**Part 1**

## **Computational Methods in Bioengineering**

**1. Introduction**

Electrical Bioimpedance Analysis (BIA) is an important tool in the characterization of organic and biological material. For instance, its use may be mainly observed in the characterization of biological tissues in medical diagnosis (Brown, 2003), in the evaluation of organic and biological material suspensions in biophysics (Cole, 1968; Grimnes & Martinsen, 2008), in the determination of fat-water content in the body (Kyle et al., 2004) and in *in vivo* identification of cancerous tissues (Aberg et al., 2004), to name a few important works. It is also natural to have different computational approaches to bioimpedance systems since more complex computational techniques are required to reconstruct images in electrical impedance tomography (Holder, 2004), and this would open a myriad of other computational and

Aleksander Paterno, Lucas Hermann Negri and Pedro Bertemes-Filho

**Efficient Computational Techniques in** 

*Department of Electrical Engineering, Center of Technological Sciences* 

**Bioimpedance Spectroscopy** 

*Santa Catarina State University, Joinville,* 

**1**

*Brazil* 

In many practical cases, the obtained bioimpedance spectrum requires that the produced signal be computationally processed to guarantee the quality of the information contained in it, or to extract the information in a more convenient way. Such algorithms would allow the removal of redundant data or even the suppression of invalid data caused by artifacts in the data acquisition process. Many of the discussed computational methods are also applied in other areas that use electrical impedance spectroscopy, as in chemistry, materials sciences and

BIA systems allow the measurement of an unknown impedance across a predetermined frequency interval. In a typical BIA system, the organic or biological material suspension or tissue sample to be characterized is excited by a constant amplitude sine voltage or current and the impedance is calculated at each frequency after the other parameter, current or voltage, is measured. This technique is called sine-correlation response analysis and can provide a high degree of accuracy in the determination of impedances. By using the sine-correlation technique, the spectrum is determined either by obtaining the impedance real and imaginary parts, or by directly obtaining its modulus and phase. For this purpose, analog precision amplifiers and phase detectors provide signals proportional to modulus and phase at each frequency, and the interrogated frequency range is usually between 100 Hz up to 10 MHz. In such BIA systems the current signal used in the sample excitation is band-limited, because the output impedance of the current source and the open-loop gain of its amplifiers are low, especially at high frequencies (Bertemes-Filho, 2002). Some of these limitations may be

mathematical questions based on inverse reconstruction problems.

biomedical engineering (Barsoukov & Macdonald, 2005).

## **Efficient Computational Techniques in Bioimpedance Spectroscopy**

Aleksander Paterno, Lucas Hermann Negri and Pedro Bertemes-Filho *Department of Electrical Engineering, Center of Technological Sciences Santa Catarina State University, Joinville, Brazil* 

## **1. Introduction**

Electrical Bioimpedance Analysis (BIA) is an important tool in the characterization of organic and biological material. For instance, its use may be mainly observed in the characterization of biological tissues in medical diagnosis (Brown, 2003), in the evaluation of organic and biological material suspensions in biophysics (Cole, 1968; Grimnes & Martinsen, 2008), in the determination of fat-water content in the body (Kyle et al., 2004) and in *in vivo* identification of cancerous tissues (Aberg et al., 2004), to name a few important works. It is also natural to have different computational approaches to bioimpedance systems since more complex computational techniques are required to reconstruct images in electrical impedance tomography (Holder, 2004), and this would open a myriad of other computational and mathematical questions based on inverse reconstruction problems.

In many practical cases, the obtained bioimpedance spectrum requires that the produced signal be computationally processed to guarantee the quality of the information contained in it, or to extract the information in a more convenient way. Such algorithms would allow the removal of redundant data or even the suppression of invalid data caused by artifacts in the data acquisition process. Many of the discussed computational methods are also applied in other areas that use electrical impedance spectroscopy, as in chemistry, materials sciences and biomedical engineering (Barsoukov & Macdonald, 2005).

BIA systems allow the measurement of an unknown impedance across a predetermined frequency interval. In a typical BIA system, the organic or biological material suspension or tissue sample to be characterized is excited by a constant amplitude sine voltage or current and the impedance is calculated at each frequency after the other parameter, current or voltage, is measured. This technique is called sine-correlation response analysis and can provide a high degree of accuracy in the determination of impedances. By using the sine-correlation technique, the spectrum is determined either by obtaining the impedance real and imaginary parts, or by directly obtaining its modulus and phase. For this purpose, analog precision amplifiers and phase detectors provide signals proportional to modulus and phase at each frequency, and the interrogated frequency range is usually between 100 Hz up to 10 MHz. In such BIA systems the current signal used in the sample excitation is band-limited, because the output impedance of the current source and the open-loop gain of its amplifiers are low, especially at high frequencies (Bertemes-Filho, 2002). Some of these limitations may be

presence of an illegal adulterant, like hydrogen peroxide (Belloque et al., 2008). The problem was then to characterize the raw milk with such adulterants using the bioimpedance spectrum either fitted to a Cole-Cole function or not (Bertemes-Filho, Valicheski, Pereira & Paterno, 2010). The neural network algorithm may be in this particular case a useful technique to

Efficient Computational Techniques in Bioimpedance Spectroscopy 5

As a summary, the authors provided a compilation of problems into which computational intelligence and digital signal processing techniques may be used, as well as the illustration of new methodologies to evaluate the processed data and consequently the proposed

The used BIA system is based on a bioimpedance spectrometer consisting of a current source that injects a variable frequency signal into a load by means of two electrodes. It then measures the resulting potential in the biological material sample with two other electrodes and calculates the transfer impedance of the sample. The complete block diagram of the spectrometer system is shown in fig. 1. A waveform generator (FGEN) board supplies a sinusoidal signal with amplitude of 1 V*pp* (peak-to-peak) in the frequency range of 100 Hz to 1 MHz. The input voltage (*Vinput*) is converted to a current (+*I* and −*I*) by a modified bipolar Howland current source (also known as voltage controlled current source) (Stiz et al., 2009), which injects an output current of 1 mA*pp* by two electrodes to the biological material under study. The resulting voltage is measured with a differential circuit between the other two electrodes by using a wide bandwidth instrumentation amplifier (Inst. Amp. 02). The amplitude of the injecting current is measured by another instrumentation amplifier (Inst. Amp. 01) while using a precision shunt resistor (*Rshunt*) of 100 Ω. A custom made tetrapolar impedance probe was used to measure the bioimpedance and is composed of 4 triaxial cables. The outer and inner shields of the cables are connected together to the ground of the instrumentation. The tip of the probe has a diameter of 8 mm (D), and the electrode material is a wire of 9 carat gold with a diameter of 1 mm (d). The wires are disposed in a circular formation about the longitudinal axis. Finally, a data acquisition (DAQ) board measures both voltage load and output current by sampling the signals at a maximum sampling frequency of 1.25 MSamples/s for each of the possible 33 frequencies in the range. Data are stored in the computer for the processing of the bioimpedance spectra. Although the modulus and phase of the load are electronically obtained, one of the parameters can be used to experimentally validate the phase/modulus retrieval technique while comparing the

For completeness purposes, if one decides to use the bioimpedance spectrum points at frequencies which were not used in the excitation or were not acquired, the value at this frequency can be determined by means of interpolation, since the evaluated spectra are

The nature of the experimental bioimpedance spectra is important for the use of the algorithms described in this work. It is assumed here that the experimental sample bioimpedance spectrum may have its points represented by a Cole-Cole function in the interrogated frequency range. This is a plausible supposition, since it is a function that represents well many types of bioimpedance spectra associated with cell suspensions and

classify the milk with hydrogen peroxide (Bertemes-Filho, Negri & Paterno, 2010).

computational techniques in bioimpedance spectroscopy.

**2.1 The BIA system to interrogate bioimpedances**

**2. Materials and methods**

calculated and measured values.

usually well-behaved.

avoided by using digital signal processing techniques that may take the place of the electronic circuitry that have frequency constraints.

In the BIA electronics, when considering the phase detection part of analog circuits used, a high-precision analog multiplier provides a constant signal proportional to the phase of its input. However, the frequency response of the circuit is usually limited, for example, to 1 MHz and such multipliers require the excitation source signal as a reference. A software solution would provide an alternative to the use of such phase detectors, where in some cases an algorithm may be capable of calculating the phase spectrum from the acquired modulus values. With this system configuration, phase/modulus retrieval algorithms may be used to obtain the phase or modulus of an impedance, considering that one of these sets of values has been electronically obtained.

In electrical bioimpedance spectroscopy applied to medical diagnosis, research groups cite the use of the Kramers-Kronig causality relations Kronig (1929) to obtain the imaginary part from the real part (or equivalently phase/modulus from modulus/phase parts) of a causal spectrum (Brown, 2003; Nordbotten et al., 2011; Riu & Lapaz, 1999; Waterworth, 2000). A similar procedure occurs when obtaining the modulus from the phase, or vice-versa, using the Hilbert transform in a causal signal (Hayes et al., 1980). With constraints on the characteristics of the acquired phase or modulus spectrum, the use of these algorithms may allow the calculation of the missing part of an electrical bioimpedance spectrum. In addition, such algorithms may be used to validate the obtained experimental impedance spectrum (Riu & Lapaz, 1999). However, there may be restrictions to the signals that can be processed with these techniques, specifically with the Fourier-transform based phase/modulus-retrieval algorithms (Paterno et al., 2009), even though it may provide a computationally efficient solution to the problem.

Still related to the multi-frequency BIA systems, after the raw non-processed information is acquired, the choice of an appropriate numerical model function to fit the experimental data and generate a summary of the information in the spectrum condensed in a few parameters is also another niche where computational techniques may be used. The choice of an efficient fitting method to be used with experimental data and with a non-linear function, as the Cole-Cole function, is a problem that has been previously discussed in the literature (Halter et al., 2008; Kun et al., 2003; 1999). It is natural to think that once such algorithms work for the fitting with a non-linear Cole-Cole function, they will also work with other different non-linear functions in bioimpedance experimental data. With this in focus, an algorithm is demonstrated that shows novelties in terms of computational performance while fitting experimental data using the Cole-Cole function as part of the fitness function and particle-swarm optimization techniques to optimally adjust the model function parameters (Negri et al., 2010). Other computational intelligence algorithms are also used for comparison purposes and a methodology to evaluate the results of the fitting algorithms is proposed that uses a neural network.

The experimental data in this work were obtained with a custom-made multi-frequency bioimpedance spectrometer (Bertemes-Filho et al., 2009; Stiz et al., 2009). Samples of biological materials were used like bovine flesh tissue and also raw milk, that may constitute a suspension of cells, since the samples of raw milk may have cells, for example, due to mastitis infection in sick animals. Other characteristics of milk, which are currently important in the dairy industry, could be evaluated, as, for instance, a change in the water content or even the presence of an illegal adulterant, like hydrogen peroxide (Belloque et al., 2008). The problem was then to characterize the raw milk with such adulterants using the bioimpedance spectrum either fitted to a Cole-Cole function or not (Bertemes-Filho, Valicheski, Pereira & Paterno, 2010). The neural network algorithm may be in this particular case a useful technique to classify the milk with hydrogen peroxide (Bertemes-Filho, Negri & Paterno, 2010).

As a summary, the authors provided a compilation of problems into which computational intelligence and digital signal processing techniques may be used, as well as the illustration of new methodologies to evaluate the processed data and consequently the proposed computational techniques in bioimpedance spectroscopy.

#### **2. Materials and methods**

2 Will-be-set-by-IN-TECH

avoided by using digital signal processing techniques that may take the place of the electronic

In the BIA electronics, when considering the phase detection part of analog circuits used, a high-precision analog multiplier provides a constant signal proportional to the phase of its input. However, the frequency response of the circuit is usually limited, for example, to 1 MHz and such multipliers require the excitation source signal as a reference. A software solution would provide an alternative to the use of such phase detectors, where in some cases an algorithm may be capable of calculating the phase spectrum from the acquired modulus values. With this system configuration, phase/modulus retrieval algorithms may be used to obtain the phase or modulus of an impedance, considering that one of these sets of values has

In electrical bioimpedance spectroscopy applied to medical diagnosis, research groups cite the use of the Kramers-Kronig causality relations Kronig (1929) to obtain the imaginary part from the real part (or equivalently phase/modulus from modulus/phase parts) of a causal spectrum (Brown, 2003; Nordbotten et al., 2011; Riu & Lapaz, 1999; Waterworth, 2000). A similar procedure occurs when obtaining the modulus from the phase, or vice-versa, using the Hilbert transform in a causal signal (Hayes et al., 1980). With constraints on the characteristics of the acquired phase or modulus spectrum, the use of these algorithms may allow the calculation of the missing part of an electrical bioimpedance spectrum. In addition, such algorithms may be used to validate the obtained experimental impedance spectrum (Riu & Lapaz, 1999). However, there may be restrictions to the signals that can be processed with these techniques, specifically with the Fourier-transform based phase/modulus-retrieval algorithms (Paterno et al., 2009), even though it may provide a computationally efficient

Still related to the multi-frequency BIA systems, after the raw non-processed information is acquired, the choice of an appropriate numerical model function to fit the experimental data and generate a summary of the information in the spectrum condensed in a few parameters is also another niche where computational techniques may be used. The choice of an efficient fitting method to be used with experimental data and with a non-linear function, as the Cole-Cole function, is a problem that has been previously discussed in the literature (Halter et al., 2008; Kun et al., 2003; 1999). It is natural to think that once such algorithms work for the fitting with a non-linear Cole-Cole function, they will also work with other different non-linear functions in bioimpedance experimental data. With this in focus, an algorithm is demonstrated that shows novelties in terms of computational performance while fitting experimental data using the Cole-Cole function as part of the fitness function and particle-swarm optimization techniques to optimally adjust the model function parameters (Negri et al., 2010). Other computational intelligence algorithms are also used for comparison purposes and a methodology to evaluate the results of the fitting algorithms is

The experimental data in this work were obtained with a custom-made multi-frequency bioimpedance spectrometer (Bertemes-Filho et al., 2009; Stiz et al., 2009). Samples of biological materials were used like bovine flesh tissue and also raw milk, that may constitute a suspension of cells, since the samples of raw milk may have cells, for example, due to mastitis infection in sick animals. Other characteristics of milk, which are currently important in the dairy industry, could be evaluated, as, for instance, a change in the water content or even the

circuitry that have frequency constraints.

been electronically obtained.

solution to the problem.

proposed that uses a neural network.

#### **2.1 The BIA system to interrogate bioimpedances**

The used BIA system is based on a bioimpedance spectrometer consisting of a current source that injects a variable frequency signal into a load by means of two electrodes. It then measures the resulting potential in the biological material sample with two other electrodes and calculates the transfer impedance of the sample. The complete block diagram of the spectrometer system is shown in fig. 1. A waveform generator (FGEN) board supplies a sinusoidal signal with amplitude of 1 V*pp* (peak-to-peak) in the frequency range of 100 Hz to 1 MHz. The input voltage (*Vinput*) is converted to a current (+*I* and −*I*) by a modified bipolar Howland current source (also known as voltage controlled current source) (Stiz et al., 2009), which injects an output current of 1 mA*pp* by two electrodes to the biological material under study. The resulting voltage is measured with a differential circuit between the other two electrodes by using a wide bandwidth instrumentation amplifier (Inst. Amp. 02). The amplitude of the injecting current is measured by another instrumentation amplifier (Inst. Amp. 01) while using a precision shunt resistor (*Rshunt*) of 100 Ω. A custom made tetrapolar impedance probe was used to measure the bioimpedance and is composed of 4 triaxial cables. The outer and inner shields of the cables are connected together to the ground of the instrumentation. The tip of the probe has a diameter of 8 mm (D), and the electrode material is a wire of 9 carat gold with a diameter of 1 mm (d). The wires are disposed in a circular formation about the longitudinal axis. Finally, a data acquisition (DAQ) board measures both voltage load and output current by sampling the signals at a maximum sampling frequency of 1.25 MSamples/s for each of the possible 33 frequencies in the range. Data are stored in the computer for the processing of the bioimpedance spectra. Although the modulus and phase of the load are electronically obtained, one of the parameters can be used to experimentally validate the phase/modulus retrieval technique while comparing the calculated and measured values.

For completeness purposes, if one decides to use the bioimpedance spectrum points at frequencies which were not used in the excitation or were not acquired, the value at this frequency can be determined by means of interpolation, since the evaluated spectra are usually well-behaved.

The nature of the experimental bioimpedance spectra is important for the use of the algorithms described in this work. It is assumed here that the experimental sample bioimpedance spectrum may have its points represented by a Cole-Cole function in the interrogated frequency range. This is a plausible supposition, since it is a function that represents well many types of bioimpedance spectra associated with cell suspensions and

a bioimpedance. This relation is given by:

represented by Cole & Cole (1941):

model for dielectrics (Cole & Cole, 1941).

By using eq.2, the relation between *Z*(*s*) and *G*(*τ*) is stressed:

*<sup>G</sup>*(*τ*) = <sup>1</sup>

2*π*

⎡ ⎣

cosh �

*ZCole*(*ω*) = *R*<sup>∞</sup> +

*Zf rac*(*s*) = *<sup>R</sup>*<sup>0</sup> <sup>−</sup> *<sup>R</sup>*<sup>∞</sup>

*<sup>Z</sup>*(*s*) = � <sup>∞</sup> 0

<sup>1</sup> + (*sτ*0)*<sup>α</sup>* = (*R*<sup>0</sup> <sup>−</sup> *<sup>R</sup>*∞)

In eq. 3, the frequency dependent part of the impedance in the Cole-Cole type model function, *Zf rac*(*s*), is represented, where *R*<sup>0</sup> is the impedance resistance at very low frequencies, *R*<sup>∞</sup> is the resistance at very high frequencies, and the function containing the fractional order term, (*sτ*0)*<sup>α</sup>* can be represented by an integral of the distribution function *G*(*τ*) (Cole & Cole, 1941), and *α* is a constant in the interval [0, 1] and *τ*<sup>0</sup> is the generalized relaxation time. *G*(*τ*) is a distribution function for the fractional order Cole-Cole model function and is explicitly

Efficient Computational Techniques in Bioimpedance Spectroscopy 7

*α* log( *<sup>τ</sup> τ*0 ) �

The complete model developed by Cole and Cole consists of an equation, an equivalent circuit and a complex impedance circular arc locus, and in terms of impedances, after integrating eq. 3, one obtains the Cole-Cole function to represent the evaluated impedance spectrum:

In eq. 5, the variable *ZCole*(*ω*) is a complex impedance and is a function of the angular frequency *ω*. The Cole-Cole function was obtained by the Cole and Cole brothers when they also introduced the distribution function of eq. (4). It is worth noticing that the function containing the fractional order term, (*sτ*0)1−*<sup>α</sup>* instead of the (*sτ*0)*α*, was originally used in a

For the use of the phase/modulus retrieval algorithm in *ZCole*(*s*) the independent term corresponding to the resistance, *R*∞, causes the frequency dependent function to satisfy neither the phase- nor the modulus-retrieval algorithm conditions (Hayes et al., 1980; Paterno et al., 2009). In other words, the experimental points to be used with the phase/modulus retrieval algorithm must be previously tested with known bioimpedance spectrum data to verify if the process is applicable. Consequently, the algorithm has limitations of use if the resistance at very high frequencies is not zero, or if the condition of minimum phase in the spectrum is not satisfied. In addition to that, for the reconstruction of phase and modulus of *ZCole*(*s*), the experimental data must correspond to a Cole-Cole spectrum that may be fitted to a specific set of values of *α* (Paterno et al., 2009), otherwise the algorithm may not converge to the correct values. Fortunately, these values of *α* with which the algorithm properly works correspond to a broad class of tissues, cell suspensions and organic materials to be evaluated in practical cases. In the limit, when *α* ≈ 0, *Zf rac*(*s*) becomes a pure resistance having minimum-phase. For values of *α* in the interval (0, 1), the modulus retrieval algorithm may be capable of producing a limited error, as demonstrated elsewhere (Paterno et al.,

*G*(*τ*) 1 + *sτ*

sin [(1 − *α*)*π*]

*R*<sup>0</sup> − *R*<sup>∞</sup>

� ∞ 0

− cos [(1 − *α*)*π*]

⎤

<sup>1</sup> + (*jωτ*0)*<sup>α</sup>* (5)

*G*(*τ*) 1 + *sτ*

*dτ* (2)

*dτ* (3)

⎦ (4)

many types of organic tissues and materials (Cole, 1940; 1968; Grimnes & Martinsen, 2008). When the Cole-Cole function shown in the following equations is not an appropriate model function to fit the experimental data, the data are not processed with these algorithms and are used in phase/modulus retrieval or in the neural network without further processing.

#### **2.2 Cole-Cole fractional order impedance function**

Tissues or non-uniform cell suspensions have bioimpedance spectra that are not well represented by a Debye-type single-pole (single-relaxation) function. In any case, the bioimpedance may be represented as a complex number in polar or cartesian, as in eq. 1:

$$Z(\mathbf{s}) = |Z(\mathbf{s})|e^{j\theta} = Z\_{\mathbb{R}}(\mathbf{s}) + jZ\_{\mathbb{I}}(\mathbf{s})\tag{1}$$

where *<sup>s</sup>* <sup>=</sup> *<sup>j</sup>ω*, *<sup>ω</sup>* represents the angular frequency and *<sup>j</sup>* <sup>=</sup> √−1. The cartesian form takes its graphical representation in the complex impedance plane where the ordinate axis is the negative of the impedance imaginary part (-reactance) and the abscissa axis is the real part of the impedance. Usually different configurations of a semi-circular arc in the complex impedance plane may represent the experimental bioimpedances spectra or they may be depicted by plotting the modulus and phase versus frequency.

In addition, the bioimpedance function used in this work is going to be represented within a limited frequency range in terms of a distribution function of relaxation times, *τ*, which would correspond to the spectrum of cell sizes, particles or molecules in a suspension or tissue. This distribution function approach was proposed by Fuoss and Kirkwood (Fuoss & Kirkwood, 1941) where they extended the Debye theory from which a relation can be obtained between the distribution function, *G*(*τ*), and a transfer function, *Z*(*s*), that corresponds in this case to a bioimpedance. This relation is given by:

4 Will-be-set-by-IN-TECH

,QVW \$PS 

,QVW \$PS 

 

 ,QVW \$PS 

Fig. 1. BIA system complete block diagram for the interrogation of electrical bioimpedances.

many types of organic tissues and materials (Cole, 1940; 1968; Grimnes & Martinsen, 2008). When the Cole-Cole function shown in the following equations is not an appropriate model function to fit the experimental data, the data are not processed with these algorithms and are used in phase/modulus retrieval or in the neural network without further processing.

Tissues or non-uniform cell suspensions have bioimpedance spectra that are not well represented by a Debye-type single-pole (single-relaxation) function. In any case, the bioimpedance may be represented as a complex number in polar or cartesian, as in eq. 1:

where *<sup>s</sup>* <sup>=</sup> *<sup>j</sup>ω*, *<sup>ω</sup>* represents the angular frequency and *<sup>j</sup>* <sup>=</sup> √−1. The cartesian form takes its graphical representation in the complex impedance plane where the ordinate axis is the negative of the impedance imaginary part (-reactance) and the abscissa axis is the real part of the impedance. Usually different configurations of a semi-circular arc in the complex impedance plane may represent the experimental bioimpedances spectra or they may be

In addition, the bioimpedance function used in this work is going to be represented within a limited frequency range in terms of a distribution function of relaxation times, *τ*, which would correspond to the spectrum of cell sizes, particles or molecules in a suspension or tissue. This distribution function approach was proposed by Fuoss and Kirkwood (Fuoss & Kirkwood, 1941) where they extended the Debye theory from which a relation can be obtained between the distribution function, *G*(*τ*), and a transfer function, *Z*(*s*), that corresponds in this case to

*<sup>Z</sup>*(*s*) = <sup>|</sup>*Z*(*s*)|*ej<sup>θ</sup>* <sup>=</sup> *ZR*(*s*) + *jZI*(*s*) (1)

G

'

V

 

,

, 5VKXQW

'\$4 ERDUG

**2.2 Cole-Cole fractional order impedance function**

depicted by plotting the modulus and phase versus frequency.

,1 ,1

YLQSXW

)\*(1 ERDUG

$$Z(s) = \int\_0^\infty \frac{G(\tau)}{1 + s\tau} d\tau \tag{2}$$

By using eq.2, the relation between *Z*(*s*) and *G*(*τ*) is stressed:

$$Z\_{frac}(s) = \frac{R\_0 - R\_{\infty}}{1 + (s\tau\_0)^a} = (R\_0 - R\_{\infty}) \int\_0^{\infty} \frac{G(\tau)}{1 + s\tau} d\tau \tag{3}$$

In eq. 3, the frequency dependent part of the impedance in the Cole-Cole type model function, *Zf rac*(*s*), is represented, where *R*<sup>0</sup> is the impedance resistance at very low frequencies, *R*<sup>∞</sup> is the resistance at very high frequencies, and the function containing the fractional order term, (*sτ*0)*<sup>α</sup>* can be represented by an integral of the distribution function *G*(*τ*) (Cole & Cole, 1941), and *α* is a constant in the interval [0, 1] and *τ*<sup>0</sup> is the generalized relaxation time. *G*(*τ*) is a distribution function for the fractional order Cole-Cole model function and is explicitly represented by Cole & Cole (1941):

$$G(\tau) = \frac{1}{2\pi} \left[ \frac{\sin\left[ (1-\mathfrak{a})\pi \right]}{\cosh\left[ \mathfrak{a} \log\left(\frac{\tau}{\mathfrak{a}\_0}\right) \right] - \cos\left[ (1-\mathfrak{a})\pi \right]} \right] \tag{4}$$

The complete model developed by Cole and Cole consists of an equation, an equivalent circuit and a complex impedance circular arc locus, and in terms of impedances, after integrating eq. 3, one obtains the Cole-Cole function to represent the evaluated impedance spectrum:

$$Z\_{\rm Col}(\omega) = R\_{\infty} + \frac{R\_0 - R\_{\infty}}{1 + (j\omega \tau\_0)^a} \tag{5}$$

In eq. 5, the variable *ZCole*(*ω*) is a complex impedance and is a function of the angular frequency *ω*. The Cole-Cole function was obtained by the Cole and Cole brothers when they also introduced the distribution function of eq. (4). It is worth noticing that the function containing the fractional order term, (*sτ*0)1−*<sup>α</sup>* instead of the (*sτ*0)*α*, was originally used in a model for dielectrics (Cole & Cole, 1941).

For the use of the phase/modulus retrieval algorithm in *ZCole*(*s*) the independent term corresponding to the resistance, *R*∞, causes the frequency dependent function to satisfy neither the phase- nor the modulus-retrieval algorithm conditions (Hayes et al., 1980; Paterno et al., 2009). In other words, the experimental points to be used with the phase/modulus retrieval algorithm must be previously tested with known bioimpedance spectrum data to verify if the process is applicable. Consequently, the algorithm has limitations of use if the resistance at very high frequencies is not zero, or if the condition of minimum phase in the spectrum is not satisfied. In addition to that, for the reconstruction of phase and modulus of *ZCole*(*s*), the experimental data must correspond to a Cole-Cole spectrum that may be fitted to a specific set of values of *α* (Paterno et al., 2009), otherwise the algorithm may not converge to the correct values. Fortunately, these values of *α* with which the algorithm properly works correspond to a broad class of tissues, cell suspensions and organic materials to be evaluated in practical cases. In the limit, when *α* ≈ 0, *Zf rac*(*s*) becomes a pure resistance having minimum-phase. For values of *α* in the interval (0, 1), the modulus retrieval algorithm may be capable of producing a limited error, as demonstrated elsewhere (Paterno et al.,

Causality is imposed in the fourth block while a finite length constraint on the time-domain sequence sets *zest*(*n*) to zero for *n > N* − 1. The *M*-point FFT of the data set containing *z*(*n*) produces the estimates of the bioimpedance spectrum. This flowchart indicates the process that is repeated until the root-mean squared value of the difference between two consecutive estimated vectors is less than a stopping parameter, *�*. It was set equal to *�* = 10−6, which is a much lower value than the necessary modulus or phase resolution in BIA systems. The length of the input vector sequences is a power of 2, since the iterative solution uses uniformly spaced samples Quartieri & Oppenheim (1981) and the Fast-Fourier Transform (FFT) radix-2

Efficient Computational Techniques in Bioimpedance Spectroscopy 9

**2.4 Computational intelligence algorithms in electrical bioimpedance spectroscopy**

*α*) as in eq.5 with the information of the electrical bioimpedance spectrum.

**2.4.1 The Particle-Swarm Optimization (PSO) experiment**

PSO algorithm.

2.4.1.1 The PSO algorithm

1. Population initialization;

In this section computational intelligence algorithms will be briefly described such as to be used in an application to fit experimental data obtained with BIA systems using particle swarm optimization techniques; additionally, artificial neural networks (ANN) are described to provide a methodology to evaluate the fitting algorithms. The performance testing is implemented by associating the training phase of the ANN to previously known information contained in the bioimpedance spectrum. For example, in the evaluated sample. The presence of different adulterants in raw milk, specifically water and hydrogen peroxide, and the characterization of the type of bovine flesh tissue are samples that were interrogated with the BIA system. The ANN is used to evaluate how much information the fitting process may extract from the experimental data such as to condense it into the parameters of the used function model, namely, the Cole-Cole function that contains four parameters (*R*0, *R*∞, *τ* and

The particle swarm optimization algorithm was used to extract the Cole-Cole function parameters, *R*0, *R*∞, *τ*<sup>0</sup> and *α* from experimental data. For this experiment, the previously described bioimpedance spectrometer injected a sinusoidal current via the two electrodes of a tetrapolar probe into bovine liver, heart, topside, and back muscle samples. A cow was killed in a slaughterhouse, where the samples were extracted and immediately headed to the laboratory where the bioimpedance measurements were performed. The measured bioimpedance spectrum points contained 32 modulus and phase values at frequencies in the range from 500 Hz up to 1 MHz. A set of 20 pairs of reactance and resistance points corresponding to the lowest frequencies (from 500 Hz up to 60 kHz) was processed with a

PSO is inspired by bird flocking, where one may consider a group of birds that moves through the space searching for food, and that uses the birds nearer to the goal (food) as references (Xiaohui et al., 2004). PSO algorithms to fit a known function to experimental data is a technique similar to the one using genetic algorithms (GA). PSO has however a faster convergence for unconstrained problems with continuous variables such as the addressed fitting problem of the Cole-Cole function and has a simple arithmetic complexity (Hassan

et al., 2005). Briefly, the PSO algorithm can be separated in the following steps:

algorithm (Proakis & Manolakis, 2006).

2009). For the use of instrumentation to characterize the spectrum of organic material, this conditions are usually met, as in the illustration case of bioimpedances obtained from mango, banana, potato and guava, shown in the results in section 3. These are illustrative examples of organic material to have its impedance phase measured and used as input to the algorithm that determines the bioimpedance modulus. In this case, both parameters were measured to validate the results (Paterno & Hoffmann, 2008).

#### **2.3 Phase/modulus retrieval algorithm description**

The algorithm is based on the flowchart in fig. 2. It starts by being fed with the modulus sequence vector (in the phase retrieval algorithm) provided by electronic means. In the case of using the modulus retrieval procedure, phase and modulus must be interchanged in the algorithm. A vector containing the *N* modulus samples equally spaced in frequency is saved in |*ZOR*(*k*)| and a vector that contains the estimated phase samples is initialized with random values. The initial impedance Fourier transform spectrum is a vector represented by the *N* values, *ZOR*(*k*) = <sup>|</sup>*ZOR*(*k*)|*ejθest* . In the following step, the real part of an *<sup>M</sup>*-point inverse fast-Fourier transform (IFFT) algorithm is used to produce a sequence in the time-domain, *zest*[*n*]. An *M*-point IFFT is used, where the constraint *M* ≥ 2*N* guarantees the algorithm convergence. Only the real part of the *M*-point IFFT is used because the input signal is real in the time-domain Quartieri & Oppenheim (1981), and has an even Fourier transform, allowing half of the samples (*N* samples) to represent the bioimpedance spectrum.

Fig. 2. Flowchart representing the processing steps in the modulus-retrieval algorithm for the BIA system.

6 Will-be-set-by-IN-TECH

2009). For the use of instrumentation to characterize the spectrum of organic material, this conditions are usually met, as in the illustration case of bioimpedances obtained from mango, banana, potato and guava, shown in the results in section 3. These are illustrative examples of organic material to have its impedance phase measured and used as input to the algorithm that determines the bioimpedance modulus. In this case, both parameters were measured to

The algorithm is based on the flowchart in fig. 2. It starts by being fed with the modulus sequence vector (in the phase retrieval algorithm) provided by electronic means. In the case of using the modulus retrieval procedure, phase and modulus must be interchanged in the algorithm. A vector containing the *N* modulus samples equally spaced in frequency is saved in |*ZOR*(*k*)| and a vector that contains the estimated phase samples is initialized with random values. The initial impedance Fourier transform spectrum is a vector represented by the *N* values, *ZOR*(*k*) = <sup>|</sup>*ZOR*(*k*)|*ejθest* . In the following step, the real part of an *<sup>M</sup>*-point inverse fast-Fourier transform (IFFT) algorithm is used to produce a sequence in the time-domain, *zest*[*n*]. An *M*-point IFFT is used, where the constraint *M* ≥ 2*N* guarantees the algorithm convergence. Only the real part of the *M*-point IFFT is used because the input signal is real in the time-domain Quartieri & Oppenheim (1981), and has an even Fourier transform, allowing

z (n) est

0

Z (k)=|Z (k)|e est+1 est

Causal z (n) est

Z (k)=|Z (k)|e est+1 OR

j (k) est+1

jest+1(k)

Z (k)=|Z (k)|e OR OR

j (k) est

M-point IFFT

z

est(n)=0 if N n M-1 and n 

M-point FFT


BIA system.

Fig. 2. Flowchart representing the processing steps in the modulus-retrieval algorithm for the

half of the samples (*N* samples) to represent the bioimpedance spectrum.

validate the results (Paterno & Hoffmann, 2008).

**2.3 Phase/modulus retrieval algorithm description**

Causality is imposed in the fourth block while a finite length constraint on the time-domain sequence sets *zest*(*n*) to zero for *n > N* − 1. The *M*-point FFT of the data set containing *z*(*n*) produces the estimates of the bioimpedance spectrum. This flowchart indicates the process that is repeated until the root-mean squared value of the difference between two consecutive estimated vectors is less than a stopping parameter, *�*. It was set equal to *�* = 10−6, which is a much lower value than the necessary modulus or phase resolution in BIA systems. The length of the input vector sequences is a power of 2, since the iterative solution uses uniformly spaced samples Quartieri & Oppenheim (1981) and the Fast-Fourier Transform (FFT) radix-2 algorithm (Proakis & Manolakis, 2006).

#### **2.4 Computational intelligence algorithms in electrical bioimpedance spectroscopy**

In this section computational intelligence algorithms will be briefly described such as to be used in an application to fit experimental data obtained with BIA systems using particle swarm optimization techniques; additionally, artificial neural networks (ANN) are described to provide a methodology to evaluate the fitting algorithms. The performance testing is implemented by associating the training phase of the ANN to previously known information contained in the bioimpedance spectrum. For example, in the evaluated sample. The presence of different adulterants in raw milk, specifically water and hydrogen peroxide, and the characterization of the type of bovine flesh tissue are samples that were interrogated with the BIA system. The ANN is used to evaluate how much information the fitting process may extract from the experimental data such as to condense it into the parameters of the used function model, namely, the Cole-Cole function that contains four parameters (*R*0, *R*∞, *τ* and *α*) as in eq.5 with the information of the electrical bioimpedance spectrum.

#### **2.4.1 The Particle-Swarm Optimization (PSO) experiment**

The particle swarm optimization algorithm was used to extract the Cole-Cole function parameters, *R*0, *R*∞, *τ*<sup>0</sup> and *α* from experimental data. For this experiment, the previously described bioimpedance spectrometer injected a sinusoidal current via the two electrodes of a tetrapolar probe into bovine liver, heart, topside, and back muscle samples. A cow was killed in a slaughterhouse, where the samples were extracted and immediately headed to the laboratory where the bioimpedance measurements were performed. The measured bioimpedance spectrum points contained 32 modulus and phase values at frequencies in the range from 500 Hz up to 1 MHz. A set of 20 pairs of reactance and resistance points corresponding to the lowest frequencies (from 500 Hz up to 60 kHz) was processed with a PSO algorithm.

#### 2.4.1.1 The PSO algorithm

PSO is inspired by bird flocking, where one may consider a group of birds that moves through the space searching for food, and that uses the birds nearer to the goal (food) as references (Xiaohui et al., 2004). PSO algorithms to fit a known function to experimental data is a technique similar to the one using genetic algorithms (GA). PSO has however a faster convergence for unconstrained problems with continuous variables such as the addressed fitting problem of the Cole-Cole function and has a simple arithmetic complexity (Hassan et al., 2005). Briefly, the PSO algorithm can be separated in the following steps:

1. Population initialization;

An ANN is composed of interconnected artificial neurons, each neuron being a simple computer unit (Haykin, 1999). Although a single neuron can perform only a simple operation, the network computational power is significant (Cybenko, 1989; Gorban, 1998) and can tackle

Efficient Computational Techniques in Bioimpedance Spectroscopy 11

In a perceptron-like network such as the ones employed in this work, each neuron performs the operation shown in eq. 8, where *y* is the output value, defined as the result of the activation function *φ* evaluated with the summation of *m* input signals *xi*, each one multiplied by a weight *wi* (also seen in fig. 4). All neural networks had neurons using the symmetric sigmoid activation function (Haykin, 1999). It is mathematically represented with its input in eq. 8. In eq. 9, the description of the sigmoid function is shown, and in fig. 3 a graphical illustration of its output is depicted as a function of its input for different steepness parameters. For this work, the steepness parameters were determined empirically. In the classification experiments, the parameter is *stp* = 0.65 in the bovine flesh classification and *stp* = 0.5 in

any computable problem (Siegelmann & Sontag, 1991), under certain circumstances.

*y* = *φ*

*<sup>φ</sup>*(*x*) = <sup>2</sup>


Fig. 4. Artificial neuron diagrammatic representation.



The ANN learns by adjusting its weights *wi*. These weight changes are performed by using a training algorithm in the training stage (offline training), feeding the network with the input values and comparing the outputs with the expected result values, which would provide an

Fig. 3. Symmetric sigmoid function for distinct steepness *stp* values. In the experiments,

 


 *m* ∑ *i xiwi* 

<sup>1</sup> <sup>+</sup> *<sup>e</sup>*−2*stp <sup>x</sup>* <sup>−</sup> <sup>1</sup> (9)

(8)

the milk classification.

*stp* = 0.65 and *stp* = 0.5.


Each parameter of the optimized function, in this case the fitting of the Cole-Cole function in eq. 5 to an experimental bioimpedance spectrum, can be represented as one dimension in the search space. The velocity update rule for the *i*-th particle is given by:

$$v\_{\rm id} = w \times v\_{\rm id} + c\_1 \times rand() \times (p\_{\rm id} - \mathbf{x}\_{\rm id}) + c\_2 \times rand() \times (p\_{\rm nd} - \mathbf{x}\_{\rm id})\tag{6}$$

where *vid* is the velocity of the *i*-th particle in the dimension *d*; *w* is the inertia weight, in the [0, 1) range; *c*<sup>1</sup> and *c*<sup>2</sup> are the learning rates, usually in the [1, 3] range; *rand*() is a random number in the [0, 1] interval, *pid* is the best position of the *i*-th particle for the *d*-th dimension and *pnd* is the best neighborhood position for the *d*-th dimension. The particle position is updated by summing the present position to the velocity.

Each particle is made by a vector with the parameters [*R*0, *R*∞, *τ*0, *α*] of the Cole-Cole function, that are randomly initialized with arbitrary values in an interval corresponding to the physical limits of the system. A parameter restart step for the global search, inspired by the genetic algorithm mutation operator, was added to the code to prevent the premature convergence of the algorithm.

Like a genetic algorithm, the PSO enhances the solution based on a heuristic function, named fitness function, that measures the difference between the experimental spectrum and the fitted one. The fitness function is shown in eq. 7

$$fitness(p) = -\frac{1}{N} \sum\_{i=1}^{N} abs(Z\_i - A\_i)^2\tag{7}$$

It is defined by the modulus of the difference between the original complex bioimpedance experimental points, *Zi*, and the fitted spectrum, *Ai*. As a consequence, resistance and reactance are taken into account in the function, and therefore, in the fitting.

#### **2.4.2 Artificial neural networks and the fitted functions of the bioimpedance spectrum**

Artificial neural networks (ANN) were implemented such as to evaluate the behavior of the fitting algorithms to experimental data. This was developed to determine, comparatively, how much information the extracted parameters from the fitted Cole-Cole function may contain that represents correctly the experimental bioimpedances.

#### 2.4.2.1 ANN as used in BIA

One of the important features of a neural network resides in its capability to learn the relationships in a given data mapping, such as the mapping from the bioimpedance spectra to the type of the analyzed sample. This feature allows the network to be trained to perform estimations and classify new samples according to the learned pattern.

8 Will-be-set-by-IN-TECH

2. Evaluation of the particles in the population by a heuristic function, where in this case the

3. Selection of the fittest particles (set of parameters) to lead the population towards the best

4. Update of the position and velocity of each particle by repeating the steps from 2 to 4 until

Each parameter of the optimized function, in this case the fitting of the Cole-Cole function in eq. 5 to an experimental bioimpedance spectrum, can be represented as one dimension in the

where *vid* is the velocity of the *i*-th particle in the dimension *d*; *w* is the inertia weight, in the [0, 1) range; *c*<sup>1</sup> and *c*<sup>2</sup> are the learning rates, usually in the [1, 3] range; *rand*() is a random number in the [0, 1] interval, *pid* is the best position of the *i*-th particle for the *d*-th dimension and *pnd* is the best neighborhood position for the *d*-th dimension. The particle position is

Each particle is made by a vector with the parameters [*R*0, *R*∞, *τ*0, *α*] of the Cole-Cole function, that are randomly initialized with arbitrary values in an interval corresponding to the physical limits of the system. A parameter restart step for the global search, inspired by the genetic algorithm mutation operator, was added to the code to prevent the premature convergence of

Like a genetic algorithm, the PSO enhances the solution based on a heuristic function, named fitness function, that measures the difference between the experimental spectrum and the

*N*

It is defined by the modulus of the difference between the original complex bioimpedance experimental points, *Zi*, and the fitted spectrum, *Ai*. As a consequence, resistance and

Artificial neural networks (ANN) were implemented such as to evaluate the behavior of the fitting algorithms to experimental data. This was developed to determine, comparatively, how much information the extracted parameters from the fitted Cole-Cole function may contain

One of the important features of a neural network resides in its capability to learn the relationships in a given data mapping, such as the mapping from the bioimpedance spectra to the type of the analyzed sample. This feature allows the network to be trained to perform

**2.4.2 Artificial neural networks and the fitted functions of the bioimpedance spectrum**

*N* ∑ *i*=1

*abs*(*Zi* <sup>−</sup> *Ai*)<sup>2</sup> (7)

*fitness*(*p*) = <sup>−</sup> <sup>1</sup>

reactance are taken into account in the function, and therefore, in the fitting.

estimations and classify new samples according to the learned pattern.

that represents correctly the experimental bioimpedances.

2.4.2.1 ANN as used in BIA

*vid* = *w* × *vid* + *c*<sup>1</sup> × *rand*() × (*pid* − *xid*) + *c*<sup>2</sup> × *rand*() × (*pnd* − *xid*) (6)

particles are formed by a vector with the Cole-Cole function parameters;

a stopping condition is satisfied (Xiaohui et al., 2004).

updated by summing the present position to the velocity.

fitted one. The fitness function is shown in eq. 7

search space. The velocity update rule for the *i*-th particle is given by:

set and

the algorithm.

An ANN is composed of interconnected artificial neurons, each neuron being a simple computer unit (Haykin, 1999). Although a single neuron can perform only a simple operation, the network computational power is significant (Cybenko, 1989; Gorban, 1998) and can tackle any computable problem (Siegelmann & Sontag, 1991), under certain circumstances.

In a perceptron-like network such as the ones employed in this work, each neuron performs the operation shown in eq. 8, where *y* is the output value, defined as the result of the activation function *φ* evaluated with the summation of *m* input signals *xi*, each one multiplied by a weight *wi* (also seen in fig. 4). All neural networks had neurons using the symmetric sigmoid activation function (Haykin, 1999). It is mathematically represented with its input in eq. 8. In eq. 9, the description of the sigmoid function is shown, and in fig. 3 a graphical illustration of its output is depicted as a function of its input for different steepness parameters. For this work, the steepness parameters were determined empirically. In the classification experiments, the parameter is *stp* = 0.65 in the bovine flesh classification and *stp* = 0.5 in the milk classification.

$$y = \phi\left(\sum\_{i}^{m} x\_i w\_i\right) \tag{8}$$

$$\phi(\mathbf{x}) = \frac{2}{1 + e^{-2s\_{lp}\mathbf{x}}} - 1 \tag{9}$$

Fig. 3. Symmetric sigmoid function for distinct steepness *stp* values. In the experiments, *stp* = 0.65 and *stp* = 0.5.

Fig. 4. Artificial neuron diagrammatic representation.

The ANN learns by adjusting its weights *wi*. These weight changes are performed by using a training algorithm in the training stage (offline training), feeding the network with the input values and comparing the outputs with the expected result values, which would provide an


Efficient Computational Techniques in Bioimpedance Spectroscopy 13

 

 

box or 20 times 2 ('x20').


(b) 40–2–4 FCC topology employed in the bovine tissue classification experiment. The input layer has 40 neurons condensed in the


 -

 

(a) 3–2–4 FCC topology employed in the bovine tissue classification experiment.


classification with bovine tissue and adulterated milk.

15 times 2 ('x15').

spectrum data.

 

(c) 30–2–4 MLP topology employed in the milk adulterant detection experiment. The input layer has 30 neurons condensed in the box or

Fig. 5. Topology of artificial neural networks used in the experiment of bioimpedance spectra

executed several times with the same set of experimental data. This would happen if the Cole-Cole function were an appropriate representation of the acquired bioimpedance

The resulting fitted parameters were used as input to the neural networks such as to classify the data by means of its known type (liver, heart, topside, or back muscle). Another neural network performed the same classification, but using the unprocessed spectrum points as inputs. The input signal was incrementally added to white-gaussian noise (AWGN) such as to produce different signal to noise ratios. A total of 24 electrical impedance measurements

error measure. The calculated error is the information used to modify the weights of the connections, in order to reduce the errors on the next run. This procedure can be executed many times until the error converges to a minimum. The training procedure for the networks employed in this work are based on the following steps (error backpropagation procedure):


Different training algorithms can be used to adjust the weights of an ANN. It is common to supervised training algorithms to follow the same steps as the error backpropagation procedure, differing only in the weight adjusting step (Haykin, 1999). As an example, while the classical backpropagation has only a centralized learning rate, the iRPROP algorithm (Anastasiadis & Ph, 2003) has a learning rate for each connections and uses only the sign changes in the local error to guide the training. Other algorithms like NBN (Neuron by Neuron) uses the local errors to estimate second-order partial derivatives, which in some cases can lead to a faster training (Wilamowski, 2009).

In the bovine tissue classification experiment, two different fully connected cascade (FCC) topologies were employed. Both topologies had two hidden layers (with one neuron each) and an output layer with 4 neurons. The first one diagrammatically depicted in fig. 5(a) employed only 3 neurons in the input layer, for the *R*0, *τ* and *α* fitted Cole-Cole parameters, while the other one depicted in fig. 5(b) used 40 input neurons, corresponding to 20 impedance and reactance pairs. Both topologies had the goal of mapping the input data into one of 4 classes. To implement this, 4 output neurons were used, each one corresponding to a class. The NBN training algorithm was used to adjust the synaptic weights for the network to predict the correct beef classes.

The milk adulterant detection experiment employed a multilayer perceptron (MLP) topology (as in fig. 5(c)), with 30 input neurons (15 impedance and reactance pairs), one hidden layer with two neurons and an output layer with 3 neurons. Each output neuron corresponds to one class (one of C classes coding). The ANN was trained with the NBN algorithm.

#### 2.4.2.2 Experiments with the ANN testing

The evaluated experimental data were also added to artificial noise such as to determine the robustness of the ANN classification when trained with the raw experimental points, with and without artificial noise, and also with the extracted parameters using different fitting techniques. Additionally, a genetic algorithm to similarly extract Cole-Cole function parameters (Halter et al., 2008) and the least-squares minimization algorithm for the fitting (Kun et al., 2003; 1999) were implemented to provide comparative results using the same methodology. It is expected that the stochastic algorithms may produce a set of parameters with small variances and with approximately the same mean values when

10 Will-be-set-by-IN-TECH

error measure. The calculated error is the information used to modify the weights of the connections, in order to reduce the errors on the next run. This procedure can be executed many times until the error converges to a minimum. The training procedure for the networks employed in this work are based on the following steps (error backpropagation procedure):

1. Feed the input data (Cole-Cole parameters or raw bioimpedance spectrum points) to the

2. Compute the output value of all neurons from the current layer and then propagate the

3. Compare the network outputs at the output layer with the expected ones to have an error

4. Propagate the measured errors to the previous layers, in a way that each neuron has a local

Different training algorithms can be used to adjust the weights of an ANN. It is common to supervised training algorithms to follow the same steps as the error backpropagation procedure, differing only in the weight adjusting step (Haykin, 1999). As an example, while the classical backpropagation has only a centralized learning rate, the iRPROP algorithm (Anastasiadis & Ph, 2003) has a learning rate for each connections and uses only the sign changes in the local error to guide the training. Other algorithms like NBN (Neuron by Neuron) uses the local errors to estimate second-order partial derivatives, which in some

In the bovine tissue classification experiment, two different fully connected cascade (FCC) topologies were employed. Both topologies had two hidden layers (with one neuron each) and an output layer with 4 neurons. The first one diagrammatically depicted in fig. 5(a) employed only 3 neurons in the input layer, for the *R*0, *τ* and *α* fitted Cole-Cole parameters, while the other one depicted in fig. 5(b) used 40 input neurons, corresponding to 20 impedance and reactance pairs. Both topologies had the goal of mapping the input data into one of 4 classes. To implement this, 4 output neurons were used, each one corresponding to a class. The NBN training algorithm was used to adjust the synaptic weights for the network to predict the

The milk adulterant detection experiment employed a multilayer perceptron (MLP) topology (as in fig. 5(c)), with 30 input neurons (15 impedance and reactance pairs), one hidden layer with two neurons and an output layer with 3 neurons. Each output neuron corresponds to

The evaluated experimental data were also added to artificial noise such as to determine the robustness of the ANN classification when trained with the raw experimental points, with and without artificial noise, and also with the extracted parameters using different fitting techniques. Additionally, a genetic algorithm to similarly extract Cole-Cole function parameters (Halter et al., 2008) and the least-squares minimization algorithm for the fitting (Kun et al., 2003; 1999) were implemented to provide comparative results using the same methodology. It is expected that the stochastic algorithms may produce a set of parameters with small variances and with approximately the same mean values when

one class (one of C classes coding). The ANN was trained with the NBN algorithm.

5. Adjust the connection weights of the network, based on the local errors;

network;

measure;

correct beef classes.

2.4.2.2 Experiments with the ANN testing

results to the next layer (forward propagation);

cases can lead to a faster training (Wilamowski, 2009).

error measure (back propagation);

(a) 3–2–4 FCC topology employed in the bovine tissue classification experiment.

(b) 40–2–4 FCC topology employed in the bovine tissue classification experiment. The input layer has 40 neurons condensed in the box or 20 times 2 ('x20').

(c) 30–2–4 MLP topology employed in the milk adulterant detection experiment. The input layer has 30 neurons condensed in the box or 15 times 2 ('x15').

Fig. 5. Topology of artificial neural networks used in the experiment of bioimpedance spectra classification with bovine tissue and adulterated milk.

executed several times with the same set of experimental data. This would happen if the Cole-Cole function were an appropriate representation of the acquired bioimpedance spectrum data.

The resulting fitted parameters were used as input to the neural networks such as to classify the data by means of its known type (liver, heart, topside, or back muscle). Another neural network performed the same classification, but using the unprocessed spectrum points as inputs. The input signal was incrementally added to white-gaussian noise (AWGN) such as to produce different signal to noise ratios. A total of 24 electrical impedance measurements

2.4.3.1 Detection of water and hydrogen peroxide in raw milk

compared with each other.

output among the other two output neurons.

of correct classifications were calculated.

2.4.3.2 Evaluation of mastitic milk

4 hours.

Milk may be adulterated by the addition of water, food coloring, conservants and substances used for the milk thickening, as for example the hydrogen peroxide. The commonest method of adulterating milk may be the dilution of water and a common method to detect it is by measuring its freezing point and use this value to calculate the percentage of the diluted water (Belloque et al., 2008). Another indication of water content would be provided by changes of bioimpedance spectra from the milk. To illustrate it, the bioimpedance spectra from raw milk with and without added water and hydrogen peroxide were determined and

Efficient Computational Techniques in Bioimpedance Spectroscopy 15

An ANN is subsequently used to classify the milk sample by using the points of the bioimpedance spectrum. For this purpose, samples of raw milk from 27 Holstein cows in lactation were obtained in a local farm. The sample sets were divided into two groups. The first group (A) was used to train the neural network with 16 samples. From this set, 4 samples were randomly taken and had distilled water added to them in a volumetric concentration of 10%; other 4 samples had hydrogen peroxide added to them in a volumetric concentration of 3%. In the second group (B), 11 samples were used for the ANN validation, this is, to test if the trained algorithm correctly classifies the samples, that were also equivalently adulterated. Before the measurements, the samples were kept in a refrigerator at a temperature of 4◦C for

The ANN used the multilayer perceptron topology of fig.5(c) with 30 neurons corresponding to resistance and reactance input values at 15 different frequency points in the bioimpedance spectrum. The output layer was formed by 3 neurons corresponding to a defined class (raw milk, milk with water and milk with hydrogen peroxide). If the bioimpedance spectrum of a sample containing H2O2 is fed to the ANN, this output neuron must have the largest value

The ANN was trained using the Neuron by Neuron (NBN) algorithm by using 24 spectra, in which 4 samples were adulterated with water and other 4 with H2O2. For the ANN validation, 30 milk bioimpedance spectra were measured in a different data set producing another data set different from the one used in the training. The validation spectra were then separated into three different classes associated with the evaluated types of samples and the percentage

The bioimpedance spectra of raw milk were acquired in samples from 17 Holstein cows, three of them with mastitis infection. Three milk samples of 100 ml from each animal were collected and stored in a refrigerator at a temperature of 4◦C. Four hours later, the bioimpedance spectrum from each sample was collected and the material was sent to an accredited laboratory to characterize the presence of somatic cells and bacteria by using flow cytometry1. Selected samples had the acquired bioimpedance spectrum data points processed and the experimental points and Cole-Cole parameters analyzed and shown for illustration

<sup>1</sup> The laboratory managed to follow the International Dairy Federation Standards 148:2008 and 196:2004. These standards specify, respectively, methods for the counting of somatic cells and for the quantitative

purposes of the changes presented in the mastitic and raw milk spectra.

determination of bacteriological quality in raw milk.

were divided into two sets. The first set is formed by 15 measured spectra and is used for the neural network training, while the second set formed by the remaining 9 measurements were used for the neural network validation test. Another 11 sets were created with AWGN having signal-to-noise ratio (SNR) from 2 to 32 dB with steps of 2 dB, forming the base validation set where each spectrum was used more than once to sum a total of 20 spectra in each set. Four ANN were created, one for each fitting algorithm and another for the raw spectra. Each neural network was trained with the spectra from the training set and tested with the validation sets, using the corresponding results from the extracted Cole-Cole parameter output or the raw spectra as input. The neural networks for the use with the testing of fitting algorithms have a 3 − 2 − 4 fully connected cascade (FCC) topology to allow a better generalization in the ANN (Wilamowski, 2009), as diagrammatically illustrated in fig. 5, with the 3 input neurons corresponding to the [*R*0, *τ*0, *α*] parameters and the 4 output neurons corresponding to the confidence level of each bovine tissue type.

The neural network that uses the set of bioimpedance spectrum points as input with a 40 − 2 − 4 FCC topology had the 40 inputs corresponding to the real and imaginary parts of the 20 input spectrum points associated with the lowest frequencies in the experimental spectrum which would correspond to a maximum frequency of 60 kHz.

One ANN was trained with the parameters fitted by the PSO algorithm using the training set, by exposing the ANN to the sample values associated with the input that corresponds to the extracted Cole-Cole parameters. After that, the neural network performance was measured to classify the sample type correctly. The rate of correct classifications was calculated by using the extracted parameters and also the raw data from 11 spectrum and using the corresponding trained ANN.

#### **2.4.3 Raw milk evaluation through bioimpedance spectra**

In the dairy industry, conductivity measurements are made to test for abnormal milk. This is somehow similar to the process of obtaining a bioimpedance spectrum from a milk sample. However, in conductivity tests the sample is usually interrogated at a single frequency and the results give false positives and negatives (Belloque et al., 2008). Conductivity, therefore bioimpedance (Piton et al., 1988), and acidity measurements are also used to measure microbial contents of the milk, being indirect and rapid methods (Belloque et al., 2008; Hamann & Zecconi, 1998). The drawbacks of these methods are associated with the lack of sensitivity and specificity. In addition, the conductivity test is also included in screening tests to detect mastitis. Since mastitic milk contains pathogens and spoilage microorganisms, and it is also characterized by an increase in Na<sup>+</sup> and Cl<sup>−</sup> as well as leucocytes (Kitchen, 1981), this may be indicated by changes in bioimpedance spectrum (Bertemes-Filho, Negri & Paterno, 2010) as discussed here, and it would also characterize the analysis of raw milk as of a cell suspension.

Other changes in the milk, which may not have its causes in a sick animal, could also be indicated by changes in the bioimpedance spectrum, as when the milk has water or hydrogen peroxide, for example, added to it for fraudulent purposes (Bertemes-Filho et al., 2011). The modulus and phase of the bioimpedance along a frequency range containing more than one frequency point is therefore an extension of the typical measurement of conductivity in the process of milk quality evaluation and is justified by previous published results.

12 Will-be-set-by-IN-TECH

were divided into two sets. The first set is formed by 15 measured spectra and is used for the neural network training, while the second set formed by the remaining 9 measurements were used for the neural network validation test. Another 11 sets were created with AWGN having signal-to-noise ratio (SNR) from 2 to 32 dB with steps of 2 dB, forming the base validation set where each spectrum was used more than once to sum a total of 20 spectra in each set. Four ANN were created, one for each fitting algorithm and another for the raw spectra. Each neural network was trained with the spectra from the training set and tested with the validation sets, using the corresponding results from the extracted Cole-Cole parameter output or the raw spectra as input. The neural networks for the use with the testing of fitting algorithms have a 3 − 2 − 4 fully connected cascade (FCC) topology to allow a better generalization in the ANN (Wilamowski, 2009), as diagrammatically illustrated in fig. 5, with the 3 input neurons corresponding to the [*R*0, *τ*0, *α*] parameters and the 4 output neurons corresponding to the

The neural network that uses the set of bioimpedance spectrum points as input with a 40 − 2 − 4 FCC topology had the 40 inputs corresponding to the real and imaginary parts of the 20 input spectrum points associated with the lowest frequencies in the experimental spectrum

One ANN was trained with the parameters fitted by the PSO algorithm using the training set, by exposing the ANN to the sample values associated with the input that corresponds to the extracted Cole-Cole parameters. After that, the neural network performance was measured to classify the sample type correctly. The rate of correct classifications was calculated by using the extracted parameters and also the raw data from 11 spectrum and using the corresponding

In the dairy industry, conductivity measurements are made to test for abnormal milk. This is somehow similar to the process of obtaining a bioimpedance spectrum from a milk sample. However, in conductivity tests the sample is usually interrogated at a single frequency and the results give false positives and negatives (Belloque et al., 2008). Conductivity, therefore bioimpedance (Piton et al., 1988), and acidity measurements are also used to measure microbial contents of the milk, being indirect and rapid methods (Belloque et al., 2008; Hamann & Zecconi, 1998). The drawbacks of these methods are associated with the lack of sensitivity and specificity. In addition, the conductivity test is also included in screening tests to detect mastitis. Since mastitic milk contains pathogens and spoilage microorganisms, and it is also characterized by an increase in Na<sup>+</sup> and Cl<sup>−</sup> as well as leucocytes (Kitchen, 1981), this may be indicated by changes in bioimpedance spectrum (Bertemes-Filho, Negri & Paterno, 2010) as discussed here, and it would also characterize the analysis of raw milk as of a cell

Other changes in the milk, which may not have its causes in a sick animal, could also be indicated by changes in the bioimpedance spectrum, as when the milk has water or hydrogen peroxide, for example, added to it for fraudulent purposes (Bertemes-Filho et al., 2011). The modulus and phase of the bioimpedance along a frequency range containing more than one frequency point is therefore an extension of the typical measurement of conductivity in the

process of milk quality evaluation and is justified by previous published results.

confidence level of each bovine tissue type.

trained ANN.

suspension.

which would correspond to a maximum frequency of 60 kHz.

**2.4.3 Raw milk evaluation through bioimpedance spectra**

## 2.4.3.1 Detection of water and hydrogen peroxide in raw milk

Milk may be adulterated by the addition of water, food coloring, conservants and substances used for the milk thickening, as for example the hydrogen peroxide. The commonest method of adulterating milk may be the dilution of water and a common method to detect it is by measuring its freezing point and use this value to calculate the percentage of the diluted water (Belloque et al., 2008). Another indication of water content would be provided by changes of bioimpedance spectra from the milk. To illustrate it, the bioimpedance spectra from raw milk with and without added water and hydrogen peroxide were determined and compared with each other.

An ANN is subsequently used to classify the milk sample by using the points of the bioimpedance spectrum. For this purpose, samples of raw milk from 27 Holstein cows in lactation were obtained in a local farm. The sample sets were divided into two groups. The first group (A) was used to train the neural network with 16 samples. From this set, 4 samples were randomly taken and had distilled water added to them in a volumetric concentration of 10%; other 4 samples had hydrogen peroxide added to them in a volumetric concentration of 3%. In the second group (B), 11 samples were used for the ANN validation, this is, to test if the trained algorithm correctly classifies the samples, that were also equivalently adulterated. Before the measurements, the samples were kept in a refrigerator at a temperature of 4◦C for 4 hours.

The ANN used the multilayer perceptron topology of fig.5(c) with 30 neurons corresponding to resistance and reactance input values at 15 different frequency points in the bioimpedance spectrum. The output layer was formed by 3 neurons corresponding to a defined class (raw milk, milk with water and milk with hydrogen peroxide). If the bioimpedance spectrum of a sample containing H2O2 is fed to the ANN, this output neuron must have the largest value output among the other two output neurons.

The ANN was trained using the Neuron by Neuron (NBN) algorithm by using 24 spectra, in which 4 samples were adulterated with water and other 4 with H2O2. For the ANN validation, 30 milk bioimpedance spectra were measured in a different data set producing another data set different from the one used in the training. The validation spectra were then separated into three different classes associated with the evaluated types of samples and the percentage of correct classifications were calculated.

#### 2.4.3.2 Evaluation of mastitic milk

The bioimpedance spectra of raw milk were acquired in samples from 17 Holstein cows, three of them with mastitis infection. Three milk samples of 100 ml from each animal were collected and stored in a refrigerator at a temperature of 4◦C. Four hours later, the bioimpedance spectrum from each sample was collected and the material was sent to an accredited laboratory to characterize the presence of somatic cells and bacteria by using flow cytometry1. Selected samples had the acquired bioimpedance spectrum data points processed and the experimental points and Cole-Cole parameters analyzed and shown for illustration purposes of the changes presented in the mastitic and raw milk spectra.

<sup>1</sup> The laboratory managed to follow the International Dairy Federation Standards 148:2008 and 196:2004. These standards specify, respectively, methods for the counting of somatic cells and for the quantitative determination of bacteriological quality in raw milk.

0 100 200 300 400 500

 Mango Experimental Modulus Mango Estimated Modulus Absolute Error

 Banana Experimental Modulus Banana Estimated Modulus Absolute Error

 Potato Experimental Modulus Potato Estimated Modulus Absolute Error

 Guava Experimental Modulus Guava Estimated Modulus Absolute Error

0 100 200 300 400 500

0 100 200 300 400 500

0 100 200 300 400 500

Frequency (kHz)

0 100 200 300 400 500

Mango Experimental Phase

Banana Experimental Phase

Potato Experimental Phase

Guava Experimental Phase

0 100 200 300 400 500

0 100 200 300 400 500

0 100 200 300 400 500

Frequency (kHz)


Phase (rad)

Efficient Computational Techniques in Bioimpedance Spectroscopy 17


Phase (rad)


Phase (rad)


Phase (rad)

Fig. 6. Modulus retrieval obtained with the phase/modulus retrieval algorithm previously described. The input data was the interpolated 64 points of phase from the mango, banana,

Least-Squares (LS) fitting. Since the LS method is not stochastic, the deviation statistic is not applicable in this case. In fig. 7, the percentage of correct classification rate is depicted for the trained artificial neural networks using as inputs the parameter sets resulting from each of the fitting methods. The unprocessed bioimpedance spectrum points (raw) were used as inputs to an ANN with 40 input neurons, and the classification rate is also depicted in fig.7 together with the results from the testing of the PSO, LS and GA for an ANN with three input neurons.

> Fitting Method *n*¯ *σ<sup>n</sup>* PSO 30 5.63 LS 134 Not applicable GA 600 402.33

Table 2. Mean number of iterations, *n*¯, for convergence of each fitting method producing a parameter set for the ANN input and its standard deviation for the stochastic fitting

From fig. 7, one may infer that the GA and proposed PSO methods demonstrate a higher accuracy and noise tolerance than the LS method, since under a higher SNR the used parameters provide the information for the correct classification of the samples. The LS method does not provide a better accuracy since for higher values of SNR, the experimental

0,0 0,2 0,4 0,6 0,8 1,0

Normalized

Normalized

Normalized

Normalized

Modulus

Modulus

Modulus

Modulus

0,0 0,2 0,4 0,6 0,8 1,0

0,0 0,2 0,4 0,6 0,8 1,0

0,0 0,2 0,4 0,6 0,8 1,0

potato and guava.

methods, *σn*.

## **3. Results and discussion**

## **3.1 Retrieving modulus from phase in experimental bioimpedance spectra**

In the experiment to illustrate the effectiveness of modulus retrieval from the data acquired by the bioimpedance spectrometer, four vegetables were excited by a signal from the tetrapolar probe. Phase and modulus were acquired in the previously specified range at non-uniformly distributed frequencies. The first procedure in the experimental data was the interpolation to produce uniformly spaced points in the frequency range. The values of phase from the bioimpedance spectrum fed the algorithm to retrieve modulus. It is seen that the impedance at high frequencies is a small value tending to zero in one of the vegetables. However both data allowed the recovery of modulus from phase with an average error as shown in table 1 and as shown in fig. 6, where the behavior of the estimated modulus error is shown with the modulus from phase and the actual acquired phase for mango, banana, potato and guava. A higher error was observe in low frequencies since the lowest measured frequency was 500 Hz. In this experiment, the constraints for the use of the algorithm are such that it allowed the modulus recovery from the phase with a well-behaved error, and one can also infer that depending on the evaluated sample, the response of the algorithm may provide smaller errors.

As a general rule, the resistance at infinite frequencies must tend to zero for the algorithm to converge. In the case of an organic material suspension or a sample with a previously known bioimpedance and whose spectrum are not supposed to change much during its interrogation, the algorithm may be a convenient choice to substitute modulus measurements in bioimpedance interrogations while reading only phase. The resulting magnitude value associated with the modulus is normalized, since it is produced differently from the actual impedance value to a scale factor, requiring calibration.


Table 1. Mean errors in modulus retrieval and standard deviation for the evaluated interval for mango, banana, potato and guava.

#### **3.2 PSO fitting using the Cole-Cole function in bovine flesh bioimpedance**

Due to the noise incorporation characteristics (convergence to the mean noise level) caused by the presence of a constant value in the model function, the *R*∞ parameter is neither included in the results, nor in the classification experiment. Since the signal-to-noise ratio (SNR) of the experimental data was changed by adding white gaussian noise to the experimental data points, this would be another reason not to include the *R*∞ parameter in the performance tests. The *R*<sup>0</sup> and *α* parameters did not show any significant fluctuation differences when they resulted from any of the tested fitting algorithms, either the PSO or the Genetic Algorithm or the Least-Squares ordinary fitting, implemented as proposed in the literature (Halter et al., 2008; Kun et al., 2003; 1999). The results of the computational performance experiment depicted in table 2 contains both the mean and sample standard deviation of the required iterations for the convergence of the PSO algorithm and also for comparison purposes, the iterations needed for the convergence of the Genetic Algorithm and for the execution of the 14 Will-be-set-by-IN-TECH

In the experiment to illustrate the effectiveness of modulus retrieval from the data acquired by the bioimpedance spectrometer, four vegetables were excited by a signal from the tetrapolar probe. Phase and modulus were acquired in the previously specified range at non-uniformly distributed frequencies. The first procedure in the experimental data was the interpolation to produce uniformly spaced points in the frequency range. The values of phase from the bioimpedance spectrum fed the algorithm to retrieve modulus. It is seen that the impedance at high frequencies is a small value tending to zero in one of the vegetables. However both data allowed the recovery of modulus from phase with an average error as shown in table 1 and as shown in fig. 6, where the behavior of the estimated modulus error is shown with the modulus from phase and the actual acquired phase for mango, banana, potato and guava. A higher error was observe in low frequencies since the lowest measured frequency was 500 Hz. In this experiment, the constraints for the use of the algorithm are such that it allowed the modulus recovery from the phase with a well-behaved error, and one can also infer that depending on

**3.1 Retrieving modulus from phase in experimental bioimpedance spectra**

the evaluated sample, the response of the algorithm may provide smaller errors.

**3.2 PSO fitting using the Cole-Cole function in bovine flesh bioimpedance**

impedance value to a scale factor, requiring calibration.

for mango, banana, potato and guava.

As a general rule, the resistance at infinite frequencies must tend to zero for the algorithm to converge. In the case of an organic material suspension or a sample with a previously known bioimpedance and whose spectrum are not supposed to change much during its interrogation, the algorithm may be a convenient choice to substitute modulus measurements in bioimpedance interrogations while reading only phase. The resulting magnitude value associated with the modulus is normalized, since it is produced differently from the actual

Vegetable Mean Error Deviation *σ* Mango 2.34% 2.84% Banana 1.54% 2.86% Potato 5.2% 6.06% Guava 2.94% 1.96% Table 1. Mean errors in modulus retrieval and standard deviation for the evaluated interval

Due to the noise incorporation characteristics (convergence to the mean noise level) caused by the presence of a constant value in the model function, the *R*∞ parameter is neither included in the results, nor in the classification experiment. Since the signal-to-noise ratio (SNR) of the experimental data was changed by adding white gaussian noise to the experimental data points, this would be another reason not to include the *R*∞ parameter in the performance tests. The *R*<sup>0</sup> and *α* parameters did not show any significant fluctuation differences when they resulted from any of the tested fitting algorithms, either the PSO or the Genetic Algorithm or the Least-Squares ordinary fitting, implemented as proposed in the literature (Halter et al., 2008; Kun et al., 2003; 1999). The results of the computational performance experiment depicted in table 2 contains both the mean and sample standard deviation of the required iterations for the convergence of the PSO algorithm and also for comparison purposes, the iterations needed for the convergence of the Genetic Algorithm and for the execution of the

**3. Results and discussion**

Fig. 6. Modulus retrieval obtained with the phase/modulus retrieval algorithm previously described. The input data was the interpolated 64 points of phase from the mango, banana, potato and guava.

Least-Squares (LS) fitting. Since the LS method is not stochastic, the deviation statistic is not applicable in this case. In fig. 7, the percentage of correct classification rate is depicted for the trained artificial neural networks using as inputs the parameter sets resulting from each of the fitting methods. The unprocessed bioimpedance spectrum points (raw) were used as inputs to an ANN with 40 input neurons, and the classification rate is also depicted in fig.7 together with the results from the testing of the PSO, LS and GA for an ANN with three input neurons.


Table 2. Mean number of iterations, *n*¯, for convergence of each fitting method producing a parameter set for the ANN input and its standard deviation for the stochastic fitting methods, *σn*.

From fig. 7, one may infer that the GA and proposed PSO methods demonstrate a higher accuracy and noise tolerance than the LS method, since under a higher SNR the used parameters provide the information for the correct classification of the samples. The LS method does not provide a better accuracy since for higher values of SNR, the experimental


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bioimpedance spectrum

**3.3.1 Spectra of adulterated milk**

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(a) Modulus and Phase of bovine liver

**3.3 Abnormal milk testing with bioimpedance**

inserted by the BIA system and the probe.

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curves associated with the fitted Cole-Cole functions using PSO, LS and GA.




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(b) Modulus and Phase of bovine heart



 

 

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Efficient Computational Techniques in Bioimpedance Spectroscopy 19

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Fig. 8. Experimental data points containing modulus and phase of bioimpedance spectra of liver and heart samples from bovine flesh tissue. Experimental points are shown with the

In fig. 9(a),(b) and (c), the bioimpedance spectra from the pure raw milk, and raw milk adulterated with water and hydrogen peroxide are depicted. The data were processed with the three fitting algorithms, and it is evidenced that the LS algorithm did not allow a proper fitting to the experimental points since one may observe a larger error along a wide frequency interval in the fitting. Since the PSO and GA have an equivalent qualitative performance, but a better computational performance in the PSO, the Cole-Cole parameters may represent more properly the information contained in the bioimpedance spectra. For higher frequencies, the Cole-Cole function is not capable of representing the experimental points characteristics in the phase spectrum, due to non-ideal characteristics and intrinsic artifacts and distortions

Comparatively one can observe some improvement in the fitting while using the PSO/GA algorithms in these data. However, distortions and artifacts produced by stray capacitance may cause a deviation in the resistance at high frequencies while obtaining the Cole-Cole parameters. Such changes may be observed in the complex impedance arc locus diagram plotted as the imaginary part of the bioimpedance as a function of its real part. The capacitive effect causes a hook like form in this diagram and the fitting process it may also produce a set of Cole-Cole parameters with negative resistances at high frequencies, as illustrated in

In fig.10(a), the proportion of correct classification when using the raw data points to the trained ANN that classify adulterated milk is depicted and the average value of correct classifications is depicted as the total rate. It is observed that, if no other substance in the milk is related to the bioimpedance changes, except for the adulterants, the ANN is capable of properly characterizing the presence of water or hydrogen peroxide with a low error rate. The

 -

 -

   -

Fig. 7. Neural network classification rate when using as inputs the parameters from the fitting methods (PSO, GA and LS) and also the unprocessed bioimpedance spectrum points (Raw).

data still have distortions caused by artifacts or external effects in the system that may cause its parameters to provide a wrong guess in the classification. The Cole-Cole parameters with any fitting technique also produce improved results than when using a data set with the raw spectrum points in the classification. The quality of the LS fitting performance is influenced by its noise sensitivity. When tested with experimental points that have distortions from the electronic system or errors caused during the acquisition process from the material sample, the LS algorithm converged prematurely, producing parameter sets that deteriorated the classification. As the inputs provided by the PSO and GA methods produced a better classification rate and resulted in networks with reduced neurons and synaptic connections than using the full spectrum points, it is possible to recommend their use for bioimpedance classification systems even under worse SNR then usual.

In addition, the used model function was such that it was appropriate for the proposed methodology and allowed the verification of a conformity between the experimental bioimpedance spectrum and the Cole-Cole function to a certain degree, even with AWGN and other unavoidable artifacts. In the case of the experimental points without artificial AWGN added to the data, the results of the fitted spectra are depicted in fig. 8. In this case, it is also observed that the PSO/GA methods produce a better approximation to the experimental data, intrinsic distortion of the used BIA system notwithstanding.

It is equivalently shown in table 2, about the performance of the algorithms, that the PSO method converges faster, requiring less iterations than the GA method. The PSO algorithm also has a linear complexity per iteration with respect to the input data vector size. Due to implementation characteristics and its deterministic nature, the LS algorithm has the fastest performance, two orders of magnitude faster than what is obtained with the PSO and GA. It is possible to infer that the LS method has a superior computational performance than the other two fitting methods, and is followed respectively by the PSO and GA methods.

(a) Modulus and Phase of bovine liver bioimpedance spectrum (b) Modulus and Phase of bovine heart bioimpedance spectrum

Fig. 8. Experimental data points containing modulus and phase of bioimpedance spectra of liver and heart samples from bovine flesh tissue. Experimental points are shown with the curves associated with the fitted Cole-Cole functions using PSO, LS and GA.

#### **3.3 Abnormal milk testing with bioimpedance**

#### **3.3.1 Spectra of adulterated milk**

16 Will-be-set-by-IN-TECH


Fig. 7. Neural network classification rate when using as inputs the parameters from the fitting methods (PSO, GA and LS) and also the unprocessed bioimpedance spectrum points

data still have distortions caused by artifacts or external effects in the system that may cause its parameters to provide a wrong guess in the classification. The Cole-Cole parameters with any fitting technique also produce improved results than when using a data set with the raw spectrum points in the classification. The quality of the LS fitting performance is influenced by its noise sensitivity. When tested with experimental points that have distortions from the electronic system or errors caused during the acquisition process from the material sample, the LS algorithm converged prematurely, producing parameter sets that deteriorated the classification. As the inputs provided by the PSO and GA methods produced a better classification rate and resulted in networks with reduced neurons and synaptic connections than using the full spectrum points, it is possible to recommend their use for bioimpedance

In addition, the used model function was such that it was appropriate for the proposed methodology and allowed the verification of a conformity between the experimental bioimpedance spectrum and the Cole-Cole function to a certain degree, even with AWGN and other unavoidable artifacts. In the case of the experimental points without artificial AWGN added to the data, the results of the fitted spectra are depicted in fig. 8. In this case, it is also observed that the PSO/GA methods produce a better approximation to the experimental data,

It is equivalently shown in table 2, about the performance of the algorithms, that the PSO method converges faster, requiring less iterations than the GA method. The PSO algorithm also has a linear complexity per iteration with respect to the input data vector size. Due to implementation characteristics and its deterministic nature, the LS algorithm has the fastest performance, two orders of magnitude faster than what is obtained with the PSO and GA. It is possible to infer that the LS method has a superior computational performance than the other

two fitting methods, and is followed respectively by the PSO and GA methods.



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classification systems even under worse SNR then usual.

intrinsic distortion of the used BIA system notwithstanding.







 

(Raw).


 -

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> In fig. 9(a),(b) and (c), the bioimpedance spectra from the pure raw milk, and raw milk adulterated with water and hydrogen peroxide are depicted. The data were processed with the three fitting algorithms, and it is evidenced that the LS algorithm did not allow a proper fitting to the experimental points since one may observe a larger error along a wide frequency interval in the fitting. Since the PSO and GA have an equivalent qualitative performance, but a better computational performance in the PSO, the Cole-Cole parameters may represent more properly the information contained in the bioimpedance spectra. For higher frequencies, the Cole-Cole function is not capable of representing the experimental points characteristics in the phase spectrum, due to non-ideal characteristics and intrinsic artifacts and distortions inserted by the BIA system and the probe.

> Comparatively one can observe some improvement in the fitting while using the PSO/GA algorithms in these data. However, distortions and artifacts produced by stray capacitance may cause a deviation in the resistance at high frequencies while obtaining the Cole-Cole parameters. Such changes may be observed in the complex impedance arc locus diagram plotted as the imaginary part of the bioimpedance as a function of its real part. The capacitive effect causes a hook like form in this diagram and the fitting process it may also produce a set of Cole-Cole parameters with negative resistances at high frequencies, as illustrated in fig. 9 (d).

> In fig.10(a), the proportion of correct classification when using the raw data points to the trained ANN that classify adulterated milk is depicted and the average value of correct classifications is depicted as the total rate. It is observed that, if no other substance in the milk is related to the bioimpedance changes, except for the adulterants, the ANN is capable of properly characterizing the presence of water or hydrogen peroxide with a low error rate. The

(a) Modulus and Phase of bioimpedance spectrum from raw milk

(b) Modulus and Phase of the bioimpedance spectrum from milk adulterated with water

Fig. 10. ANN correct classification rate for adulterated milk when using raw spectrum points

Efficient Computational Techniques in Bioimpedance Spectroscopy 21

In the evaluation of the mastitic milk with different concentrations of cells, the graphs showing two examples of complex impedance arc locus are depicted in fig.11 (a) and (b). The somatic cell concentration (SCC) of the 17 milk samples as obtained from the accredited laboratory is shown in fig.11(c). The concentrations of 3000 cells per milliliter and 1.274 millions of cells per milliliter, as determined by the characterization in the laboratory, illustrate that the impedance spectra may confirm the differences between a mastitic milk sample with low cell concentration and mastitic milk. The impedance spectrum differences may be observed in the Cole-Cole parameters obtained in the fitting with the PSO technique while using also the compensation to reduce stray impedance effects, as depicted in fig. 11(a) and (b). The values of the fitting are depicted in table 3 for illustration purposes only and not to be used as references of mastitic milk bioimpedances. The compensation of stray impedance effects, however, may be used in any bioimpedance spectrum containing distortions due to stray impedances at high frequencies. The technique that shows how the optimal time delay for this compensation is obtained will be published elsewhere. The used *Td* s are also shown in table 3 together with the mean squared error after the convergence of the algorithm and visually shows that the mean squared error between experimental points and fitted curves are reduced after correction. The resistances obtained by the model function fitting are also naturally reduced to zero, as observed in table 3. The parameters that change after time delay compensation may be

Parameters Mastitic milk Compensated mastitic milk Raw milk Compensated raw milk

*R*<sup>∞</sup> [Ω] −14.6 0 −11.7 0 *R*<sup>0</sup> [Ω] 94.9 94.8 100.3 100.7 *α* 1 1 0.99 0.96 *τ* [*μ*s] 0.552 0.515 0.711 0.672 *Td* [*μ*s] 0 0.100726 0 0.110161

Mean Squared Error 14.6 9.2 31.6 26.9

Table 3. Cole-Cole parameters and final fitting mean squared error from the fitting with PSO algorithm for the spectra of mastitic milk samples and the bioimpedance from the raw milk sample, also containing the parameters from the fitted spectra compensated with specific

as inputs to the ANN.

time delays *Td*.

**3.3.2 Spectra of mastitic milk**

(c) Modulus and Phase of the bioimpedance spectrum from milk adulterated with hydrogen peroxide (d) Complex impedance arc locus plot example of the bioimpedance spectrum from raw milk

Fig. 9. Experimental bioimpedance spectrum and the results from the fitting with PSO, GA and LS algorithms. Data were obtained from raw milk and from raw milk adulterated with distilled water and with hydrogen peroxide. The complex impedance arc locus plot is depicted in fig. 9(d) associated with the raw milk sample.

used bioimpedance data have artifacts that were not corrected, and this was partly responsible for the non-null error in the classification rate.

In this evaluation of raw milk, it is possible to evidence the presence of artifacts that may invalidate the bioimpedance spectra. In order to avoid discarding spectra that may be corrupted mainly by impedance stray effects, usually the experimental data shown to have a hook-like form in the impedance plot at high frequencies requires that the data points be multiplied by a linear phase factor corresponding to a delay in the time domain. This would fit the experimental data with such distortions by multiplying the impedance function, i.e., an exponential factor *e*−*jωTd* (De Lorenzo et al., 1997). It would be equivalent to a delay of *Td* s in the impedance time domain function if *Td* is real and it would partly compensate the high frequency artifacts. The only problem in this compensation resides in the choice of the optimal *Td* value, which is usually done on a trial-and-error basis.

Fig. 10. ANN correct classification rate for adulterated milk when using raw spectrum points as inputs to the ANN.

#### **3.3.2 Spectra of mastitic milk**

18 Will-be-set-by-IN-TECH

 - 

+, 


 


+ +, + +-, +-


from raw milk

 -

 -

Fig. 9. Experimental bioimpedance spectrum and the results from the fitting with PSO, GA and LS algorithms. Data were obtained from raw milk and from raw milk adulterated with distilled water and with hydrogen peroxide. The complex impedance arc locus plot is

used bioimpedance data have artifacts that were not corrected, and this was partly responsible

In this evaluation of raw milk, it is possible to evidence the presence of artifacts that may invalidate the bioimpedance spectra. In order to avoid discarding spectra that may be corrupted mainly by impedance stray effects, usually the experimental data shown to have a hook-like form in the impedance plot at high frequencies requires that the data points be multiplied by a linear phase factor corresponding to a delay in the time domain. This would fit the experimental data with such distortions by multiplying the impedance function, i.e., an exponential factor *e*−*jωTd* (De Lorenzo et al., 1997). It would be equivalent to a delay of *Td* s in the impedance time domain function if *Td* is real and it would partly compensate the high frequency artifacts. The only problem in this compensation resides in the choice of the

 -

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adulterated with water




 

(d) Complex impedance arc locus plot example of the bioimpedance spectrum

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(b) Modulus and Phase of the bioimpedance spectrum from milk

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spectrum from raw milk

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(c) Modulus and Phase of the bioimpedance spectrum from milk adulterated with hydrogen peroxide

depicted in fig. 9(d) associated with the raw milk sample.

optimal *Td* value, which is usually done on a trial-and-error basis.

for the non-null error in the classification rate.

(a) Modulus and Phase of bioimpedance

 -

 -

 -

 - In the evaluation of the mastitic milk with different concentrations of cells, the graphs showing two examples of complex impedance arc locus are depicted in fig.11 (a) and (b). The somatic cell concentration (SCC) of the 17 milk samples as obtained from the accredited laboratory is shown in fig.11(c). The concentrations of 3000 cells per milliliter and 1.274 millions of cells per milliliter, as determined by the characterization in the laboratory, illustrate that the impedance spectra may confirm the differences between a mastitic milk sample with low cell concentration and mastitic milk. The impedance spectrum differences may be observed in the Cole-Cole parameters obtained in the fitting with the PSO technique while using also the compensation to reduce stray impedance effects, as depicted in fig. 11(a) and (b). The values of the fitting are depicted in table 3 for illustration purposes only and not to be used as references of mastitic milk bioimpedances. The compensation of stray impedance effects, however, may be used in any bioimpedance spectrum containing distortions due to stray impedances at high frequencies. The technique that shows how the optimal time delay for this compensation is obtained will be published elsewhere. The used *Td* s are also shown in table 3 together with the mean squared error after the convergence of the algorithm and visually shows that the mean squared error between experimental points and fitted curves are reduced after correction. The resistances obtained by the model function fitting are also naturally reduced to zero, as observed in table 3. The parameters that change after time delay compensation may be


Table 3. Cole-Cole parameters and final fitting mean squared error from the fitting with PSO algorithm for the spectra of mastitic milk samples and the bioimpedance from the raw milk sample, also containing the parameters from the fitted spectra compensated with specific time delays *Td*.


milk



properly chosen time delay parameter.

Mean Squared Error

time delays *Td*.

Parameters Raw milk Compensated

 

(a) Complex impedance diagram of raw

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Raw Milk

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  -

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with water

Efficient Computational Techniques in Bioimpedance Spectroscopy 23


Fig. 12. The complex impedance arc locus diagram for samples of milk adulterated with water and hydrogen peroxide. The plots show the experimental points, the curve fitting with the Cole-Cole model function, and also the curve fitting containing the phase factor with the

> Milk + H2O

*R*<sup>∞</sup> [Ω] −8.8 0 −9.7 0 −5.9 0 *R*<sup>0</sup> [Ω] 60.6 59.9 83.5 82.7 62 62.4 *α* 1 1 1 1 1 0.95 *τ* [*μ*s] 2.446 2.014 3.019 2.575 1.882 1.733 *Td* [*μ*s] 0 0.595 0 0.631 0 0.301

Table 4. Cole-Cole parameters and final fitting mean squared error from the fitting with PSO algorithm for the spectra of adulterated milk samples and the bioimpedance from a raw milk sample, also containing the parameters from the fitted spectra compensated with specific

of the mastitic milk data. The complex impedance arc locus of the evaluated cases can be seen in fig. 12. It is evident from fig. 12 that the compensating time delay improves the fitting, indicating that the stray impedance effect is responsible for an important contribution to the

24 4.7 39.3 13.4 10.8 6.7

with hydrogen peroxide

 

(c) Complex impedance diagram of milk

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(b) Complex impedance diagram of milk

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> 

 

Compensated Milk + H2O

Milk + H2O2

Compensated Milk + H2O2

(a) Complex impedance diagram of mastitic milk with 3000 cells per milliliter (b) Complex impedance diagram of mastitic milk with 1, 274 millions of cells per milliliter

(c) Somatic cells concentration (SCC) for the 17 Holstein cows milk samples, given in thousands of cells per milliliter for each cow sample.

Fig. 11. The complex impedance arc locus diagram for two samples of milk with tolerable concentration of mastitis cells in fig. 11(a), a concentration above the limit characterizing mastitic milk in fig. 11(b). Experimental points and fitted curves with PSO and with the modified model function using the *Td* parameter. In fig. 11(c), SCC for the evaluated samples.

markedly observed in the relaxation constant in the Cole-Cole function. The reciprocal of the relaxation constant would be related to the characteristic frequency of the sample that changes from 1.811 MHz to 1.941 MHz in the mastitic milk and in the compensated parameters. This indicates also that the experimental bioimpedance spectrum does not contain this frequency, requiring a wider frequency interval to evaluate more accurately the characteristics of the sample. In the low cell concentration mastitic milk, the parameters reflect a change in the frequency from 1.406 MHz to 1.488 MHz, that shows the same limitation in the experimental points, requiring a more detailed study where the spectrum will be analyzed with an analyzer in a wider frequency spectrum range.

In the results shown in table 4, the same compensation with a proper chosen time delay is applied to the Cole-Cole fitting and is compared to the parameters fitted with the PSO algorithm without compensation. One may observe that the low frequency resistance and the dispersion parameter *α* is not affected by the compensation, but the compensated high frequency resistances are no longer negative. The improvement in the mean squared error of the final fitting procedure is significantly reduced, more than in the case of the compensation 20 Will-be-set-by-IN-TECH

 -

 - 

per milliliter

(c) Somatic cells concentration (SCC) for the 17 Holstein cows milk samples, given in thousands of cells per milliliter for

Fig. 11. The complex impedance arc locus diagram for two samples of milk with tolerable concentration of mastitis cells in fig. 11(a), a concentration above the limit characterizing mastitic milk in fig. 11(b). Experimental points and fitted curves with PSO and with the modified model function using the *Td* parameter. In fig. 11(c), SCC for the evaluated samples. markedly observed in the relaxation constant in the Cole-Cole function. The reciprocal of the relaxation constant would be related to the characteristic frequency of the sample that changes from 1.811 MHz to 1.941 MHz in the mastitic milk and in the compensated parameters. This indicates also that the experimental bioimpedance spectrum does not contain this frequency, requiring a wider frequency interval to evaluate more accurately the characteristics of the sample. In the low cell concentration mastitic milk, the parameters reflect a change in the frequency from 1.406 MHz to 1.488 MHz, that shows the same limitation in the experimental points, requiring a more detailed study where the spectrum will be analyzed with an analyzer

In the results shown in table 4, the same compensation with a proper chosen time delay is applied to the Cole-Cole fitting and is compared to the parameters fitted with the PSO algorithm without compensation. One may observe that the low frequency resistance and the dispersion parameter *α* is not affected by the compensation, but the compensated high frequency resistances are no longer negative. The improvement in the mean squared error of the final fitting procedure is significantly reduced, more than in the case of the compensation

each cow sample.

 -

(b) Complex impedance diagram of mastitic milk with 1, 274 millions of cells

 !"

> 

 - 

in a wider frequency spectrum range.

 -

 !"

> 

(a) Complex impedance diagram of mastitic milk with 3000 cells per milliliter

(a) Complex impedance diagram of raw milk (b) Complex impedance diagram of milk with water

(c) Complex impedance diagram of milk with hydrogen peroxide

Fig. 12. The complex impedance arc locus diagram for samples of milk adulterated with water and hydrogen peroxide. The plots show the experimental points, the curve fitting with the Cole-Cole model function, and also the curve fitting containing the phase factor with the properly chosen time delay parameter.


Table 4. Cole-Cole parameters and final fitting mean squared error from the fitting with PSO algorithm for the spectra of adulterated milk samples and the bioimpedance from a raw milk sample, also containing the parameters from the fitted spectra compensated with specific time delays *Td*.

of the mastitic milk data. The complex impedance arc locus of the evaluated cases can be seen in fig. 12. It is evident from fig. 12 that the compensating time delay improves the fitting, indicating that the stray impedance effect is responsible for an important contribution to the

evidence the interesting characteristic. During the evaluation of adulterated milk with typical adulterants, like water and hydrogen peroxide, the information would be present in the bioimpedance spectrum, but an identification of the exact adulterant or its quantity would

Efficient Computational Techniques in Bioimpedance Spectroscopy 25

The experimental data produced with the milk evaluation have also other characteristics not related to the sample itself, but to the instrumentation and also to reactions occurring between the sample and the electrode. The hook like figure in the complex plane arc locus in the milk measurements demonstrate the effect. Such a behavior may be considered due to adsorption in the impedance electrode in some types of samples. However, the hook-like characteristic of the spectrum may be due to impedance stray effects, either from the cables, electrodes or the electronic circuitry. This may be corrected in some cases with a change in the model, by considering the effect of a phase corresponding to a complex exponential in the model function. The optimal values were determined for the correction and the error in the fitting was significantly reduced in those sets of data. Specifically in the raw mastitic and adulterated milk, the Cole-Cole parameters were compared and the fitting algorithms are once again shown to be efficient in illustrating the computational power of the techniques in

The idea of determining efficient and simple algorithms to process bioimpedance spectra is a topic that may allow the implementation of sophisticated algorithms in embedded systems and could also improve the quality of the analysis produced by simple equipment. One can mention that in the case of the phase/modulus retrieval algorithms, since the technique is based on the use of the well-known fast-Fourier transform algorithm, it would be natural to implement it in embedded systems. However, the applications could not be restricted to such systems, since the use of the proposed algorithms may help improve the bioimpedance spectrum analysis while correcting experimental data and retrieving the more convenient information from the improved fitting algorithms. The methodology that uses artificial neural networks to evaluate the performance of the algorithms could also be used in systems that require automated analysis of bioimpedance spectra, as in an industrial environment to

As a direction to the future research efforts, a final goal for the use of such algorithms would be their implementation in reconfigurable hardware, more specifically, in field-programmable gate arrays (FPGA). Commercial systems already use such technologies, like the FPGA in bioimpedance spectrometers (Nacke et al., 2011). Therefore the evaluated techniques are suggested to be implemented in hardware, since the particle swarm optimization algorithms would be a good choice for this purpose. The arithmetic operations in the particle-swarm optimization update step requires only random number generation, and a series of summations and multiplications. In the phase/modulus retrieval algorithm case, the

The authors gratefully acknowledge the experimental data collected by Rogerio Martins Pereira, Rodrigo Stiz and Guilherme Martignago Zilli as students supervised in the

FFT could also be easily instantiated from the core provided by the FPGA company.

Laboratories of the Santa Catarina State University in Joinville City.

require other sensing systems.

bioimpedance spectroscopy.

characterize samples of milk or beef, for example.

**5. Future directions**

**6. Acknowledgements**

hook-like behavior of the complex impedance arc locus. Observing the dispersion parameter *α*, it is usually close to unity in every sample, compensated or not. This is an indication that the milk may be modeled by a single pole function with fitting errors of the same order of magnitude as shown in table 4 and 3. Differently from the mastitic milk analysis, the reciprocal of the relaxation constant is in the experimental frequency interval obtained with the BIA system. The characteristic frequency of the samples in the raw milk changes from 408 kHz to 496 kHz after compensation. Equivalently for adulterated milk with water and hydrogen peroxide, the changes occur from 331 kHz to 388 kHz and from 531 kHz to 577 kHz, respectively. These variations indicate an increase in the compensated characteristic frequency when the stray effects are compensated this way.

#### **4. Conclusion**

The authors report the use of computational intelligence and also well known digital signal processing algorithms in bioimpedance spectroscopy. The BIA analysis of data obtained from a custom made spectrometer were processed with a modulus retrieval algorithm from phase of bioimpedance spectra of vegetables showing the feasibility of using this specific and well known algorithm in a practical case. This would also allow the BIA system hardware to be simplified. In this case, since only the phase of the bioimpedance is going to be acquired to obtain the complete modulus of the bioimpedance spectrum, the involved electronic circuitry, as expected, may be reduced and the instrumentation amplifiers to measure modulus would be unnecessary. This would pave the way to embed algorithms in a much more simplified electronics for bioimpedance systems designed for specific applications as in the characterization of fruits, for example.

The bioimpedance data may also be processed with computational intelligence techniques. The authors improved already known techniques to fit experimental bioimpedance spectrum data to a specific model function. This is common practice in bioimpedance spectroscopy and is already implemented in commercial systems, however they do not use the techniques proposed here, only the least-squares algorithms, but no other more elaborate algorithms, like evolutionary techniques and particle-swarm optimization procedures. It is shown that the PSO technique has advantages over the already proposed procedures. The comparison of such techniques was implemented and artificial neural networks were used for the specific purpose of comparing them. The use of an Artificial Neural Network that receives as input the parameters produced by the fitting illustrates that different techniques, specifically the least-square fitting, simply would not be capable of allowing the identification of the correct tissue or the sample experimentally evaluated. The genetic algorithm and the particle-swarm optimization were capable of allowing the correct classification of the samples with experimental data added to noise in a much better proportion than the least-squares algorithm. Considering that the number of iterations in the PSO is much less than the genetic algorithm, and since they provide the same qualitative results in terms of classification, the PSO shows a superiority with respect to performance. The arithmetic complexity of the PSO is also an important characteristic that could facilitate embedded implementations.

Still in the dairy food applications, the idea of using bioimpedance to classify milk with the previously described techniques was also illustrated. Milk with different concentrations of mastitis cells were evaluated and the differences in the phase and modulus of the bioimpedance spectrum are noticed. However, the selectivity of the BIA system could not be demonstrated, and this would force one to use other additional sensing systems to evidence the interesting characteristic. During the evaluation of adulterated milk with typical adulterants, like water and hydrogen peroxide, the information would be present in the bioimpedance spectrum, but an identification of the exact adulterant or its quantity would require other sensing systems.

The experimental data produced with the milk evaluation have also other characteristics not related to the sample itself, but to the instrumentation and also to reactions occurring between the sample and the electrode. The hook like figure in the complex plane arc locus in the milk measurements demonstrate the effect. Such a behavior may be considered due to adsorption in the impedance electrode in some types of samples. However, the hook-like characteristic of the spectrum may be due to impedance stray effects, either from the cables, electrodes or the electronic circuitry. This may be corrected in some cases with a change in the model, by considering the effect of a phase corresponding to a complex exponential in the model function. The optimal values were determined for the correction and the error in the fitting was significantly reduced in those sets of data. Specifically in the raw mastitic and adulterated milk, the Cole-Cole parameters were compared and the fitting algorithms are once again shown to be efficient in illustrating the computational power of the techniques in bioimpedance spectroscopy.

## **5. Future directions**

22 Will-be-set-by-IN-TECH

hook-like behavior of the complex impedance arc locus. Observing the dispersion parameter *α*, it is usually close to unity in every sample, compensated or not. This is an indication that the milk may be modeled by a single pole function with fitting errors of the same order of magnitude as shown in table 4 and 3. Differently from the mastitic milk analysis, the reciprocal of the relaxation constant is in the experimental frequency interval obtained with the BIA system. The characteristic frequency of the samples in the raw milk changes from 408 kHz to 496 kHz after compensation. Equivalently for adulterated milk with water and hydrogen peroxide, the changes occur from 331 kHz to 388 kHz and from 531 kHz to 577 kHz, respectively. These variations indicate an increase in the compensated characteristic frequency

The authors report the use of computational intelligence and also well known digital signal processing algorithms in bioimpedance spectroscopy. The BIA analysis of data obtained from a custom made spectrometer were processed with a modulus retrieval algorithm from phase of bioimpedance spectra of vegetables showing the feasibility of using this specific and well known algorithm in a practical case. This would also allow the BIA system hardware to be simplified. In this case, since only the phase of the bioimpedance is going to be acquired to obtain the complete modulus of the bioimpedance spectrum, the involved electronic circuitry, as expected, may be reduced and the instrumentation amplifiers to measure modulus would be unnecessary. This would pave the way to embed algorithms in a much more simplified electronics for bioimpedance systems designed for specific applications

The bioimpedance data may also be processed with computational intelligence techniques. The authors improved already known techniques to fit experimental bioimpedance spectrum data to a specific model function. This is common practice in bioimpedance spectroscopy and is already implemented in commercial systems, however they do not use the techniques proposed here, only the least-squares algorithms, but no other more elaborate algorithms, like evolutionary techniques and particle-swarm optimization procedures. It is shown that the PSO technique has advantages over the already proposed procedures. The comparison of such techniques was implemented and artificial neural networks were used for the specific purpose of comparing them. The use of an Artificial Neural Network that receives as input the parameters produced by the fitting illustrates that different techniques, specifically the least-square fitting, simply would not be capable of allowing the identification of the correct tissue or the sample experimentally evaluated. The genetic algorithm and the particle-swarm optimization were capable of allowing the correct classification of the samples with experimental data added to noise in a much better proportion than the least-squares algorithm. Considering that the number of iterations in the PSO is much less than the genetic algorithm, and since they provide the same qualitative results in terms of classification, the PSO shows a superiority with respect to performance. The arithmetic complexity of the PSO

is also an important characteristic that could facilitate embedded implementations.

Still in the dairy food applications, the idea of using bioimpedance to classify milk with the previously described techniques was also illustrated. Milk with different concentrations of mastitis cells were evaluated and the differences in the phase and modulus of the bioimpedance spectrum are noticed. However, the selectivity of the BIA system could not be demonstrated, and this would force one to use other additional sensing systems to

when the stray effects are compensated this way.

as in the characterization of fruits, for example.

**4. Conclusion**

The idea of determining efficient and simple algorithms to process bioimpedance spectra is a topic that may allow the implementation of sophisticated algorithms in embedded systems and could also improve the quality of the analysis produced by simple equipment. One can mention that in the case of the phase/modulus retrieval algorithms, since the technique is based on the use of the well-known fast-Fourier transform algorithm, it would be natural to implement it in embedded systems. However, the applications could not be restricted to such systems, since the use of the proposed algorithms may help improve the bioimpedance spectrum analysis while correcting experimental data and retrieving the more convenient information from the improved fitting algorithms. The methodology that uses artificial neural networks to evaluate the performance of the algorithms could also be used in systems that require automated analysis of bioimpedance spectra, as in an industrial environment to characterize samples of milk or beef, for example.

As a direction to the future research efforts, a final goal for the use of such algorithms would be their implementation in reconfigurable hardware, more specifically, in field-programmable gate arrays (FPGA). Commercial systems already use such technologies, like the FPGA in bioimpedance spectrometers (Nacke et al., 2011). Therefore the evaluated techniques are suggested to be implemented in hardware, since the particle swarm optimization algorithms would be a good choice for this purpose. The arithmetic operations in the particle-swarm optimization update step requires only random number generation, and a series of summations and multiplications. In the phase/modulus retrieval algorithm case, the FFT could also be easily instantiated from the core provided by the FPGA company.

## **6. Acknowledgements**

The authors gratefully acknowledge the experimental data collected by Rogerio Martins Pereira, Rodrigo Stiz and Guilherme Martignago Zilli as students supervised in the Laboratories of the Santa Catarina State University in Joinville City.

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**2** 

**Computer Simulation and** 

Seishin Takao, Shigeru Tadano, Hiroshi Taguchi and Hiroki Shirato

*Hokkaido University* 

*Japan* 

**Analysis of Three-Dimensional** 

**Tumor Geometry in Radiotherapy** 

Radiotherapy plays an important role in the treatment for patients with solid tumors. Recently, the advantages in high-precision radiotherapy enable focusing of higher radiation energy (dose) to the tumor region while minimizing unwanted radiation exposure to surrounding normal tissue to avoid radiation injury. Intensity-modulated radiation therapy (IMRT) varies the intensities and profiles of beams from various directions to fit the tumor size and shape. This technique greatly improves dose concentration on target region and normal tissue sparing. Image-guided radiation therapy (IGRT) uses advanced imaging technology such as on-board imaging system to achieve precise and accurate dose delivery. Many studies have reported inter-fractional organ motions and efficacy of IGRT in reducing targeting errors using daily CT images (Den et al. 2009, Wang et al. 2009, Houghton et al. 2009, Pawlowski et al. 2010, Varadhan et al. 2009, Greene et al. 2009). Owing to these techniques, errors in patient set-up and dose delivery can be reduced to some extent. However, as radiotherapy typically takes several weeks, tumor and normal tissues may deform due to therapeutic effect or loss of body weight during treatment period. Shapes and locations of the tumor and the surrounding organs would be quite different from those when the treatment was planned. This results in overdosage of surrounding normal tissue or underdosage of target region. To overcome this issue, it would be useful to precisely analyse and predict the changes in three-dimensional (3D) geometries of tumors and normal

However, even methodology to evaluate 3D tumor shapes has not been established yet. At present, tumor diameter is commonly used as an indicator to evaluate therapeutic response in cancer patients. Since the 1970s, the World Health Organization (WHO) had suggested to assess tumor response by measurement of maximum diameter and largest perpendicular diameter (World Health Organization, 1979). The response evaluation criteria in solid tumor (RECIST) guideline proposed to use only maximum diameter in categorizing therapeutic response (Therasse et al. 2000, Werner-Wasik et al. 2001). Some researchers have reported that this difference in diagnostic criteria often resulted in different categorization of therapeutic response. Rohbe et al. stated that volumetric measurement with CT might help

**1. Introduction** 

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## **Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy**

Seishin Takao, Shigeru Tadano, Hiroshi Taguchi and Hiroki Shirato *Hokkaido University Japan* 

## **1. Introduction**

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reconstruction from phase or magnitude, *IEEE Transactions on Acoustics, Speech and*

to experimental bioimpedance data, *Annals of the New York Academy of Sciences*

Radiotherapy plays an important role in the treatment for patients with solid tumors. Recently, the advantages in high-precision radiotherapy enable focusing of higher radiation energy (dose) to the tumor region while minimizing unwanted radiation exposure to surrounding normal tissue to avoid radiation injury. Intensity-modulated radiation therapy (IMRT) varies the intensities and profiles of beams from various directions to fit the tumor size and shape. This technique greatly improves dose concentration on target region and normal tissue sparing. Image-guided radiation therapy (IGRT) uses advanced imaging technology such as on-board imaging system to achieve precise and accurate dose delivery. Many studies have reported inter-fractional organ motions and efficacy of IGRT in reducing targeting errors using daily CT images (Den et al. 2009, Wang et al. 2009, Houghton et al. 2009, Pawlowski et al. 2010, Varadhan et al. 2009, Greene et al. 2009). Owing to these techniques, errors in patient set-up and dose delivery can be reduced to some extent. However, as radiotherapy typically takes several weeks, tumor and normal tissues may deform due to therapeutic effect or loss of body weight during treatment period. Shapes and locations of the tumor and the surrounding organs would be quite different from those when the treatment was planned. This results in overdosage of surrounding normal tissue or underdosage of target region. To overcome this issue, it would be useful to precisely analyse and predict the changes in three-dimensional (3D) geometries of tumors and normal tissues through the treatment.

However, even methodology to evaluate 3D tumor shapes has not been established yet. At present, tumor diameter is commonly used as an indicator to evaluate therapeutic response in cancer patients. Since the 1970s, the World Health Organization (WHO) had suggested to assess tumor response by measurement of maximum diameter and largest perpendicular diameter (World Health Organization, 1979). The response evaluation criteria in solid tumor (RECIST) guideline proposed to use only maximum diameter in categorizing therapeutic response (Therasse et al. 2000, Werner-Wasik et al. 2001). Some researchers have reported that this difference in diagnostic criteria often resulted in different categorization of therapeutic response. Rohbe et al. stated that volumetric measurement with CT might help

Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy 31

represents the polar angle (-90° ≤ *φ* ≤ 90°). Radius *R*(*θ*, *φ*) was sampled at 10° intervals in both the polar and azimuthal directions. To enable a visual understanding of the features of the 3D geometry of the tumor, the values of radius *R*(*θ*, *φ*) were represented in a color scale

within the tumor. The warm colors (red and yellow) represent convex region and cool colors

Further, to evaluate changes in tumor geometry quantitatively, the image correlation was analyzed. Surface geometry maps were converted into grayscale, therefore the intensities in the maps represented the tumor radius. The intensities at every position in the maps created from CT images taken during the treatment were compared with those of the corresponding position in the map before the treatment, and correlation coefficient was calculated. Similar analysis was performed to evaluate our simulation method, especially calculation

Fig. 1. Coordinate system in radiotherapy and representation of 3D tumor geometry using

Equations for describing changes in 3D tumor geometry were established using analogy with deformation of continuous body in solid mechanics (Takao et al. 2009b) (Fig. 2). The relationship between radiation dose *D* and cell mortality fraction *M* is described as follows,

Radiation dose and mortality fraction are tentatively treated as tensor quantities in formulation process so that direction of shrinkage can be considered. *Cijkl* is the parameter of

*ij ijkl kl dM C dD* (2)

plane: red indicates the maximum radius and blue the minimum

and plotted in the

2D surface geometry map


(blue) represents concave areas (Fig. 1).

considering tumor heterogeneity (discussed later).

**3. Simulation of changes in tumor geometry** 

radioresistance and varies as the function of radiation dose.

**3.1 Equations for tumor deformation** 

to evaluate therapeutic response more accurately (Rohbe et al. 2007). For more precise assessment, it would be useful to examine 3D tumor morphological features.

For the purpose of prediction of therapeutic effect, various computational methods have been proposed for simulation of tumor growth and shrinkage as the effects of radiotherapy. Almost all of these method consider tumor as concentration of huge number of cancer cells and calculate the death or birth of these cells pursuant to some rules based on the cell biology (Dionysiou et al. 2004, Stamatakos et al. 2010, Kolokotroni et al. 2011). These approaches look attractive, however it seems to be difficult to implement them into clinical situation because therapeutic effect cannot be evaluated accurately only by the number of cancer cells. Usable method for prediction and evaluation of therapeutic response of tumors has been required strongly.

Authors have proposed novel numerical simulation method to predict changes in tumor volume in radiotherapy (Takao et al. 2009a). We have also established the methodology to evaluate 3D tumor shape visually using color map called surface geometry map (Takao et al. 2009b and 2011). From these knowledge, we proposed simulation method to predict changes in 3D tumor shape through the treatment duration and evaluated tumor geometry visually and quantitatively.

## **2. Analysis of three-dimensional tumor geometry**

It would be valuable if changes in 3D tumor shapes during treatment can be evaluated visually and quantitatively. Quantitative evaluation could be performed using geometric factors such as volume, surface area, and radius. For visual evaluation, we introduce some color map called surface geometry map to represent 3D tumor geometry (shape) into twodimensional plane. The volume of tumor is also represented as size of the map. Therefore, this surface geometry map is useful to understand how the tumor shrinks during treatment.

#### **2.1 Geometric factor**

For quantitative (or numerical) analysis of tumor geometry, volume *V*, surface area *S* were measured and evaluated based on the 3D surface models of the tumors constructed from CT image sets taken once a week during treatment. From the values of *V* and *S*, spherical shape factor (SSF) which represents degree of sphericity was calculated by following equation (Choia HJ and Choi HK 2007).

$$SSF = \frac{36\pi V^2}{S^3} \tag{1}$$

If SSF=1, the tumor has a perfect sphere. As surface roughness increase, the value of SSF decreases. Tumor radius *R*(*θ*, *φ*) was also measured in all directions from the gravitational canter of the tumor.

#### **2.2 Surface geometry map**

We introduced surface geometry map like a global map to visualyze changes in 3D tumor shape (Takao et al. 2009a). Distances from the center of the gravity to its surface, i.e. radius *R*(, *φ*) were measured in the spherical coordinate system *O*-*Rφ*, with the origin is set at the tumor center. The angle represents the azimuthal angle (-180° ≤ ≤ 180°), and the angle *φ*

to evaluate therapeutic response more accurately (Rohbe et al. 2007). For more precise

For the purpose of prediction of therapeutic effect, various computational methods have been proposed for simulation of tumor growth and shrinkage as the effects of radiotherapy. Almost all of these method consider tumor as concentration of huge number of cancer cells and calculate the death or birth of these cells pursuant to some rules based on the cell biology (Dionysiou et al. 2004, Stamatakos et al. 2010, Kolokotroni et al. 2011). These approaches look attractive, however it seems to be difficult to implement them into clinical situation because therapeutic effect cannot be evaluated accurately only by the number of cancer cells. Usable method for prediction and

Authors have proposed novel numerical simulation method to predict changes in tumor volume in radiotherapy (Takao et al. 2009a). We have also established the methodology to evaluate 3D tumor shape visually using color map called surface geometry map (Takao et al. 2009b and 2011). From these knowledge, we proposed simulation method to predict changes in 3D tumor shape through the treatment duration and evaluated tumor geometry visually

It would be valuable if changes in 3D tumor shapes during treatment can be evaluated visually and quantitatively. Quantitative evaluation could be performed using geometric factors such as volume, surface area, and radius. For visual evaluation, we introduce some color map called surface geometry map to represent 3D tumor geometry (shape) into twodimensional plane. The volume of tumor is also represented as size of the map. Therefore, this surface geometry map is useful to understand how the tumor shrinks during treatment.

For quantitative (or numerical) analysis of tumor geometry, volume *V*, surface area *S* were measured and evaluated based on the 3D surface models of the tumors constructed from CT image sets taken once a week during treatment. From the values of *V* and *S*, spherical shape factor (SSF) which represents degree of sphericity was calculated by following equation

If SSF=1, the tumor has a perfect sphere. As surface roughness increase, the value of SSF decreases. Tumor radius *R*(*θ*, *φ*) was also measured in all directions from the gravitational

We introduced surface geometry map like a global map to visualyze changes in 3D tumor shape (Takao et al. 2009a). Distances from the center of the gravity to its surface, i.e. radius

represents the azimuthal angle (-180° ≤

, *φ*) were measured in the spherical coordinate system *O*-*R*

2 3 <sup>36</sup> *<sup>V</sup> SSF S* 

(1)

*φ*, with the origin is set at the

≤ 180°), and the angle *φ*

assessment, it would be useful to examine 3D tumor morphological features.

evaluation of therapeutic response of tumors has been required strongly.

**2. Analysis of three-dimensional tumor geometry** 

and quantitatively.

**2.1 Geometric factor** 

canter of the tumor.

*R*(

**2.2 Surface geometry map** 

tumor center. The angle

(Choia HJ and Choi HK 2007).

represents the polar angle (-90° ≤ *φ* ≤ 90°). Radius *R*(*θ*, *φ*) was sampled at 10° intervals in both the polar and azimuthal directions. To enable a visual understanding of the features of the 3D geometry of the tumor, the values of radius *R*(*θ*, *φ*) were represented in a color scale and plotted in the - plane: red indicates the maximum radius and blue the minimum within the tumor. The warm colors (red and yellow) represent convex region and cool colors (blue) represents concave areas (Fig. 1).

Further, to evaluate changes in tumor geometry quantitatively, the image correlation was analyzed. Surface geometry maps were converted into grayscale, therefore the intensities in the maps represented the tumor radius. The intensities at every position in the maps created from CT images taken during the treatment were compared with those of the corresponding position in the map before the treatment, and correlation coefficient was calculated. Similar analysis was performed to evaluate our simulation method, especially calculation considering tumor heterogeneity (discussed later).

## **3. Simulation of changes in tumor geometry**

#### **3.1 Equations for tumor deformation**

Equations for describing changes in 3D tumor geometry were established using analogy with deformation of continuous body in solid mechanics (Takao et al. 2009b) (Fig. 2). The relationship between radiation dose *D* and cell mortality fraction *M* is described as follows,

$$d\mathcal{M}\_{ij} = \mathbb{C}\_{ijkl} d\mathcal{D}\_{kl} \tag{2}$$

Radiation dose and mortality fraction are tentatively treated as tensor quantities in formulation process so that direction of shrinkage can be considered. *Cijkl* is the parameter of radioresistance and varies as the function of radiation dose.

Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy 33

irradiation, which gives small radiation dose in many times, is performed for reducing radiation damage to normal tissue. Cell survival after *n* times irradiation (total dose of *D*,

> *S* exp ( )

*dM d* 

This formula is rewritten as the relationship between radiation dose and mortality fraction

Equation (9) denotes mortality fraction as the function of radiation dose in terms of radiobiology. Equally equation (2) represents same quantity based on the analogy with solid mechanics. Therefore, right-hand sides of both two equations can be equated and following

> <sup>2</sup> 31 2 1 2 <sup>1</sup> *D d* exp *d D*

Tumor shows internal heterogeneity of radiosensitivity, and it may result in uneven tumor shrinkage. For example, cancer cells under hypoxic environment are likely to be radioresistant, therefore tumor tissue in this region usually does not shrink obviously. Tumor radiosensitivity also varies depend on many other factors such as cell cycle phase or growth rate of each cell. Because of its complexity, it still seems difficult to measure or estimate the distribution of radiosensitivity in tumor tissue. In this study, intratumoral distribution of radiosensitivity is estimated from the degree of tumor shrinkage in the early stage of treatment. The site where tumor radius decreases greatly is considered to be more radiosensitive, and the site where tumor radius decrease slightly is more radioresistant. Therefore tumor radiosensitivity can be represented as the function of position within the tumor. As radiosensitivity is represented by *E* parameter in this model, heterogeneity of

Simulation flow-chart for calculation of tumor geometry is shown in Fig. 3. First, finite element (FE) models of the tumor at the start of the treatment was constructed from the CT images taken for the purpose of treatment planning. Next the values of parameters for

suggested by Thames et al. (Thames et al. 1990). Other simulations parameters were

the relationship between tumor response and radiation dose would entirely obey the LQ

, were set as

= 0.1 and

= 0.01 (

was tentatively set to 0 assuming that

/

=10.0) as

are determined, therapeutic displacement *Ri* can be calculated by means of

 

administered in fractionated dose of *d*) is denoted as follows,

*E E* 

Equation (10) gives the condition that the parameters *E* and

**3.2 Heterogeneity of tumor radiosensitivity** 

numerical discretization method such as finite element method.

radiosensitivity can be expressed by the distribution of the values of *E*.

 and 

are parameters of radiosensitivity. In standard radiotherapy, fractionated

*d D* (8)

must satisfy. When the values

(10)

exp *d D dD* (9)

 

where and 

and in incremental form as,

relationship can be derived.

of *E* and

**3.3 Simulation procedure** 

tumor radiosensitivity in LQ model,

consecutively determined The reduction resistance

Fig. 2. Tumor deformation due to radiotherapy estimated from solid mechanics. *Xi*: Exposure dose, *Dij*: absorbed dose, *Mij*: cell mortality, *Ri*: therapeutic displacement, *Ti*: external force, *ij*: stress, *ij*: strain, *ui*: displacement. Absorbed dose and cell mortality are defined as tensor quantities. Boundary conditions are prescribed on area *SX* and *SR*.

Radiation dose *D* should obey following equations in accordance with the rule in solid mechanics.

$$\frac{\partial \left( D\_{\vec{\eta}} \right)}{\partial \mathbf{x}\_{j}} = \mathbf{0} \tag{3}$$

Assuming that cancer cells killed by irradiation are removed from the tumor, decrease in the number of cancer cells, i.e., cell mortality directly relates to the changes in tumor volume and shape. The relationship between cell mortality *M* and the displacement of tumor boundary *R* is formulated as follows,

$$d\mathcal{M}\_{ij} = \frac{1}{2} \left| \frac{\partial \left( d\mathcal{R}\_i \right)}{\partial \mathbf{x}\_j} + \frac{\partial \left( d\mathcal{R}\_j \right)}{\partial \mathbf{x}\_i} \right| \tag{4}$$

The boundary condition that prescribes the amount of radiation dose transmitted through the tumor boundary is given by

$$d\overline{X}\_i = dD\_{\overline{\eta}}\eta\_j \text{ (on } S\_{\mathcal{X}} \text{ } S\_{\mathcal{X}} \text{ irradiation boundary)}\tag{5}$$

The geometrical boundary condition is given by

$$d\overline{R}\_i = d\mathbb{R}\_i \text{ (on } \text{Sı: } \text{Sı: } \text{geometric} \text{ 1 boundary)}\tag{6}$$

Equations (2)-(6) express tumor response to irradiation in clinical situation. These equations can be solved numerically by means of discretization method such as finite element method (FEM). Assuming that tumors locally (in a sub-millimeter scale) have an isotropic property, *Cijkl* parameter in Eq. (2) for radioresistance is represented by two parameters; reduction resistance *E* and reduction ratio . The values of *E* and should be determined based on the radiobiological model describing the relationship between radiation dose and therapeutic effect. Here we use the linear-quadratic (LQ) model, which is widely accepted and used in the field of radiobiology. According to the LQ model, cell survival fraction S is expressed by following equation,

$$S = \exp(-aD - \beta D^2) \tag{7}$$

where and are parameters of radiosensitivity. In standard radiotherapy, fractionated irradiation, which gives small radiation dose in many times, is performed for reducing radiation damage to normal tissue. Cell survival after *n* times irradiation (total dose of *D*, administered in fractionated dose of *d*) is denoted as follows,

$$S = \exp\left\{-(\alpha + \beta d)D\right\} \tag{8}$$

This formula is rewritten as the relationship between radiation dose and mortality fraction and in incremental form as,

$$dM = (a + \beta d) \exp\{-(a + \beta d)D\} dD \tag{9}$$

Equation (9) denotes mortality fraction as the function of radiation dose in terms of radiobiology. Equally equation (2) represents same quantity based on the analogy with solid mechanics. Therefore, right-hand sides of both two equations can be equated and following relationship can be derived.

$$\frac{\Re(1-2\nu)}{E}\left(1-\frac{1-2\nu}{E}D\right)^2=(\alpha+\beta d)\exp\left\{-(\alpha+\beta d)D\right\}\tag{10}$$

Equation (10) gives the condition that the parameters *E* and must satisfy. When the values of *E* and are determined, therapeutic displacement *Ri* can be calculated by means of numerical discretization method such as finite element method.

#### **3.2 Heterogeneity of tumor radiosensitivity**

Tumor shows internal heterogeneity of radiosensitivity, and it may result in uneven tumor shrinkage. For example, cancer cells under hypoxic environment are likely to be radioresistant, therefore tumor tissue in this region usually does not shrink obviously. Tumor radiosensitivity also varies depend on many other factors such as cell cycle phase or growth rate of each cell. Because of its complexity, it still seems difficult to measure or estimate the distribution of radiosensitivity in tumor tissue. In this study, intratumoral distribution of radiosensitivity is estimated from the degree of tumor shrinkage in the early stage of treatment. The site where tumor radius decreases greatly is considered to be more radiosensitive, and the site where tumor radius decrease slightly is more radioresistant. Therefore tumor radiosensitivity can be represented as the function of position within the tumor. As radiosensitivity is represented by *E* parameter in this model, heterogeneity of radiosensitivity can be expressed by the distribution of the values of *E*.

#### **3.3 Simulation procedure**

32 Applied Biological Engineering – Principles and Practice

*ij*: strain, *ui*: displacement. Absorbed dose and cell mortality are

(3)

(4)

should be determined based on the

(7)

Fig. 2. Tumor deformation due to radiotherapy estimated from solid mechanics. *Xi*: Exposure dose, *Dij*: absorbed dose, *Mij*: cell mortality, *Ri*: therapeutic displacement,

defined as tensor quantities. Boundary conditions are prescribed on area *SX* and *SR*.

Radiation dose *D* should obey following equations in accordance with the rule in solid

 <sup>0</sup> *ij j*

Assuming that cancer cells killed by irradiation are removed from the tumor, decrease in the number of cancer cells, i.e., cell mortality directly relates to the changes in tumor volume and shape. The relationship between cell mortality *M* and the displacement of tumor

1

The boundary condition that prescribes the amount of radiation dose transmitted through

Equations (2)-(6) express tumor response to irradiation in clinical situation. These equations can be solved numerically by means of discretization method such as finite element method (FEM). Assuming that tumors locally (in a sub-millimeter scale) have an isotropic property, *Cijkl* parameter in Eq. (2) for radioresistance is represented by two parameters; reduction

. The values of *E* and

radiobiological model describing the relationship between radiation dose and therapeutic effect. Here we use the linear-quadratic (LQ) model, which is widely accepted and used in the field of radiobiology. According to the LQ model, cell survival fraction S is expressed by

> <sup>2</sup> *S DD* exp( )

*j i*

*<sup>i</sup> ij j dX dD n* (on *SX*, *SX*; irradiation boundary) (5)

*<sup>i</sup> <sup>i</sup> dR dR* (on *SR*, *SR*; geometrical boundary) (6)

*j i dR dR*

*x x* 

2

*ij*

*dM*

*D x*

*Ti*: external force,

mechanics.

boundary *R* is formulated as follows,

the tumor boundary is given by

resistance *E* and reduction ratio

following equation,

The geometrical boundary condition is given by

*ij*: stress,

Simulation flow-chart for calculation of tumor geometry is shown in Fig. 3. First, finite element (FE) models of the tumor at the start of the treatment was constructed from the CT images taken for the purpose of treatment planning. Next the values of parameters for tumor radiosensitivity in LQ model, and , were set as = 0.1 and = 0.01 (/=10.0) as suggested by Thames et al. (Thames et al. 1990). Other simulations parameters were consecutively determined The reduction resistance was tentatively set to 0 assuming that the relationship between tumor response and radiation dose would entirely obey the LQ

Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy 35

After that, similar process was performed to determine the distribution of the parameter *E* (reduction resistance) to represent intratumoral heterogeneity of radiosensitivity. The *E* parameter was so far considered to be uniform throughout the tumor. In following calculation, the value of *E* parameter was set for each element, which constitutes the whole 3D tumor model for FEA calculation, as the function of azimuthal angle and polar angle *φ*. Depending on the distance from the gravity center of the tumor to surface, the value of *E* at

> <sup>1</sup> (,) (,) (,) (,) *n n M C*

where, superscript represents the number of iteration, *R*(*θ*, *φ*)*M* is measured tumor radius at

The subjects of this study were three clinical cases (case A, B, and C) of metastatic cervical lymph nodes in three patients with nasopharyngeal cancer treated at the Hokkaido University Hospital, Sapporo, Japan between February 2007 and August 2007. Of the patients, case A and B were undifferentiated carcinoma and case C was squamous cell carcinoma. Initial volumes of lymph nodes were 3.5, 55.1, and 10.4 cm3, respectively. Case A and C were treated with IMRT; patient B received conventional radiotherapy. The dose distribution before radiotherapy intended each node in this study to be homogeneously irradiated with a dose of 66 Gy (case A) to 70 Gy (case B, C) in 2.0 Gy fractions delivered five

Pre-treatment CT images (CT0) were taken for the treatment planning. The slice thickness of the pre-treatment CT images was 2 mm. After the start of treatment, follow-up CT images were taken at weekly intervals (CT1, CT2, CT3, etc). The slice thickness of the follow-up CT images was 5 mm. All patients were immobilized by thermoplastic masks during the CT scanning and treatment. Additionally, in the head and neck IMRT treatments in our hospital, A mouthpiece with three fiducial markers (2 mm diameter gold pellets) was used for the fluoroscopic verification of the patient set-up by means of real-time tumor-tracking radiotherapy (RTRT) system. This study was conducted with written informed consent obtained from all patients and was approved by the institutional ethical committee at

Three-dimensional finite element (FE) models of tumors were constructed based on the CT images taken before and during treatment (Fig. 4). One radiation oncologist determined and contoured the boundary of metastatic cervical lymph nodes on the CT images by means of a treatment planning system (Xio). A group of sequential cross-sectional profiles of the tumor was then loaded into biomedical imaging software and interpolated to 1 mm intervals. After file format conversion with in-house software, the data was imported into the finite element analysis software (ANSYS 11.0), and the 3D FE models of the tumors were constructed.

   

(11)

*<sup>R</sup> E E R* 

 

(*θ*, *φ*), and *R*(*θ*, *φ*)*C* is calculated tumor radius at the corresponding point.

(*θ*, *φ*) was determined by following equation.

**4. Clinical cases** 

times a week.

**4.1 Patient characteristics** 

Hokkaido University Hospital.

**4.2 Finite element modeling of tumors** 

model. After then, the reduction resistance *E* was calculated from Eq. (10) using , , cumulative dose *D*, and daily dose *d*. The *E* parameter was initially considered to be uniform throughout the tumor. Using these parameters, changes in tumor volume was calculated by means of FE analysis software. Calculated tumor volumes were compared with corresponding tumor volumes measured from CT image sets for treatment follow-up. Followed by this process, the value of reduction ratio , which represents interpatient variation in radiosensitivity, was adjusted for each case so that the discrepancy between the calculated and the actual tumor volumes obtained from follow-up CT would decrease. If the calculated volume was less than the actual volume, the value of was incremented and then the tumor volume was recalculated. This iterative process was continued till the root mean square (RMS) error of the calculated and actual tumor volumes reached a minimum.

\*VM : Measured tumor volume, VC : Calculated volume \*\* RM : Measured tumor radius, RC : Calculated radius

Fig. 3. Flow chart illustrating simulation steps to calculate and predict changes in 3D tumor shape during radiotherapy.

After that, similar process was performed to determine the distribution of the parameter *E* (reduction resistance) to represent intratumoral heterogeneity of radiosensitivity. The *E* parameter was so far considered to be uniform throughout the tumor. In following calculation, the value of *E* parameter was set for each element, which constitutes the whole 3D tumor model for FEA calculation, as the function of azimuthal angle and polar angle *φ*. Depending on the distance from the gravity center of the tumor to surface, the value of *E* at (*θ*, *φ*) was determined by following equation.

$$E(\theta,\varphi)^{n+1} = \frac{R(\theta,\varphi)\_{\text{M}}}{R(\theta,\varphi)\_{\text{C}}} E(\theta,\varphi)^{n} \tag{11}$$

where, superscript represents the number of iteration, *R*(*θ*, *φ*)*M* is measured tumor radius at (*θ*, *φ*), and *R*(*θ*, *φ*)*C* is calculated tumor radius at the corresponding point.

## **4. Clinical cases**

34 Applied Biological Engineering – Principles and Practice

cumulative dose *D*, and daily dose *d*. The *E* parameter was initially considered to be uniform throughout the tumor. Using these parameters, changes in tumor volume was calculated by means of FE analysis software. Calculated tumor volumes were compared with corresponding tumor volumes measured from CT image sets for treatment follow-up.

variation in radiosensitivity, was adjusted for each case so that the discrepancy between the calculated and the actual tumor volumes obtained from follow-up CT would decrease. If the

the tumor volume was recalculated. This iterative process was continued till the root mean

START

Construct the FE model

 and 

Calculate E

Calculation

Compare calculated and measured tumor volumes

Yes

Compare calculated and measured tumor radius at each evaluation point Modify

)2 is minimized\*

)2 is minimized\*\*

Yes

Calculation

Compare calculated and measured tumor geometry for evaluation

END

Determine

Set = 0

from , , D, and d

(VM – VC

(RM – RC

square (RMS) error of the calculated and actual tumor volumes reached a minimum.

Modify 

> E at each element

No

No

, ,

, which represents interpatient

was incremented and then

model. After then, the reduction resistance *E* was calculated from Eq. (10) using

Followed by this process, the value of reduction ratio

CT Images during RT (CT1)

CT Images during RT (CT2)

CT Images during RT (CT3)

> CT Images at the end of RT

shape during radiotherapy.

CT Images before RT (CT0)

> \*VM

\*\* RM

: Measured tumor volume,

: Measured tumor radius,

Fig. 3. Flow chart illustrating simulation steps to calculate and predict changes in 3D tumor

VC

> RC

: Calculated volume

: Calculated radius

calculated volume was less than the actual volume, the value of

#### **4.1 Patient characteristics**

The subjects of this study were three clinical cases (case A, B, and C) of metastatic cervical lymph nodes in three patients with nasopharyngeal cancer treated at the Hokkaido University Hospital, Sapporo, Japan between February 2007 and August 2007. Of the patients, case A and B were undifferentiated carcinoma and case C was squamous cell carcinoma. Initial volumes of lymph nodes were 3.5, 55.1, and 10.4 cm3, respectively. Case A and C were treated with IMRT; patient B received conventional radiotherapy. The dose distribution before radiotherapy intended each node in this study to be homogeneously irradiated with a dose of 66 Gy (case A) to 70 Gy (case B, C) in 2.0 Gy fractions delivered five times a week.

Pre-treatment CT images (CT0) were taken for the treatment planning. The slice thickness of the pre-treatment CT images was 2 mm. After the start of treatment, follow-up CT images were taken at weekly intervals (CT1, CT2, CT3, etc). The slice thickness of the follow-up CT images was 5 mm. All patients were immobilized by thermoplastic masks during the CT scanning and treatment. Additionally, in the head and neck IMRT treatments in our hospital, A mouthpiece with three fiducial markers (2 mm diameter gold pellets) was used for the fluoroscopic verification of the patient set-up by means of real-time tumor-tracking radiotherapy (RTRT) system. This study was conducted with written informed consent obtained from all patients and was approved by the institutional ethical committee at Hokkaido University Hospital.

#### **4.2 Finite element modeling of tumors**

Three-dimensional finite element (FE) models of tumors were constructed based on the CT images taken before and during treatment (Fig. 4). One radiation oncologist determined and contoured the boundary of metastatic cervical lymph nodes on the CT images by means of a treatment planning system (Xio). A group of sequential cross-sectional profiles of the tumor was then loaded into biomedical imaging software and interpolated to 1 mm intervals. After file format conversion with in-house software, the data was imported into the finite element analysis software (ANSYS 11.0), and the 3D FE models of the tumors were constructed.

Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy 37

case B, and 23% in case C. Changes in tumor surface area showed similar tendency with changes in tumor volume. Tumor surface areas at the end of the treatment were 20%, 28%, and 37% for case A, B, and C, respectively. Changes in SSF are shown in Fig. 7. The values of SSF were about 0.8 through the treatment duration and did not vary widely in all three

Fig. 8 shows changes in average, maximum, and minimum tumor radius through the treatment period. At the start of treatment, each average radius was 9.8 mm, 24.6 mm, and 14.4 mm in tumor A, B, and C. The tumor radius ranged from 7.3 mm to 13.3 mm (75 % to 137 % of average radius) in tumor A, 17.4 mm to 34.4 mm (71 % to 140 %) in tumor B, 9.2 mm to 20.3 mm (64 % to 142 %) in tumor C, respectively. At the end of the treatment, average radius decreased to 4.5 mm, 13.5 mm, and 8.9 mm, respectively. The ranges of radius were 3.3 mm to 5.8 mm (73 % to 129 % of the average radius at the end of the treatment) in tumor A, 9.4 mm to 18.2 mm (70 % to 135 %) in tumor B, 6.3 mm to 12.5 mm (71 % to 140 %) in tumor C, respectively. In Fig. 8, all values are represented as percentages

0 10 20 30 40 50

Tumor A Tumor B Tumor C

Tumor A Tumor B Tumor C

Treatment days

0 10 20 30 40 50

Treatment days

evaluation point are represented as the percentage of initial surface area.

Fig. 6. Changes in tumor surface are during radiotherapy. Tumor surface area at each

Fig. 5. Changes in tumor volume during radiotherapy. Tumor volumes at each evaluation

cases.

of each initial average radius.

0%

0%

20%

40%

60%

% of initial surface area

80%

100%

point are represented as the percentage of initial volume.

20%

40%

60%

% of initial volume

80%

100%

Fig. 4. Process of finite element modelling of tumor. (a) tumor region (red edging) on CT images (b) tumor profiles in each sectional image (c) 3D surface model (d) 3D finite element model

## **5. Results**

This study first aimed to evaluate changes in 3D tumor shapes during treatment visually and quantitatively. We constructed surface model of tumors and then analysed the 3D shapes by geometric factors for quantitative evaluation. Two-dimensional surface geometry map was also proposed for visual evaluation of 3D morphological features of tumors. Other main aims of this study was to propose simulation method to predict changes in 3D tumor shape during radiotherapy.

#### **5.1 Analysis of three-dimensional tumor geometry**

## **5.1.1 Geometric factors**

This study investigated geometric factors to accurately evaluate therapeutic response in radiotherapy. Tumor volume, surface area, radius, and spherical shape factor (SSF) were used to quantitatively evaluate tumor geometry. Fig. 5-7 show changes in geometric factors of tumors through treatment duration for quantitative analysis of 3D tumor morphology. Changes in tumor volume and surface area are shown in Fig. 5 and 6. Tumor volume at the end of the treatment period was 8.7% of its initial volume in case A, 15% in

Fig. 4. Process of finite element modelling of tumor. (a) tumor region (red edging) on CT images (b) tumor profiles in each sectional image (c) 3D surface model (d) 3D finite element

This study first aimed to evaluate changes in 3D tumor shapes during treatment visually and quantitatively. We constructed surface model of tumors and then analysed the 3D shapes by geometric factors for quantitative evaluation. Two-dimensional surface geometry map was also proposed for visual evaluation of 3D morphological features of tumors. Other main aims of this study was to propose simulation method to predict changes in 3D tumor

This study investigated geometric factors to accurately evaluate therapeutic response in radiotherapy. Tumor volume, surface area, radius, and spherical shape factor (SSF) were used to quantitatively evaluate tumor geometry. Fig. 5-7 show changes in geometric factors of tumors through treatment duration for quantitative analysis of 3D tumor morphology. Changes in tumor volume and surface area are shown in Fig. 5 and 6. Tumor volume at the end of the treatment period was 8.7% of its initial volume in case A, 15% in

model

**5. Results** 

shape during radiotherapy.

**5.1.1 Geometric factors** 

**5.1 Analysis of three-dimensional tumor geometry** 

case B, and 23% in case C. Changes in tumor surface area showed similar tendency with changes in tumor volume. Tumor surface areas at the end of the treatment were 20%, 28%, and 37% for case A, B, and C, respectively. Changes in SSF are shown in Fig. 7. The values of SSF were about 0.8 through the treatment duration and did not vary widely in all three cases.

Fig. 8 shows changes in average, maximum, and minimum tumor radius through the treatment period. At the start of treatment, each average radius was 9.8 mm, 24.6 mm, and 14.4 mm in tumor A, B, and C. The tumor radius ranged from 7.3 mm to 13.3 mm (75 % to 137 % of average radius) in tumor A, 17.4 mm to 34.4 mm (71 % to 140 %) in tumor B, 9.2 mm to 20.3 mm (64 % to 142 %) in tumor C, respectively. At the end of the treatment, average radius decreased to 4.5 mm, 13.5 mm, and 8.9 mm, respectively. The ranges of radius were 3.3 mm to 5.8 mm (73 % to 129 % of the average radius at the end of the treatment) in tumor A, 9.4 mm to 18.2 mm (70 % to 135 %) in tumor B, 6.3 mm to 12.5 mm (71 % to 140 %) in tumor C, respectively. In Fig. 8, all values are represented as percentages of each initial average radius.

Fig. 5. Changes in tumor volume during radiotherapy. Tumor volumes at each evaluation point are represented as the percentage of initial volume.

Fig. 6. Changes in tumor surface are during radiotherapy. Tumor surface area at each evaluation point are represented as the percentage of initial surface area.

Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy 39

shows the changes in tumor geometry through treatment duration using surface geometry map. The red end of the color scale is convex region and blue is concave region. Therefore surface geometry map can provide information about 3D geometrical feature of the tumor. The patterns of color distribution are found to be similar in each case. This result means that tumor shrunk uniformly keeping their original morphological features

A computational simulation method to predict changes in 3D tumor geometry during radiotherapy was proposed. Simulation parameters were determined based on the changes in tumor geometry in the early stage of the treatment (first 19 days in case A and B, 22 days in case C). Using these parameters, tumor geometries in the latter half of the treatment

Simulation results are shown in Fig. 10-12. Simulation could represent tendencies of tumor geometrical changes in the first 19 or 22 days in each case. Calculation to predict tumor geometries in the rest of the treatment was performed subsequently. The predicted tumor geometries were compared with corresponding actual tumor geometries by surface geometry maps. The calculated tumor geometry at the end of the treatment was found to conform to actual tumor geometry. The discrepancy between calculated and actual tumor geometry could be quantitatively evaluated by tumor radius *R*(*θ*, *φ*). The discrepancies between calculated and actual tumor radius (calculated tumor radius - actual tumor radius) at the end of the treatment were 0.2 mm (maximum), -1.4 mm (minimum), and 0.5 mm (average absolute value) for tumor A, 3.4 mm, -6.3 mm, and 2.1 mm for tumor B, 0.4 mm, - 4.3 mm, and 1.3 mm for tumor C, respectively, while average of actual tumor radius was 5.4

Precise assessment of therapeutic response in radiotherapy has been an important issue in the field of radiation oncology. To understand how tumor geometries change during the treatment would be useful for not only determination of prognosis but for treatment plans as well. However, there has been no research which visualized 3D tumor geometries and evaluated the therapeutic response based on the changes of tumor geometries. In this study, we proposed a method to represent 3D tumor geometry in 2D color map, and evaluated therapeutic response through the treatment period, as well as geometric factors representing

Surface geometry map introduced in this study could indicate 3D morphological features of the tumors in color scale. These figures show that tumors shrank evenly maintaining their original shape. This would be valuable information for determining the optimal radiation field in the latter half of the treatment. The degree of tumor shrinkage, i.e. decrease in tumor radius (shown in Fig. 8), varied approximately plus or minus 20 % depending on tumor region. This variation was considered to represent intratumoral heterogeneity. These findings cannot be obtained from commonly-used geometric factor, i. e., tumor volume or

mm for tumor A, and 13.2 mm for tumor B, 8.4 mm tumor C, respectively.

through the treatment duration.

period were calculated sequentially.

therapeutic response quantitatively.

maximum diameter measured on CT images.

**6. Discussion** 

**5.2 Simulation of changes in tumor geometry** 

Fig. 7. Changes in spherical shape factors in radiotherapy.

Fig. 8. Changes of average tumor radius during the treatment in tumor A, B, and C. Vertical lines represent ranges from minimum to maximum.

#### **5.1.2 Surface geometry map**

This study also proposed representation and evaluation method for changes in 3D tumor geometry using 2D surface geometry map. Distances from the geometrical center to surface were represented in color scale for visual understanding of 3D tumor shape. Fig. 9 shows the changes in tumor geometry through treatment duration using surface geometry map. The red end of the color scale is convex region and blue is concave region. Therefore surface geometry map can provide information about 3D geometrical feature of the tumor. The patterns of color distribution are found to be similar in each case. This result means that tumor shrunk uniformly keeping their original morphological features through the treatment duration.

## **5.2 Simulation of changes in tumor geometry**

A computational simulation method to predict changes in 3D tumor geometry during radiotherapy was proposed. Simulation parameters were determined based on the changes in tumor geometry in the early stage of the treatment (first 19 days in case A and B, 22 days in case C). Using these parameters, tumor geometries in the latter half of the treatment period were calculated sequentially.

Simulation results are shown in Fig. 10-12. Simulation could represent tendencies of tumor geometrical changes in the first 19 or 22 days in each case. Calculation to predict tumor geometries in the rest of the treatment was performed subsequently. The predicted tumor geometries were compared with corresponding actual tumor geometries by surface geometry maps. The calculated tumor geometry at the end of the treatment was found to conform to actual tumor geometry. The discrepancy between calculated and actual tumor geometry could be quantitatively evaluated by tumor radius *R*(*θ*, *φ*). The discrepancies between calculated and actual tumor radius (calculated tumor radius - actual tumor radius) at the end of the treatment were 0.2 mm (maximum), -1.4 mm (minimum), and 0.5 mm (average absolute value) for tumor A, 3.4 mm, -6.3 mm, and 2.1 mm for tumor B, 0.4 mm, - 4.3 mm, and 1.3 mm for tumor C, respectively, while average of actual tumor radius was 5.4 mm for tumor A, and 13.2 mm for tumor B, 8.4 mm tumor C, respectively.

## **6. Discussion**

38 Applied Biological Engineering – Principles and Practice

Tumor A Tumor B Tumor C

(B)

0 10 20 30 40 50

Treatment days

0 10 20 30 40 50

Treatment days

Fig. 8. Changes of average tumor radius during the treatment in tumor A, B, and C. Vertical

0% 20% 40% 60% 80% 100% 120% 140%

Average tumor radius

This study also proposed representation and evaluation method for changes in 3D tumor geometry using 2D surface geometry map. Distances from the geometrical center to surface were represented in color scale for visual understanding of 3D tumor shape. Fig. 9

0.0

(A)

Fig. 7. Changes in spherical shape factors in radiotherapy.

lines represent ranges from minimum to maximum.

0 10 20 30 40 50

Treatment days

0 10 20 30 40 Treatment days

(C)

**5.1.2 Surface geometry map** 

0% 20% 40% 60% 80% 100% 120% 140%

0% 20% 40% 60% 80% 100% 120% 140%

Average tumor radius

Average tumor radius

0.2

0.4

SSF (Spherical shape factor)

0.6

0.8

1.0

Precise assessment of therapeutic response in radiotherapy has been an important issue in the field of radiation oncology. To understand how tumor geometries change during the treatment would be useful for not only determination of prognosis but for treatment plans as well. However, there has been no research which visualized 3D tumor geometries and evaluated the therapeutic response based on the changes of tumor geometries. In this study, we proposed a method to represent 3D tumor geometry in 2D color map, and evaluated therapeutic response through the treatment period, as well as geometric factors representing therapeutic response quantitatively.

Surface geometry map introduced in this study could indicate 3D morphological features of the tumors in color scale. These figures show that tumors shrank evenly maintaining their original shape. This would be valuable information for determining the optimal radiation field in the latter half of the treatment. The degree of tumor shrinkage, i.e. decrease in tumor radius (shown in Fig. 8), varied approximately plus or minus 20 % depending on tumor region. This variation was considered to represent intratumoral heterogeneity. These findings cannot be obtained from commonly-used geometric factor, i. e., tumor volume or maximum diameter measured on CT images.

Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy 41

90



5.7 11.0 (mm)

5.4 9.7 (mm)

5.0 8.3 (mm)

4.4 8.0 (mm)

4.1 6.7 (mm)

3.9 6.6 (mm)

geometries using 2D surface geometry map (case A).

*<sup>R</sup>* 7.3 13.3 (mm)

Measuerment Simulation

Day 12

Day 19

Day 26

Day 33

Day 40

Day 48

Fig. 10. Comparison of tumor geometries calculated in this method with actual tumor

6.1 11.1 (mm)

5.4 9.8 (mm)

4.8 8.7 (mm)

4.4 7.9 (mm)

3.9 7.0 (mm)

3.5 6.1 (mm)

Fig. 9. Changes in 3D tumor geometries represented in surface geometry maps.

Fig. 9. Changes in 3D tumor geometries represented in surface geometry maps.

Fig. 10. Comparison of tumor geometries calculated in this method with actual tumor geometries using 2D surface geometry map (case A).

Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy 43

90



9.2 20.3

Measureme Simulation

Day 9

Day 15

Day 22

Day 29

Day 36

Day 43

Day 50

Fig. 12. Comparison of tumor geometries calculated in this method with actual tumor

R

9.8 19.3

8.2 15.9

8.0 14.7

6.5 12.7

6.9 11.6

6.3 12.5

6.3 12.5

geometries using 2D surface geometry map (case B).

8.4 17.4

7.9 16.0

7.4 14.4

6.9 13.0

6.4 11.8

5.7 10.9

4.7 12.5

Fig. 11. Comparison of tumor geometries calculated in this method with actual tumor geometries using 2D surface geometry map (case B).

90



17.4 34.4

Day 9

Measurement Simulation

Day 19

Day 30

Day 34

Day 44

Fig. 11. Comparison of tumor geometries calculated in this method with actual tumor

R

12.8 31.3

10.8 28.2

9.8 24.9

9.0 24.5

9.4 18.2

geometries using 2D surface geometry map (case B).

14.5 29.2

12.1 25.7

8.8 21.8

8.1 20.9

5.9 18.0

Fig. 12. Comparison of tumor geometries calculated in this method with actual tumor geometries using 2D surface geometry map (case B).

Computer Simulation and Analysis of Three-Dimensional Tumor Geometry in Radiotherapy 45

Technology (FIRST Program)," initiated by the Council for Science and Technology Policy (CSTP), Grant-in-Aid for JSPS Fellows (NO. 09J02587), and Grant-in-Aid for Scientific

Choia, H.J. and Choi, H.K. (2007), Grading of renal cell carcinoma by 3D morphological analysis of cell nuclei. *Comput Biol Med*,Vol. 37 (2007), pp. 1334–1341 Den, R.B., et al. (2010). Daily image guidance with cone-beam computed tomography for

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Thames, H.D., et al. (1990). Time-dose factors in radiotherapy: a review of the human data,

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**10. References** 

1989-2006.

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(2009), pp. 56–74.

A simulation method proposed here enabled to predict changes in 3D tumor geometry considering intratumoral heterogeneity of radiosensitivity therefore would be more valuable for treatment planning or diagnosis of prognosis. The simulation method could predict tumor shapes at the end of the treatment within 2.1 mm discrepancy in radius (absolute average) by considering tumor heterogeneity. As the limitation of present method, these calculations were performed on the assumption that tumors were irradiated evenly. Although dose distribution in IMRT is considered to be uniform to a certain extent, actual dose distribution should be taken into consideration for more precise calculation.

Calculated tumor geometries in the latter half of the treatment strongly depended on changes in tumor geometries in the early stage of the treatment, because values of parameter *E* were determined only from early tumor geometries. Our present method cannot handle the cases that tumor geometry changes drastically during treatment. We should investigate factors affecting tumor radiosensitivity e.g. angiogenesis, hypoxia, or cell cycle, and appropriately determine the values of *E* parameter considering these factors.

## **7. Conclusion**

In this work, tumor geometries were analysed visually and quantitatively from several perspectives. The effectiveness of surface geometry map proposed here was confirmed as the tool for precise assessment of therapeutic response based on the 3D tumor geometry. It was revealed that tumors shrunk uniformly keeping their initial morphological features during radiotherapy. This finding cannot be obtained from traditional evaluation by measuring diameters of the tumors on CT images. This study also proposed a novel simulation method to predict changes in 3D tumor geometries during radiotherapy considering intratumoral heterogeneity of radiosensitivity. The simulation results were found to conform to actual changes in tumor geometry. Although some difficulties still remain to be solved, tumor geometries could be predicted using our approach. It would lead to the idea of "Computer associated radiotherapy (CART)", which is the highly-advanced integration of computational technology and radiotherapy to achieve more precise and safety treatment.

## **8. Future directions**

The role of computer technology in recent advanced radiotherapy has rapidly increased. Calculation of 3D dose distribution in patient is indispensable for precise treatment. Imaging techniques, especially image registration technique, are expected as tools for adaptive radiotherapy, which modifies original treatment plan to fit the actual patient condition. Through this research, great contribution of our computational analysis and simulation method for changes in 3D tumor geometry has been confirmed. These methods are expected to play a great important role in putting adaptive radiotherapy into practice. It would be a first step for achievement of computer associated radiotherapy (CART), and attainment of more effective and safety treatment.

## **9. Acknowledgment**

This research is partly granted by the Japan Society for the Promotion of Science (JSPS) through the "Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)," initiated by the Council for Science and Technology Policy (CSTP), Grant-in-Aid for JSPS Fellows (NO. 09J02587), and Grant-in-Aid for Scientific Research (A), MEXT (NO. 21249065).

## **10. References**

44 Applied Biological Engineering – Principles and Practice

A simulation method proposed here enabled to predict changes in 3D tumor geometry considering intratumoral heterogeneity of radiosensitivity therefore would be more valuable for treatment planning or diagnosis of prognosis. The simulation method could predict tumor shapes at the end of the treatment within 2.1 mm discrepancy in radius (absolute average) by considering tumor heterogeneity. As the limitation of present method, these calculations were performed on the assumption that tumors were irradiated evenly. Although dose distribution in IMRT is considered to be uniform to a certain extent, actual

Calculated tumor geometries in the latter half of the treatment strongly depended on changes in tumor geometries in the early stage of the treatment, because values of parameter *E* were determined only from early tumor geometries. Our present method cannot handle the cases that tumor geometry changes drastically during treatment. We should investigate factors affecting tumor radiosensitivity e.g. angiogenesis, hypoxia, or cell cycle, and

In this work, tumor geometries were analysed visually and quantitatively from several perspectives. The effectiveness of surface geometry map proposed here was confirmed as the tool for precise assessment of therapeutic response based on the 3D tumor geometry. It was revealed that tumors shrunk uniformly keeping their initial morphological features during radiotherapy. This finding cannot be obtained from traditional evaluation by measuring diameters of the tumors on CT images. This study also proposed a novel simulation method to predict changes in 3D tumor geometries during radiotherapy considering intratumoral heterogeneity of radiosensitivity. The simulation results were found to conform to actual changes in tumor geometry. Although some difficulties still remain to be solved, tumor geometries could be predicted using our approach. It would lead to the idea of "Computer associated radiotherapy (CART)", which is the highly-advanced integration of computational

The role of computer technology in recent advanced radiotherapy has rapidly increased. Calculation of 3D dose distribution in patient is indispensable for precise treatment. Imaging techniques, especially image registration technique, are expected as tools for adaptive radiotherapy, which modifies original treatment plan to fit the actual patient condition. Through this research, great contribution of our computational analysis and simulation method for changes in 3D tumor geometry has been confirmed. These methods are expected to play a great important role in putting adaptive radiotherapy into practice. It would be a first step for achievement of computer associated radiotherapy (CART), and

This research is partly granted by the Japan Society for the Promotion of Science (JSPS) through the "Funding Program for World-Leading Innovative R&D on Science and

dose distribution should be taken into consideration for more precise calculation.

appropriately determine the values of *E* parameter considering these factors.

technology and radiotherapy to achieve more precise and safety treatment.

attainment of more effective and safety treatment.

**7. Conclusion** 

**8. Future directions** 

**9. Acknowledgment** 


**3** 

*Brazil* 

**Frequency-Domain Objective** 

and Antonio Fernando Catelli Infantosi1

**Response Detection Techniques** 

**Applied to Evoked Potentials: A Review** 

*1Biomedical Engineering Program, Federal University of Rio de Janeiro (UFRJ) 2Electrical Engineering Department, Federal University of Minas Gerais (UFMG)* 

Danilo Barbosa Melges1,2, Antonio Mauricio Ferreira Leite Miranda de Sá1

The Electroencephalogram (EEG) is the biological signal collected at the scalp as a summation result of ionic currents generated from the post-synaptic potentials of the brain neurons. Differently from some other biosignals such as the electrocardiogram, which presents a visual identifiable pattern – particularly the QRS complex, the EEG exhibits a very large random variability. It is indeed quite often assumed to be a white Gaussian noise, and this stochastic behavior turns the analysis of EEG signals by visual inspection a very difficult task. In spite of this, the EEG is known to be correlated with sensorial information processing, and it is widely used for neurophysiologic assessment and neuropathies

The cortical response obtained by sensorial excitation consists of a neurological evaluation paradigm that produces a pattern related to a stimulation that is often rhythmic, such as electric pulses, auditory clicks or intermittent light. The elicited cortical activity is usually synchronized with the stimulation, but it is embedded in the spontaneous EEG, which has much higher amplitude values. An estimation of this evoked response is frequently obtained by averaging EEG epochs stimuli-synchronized. The resulting waveform is visually inspected and evaluated by a neurologist or a technical specialist for both diagnosis/prognosis and surgical monitoring purposes. Such response is locked in time and phase with the stimulation, which can lead to a clear pattern that is usually called evoked

The most employed evoked potentials are the visual (VEP) – elicited by intermittent photic stimuli-, the auditory (AEP) – obtained by tones or clicks-, and the somatosensory ones (SEP), evoked by electric current pulses. Among many applications, the VEP is commonly applied for visual acuity evaluation of infants and newborns (Linden *et al.*, 1997); the AEP is often used for monitoring the depth of anesthesia (Cagy, 2003) and auditory screening of newborns (Ramos *et al.*, 2000); whilst the SEP is frequently employed for monitoring spine

(Cruccu *et al.*, 2008) and vascular surgeries (Keyhani *et al.*, 2009).

**1. Introduction** 

diagnosis.

potential (EP).


## **Frequency-Domain Objective Response Detection Techniques Applied to Evoked Potentials: A Review**

## Danilo Barbosa Melges1,2, Antonio Mauricio Ferreira Leite Miranda de Sá1 and Antonio Fernando Catelli Infantosi1

*1Biomedical Engineering Program, Federal University of Rio de Janeiro (UFRJ) 2Electrical Engineering Department, Federal University of Minas Gerais (UFMG) Brazil* 

## **1. Introduction**

46 Applied Biological Engineering – Principles and Practice

Werner-Wasik, M., et al. (2001). Assessment of lung cancer response after nonoperative

World Health Organization (1979). *WHO handbook for reporting results of cancer treatment*, pp.

based study. *Int J Radiat Oncol Biol Phys*, Vol.51 (2001), pp. 56–61.

48, Offset Publication, Geneva, Switzerland.

therapy: tumor diameter, bidimensional product, and volume. A serial CT scan-

The Electroencephalogram (EEG) is the biological signal collected at the scalp as a summation result of ionic currents generated from the post-synaptic potentials of the brain neurons. Differently from some other biosignals such as the electrocardiogram, which presents a visual identifiable pattern – particularly the QRS complex, the EEG exhibits a very large random variability. It is indeed quite often assumed to be a white Gaussian noise, and this stochastic behavior turns the analysis of EEG signals by visual inspection a very difficult task. In spite of this, the EEG is known to be correlated with sensorial information processing, and it is widely used for neurophysiologic assessment and neuropathies diagnosis.

The cortical response obtained by sensorial excitation consists of a neurological evaluation paradigm that produces a pattern related to a stimulation that is often rhythmic, such as electric pulses, auditory clicks or intermittent light. The elicited cortical activity is usually synchronized with the stimulation, but it is embedded in the spontaneous EEG, which has much higher amplitude values. An estimation of this evoked response is frequently obtained by averaging EEG epochs stimuli-synchronized. The resulting waveform is visually inspected and evaluated by a neurologist or a technical specialist for both diagnosis/prognosis and surgical monitoring purposes. Such response is locked in time and phase with the stimulation, which can lead to a clear pattern that is usually called evoked potential (EP).

The most employed evoked potentials are the visual (VEP) – elicited by intermittent photic stimuli-, the auditory (AEP) – obtained by tones or clicks-, and the somatosensory ones (SEP), evoked by electric current pulses. Among many applications, the VEP is commonly applied for visual acuity evaluation of infants and newborns (Linden *et al.*, 1997); the AEP is often used for monitoring the depth of anesthesia (Cagy, 2003) and auditory screening of newborns (Ramos *et al.*, 2000); whilst the SEP is frequently employed for monitoring spine (Cruccu *et al.*, 2008) and vascular surgeries (Keyhani *et al.*, 2009).

Frequency-Domain Objective Response

and its multiples.

Detection Techniques Applied to Evoked Potentials: A Review 49

background EEG is assumed to be a zero-mean white Gaussian noise. Hence, the measured EEG *y*[*k*] is composed by evoked and background activities. In this linear model, a correlation between stimulus and EEG is expected at the stimulation frequency

*b*[*k*]

*y*[*k*]

*<sup>x</sup>*[*k*] *<sup>v</sup>*[*k*]

*b*[*k*] is the background EEG and *y*[*k*] is the measured EEG.

provides an estimate of the evoked potential, being calculated by:

**3. Clinical and surgical application of the evoked potentials** 

and the continuous neuromonitoring in order to avoid neurological damages.

the signal-to-noise ratio as shown next.

can be given by:

terms will vanish.

*H*(*f*)

Fig. 1. Linear Model of evoked potential generation: *x*[*k*] is the stimulus, *H*(*f*) is the frequency-domain transfer function of the sensory pathways, *v*[*k*] is the stimuli-response,

This model reflects the scalp electrical activity registration, where the evoked potentials are usually embedded in the spontaneous (or background) EEG. Since the EP is tens of times lower than the background EEG, it cannot be visualized; therefore, it is common to perform the averaging of many epochs, taken the stimulus instant as the fiducial point. As mentioned above, assuming that the background EEG is a zero-mean Gaussian noise and the responses are synchronized with the stimulation and identical from stimulus to stimulus (Lopes da Silva, 1999), this procedure, known as coherent average, leads to an increase in

Considering the linear model presented in Figure 1, the *ith* EEG epoch during stimulation

[] [] [] *i i y k vk n k*

where *v k*[ ] is the evoked response and *n k*[ ] is the background EEG. The coherent average

where the superscript ^ denotes estimation and *M* is the number of EEG epochs. When *M* tends to infinity, *v k* ˆ[ ] tends to *v k*[ ] , since the parcel due to summation involving the *ni*[*k*]

The evoked potentials obtained by different kinds of stimulation have been applied to a broad range of clinical and intra-operative conditions. It is increasing the number of studies that shows the advantages of EP application for supporting the diagnosis of neuropathies

1 11 1 11 ˆ[] [] [] [] *M MM i i i ii vk y k vk n k M MM* 

Although the EP has been widely applied, the conventional procedure is based on the physician experience and ability, as well as in informal criteria (Dobie and Wilson, 1993). The analysis is also hampered by the EEG recording quality, anesthesia regimen, and the high variability inter-observer and inter-patient (Martin *et al.*, 2002). In order to overcome these limitations and aiming at widening the employment of the evoked potentials, the use of Objective Response Detection (ORD) techniques has been proposed. One of the first works applying the ORD to evoked potentials was described in Galambos *et al.* (1984 apud Stapells *et al.*, 1987), which introduced the Phase Coherence. Since then, many other ORD techniques have been investigated.

These methods are based on statistical tests that allow inferring about the presence (or absence) of sensory response with a maximum false-positive rate previously established, which is the significance level of the statistical test. The ORD techniques at the frequency domain are useful, particularly in the presence of narrow band noises, such as network noise and its harmonics. This kind of noise corrupts the EP waveform, yielding to a misleading analysis and, consequently, to a mistaken diagnose or monitoring. However, it only affects the frequency-domain ORD in specific frequencies that can be disregarded in the analysis. Hence, these techniques are more suitable for medical environments (hospitals and intensive care units), which are usually electrically noisy, due to the presence of many electrical and electro-mechanical devices.

Although the ORD allows reducing the subjectivity of neurophysiologic assessment, the probability and rapidness of detection are still aspects to be optimized. The fast detection with high hit rate is a requirement specially for intra-operative monitoring, since it can help the physicians to avoid iatrogenic neurological damages. Methods to accelerate the detection such as the application of a decreasing exponential (Tierra-Criollo *et al.*, 1998) to the ORD techniques have been proposed. More recently, the employment of more than one EEG derivation in a multivariate ORD approach has been suggested in order to improve the detection probability (Miranda de Sá and Felix, 2002). These techniques constitute the state of the art for objectively identify sensorial responses to a stimulation.

This work aims at reviewing the most employed frequency-domain techniques applied to evoked potentials. Besides the Introduction, this chapter will be subdivided into six sections. The second one introduces the model of evoked response generation. Section 3 presents a brief description of the principal applications of the cortical (brain) responses obtained by different types of stimulation (visual, auditory and somatosensory). Both clinical diagnosis and surgical monitoring references are included. In the next section, the mathematical definition of uni- and multivariate techniques is provided. A chronological literature review of applying the ORD to EP is described in Section 5. The subsequent section presents examples of using these techniques, including recent findings. Finally, the last section discloses a discussion about ORD.

## **2. The model of evoked potential generation and the coherent average**

The evoked potential (EP) generation model is shown in Figure 1, where *v*[*k*] is the response elicited by the sensory stimulation *x*[*k*], *b*[*k*] is the spontaneous EEG and *H*(*f*) is the transfer function of the sensory pathways. The evoked response v[k] is considered to be identical from stimulus-to-stimulus (i.e. *H*(*f*) is assumed to be deterministic) and the

Although the EP has been widely applied, the conventional procedure is based on the physician experience and ability, as well as in informal criteria (Dobie and Wilson, 1993). The analysis is also hampered by the EEG recording quality, anesthesia regimen, and the high variability inter-observer and inter-patient (Martin *et al.*, 2002). In order to overcome these limitations and aiming at widening the employment of the evoked potentials, the use of Objective Response Detection (ORD) techniques has been proposed. One of the first works applying the ORD to evoked potentials was described in Galambos *et al.* (1984 apud Stapells *et al.*, 1987), which introduced the Phase Coherence. Since then, many other ORD

These methods are based on statistical tests that allow inferring about the presence (or absence) of sensory response with a maximum false-positive rate previously established, which is the significance level of the statistical test. The ORD techniques at the frequency domain are useful, particularly in the presence of narrow band noises, such as network noise and its harmonics. This kind of noise corrupts the EP waveform, yielding to a misleading analysis and, consequently, to a mistaken diagnose or monitoring. However, it only affects the frequency-domain ORD in specific frequencies that can be disregarded in the analysis. Hence, these techniques are more suitable for medical environments (hospitals and intensive care units), which are usually electrically noisy, due to the presence of many

Although the ORD allows reducing the subjectivity of neurophysiologic assessment, the probability and rapidness of detection are still aspects to be optimized. The fast detection with high hit rate is a requirement specially for intra-operative monitoring, since it can help the physicians to avoid iatrogenic neurological damages. Methods to accelerate the detection such as the application of a decreasing exponential (Tierra-Criollo *et al.*, 1998) to the ORD techniques have been proposed. More recently, the employment of more than one EEG derivation in a multivariate ORD approach has been suggested in order to improve the detection probability (Miranda de Sá and Felix, 2002). These techniques constitute the state

This work aims at reviewing the most employed frequency-domain techniques applied to evoked potentials. Besides the Introduction, this chapter will be subdivided into six sections. The second one introduces the model of evoked response generation. Section 3 presents a brief description of the principal applications of the cortical (brain) responses obtained by different types of stimulation (visual, auditory and somatosensory). Both clinical diagnosis and surgical monitoring references are included. In the next section, the mathematical definition of uni- and multivariate techniques is provided. A chronological literature review of applying the ORD to EP is described in Section 5. The subsequent section presents examples of using these techniques, including recent findings. Finally, the last section

**2. The model of evoked potential generation and the coherent average** 

The evoked potential (EP) generation model is shown in Figure 1, where *v*[*k*] is the response elicited by the sensory stimulation *x*[*k*], *b*[*k*] is the spontaneous EEG and *H*(*f*) is the transfer function of the sensory pathways. The evoked response v[k] is considered to be identical from stimulus-to-stimulus (i.e. *H*(*f*) is assumed to be deterministic) and the

of the art for objectively identify sensorial responses to a stimulation.

techniques have been investigated.

electrical and electro-mechanical devices.

discloses a discussion about ORD.

background EEG is assumed to be a zero-mean white Gaussian noise. Hence, the measured EEG *y*[*k*] is composed by evoked and background activities. In this linear model, a correlation between stimulus and EEG is expected at the stimulation frequency and its multiples.

Fig. 1. Linear Model of evoked potential generation: *x*[*k*] is the stimulus, *H*(*f*) is the frequency-domain transfer function of the sensory pathways, *v*[*k*] is the stimuli-response, *b*[*k*] is the background EEG and *y*[*k*] is the measured EEG.

This model reflects the scalp electrical activity registration, where the evoked potentials are usually embedded in the spontaneous (or background) EEG. Since the EP is tens of times lower than the background EEG, it cannot be visualized; therefore, it is common to perform the averaging of many epochs, taken the stimulus instant as the fiducial point. As mentioned above, assuming that the background EEG is a zero-mean Gaussian noise and the responses are synchronized with the stimulation and identical from stimulus to stimulus (Lopes da Silva, 1999), this procedure, known as coherent average, leads to an increase in the signal-to-noise ratio as shown next.

Considering the linear model presented in Figure 1, the *ith* EEG epoch during stimulation can be given by:

$$y\_i[k] = v[k] + n\_i[k]$$

where *v k*[ ] is the evoked response and *n k*[ ] is the background EEG. The coherent average provides an estimate of the evoked potential, being calculated by:

$$\hat{v}[k] = \frac{1}{M} \sum\_{i=1}^{M} y\_i[k] = \frac{1}{M} \sum\_{i=1}^{M} v[k] + \frac{1}{M} \sum\_{i=1}^{M} n\_i[k]$$

where the superscript ^ denotes estimation and *M* is the number of EEG epochs. When *M* tends to infinity, *v k* ˆ[ ] tends to *v k*[ ] , since the parcel due to summation involving the *ni*[*k*] terms will vanish.

## **3. Clinical and surgical application of the evoked potentials**

The evoked potentials obtained by different kinds of stimulation have been applied to a broad range of clinical and intra-operative conditions. It is increasing the number of studies that shows the advantages of EP application for supporting the diagnosis of neuropathies and the continuous neuromonitoring in order to avoid neurological damages.

Frequency-Domain Objective Response

procedures (Guérit and Dion, 2002).

ischemia.

2000).

1999).

Detection Techniques Applied to Evoked Potentials: A Review 51

The somatosensory evoked potential (SEP) is often obtained by applying electric current pulses and is useful for detecting peripheral nerve lesions, plexopathies and radiculopathies (Linden *et al.*, 1997), and for monitoring vascular and spine surgeries such as desobstruction of the carotid artery (Liu *et al.*, 2010), aortic aneurism repair (Keyhani *et al.*, 2009, Van Dongen *et al.*, 2001), aortic coarctation repair (Faberowski *et al.*, 1999), scoliosis correction procedures (Cruccu *et al.*, 2008) and lumbar pedicle screw placement for in situ posterior spinal fusion (Gundanna, 2003), due to its sensitivity to mechanical stress, hypotension and

The neuromonitoring is considered important in the prevention of immediate and late paraplegia caused by medullary ischemia, since it is capable of detecting the "ischemic penumbra", status pathophysiologic present in the acute ischemia, when the neurons are not at functional state, but alive and recoverable by the application of appropriate

Due to its sensitivity to temperature, the SEP has been used as optimal temperature identifier during surgeries that require profound hypothermia (Ghariani *et al.*, 1999), being considered as a secure and efficient method (Ghariani *et al.*, 2000). The hypothermia is employed in order to reduce the cerebral metabolism, during surgeries of ascending aorta and aortic arch repair, which require circulatory arrest (Ghariani *et al.*, 1998). This procedure allows the reduction of neurological sequels arising from hypoxia. On the other hand, excessively low temperatures can lead to iatrogenic complications, such as coagulation disorders, hemolysis, increased blood viscosity, among others (Ghariani *et al.*,

The need of monitoring upper and lower limbs during surgeries has been reported due to the occurrence of paraplegia by unpredicted intra-operative evaluation of only median nerve SEP (Ghariani et al., 1999). The advantages that the monitoring of the four limbs SEP can provide for a low cost, reducing the occurrence of transient and persistent neurological complications, has been also reported by Jones et al. (2004). In a survey conducted with members of the Scoliosis Research Society, Nuwer et al. (1995) reported that 88% of the north-American surgeons used the SEP in more than a half of the surgeries. According to Bose et al. (2004), the neurophysiologic monitoring during lumbar and thoracic surgery has become a routine procedure for years, but its employment during cervical surgeries is more recent and seems to be a sensitive method for detecting neurological insults caused by

Since it is related with variations in the cerebral blood flow, the SEP presents identifiable changes associated with variation in the hemodynamics (Florence et al., 2004). Moreover, the SEP is not influenced by muscular blockers and present gradual changes with the increase of anesthetic concentration (Angel et al., 1999). Frequently registered over the somatosensory cortex, region vascularized by the carotid artery, the SEP is often used during the carotid endarterectomy (Florence et al., 2004), performed for the treatment of vascular obstructive disease and that presents potential risk of ischemia for the ipsilateral hemisphere during internal carotid artery occlusion (Linden et al., 1997). The absence of the cortical function and of the subcortical EP, in cases of cerebral hemorrhages, is a negative prognostic predictor, although its preservation does not present prognostic value (Guérit,

mechanical stress, surgical manipulation, hypotension and ischemia.

The Brainstem Auditory Evoked Potential (BAEP), elicited by click (sound pulses), is an important tool in the child auditory screening (Ramos *et al.*, 2000, Infantosi *et al.*, 2004), since it can assess the auditory pathways down to the brainstem. It is usually performed by obtaining the auditory neurophysiologic threshold by means of the BERA (Brainstem Evoked Response Audiometry). The most widely employed screening method is the optoacoustic emission (OE). Although this latter has been applied in many hospital units, due to its technical and operational facility (Zaeyen, 2005), the OE evaluate the integrity only up to the cochlea, whereas the BAEP can access the auditory pathways up to the brainstem. Moreover, there are cases in which the BAEP is absent or impaired, but the OE are preserved (Infantosi *et al.*, 2004). Thus, a question that naturally arises is whether the OE is a suitable method for auditory screening in newborn intensive care units (Infantosi *et al.*, 2004).

On the other hand, the BAEP has been also employed for intra-operative monitoring during removal of cerebello-pontine tumors, microvascular decompression of cranial nerves and ischemic complications due the manipulation of the posterior fossa circulation, since this potential is stable to a variety of anesthetics and pharmacological agents and presents adequate reproducibility (Linden *et al.*, 1997).

When the impairment is located in structures above the brainstem, the investigation of late potentials such as the Middle Latency Auditory Evoked Potential (MLAEP) can be suitable for functional evaluation up to the primary auditory cortex (Zaeyen, 2005). The MLAEP has been also applied for monitoring the depth anesthetic plan (Nayak and Roy, 1998, Gemal, 1999, Cagy and Infantosi, 2002, Cagy, 2003), because it presents changes that are dosedependent with the anesthesia. The anesthetic plan monitoring is particularly important because the clinical signs usually applied for this purpose are masked by the employment of vasodilators, vasoconstrictors, calcium channel blockers and neuromuscular blockers during surgeries (Nayak and Roy, 1998).

The application of the Visual Evoked Potential (VEP) for monitoring is limited due to the need of controlling parameters such as surgical room light and distance between the eye and the stimulator. Although it has been used during surgeries of pituitary tumors and brain aneurisms, the recording of VEP for intra-operative functional evaluation presents low success rate (Linden et al., 1997). Flash-VEP is one of the potentials with the highest signalto-noise ratio (SNR) , some characteristics of its waveform can be even visually identified with only 100 stimuli. Nevertheless, this potential shows high inter- and intra-observer variability, which makes difficult its evaluation with the administration of anesthetics. Moreover, since the quantity of light is a function of the pupil size, agents causing mydriasis (pupil dilatation) should be applied when anesthetics are administered (Linden et al., 1997). On the other hand, the VEP has been used, especially in pediatrics, for evaluating the visual acuity, detecting amblyopia, and as a useful tool for prognosis of comatose patients, newborn asphyxia and cortical blindness (Linden et al., 1997). Other applications of VEP includes diagnosis of migraine in children and adolescents (Jancic-Stefanovic *et al.*, 2003), childhood optical glioma (Trisciuzzi *et al.*, 2004) and functional visual loss (Xu *et al.*, 2001). It has also been used in studies of dyslexia (Schulte-Körne *et al.*, 2004), periventricular leukomalacia (Kato *et al.*, 2005), retinitis pigmentosa (Holopigian *et al.*, 2005), macular degeneration (Nemoto *et al.*, 2002), schizophrenia (Krishnan *et al.*, 2005), glaucoma (Parisi *et al.*, 2001) and nystagmus (Hoffmann *et al.*, 2004).

The Brainstem Auditory Evoked Potential (BAEP), elicited by click (sound pulses), is an important tool in the child auditory screening (Ramos *et al.*, 2000, Infantosi *et al.*, 2004), since it can assess the auditory pathways down to the brainstem. It is usually performed by obtaining the auditory neurophysiologic threshold by means of the BERA (Brainstem Evoked Response Audiometry). The most widely employed screening method is the optoacoustic emission (OE). Although this latter has been applied in many hospital units, due to its technical and operational facility (Zaeyen, 2005), the OE evaluate the integrity only up to the cochlea, whereas the BAEP can access the auditory pathways up to the brainstem. Moreover, there are cases in which the BAEP is absent or impaired, but the OE are preserved (Infantosi *et al.*, 2004). Thus, a question that naturally arises is whether the OE is a suitable method for auditory screening in newborn intensive care units (Infantosi *et al.*,

On the other hand, the BAEP has been also employed for intra-operative monitoring during removal of cerebello-pontine tumors, microvascular decompression of cranial nerves and ischemic complications due the manipulation of the posterior fossa circulation, since this potential is stable to a variety of anesthetics and pharmacological agents and presents

When the impairment is located in structures above the brainstem, the investigation of late potentials such as the Middle Latency Auditory Evoked Potential (MLAEP) can be suitable for functional evaluation up to the primary auditory cortex (Zaeyen, 2005). The MLAEP has been also applied for monitoring the depth anesthetic plan (Nayak and Roy, 1998, Gemal, 1999, Cagy and Infantosi, 2002, Cagy, 2003), because it presents changes that are dosedependent with the anesthesia. The anesthetic plan monitoring is particularly important because the clinical signs usually applied for this purpose are masked by the employment of vasodilators, vasoconstrictors, calcium channel blockers and neuromuscular blockers during

The application of the Visual Evoked Potential (VEP) for monitoring is limited due to the need of controlling parameters such as surgical room light and distance between the eye and the stimulator. Although it has been used during surgeries of pituitary tumors and brain aneurisms, the recording of VEP for intra-operative functional evaluation presents low success rate (Linden et al., 1997). Flash-VEP is one of the potentials with the highest signalto-noise ratio (SNR) , some characteristics of its waveform can be even visually identified with only 100 stimuli. Nevertheless, this potential shows high inter- and intra-observer variability, which makes difficult its evaluation with the administration of anesthetics. Moreover, since the quantity of light is a function of the pupil size, agents causing mydriasis (pupil dilatation) should be applied when anesthetics are administered (Linden et al., 1997). On the other hand, the VEP has been used, especially in pediatrics, for evaluating the visual acuity, detecting amblyopia, and as a useful tool for prognosis of comatose patients, newborn asphyxia and cortical blindness (Linden et al., 1997). Other applications of VEP includes diagnosis of migraine in children and adolescents (Jancic-Stefanovic *et al.*, 2003), childhood optical glioma (Trisciuzzi *et al.*, 2004) and functional visual loss (Xu *et al.*, 2001). It has also been used in studies of dyslexia (Schulte-Körne *et al.*, 2004), periventricular leukomalacia (Kato *et al.*, 2005), retinitis pigmentosa (Holopigian *et al.*, 2005), macular degeneration (Nemoto *et al.*, 2002), schizophrenia (Krishnan *et al.*, 2005), glaucoma (Parisi *et* 

2004).

adequate reproducibility (Linden *et al.*, 1997).

*al.*, 2001) and nystagmus (Hoffmann *et al.*, 2004).

surgeries (Nayak and Roy, 1998).

The somatosensory evoked potential (SEP) is often obtained by applying electric current pulses and is useful for detecting peripheral nerve lesions, plexopathies and radiculopathies (Linden *et al.*, 1997), and for monitoring vascular and spine surgeries such as desobstruction of the carotid artery (Liu *et al.*, 2010), aortic aneurism repair (Keyhani *et al.*, 2009, Van Dongen *et al.*, 2001), aortic coarctation repair (Faberowski *et al.*, 1999), scoliosis correction procedures (Cruccu *et al.*, 2008) and lumbar pedicle screw placement for in situ posterior spinal fusion (Gundanna, 2003), due to its sensitivity to mechanical stress, hypotension and ischemia.

The neuromonitoring is considered important in the prevention of immediate and late paraplegia caused by medullary ischemia, since it is capable of detecting the "ischemic penumbra", status pathophysiologic present in the acute ischemia, when the neurons are not at functional state, but alive and recoverable by the application of appropriate procedures (Guérit and Dion, 2002).

Due to its sensitivity to temperature, the SEP has been used as optimal temperature identifier during surgeries that require profound hypothermia (Ghariani *et al.*, 1999), being considered as a secure and efficient method (Ghariani *et al.*, 2000). The hypothermia is employed in order to reduce the cerebral metabolism, during surgeries of ascending aorta and aortic arch repair, which require circulatory arrest (Ghariani *et al.*, 1998). This procedure allows the reduction of neurological sequels arising from hypoxia. On the other hand, excessively low temperatures can lead to iatrogenic complications, such as coagulation disorders, hemolysis, increased blood viscosity, among others (Ghariani *et al.*, 2000).

The need of monitoring upper and lower limbs during surgeries has been reported due to the occurrence of paraplegia by unpredicted intra-operative evaluation of only median nerve SEP (Ghariani et al., 1999). The advantages that the monitoring of the four limbs SEP can provide for a low cost, reducing the occurrence of transient and persistent neurological complications, has been also reported by Jones et al. (2004). In a survey conducted with members of the Scoliosis Research Society, Nuwer et al. (1995) reported that 88% of the north-American surgeons used the SEP in more than a half of the surgeries. According to Bose et al. (2004), the neurophysiologic monitoring during lumbar and thoracic surgery has become a routine procedure for years, but its employment during cervical surgeries is more recent and seems to be a sensitive method for detecting neurological insults caused by mechanical stress, surgical manipulation, hypotension and ischemia.

Since it is related with variations in the cerebral blood flow, the SEP presents identifiable changes associated with variation in the hemodynamics (Florence et al., 2004). Moreover, the SEP is not influenced by muscular blockers and present gradual changes with the increase of anesthetic concentration (Angel et al., 1999). Frequently registered over the somatosensory cortex, region vascularized by the carotid artery, the SEP is often used during the carotid endarterectomy (Florence et al., 2004), performed for the treatment of vascular obstructive disease and that presents potential risk of ischemia for the ipsilateral hemisphere during internal carotid artery occlusion (Linden et al., 1997). The absence of the cortical function and of the subcortical EP, in cases of cerebral hemorrhages, is a negative prognostic predictor, although its preservation does not present prognostic value (Guérit, 1999).

Frequency-Domain Objective Response

 **test** 

the limits for the occurrence of the population mean:

Transformed EEG epochs and *Y*( ) *f* the mean vector.

**4.1.2 Hotelling's T<sup>2</sup>**

freedom.

response detection.

as follows:

**4.1.3 Spectral F Test (SFT)** 

Detection Techniques Applied to Evoked Potentials: A Review 53

According to Picton et al. (1987), the Hotelling T2 Test (HT2) is the multivariate analogue of the Student's t test. If *M* samples of a uni-variate distribution is taken, one can estimate its mean *y* and standard deviation *s*. Based on this two parameters, it is possible to calculate

> *y y <sup>M</sup> <sup>t</sup> s*

where t are the limits taken from the two-tailed Student's t distribution with M-1 degrees of

1 2 <sup>ˆ</sup> () () () () ()

where the superscript H and ^ denote Hermitian and estimation, respectively, S-1 is the inverse of the covariance matrix of the sample, Y(f) is the vector of the *M* Fourier

*M Y f Y f S Y f Y f T f* (2)

,2, 2,

2

2

(3)

.

(4)

For a bidimensional distribution, the confidence region for the mean vector is given by:

*H*

The statistics T2 can be related to the Fisher's F distribution by (Picton et al., 1987):

value of the F-distribution with 2 and M-2 degrees of freedom at the significance level

( 1)2 <sup>ˆ</sup> ( ) ( 2) *crit crit M <sup>M</sup> Tf F <sup>M</sup>*

where *M* is the number of epochs used to calculate the *T2* estimate and Fcrit,2,M-2,α is the critical

Considering that the Fourier Transformed EEG epochs are bidimensional variables (complex variables with real and imaginary parts), the confidence region for the mean vector leads to an ellipse of confidence. When the ellipse encompasses the origin of the plan (0,0), which represents the response absence condition, one can assume that there is no response to the stimulation. On the other hand, if the origin is not included in the confidence region, the null hypothesis of response absence can be rejected, and one can assume the

The Spectral F Test (SFT) is given by the ratio between the Power Spectrum Density (PSD) of the EEG during stimulation *y*[*k*] and the background EEG *b*[*k*] (Dobie and Wilson, 1996). For windowed EEG signals, the SFT can be estimated by the ratio of the Bartlett periodograms,

1

*Y f <sup>M</sup>*

*y*

*x*

*M*

*y i M*

*b i*

ˆ( )

*f*

<sup>1</sup> ( )

*i*

*i*

1

*B f <sup>M</sup>*

<sup>1</sup> ( )

2

For monitoring intracranial aneurysms repair surgeries, the real time detection of cerebral ischemia can help the surgeon, for example, to determine the duration of the temporary vascular occlusion and the optimal systemic arterial pressure (Martin et al., 2002). The SEP and the cortical EEG are the techniques most frequently employed for this purpose in anterior circulation aneurysm surgeries (Martin et al., 2002).

Apart from the cited surgeries, the SEP monitoring was also successfully applied in many other surgical procedures, such as interventional neuroradiology, stereotaxic surgery of the brainstem, thalamus, cerebral cortex, thalamotomy, cortical localization, brachial plexus surgery and pelvic fracture surgery (Linden et. al, 1997). SEP also presents prognostic value in cases of intracranial hypertension (Giugno et al., 2003) and coma (Logi et al., 2003).

Even when post-operative squeals cannot be avoided by monitoring, the detection of neurophysiologic intra-operative changes can make the surgery staff aware of the risk and avoid the exacerbation of the damage (Bose et al., 2004). However, it is important selecting the patients for whom the EP monitoring can be useful, because if the patient does not present pre-operative EP, this technique is not suitable for intra-operative neuro-evaluation (Linden et al., 1997).

Finally, as the neuromonitoring represents only the current status of the patient, many studies point out the importance of the post-surgery SEP monitoring in order to detect late neurological complications (Guérit and Dion, 2002, Dong et al., 2002, Ghariani et al., 2000).

## **4. Frequency–domain Objective Response Detection (ORD) techniques**

This section describes some of the most used frequency-domain Objective Response Detection (ORD) techniques, both in its univariate and multivariate versions. Details about *a priori* assumptions related to the signals are included.

## **4.1 Univariate ORD techniques**

## **4.1.1 Phase Coherence**

The Phase Coherence (PC) was introduced in the analysis of the evoked potentials by Galambos *et al.* (1984) and can be seen as a statistical measure of the phase variance. It can be mathematically defined by:

$$\hat{\theta}\_c(f) = \sqrt{\left(\sum\_{i=1}^{M} \sin \phi\_i(f)\right)^2 + \left(\sum\_{i=1}^{M} \cos \phi\_i(f)\right)^2} \Bigg/ M \tag{1}$$

where ( ) *<sup>i</sup> f* is the phase angle of the ith Fourier Transformed EEG epoch and *M* is the number of EEG epochs. This measure supposes that the presence of stimuli-response causes a phase aggregation of the Fourier Transformed EEG epochs in the complex plan. On the other hand, on the absence of response, the phase angle is assumed to be randomly distributed between 0 and 2π, and the probability of obtaining this phase angle configuration is accessed by the Rayleigh test (Mardia, 1972). This techniques only takes into account the phase of the Fourier Transform (FT) of EEG epochs.

#### **4.1.2 Hotelling's T<sup>2</sup> test**

52 Applied Biological Engineering – Principles and Practice

For monitoring intracranial aneurysms repair surgeries, the real time detection of cerebral ischemia can help the surgeon, for example, to determine the duration of the temporary vascular occlusion and the optimal systemic arterial pressure (Martin et al., 2002). The SEP and the cortical EEG are the techniques most frequently employed for this purpose in

Apart from the cited surgeries, the SEP monitoring was also successfully applied in many other surgical procedures, such as interventional neuroradiology, stereotaxic surgery of the brainstem, thalamus, cerebral cortex, thalamotomy, cortical localization, brachial plexus surgery and pelvic fracture surgery (Linden et. al, 1997). SEP also presents prognostic value

Even when post-operative squeals cannot be avoided by monitoring, the detection of neurophysiologic intra-operative changes can make the surgery staff aware of the risk and avoid the exacerbation of the damage (Bose et al., 2004). However, it is important selecting the patients for whom the EP monitoring can be useful, because if the patient does not present pre-operative EP, this technique is not suitable for intra-operative neuro-evaluation

Finally, as the neuromonitoring represents only the current status of the patient, many studies point out the importance of the post-surgery SEP monitoring in order to detect late neurological complications (Guérit and Dion, 2002, Dong et al., 2002, Ghariani et al., 2000).

This section describes some of the most used frequency-domain Objective Response Detection (ORD) techniques, both in its univariate and multivariate versions. Details about *a* 

The Phase Coherence (PC) was introduced in the analysis of the evoked potentials by Galambos *et al.* (1984) and can be seen as a statistical measure of the phase variance. It can be

> 1 1 ˆ ( ) sin ( ) cos ( ) *M M ci i i i*

 

*ff f M*

 *f* is the phase angle of the ith Fourier Transformed EEG epoch and *M* is the number of EEG epochs. This measure supposes that the presence of stimuli-response causes a phase aggregation of the Fourier Transformed EEG epochs in the complex plan. On the other hand, on the absence of response, the phase angle is assumed to be randomly distributed between 0 and 2π, and the probability of obtaining this phase angle configuration is accessed by the Rayleigh test (Mardia, 1972). This techniques only takes into

account the phase of the Fourier Transform (FT) of EEG epochs.

2 2

 

(1)

**4. Frequency–domain Objective Response Detection (ORD) techniques** 

in cases of intracranial hypertension (Giugno et al., 2003) and coma (Logi et al., 2003).

anterior circulation aneurysm surgeries (Martin et al., 2002).

*priori* assumptions related to the signals are included.

**4.1 Univariate ORD techniques** 

**4.1.1 Phase Coherence** 

mathematically defined by:

where ( ) *<sup>i</sup>* 

(Linden et al., 1997).

According to Picton et al. (1987), the Hotelling T2 Test (HT2) is the multivariate analogue of the Student's t test. If *M* samples of a uni-variate distribution is taken, one can estimate its mean *y* and standard deviation *s*. Based on this two parameters, it is possible to calculate the limits for the occurrence of the population mean:

$$\sqrt{M}\frac{\left|\overline{y}-y\right|}{s} \le t$$

where t are the limits taken from the two-tailed Student's t distribution with M-1 degrees of freedom.

For a bidimensional distribution, the confidence region for the mean vector is given by:

$$M\left(\overline{Y}(f) - Y(f)\right)^H S^{-1}\left(\overline{Y}(f) - Y(f)\right) \le \hat{T}^2(f) \tag{2}$$

where the superscript H and ^ denote Hermitian and estimation, respectively, S-1 is the inverse of the covariance matrix of the sample, Y(f) is the vector of the *M* Fourier Transformed EEG epochs and *Y*( ) *f* the mean vector.

The statistics T2 can be related to the Fisher's F distribution by (Picton et al., 1987):

$$
\hat{T}\_{crit}^2(f) = \frac{(M-1)2}{(M-2)} \mathbf{F}\_{crit,2,M-2,a} \tag{3}
$$

where *M* is the number of epochs used to calculate the *T2* estimate and Fcrit,2,M-2,α is the critical value of the F-distribution with 2 and M-2 degrees of freedom at the significance level .

Considering that the Fourier Transformed EEG epochs are bidimensional variables (complex variables with real and imaginary parts), the confidence region for the mean vector leads to an ellipse of confidence. When the ellipse encompasses the origin of the plan (0,0), which represents the response absence condition, one can assume that there is no response to the stimulation. On the other hand, if the origin is not included in the confidence region, the null hypothesis of response absence can be rejected, and one can assume the response detection.

#### **4.1.3 Spectral F Test (SFT)**

The Spectral F Test (SFT) is given by the ratio between the Power Spectrum Density (PSD) of the EEG during stimulation *y*[*k*] and the background EEG *b*[*k*] (Dobie and Wilson, 1996). For windowed EEG signals, the SFT can be estimated by the ratio of the Bartlett periodograms, as follows:

$$\hat{\phi}(f) = \frac{\frac{1}{M\_y} \sum\_{i=1}^{M\_y} \left| Y\_i(f) \right|^2}{\frac{1}{M\_b} \sum\_{i=1}^{M\_y} \left| B\_i(f) \right|^2} \tag{4}$$

Frequency-Domain Objective Response

signals *y*[*k*] and *x*[*k*], respectively.

Gaussian noise) and, therefore, <sup>2</sup>

ˆ ( )

*f*

response is present in all epochs ( () () *Y f Yf <sup>i</sup>* , *i* ), <sup>2</sup>

For the null hypothesis (H0) of response absence ( <sup>2</sup>

following expression (Simpson et al., 2000):

Detection Techniques Applied to Evoked Potentials: A Review 55

where "^" superscript denotes estimation, \* is the complex conjugate, *M* is the number of epochs, and ( ) *Y f <sup>i</sup>* and ( ) *X f <sup>i</sup>* are the Discrete Fourier Transform (DFT) of the ith epoch of

For the case of a periodic stimulation (*x*[*k*]), ( ) *X f <sup>i</sup>* is identical for all epochs and the MSC estimate depends only on the measured EEG ( ) *Y f <sup>i</sup>* , since the contribution of the periodic

*M M*

*i i M M*

1 1

1

From expression 9, it can be seen that, when there is no response to stimulation, the numerator corresponds only to background EEG (assumed to be a zero-mean white

of the MSC), it can be shown that, for *M* independent epochs of *y*[*k*] (zero-mean white Gaussian noise, by assumption), the MSC can be related to the F-distribution by the

2

for the MSC estimates for a given significance level (Simpson et al., 2000):

,

following analytical expression (Miranda de Sá and Infantosi, 2007):

reached when the estimate values exceed the critical value ( 2 2

<sup>ˆ</sup> <sup>1</sup> *crit*

crit 

<sup>ˆ</sup> ( ) ( 1) ~ (1 ( )) <sup>ˆ</sup> *<sup>M</sup> <sup>f</sup> M F*

2 2,2 2,

*F M F*

*f*

*crit M*

Hence, based on the critical values of the F-distribution, one can calculate the critical values

The critical value constitutes a detection threshold and can be alternatively calculated by the

2 1

The detection is based on rejecting the null hypothesis (H0) of response absence, which is

 

*M Y f*

*M X f Y f MX f Y f*

*i i*

*M i i M i i*

()() () ()

*XfY f X f Y f*

*i i*

()() () ()

*i i*

2

( )

*Y f*

( )

2 2,2 2

2,2 2,

ˆ 1 *<sup>M</sup>* (12)

 ˆ ˆ ( ) *f crit* ).

*crit M*

1

2

ˆ ( ) *f* tends to zero. On the other hand, if a consistent

() 0 *f* , where <sup>2</sup>

ˆ ( )*f* tends to the unity.

( ) *f* is the true value

(10)

(11)

2 2 2

2 2 2

(9)

signal to both the numerator and denominator cancels out (Dobie and Wilson, 1989):

2 1 1

2 1

ˆ ( )

*f*

where the superscript ^denotes estimation, ( ) *Y f <sup>i</sup>* and ( ) *B f <sup>i</sup>* are, respectively, the Discrete Fourier Transform (DFT) of the ith EEG epoch of *y*[*k*] and *b*[*k*], and *My* and *Mb*, are the number of EEG epochs during stimulation and at the resting condition (background EEG), respectively.

In the null hypothesis (H0) of no stimulus response, the EEG during stimulation belongs to the same population as the background EEG; hence, both *y*[*k*] and *b*[*k*] are zero-mean Gaussian noise with equal variance. Hence, it can be shown that the distribution of the SFT can be related to the Fisher F-distribution by:

$$\frac{M\_y}{M\_b}\hat{\phi}(f) \sim F\_{2M\_y, 2M\_b} \tag{5}$$

Thus, the critical value for a given significance level , *My* and *Mb* number of EEG epochs is expressed by:

$$
\hat{\phi}\_{crit}(f) = \mathcal{F}\_{crit2M\_y, 2M\_{b^\*}, \alpha} \tag{6}
$$

where 2 ,2 , *y b Fcrit M M* is the critical value of the F-distribution with *2My* and *2Mb* degrees of freedom.

The above expression for critical values calculation is not valid for DC (direct current) and Nyquist frequency, since, in these frequencies, the Fourier Transform of EEG epoch leads to purely real values.

#### **4.1.4 Magnitude-Squared Coherence (MSC)**

The squared modulus of the coherence function (also called Magnitude-squared coherence, MSC), 2 ( ) *yx f* , corresponds to the parcel of the squared mean value of the measured EEG signal *y*[*k*] caused by the stimulation *x*[*k*] for a given frequency *f* (Bendat and Piersol, 2000), and is calculated by (Dobie and Wilson, 1989):

$$\gamma\_{yx}^2(f) = \frac{\left| G\_{yx}(f) \right|^2}{G\_{yy}(f) G\_{xx}(f)} \tag{7}$$

where *Gyx*(*f*) is the cross-spectrum of *x*[*k*] and *y*[*k*] normalized by the auto-spectra, *Gyy*(*f*) and *Gxx*(*f*). It can be shown that the MSC (expression 7) is a real function that varies between 0 and 1.

The estimates of 2 ( ) *yx f* for discrete-time, finite-duration and windowed signals can be calculated by (Bendat and Piersol, 2000):

$$\hat{\boldsymbol{\gamma}}\_{yx}^{2}(f) = \frac{\left| \sum\_{i=1}^{M} \mathbf{Y}\_{i}(f)\mathbf{X}\_{i}^{\*}(f) \right|^{2}}{\sum\_{i=1}^{M} \left| \mathbf{Y}\_{i}(f) \right|^{2} \sum\_{i=1}^{M} \left| \mathbf{X}\_{i}(f) \right|^{2}} \tag{8}$$

where the superscript ^denotes estimation, ( ) *Y f <sup>i</sup>* and ( ) *B f <sup>i</sup>* are, respectively, the Discrete Fourier Transform (DFT) of the ith EEG epoch of *y*[*k*] and *b*[*k*], and *My* and *Mb*, are the number of EEG epochs during stimulation and at the resting condition (background EEG),

In the null hypothesis (H0) of no stimulus response, the EEG during stimulation belongs to the same population as the background EEG; hence, both *y*[*k*] and *b*[*k*] are zero-mean Gaussian noise with equal variance. Hence, it can be shown that the distribution of the SFT

2 ,2 ˆ( )~ *<sup>y</sup> <sup>b</sup>*

2 ,2 , <sup>ˆ</sup> ( ) *y b*

The above expression for critical values calculation is not valid for DC (direct current) and Nyquist frequency, since, in these frequencies, the Fourier Transform of EEG epoch leads to

The squared modulus of the coherence function (also called Magnitude-squared coherence,

signal *y*[*k*] caused by the stimulation *x*[*k*] for a given frequency *f* (Bendat and Piersol, 2000),

<sup>2</sup> ( ) ( ) () () *yx*

where *Gyx*(*f*) is the cross-spectrum of *x*[*k*] and *y*[*k*] normalized by the auto-spectra, *Gyy*(*f*) and *Gxx*(*f*). It can be shown that the MSC (expression 7) is a real function that varies between 0

1 1

*i i*

*M*

*i yx M M*

*yy xx G f <sup>f</sup> G fG f*

*yx*

2 1

ˆ ( )

*f*

*f* , corresponds to the parcel of the squared mean value of the measured EEG

2

*f* for discrete-time, finite-duration and windowed signals can be

2

\*

() ()

*i i*

*Y fX f*

*i i*

*Yf Xf*

() ()

2 2

(7)

*crit crit M M f F*

*M M*

is the critical value of the F-distribution with *2My* and *2Mb* degrees of

(5)

, *My* and *Mb* number of EEG epochs is

(6)

(8)

*y*

*M*

*b*

*f F <sup>M</sup>* 

respectively.

expressed by:

where 2 ,2 , *y b Fcrit M M*

purely real values.

MSC), 2 ( ) *yx* 

and 1.

The estimates of 2 ( ) *yx*

calculated by (Bendat and Piersol, 2000):

freedom.

can be related to the Fisher F-distribution by:

**4.1.4 Magnitude-Squared Coherence (MSC)** 

and is calculated by (Dobie and Wilson, 1989):

Thus, the critical value for a given significance level

where "^" superscript denotes estimation, \* is the complex conjugate, *M* is the number of epochs, and ( ) *Y f <sup>i</sup>* and ( ) *X f <sup>i</sup>* are the Discrete Fourier Transform (DFT) of the ith epoch of signals *y*[*k*] and *x*[*k*], respectively.

For the case of a periodic stimulation (*x*[*k*]), ( ) *X f <sup>i</sup>* is identical for all epochs and the MSC estimate depends only on the measured EEG ( ) *Y f <sup>i</sup>* , since the contribution of the periodic signal to both the numerator and denominator cancels out (Dobie and Wilson, 1989):

$$\hat{\kappa}^2(f) = \frac{\left| \sum\_{i=1}^M \mathbf{X}(f) Y\_i(f) \right|^2}{M \sum\_{i=1}^M \left| \mathbf{X}(f) Y\_i(f) \right|^2} = \frac{\mathbf{X}^2(f) \left| \sum\_{i=1}^M Y\_i(f) \right|^2}{M \mathbf{X}^2(f) \sum\_{i=1}^M \left| Y\_i(f) \right|^2} $$
 
$$\hat{\kappa}^2(f) = \frac{\left| \sum\_{i=1}^M Y\_i(f) \right|^2}{M \sum\_{i=1}^M \left| Y\_i(f) \right|^2} \tag{9} $$

From expression 9, it can be seen that, when there is no response to stimulation, the numerator corresponds only to background EEG (assumed to be a zero-mean white Gaussian noise) and, therefore, <sup>2</sup> ˆ ( ) *f* tends to zero. On the other hand, if a consistent response is present in all epochs ( () () *Y f Yf <sup>i</sup>* , *i* ), <sup>2</sup> ˆ ( )*f* tends to the unity.

For the null hypothesis (H0) of response absence ( <sup>2</sup> () 0 *f* , where <sup>2</sup> ( ) *f* is the true value of the MSC), it can be shown that, for *M* independent epochs of *y*[*k*] (zero-mean white Gaussian noise, by assumption), the MSC can be related to the F-distribution by the following expression (Simpson et al., 2000):

$$\hat{\kappa}^2(M-1)\frac{\hat{\kappa}^2(f)}{(1-\hat{\kappa}^2(f))} \sim F\_{2,2M-2} \tag{10}$$

Hence, based on the critical values of the F-distribution, one can calculate the critical values for the MSC estimates for a given significance level (Simpson et al., 2000):

$$
\hat{\kappa}\_{cir,a}^2 = \frac{F\_{cirt2,2M-2,a}}{M - 1 + F\_{cirt2,2M-2,a}} \tag{11}
$$

The critical value constitutes a detection threshold and can be alternatively calculated by the following analytical expression (Miranda de Sá and Infantosi, 2007):

$$
\hat{\kappa}\_{\text{crit}}^2 = 1 - \alpha^{\frac{1}{M-1}} \tag{12}
$$

The detection is based on rejecting the null hypothesis (H0) of response absence, which is reached when the estimate values exceed the critical value ( 2 2 ˆ ˆ ( ) *f crit* ).

Frequency-Domain Objective Response

where 

M/2:

where <sup>2</sup> 

**4.1.6 Component Synchrony Measure (CSM)** 

phase of its Fourier Transform (Simpson et al., 2000):

2

i and sen

2 2

0 0

2 2 22 2 0 0

 

1 1

*i i*

cos

*M M*

*i i*

2 distribution by:

*M*

*M M*

cos

 

of epochs used in the CSM estimation.

1/2 and the functions cos

and Felix, 2003), as follows:

Hence, it can be shown that:

the CSM can be related to the <sup>2</sup>

Detection Techniques Applied to Evoked Potentials: A Review 57

2 ' 1

The Component Synchrony Measure (CSM) or Phase Synchrony Measure (PSM) quantifies the degree of synchronism between frequencies of a signal, taking into account only the

> 1 1 1 1 <sup>ˆ</sup> ( ) cos ( ) sin ( ) *M M*

*<sup>i</sup>*(*f*) is the phase of the Fourier Transform of the *i*th EEG epoch and *M* is the number

*i i ff f M M*

Assuming that the phase is uniformly distributed between 0 and 2 (absence of synchronism between stimulus and response), the probability density function is given by

> 1 1 cos 0 2 2

 

*d sen d*

 

 

According to the Central Limit Theorem, the summation of sins (and co-sins) in the expression 18 tends asymptotically to a normal distribution with zero-mean and variance

cos ~ 0, ~ 0, 2 2

*N and sen N*

2 2

1 1 2

*i i*

 

<sup>~</sup> <sup>2</sup>

2 is the chi-squared distribution with 2 degrees of freedom. From this expression,

 

*sen*

*i i*

1 11

 

*M M*

 

2

 

 

2 22

*d sen d*

 

*i i*

  1

2 2

 

(18)

i present zero mean and variance ½ (Miranda de Sá

ˆ 1 *<sup>M</sup>* (17)

The critical value can be alternatively calculated by the following analytical expression:

crit 

Considering the linear model presented in Section 2, the response detection is expected in the stimulation frequency and its harmonics. Even in the no-stimulation condition, the detection is expected at the rate of , that is, the significance level of the statistical test corresponds to the maximum false positive rate. The above mentioned critical values are not valid for DC and Nyquist frequency, since the DFT of these components are purely real, while ( ) *Y f <sup>i</sup>* is complex for other frequencies.

#### **4.1.5 Magnitude-Squared Coherence (MSC) with Exponential Forgetting (MSC-EF)**

The application of an exponential forgetting to the MSC was proposed by Tierra-Criollo et al. (1998) and consists of the employment of a decreasing exponential to the EEG epochs spectra, as follows:

$$\hat{\kappa}\_p^2(i,f) = (1-b)\frac{\left|\mathcal{Y}\_i(f) + bS\_{i-1}'(f)\right|^2}{\left|\mathcal{Y}\_i(f)\right|^2 + bS\_{i-1}''(f)}\tag{13}$$

being

$$\begin{aligned} S\_i'(f) &= Y\_i(f) + bS\_{i-1}'(f) \\\\ S\_i''(f) &= \left| Y\_i(f) \right|^2 + bS\_{i-1}''(f) \end{aligned}$$

where *f* is the frequency index, ^ denotes estimation, ( ) *Y f <sup>i</sup>* represents the DFT of the ith EEG epoch and *b* is the forgetting factor (0<*b*<1).

According to Tierra-Criollo et al. (1998), for the null hypothesis of response absence (H0), similarly to the described for the MSC, 2ˆ ( ) *<sup>p</sup> f* can be related to the F-distribution:

$$(M'-1)\frac{\hat{\kappa}\_p^2(f)}{(1-\hat{\kappa}\_p^2(f))} \sim F\_{2,2M'-2} \tag{14}$$

where *F*2,2*<sup>M</sup>* '2 is the F-distribution with *2* and *2M'-2* degrees of freedom and *M'* is given by:

$$M' = \frac{1+b}{1-b} \tag{15}$$

Thus, based on the critical values of *F*2,2 2 *<sup>M</sup>* , one can obtain the critical values for 2ˆ ( ) *<sup>p</sup> f* with a given significance level :

$$
\hat{\kappa}\_{p,vi}^2 = \frac{F\_{crit2,2M'-2,\alpha}}{M'-1+F\_{crit2,2M'-2,\alpha}} \tag{16}
$$

Similarly to the mentioned for MSC, the response detection ( 2 2 ˆ ˆ ( ) *<sup>p</sup> pcrit f* ) is expected at the stimulation frequencies and its harmonics. Even in the no-stimulation condition, the detection is expected at the rate of the significance level of the statistical test.

Considering the linear model presented in Section 2, the response detection is expected in the stimulation frequency and its harmonics. Even in the no-stimulation condition, the detection is expected at the rate of , that is, the significance level of the statistical test corresponds to the maximum false positive rate. The above mentioned critical values are not valid for DC and Nyquist frequency, since the DFT of these components are purely real,

**4.1.5 Magnitude-Squared Coherence (MSC) with Exponential Forgetting (MSC-EF)** 

*p*

2 1

() () <sup>ˆ</sup> (, ) 1

*<sup>Y</sup> <sup>f</sup> bS <sup>f</sup> if b*

<sup>1</sup> () () () *Sii i f Y f bS f*

where *f* is the frequency index, ^ denotes estimation, ( ) *Y f <sup>i</sup>* represents the DFT of the ith EEG

According to Tierra-Criollo et al. (1998), for the null hypothesis of response absence (H0),

2

*p <sup>f</sup> M F*

where *F*2,2*<sup>M</sup>* '2 is the F-distribution with *2* and *2M'-2* degrees of freedom and *M'* is given

1 1 *<sup>b</sup> <sup>M</sup>*

Thus, based on the critical values of *F*2,2 2 *<sup>M</sup>* , one can obtain the critical values for 2ˆ ( ) *<sup>p</sup>*

2 2,2 2,

*F M F*

*crit M*

stimulation frequencies and its harmonics. Even in the no-stimulation condition, the

<sup>ˆ</sup> <sup>1</sup> *crit*

*p*

Similarly to the mentioned for MSC, the response detection ( 2 2 ˆ ˆ ( ) *<sup>p</sup> pcrit*

detection is expected at the rate of the significance level of the statistical test.

*b*

2,2 2,

*f*

*crit M*

*f*

<sup>ˆ</sup> ( ) ( ' 1) ~ (1 ( )) <sup>ˆ</sup> *p*

2 <sup>1</sup> () () () *S f Y f bS f ii i*

2

*i i*

2 2,2 ' 2

*M*

*Y f bS f*

*i i*

() ()

The application of an exponential forgetting to the MSC was proposed by Tierra-Criollo et al. (1998) and consists of the employment of a decreasing exponential to the EEG epochs

2

(13)

(14)

(16)

) is expected at the

*f*

(15)

1

*f* can be related to the F-distribution:

while ( ) *Y f <sup>i</sup>* is complex for other frequencies.

epoch and *b* is the forgetting factor (0<*b*<1).

similarly to the described for the MSC, 2ˆ ( ) *<sup>p</sup>*

with a given significance level :

spectra, as follows:

being

by:

The critical value can be alternatively calculated by the following analytical expression:

$$
\hat{\kappa}\_{\text{crit}}^2 = 1 - \alpha^{\frac{1}{M'-1}} \tag{17}
$$

#### **4.1.6 Component Synchrony Measure (CSM)**

The Component Synchrony Measure (CSM) or Phase Synchrony Measure (PSM) quantifies the degree of synchronism between frequencies of a signal, taking into account only the phase of its Fourier Transform (Simpson et al., 2000):

$$\hat{\rho}^2(f) = \left[\frac{1}{M} \sum\_{i=1}^M \cos \phi\_i(f)\right]^2 + \left[\frac{1}{M} \sum\_{i=1}^M \sin \phi\_i(f)\right]^2 \tag{18}$$

where *<sup>i</sup>*(*f*) is the phase of the Fourier Transform of the *i*th EEG epoch and *M* is the number of epochs used in the CSM estimation.

Assuming that the phase is uniformly distributed between 0 and 2 (absence of synchronism between stimulus and response), the probability density function is given by 1/2 and the functions cosi and seni present zero mean and variance ½ (Miranda de Sá and Felix, 2003), as follows:

$$\begin{aligned} \mu &= \int\_0^{2\pi} \cos\phi \frac{1}{2\pi} \, d\phi = \int\_0^{2\pi} \sec\phi \frac{1}{2\pi} \, d\phi = 0 \\\\ \sigma^2 &= \int\_0^{2\pi} \cos^2\phi \frac{1}{2\pi} \, d\phi = \int\_0^{2\pi} \sec^2\phi \frac{1}{2\pi} \, d\phi = \frac{1}{2\pi} \end{aligned}$$

According to the Central Limit Theorem, the summation of sins (and co-sins) in the expression 18 tends asymptotically to a normal distribution with zero-mean and variance M/2:

$$\sum\_{i=1}^{M} \cos \phi\_i \sim N\left(0, \frac{M}{2}\right) \qquad \text{and} \qquad \sum\_{i=1}^{M} \text{sen}\phi\_i \sim N\left(0, \frac{M}{2}\right).$$

Hence, it can be shown that:

$$\frac{\left(\sum\_{i=1}^{M} \cos \phi\_i\right)^2 + \left(\sum\_{i=1}^{M} \sin \phi\_i\right)^2}{M/2} \sim \chi\_2^2$$

where <sup>2</sup> 2 is the chi-squared distribution with 2 degrees of freedom. From this expression, the CSM can be related to the <sup>2</sup> 2 distribution by:

Frequency-Domain Objective Response

column element of <sup>ˆ</sup> ( ) *yy* **<sup>S</sup>** *<sup>f</sup>* is

of a set of signals that is caused by the stimulation.

2

( )

1 <sup>1</sup> cos ( ) *N i ij j C f <sup>N</sup>*

and

*i*

for the MCSM can be expressed by (Felix et al., 2007):

**4.2.2 Multiple Component Synchrony Measure (MCSM)** 

<sup>ˆ</sup> *crit*

*N*

for a significance level

where *Fcrit N M N* 

( 2 2 ˆ ˆ ( ) *N Ncrit*

Felix, 2003):

being

 

mean phase angle, ( ) *<sup>i</sup>*

2004):

Detection Techniques Applied to Evoked Potentials: A Review 59

being ( ) *Y f ki* the Fourier Transform of the *i*th epoch of the *k*th EEG derivation; *H* and *T* superscripts mean, respectively, Hermitian and the matrix transpose; and the *p*th-row, *q*th-

The distribution of the MC estimates can related to the F-distribution and the critical value

*crit N M N*

*F MNN* 

*f* ). As a multivariate extension of the MSC, MC quantifies the amount of power

,2 ,2( ) is the critical value of the F distribution with 2*N* and 2(*M*-*N*) degrees of

freedom. The detection is identified based on the rejection of the null hypothesis (H0) of response absence, which is achieved when the estimate values exceed the critical value

A multivariate extension of the CSM was proposed by Miranda de Sá and Felix (2003) as a way of measuring the synchronism of the ith epoch of the Fourier Transform of *N* EEG derivations (*y1*[*k*], *y2*[*k*],…, *yN*[*k*]) caused by a rhythmical stimulation only considering their

detecting the evoked response and can be mathematically defined by (Miranda de Sá and

1 1 1 1 <sup>ˆ</sup> ( ) cos ( ) sin ( ) *M M Ni i i i ff f M M*

 

tan 0

tan 0 *ii i*

*S C if C*

*i i i*

Assuming that the mean phase angle is uniformly distributed between 0 and 2, it can be showed, in a similar way to the performed to the CSM, that the asymptotical critical value

*S C if C <sup>f</sup>*

where the *M* is the number of EEG epochs and the mean phase angle can be calculated by:

1

1

, *M* epochs and *N* signals can be expressed as (Miranda de Sá et al.,

(24)

*f* . This technique, called Multiple CSM (MCSM), can be used for

2 2

 

(25)

1 <sup>1</sup> sin ( ) *N i ij j S f <sup>N</sup>*

 

1 ˆ () () () *M yp yq pi qi i*

*f Y fY f* **<sup>S</sup>** .

2 ,2 ,2( ) ,2 ,2( )

*crit N M N F*

$$
\hat{\rho}^2(f) \sim \frac{1}{M^2} \frac{M}{2} \chi\_2^2 = \frac{\chi\_2^2}{2M} \tag{19}
$$

Thus, for the null hypothesis of absence of synchronism, the critical value for a given significance level α and *M* EEG epochs can be obtained by (Mardia, 1972):

$$
\rho\_{crit,a}^2 = \frac{\mathcal{X}\_{2\,crit,a}^2}{2M} \tag{20}
$$

where <sup>2</sup> 2 , *crit* is the critical value of the chi-squared distribution for the significance level . It is worth noting that CSM expression corresponds to the square of the Phase Coherence (PC).

Alternatively, the critical value for CSM can be calculated based on the probability density function of the chi-squared distribution given as:

$$p\_{\chi^{\frac{z}{2}}\_2}(z) = \frac{1}{2}e^{-\frac{z}{2}}.$$

The analytical critical value of <sup>2</sup> 2 for a given significance level is obtained from

$$\int\_0^{\frac{z}{2\alpha i}} \frac{1}{2} e^{-\frac{z}{2}} dz = 1 - a\_{\prime\prime}$$

which yields to:

$$\mathcal{X}\_{2\,crit,\alpha}^2 = 2\ln\left(\frac{1}{\alpha}\right). \tag{21}$$

Hence, substituting expression (21) in (20) leads to:

$$
\rho\_{crit, \alpha}^2 = \frac{\ln\left(1/\alpha\right)}{M} \tag{22}
$$

#### **4.2 Multivariate ORD (MORD) techniques**

#### **4.2.1 Multiple Coherence (MC)**

The Multiple Coherence (MC) - which is the multivariate version of MSC - between a periodic signal and a set of *N* random ones (yj[k], j = 1..*N*) is given by (Miranda de Sá et al., 2004):

$$
\hat{\kappa}\_N^2(f) = \mathbf{V}^H(f)\hat{\mathbf{S}}\_{yy}^{-1}(f)\mathbf{V}(f)\Big/\mathcal{M}\tag{23}
$$

where \*\* \* 1 2 11 1 () () () () *<sup>T</sup> MM M i i Ni ii i f Yf Yf Y f* **<sup>V</sup>**

being ( ) *Y f ki* the Fourier Transform of the *i*th epoch of the *k*th EEG derivation; *H* and *T* superscripts mean, respectively, Hermitian and the matrix transpose; and the *p*th-row, *q*th-

$$\text{column element of } \hat{\mathbf{S}}\_{yy}(f) \text{ is } \hat{\mathbf{S}}\_{ypyq}(f) = \sum\_{i=1}^{M} Y\_{pi}^{\*}(f) Y\_{qi}(f) \dots$$

The distribution of the MC estimates can related to the F-distribution and the critical value for a significance level , *M* epochs and *N* signals can be expressed as (Miranda de Sá et al., 2004):

$$
\hat{\kappa}\_{N\_{cit}}^2 = \frac{F\_{crit\,\alpha, 2N, 2(M-N)}}{F\_{crit\,\alpha, 2N, 2(M-N)} + [M-N] \stackrel{\text{(24)}}{\text{(25)}}} \tag{24}
$$

where *Fcrit N M N* ,2 ,2( ) is the critical value of the F distribution with 2*N* and 2(*M*-*N*) degrees of freedom. The detection is identified based on the rejection of the null hypothesis (H0) of response absence, which is achieved when the estimate values exceed the critical value ( 2 2 ˆ ˆ ( ) *N Ncrit f* ). As a multivariate extension of the MSC, MC quantifies the amount of power of a set of signals that is caused by the stimulation.

#### **4.2.2 Multiple Component Synchrony Measure (MCSM)**

A multivariate extension of the CSM was proposed by Miranda de Sá and Felix (2003) as a way of measuring the synchronism of the ith epoch of the Fourier Transform of *N* EEG derivations (*y1*[*k*], *y2*[*k*],…, *yN*[*k*]) caused by a rhythmical stimulation only considering their mean phase angle, ( ) *<sup>i</sup> f* . This technique, called Multiple CSM (MCSM), can be used for detecting the evoked response and can be mathematically defined by (Miranda de Sá and Felix, 2003):

$$\hat{\rho}\_N^2(f) = \left[\frac{1}{M} \sum\_{i=1}^M \cos\left(\overline{\theta}\_i(f)\right)\right]^2 + \left[\frac{1}{M} \sum\_{i=1}^M \sin\left(\overline{\theta}\_i(f)\right)\right]^2 \tag{25}$$

where the *M* is the number of EEG epochs and the mean phase angle can be calculated by:

$$
\overline{\partial}\_i(f) = \begin{cases}
\tan^{-1}\left(\overline{S}\_i / \overline{C}\_i\right) & \text{if} \quad \overline{C}\_i \ge 0 \\
\tan^{-1}\left(\overline{S}\_i / \overline{C}\_i\right) + \pi & \text{if} \quad \overline{C}\_i < 0
\end{cases}
$$

being

58 Applied Biological Engineering – Principles and Practice

2 2 2 2 2 <sup>1</sup> <sup>ˆ</sup> ( )~ 2 2 *<sup>M</sup> <sup>f</sup> <sup>M</sup> <sup>M</sup>*

Thus, for the null hypothesis of absence of synchronism, the critical value for a given

*crit M*

It is worth noting that CSM expression corresponds to the square of the Phase Coherence

Alternatively, the critical value for CSM can be calculated based on the probability density

*p z e* 

2

<sup>1</sup> 1 , <sup>2</sup>

<sup>1</sup> 2ln .

<sup>2</sup>

The Multiple Coherence (MC) - which is the multivariate version of MSC - between a periodic signal and a set of *N* random ones (yj[k], j = 1..*N*) is given by (Miranda de Sá et al., 2004):

> 2 1 ˆ ˆ () () ()() *<sup>H</sup> N yy*

ln 1 *crit M* 

,

*<sup>T</sup> MM M i i Ni*

11 1 () () () ()

*ii i f Yf Yf Y f*   

<sup>2</sup> <sup>1</sup> () . <sup>2</sup>

2 2

*crit z e dz*

2 2

0

2 2 ,

 *crit* 

 

2 2 2 , , 2

*crit*

is the critical value of the chi-squared distribution for the significance level

*z*

2 for a given significance level is obtained from

 

function of the chi-squared distribution given as:

Hence, substituting expression (21) in (20) leads to:

**4.2 Multivariate ORD (MORD) techniques** 

where \*\* \* 1 2

**<sup>V</sup>**

**4.2.1 Multiple Coherence (MC)** 

The analytical critical value of <sup>2</sup>

which yields to:

where <sup>2</sup> 2 , *crit* 

(PC).

significance level α and *M* EEG epochs can be obtained by (Mardia, 1972):

2

(19)

(21)

(22)

*f f f fM* **VS V** (23)

.

(20)

$$\overline{\mathbf{C}}\_i = \frac{1}{N} \sum\_{j=1}^{N} \cos \theta\_{ij}(f) \quad \text{and} \quad \overline{S}\_i = \frac{1}{N} \sum\_{j=1}^{N} \sin \theta\_{ij}(f).$$

Assuming that the mean phase angle is uniformly distributed between 0 and 2, it can be showed, in a similar way to the performed to the CSM, that the asymptotical critical value for the MCSM can be expressed by (Felix et al., 2007):

Frequency-Domain Objective Response

1985, Beagley *et al.*, 1979).

performance than any technique.

Detection Techniques Applied to Evoked Potentials: A Review 61

be statistically more powerful than the PC. However, Picton *et al.* (1987) have found small difference between the two methods when the auditory threshold was measured by means of the steady state AEP. Based on these results, the authors have reported that, for intensities near the threshold, most of the information about the signal is in the phase, since using the amplitude information (HT2) didn't result in an improvement in the response detection. Other studies also found that the phase is more important than magnitude (Greenblat *et al.*,

In 1989, Dobie and Wilson have proposed the use of the Magnitude-Squared Coherence (MSC), an ORD technique that uses magnitude and phase of the Fourier Transform of EEG epochs, for identifying the frequencies that significantly contribute to the auditory EP. In this work, the MSC was considered more sensible than the simple visual inspection of the replicated responses. In a later work, Dobie and Wilson (1990) have applied the coherence (MSC) to the AEP filtered with the "Optimum" Wiener Filtering and, compared to the nonfiltered version, it was verified that this procedure can be advantageous for signals with low signal-to-noise ratio, such as the obtained with stimulation near the auditory threshold.

Later, Victor and Mast (1991) have proposed a variant of HT2, named T2 circular (T2C). This method assumes that the real and imaginary parts of the Fourier Transform of the EEG epochs are independent and present equal variance. This assumption results in a simpler statistical approach, and the ellipse of confidence of HT2 becomes a circle of confidence in T2C. Moreover, in this study, a comparison between the performances of three ORD methods was performed: the HT2, the T2C and the Phase Rayleigh Criterion (PRC) – a technique that uses only the phase of the signal. The comparison was based on simulation and application to the steady state visual evoked potential. As a result, it was observed that, for low signal-to-noise (SNR) ratio values, HT2 and T2C have shown to be superior to the PRC. The authors consider that this result is due to the fact that the first two methods use information of amplitude, while the PRC discard it. Furthermore, it was verified that for low SNR, a high number of EEG epochs is needed in order to achieve statistical significance. On the other hand, for a low number of EEG segments, T2C and PRC presented advantage over HT2 and for intermediate SNR values T2C showed better

Dobie and Wilson (1993) also compared the performance of T2C, PC and MSC using simulated signals. Additionally, a variant version of the MSC, the MSC-WA (WA, of Weighted Averaging), which consists of the multiplication of each epoch by the inverse of its power, was investigated. This weighting assumes that epochs with high power are the ones that present lower SNR and, therefore, should have their weight reduced. This procedure can be particularly interesting in the cases of non-stationary noises, which can harm the performance of the MSC, leading it to have inferior results to the PC (Dobie and Wilson, 1993). According to these authors, the T2C is mathematically related to the MSC, and it is possible to obtain one estimator from the other, although the MSC is computationally simpler. The MSC (or T2C) weighted averaging was the technique that presented the best performance in the detection of response to the auditory stimulus. In a later study (Dobie and Wilson, 1994a), the MSC, the MSC-WA and the PC were applied to the steady state 40Hz AEP. The three techniques presented similar performance in the response detection, although a slightly advantage for the MSC-WA over the MSC and for

the MSC over the PC has been observed (Dobie and Wilson, 1994b).

$$
\rho\_{N\,crit,\alpha}^2 = \frac{\chi\_{2\,crit,\alpha}^2}{2M} = \frac{\ln\left(1/\alpha\right)}{M} \tag{26}
$$

where <sup>2</sup> 2 , *crit* is the critical value of the chi-squared distribution with 2 degrees of freedom for the significance level *α* and *M* is the number of EEG epochs used in the estimation. Also for this technique, the detection is based on the null hypothesis (H0) rejection of synchronism absence, which is achieved when the estimate values exceed the corresponding critical value ( 2 2 ˆ*N N crit f* ).

## **5. A chronological review of ORD applied to the evoked potentials**

The waveform analysis of the evoked potential (EP) is based on the physician experience, ability and attention level, as well as in informal criteria (Dobie and Wilson, 1993). For the case of the somatosensory evoked potential used in surgical monitoring, for example, one considers a significant modification in its waveform, a reduction of 30% to 50% in the amplitude, an increase of 5% to 10% in the latency, or a combination of these criteria (Linden *et al.*, 1997). Such criteria, used as parameters of modification on the intra-operative strategy, are clearly subjective once they depend on the EEG recording quality, anesthesia regimen, and are hampered by the high variability inter-observer and inter-patient (Martin et al., 2002).

On the other hand, the techniques known as Objective Response Detection (ORD) have been suggested as a way to overcome this subjectivity and allow the stimuli-response detection with a maximum false positive rate *a priori* established. Dobie and Wilson (1993) numbered the advantages of the ORD application compared to the conventional analysis by visual inspection, such as avoiding the persistence of the trained observer and obtaining relevant information even for experienced observers in the judgment of questionable cases.

#### **5.1 Univariate ORD techniques**

In 1984, Galambos *et al.* (apud Stapells, 1987) introduced the ORD technique Phase Coherence (PC) in the analysis of the steady state auditory responses. This technique can be seen as a statistical measure of the phase variance and uses only the phase information of the Fourier Transform of the EEG epochs. Two years later, Stapells *et al.* (1987) have applied the PC for obtaining the auditory threshold of normal adults. This method showed to be accurate to establish the behavioral auditory threshold, being considered as fast as obtaining the brainstem responses by tones. Moreover, these authors pointed out that the PC showed better results for determining the optimal stimulation rate when compared to the amplitude inspection of the coherent average, since the latter presents higher variability than the PC.

Still in 1987, Picton *et al.* have applied the Hotelling T2 Test (HT2) and the PC to the steady state auditory evoked potential (AEP). The HT2 (Hotelling, 1931) takes into account both amplitude and phase of the Fourier Transformed EEG epochs and allows the calculation of a confidence ellipse for the response vectors (EP). In the case in which the ellipse do not encompass the origin (0,0), which corresponds to the absence response condition, its presence is assumed (Dobie and Wilson, 1993). Since the PC represents a kind of HT2 without considering the amplitude information (Picton *et al.*, 1987), theoretically, HT2 would 1985, Beagley *et al.*, 1979).

60 Applied Biological Engineering – Principles and Practice

2 2 , ,

**5. A chronological review of ORD applied to the evoked potentials** 

hampered by the high variability inter-observer and inter-patient (Martin et al., 2002).

information even for experienced observers in the judgment of questionable cases.

where <sup>2</sup> 2 , *crit* 

critical value ( 2 2 ˆ*N N crit* 

**5.1 Univariate ORD techniques** 

 *f* ).

2 *crit N crit M M* 

for the significance level *α* and *M* is the number of EEG epochs used in the estimation. Also for this technique, the detection is based on the null hypothesis (H0) rejection of synchronism absence, which is achieved when the estimate values exceed the corresponding

The waveform analysis of the evoked potential (EP) is based on the physician experience, ability and attention level, as well as in informal criteria (Dobie and Wilson, 1993). For the case of the somatosensory evoked potential used in surgical monitoring, for example, one considers a significant modification in its waveform, a reduction of 30% to 50% in the amplitude, an increase of 5% to 10% in the latency, or a combination of these criteria (Linden *et al.*, 1997). Such criteria, used as parameters of modification on the intra-operative strategy, are clearly subjective once they depend on the EEG recording quality, anesthesia regimen, and are

On the other hand, the techniques known as Objective Response Detection (ORD) have been suggested as a way to overcome this subjectivity and allow the stimuli-response detection with a maximum false positive rate *a priori* established. Dobie and Wilson (1993) numbered the advantages of the ORD application compared to the conventional analysis by visual inspection, such as avoiding the persistence of the trained observer and obtaining relevant

In 1984, Galambos *et al.* (apud Stapells, 1987) introduced the ORD technique Phase Coherence (PC) in the analysis of the steady state auditory responses. This technique can be seen as a statistical measure of the phase variance and uses only the phase information of the Fourier Transform of the EEG epochs. Two years later, Stapells *et al.* (1987) have applied the PC for obtaining the auditory threshold of normal adults. This method showed to be accurate to establish the behavioral auditory threshold, being considered as fast as obtaining the brainstem responses by tones. Moreover, these authors pointed out that the PC showed better results for determining the optimal stimulation rate when compared to the amplitude inspection of the coherent average, since the latter presents higher variability than the PC. Still in 1987, Picton *et al.* have applied the Hotelling T2 Test (HT2) and the PC to the steady state auditory evoked potential (AEP). The HT2 (Hotelling, 1931) takes into account both amplitude and phase of the Fourier Transformed EEG epochs and allows the calculation of a confidence ellipse for the response vectors (EP). In the case in which the ellipse do not encompass the origin (0,0), which corresponds to the absence response condition, its presence is assumed (Dobie and Wilson, 1993). Since the PC represents a kind of HT2 without considering the amplitude information (Picton *et al.*, 1987), theoretically, HT2 would

<sup>2</sup>

ln 1

is the critical value of the chi-squared distribution with 2 degrees of freedom

(26)

In 1989, Dobie and Wilson have proposed the use of the Magnitude-Squared Coherence (MSC), an ORD technique that uses magnitude and phase of the Fourier Transform of EEG epochs, for identifying the frequencies that significantly contribute to the auditory EP. In this work, the MSC was considered more sensible than the simple visual inspection of the replicated responses. In a later work, Dobie and Wilson (1990) have applied the coherence (MSC) to the AEP filtered with the "Optimum" Wiener Filtering and, compared to the nonfiltered version, it was verified that this procedure can be advantageous for signals with low signal-to-noise ratio, such as the obtained with stimulation near the auditory threshold.

Later, Victor and Mast (1991) have proposed a variant of HT2, named T2 circular (T2C). This method assumes that the real and imaginary parts of the Fourier Transform of the EEG epochs are independent and present equal variance. This assumption results in a simpler statistical approach, and the ellipse of confidence of HT2 becomes a circle of confidence in T2C. Moreover, in this study, a comparison between the performances of three ORD methods was performed: the HT2, the T2C and the Phase Rayleigh Criterion (PRC) – a technique that uses only the phase of the signal. The comparison was based on simulation and application to the steady state visual evoked potential. As a result, it was observed that, for low signal-to-noise (SNR) ratio values, HT2 and T2C have shown to be superior to the PRC. The authors consider that this result is due to the fact that the first two methods use information of amplitude, while the PRC discard it. Furthermore, it was verified that for low SNR, a high number of EEG epochs is needed in order to achieve statistical significance. On the other hand, for a low number of EEG segments, T2C and PRC presented advantage over HT2 and for intermediate SNR values T2C showed better performance than any technique.

Dobie and Wilson (1993) also compared the performance of T2C, PC and MSC using simulated signals. Additionally, a variant version of the MSC, the MSC-WA (WA, of Weighted Averaging), which consists of the multiplication of each epoch by the inverse of its power, was investigated. This weighting assumes that epochs with high power are the ones that present lower SNR and, therefore, should have their weight reduced. This procedure can be particularly interesting in the cases of non-stationary noises, which can harm the performance of the MSC, leading it to have inferior results to the PC (Dobie and Wilson, 1993). According to these authors, the T2C is mathematically related to the MSC, and it is possible to obtain one estimator from the other, although the MSC is computationally simpler. The MSC (or T2C) weighted averaging was the technique that presented the best performance in the detection of response to the auditory stimulus. In a later study (Dobie and Wilson, 1994a), the MSC, the MSC-WA and the PC were applied to the steady state 40Hz AEP. The three techniques presented similar performance in the response detection, although a slightly advantage for the MSC-WA over the MSC and for the MSC over the PC has been observed (Dobie and Wilson, 1994b).

Frequency-Domain Objective Response

normalizing transform in it.

the MLAEP's (L+15).

Detection Techniques Applied to Evoked Potentials: A Review 63

Miranda de Sá *et al.* (2001) proposed a coherence-based method to emphasize the stimulisynchronized responses and reduce the background EEG influence. Later (Miranda de Sá *et al.*, 2002), the confidence limits for the coherence estimates between one random and one periodic signal were calculated based on a monotonically increasing function of the estimates, which involves the non-central F-distribution. Miranda de Sá (2004) obtained the sampling distribution of this coherence estimate itself and found it to be non-central beta distributed. This allowed further investigations to be carried out (Miranda de Sá *et al.*, 2009) for assessing both bias and variance of the estimate as well as the performance of the

The MSC and the CSM were also applied for monitoring the anesthetic plan (Cagy *et al.*, 2000, Cagy, 2003). These studies showed that, during infusion of anesthetic, a reduction in values of both estimates is verified. Moreover, the results for MSC and CSM were quite similar, indicating the phase to be more important than the magnitude, as previously reported by Dobie and Wilson (1993). The MSC was also used to identify the maximum response band for the Brainstem Auditory Evoked Potential (BAEP) (Pacheco, 2003, Pacheco and Infantosi, 2005). Infantosi *et al.* (2004) applied the MSC to the Middle Latency Auditory Evoked Potential (MLAEP) of normal individuals for different sound pressure levels aiming at investigating the frequency bands that better characterize this evoked response for distinct stimulation intensities. They have found consistent response detection for frequencies within the gamma band (30-50 Hz). Furthermore, the application of the MSC to the AEP for determining the auditory threshold L, defined as the volunteer response to a click stimulation, resulted in the detection near the visual identification by a specialist of the BAEP waves (L and L+5) or of

Melges *et al.* (2005) employed the methodology suggested by Tierra-Criollo (2001), and used the temporal evolution of the MSC for a given frequency in order to evidence the transitions from tibial nerve somatosensory stimulation to resting condition, and conversely. The transition from a responsive to a no-responsive status is very important for surgical monitoring and this work have mimicked these statuses by presenting and omitting the stimulus. At the same year, Miranda de Sá *et al.* (2005) have investigated the coherence between two EEG derivations due to a visual rhythmic stimulation and the partial coherence (after removing the contribution of the stimulus) applied to the same signals. They concluded that these techniques present complementary role, since the coherence quantifies the degree of synchronism between the derivations, whereas the partial coherence informs about the relationship due to the non-phase locked activities, suggesting its use in

In 2006, Campos *et al.* (2006) applied the SFT to the EEG of epileptic patients during intermittent photic stimulation, and concluded that this technique should be employed as a complement to the traditional identification methods of photo-recruited responses, such as spectral analysis. By using EEG signals during the same type of stimulation, Miranda de Sá *et al.* (2006) studied the SFT applied to the signals of normal individuals. Moreover, they investigated the probability distribution of this test, as well as the confidence limits for its estimates, using simulated signals with different signal-to-noise ratio and *M*-values. Since the majority of the EP applications use periodic stimulation (intermittent photic stimulation, train of current pulses or clicks), Miranda de Sá (2006a) developed analytical expressions for calculating the trend, variance and probability density function for the coherence (MSC), in

ERD/ERS (event related desynchronization/synchronization) studies.

the particular case in which the input signal (stimulus) is periodic.

At the same year, Dobie and Wilson (1994b) have applied the MSC and the MSC-PW (PW, of Phase Weighting) to the steady state 40Hz AEP. In the MSC-PW, a weighting is applied and it is related to the phase error calculated as the difference between the phase of the averaged signal (coherent average) and an expected phase (or target-phase). The targetphase is calculated from the coherent average with a high M number of EEG epochs during stimulation with intensities higher than the commonly used for obtaining the AEP. As a result, it was verified that the phase weighting improved the performance of the MSC. At the same year, Miranda de Sá et al. (1994) investigated the theoretical confidence limits for the coherence estimate (MSC) comparing them to the limits obtained by simulation with random signals.

In 1995, Dobie and Wilson (1995) verified the superior performance for the MSC-WA, when compared to the human inspection. The MSC-WA allowed detecting the responses to auditory stimulation with a lower number of stimuli and with lower stimulation intensity. At the same year, Thakor *et al.* (1995) have proposed an adaptive algorithm for the coherence estimate, in order to detect changes in the somatosensory evoked response. This study showed that, during hypoxia in cats, the MSC presents a sharp decrease, confirming the applicability of the adaptive MSC for monitoring purposes.

In 1996, Dobie and Wilson (1996) compared the Spectral F Test (SFT) and the MSC in the detection of the steady state AEP and concluded that, as they presented the same performance, the choice for using one technique or other would be a convenience issue. Two years later, Liavas *et al.* (1998) used successfully an ORD technique based on the periodogram for detecting the steady state visual evoked potential, aiming at investigating neuropathies related to the visual system.

Applying a decreasing exponential weighting to the spectral estimates of the EEG epochs during somatosensory stimulation used for MSC calculation, Tierra-Criollo *et al.* (1998) showed that this technique leads to the detection of the evoked responses faster than its simple version. This weighting emphasizes the latest spectral estimates, making the MSC more representative of the current status of the patient. This technique was named MSC with exponential forgetting (MSC-EF). Due to its promising results, Tierra-Criollo (2001) suggested the application of both the MSC and MSC-EF to the posterior tibial nerve SEP as a method to be evaluated for real-time monitoring of surgical procedures.

In 2000, Ramos et al. compared the MSC and the CSM (Component Synchrony Measure), which corresponds to the square of the PC (Phase Coherence). They reported that there is no statistical difference in performance for response detection when applied to the EEG of children and newborns during click stimulation. However, the MSC showed higher specificity in the detection of auditory deficiency, which gives to this technique greater clinical interest. Moreover, this method presented higher potentiality for determining the auditory threshold in the studied age group (Ramos et al., 2000). Also in the detection of the somatosensory response, the MSC presented better performance when compared to the CSM and the SFT (Simpson *et al.*, 2000, Tierra-Criollo, 2001). The MSC was also applied to the EEG during intermittent photic stimulation in order to quantify the degree of cortical activation (Miranda de Sá, 2000) and in the identification of inter-hemisphere symmetry between homologues regions of the visual cortex at the stimulation frequency and its harmonics (Miranda de Sá and Infantosi, 2002).

At the same year, Dobie and Wilson (1994b) have applied the MSC and the MSC-PW (PW, of Phase Weighting) to the steady state 40Hz AEP. In the MSC-PW, a weighting is applied and it is related to the phase error calculated as the difference between the phase of the averaged signal (coherent average) and an expected phase (or target-phase). The targetphase is calculated from the coherent average with a high M number of EEG epochs during stimulation with intensities higher than the commonly used for obtaining the AEP. As a result, it was verified that the phase weighting improved the performance of the MSC. At the same year, Miranda de Sá et al. (1994) investigated the theoretical confidence limits for the coherence estimate (MSC) comparing them to the limits obtained by simulation with

In 1995, Dobie and Wilson (1995) verified the superior performance for the MSC-WA, when compared to the human inspection. The MSC-WA allowed detecting the responses to auditory stimulation with a lower number of stimuli and with lower stimulation intensity. At the same year, Thakor *et al.* (1995) have proposed an adaptive algorithm for the coherence estimate, in order to detect changes in the somatosensory evoked response. This study showed that, during hypoxia in cats, the MSC presents a sharp decrease, confirming

In 1996, Dobie and Wilson (1996) compared the Spectral F Test (SFT) and the MSC in the detection of the steady state AEP and concluded that, as they presented the same performance, the choice for using one technique or other would be a convenience issue. Two years later, Liavas *et al.* (1998) used successfully an ORD technique based on the periodogram for detecting the steady state visual evoked potential, aiming at investigating

Applying a decreasing exponential weighting to the spectral estimates of the EEG epochs during somatosensory stimulation used for MSC calculation, Tierra-Criollo *et al.* (1998) showed that this technique leads to the detection of the evoked responses faster than its simple version. This weighting emphasizes the latest spectral estimates, making the MSC more representative of the current status of the patient. This technique was named MSC with exponential forgetting (MSC-EF). Due to its promising results, Tierra-Criollo (2001) suggested the application of both the MSC and MSC-EF to the posterior tibial nerve SEP as a

In 2000, Ramos et al. compared the MSC and the CSM (Component Synchrony Measure), which corresponds to the square of the PC (Phase Coherence). They reported that there is no statistical difference in performance for response detection when applied to the EEG of children and newborns during click stimulation. However, the MSC showed higher specificity in the detection of auditory deficiency, which gives to this technique greater clinical interest. Moreover, this method presented higher potentiality for determining the auditory threshold in the studied age group (Ramos et al., 2000). Also in the detection of the somatosensory response, the MSC presented better performance when compared to the CSM and the SFT (Simpson *et al.*, 2000, Tierra-Criollo, 2001). The MSC was also applied to the EEG during intermittent photic stimulation in order to quantify the degree of cortical activation (Miranda de Sá, 2000) and in the identification of inter-hemisphere symmetry between homologues regions of the visual cortex at the stimulation frequency and its

the applicability of the adaptive MSC for monitoring purposes.

method to be evaluated for real-time monitoring of surgical procedures.

neuropathies related to the visual system.

harmonics (Miranda de Sá and Infantosi, 2002).

random signals.

Miranda de Sá *et al.* (2001) proposed a coherence-based method to emphasize the stimulisynchronized responses and reduce the background EEG influence. Later (Miranda de Sá *et al.*, 2002), the confidence limits for the coherence estimates between one random and one periodic signal were calculated based on a monotonically increasing function of the estimates, which involves the non-central F-distribution. Miranda de Sá (2004) obtained the sampling distribution of this coherence estimate itself and found it to be non-central beta distributed. This allowed further investigations to be carried out (Miranda de Sá *et al.*, 2009) for assessing both bias and variance of the estimate as well as the performance of the normalizing transform in it.

The MSC and the CSM were also applied for monitoring the anesthetic plan (Cagy *et al.*, 2000, Cagy, 2003). These studies showed that, during infusion of anesthetic, a reduction in values of both estimates is verified. Moreover, the results for MSC and CSM were quite similar, indicating the phase to be more important than the magnitude, as previously reported by Dobie and Wilson (1993). The MSC was also used to identify the maximum response band for the Brainstem Auditory Evoked Potential (BAEP) (Pacheco, 2003, Pacheco and Infantosi, 2005).

Infantosi *et al.* (2004) applied the MSC to the Middle Latency Auditory Evoked Potential (MLAEP) of normal individuals for different sound pressure levels aiming at investigating the frequency bands that better characterize this evoked response for distinct stimulation intensities. They have found consistent response detection for frequencies within the gamma band (30-50 Hz). Furthermore, the application of the MSC to the AEP for determining the auditory threshold L, defined as the volunteer response to a click stimulation, resulted in the detection near the visual identification by a specialist of the BAEP waves (L and L+5) or of the MLAEP's (L+15).

Melges *et al.* (2005) employed the methodology suggested by Tierra-Criollo (2001), and used the temporal evolution of the MSC for a given frequency in order to evidence the transitions from tibial nerve somatosensory stimulation to resting condition, and conversely. The transition from a responsive to a no-responsive status is very important for surgical monitoring and this work have mimicked these statuses by presenting and omitting the stimulus. At the same year, Miranda de Sá *et al.* (2005) have investigated the coherence between two EEG derivations due to a visual rhythmic stimulation and the partial coherence (after removing the contribution of the stimulus) applied to the same signals. They concluded that these techniques present complementary role, since the coherence quantifies the degree of synchronism between the derivations, whereas the partial coherence informs about the relationship due to the non-phase locked activities, suggesting its use in ERD/ERS (event related desynchronization/synchronization) studies.

In 2006, Campos *et al.* (2006) applied the SFT to the EEG of epileptic patients during intermittent photic stimulation, and concluded that this technique should be employed as a complement to the traditional identification methods of photo-recruited responses, such as spectral analysis. By using EEG signals during the same type of stimulation, Miranda de Sá *et al.* (2006) studied the SFT applied to the signals of normal individuals. Moreover, they investigated the probability distribution of this test, as well as the confidence limits for its estimates, using simulated signals with different signal-to-noise ratio and *M*-values. Since the majority of the EP applications use periodic stimulation (intermittent photic stimulation, train of current pulses or clicks), Miranda de Sá (2006a) developed analytical expressions for calculating the trend, variance and probability density function for the coherence (MSC), in the particular case in which the input signal (stimulus) is periodic.

Frequency-Domain Objective Response

allowing a faster detection of the elicited responses.

advantageous using only the 6th signal for estimating the MSC.

both simulated and real EEG signals.

2007).

Detection Techniques Applied to Evoked Potentials: A Review 65

named MORD (Multivariate ORD), which use information of more than one EEG derivation. In this study, they introduced the Multiple Coherence (MC), a multivariate version of the MSC, and verified that the detection percentages can be improved by augmenting the number of EEG channels used. These authors also verified that, similar to the proved to the uni-variate version (MSC), the estimate of the MC, for a periodic and deterministic stimulation, is independent of the stimulation signal. Moreover, they showed, by means of simulation, that even the addition of a second EEG signal with lower signal to noise-ratio than the first could result in an increase in the probability detection. Since the MORD does not require increasing the number of epochs for obtaining higher detection rates, the MC has been suggested as a useful tool to be applied in the surgical monitoring,

In the following year, Miranda de Sá and Felix (2003) proposed a multivariate extension for the Component Synchrony Measure (CSM), the MCSM (Multiple CSM), for which it was verified that the detection rates for the intermittent photic stimulation responses increase by augmenting the number of signals used in its calculation. Such results were observed for

In 2004, Miranda de Sá *et al.* (2004) proposed a matrix-based algorithm for the calculation of the Multiple Coherence. The results obtained by simulation showed that for achieving a detection probability of 95%, for example, the signals added to the set of EEG channels used for the MC estimate can present SNR lower than the first one. This can be observed until the 6th signal, from which a signal with SNR higher than the first one should be employed in order to maintain the detection rate (95%). However, in this case it would be more

Later, Ferreira and Miranda de Sá (2005) compared the simple, multiple and partial coherences applied to the EEG during intermittent photic stimulation and consider these techniques promising in the analysis of the EEG during sensory stimulation. In the same year, Infantosi *et al.* (2005) verified, as theoretically predicted (Miranda de Sá and Felix, 2002, Miranda de Sá *et al.*, 2004), a better performance of the MC when compared to the MSC applied to the EEG during somatosensory stimulation of the tibial nerve. In this study, the MSC was applied to the bipolar derivations [Cz'-Fpz'] and [C3'-C4'] (where [Fpz'] is midway between [Fpz] and [Fz]; [Cz'], [C3'], and [C4'] are 2 cm posterior to [Cz], [C3] and [C4], respectively) - very often used for scalp SEP recording - and the MC was applied to both derivations. Using EEG signals from the same derivations during electric stimulation, Melges *et al.* (2006a) have found the MCSM to be useful for tibial nerve SEP detection. At the same year, Melges *et al.* (2006b) compared the performance of the MC and the MCSM, observing higher detection rates for the former. This result was observed for different values of *M* epochs (100, 200, 400, 800) used in the calculation of the estimates. A comparison between the two techniques applied to the EEG during intermittent photic stimulation (Felix *et al.*, 2007) has also resulted in higher detection percentages for the MC over the MCSM. By means of simulation, it was observed that the presence of noise correlated with the responses degrades the detection rates (Felix *et al.*,

In 2008, Miranda de Sá *et al.* (2008) derived the probability density function of the MC and a set of evoked responses embedded in additive noise for the zero-coherence case (null hypothesis of response absence). In this work, it was also demonstrated the influence of the

Tierra-Criollo (2001) and Infantosi *et al.* (2006), by applying the MSC to the responses evoked by electric stimulation, identified the low gamma band (30-60 Hz) as the one that better represents the short-latency components of the somatosensory evoked potential. Also in 2006, Klein *et al.* (2006) have introduced a variant of the MSC, the Wavelet Coherence (WC), which allowed obtaining the temporal information that is lost when frequencydomain techniques are used.

Infantosi and Miranda de Sá (2006) proposed a methodology based on the MSC in order to study EEG activities that are synchronized in time (time-locked) with the stimulation signal, but non-synchronized in phase (non phase-locked). Such technique was investigated using the visual evoked potential, elicited by intermittent photic stimulation. In another study, Miranda de Sá (2006b) developed an expression for the partial coherence between two signals, removing the contribution of the stimulation, and showing that this estimates is independent of the stimulus signal. In 2007, Miranda de Sá and Infantosi (2007) introduced a method based on the estimates of the MSC and the Partial Coherence in order to quantify the similarity between two EEG activities that are not synchronized in phase with the stimulation signal. At the same year, Cagy and Infantosi (2007) showed that the MSC is capable of indicating modification both in amplitude and latency of the MLAEP.

Later, Melges *et al.* (2008a) investigated the topographic distribution of the tibial nerve somatosensory evoked potential (SEP) using the MSC and verified that the best regions for SEP recording, in an ORD approach, includes the central and parietal leads at the midline and parasagittal line ipsilateral to the stimulated limb. Two years later, Farina *et al.* (2010) proposed a novel ORD technique based on the Rice distribution, obtaining the analytical critical values and using simulated signals to calculate the probability of detection for different values of signal-to-noise ratio.

More recently, Melges *et al.* (2011a) showed that, although the variation of the stimulation frequency to values higher than 5 Hz produces distortion in the tibial nerve SEP waveform, hampering the visual inspection, the detection rates obtained with the MSC (and CSM) are statistically equivalent for different stimulation frequencies. Hence, higher values can be used in order to fasten the detection. The maximum frequency, however, is limited to about 10 Hz, since higher values could lead to steady state tibial nerve SEP, instead of transient one.

## **5.2 Multivariate ORD (MORD) techniques**

The introduction of the ORD techniques represented an advance in the study of the evoked potentials, since these methods are based in statistical tests for inferring about the absence of stimulus-response (Dobie and Wilson, 1989). These techniques present the advantage (over traditional methods of identification of response), since they have a maximum false-positive rate (false alarm) a priori defined. However, for a fixed signal-to-noise ratio, it is only possible to improve the response detection rates, at the expense of increasing the recording length (number *M* of EEG epochs). This aspect may limit the application of ORD techniques, especially for surgical monitoring, case in which a fast detection of EP variations is needed, aiming at modifying the intra-operative strategy to avoid the occurrence of neurological damages.

In order to overcome this drawback and improve the detection rates, Miranda de Sá and Felix (2002) suggested the employment of multivariate extensions of the ORD techniques,

Tierra-Criollo (2001) and Infantosi *et al.* (2006), by applying the MSC to the responses evoked by electric stimulation, identified the low gamma band (30-60 Hz) as the one that better represents the short-latency components of the somatosensory evoked potential. Also in 2006, Klein *et al.* (2006) have introduced a variant of the MSC, the Wavelet Coherence (WC), which allowed obtaining the temporal information that is lost when frequency-

Infantosi and Miranda de Sá (2006) proposed a methodology based on the MSC in order to study EEG activities that are synchronized in time (time-locked) with the stimulation signal, but non-synchronized in phase (non phase-locked). Such technique was investigated using the visual evoked potential, elicited by intermittent photic stimulation. In another study, Miranda de Sá (2006b) developed an expression for the partial coherence between two signals, removing the contribution of the stimulation, and showing that this estimates is independent of the stimulus signal. In 2007, Miranda de Sá and Infantosi (2007) introduced a method based on the estimates of the MSC and the Partial Coherence in order to quantify the similarity between two EEG activities that are not synchronized in phase with the stimulation signal. At the same year, Cagy and Infantosi (2007) showed that the MSC is

Later, Melges *et al.* (2008a) investigated the topographic distribution of the tibial nerve somatosensory evoked potential (SEP) using the MSC and verified that the best regions for SEP recording, in an ORD approach, includes the central and parietal leads at the midline and parasagittal line ipsilateral to the stimulated limb. Two years later, Farina *et al.* (2010) proposed a novel ORD technique based on the Rice distribution, obtaining the analytical critical values and using simulated signals to calculate the probability of detection for

More recently, Melges *et al.* (2011a) showed that, although the variation of the stimulation frequency to values higher than 5 Hz produces distortion in the tibial nerve SEP waveform, hampering the visual inspection, the detection rates obtained with the MSC (and CSM) are statistically equivalent for different stimulation frequencies. Hence, higher values can be used in order to fasten the detection. The maximum frequency, however, is limited to about 10 Hz,

The introduction of the ORD techniques represented an advance in the study of the evoked potentials, since these methods are based in statistical tests for inferring about the absence of stimulus-response (Dobie and Wilson, 1989). These techniques present the advantage (over traditional methods of identification of response), since they have a maximum false-positive rate (false alarm) a priori defined. However, for a fixed signal-to-noise ratio, it is only possible to improve the response detection rates, at the expense of increasing the recording length (number *M* of EEG epochs). This aspect may limit the application of ORD techniques, especially for surgical monitoring, case in which a fast detection of EP variations is needed, aiming at modifying the intra-operative strategy to avoid the occurrence of neurological

In order to overcome this drawback and improve the detection rates, Miranda de Sá and Felix (2002) suggested the employment of multivariate extensions of the ORD techniques,

since higher values could lead to steady state tibial nerve SEP, instead of transient one.

capable of indicating modification both in amplitude and latency of the MLAEP.

domain techniques are used.

different values of signal-to-noise ratio.

**5.2 Multivariate ORD (MORD) techniques** 

damages.

named MORD (Multivariate ORD), which use information of more than one EEG derivation. In this study, they introduced the Multiple Coherence (MC), a multivariate version of the MSC, and verified that the detection percentages can be improved by augmenting the number of EEG channels used. These authors also verified that, similar to the proved to the uni-variate version (MSC), the estimate of the MC, for a periodic and deterministic stimulation, is independent of the stimulation signal. Moreover, they showed, by means of simulation, that even the addition of a second EEG signal with lower signal to noise-ratio than the first could result in an increase in the probability detection. Since the MORD does not require increasing the number of epochs for obtaining higher detection rates, the MC has been suggested as a useful tool to be applied in the surgical monitoring, allowing a faster detection of the elicited responses.

In the following year, Miranda de Sá and Felix (2003) proposed a multivariate extension for the Component Synchrony Measure (CSM), the MCSM (Multiple CSM), for which it was verified that the detection rates for the intermittent photic stimulation responses increase by augmenting the number of signals used in its calculation. Such results were observed for both simulated and real EEG signals.

In 2004, Miranda de Sá *et al.* (2004) proposed a matrix-based algorithm for the calculation of the Multiple Coherence. The results obtained by simulation showed that for achieving a detection probability of 95%, for example, the signals added to the set of EEG channels used for the MC estimate can present SNR lower than the first one. This can be observed until the 6th signal, from which a signal with SNR higher than the first one should be employed in order to maintain the detection rate (95%). However, in this case it would be more advantageous using only the 6th signal for estimating the MSC.

Later, Ferreira and Miranda de Sá (2005) compared the simple, multiple and partial coherences applied to the EEG during intermittent photic stimulation and consider these techniques promising in the analysis of the EEG during sensory stimulation. In the same year, Infantosi *et al.* (2005) verified, as theoretically predicted (Miranda de Sá and Felix, 2002, Miranda de Sá *et al.*, 2004), a better performance of the MC when compared to the MSC applied to the EEG during somatosensory stimulation of the tibial nerve. In this study, the MSC was applied to the bipolar derivations [Cz'-Fpz'] and [C3'-C4'] (where [Fpz'] is midway between [Fpz] and [Fz]; [Cz'], [C3'], and [C4'] are 2 cm posterior to [Cz], [C3] and [C4], respectively) - very often used for scalp SEP recording - and the MC was applied to both derivations. Using EEG signals from the same derivations during electric stimulation, Melges *et al.* (2006a) have found the MCSM to be useful for tibial nerve SEP detection. At the same year, Melges *et al.* (2006b) compared the performance of the MC and the MCSM, observing higher detection rates for the former. This result was observed for different values of *M* epochs (100, 200, 400, 800) used in the calculation of the estimates. A comparison between the two techniques applied to the EEG during intermittent photic stimulation (Felix *et al.*, 2007) has also resulted in higher detection percentages for the MC over the MCSM. By means of simulation, it was observed that the presence of noise correlated with the responses degrades the detection rates (Felix *et al.*, 2007).

In 2008, Miranda de Sá *et al.* (2008) derived the probability density function of the MC and a set of evoked responses embedded in additive noise for the zero-coherence case (null hypothesis of response absence). In this work, it was also demonstrated the influence of the

Frequency-Domain Objective Response

**ORD and MORD application:** <sup>2</sup>

respectively. The significance level

values exceeded the critical value.

**6.2 The tibial nerve somatosensory evoked potential waveform** 

even for an untrained observer at 40 ms and 50 ms.

frequencies 29.0 and 33.8 Hz (nominal values: 30 and 35 Hz).

evidences the importance of phase in the Objective Detection.

it can be visualized the similarity of values of <sup>2</sup>

ˆ ( ) *f* , 2ˆ *crit* , <sup>2</sup> ˆ*<sup>N</sup>* ( ) *f* , 2ˆ *N crit* , <sup>2</sup> 

Infantosi *et al* (2006).

analysis.

Detection Techniques Applied to Evoked Potentials: A Review 67

epoch to ensure that the late components of the artifact are also attenuated. Noisy epochs were next discarded by a semi-automatic artifact rejection algorithm, which rejects epochs with more than 5% of continuous samples or more than 10% of samples exceeding ± 3 SD (where SD is the standard deviation of 20 s of noise-free background EEG selected as reference signal). Details about the windowing and artifact rejection can be found in

were calculated for the EEG signals using expressions (9),(11),(23),(24),(18),(20), (25), (26),

and is cited for each illustration that follows. The detection was achieved when the estimate

As mentioned in the Section 2, the waveform quality of SEP is very dependent on the number of stimulus presented. Figure 2 illustrates this characteristic of the analysis performed by visual inspection. For the coherent average obtained with *M*=50 epochs for derivation Cz of volunteer #35, the tibial nerve SEP waveform is very noisy and it is difficult to identify its characteristic waves. For *M*=200 epochs, the P37 (at 40 ms) and N45 (at 52 ms) are visible, respectively with amplitudes equal to -2.86 μV and 0.86 μV. However, it can be seen that, when a higher number of epochs (*M* = 500 epochs) is used, the waveform is smoother and the identification of the short-latency SEP components can be easily pointed

Even for the SEP obtained with high signal-to-noise ratio, the components P37 and N45 presents high amplitude and latency (time duration from the stimulus to a peak or valley occurrence) variability, as it can be observed in Figure 3, which presents the SEP for six individuals calculated by averaging 500 epochs. This variability, associated with low signalto-noise SEP recording obtained in hospital units, reinforces the subjectivity of such

The application of MSC to the EEG of volunteer #40 (stimulated at 6 mA) is illustrated in Figure 4. The horizontal black dashed line represents the detection threshold; when the corresponding MSC tracing surpasses its critical value, the detection is assumed for that (those) specific frequency (frequencies). As it can be observed, the MSC presents low values for derivation [C3] and higher values for [C4], that is, the higher response effects occur ipsilateral to the stimulated limb (the well known paradoxical lateralization (Cruse et al., 1982)). For derivation [C4], the detection is evident, predominantly at the frequencies from 30 to 65 Hz. On the other hand, for [C3], MSC exceeds the critical value only for the

Both the CSM and MSC of derivation [C4] of volunteer #38 are showed in Figure 5, in which

obtained from the MSC when the amplitude information is discarded, this similarity

ˆ [ 4] *C* and <sup>2</sup>

ˆ [ 4] *C* . Since the CSM can be

**6.3 ORD techniques applied to the somatosensory evoked response detection** 

ˆ ( ) *f* , <sup>2</sup> ˆ *crit* , <sup>2</sup> 

= 5% was generally adopted, but the *M*-value varied

ˆ*<sup>N</sup>* ( ) *f* , <sup>2</sup> ˆ*N crit*

number of EEG epochs (*M*) in both bias and variance of the MC estimates. At the same year, Melges *et al.* (2008b) compared the performance of MSC applied to the bipolar derivations [Cz-Fz] and [C3-C4] with the MC applied to the pairs of unipolar derivations [Cz][Fz] and [C3][C4]. The results showed that if two leads are available, it is better to use the MC of unipolar recordings than the MSC applied to the difference of the leads (bipolar derivation).

Since the use of unipolar derivations seemed to be more adequate, the performance for the MC and MCSM were compared, by applying both techniques to the pairs of unipolar derivations [Cz][Fz] and [C3][C4] (Melges *et al.*, 2010). The comparison was performed for *M*=100 and 800 epochs. The MC outperformed the MCSM, regardless the pair of derivations or the number of EEG epochs used for the estimates calculation.

More recently, Melges *et al.* (2011b) compared the MSC applied to the unipolar derivations [Cz], [Fz], [C3] and [C4] - usually employed in a bipolar SEP recording, as above mentioned - and the MC applied to the pairs [Cz][Fz] and [C3][C4]. The results evidenced the detection improvement by using synergically the information of two derivations, showing to be more advantageous using the MC than the MSC.

## **6. Examples and applications of ORD and MORD techniques**

This section presents examples of using ORD and MORD techniques to the EEG during somatosensory stimulation. Following, the experimental protocol of EEG acquisition, the pre-processing and processing steps, and some results are shown.

## **6.1 EEG acquisition, pre-processing and processing**

**EEG Acquisition:** EEG signals during somatosensory stimulation were collected from forty adult volunteers aging from 21 to 41 years old (mean ± standard deviation: 28.6 ± 4.6 years), without history of neurological pathology and with normal SEP. The signals were collected using the EEG BNT-36 (EMSA, Brazil, www.emsamed.com.br) according to the 10-20 International System and all leads referenced to the earlobe average. The volunteers were laid down in the supine position with eyes closed. The stimuli were applied by means of current pulses (200 µs width) to the right posterior tibial nerve using the Atlantis Four (EMSA, Brazil, www.emsamed.com.br). About 1000 to 1400 stimuli were applied at the motor threshold (the lowest intensity that produces toe oscillations) and at the rates of 1.99, 4.83, 6.68, 8.51 Hz (nominal values: 2, 5, 7, 9 Hz). The motor threshold was determined by an accelerometer tied in the toe that allowed the recording of the oscillations. The stimuli in the frequencies of 7 and 9 Hz were applied to 32 of the 40 volunteers. The ground electrode was attached to the poplitea fossa. Surface silver and gold electrodes were used, respectively, for recording and stimulation. An Institutional Review Board approved this research and all volunteers signed informed consent forms.

**Pre-processing:** The signals were band-filtered (0.5 – 100 Hz) and digitized (16-bits resolution) with BNT-36 at the sampling rate of 600 Hz. Then, the EEG was segmented into epochs of 501, 207, 149 and 117 ms, stimuli-synchronized, leading to spectral resolution of 2.0, 4.83, 6.71 and 8.55 Hz, respectively. In order to minimize the interference of the stimulus artifact in the ORD and MORD techniques we have set to zero the first 5 ms after each stimulus. Furthermore, the final 5 ms were zero padded to ensure window symmetry. A Tukey window with 7 ms rising (falling) time has been next applied to each

number of EEG epochs (*M*) in both bias and variance of the MC estimates. At the same year, Melges *et al.* (2008b) compared the performance of MSC applied to the bipolar derivations [Cz-Fz] and [C3-C4] with the MC applied to the pairs of unipolar derivations [Cz][Fz] and [C3][C4]. The results showed that if two leads are available, it is better to use the MC of unipolar recordings than the MSC applied to the difference of the leads (bipolar derivation). Since the use of unipolar derivations seemed to be more adequate, the performance for the MC and MCSM were compared, by applying both techniques to the pairs of unipolar derivations [Cz][Fz] and [C3][C4] (Melges *et al.*, 2010). The comparison was performed for *M*=100 and 800 epochs. The MC outperformed the MCSM, regardless the pair of derivations

More recently, Melges *et al.* (2011b) compared the MSC applied to the unipolar derivations [Cz], [Fz], [C3] and [C4] - usually employed in a bipolar SEP recording, as above mentioned - and the MC applied to the pairs [Cz][Fz] and [C3][C4]. The results evidenced the detection improvement by using synergically the information of two derivations, showing to be more

This section presents examples of using ORD and MORD techniques to the EEG during somatosensory stimulation. Following, the experimental protocol of EEG acquisition, the

**EEG Acquisition:** EEG signals during somatosensory stimulation were collected from forty adult volunteers aging from 21 to 41 years old (mean ± standard deviation: 28.6 ± 4.6 years), without history of neurological pathology and with normal SEP. The signals were collected using the EEG BNT-36 (EMSA, Brazil, www.emsamed.com.br) according to the 10-20 International System and all leads referenced to the earlobe average. The volunteers were laid down in the supine position with eyes closed. The stimuli were applied by means of current pulses (200 µs width) to the right posterior tibial nerve using the Atlantis Four (EMSA, Brazil, www.emsamed.com.br). About 1000 to 1400 stimuli were applied at the motor threshold (the lowest intensity that produces toe oscillations) and at the rates of 1.99, 4.83, 6.68, 8.51 Hz (nominal values: 2, 5, 7, 9 Hz). The motor threshold was determined by an accelerometer tied in the toe that allowed the recording of the oscillations. The stimuli in the frequencies of 7 and 9 Hz were applied to 32 of the 40 volunteers. The ground electrode was attached to the poplitea fossa. Surface silver and gold electrodes were used, respectively, for recording and stimulation. An Institutional Review Board approved this research and all

**Pre-processing:** The signals were band-filtered (0.5 – 100 Hz) and digitized (16-bits resolution) with BNT-36 at the sampling rate of 600 Hz. Then, the EEG was segmented into epochs of 501, 207, 149 and 117 ms, stimuli-synchronized, leading to spectral resolution of 2.0, 4.83, 6.71 and 8.55 Hz, respectively. In order to minimize the interference of the stimulus artifact in the ORD and MORD techniques we have set to zero the first 5 ms after each stimulus. Furthermore, the final 5 ms were zero padded to ensure window symmetry. A Tukey window with 7 ms rising (falling) time has been next applied to each

or the number of EEG epochs used for the estimates calculation.

**6. Examples and applications of ORD and MORD techniques** 

pre-processing and processing steps, and some results are shown.

**6.1 EEG acquisition, pre-processing and processing** 

advantageous using the MC than the MSC.

volunteers signed informed consent forms.

epoch to ensure that the late components of the artifact are also attenuated. Noisy epochs were next discarded by a semi-automatic artifact rejection algorithm, which rejects epochs with more than 5% of continuous samples or more than 10% of samples exceeding ± 3 SD (where SD is the standard deviation of 20 s of noise-free background EEG selected as reference signal). Details about the windowing and artifact rejection can be found in Infantosi *et al* (2006).

**ORD and MORD application:** <sup>2</sup> ˆ ( ) *f* , 2ˆ *crit* , <sup>2</sup> ˆ *<sup>N</sup>* ( ) *f* , 2ˆ *N crit* , <sup>2</sup> ˆ ( ) *f* , <sup>2</sup> ˆ *crit* , <sup>2</sup> ˆ*<sup>N</sup>* ( ) *f* , <sup>2</sup> ˆ *N crit* were calculated for the EEG signals using expressions (9),(11),(23),(24),(18),(20), (25), (26), respectively. The significance level = 5% was generally adopted, but the *M*-value varied and is cited for each illustration that follows. The detection was achieved when the estimate values exceeded the critical value.

## **6.2 The tibial nerve somatosensory evoked potential waveform**

As mentioned in the Section 2, the waveform quality of SEP is very dependent on the number of stimulus presented. Figure 2 illustrates this characteristic of the analysis performed by visual inspection. For the coherent average obtained with *M*=50 epochs for derivation Cz of volunteer #35, the tibial nerve SEP waveform is very noisy and it is difficult to identify its characteristic waves. For *M*=200 epochs, the P37 (at 40 ms) and N45 (at 52 ms) are visible, respectively with amplitudes equal to -2.86 μV and 0.86 μV. However, it can be seen that, when a higher number of epochs (*M* = 500 epochs) is used, the waveform is smoother and the identification of the short-latency SEP components can be easily pointed even for an untrained observer at 40 ms and 50 ms.

Even for the SEP obtained with high signal-to-noise ratio, the components P37 and N45 presents high amplitude and latency (time duration from the stimulus to a peak or valley occurrence) variability, as it can be observed in Figure 3, which presents the SEP for six individuals calculated by averaging 500 epochs. This variability, associated with low signalto-noise SEP recording obtained in hospital units, reinforces the subjectivity of such analysis.

## **6.3 ORD techniques applied to the somatosensory evoked response detection**

The application of MSC to the EEG of volunteer #40 (stimulated at 6 mA) is illustrated in Figure 4. The horizontal black dashed line represents the detection threshold; when the corresponding MSC tracing surpasses its critical value, the detection is assumed for that (those) specific frequency (frequencies). As it can be observed, the MSC presents low values for derivation [C3] and higher values for [C4], that is, the higher response effects occur ipsilateral to the stimulated limb (the well known paradoxical lateralization (Cruse et al., 1982)). For derivation [C4], the detection is evident, predominantly at the frequencies from 30 to 65 Hz. On the other hand, for [C3], MSC exceeds the critical value only for the frequencies 29.0 and 33.8 Hz (nominal values: 30 and 35 Hz).

Both the CSM and MSC of derivation [C4] of volunteer #38 are showed in Figure 5, in which it can be visualized the similarity of values of <sup>2</sup> ˆ [ 4] *C* and <sup>2</sup> ˆ [ 4] *C* . Since the CSM can be obtained from the MSC when the amplitude information is discarded, this similarity evidences the importance of phase in the Objective Detection.

Frequency-Domain Objective Response

the stimulation frequency.

**0.00**

represent the critical value: 2ˆ 0.006

ˆ [ 3] *C* and <sup>2</sup>

**0.02**

**0.04**

**0.06**

**MSC**

Fig. 4. <sup>2</sup> 

dimensionless.

**0.08**

**0.10**

**0.12**

positive alarm can be as lower as desired, setting up

**6.4 Topographic distribution of the evoked responses** 

Detection Techniques Applied to Evoked Potentials: A Review 69

As it should be clear, establishing a statistical threshold for identifying the response detection reduces the subjectivity of the analysis. It is worth noting that the maximum false

The localization on the scalp of the response to a specific kind of stimulation is a critical issue for the detection performance, since it determines the best regions for the evoked potential recording. In Melges et al. (2008), we have described that the leads with best signal-to-noise ratio for electrical stimulation of the right posterior tibial nerve are [Pz], [P4], [Cz], [C4] that is, leads at the parietal and central regions midsagital and ipsilateral to the stimulated limb. The results were obtained with the MSC applied to the SEP using 5 Hz as frequency of stimulation (fstim). In fact, although the SEP is known to change its waveform characteristics with the stimulation frequency, the best detection percentages were obtained in the same leads for all investigated frequencies (2, 5, 7 and 9 Hz). Figure 6 shows the performance of the MSC for all the casuistry stimulated at the motor threshold and with fstim = 9 Hz. As it can be seen, the same leads [Pz], [P4], [Cz], [C4] present the best detection rates. The ordinate presents the percentage of volunteers for whom it was possible to detect the evoked response for each frequency from the 1st to 12nd harmonics of

**10 20 30 40 50 60 70 80 90 100**

ˆ [ 4] *C* of volunteer #40, stimulated at 6 mA and 5 Hz. Horizontal line

=0.05). Vertical axis (MSC) is

**Frequency (Hz)**

*crit* (*M* = 500 epochs and

for the corresponding value.

 crit [C3] [C4]

^

^ ^

Fig. 2. Coherent Average (M = 50, 200 and 500 epochs) of derivation [Cz] of volunteer #35, stimulated at 24 mA and 5 Hz.

Fig. 3. Coherent Average (M = 500 epochs) of derivation [Cz] of volunteers #12, #13, #14, #22, #24, #26, respectively stimulated at 10, 10.5, 18, 12.5, 16 and 15 mA (these currents correspond to the individual motor threshold) and 5 Hz.

 M=50 M=200 M=500

**10 20 30 40 50 60 70 80 90 100**

**10 20 30 40 50 60 70 80 90 100**

**Time (ms)**

Fig. 3. Coherent Average (M = 500 epochs) of derivation [Cz] of volunteers #12, #13, #14, #22, #24, #26, respectively stimulated at 10, 10.5, 18, 12.5, 16 and 15 mA (these currents

**Time (ms)**

Fig. 2. Coherent Average (M = 50, 200 and 500 epochs) of derivation [Cz] of volunteer #35,

 #12 #13 #14 #22 #24 #26

**-4**

stimulated at 24 mA and 5 Hz.

**-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8**

correspond to the individual motor threshold) and 5 Hz.

**SEP (**

**V)**

**-2**

**0**

**SEP (**

**V)**

**2**

**4**

As it should be clear, establishing a statistical threshold for identifying the response detection reduces the subjectivity of the analysis. It is worth noting that the maximum false positive alarm can be as lower as desired, setting up for the corresponding value.

#### **6.4 Topographic distribution of the evoked responses**

The localization on the scalp of the response to a specific kind of stimulation is a critical issue for the detection performance, since it determines the best regions for the evoked potential recording. In Melges et al. (2008), we have described that the leads with best signal-to-noise ratio for electrical stimulation of the right posterior tibial nerve are [Pz], [P4], [Cz], [C4] that is, leads at the parietal and central regions midsagital and ipsilateral to the stimulated limb. The results were obtained with the MSC applied to the SEP using 5 Hz as frequency of stimulation (fstim). In fact, although the SEP is known to change its waveform characteristics with the stimulation frequency, the best detection percentages were obtained in the same leads for all investigated frequencies (2, 5, 7 and 9 Hz). Figure 6 shows the performance of the MSC for all the casuistry stimulated at the motor threshold and with fstim = 9 Hz. As it can be seen, the same leads [Pz], [P4], [Cz], [C4] present the best detection rates. The ordinate presents the percentage of volunteers for whom it was possible to detect the evoked response for each frequency from the 1st to 12nd harmonics of the stimulation frequency.

Fig. 4. <sup>2</sup> ˆ [ 3] *C* and <sup>2</sup> ˆ [ 4] *C* of volunteer #40, stimulated at 6 mA and 5 Hz. Horizontal line represent the critical value: 2ˆ 0.006 *crit* (*M* = 500 epochs and =0.05). Vertical axis (MSC) is dimensionless.

Frequency-Domain Objective Response

Detection Techniques Applied to Evoked Potentials: A Review 71

(Melges *et al.*, 2011a). In this case, the use of the higher investigated frequency 9 Hz, represent a gain of 9:5 in the time of detection, if we consider the very often used stimulation frequency (5 Hz). Figure 7 presents the detection rates for derivation [Cz] and *M* = 200 epochs. In this figure it is possible to visualize the similarity in the profile of the detection percentage tracings, showed to be statistically equivalent for the maximum

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

**F8**

**T4**

**T6**

**Fp2**

**F4**

**C4**

**P4**

**O2**

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

After identifying the more responsive frequencies and have optimized the stimulation frequency aiming the fast detection, it is possible to choose one or some frequencies for monitoring its temporal evolution. In Figure 8A, a modulus of a Virtual Instrument

Fig. 6. Percentage of volunteers whose response to the stimulation could be detected using the MSC for multiples from 1 to 12 (9 to 100 Hz) of the stimulation frequency (9 Hz). Horizontal lines indicate 70, 80 and 90% of detection. For derivations Fp2 (31), F8 (31) and C4 (31), it was not possible to obtain 500 artifact-free epochs for the 32 volunteers, hence, the percentages were calculated with the number of volunteers

**Fz**

**Cz**

**Pz**

**Oz**

response frequency band, for both M = 100 and 500 epochs (Melges *et al.*, 2011a).

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

**Fp1**

**F3**

**C3**

**P3**

**O1**

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

2 3 4 5 6 7 8 9 101112

in parenthesis.

**6.7 ORD temporal evolution** 

**F7**

**T3**

**T5**

Fig. 5. <sup>2</sup> ˆ [ 4] *C* and <sup>2</sup> ˆ [ 4] *C* of volunteer #38, stimulated at 14 mA and 5 Hz. Horizontal lines represent the critical values: <sup>2</sup> ˆ 0.005 *crit* and 2ˆ 0.006 *crit* (*M* = 500 epochs and =0.05). Vertical axis (ORD) is dimensionless.

#### **6.5 Maximum response frequency band**

Apart from choosing suitable sites for EP recording, selecting the frequencies that are more responsive to a specific kind of stimulation is also important, since it leads to a more reliable objective neurophysiologic evaluation during surgical procedures.

From Figure 6, it is also possible to identify, in the derivations with best detection percentages, that the frequency range that includes from 2nd to the 6th harmonics of the stimulation frequency (9Hz) - frequencies from 18 to 54 Hz - is the more responsive. Hence, the presence of stimuli-response leads to positive detection in these frequencies, which were classified as the maximum response frequency band (Tierra-Criollo, 2001, Infantosi *et al.*, 2006); that is, frequencies within this range should be selected in order to augment the probability and rapidness of detection.

#### **6.6 Stimulation frequency**

The increase of the stimulation frequency is the simplest way of obtaining faster the response to a set of *M* stimuli, and enhances the time of detection. However, this frequency increase is known to cause changes in the SEP waveform (Chiappa, 1997, p. 307 and 323), whose characteristics are the basis for neurophysiologic monitoring. Fortunately, the detection rates obtained with an ORD approach is not statistically modified for different stimulation frequencies, as it was shown in a recent study of ours

**10 20 30 40 50 60 70 80 90 100**

ˆ [ 4] *C* of volunteer #38, stimulated at 14 mA and 5 Hz. Horizontal lines

*crit* (*M* = 500 epochs and

=0.05).

**Frequency (Hz)**

*crit* and 2ˆ 0.006 

Apart from choosing suitable sites for EP recording, selecting the frequencies that are more responsive to a specific kind of stimulation is also important, since it leads to a more reliable

From Figure 6, it is also possible to identify, in the derivations with best detection percentages, that the frequency range that includes from 2nd to the 6th harmonics of the stimulation frequency (9Hz) - frequencies from 18 to 54 Hz - is the more responsive. Hence, the presence of stimuli-response leads to positive detection in these frequencies, which were classified as the maximum response frequency band (Tierra-Criollo, 2001, Infantosi *et al.*, 2006); that is, frequencies within this range should be selected in order to augment the

The increase of the stimulation frequency is the simplest way of obtaining faster the response to a set of *M* stimuli, and enhances the time of detection. However, this frequency increase is known to cause changes in the SEP waveform (Chiappa, 1997, p. 307 and 323), whose characteristics are the basis for neurophysiologic monitoring. Fortunately, the detection rates obtained with an ORD approach is not statistically modified for different stimulation frequencies, as it was shown in a recent study of ours

 2 crit 2 [C4] 2 crit [C4]

^

^ ^ ^

**0.00**

represent the critical values: <sup>2</sup> ˆ 0.005

**6.5 Maximum response frequency band** 

probability and rapidness of detection.

**6.6 Stimulation frequency** 

Vertical axis (ORD) is dimensionless.

objective neurophysiologic evaluation during surgical procedures.

ˆ [ 4] *C* and <sup>2</sup>

**0.02**

**0.04**

**0.06**

**ORD**

Fig. 5. <sup>2</sup> 

**0.08**

**0.10**

**0.12**

**0.14**

(Melges *et al.*, 2011a). In this case, the use of the higher investigated frequency 9 Hz, represent a gain of 9:5 in the time of detection, if we consider the very often used stimulation frequency (5 Hz). Figure 7 presents the detection rates for derivation [Cz] and *M* = 200 epochs. In this figure it is possible to visualize the similarity in the profile of the detection percentage tracings, showed to be statistically equivalent for the maximum response frequency band, for both M = 100 and 500 epochs (Melges *et al.*, 2011a).

Fig. 6. Percentage of volunteers whose response to the stimulation could be detected using the MSC for multiples from 1 to 12 (9 to 100 Hz) of the stimulation frequency (9 Hz). Horizontal lines indicate 70, 80 and 90% of detection. For derivations Fp2 (31), F8 (31) and C4 (31), it was not possible to obtain 500 artifact-free epochs for the 32 volunteers, hence, the percentages were calculated with the number of volunteers in parenthesis.

1 2 3 4 5 6 7 8 9 101112

1 2 3 4 5 6 7 8 9 101112

1 2 3 4 5 6 7 8 9 101112

#### **6.7 ORD temporal evolution**

After identifying the more responsive frequencies and have optimized the stimulation frequency aiming the fast detection, it is possible to choose one or some frequencies for monitoring its temporal evolution. In Figure 8A, a modulus of a Virtual Instrument

Frequency-Domain Objective Response

operative application.

**A** 

**B** 

Fig. 8. <sup>2</sup> 

ˆ ( ) *f* of the frequency 36.8 Hz (

B) *M*=400 epochs ( 2ˆ 0.0075 

Portuguese Regional Settings.

**6.8 MORD techniques applied to SEP** 

stimulated at MT and IT for A) *M*=50 epochs (Horizontal orange line: 2ˆ 0.0593

condition at: A) t=830, 2296, 3164, 4591, 5459, 6889, 7781 and 9204 elapsed epochs. B) t=480, 1946, 2814, 4241, 5109, 6539, 7431 and 8854 elapsed epochs. Horizontal scale in elapsed epochs. Vertical axis (ORD-MSC) is dimensionless. The decimal separator in the coordinates scale is "comma", since the virtual instrument was developed using Brazilian

The use of more than one derivation, as suggested by Miranda de Sá and Felix (2002), can improve the detection rates without the need of augmenting the exam duration (the number of EEG epochs used for ORD estimation). Figure 9 shows the MSC (*M* = 100 epochs) for [C3] and [C4], and the MC (*M* = 100 epochs) using both leads of volunteer #17. Since the somatosensory region on the contralateral hemisphere presents SEP with very low

=0.05) for derivation [Fpz'-Cz'] of volunteer

*crit* ). Transitions from/to stimulated to/from no-stimulated

*crit* );

i.e., the first line of it, by the new epoch and return to step 1.

Detection Techniques Applied to Evoked Potentials: A Review 73

expression 9; 3) When a new EEG epoch is acquired, substitute the older EEG epoch of AEEG,

From Figure 8A, one can note that even for a low *M*-value (*M*=50 epochs), the MSC was capable to follow the transition from rest to stimulated condition (Figure legend indicates the instant when the stimulus started and stopped), and conversely. Since the increase of *M* is known to improve the detection rate, the time evolution of MSC was also evaluated using *M*=400 epochs (Figure 8B). As it can be noted, the MSC estimate with *M*=50 epochs (MSCM50) presents higher variability than the obtained with *M*=400 epochs (MSCM400). On the other hand, MSC400 presents a higher inertia to change from one status to the other. Hence, the *M*-value should be parsimoniously chosen for the clinical or intra-

(software) for Evoked Potential Objective Detection developed in Melges (2005) is shown, containing the temporal evolution of the MSC for the frequency of 36.8 Hz (Horizontal line represents the detection threshold). This signal was collected from volunteer #6, using parameters very commonly applied during surgical procedures. That is, the EEG was collected from derivation [Fpz'-Cz'] and with stimulation frequency of 5 Hz. In order to evaluate the capability of the MSC to reflect the transition of a responsive status to a noresponsive one, these conditions were mimicked by periods with and without electrical stimulation, respectively. Moreover, four periods with stimulation (S) were alternated with no-stimulation (NS) periods (starting without stimulation). The first S-period corresponds to the stimulation with the motor threshold intensity level (MT). In the following three Speriods, an intermediary intensity (IT) level was used; this intensity value was obtained by the arithmetic mean between MT and the sensitivity threshold, which corresponds to the lowest current level that is felt by the individual.

Fig. 7. Percentage of volunteers for whom the stimulation response was detected using the MSC (*M* = 200 epochs) for the frequencies from 2 to 100 Hz at the derivation [Cz] for the stimulation frequencies 2, 5, 7, 9 Hz.

The MSC estimates can be dynamically estimate as follows: 1) Store *M* EEG epochs in a matrix (AEEG); 2) Calculate the MSC estimate using the *M* EEG epochs of AEEG and

(software) for Evoked Potential Objective Detection developed in Melges (2005) is shown, containing the temporal evolution of the MSC for the frequency of 36.8 Hz (Horizontal line represents the detection threshold). This signal was collected from volunteer #6, using parameters very commonly applied during surgical procedures. That is, the EEG was collected from derivation [Fpz'-Cz'] and with stimulation frequency of 5 Hz. In order to evaluate the capability of the MSC to reflect the transition of a responsive status to a noresponsive one, these conditions were mimicked by periods with and without electrical stimulation, respectively. Moreover, four periods with stimulation (S) were alternated with no-stimulation (NS) periods (starting without stimulation). The first S-period corresponds to the stimulation with the motor threshold intensity level (MT). In the following three Speriods, an intermediary intensity (IT) level was used; this intensity value was obtained by the arithmetic mean between MT and the sensitivity threshold, which corresponds to the

**0 10 20 30 40 50 60 70 80 90 100**

 7Hz 5Hz 2Hz

9Hz

**Frequency (Hz)**

Fig. 7. Percentage of volunteers for whom the stimulation response was detected using the MSC (*M* = 200 epochs) for the frequencies from 2 to 100 Hz at the derivation [Cz] for the

The MSC estimates can be dynamically estimate as follows: 1) Store *M* EEG epochs in a matrix (AEEG); 2) Calculate the MSC estimate using the *M* EEG epochs of AEEG and

lowest current level that is felt by the individual.

**0**

stimulation frequencies 2, 5, 7, 9 Hz.

**10**

**20**

**30**

**40**

**50**

**% detection**

**60**

**70**

**80**

**90**

**100**

expression 9; 3) When a new EEG epoch is acquired, substitute the older EEG epoch of AEEG, i.e., the first line of it, by the new epoch and return to step 1.

From Figure 8A, one can note that even for a low *M*-value (*M*=50 epochs), the MSC was capable to follow the transition from rest to stimulated condition (Figure legend indicates the instant when the stimulus started and stopped), and conversely. Since the increase of *M* is known to improve the detection rate, the time evolution of MSC was also evaluated using *M*=400 epochs (Figure 8B). As it can be noted, the MSC estimate with *M*=50 epochs (MSCM50) presents higher variability than the obtained with *M*=400 epochs (MSCM400). On the other hand, MSC400 presents a higher inertia to change from one status to the other. Hence, the *M*-value should be parsimoniously chosen for the clinical or intraoperative application.

Fig. 8. <sup>2</sup> ˆ ( ) *f* of the frequency 36.8 Hz (=0.05) for derivation [Fpz'-Cz'] of volunteer stimulated at MT and IT for A) *M*=50 epochs (Horizontal orange line: 2ˆ 0.0593 *crit* ); B) *M*=400 epochs ( 2ˆ 0.0075 *crit* ). Transitions from/to stimulated to/from no-stimulated condition at: A) t=830, 2296, 3164, 4591, 5459, 6889, 7781 and 9204 elapsed epochs. B) t=480, 1946, 2814, 4241, 5109, 6539, 7431 and 8854 elapsed epochs. Horizontal scale in elapsed epochs. Vertical axis (ORD-MSC) is dimensionless. The decimal separator in the coordinates scale is "comma", since the virtual instrument was developed using Brazilian Portuguese Regional Settings.

### **6.8 MORD techniques applied to SEP**

The use of more than one derivation, as suggested by Miranda de Sá and Felix (2002), can improve the detection rates without the need of augmenting the exam duration (the number of EEG epochs used for ORD estimation). Figure 9 shows the MSC (*M* = 100 epochs) for [C3] and [C4], and the MC (*M* = 100 epochs) using both leads of volunteer #17. Since the somatosensory region on the contralateral hemisphere presents SEP with very low

Frequency-Domain Objective Response

Fig. 10. Detection rates (*M* = 100 epochs) for A) <sup>2</sup>

**% detection**

ˆ [ 4] *C* and <sup>2</sup>

2 

[Cz][C4] were calculated over 39.

**% detection**

Detection Techniques Applied to Evoked Potentials: A Review 75

**10 20 30 40 50 60 70 80 90 100**

**10 20 30 40 50 60 70 80 90 100**

ˆ [ ] *Cz* , <sup>2</sup> 

ˆ [ 3][ 4] *C C* . For derivation [Cz], it was only possible to obtain 100 artifact-free

ˆ [ 4] *C* and <sup>2</sup>

2 

ˆ [ ][ 4] *Cz C* ; B) <sup>2</sup>

**Frequency (Hz)**

B

<sup>ˆ</sup> [ 3] *<sup>C</sup>* , 2

epochs for 39 from the 40 volunteers, hence, the percentages of detection for [Cz] and

 [Cz] [C4] [Cz][C4]

> [C3] [C4] [C3][C4]

**Frequency (Hz)**

A

amplitude, as expected, the MSC values are low and under the detection threshold. On the other hand, the lead ipsilateral to the stimulated limb, [C4], shows detection for the nominal frequencies 35, 40, 50-60 Hz. It is worth noting that the employment of the <sup>2</sup> 2 ˆ [ 3][ 4] *C C* resulted in estimate values higher than <sup>2</sup> ˆ [ 3] *C* and <sup>2</sup> ˆ [ 4] *C* , and the MC tracing surpasses its corresponding critical value for 35-60 Hz.

Fig. 9. <sup>2</sup> ˆ [ 3] *C* , <sup>2</sup> ˆ [ 4] *C* and <sup>2</sup> 2 ˆ [ 3][ 4] *C C* of volunteer #17, stimulated at 10 mA and 5 Hz. Horizontal lines represent the critical values: 2ˆ 0.0300 *crit* and <sup>2</sup> 2ˆ 0.0470 *crit* for =0.05, *M* = 100 epochs and *N*=2. Vertical axis (MSC and MC) is dimensionless.

The detection rates for the MSC applied to [Cz] and [C4] and for MC applied to [Cz][C4] is showed in Figure 10A. It is easy to note that the percentages for <sup>2</sup> ˆ [ ] *Cz* are higher than the observed for <sup>2</sup> ˆ [ 4] *C* , and both are lower than <sup>2</sup> 2 ˆ [ ][ 4] *Cz C* . Hence, "adding" the information from [Cz] to the [C4] resulted in an increase in the overall response detection performance.

In fact, even when a derivation with lower signal-to-noise ratio ([C3]) is added to the estimation of the Multiple Coherence, the detection rates can be improved (Figure 10B), as theoretically predicted by Miranda de Sá and Félix (2002).

amplitude, as expected, the MSC values are low and under the detection threshold. On the other hand, the lead ipsilateral to the stimulated limb, [C4], shows detection for the nominal

ˆ [ 3] *C* and <sup>2</sup>

**10 20 30 40 50 60 70 80 90 100**

ˆ [ 3][ 4] *C C* of volunteer #17, stimulated at 10 mA and 5 Hz.

2 

*crit* and <sup>2</sup>

**Frequency (Hz)**

The detection rates for the MSC applied to [Cz] and [C4] and for MC applied to [Cz][C4]

information from [Cz] to the [C4] resulted in an increase in the overall response detection

In fact, even when a derivation with lower signal-to-noise ratio ([C3]) is added to the estimation of the Multiple Coherence, the detection rates can be improved (Figure 10B), as

2 

ˆ [ 4] *C* , and the MC tracing surpasses

 2 crit 2 [C3]

 [C4] 2 2 crit 

C3C4

2ˆ 0.0470

*crit* for

ˆ [ ][ 4] *Cz C* . Hence, "adding" the

=0.05,

ˆ [ ] *Cz* are higher than

ˆ [ 3][ 4] *C C*

frequencies 35, 40, 50-60 Hz. It is worth noting that the employment of the <sup>2</sup>

resulted in estimate values higher than <sup>2</sup>

**0.00**

ˆ [ 3] *C* , <sup>2</sup> 

the observed for <sup>2</sup>

performance.

ˆ [ 4] *C* and <sup>2</sup>

2 

*M* = 100 epochs and *N*=2. Vertical axis (MSC and MC) is dimensionless.

is showed in Figure 10A. It is easy to note that the percentages for <sup>2</sup>

ˆ [ 4] *C* , and both are lower than <sup>2</sup>

Horizontal lines represent the critical values: 2ˆ 0.0300

theoretically predicted by Miranda de Sá and Félix (2002).

**0.02**

**0.04**

**0.06**

**0.08**

**MSC and MC**

Fig. 9. <sup>2</sup> 

**0.10**

**0.12**

**0.14**

**0.16**

**0.18**

its corresponding critical value for 35-60 Hz.

Fig. 10. Detection rates (*M* = 100 epochs) for A) <sup>2</sup> ˆ [ ] *Cz* , <sup>2</sup> ˆ [ 4] *C* and <sup>2</sup> 2 ˆ [ ][ 4] *Cz C* ; B) <sup>2</sup> <sup>ˆ</sup> [ 3] *<sup>C</sup>* , 2 ˆ [ 4] *C* and <sup>2</sup> 2 ˆ [ 3][ 4] *C C* . For derivation [Cz], it was only possible to obtain 100 artifact-free epochs for 39 from the 40 volunteers, hence, the percentages of detection for [Cz] and [Cz][C4] were calculated over 39.

Frequency-Domain Objective Response

**9. Abbreviations** 

**11. References** 

**10. Acknowledgements** 

providing infrastructure support.

York, Wiley-Interscience.

Mar/Apr, pp. 202-207.

17, No.6, pp. 362-366.

Detection Techniques Applied to Evoked Potentials: A Review 77

derivations to be employed for both MC and MCSM estimation for each kind of stimulation, since the presence of a massive number of leads is undesirable for clinical and surgical monitoring purposes. Moreover, the exponential forgetting, suggested by Tierra-Criollo *et al.* (1998), should be applied for multivariate ORD in order to increase the rapidness of response detection. Finally, both ORD and MORD techniques should be incorporated in the EP analysis software to have their efficacy evaluated for diagnosis and neuro-monitoring.

EEG – Electroencephalogram; EP – Evoked Potential; AEP – auditory EP; SEP – somatosensory EP; VEP – Visual EP; ORD – Objective Response Detection; MORD – Multivariate ORD.

To the Brazilian research and education agencies, the Rio de Janeiro State Research Council (FAPERJ), the National Council for Scientific and Technological Development (CNPq - Ministry of Science and Technology) and CAPES (Ministry of Education) for the financial support. We also acknowledge the Military Police Central Hospital of Rio de Janeiro for

Angel, A, Linkens, DA, Ting, CH. 1999. Estimation of latency changes and relative

Beagley, HA, Sayers, BMcA, Ross, AJ. 1979. Fully objective ERA by phase spectral analysis,

Bendat, JS, Piersol, AG. 2000. *Random Data Analysis and Measurement Procedures* (3 ed), New

Bose, B, Sestokas, AK, Schwartz, DM. 2004. Neuropsychological monitoring of spinal cord

Cagy, M, Infantosi, AFC, Gemal, AE. 2000. Monitoring depth of anaesthesia by frequencydomain statistical techniques, *Braz J Biomed Eng*, Vol. 16, No. 2, pp. 95-107. Cagy, M, Infantosi, AFC. 2002. Unconsciousness indication using time-domain parameters

Cagy, M., 2003, Monitorização do plano anestésico usando o potencial evocado auditivo de

Cagy, M, Infantosi, AFC. 2007. Objective response detection technique in frequency-domain for reflecting changes in MLAEP, Medl Eng Phy, Vol 29, No 8, Oct, pp. 910-917. Campos, DV, Infantosi, AFC, Lazarev, VV. 2006. Aplicação do Teste F spectral na detecção

*Comput Biomed Res*, Vol. 32, No. 3, Jun, pp. 209-251.

COPPE/UFRJ, Rio de Janeiro, Rio de Janeiro, Brazil.

(CDROM), pp. 318-321, São Pedro, São Paulo, Brazil, Oct 2006.

*Acta otolaryngol*, Vol. 87, No. 3, Jan, pp. 270-278.

amplitudes in somatosensory evoked potentials using wavelets and regression,

function during instrumented anterior cervical fusion, *Spine J*, Vol. 4, No. 2,

extracted from mid-latency auditory evoked potentials, *J Clin Monit Comput*, Vol.

média latência: técnicas no domínio do tempo e coerência espectral. D.Sc. Thesis.,

de respostas fotorecrutantes no eletroencefalograma multicanal de pacientes epilépticos, *Anais do XX Congresso Brasileiro de Engenharia Biomédica - CBEB2006*

## **7. Conclusion**

The ORD approach allows the detection of sensory response with a maximum false-positive rate () that can be defined as strict as desired. This leads to techniques that can be employed for a variety of occasions ranging from children auditory screening to the fast intra-operative monitoring in order to avoid early or late neurological sequels, including the ones arising from surgical manipulation. The wide applicability of the ORD comes from its computational simplicity, being usually based on the calculation of parameters derived from the Fourier Transform of EEG epochs.

When a very low signal-to-noise ratio is observed, which is the circumstance expected in hospital units due to the presence of electrical/electro-mechanic devices that generate electrical/electromagnetic interference, the use of more than one derivation, in a multivariate ORD approach, may improve the probability of detection without increasing in the exam duration. For this purpose, both scalp regions and frequencies more responsive should be employed in the objective detection. Moreover, in order to obtain faster response detection, the most higher stimulation frequency that does not result in decrease in the detection rates should be used.

For the right posterior tibial nerve SEP, presented as an illustration in this review, the maximum response frequency range is within the high beta and low gamma band (20- 60 Hz); the best regions for SEP recording includes the central and parietal leads at the midline and parasagital line ipsilateral to the stimulated limb ([Cz], [C4] [Pz] and [P4]). The stimulation frequency of 9 Hz, instead of the often employed 5 Hz, can be used without diminishes the probability of detection. Hence, once the application of MORD produces an increase in the detection percentages compared to the MSC for the same *M*-value, it can, on the other hand, be employed to reduce the exam duration (*M*), whereas the detection probability is maintained.

Analogue results are expected for SEP obtained for the left tibial nerve and even for upper limbs, since the anatomical pathways follow similar routes, including decussation and somatotopic mapping. However, it should be effectively measured.

This review presented the theoretical background of ORD and MORD techniques applied to the Evoked Potential field. The historical aspects together with the included examples may be useful to many researches, since they encompass applications ranging from elementary goals up to the state of art in biosignal detection.

## **8. Future directions**

Based on the prominent results found by using multivariate objective response detection techniques, it would be useful to investigate it for a number of derivations higher than *N* = 2. The MCSM critical value does not vary with *N*, as stated on expression (26) (Felix and Miranda de Sá, 2003). Thus, augmenting the number of derivations would imply increasing the detection rate. However, it did not occur in practical applications (Melges, 2009, Felix *et al.*, 2007). This could be explained by the fact that the background activities are correlated and hence there would be no improvement by continuously adding new derivations. However, this hypothesis of correlated activities should be verified for different kinds of evoked potentials. Additionally, it would be worth to identify the optimal number of derivations to be employed for both MC and MCSM estimation for each kind of stimulation, since the presence of a massive number of leads is undesirable for clinical and surgical monitoring purposes. Moreover, the exponential forgetting, suggested by Tierra-Criollo *et al.* (1998), should be applied for multivariate ORD in order to increase the rapidness of response detection. Finally, both ORD and MORD techniques should be incorporated in the EP analysis software to have their efficacy evaluated for diagnosis and neuro-monitoring.

## **9. Abbreviations**

76 Applied Biological Engineering – Principles and Practice

The ORD approach allows the detection of sensory response with a maximum false-positive

When a very low signal-to-noise ratio is observed, which is the circumstance expected in hospital units due to the presence of electrical/electro-mechanic devices that generate electrical/electromagnetic interference, the use of more than one derivation, in a multivariate ORD approach, may improve the probability of detection without increasing in the exam duration. For this purpose, both scalp regions and frequencies more responsive should be employed in the objective detection. Moreover, in order to obtain faster response detection, the most higher stimulation frequency that does not result in decrease in the

For the right posterior tibial nerve SEP, presented as an illustration in this review, the maximum response frequency range is within the high beta and low gamma band (20- 60 Hz); the best regions for SEP recording includes the central and parietal leads at the midline and parasagital line ipsilateral to the stimulated limb ([Cz], [C4] [Pz] and [P4]). The stimulation frequency of 9 Hz, instead of the often employed 5 Hz, can be used without diminishes the probability of detection. Hence, once the application of MORD produces an increase in the detection percentages compared to the MSC for the same *M*-value, it can, on the other hand, be employed to reduce the exam duration (*M*), whereas the detection

Analogue results are expected for SEP obtained for the left tibial nerve and even for upper limbs, since the anatomical pathways follow similar routes, including decussation and

This review presented the theoretical background of ORD and MORD techniques applied to the Evoked Potential field. The historical aspects together with the included examples may be useful to many researches, since they encompass applications ranging from elementary

Based on the prominent results found by using multivariate objective response detection techniques, it would be useful to investigate it for a number of derivations higher than *N* = 2. The MCSM critical value does not vary with *N*, as stated on expression (26) (Felix and Miranda de Sá, 2003). Thus, augmenting the number of derivations would imply increasing the detection rate. However, it did not occur in practical applications (Melges, 2009, Felix *et al.*, 2007). This could be explained by the fact that the background activities are correlated and hence there would be no improvement by continuously adding new derivations. However, this hypothesis of correlated activities should be verified for different kinds of evoked potentials. Additionally, it would be worth to identify the optimal number of

somatotopic mapping. However, it should be effectively measured.

goals up to the state of art in biosignal detection.

) that can be defined as strict as desired. This leads to techniques that can be employed for a variety of occasions ranging from children auditory screening to the fast intra-operative monitoring in order to avoid early or late neurological sequels, including the ones arising from surgical manipulation. The wide applicability of the ORD comes from its computational simplicity, being usually based on the calculation of parameters derived from

**7. Conclusion** 

the Fourier Transform of EEG epochs.

detection rates should be used.

probability is maintained.

**8. Future directions** 

rate (

> EEG – Electroencephalogram; EP – Evoked Potential; AEP – auditory EP; SEP – somatosensory EP; VEP – Visual EP; ORD – Objective Response Detection; MORD – Multivariate ORD.

## **10. Acknowledgements**

To the Brazilian research and education agencies, the Rio de Janeiro State Research Council (FAPERJ), the National Council for Scientific and Technological Development (CNPq - Ministry of Science and Technology) and CAPES (Ministry of Education) for the financial support. We also acknowledge the Military Police Central Hospital of Rio de Janeiro for providing infrastructure support.

## **11. References**


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**4** 

*Poland* 

**Extraction of 3D Geometrical** 

Michal Rychlik and Witold Stankiewicz

*Poznan University of Technology Division of Machine Design Methods* 

**Features of Biological Objects with** 

**3D PCA Analysis and Applications of Results** 

The Computer Aided Design (CAD) systems are very well known by designers in their every day practice and numerical analysis. Computer models of real objects with advanced numerical tools, significantly improves the quality and reduce time of design process. In addition to the three-dimensional modeling systems, there are many other tools and techniques (such as reverse engineering, rapid prototyping), which will further enhance the

Many of those engineering technologies, especially CAD/CAM techniques, have an application not only in mechanical design. These tools also can be used in different disciplines, like biomechanics, bioengineering, biometrics, etc. This interdisciplinary area of knowledge takes advantage of Reverse Engineering, three-dimensional modeling and simulation, FEM1 analysis and is equipped with Rapid Prototyping and CNC machines. The acquisition and processing of three-dimensional models with complicated shapes becomes the important issue in applications mentioned above. The 3D virtual models have numerous applications, simply such as visualization, but also more advanced like medical diagnostics (virtual endoscopes), pre-surgical planning (simulations of surgical operations), FEM and CFD2 analysis, CNC machining, Rapid Prototyping, preparation and fabrication of implants, etc. Several engineering technologies and tools can be used for advanced analysis of biological objects.

The first step in computer analysis of biological/medical objects is to obtain the correct and high accurate 3D model. This 3D modeling generally is made by reconstruction procedure. 3D reconstruction can be done by usage of medical imagining systems (such as CT, NMR) or 3D scanning systems. Reconstruction of 3D model based on DICOM3 images must be supported by image processing (segmentation of the region of interest) to extract 3D shape of the object. Dependent on the area of interest the bones, blood vessels or other soft tissues

**1. Introduction** 

capabilities of engineers.

can be searched.

1FEM – finite element method 2CFD – computational fluid dynamics

3DICOM – Digital Imaging in Communications in Medicine


## **Extraction of 3D Geometrical Features of Biological Objects with 3D PCA Analysis and Applications of Results**

Michal Rychlik and Witold Stankiewicz *Poznan University of Technology Division of Machine Design Methods Poland* 

## **1. Introduction**

84 Applied Biological Engineering – Principles and Practice

Victor, JD, Mast, J. 1991. A new statistic for steady-state evoked potentials, Electroencephalogr Clin Neurophysiol, Vol. 78, No. 5, May, pp. 378-388. Xu, S, Meyer, D, Yoser, S, Mathews, D, Elfervig, JL. 2001.Pattern visual evoked potential in

Zaeyen, EJB. 2005. Aplicação da Coerência ao eletroencefalograma para investigar

http://www.dominiopublico.gov.br/)

the diagnosis of functional visual loss, *Ophthalmology*, Vol. 108, No. 1, Jan, pp. 76-80.

características do Potencial Evocado Auditivo de Média Latência. M.Sc. Dissertation, COPPE/UFRJ, Rio de Janeiro, Rio de Janeiro, Brazil. (Available at:

> The Computer Aided Design (CAD) systems are very well known by designers in their every day practice and numerical analysis. Computer models of real objects with advanced numerical tools, significantly improves the quality and reduce time of design process. In addition to the three-dimensional modeling systems, there are many other tools and techniques (such as reverse engineering, rapid prototyping), which will further enhance the capabilities of engineers.

> Many of those engineering technologies, especially CAD/CAM techniques, have an application not only in mechanical design. These tools also can be used in different disciplines, like biomechanics, bioengineering, biometrics, etc. This interdisciplinary area of knowledge takes advantage of Reverse Engineering, three-dimensional modeling and simulation, FEM1 analysis and is equipped with Rapid Prototyping and CNC machines. The acquisition and processing of three-dimensional models with complicated shapes becomes the important issue in applications mentioned above. The 3D virtual models have numerous applications, simply such as visualization, but also more advanced like medical diagnostics (virtual endoscopes), pre-surgical planning (simulations of surgical operations), FEM and CFD2 analysis, CNC machining, Rapid Prototyping, preparation and fabrication of implants, etc. Several engineering technologies and tools can be used for advanced analysis of biological objects.

> The first step in computer analysis of biological/medical objects is to obtain the correct and high accurate 3D model. This 3D modeling generally is made by reconstruction procedure. 3D reconstruction can be done by usage of medical imagining systems (such as CT, NMR) or 3D scanning systems. Reconstruction of 3D model based on DICOM3 images must be supported by image processing (segmentation of the region of interest) to extract 3D shape of the object. Dependent on the area of interest the bones, blood vessels or other soft tissues can be searched.

<sup>1</sup>FEM – finite element method

<sup>2</sup>CFD – computational fluid dynamics

<sup>3</sup>DICOM – Digital Imaging in Communications in Medicine

Extraction of 3D Geometrical Features of

of ellipsoids [Syn and Prager, 1994]

of decreasing of the accuracy.

1996].

description

**3. Principal Component Analysis (empirical modes)** 

(Fig. 2.).

Biological Objects with 3D PCA Analysis and Applications of Results 87

Application of spherical modes is not "optimal" solution and sometimes cause of increasing complication of the computation because all objects are approximated by deformed sphere. Reconstruction of cube geometry can be done by very many numbers of spherical harmonics. This problem is analogous to Fourier decomposition of rectangular signal.

The second group of modal decomposition of 3D objects is present by physical modes (mechanical modes). This modes – known also as the vibration modes – are obtained by solution of equitation of own issue for resilience model of analyzing object. Vibration modal decomposition provides alternative parameterization of degree of freedom of the structure (only translation of the nodes in x, y, z directions) based on proper vibration of the objects and correlated frequencies. The most often are used low frequencies of the modes which described vectors of deformations for individual nodes of FEM grid. This way is possible the deformation of geometry of basic object and to fit it into searched object. Vibration modes compute for rigid body are responsible for translations and rotations of 3D model. Vibration modes compute for spring body describe different variation of the shape of basic model

Fig. 2. Graphical representation of seven low frequencies vibration modes for surface model

PCA transformation gives orthogonal directions of principal variation of input data. Principal component which are connected with the largest eigenvalue4, represent factor (direction) of the largest variation of data in data space. Variation is described by eigenvalue connected with the first principal component. The second principal component describes the next in order, orthogonal direction in the space with the next largest variation of data. Usually only few first principal components are responsible for a majority variations of the data. Data projected onto other principal components often have small amplitude and don't cross a amplitude of measurement noise. Therefore they can be deleted, without dangerous

For reconstruction of the 3D geometry, "low-dimensional" decomposition based on Principal Component Analysis (PCA) can be used [Benameur S., Mignote M., Parent S., Labelle H., Skalli W., De Gusie J., 2001]. PCA provides a "relevant" set of basis functions, which allow identification of a low-dimensional subspace [Holmes, Lumley and Berkooz,

4The prefix **eigen-** is adopted from the German word "eigen" for "own" in the sense of a characteristic

The used algorithm is based on statistical representation of the random variables.

The main objective of this chapter is to present the possibility of a new use of "tools", known from engineering area, in the biomedical applications. One of the useful tools, known from technical applications (mainly in images and signal analysis) is Principal Component Analysis. This method is usually used for one or two dimensional "statistical" analysis, but three or more dimensions also can be analyzed. That multidimensional PCA analysis supported by other "high-tech" technologies (Reverse Engineering - 3D scanners, thermal camera, CT or NMR imagining), can generate very interesting results especially for 3D biomedical objects. In further sections the three applications (in anthropometrics, biometricsand for 3D geometry reconstruction procedure) of three-dimensional PCA analysis of biological objects will be presented and discussed.

## **2. Methods of modal analysis**

In this chapter authors present modal analysis methods which can be used for geometry description of three dimensional objects. This methods are used for simplify and minimize the number of parameters which describe 3D objects.

The kinds of modal method (mathematical, physical or empirical) which are applied to analysis have a fundamental importance onto results. One of the method which based on modal decomposition is PCA (Principal Component Analysis, known also as POD – Proper Orthogonal Decomposition). If empirical modes (PCA) are optimal from viewpoint of information included inside of the each modes [Holmes, Lumley and Berkooz, 1998], also others decompositions based on mathematical (e.g. spherical harmonics) or physical modes (vibration modes) are also used.

The goal of using mathematical modes is conversion physical features onto mathematical features (synthetic form). In the event of the mathematical modes usually the features which describing geometry of 3D object is save as the vectors. Each vector is obtained through splitting of the 3D model on the several classes (different diameter spheres) and calculates common areas for 3D object and surface of individual spheres. All areas are described by set of vectors (spherical functions). For spherical functions Fourier transformation is used. After this operation the new unit is inserting. Goal of unit is made easier multidimensional description of features vectors. For representation of features vectors spherical harmonics are used (Fig. 1.).

Fig. 1. Example of spherical harmonics of 3D model of plane (a) and application spherical harmonic to reconstruction of geometry of the cube (b) [Vranic and Saupe, 2002]

The main objective of this chapter is to present the possibility of a new use of "tools", known from engineering area, in the biomedical applications. One of the useful tools, known from technical applications (mainly in images and signal analysis) is Principal Component Analysis. This method is usually used for one or two dimensional "statistical" analysis, but three or more dimensions also can be analyzed. That multidimensional PCA analysis supported by other "high-tech" technologies (Reverse Engineering - 3D scanners, thermal camera, CT or NMR imagining), can generate very interesting results especially for 3D biomedical objects. In further sections the three applications (in anthropometrics, biometricsand for 3D geometry reconstruction procedure) of three-dimensional PCA

In this chapter authors present modal analysis methods which can be used for geometry description of three dimensional objects. This methods are used for simplify and minimize

The kinds of modal method (mathematical, physical or empirical) which are applied to analysis have a fundamental importance onto results. One of the method which based on modal decomposition is PCA (Principal Component Analysis, known also as POD – Proper Orthogonal Decomposition). If empirical modes (PCA) are optimal from viewpoint of information included inside of the each modes [Holmes, Lumley and Berkooz, 1998], also others decompositions based on mathematical (e.g. spherical harmonics) or physical modes

The goal of using mathematical modes is conversion physical features onto mathematical features (synthetic form). In the event of the mathematical modes usually the features which describing geometry of 3D object is save as the vectors. Each vector is obtained through splitting of the 3D model on the several classes (different diameter spheres) and calculates common areas for 3D object and surface of individual spheres. All areas are described by set of vectors (spherical functions). For spherical functions Fourier transformation is used. After this operation the new unit is inserting. Goal of unit is made easier multidimensional description of features vectors. For representation of features vectors spherical harmonics are used (Fig. 1.).

(a) (b)

Fig. 1. Example of spherical harmonics of 3D model of plane (a) and application spherical

harmonic to reconstruction of geometry of the cube (b) [Vranic and Saupe, 2002]

analysis of biological objects will be presented and discussed.

the number of parameters which describe 3D objects.

**2. Methods of modal analysis** 

(vibration modes) are also used.

Application of spherical modes is not "optimal" solution and sometimes cause of increasing complication of the computation because all objects are approximated by deformed sphere. Reconstruction of cube geometry can be done by very many numbers of spherical harmonics. This problem is analogous to Fourier decomposition of rectangular signal.

The second group of modal decomposition of 3D objects is present by physical modes (mechanical modes). This modes – known also as the vibration modes – are obtained by solution of equitation of own issue for resilience model of analyzing object. Vibration modal decomposition provides alternative parameterization of degree of freedom of the structure (only translation of the nodes in x, y, z directions) based on proper vibration of the objects and correlated frequencies. The most often are used low frequencies of the modes which described vectors of deformations for individual nodes of FEM grid. This way is possible the deformation of geometry of basic object and to fit it into searched object. Vibration modes compute for rigid body are responsible for translations and rotations of 3D model. Vibration modes compute for spring body describe different variation of the shape of basic model (Fig. 2.).

Fig. 2. Graphical representation of seven low frequencies vibration modes for surface model of ellipsoids [Syn and Prager, 1994]

PCA transformation gives orthogonal directions of principal variation of input data. Principal component which are connected with the largest eigenvalue4, represent factor (direction) of the largest variation of data in data space. Variation is described by eigenvalue connected with the first principal component. The second principal component describes the next in order, orthogonal direction in the space with the next largest variation of data. Usually only few first principal components are responsible for a majority variations of the data. Data projected onto other principal components often have small amplitude and don't cross a amplitude of measurement noise. Therefore they can be deleted, without dangerous of decreasing of the accuracy.

## **3. Principal Component Analysis (empirical modes)**

For reconstruction of the 3D geometry, "low-dimensional" decomposition based on Principal Component Analysis (PCA) can be used [Benameur S., Mignote M., Parent S., Labelle H., Skalli W., De Gusie J., 2001]. PCA provides a "relevant" set of basis functions, which allow identification of a low-dimensional subspace [Holmes, Lumley and Berkooz, 1996].

The used algorithm is based on statistical representation of the random variables.

 4The prefix **eigen-** is adopted from the German word "eigen" for "own" in the sense of a characteristic description

Extraction of 3D Geometrical Features of

**4.1 Biometric application of 3D PCA** 

biometrics can be sorted into two types [Mainguet J-F. , 2004]:

support information.

dental, lips, nail;

primate ancestors.

[Anil K. J., at al., 2002].

twins.

**4.1.1 Materials – Acquisition of input data** 

Biological Objects with 3D PCA Analysis and Applications of Results 89

Several engineering technologies can be used for advanced analysis of biological objects. In further chapters the three applications, anthropometric (femur bones), biometric (human faces), geometry reconstruction (lumbar vertebra) of three-dimensional models will be presented and discussed. For biometric database the thermal (infrared) images was tested as

The security and access systems are very important and rapidly advancing, not only in computer vision. Such systems are used obviously during passenger control on the airport or boundary crossing [Schneider W., 2007]. Biometrics identify people by measuring some aspects of individual anatomy or physiology – such as hand geometry or fingerprint, some deeply ingrained skill, or other behavioral characteristic – handwritten signature, or something that is a combination of the two – voice [Anderson, R. J., 2008]. In generally the

a. physical – face, fingerprint, hand/finger, iris, ear, retinal, DNA, vein, blood pulse,

The face recognition method is the oldest and the most "natural" method of identification person's. Recognizing people by their facial features is going back at least to our early

The disadvantage of the most commonly used recognition techniques is their insufficient reliability. A 2D dimensional photo cannot be measured like a landscape and simply doesn't contain the same amount of information as the 3D "photo" [Xiaoguang Lu, 2006]. This problem is especially essential for twins, when the similarity of face shape is very high

Facial identification reads the peaks and valleys of facial features. These peaks and valleys are known as nodal points (80 nodal points exist in a human face, but usually only 15-20 are used for identification – known as "Golden triangle" region between the temples and the lips.

For obtain the 3D input data the 3D scanning system (the structural light scanner) was used. The two groups of biological models were measured: set of human faces and set of femur

To increase the accuracy of PCA analysis, each face was described (Fig. 4.) by individual

Database for biometric PCA analysis is prepared onto the multiple human faces. There are 39 faces (Fig. 5.) with neutral expression of different persons. To improve sensitivity of presented method, three sets (6 faces) of the twin's faces in the database were included. There are two sets of identical – monozygotic twins and one set of fraternal – dizygotic

bones. Each input object was scanned and 3D surface model was computed.

points cloud (40k points) instead of few markers from "Golden triangle" area.

b. behavioral – voice, gait, tapping, signature, keystroke dynamics, mouse dynamics.

**4. Applications of Principal Component Analysis of 3D biological objects** 

The shape of the each object is represented in the data base as the set of 3D point clouds. Each point clouds is described by a vector (1):

$$S\_i = \left[ \mathbf{s}\_{i1}, \mathbf{s}\_{i2}, \dots, \mathbf{s}\_{iN} \right]^T, \text{ i } = \mathbf{1}, \mathbf{2}, \dots, M,\tag{1}$$

where *s xyz ij* , , describes coordinates of the points in Cartesian system, *M* is the number of the objects which are in database, *N* is the number of the points in single point cloud. In the next step the mean shape *S* and covariance matrix *C* are computed (2):

1 1 *<sup>M</sup> i i S S M* , 1 1 *<sup>M</sup> T i i i C SS M* , (2)

The difference between mean and object that is in data base are describe by the deformation vector *SSS i i* . The statistical analysis of the deformation vectors gives us the information about the empirical modes. Modes represent the geometrical features (shape) but also can carry other information like texture, map of temperature and others. Only few first modes contains most information, therefore each original object *Si* is reconstructed by using some *K* principal components (3):

$$S\_i = \overline{S} + \sum\_{k=1}^{K} a\_{ki} \Psi\_{k \text{ \textquotedblleft \textquotedblright}} \text{ \textquotedblright} = 1, 2, \dots, M \text{ \textquotedblleft} \tag{3}$$

where *k* is an eigenvector representing the orthogonal mode (the feature computed from data base), *ki a* is coefficient of eigenvector.

Energy (equivalent of quantity of information) transmitted by eigenvector *m* is appointed on following equation:

$$E = \frac{\Psi\_m}{\sum\_{k=1}^{M} \Psi\_k},\tag{4}$$

The example of the low dimensional reconstruction for three different values of the coefficients is presented on the Figure 3. Every manipulations of coefficients value of the modes, changing geometry of the objects.

Fig. 3. The visualization ofthe low dimensional reconstruction for L4 vertebra: average value (left side) and two different deformation which are compute for different values of the coefficients (middle and right side).

## **4. Applications of Principal Component Analysis of 3D biological objects**

Several engineering technologies can be used for advanced analysis of biological objects. In further chapters the three applications, anthropometric (femur bones), biometric (human faces), geometry reconstruction (lumbar vertebra) of three-dimensional models will be presented and discussed. For biometric database the thermal (infrared) images was tested as support information.

## **4.1 Biometric application of 3D PCA**

88 Applied Biological Engineering – Principles and Practice

The shape of the each object is represented in the data base as the set of 3D point clouds.

where *s xyz ij* , , describes coordinates of the points in Cartesian system, *M* is the number of the objects which are in database, *N* is the number of the points in single point

The difference between mean and object that is in data base are describe by the deformation vector *SSS i i* . The statistical analysis of the deformation vectors gives us the information about the empirical modes. Modes represent the geometrical features (shape) but also can carry other information like texture, map of temperature and others. Only few first modes contains most information, therefore each original object *Si* is reconstructed by

where *k* is an eigenvector representing the orthogonal mode (the feature computed from

Energy (equivalent of quantity of information) transmitted by eigenvector *m* is appointed

1

The example of the low dimensional reconstruction for three different values of the coefficients is presented on the Figure 3. Every manipulations of coefficients value of

<sup>0</sup> *ki <sup>a</sup>* <sup>6</sup> 5 10 *ki <sup>a</sup>* <sup>6</sup> 5 10 *ki <sup>a</sup>* Fig. 3. The visualization ofthe low dimensional reconstruction for L4 vertebra: average value

(left side) and two different deformation which are compute for different values

*k*

 

*E*

*m M*

*k*

1

*T i i*

, *i M* 1,2, , , (3)

, (2)

, (4)

1 *<sup>M</sup>*

*i C SS M*

cloud. In the next step the mean shape *S* and covariance matrix *C* are computed (2):

*i i S S M* ,

1

1

*K i ki k k SS a* 

1 *<sup>M</sup>*

1 2 , ,, , *<sup>T</sup> S ss s i i i iN i M* 1,2, , , (1)

Each point clouds is described by a vector (1):

using some *K* principal components (3):

data base), *ki a* is coefficient of eigenvector.

the modes, changing geometry of the objects.

of the coefficients (middle and right side).

on following equation:

The security and access systems are very important and rapidly advancing, not only in computer vision. Such systems are used obviously during passenger control on the airport or boundary crossing [Schneider W., 2007]. Biometrics identify people by measuring some aspects of individual anatomy or physiology – such as hand geometry or fingerprint, some deeply ingrained skill, or other behavioral characteristic – handwritten signature, or something that is a combination of the two – voice [Anderson, R. J., 2008]. In generally the biometrics can be sorted into two types [Mainguet J-F. , 2004]:


The face recognition method is the oldest and the most "natural" method of identification person's. Recognizing people by their facial features is going back at least to our early primate ancestors.

The disadvantage of the most commonly used recognition techniques is their insufficient reliability. A 2D dimensional photo cannot be measured like a landscape and simply doesn't contain the same amount of information as the 3D "photo" [Xiaoguang Lu, 2006]. This problem is especially essential for twins, when the similarity of face shape is very high [Anil K. J., at al., 2002].

Facial identification reads the peaks and valleys of facial features. These peaks and valleys are known as nodal points (80 nodal points exist in a human face, but usually only 15-20 are used for identification – known as "Golden triangle" region between the temples and the lips.

## **4.1.1 Materials – Acquisition of input data**

For obtain the 3D input data the 3D scanning system (the structural light scanner) was used. The two groups of biological models were measured: set of human faces and set of femur bones. Each input object was scanned and 3D surface model was computed.

To increase the accuracy of PCA analysis, each face was described (Fig. 4.) by individual points cloud (40k points) instead of few markers from "Golden triangle" area.

Database for biometric PCA analysis is prepared onto the multiple human faces. There are 39 faces (Fig. 5.) with neutral expression of different persons. To improve sensitivity of presented method, three sets (6 faces) of the twin's faces in the database were included. There are two sets of identical – monozygotic twins and one set of fraternal – dizygotic twins.

Extraction of 3D Geometrical Features of

network.

coefficients (Tab. 1.).

Average face (mean value)

Coefficient value max

Coefficient value min

Biological Objects with 3D PCA Analysis and Applications of Results 91

(a) (b) (c)

The second step is connected with curves extraction. Independently from face size, always 201 curves on face are only. To achieve this, scaling of space between curves is used.

For prepared database of human faces (39 faces of young persons) the PCA analysis was performed. The result of this operation is the mean object, thirty nine modes (Fig. 7) and

The first thirty eight modes include one hundred percent of information about decomposed geometry. Mode thirty nine contains only a numerical noise. For further reconstruction of

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6

Fig. 7. Visualization of the average value and first nine empirical modes of faces

Fig. 6. Data registration: a) origin point, b) three point of rigid registration, c) 3D curves

For infrared images only the first step of registration was done.

**4.1.3 Results of 3D PCA analysis – Face print** 

face geometry only first twenty five modes are used.

(for maximum and minimum values of coefficient).

Fig. 4. Data acquisition process (from left): hardware configuration, captured image, input data set (points cloud).

Second part of input data for biometric database is set of two-dimensional infrared images (thermal images). In this research the thermal images of 17 different persons were collected (Fig. 5.). For acquisition of infrared images the thermal camera was used. All pictures were collected in the same conditions of the measurement: room (+220C) and camera settings: matrix VOx 320x240 pixels, thermal resolution +/0.030C, range of measured temperature: 26-400C.

Fig. 5. An example of the models in database (from the left): 3D faces, 2D thermal images.

## **4.1.2 Data registration**

The Principal Component Analysis requires the same position, orientation and topology of the data input (the same number of nodes, matrix connection, etc.) for all objects. To achieve this, each new object added to database must be registered.

For face the origin point (0, 0, 0) of coordinate system is arranged in cross section of two lines: vertical middle line on the face, horizontal – eyes line. The registration is made in two steps. First step (preliminary registration) is the rigid registration. It consists of simple, affine geometrical transformation of object in three-dimensional space (rotation and transformation). For control of this process three points are used: two points in the centers of the eyes, one on the top of the nose (Fig.6.).

Fig. 4. Data acquisition process (from left): hardware configuration, captured image, input

Second part of input data for biometric database is set of two-dimensional infrared images (thermal images). In this research the thermal images of 17 different persons were collected (Fig. 5.). For acquisition of infrared images the thermal camera was used. All pictures were collected in the same conditions of the measurement: room (+220C) and camera settings: matrix VOx 320x240 pixels, thermal resolution +/0.030C, range of measured temperature:

Fig. 5. An example of the models in database (from the left): 3D faces, 2D thermal images.

The Principal Component Analysis requires the same position, orientation and topology of the data input (the same number of nodes, matrix connection, etc.) for all objects. To achieve

For face the origin point (0, 0, 0) of coordinate system is arranged in cross section of two lines: vertical middle line on the face, horizontal – eyes line. The registration is made in two steps. First step (preliminary registration) is the rigid registration. It consists of simple, affine geometrical transformation of object in three-dimensional space (rotation and transformation). For control of this process three points are used: two points in the centers of

this, each new object added to database must be registered.

the eyes, one on the top of the nose (Fig.6.).

data set (points cloud).

**4.1.2 Data registration** 

26-400C.

Fig. 6. Data registration: a) origin point, b) three point of rigid registration, c) 3D curves network.

The second step is connected with curves extraction. Independently from face size, always 201 curves on face are only. To achieve this, scaling of space between curves is used. For infrared images only the first step of registration was done.

## **4.1.3 Results of 3D PCA analysis – Face print**

For prepared database of human faces (39 faces of young persons) the PCA analysis was performed. The result of this operation is the mean object, thirty nine modes (Fig. 7) and coefficients (Tab. 1.).

The first thirty eight modes include one hundred percent of information about decomposed geometry. Mode thirty nine contains only a numerical noise. For further reconstruction of face geometry only first twenty five modes are used.


Fig. 7. Visualization of the average value and first nine empirical modes of faces (for maximum and minimum values of coefficient).

Extraction of 3D Geometrical Features of

Coefficient values for Face 13


mode 01

mode 02

mode 03

mode 04

mode 05

mode 06

mode 07

mode 08

mode 09

mode 10

mode 11

mode 12

mode 13

mode 14

mode 15

mode 16

mode 17

mode 18

mode 19

mode 20

mode 21

mode 22

mode 23

mode 24

mode 25

of coefficient values, original photo and 3D face model).


mode 01

mode 02

mode 03

mode 04

mode 05

mode 06

mode 07

mode 08

mode 09

mode 10

mode 11

mode 12

mode 13

mode 14

mode 15

mode 16

mode 17

mode 18

mode 19

mode 20

mode 21

mode 22

mode 23

mode 24

mode 25

Coefficient values for Face 4

**4.1.4 Results of 2D PCA analysis – Thermal images** 

Number of the mode

Biological Objects with 3D PCA Analysis and Applications of Results 93

Faces of different people


mode 01

mode 02

mode 03

mode 04

mode 05

mode 06

mode 07

mode 08

mode 09

mode 10

mode 11

mode 12

mode 13

mode 14

mode 15

mode 16

mode 17

mode 18

mode 19

mode 20

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mode 22

mode 23

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mode 25


mode 01

mode 02

mode 03

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mode 05

mode 06

mode 07

mode 08

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mode 17

mode 18

mode 19

Coefficient values for Face 5

Coefficient values for Face 27

Fig. 8. Faceprints (ID codes) for few faces from database (for each object is presented – graph

As a support for three-dimensional face recognition, additional information – the thermal images – can be used [Akhloufi, M, Bendada A., 2008, Prokoski. F., 2000]. The twodimensional infrared images can be added to database as a "fourth" dimension. For prepared infrared images of human faces the 2D PCA analysis was done. The result of this

Mean face Mode 1 Mode 2 Mode 3 Mode 4

Fig. 9. Visualization of the mean face and first four empirical modes of infrared images.

Participation of the mode [%]

Table 2. Participation of the first 10 modes PCA decomposition of thermal images.

For presented analysis the sixteen modes include one hundred percent of information about decomposed thermal images (Table 2.). Seventeenth mode contains only a numerical noise.

> 1 26.4191478 26.4191478 2 16.7302890 43.1494367 3 10.9104597 54.0598965 4 8.3397586 62.3996550 5 6.5525733 68.9522283 6 5.6298384 74.5820668 7 4.4142731 78.9963398 8 3.6441677 82.6405075 9 3.3063140 85.9468215 10 2.7908036 88.7376251

Total participation of the modes [%]

operation is the mean face (Fig. 9.), seventeen modes and set of coefficients.


Table 1. Participation of the modes in faces geometry reconstruction.

Modes describe the features of the faces. Two first modes characterize global transformation: first mode changing of the face size in vertical direction, second mode changing the size in horizontal direction. Further modes describe more complex, local deformations. For example third mode is responsible for changes in nose and eyes areas. Results of the statistical analysis (empirical modes) can be used for reconstruction of geometry (in CAD systems) of individual features of the object. Those 3D models of faces can be used in many applications: 3D visualizations, Rapid Prototyping technologies, surgical planning, archivisation and many others.

Each face in database has unique set of coefficient values "faceprint" (Fig. 8.) – individual ID code like fingerprints. As the authorization key the set of coefficient values for the faces can be used. Each key describes individual shape of face and can be decoded and compared with the original data of user to obtain access to restricted area or data files.

1 57,2010066 57,2010066 2 13,4976482 70,6986548 3 5,9128812 76,6115360 4 4,3703630 80,9818990 5 4,0161309 84,9980299 6 3,1945602 88,1925901 7 2,6277538 90,8203439 8 1,3584618 92,1788057 9 1,2914768 93,4702825 10 0,9734244 94,4437069 11 0,8401794 95,2838863 12 0,6097119 95,8935982 13 0,4819451 96,3755433 14 0,4433567 96,8189000 15 0,3511382 97,1700382 16 0,3001483 97,4701865 17 0,2681638 97,7383503 18 0,2577919 97,9961422 19 0,2179374 98,2140797 20 0,1973631 98,4114428 21 0,1767063 98,5881491 22 0,1608646 98,7490137 23 0,1512224 98,9002361 24 0,1311154 99,0313516 25 0,1250506 99,1564022

Total participation of the modes [%]

Participation of the mode [%]

Table 1. Participation of the modes in faces geometry reconstruction.

surgical planning, archivisation and many others.

Modes describe the features of the faces. Two first modes characterize global transformation: first mode changing of the face size in vertical direction, second mode changing the size in horizontal direction. Further modes describe more complex, local deformations. For example third mode is responsible for changes in nose and eyes areas. Results of the statistical analysis (empirical modes) can be used for reconstruction of geometry (in CAD systems) of individual features of the object. Those 3D models of faces can be used in many applications: 3D visualizations, Rapid Prototyping technologies,

Each face in database has unique set of coefficient values "faceprint" (Fig. 8.) – individual ID code like fingerprints. As the authorization key the set of coefficient values for the faces can be used. Each key describes individual shape of face and can be decoded and compared

with the original data of user to obtain access to restricted area or data files.

Number of the mode

Fig. 8. Faceprints (ID codes) for few faces from database (for each object is presented – graph of coefficient values, original photo and 3D face model).

## **4.1.4 Results of 2D PCA analysis – Thermal images**

As a support for three-dimensional face recognition, additional information – the thermal images – can be used [Akhloufi, M, Bendada A., 2008, Prokoski. F., 2000]. The twodimensional infrared images can be added to database as a "fourth" dimension. For prepared infrared images of human faces the 2D PCA analysis was done. The result of this operation is the mean face (Fig. 9.), seventeen modes and set of coefficients.

Fig. 9. Visualization of the mean face and first four empirical modes of infrared images.

For presented analysis the sixteen modes include one hundred percent of information about decomposed thermal images (Table 2.). Seventeenth mode contains only a numerical noise.


Table 2. Participation of the first 10 modes PCA decomposition of thermal images.

Extraction of 3D Geometrical Features of

Common shape

– "ID code" (Fig. 13.).

Coefficient values for Face 1


mode 01

mode 02

mode 03

mode 04

mode 05

mode 06

mode 07

mode 08

mode 09

mode 10

mode 11

mode 12

mode 13

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mode 15

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mode 01

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mode 19

values, original photo, 3D face mode.

far from each other.

for each one face similar like for fingerprints (Anil K., 2002 ).

Biological Objects with 3D PCA Analysis and Applications of Results 95

Faces of dizygotic twins

Surface map of differences

Coefficient values for Face 4

Differences Max Min

Fig. 12. Visualizations of the common shape (mean face) and differences (empirical mode

For comparison of similarity of twins faces the value of surface deviation was done. For faces of monozygotic couple the value of standard deviation was 1,19mm and average distance 0,29mm. For faces of dizygotic twins standard deviation is near 1,79mm and average distance 0,83. Each twin's face in database has unique set of coefficient values

Faces of monozygotic twins Faces of dizygotic twins


mode 01

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Coefficient values for Face 3

Fig. 13. Face ID code for faces of two types of twins (from upper left): face code – coefficient

Also for identical (for human eye view) monozygotic twins this "face-code" is incomparable

Trend curves (Fig. 14) of coefficients values showing how faces of twins are similar between each other. In general shape, curves (trends) are the same but in local values they have small differences. By this way the description ofsimilarity level between faces of the same couple of twins. As much faces are different from each other, than curves are automatically more

When we try comparing two trends curves from different couple of twins, we can observe

very big difference. Each face have own unique trend curve even for twins.

and surface map of difference) for dizygotic twins (gender: male).

Coefficient values for Face 2

Similarly to 3D data, each infrared image of the face in database has unique set of coefficient values – "thermal faceprints" (Fig. 10.). This additional information can be associated with 3D data to increase the level of security and can complicate the trials of fake the system.

Fig. 10. Thermal faceprint for few faces from infrared database (for each object is presented – graph of coefficient values, original photo and thermal image).

## **4.1.5 Analysis of similarity and differences of twin's faces**

For testing of sensitivity level of presented faceprint method the twin's faces was used. For numerical experiment the database with 19 faces (which include three couples of twins – two couples of monozygotic twins and one couple of dizygotic twins) was prepared.

For better comparison and computation of similarity of twin's faces the additional analysis was done. PCA analysis give information about common shape and differences between each face of twins couple. Results of this analysis (surface map of differences are presented) is presented for one monozigotic and one dizygotic twins (Fig. 11., Fig. 12.).



Fig. 11. Visualizations of the common shape (average face) and differences (empirical mode and surface map of difference) for monozygotic twins (gender: female).

Similarly to 3D data, each infrared image of the face in database has unique set of coefficient values – "thermal faceprints" (Fig. 10.). This additional information can be associated with 3D data to increase the level of security and can complicate the trials of

Thermal faceprint of few faces of different person


**Coefficient value**

Coefficient values for Face 10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 **Number of mode**

Fig. 10. Thermal faceprint for few faces from infrared database (for each object is presented –

For testing of sensitivity level of presented faceprint method the twin's faces was used. For numerical experiment the database with 19 faces (which include three couples of twins – two couples of monozygotic twins and one couple of dizygotic twins) was prepared.

For better comparison and computation of similarity of twin's faces the additional analysis was done. PCA analysis give information about common shape and differences between each face of twins couple. Results of this analysis (surface map of differences are presented)

Faces of monozygotic twins

Surface map of differences

Coefficient values for Face 12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 **Number of mode**


**Coefficient value**

Differences Max Min

Fig. 11. Visualizations of the common shape (average face) and differences (empirical mode

and surface map of difference) for monozygotic twins (gender: female).

is presented for one monozigotic and one dizygotic twins (Fig. 11., Fig. 12.).

graph of coefficient values, original photo and thermal image).

Coefficient values for Face 8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 **Number of mode**


**Coefficient value**

**4.1.5 Analysis of similarity and differences of twin's faces** 

fake the system.


**Coefficient value**

Coefficient values for Face 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 **Number of mode**

Common shape


Faces of dizygotic twins

Fig. 12. Visualizations of the common shape (mean face) and differences (empirical mode and surface map of difference) for dizygotic twins (gender: male).

For comparison of similarity of twins faces the value of surface deviation was done. For faces of monozygotic couple the value of standard deviation was 1,19mm and average distance 0,29mm. For faces of dizygotic twins standard deviation is near 1,79mm and average distance 0,83. Each twin's face in database has unique set of coefficient values – "ID code" (Fig. 13.).

Fig. 13. Face ID code for faces of two types of twins (from upper left): face code – coefficient values, original photo, 3D face mode.

Also for identical (for human eye view) monozygotic twins this "face-code" is incomparable for each one face similar like for fingerprints (Anil K., 2002 ).

Trend curves (Fig. 14) of coefficients values showing how faces of twins are similar between each other. In general shape, curves (trends) are the same but in local values they have small differences. By this way the description ofsimilarity level between faces of the same couple of twins. As much faces are different from each other, than curves are automatically more far from each other.

When we try comparing two trends curves from different couple of twins, we can observe very big difference. Each face have own unique trend curve even for twins.

Extraction of 3D Geometrical Features of

Biological Objects with 3D PCA Analysis and Applications of Results 97

Fig. 15. Hand biometrics (from left): 2D biometric hand reader, segmentation of length and

Basis on faceprint methodology (described in chapter 4.1.3.) the 3D hand biometric

The data input for numerical experiment was obtained by using the 3D optical scanner analogues to obtain the geometry of the bones. Measurements of hand geometry are easy to collect but for obtain full 3D information the special platform with mirrors was created. The system of mirrors and settings for localization of fingers (Fig. 16.) are comparable like

For test the database contains of 10 different 3D models of human hand (Fig. 17.). For each hand the registration procedure was done. As final result the set of polygon meshes (6,5k

Fig. 17. Input data for 3D hand PCA analysis: five 3D models of different hands, example of

weight of the hand fingers features [Sanchez-Reillo R. at al., 2000].

used in regular 2D silhouette scanners [Jain A.K., at al., 1999].

Fig. 16. Hand positioning system with mirror [Jain A.K., at al., 1999]

triangles) describing hands was obtained and used in further 3D PCA analysis.

identification system was prepared and tested.

mesh grid.

(a)

Fig. 14. Comparison of trend curves of coefficient values of modes: a) monozygotic twins, b) dizygotic twins.

#### **4.1.6 Results of 3D PCA analysis – Hand shape biometrics**

For identity of persons as a input data the many different information can be used. One of them is the hand shape. Hand geometry verification systems use geometric measurements of hand as the features for the verification of individuals. Usually they measure and analyze the overall structure, 2D shape (silhouette) and proportions of the hand e.g. length, width and thickness of hand, fingers and joints [Sanchez-Reillo R. at al., 2000]. Hand geometry biometrics systems measure up to 90 parameters (Fig. 15). Hand biometrics systems have some limitations, especially for people with severe arthristis who cannot spread their hands on the special hand reader.

(a)

(b) Fig. 14. Comparison of trend curves of coefficient values of modes: a) monozygotic twins,

For identity of persons as a input data the many different information can be used. One of them is the hand shape. Hand geometry verification systems use geometric measurements of hand as the features for the verification of individuals. Usually they measure and analyze the overall structure, 2D shape (silhouette) and proportions of the hand e.g. length, width and thickness of hand, fingers and joints [Sanchez-Reillo R. at al., 2000]. Hand geometry biometrics systems measure up to 90 parameters (Fig. 15). Hand biometrics systems have some limitations, especially for people with severe arthristis who cannot spread their hands

**4.1.6 Results of 3D PCA analysis – Hand shape biometrics** 

b) dizygotic twins.

on the special hand reader.

Fig. 15. Hand biometrics (from left): 2D biometric hand reader, segmentation of length and weight of the hand fingers features [Sanchez-Reillo R. at al., 2000].

Basis on faceprint methodology (described in chapter 4.1.3.) the 3D hand biometric identification system was prepared and tested.

The data input for numerical experiment was obtained by using the 3D optical scanner analogues to obtain the geometry of the bones. Measurements of hand geometry are easy to collect but for obtain full 3D information the special platform with mirrors was created. The system of mirrors and settings for localization of fingers (Fig. 16.) are comparable like used in regular 2D silhouette scanners [Jain A.K., at al., 1999].

Fig. 16. Hand positioning system with mirror [Jain A.K., at al., 1999]

For test the database contains of 10 different 3D models of human hand (Fig. 17.). For each hand the registration procedure was done. As final result the set of polygon meshes (6,5k triangles) describing hands was obtained and used in further 3D PCA analysis.

Fig. 17. Input data for 3D hand PCA analysis: five 3D models of different hands, example of mesh grid.

Extraction of 3D Geometrical Features of

Coefficient values for Hand 2

12345678 **Number of mode**


**Coefficient value**

Biological Objects with 3D PCA Analysis and Applications of Results 99

Hands of different people

Coefficient values for Hand 6

Coefficient values for Hand 10

12345678 **Number of mode**


**Coefficient value**

12345678 **Number of mode**

Fig. 19. Handprints (ID codes) for few hands from database (for each object is presented –

Anthropometry is the science of measuring the human body (e.g. height, weight) and size of component parts, including skinfold thickness, to study and compare the relative proportions. Measurements can be done under normal and abnormal conditions. The results of measurements done for group or population of people are organised in special databases. The basic problem which exists in most of databases is not enough information. Most of them are old and not includes all interesting dimensions. Traditional anthropometric database contains information only about some characteristic points (other parameters are not described). The set of the bones are described only in two dimensional space [Jantz, R.L. and P.H. Moore-Jansen, 1988], by the collection of linear

Fig. 20. Example of measurement process and view on a few characteristic points for femur

Three dimensional knowledge about mean geometry of the bones are not exist. Usually data acquisition process is prepared with usage of the conventional osteological instruments (measurements equipment like: caliper, spreading calliper, or osteometric board – Fig.21.).

graph of coefficient values, two views of 3D hand model).


**Coefficient value**

**4.2 Anthropometric application of 3D PCA** 

and angular dimensions (Fig.20.).

bone [Moore-Jansen at al., 1994]


For this analysis the nine modes include one hundred percent of information about hand geometry (Table 3.). The last, tenth mode, contain only a numerical noise.

Table 3. Participation of the first 10 modes PCA decomposition of handgeometry.

Comparable like it was for 3D faces, the same situation is for hands. Individual modes characterize principal features of hand: size of hand, length of fingers, thickness of fingers and shape of hand regions (Fig. 18).


Fig. 18. Visualization of the average value and first nine empirical modes of faces (for maximum and minimum values of coefficient).

Each hand in database has unique set of coefficient values "handprint" (Fig. 19.) – individual ID code like fingerprints just based on full 3D hand geometry. As the authorization key the set of coefficient values for the hands can be used. Each key describes individual 3D geometry of hand and can be decoded and compared with the original data of user to obtain access to restricted area or data files.

For this analysis the nine modes include one hundred percent of information about hand

1 94.2193186 94.2193186 2 1.9215473 96.1408659 3 1.4766160 97.6174819 4 0.8838991 98.5013809 5 0.8546490 99.3560300 6 0.3615261 99.7175561 7 0.1225032 99.8400593 8 0.0912159 99.9312752 9 0.0687248 100.0000000 10 0.0000000 100.0000000

Total participation of the modes [%]

Participation of the mode [%]

Table 3. Participation of the first 10 modes PCA decomposition of handgeometry.

Fig. 18. Visualization of the average value and first nine empirical modes of faces

Each hand in database has unique set of coefficient values "handprint" (Fig. 19.) – individual ID code like fingerprints just based on full 3D hand geometry. As the authorization key the set of coefficient values for the hands can be used. Each key describes individual 3D geometry of hand and can be decoded and compared with the original data of

(for maximum and minimum values of coefficient).

user to obtain access to restricted area or data files.

Comparable like it was for 3D faces, the same situation is for hands. Individual modes characterize principal features of hand: size of hand, length of fingers, thickness of fingers

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6

geometry (Table 3.). The last, tenth mode, contain only a numerical noise.

Number of the mode

and shape of hand regions (Fig. 18).

Average face (mean value)

Coefficient value max

Coefficient value min

Fig. 19. Handprints (ID codes) for few hands from database (for each object is presented – graph of coefficient values, two views of 3D hand model).

## **4.2 Anthropometric application of 3D PCA**

Anthropometry is the science of measuring the human body (e.g. height, weight) and size of component parts, including skinfold thickness, to study and compare the relative proportions. Measurements can be done under normal and abnormal conditions. The results of measurements done for group or population of people are organised in special databases. The basic problem which exists in most of databases is not enough information. Most of them are old and not includes all interesting dimensions. Traditional anthropometric database contains information only about some characteristic points (other parameters are not described). The set of the bones are described only in two dimensional space [Jantz, R.L. and P.H. Moore-Jansen, 1988], by the collection of linear and angular dimensions (Fig.20.).

Fig. 20. Example of measurement process and view on a few characteristic points for femur bone [Moore-Jansen at al., 1994]

Three dimensional knowledge about mean geometry of the bones are not exist. Usually data acquisition process is prepared with usage of the conventional osteological instruments (measurements equipment like: caliper, spreading calliper, or osteometric board – Fig.21.).

Extraction of 3D Geometrical Features of

**4.2.2 Data registration** 

where

Gramkow, C., 1996]) is used (5):

integration of the velocity field.

around bone– the transfer area).

viscosity.

viscosity. In this application, parameters

Biological Objects with 3D PCA Analysis and Applications of Results 101

The registration procedure forbones was made also in two steps. First step (preliminary registration) is simply rigid registration. The second step is the viscous fluid registration. For this registration the modified Navier-Stokes equation in penalty function formulation (existing numerical code [Morzynski M., at al., 1999]; source segment [Bro-Nielsen, M.,

,, , , <sup>1</sup> <sup>0</sup>

(5)

are used to control the fluid


Re *i i j j i jj j ji <sup>i</sup> source segment existing numerical code*


and

compressibility, *f* is the base object and *g* is the target object (input model). The object is described by the grid nodes (FEM grid). The displacements of the nodes are computed from

Every based and new model is represented by several cross-sections with the same transfer

Fig. 25. Cross sections of the vertebra – orientation of the planes and two examples of 2D slices (from left): based vertebra geometry, new geometry of input vertebra (dark colour

where *f* and *g* are areas in grayscale *f* - base image (base vertebra), *g -* target image (input vertebra). The parameters of the flow are the same as for the compressible fluid with very

Source term is calculated from the difference of the two images in grey scale (6):

area (Fig. 25.). The transfer area is needed for topology conservation.

, ( ) *F f gf i i* (6)

*V VV V V f gf* 

Fig. 24. Complete points cloud (1,5 mln points) and final triangle surface grid.

Fig. 21. Osteological instruments usually used for measuring the femur bone [Vitek C., 2005]

The solution of presented problem is proposition to use the Reverse Engineering techniques for measurement process (to achieve precision 3D data) and modal analysis (PCA) to compute the 3D anthropometric database. These aspects are presented further in details.

## **4.2.1 Acquisition of input data**

For creation of database, the set of real bones was used. In this work was used the 15 femur bones (Fig. 22) – 6 female, 9 male – which are obtained from Poznan University of Medical Science.

Fig. 22. View of two different female femur bones.

For acquisition of data the 3D structural light scanner was used (Fig. 23.). To acquire full 3D geometry, each bone was measured from 15 different directions with accuracy 0,05mm. Effect of measure process, is set of 3D points clouds (Fig. 23). All points clouds must be registered (orientation and connection between clouds).

Fig. 23. Data acquisition process on 3D structural light scanner and set of points clouds.

The result of registration is one points cloud which consist about 1,5 mln points (Fig. 24). As the final step is generated 3D triangle surface grid.

Fig. 24. Complete points cloud (1,5 mln points) and final triangle surface grid.

### **4.2.2 Data registration**

100 Applied Biological Engineering – Principles and Practice

Fig. 21. Osteological instruments usually used for measuring the femur bone [Vitek C., 2005]

The solution of presented problem is proposition to use the Reverse Engineering techniques for measurement process (to achieve precision 3D data) and modal analysis (PCA) to compute the 3D anthropometric database. These aspects are presented further in details.

For creation of database, the set of real bones was used. In this work was used the 15 femur bones (Fig. 22) – 6 female, 9 male – which are obtained from Poznan University of Medical

For acquisition of data the 3D structural light scanner was used (Fig. 23.). To acquire full 3D geometry, each bone was measured from 15 different directions with accuracy 0,05mm. Effect of measure process, is set of 3D points clouds (Fig. 23). All points clouds must be

Fig. 23. Data acquisition process on 3D structural light scanner and set of points clouds.

The result of registration is one points cloud which consist about 1,5 mln points (Fig. 24). As

**4.2.1 Acquisition of input data** 

Fig. 22. View of two different female femur bones.

registered (orientation and connection between clouds).

the final step is generated 3D triangle surface grid.

Science.

The registration procedure forbones was made also in two steps. First step (preliminary registration) is simply rigid registration. The second step is the viscous fluid registration. For this registration the modified Navier-Stokes equation in penalty function formulation (existing numerical code [Morzynski M., at al., 1999]; source segment [Bro-Nielsen, M., Gramkow, C., 1996]) is used (5):

$$\underbrace{\dot{V}\_{i} + V\_{i,j}V\_{j} - \frac{1}{\text{Re}}V\_{i,jj} + \frac{\varepsilon - \lambda}{\rho}V\_{j,ji}}\_{\text{existing numerical code}} + \underbrace{\left(f - \text{g}\right)f\_{,i}}\_{\text{source segment}} = 0 \tag{5}$$

where - is fluid density, *Vi* - velocity component, Re - Reynolds number, - bulk viscosity. In this application, parameters and are used to control the fluid compressibility, *f* is the base object and *g* is the target object (input model). The object is described by the grid nodes (FEM grid). The displacements of the nodes are computed from integration of the velocity field.

Every based and new model is represented by several cross-sections with the same transfer area (Fig. 25.). The transfer area is needed for topology conservation.

Fig. 25. Cross sections of the vertebra – orientation of the planes and two examples of 2D slices (from left): based vertebra geometry, new geometry of input vertebra (dark colour around bone– the transfer area).

Source term is calculated from the difference of the two images in grey scale (6):

$$F\_i = -(f - \mathbf{g})f\_{,i} \tag{6}$$

where *f* and *g* are areas in grayscale *f* - base image (base vertebra), *g -* target image (input vertebra). The parameters of the flow are the same as for the compressible fluid with very viscosity.

Extraction of 3D Geometrical Features of

Number of the mode

Table 4. Participation of the modes in decomposition.

the anterior and posterior view is shown).

Biological Objects with 3D PCA Analysis and Applications of Results 103

1 74.9212416 74.9212416 2 10.5438352 85.4650767 3 4.2699519 89.7350286 4 3.3128685 93.0478971 5 1.6659793 94.7138765 6 1.4234329 96.1373093 7 1.0359034 97.1732127 8 0.6781645 97.8513772 9 0.5866122 98.4379894 10 0.4796167 98.9176061 11 0.3301463 99.2477523 12 0.3080968 99.5558492 13 0.2516839 99.8075330 14 0.1924670 100.0000000 15 0.0000000 100.0000000

Fig. 28. 3D visualization of mean value and first eight modes of femur bones (for each bone

Total participation of the modes [%]

Participation of the mode [%]

Computed flow field provides information about translations of the nodes in both sections. After computation we obtain dislocation of nodes of the base grid onto new geometry (Fig. 26.).

Fig. 26. Grid deformation (from the left): base object (base grid), new object inserted to database, base grid on geometry of the new objects.

## **4.2.3 Results of 3D PCA analysis – Femur bones**

The database used in analysis contains 15 femur bones. Each bone has different geometry and is described by triangle surface grid (Fig. 27) with the same structure (14 thousands nodes, 30 thousands elements).

Fig. 27. Triangle surface grid of femur bone.

For this database the Principal Component Analysis was done. The result of this operation is the mean object, fifteen modes and coefficients.

The first fourteen modes include 100% of information about decomposed geometry (Table 4). Mode fifteen contain only a numerical noise and they are not used for further calculations.

Modes describing the features of the femur bones (Fig. 28). The first mode describes transformation of the length of the femur bone. Second mode represent position conversion of the head of the bone, third describe change the arc of the shaft (body). Next modes describing more complex deformations, e.g. fourth mod describe change the position of the greater trochanter and lesser trochanter, also thickness of the shaft (body).

In this experiment the value of average error for reconstructed geometry of the bone was equal 0,3mm (reconstruction done with using of 14 modes).

Study of the value of the coefficients, give us additional information about the analyzed bones. For presented database we can found, correlation between coefficient value of first mode and gender. Negative coefficient value "-" of first mode is connected with female bones (one exception bone nr 8), when positive coefficient value "+" describe male bones (Fig. 29.).

Computed flow field provides information about translations of the nodes in both sections. After computation we obtain dislocation of nodes of the base grid onto new geometry

Fig. 26. Grid deformation (from the left): base object (base grid), new object inserted to

The database used in analysis contains 15 femur bones. Each bone has different geometry and is described by triangle surface grid (Fig. 27) with the same structure (14 thousands

For this database the Principal Component Analysis was done. The result of this operation is

The first fourteen modes include 100% of information about decomposed geometry (Table 4). Mode fifteen contain only a numerical noise and they are not used for further

Modes describing the features of the femur bones (Fig. 28). The first mode describes transformation of the length of the femur bone. Second mode represent position conversion of the head of the bone, third describe change the arc of the shaft (body). Next modes describing more complex deformations, e.g. fourth mod describe change the position of the

In this experiment the value of average error for reconstructed geometry of the bone was

Study of the value of the coefficients, give us additional information about the analyzed bones. For presented database we can found, correlation between coefficient value of first mode and gender. Negative coefficient value "-" of first mode is connected with female bones (one exception bone nr 8), when positive coefficient value "+" describe male bones

greater trochanter and lesser trochanter, also thickness of the shaft (body).

equal 0,3mm (reconstruction done with using of 14 modes).

database, base grid on geometry of the new objects.

**4.2.3 Results of 3D PCA analysis – Femur bones** 

Fig. 27. Triangle surface grid of femur bone.

the mean object, fifteen modes and coefficients.

nodes, 30 thousands elements).

calculations.

(Fig. 29.).

(Fig. 26.).


Table 4. Participation of the modes in decomposition.


Fig. 28. 3D visualization of mean value and first eight modes of femur bones (for each bone the anterior and posterior view is shown).

Extraction of 3D Geometrical Features of

**empirical modes database** 

this method more common.

CAD system.

**4.3.1 Alghorithm of the reconstruction method** 

Fig. 31. Algorithm of the reconstruction method.

[Milickovic N. at al. 2000, Russacof D. B. 2003] from database.

Biological Objects with 3D PCA Analysis and Applications of Results 105

Another advantage of property of real 3D anthropometric database is possibility of using this information as the "knowledge base". Knowledge base is necessary for the reconstruction of 3D geometry, basing on few RTG images (e.g. two or three ,depends from complication of the object shape). Method developed by authors [Rychlik M., 2004, Rychlik M. at al., 2005] can be used instead of CT images processing. The result of the reconstruction is 3D virtual model which can be used for develop individual prosthesis. The high accuracy (comparison with CT and contact 3D scanners) and low costs, making

The Algorithm of the method is following (Fig. 31.). Searched three-dimensional object are represented by the set of RTG images (minimum two images from different directions). These RTG images are compared with DRR - Digitally Reconstructed Radiographs

Data base includes DRR images and set of the modes and coefficients. Modes and coefficients are received from Principal Component Analysis. After comparison of images, the most similar objects from database are selected. In the next step we manipulate the coefficients of modes as long as the minimization of the mean square deviation of the images RTG and DRR is accomplished. Finally we receive reconstructed 3D model in

**4.3 Reconstruction method of 3D geometry of the bones basis on RTG images and** 

Fig. 29. Correlation between coefficient value of first mode and gender: the negative value "-" is correlated to female bone, positive value "+" is associated with male bones.

Other interesting feature of coefficients is individual set of coefficients values for each bone. This aspect is similar to "fingers prints". Because each bone have another geometry also they have individual set of coefficient values. On Figure 30 is presented graphs of coefficient values and visualization of the geometry for three different bones.

Fig. 30. Correlation between coefficient value and geometry of the bone for three different femur bones (all pictures of bones are made in the same scale).

Male bones

Fig. 29. Correlation between coefficient value of first mode and gender: the negative value

Other interesting feature of coefficients is individual set of coefficients values for each bone. This aspect is similar to "fingers prints". Because each bone have another geometry also they have individual set of coefficient values. On Figure 30 is presented graphs of coefficient

Fig. 30. Correlation between coefficient value and geometry of the bone for three different

femur bones (all pictures of bones are made in the same scale).

"-" is correlated to female bone, positive value "+" is associated with male bones.

values and visualization of the geometry for three different bones.

Female bones

#### **4.3 Reconstruction method of 3D geometry of the bones basis on RTG images and empirical modes database**

Another advantage of property of real 3D anthropometric database is possibility of using this information as the "knowledge base". Knowledge base is necessary for the reconstruction of 3D geometry, basing on few RTG images (e.g. two or three ,depends from complication of the object shape). Method developed by authors [Rychlik M., 2004, Rychlik M. at al., 2005] can be used instead of CT images processing. The result of the reconstruction is 3D virtual model which can be used for develop individual prosthesis. The high accuracy (comparison with CT and contact 3D scanners) and low costs, making this method more common.

## **4.3.1 Alghorithm of the reconstruction method**

The Algorithm of the method is following (Fig. 31.). Searched three-dimensional object are represented by the set of RTG images (minimum two images from different directions). These RTG images are compared with DRR - Digitally Reconstructed Radiographs [Milickovic N. at al. 2000, Russacof D. B. 2003] from database.

Data base includes DRR images and set of the modes and coefficients. Modes and coefficients are received from Principal Component Analysis. After comparison of images, the most similar objects from database are selected. In the next step we manipulate the coefficients of modes as long as the minimization of the mean square deviation of the images RTG and DRR is accomplished. Finally we receive reconstructed 3D model in CAD system.

Fig. 31. Algorithm of the reconstruction method.

Extraction of 3D Geometrical Features of

Number of the mode

Table 5. Participation of the modes in reconstruction.

Fig. 33. Three dimensional visualization of 11 modes.

about 0,11% and surface difference is 0,95%.

To verify the quality of the reconstruction, the anthropometric measurements [Berry J. L., 1987] of the reconstructed vertebra was done. Average inaccuracy of the reconstruction is about 0,25 mm (~1%). Volume differences between searched and reconstructed vertebra is

Biological Objects with 3D PCA Analysis and Applications of Results 107

1 60,7418270 60,7418270 2 18,7637347 79,5055617 3 8,0275130 87,5330747 4 7,5452177 95,0782924 5 1,1870943 96,2653867 6 0,9569025 97,2222892 7 0,6885226 97,9108118 8 0,5571059 98,4679177 9 0,5541704 99,0220881 10 0,5054029 99,5274910 11 0,4725086 99,9999996 12 0,0000002 99,9999998 13 0,0000001 99,9999999

Total participation of the modes [%]

Participation of the mode [%]

## **4.3.2 Input data – Artifical database**

The database used in experiment contains 99 lumbar vertebra's (Fig. 32.). Each vertebra has different geometry, and is described by FEM grid with the same structure (616 nodes, 2000 elements).


Fig. 32. Data base: DDR images (left side), 3D CAD models (right side).

## **4.3.3 Results of 3D PCA analysis – Vertebra bones**

For this database the Principal Component Analysis was done. The result of this operation is the mean object, 11 modes and coefficients.

The first five modes include 96% of information about reconstructed geometry (Table 5.). Modes: twelfth and others contain very low information (this is only a numerical noise) and they aren't used for further reconstruction.

Modes describe the features of the vertebras (Fig. 33.). The first and fourth mode describe the deformation of the vertebral body, the second, third and seventh mode represent the deformation of the spinosus process. Other modes describe the deformation of the transverse process.

To verify this method the new vertebra has been made. It is deformed by three features (spinous process, vertebral body, transverse process) but has completely new values (there is no similar shape in data base).

In the next step we compare the DRR images of the searched and created vertebra and manipulate of the coefficients of modes. To compute the values of coefficients for all modes Jacobi criterion was used.

The final result of this experiment is the solid CAD model (Fig. 34.) and FEM grid.

The database used in experiment contains 99 lumbar vertebra's (Fig. 32.). Each vertebra has different geometry, and is described by FEM grid with the same structure (616 nodes, 2000

Fig. 32. Data base: DDR images (left side), 3D CAD models (right side).

For this database the Principal Component Analysis was done. The result of this operation is

The first five modes include 96% of information about reconstructed geometry (Table 5.). Modes: twelfth and others contain very low information (this is only a numerical noise) and

Modes describe the features of the vertebras (Fig. 33.). The first and fourth mode describe the deformation of the vertebral body, the second, third and seventh mode represent the deformation of the spinosus process. Other modes describe the deformation of the

To verify this method the new vertebra has been made. It is deformed by three features (spinous process, vertebral body, transverse process) but has completely new values (there

In the next step we compare the DRR images of the searched and created vertebra and manipulate of the coefficients of modes. To compute the values of coefficients for all modes

The final result of this experiment is the solid CAD model (Fig. 34.) and FEM grid.

**4.3.3 Results of 3D PCA analysis – Vertebra bones** 

the mean object, 11 modes and coefficients.

they aren't used for further reconstruction.

transverse process.

is no similar shape in data base).

Jacobi criterion was used.

**4.3.2 Input data – Artifical database** 

elements).


Table 5. Participation of the modes in reconstruction.


Fig. 33. Three dimensional visualization of 11 modes.

To verify the quality of the reconstruction, the anthropometric measurements [Berry J. L., 1987] of the reconstructed vertebra was done. Average inaccuracy of the reconstruction is about 0,25 mm (~1%). Volume differences between searched and reconstructed vertebra is about 0,11% and surface difference is 0,95%.

Extraction of 3D Geometrical Features of

face veins is suggested.

populations or ages.

the biological objects.

Component Analysis.

method is non-invasive and non-destructive.

**6. Future directions of research** 

Biological Objects with 3D PCA Analysis and Applications of Results 109

Presented method was tested onto very specific group of data – faces of twins. Results of this analysis, was confirmed that even for very similar monozygotic twins faces (which can be very difficult for distinguish by human visual perception) the numerical ID – code of each face, was different and individual. Trends curves of coefficient values of modes have general the same trajectory but in local comparison still they are different. Them bigger difference between faces them larger distance between trend curves. For comparison of two faces of different twins the trend curves are completely different – analogical like for two different persons. The basic input information for PCA, not necessary must be limited only to geometry of the object, but can be enlarged by additional information's (e.g. thermal images) into multi-dimensional database. In presented paper the 2D infrared images of faces was added to the basic database. Also this data can be coded and used as a thermal faceprint. Big disadvantage of thermal images of face surface is strong influence of environment temperature. As the more stabile and independent from temperature of atmosphere, the system based on thermal images of

Second presented application of 3D PCA analysis is anthropometrics. 3D PCA make possible extraction of mean shape and geometrical features of biological objects set. Mean shape characterize all 3D body (not only few 2D dimensions, like it is, in traditional anthropometric database). Features are describing principal deformations of analyzed group of objects (bones). This method can be used to create of full three dimensional anthropometric database of the skeleton system. One of advantages of that three dimensional anthropometric database, is possibility of measured any necessary dimensions on the surface of the mean bone. Mean shape and geometrical features (knowledge about shape and trends of deformations) can be used for developing new, more useful types of prosthesis. Such 3D anthropometrics analysis also can be important in anthropology, gives us information about the changes that appear in the human skeletal structure in different

As a third application the method of reconstruction of three-dimensional shape of biological object was presented. The reconstructed geometry is compatible with CAD systems. Reconstruction algorithm, developed by authors, is based on the few 2D RTG images and knowledge about object geometry recorded in empirical database. Presented method use full volume information from RTG images and can be used not only for reconstruction of

Accuracy of the method is higher than reconstructions based on CT-imagining and comparable with 3D scanners (about 0,3 mm). Important characteristic of presented method is the automation of searching of the solution (elimination of landmarks) and that this

Based onthe resultsof analysis presented above, in the following chapter authors propose further directions of researches. This work would have to expand possibilities of existing 3DPCA and to examine other methods of statistical analysis, such as: ICA-Independent

Fig. 34. Correlated images (from left): RTG image of searched object, DRR image of created (deformed) model, image of CAD solid model searched vertebra (left side) & reconstructed vertebra (right side).

## **5. Conclusions**

Many modern methods and techniques known from classic mechanics and engineering solutions, they are applicable in many other disciplines of knowledge. One of such new "beneficent" is biological branch of knowledge. In presented research authors concentrate attention on present several applications of three-dimensional version of Principal Component Analysis in biological cases. However to describe geometry of 3D objects the numerous modal methods can be used; only empirical modes gives an optimal statistical database. Empirical modes, represent features of the objects composed in database. Characters of features are dependent from frequent occurrence in population.

The first presented application of 3D PCA is biometrics. Many security systems need ID key, which will be fast and guarantees high level of protection. The 3D PCA make possible using 3D faces as the access code (Faceprint). Each face has individual set of coefficient values – unique face code. That information (code) can be easily recorded onto electronic ID card – similar to 2D biometric data's. Presented method as the source of data-input, apply cheap non-contact measurement method and full 3D face information – instead of "control" points set (few nodal points in "golden triangle" area). The 3D geometry of the face (3D faceprint) is more complicated than "flat" image and by this way more proof onto fake, than 2D face recognition systems. Other advantage of this method is automatically receiving unauthorized attempt (face of unauthorized persons) without require specialist decipher. For results interpretation of verification procedure, any special equipment or knowledge is not necessary. Results of verification can be understanding for everybody (without special training) and used immediately as the image or 3D model, for further analysis, e.g.: in police departments or other 3D modeling.

Fig. 34. Correlated images (from left): RTG image of searched object, DRR image of created (deformed) model, image of CAD solid model searched vertebra (left side) & reconstructed

Many modern methods and techniques known from classic mechanics and engineering solutions, they are applicable in many other disciplines of knowledge. One of such new "beneficent" is biological branch of knowledge. In presented research authors concentrate attention on present several applications of three-dimensional version of Principal Component Analysis in biological cases. However to describe geometry of 3D objects the numerous modal methods can be used; only empirical modes gives an optimal statistical database. Empirical modes, represent features of the objects composed in database.

The first presented application of 3D PCA is biometrics. Many security systems need ID key, which will be fast and guarantees high level of protection. The 3D PCA make possible using 3D faces as the access code (Faceprint). Each face has individual set of coefficient values – unique face code. That information (code) can be easily recorded onto electronic ID card – similar to 2D biometric data's. Presented method as the source of data-input, apply cheap non-contact measurement method and full 3D face information – instead of "control" points set (few nodal points in "golden triangle" area). The 3D geometry of the face (3D faceprint) is more complicated than "flat" image and by this way more proof onto fake, than 2D face recognition systems. Other advantage of this method is automatically receiving unauthorized attempt (face of unauthorized persons) without require specialist decipher. For results interpretation of verification procedure, any special equipment or knowledge is not necessary. Results of verification can be understanding for everybody (without special training) and used immediately as the image or 3D model, for further analysis, e.g.: in police

Characters of features are dependent from frequent occurrence in population.

vertebra (right side).

**5. Conclusions** 

departments or other 3D modeling.

Presented method was tested onto very specific group of data – faces of twins. Results of this analysis, was confirmed that even for very similar monozygotic twins faces (which can be very difficult for distinguish by human visual perception) the numerical ID – code of each face, was different and individual. Trends curves of coefficient values of modes have general the same trajectory but in local comparison still they are different. Them bigger difference between faces them larger distance between trend curves. For comparison of two faces of different twins the trend curves are completely different – analogical like for two different persons. The basic input information for PCA, not necessary must be limited only to geometry of the object, but can be enlarged by additional information's (e.g. thermal images) into multi-dimensional database. In presented paper the 2D infrared images of faces was added to the basic database. Also this data can be coded and used as a thermal faceprint. Big disadvantage of thermal images of face surface is strong influence of environment temperature. As the more stabile and independent from temperature of atmosphere, the system based on thermal images of face veins is suggested.

Second presented application of 3D PCA analysis is anthropometrics. 3D PCA make possible extraction of mean shape and geometrical features of biological objects set. Mean shape characterize all 3D body (not only few 2D dimensions, like it is, in traditional anthropometric database). Features are describing principal deformations of analyzed group of objects (bones). This method can be used to create of full three dimensional anthropometric database of the skeleton system. One of advantages of that three dimensional anthropometric database, is possibility of measured any necessary dimensions on the surface of the mean bone. Mean shape and geometrical features (knowledge about shape and trends of deformations) can be used for developing new, more useful types of prosthesis. Such 3D anthropometrics analysis also can be important in anthropology, gives us information about the changes that appear in the human skeletal structure in different populations or ages.

As a third application the method of reconstruction of three-dimensional shape of biological object was presented. The reconstructed geometry is compatible with CAD systems. Reconstruction algorithm, developed by authors, is based on the few 2D RTG images and knowledge about object geometry recorded in empirical database. Presented method use full volume information from RTG images and can be used not only for reconstruction of the biological objects.

Accuracy of the method is higher than reconstructions based on CT-imagining and comparable with 3D scanners (about 0,3 mm). Important characteristic of presented method is the automation of searching of the solution (elimination of landmarks) and that this method is non-invasive and non-destructive.

## **6. Future directions of research**

Based onthe resultsof analysis presented above, in the following chapter authors propose further directions of researches. This work would have to expand possibilities of existing 3DPCA and to examine other methods of statistical analysis, such as: ICA-Independent Component Analysis.

Extraction of 3D Geometrical Features of

Tennessee.

Tennessee.

05-924-0.

Machine Intelligence.

Mainguet J-F. Biometrics, (2004), URL:

45, pp. 2787-2800.

Mechanical Engineering.

Applications (CVBVS 2000), pp 5-14.

2003, Image Processing, Proceedings SPIE Vol. 5032.

work, Poznań University of Technology, Poznan Poland.

Computer Science, vol. 1131, Hamburg

*and symmetry,* Cambridge University Press.

Biological Objects with 3D PCA Analysis and Applications of Results 111

Berry J. L., Moran J. M., Berg W. S.,Steffee A. D., (1987), *A morphometric study of human* 

Bro-Nielsen, M., Gramkow, C., (1996), *Fast fluid registration of medical images*, In: Proc.

Holmes P., Lumley J. L., Berkooz G., (1996),*Turbulence, coherent, structures dynamical systems* 

Holmes, P., Lumley, J., L., Berkooz, G., (1998), *Turbulence, Coherent Structures, Dynamical Systems and Symmetry*, Cambridge University Press, Cambridge, New Edition. Jain A.K., Ross A. and Pankanti S., (1999) , *A Prototype Hand Geometry-based Verification* 

Biometric Person Authentication (AVBPA), (Washington D.C.), pp.166-171. Jantz, R.L. and P.H. Moore-Jansen, (1988), *A Data Base for Forensic Anthropology: Structure,* 

http://pagesperso-orange.fr/fingerchip/biometrics/biometrics.htm Milickovic N., Baltas D., Giannouli S., Lahanas M., Zamboglou N., (2000)*CT imaging based* 

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Rychlik M., (2004), Original title In Polish: *Metoda odtwarzania złożonych kształtów* 

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Sanchez-Reillo R., Sanchez-Avila and Gonzales-Marcos A., (2000), *Biometric Identification* 

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Department of Defense United States of America, Washington D.C.

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*System*, Proceedings of 2nd International Conference on Audio- and Video-based

*Content and Analysis,* Report of Investigations no 47. Knoxville, TN: University of

*digitally reconstructed radiographs and its application in brachytherapy*. Phys. Med. Biol.

*Skeletal Material*. Report of Investigations no 48. Knoxville, TN: University of

*from global non-parallel flow stability analysis*, Computer Methods Applied in

Workshop on Computer Vision behind the Visible Spectrum: Methods and

*calculation of digitally reconstructed radiographs using light fields,* Medical Imagining

*przestrzennych dla systemów CAD, przy zredukowanej ilości danych pomiarowych*, PhD

*geometry reconstruction of 3D objects*, Proceedings of the 10th. International Conference Mathematical Modeling and Analysis, Vilnius, pp 123-128. ISBN 9986-

*Through Hand Geometry Measurements*, IEEE Transactions on Pattern Analysis and

*lumbar and selected thoracic vertebrae,*Spine, Volume 12, Number 4.

For application of PCA in 3D biometric systems the unified system of data recording (included areas of measurements) must develop. Furthermore, the optimal data acquisition process should be clearly defined for obtain highest accuracy level of measurement during the shortest time and the maximum simplification of the measuring equipment. An important element that should be subjected to further testing is the issue of facial expressions of the subjects. This aspect strongly influence on the obtained results. Also study of the influence of other objects such as glasses, beard, hat, etc., on the results should be examined. Considering the three-dimensional biometric system can be interesting to increase the number of dimensions included in the analysis of the PCA. Such additional information may be infrared images. However in this case, user must remember about strong impact of the ambient temperature on the obtained results. One solution to this problem may be the use of thermal images containing the facial structure of blood vessels.

Development of the PCA method in the anthropometric application should include the development of precise and effective tool of registration process. This procedure should include the specific areas of individual bones and the anatomical elements of the human body. Very interesting results can provide a PCA analysis of other human organs. Also basic research on the structure of the external shape of human body would have produced very valuable results for the ergonomic environment.

Another direction of development of the above considerations is the method of threedimensional reconstruction of the geometry of the object. Described method basis on the two-dimensional X-ray images and the 3D database generated by PCA analysis. For correct reconstruction is necessary to make set of measurements and analysis, contains: geometry measurements, PCA analysis and verification of reconstruction process performed on the of RTG images. Develop a comprehensive; coherent system for the reconstruction of geometry could allow the significantly spread the use of computer models in everyday medical practice.

## **7. Acknowledgment**

The part of this work was supported under research grant no: N518 496039 from the Polish Ministry of Science 2010-2012.

## **8. References**


For application of PCA in 3D biometric systems the unified system of data recording (included areas of measurements) must develop. Furthermore, the optimal data acquisition process should be clearly defined for obtain highest accuracy level of measurement during the shortest time and the maximum simplification of the measuring equipment. An important element that should be subjected to further testing is the issue of facial expressions of the subjects. This aspect strongly influence on the obtained results. Also study of the influence of other objects such as glasses, beard, hat, etc., on the results should be examined. Considering the three-dimensional biometric system can be interesting to increase the number of dimensions included in the analysis of the PCA. Such additional information may be infrared images. However in this case, user must remember about strong impact of the ambient temperature on the obtained results. One solution to this problem may be the use of thermal images containing the facial structure

Development of the PCA method in the anthropometric application should include the development of precise and effective tool of registration process. This procedure should include the specific areas of individual bones and the anatomical elements of the human body. Very interesting results can provide a PCA analysis of other human organs. Also basic research on the structure of the external shape of human body would have produced very

Another direction of development of the above considerations is the method of threedimensional reconstruction of the geometry of the object. Described method basis on the two-dimensional X-ray images and the 3D database generated by PCA analysis. For correct reconstruction is necessary to make set of measurements and analysis, contains: geometry measurements, PCA analysis and verification of reconstruction process performed on the of RTG images. Develop a comprehensive; coherent system for the reconstruction of geometry could allow the significantly spread the use of computer models in everyday medical

The part of this work was supported under research grant no: N518 496039 from the Polish

Akhloufi, M, Bendada A., 2008,*Infrared Face Recognition Using Distance Transforms*, World Academy of Science, Engineering and Technology Nr 40, pp. 160-163. Anderson, R. J., (2008), *Security Engineering: A Guide to Building Dependable Distributed Systems*, Wiley Publishing Inc., Indiana, USA ISBN-13: 9780470068526. Anil K. J., Prabhakar S., Pankanti S., (2002), *On the Similarity of identical twin fingerprints*, The

Benameur S., Mignote M., Parent S., Labelle H., Skalli W., De Gusie J., (December 2001), *3D* 

*Biplanar Reconstruction of Scoliotic Vertebrae Using Statistical Models.* 20th IEEE International Conference on Computer Vision and Pattern Recognition, CVPR'01,

Journal of Patter Recognition Society Nr 35, pp. 2653 –2663.

of blood vessels.

practice.

**7. Acknowledgment** 

**8. References** 

Ministry of Science 2010-2012.

volume II, pp. 577-582.

valuable results for the ergonomic environment.

http://pagesperso-orange.fr/fingerchip/biometrics/biometrics.htm


**5** 

*Croatia* 

**Mathematical Modelling** 

Ana Tušek and Želimir Kurtanjek

**of Gene Regulatory Networks** 

*Faculty of Food Technology and Biotechnology, University of Zagreb* 

Living cells can be observed as complex dynamical systems that are constantly remodelling themselves as response to changes in their environment (Zak et al., 2005). The cell metabolism includes number of reactions and products of reactions which interact forming a metabolic network. The aim of modern biology is to understand the structure and dynamic

Due to the fact that large amount of date about processes in living cells are being collected every day, it become necessary to use computers for data processing and analysis. Introducing computer technologies into biology new discipline has been develop, systems biology or computational biology. The aim of system biology is describing and understanding how parts of organism interact in one complex system; systems biology aims to develop mathematical model of biological systems by integrating experimental and theoretical techniques (Hecker et al., 2009, Albert, 2004). Systems biology studies biological systems by systematically perturbating them (biologically, genetically or chemically) monitoring the genes, proteins and informational pathway response (Strizh et al., 2007). According to Bruggeman & Westerholl, 2007 a complete systems biology approach requires (i) characterisation of organism molecular composition, (ii) components dynamics (spatial and temporal) and (iii) detail analysis of molecular response to internal

Progress in molecular biology led to development of complete maps of genomes of many organisms; it is also possible to identify and classify proteins. Although the number of completely sequenced genomes is mounting rapidly, our knowledge of transcription regulation is limited to a few model organisms (Janga & Collado-Vides, 2007). The interactive regulation of genes, working together to create gene networks has been considered the origin of many functions of organism (Mochizuki, 2008). Classical molecular method (Northern blotting, reporter genes and DNA footprinting) have provided great insight into regulatory relationship between genes; advancement in genetic experimental technologies DNA microarray analysis provide an effective and efficient way to measure the gene expression levels of up to tens of thousands of genes simultaneously under many different conditions (Xu et al., 2007). The control of the gene transcription is an integrated mechanism involving the interaction of genes and proteins (Knott et al., 2010). Every gene

**1. Introduction** 

of those complex interactions.

and external stimuli.


## **Mathematical Modelling of Gene Regulatory Networks**

Ana Tušek and Želimir Kurtanjek *Faculty of Food Technology and Biotechnology, University of Zagreb Croatia* 

## **1. Introduction**

112 Applied Biological Engineering – Principles and Practice

Syn, M., H-M., Prager, R., W., (1994), *Mesh models for three-dimensional ultrasound imagining*,

Vitek C., (2005), *A comparison in osteological measurements of two populations from East* 

Vranic, D., Saupe, D., (2002), *Description of 3D-shape using a complex function of the sphere*, Department of Computer and Information Science, University of Konstanz. Xiaoguang Lu, (2006), *3D Face Recognition across Pose and Expression*, PhD thesis, Michigan

*Tennessee*, University of Tennessee at Chattanooga.

Cambridge.

State University

CUED/F-INFENG/TR 210, Cambridge University Engineering Department,

Living cells can be observed as complex dynamical systems that are constantly remodelling themselves as response to changes in their environment (Zak et al., 2005). The cell metabolism includes number of reactions and products of reactions which interact forming a metabolic network. The aim of modern biology is to understand the structure and dynamic of those complex interactions.

Due to the fact that large amount of date about processes in living cells are being collected every day, it become necessary to use computers for data processing and analysis. Introducing computer technologies into biology new discipline has been develop, systems biology or computational biology. The aim of system biology is describing and understanding how parts of organism interact in one complex system; systems biology aims to develop mathematical model of biological systems by integrating experimental and theoretical techniques (Hecker et al., 2009, Albert, 2004). Systems biology studies biological systems by systematically perturbating them (biologically, genetically or chemically) monitoring the genes, proteins and informational pathway response (Strizh et al., 2007). According to Bruggeman & Westerholl, 2007 a complete systems biology approach requires (i) characterisation of organism molecular composition, (ii) components dynamics (spatial and temporal) and (iii) detail analysis of molecular response to internal and external stimuli.

Progress in molecular biology led to development of complete maps of genomes of many organisms; it is also possible to identify and classify proteins. Although the number of completely sequenced genomes is mounting rapidly, our knowledge of transcription regulation is limited to a few model organisms (Janga & Collado-Vides, 2007). The interactive regulation of genes, working together to create gene networks has been considered the origin of many functions of organism (Mochizuki, 2008). Classical molecular method (Northern blotting, reporter genes and DNA footprinting) have provided great insight into regulatory relationship between genes; advancement in genetic experimental technologies DNA microarray analysis provide an effective and efficient way to measure the gene expression levels of up to tens of thousands of genes simultaneously under many different conditions (Xu et al., 2007). The control of the gene transcription is an integrated mechanism involving the interaction of genes and proteins (Knott et al., 2010). Every gene

Mathematical Modelling of Gene Regulatory Networks 115

The number of genes in genome can be identified in several ways: (i) by defining open reading frames, (ii) by identifying all the mRNAs (transcriptome) or (iii) by identifying all the proteins (proteome). Due to the fact that some of the genes are presented in more then one copy or are related to one another, the number of different types of genes is less than

Over the past decade genome sequencing has generated large amount of new information. The main goal in sequencing is the identification of molecular and cellular function of all gene products. Interpretation of raw DNA sequences data includes identification and annotation of genes, proteins and metabolic and regulatory pathways (Médigue & Moszer, 2007). Accurate annotation of the human and genome of other organisms is essential for drug discovery (Rust et al., 2002). The mostly used annotation method is sequence homology recognition. According to Yakunin et al., 2004 apart sequence-based method, few others approaches can be used: (i) analysis of temporal, spatial and physiological proteins regulation, (ii) analysis of protein interactions, (iii) analysis of gene neighborhood, (iv) analysis of gene knockout phenotype, (v) analysis of the protein activities, (vi) analysis of

More information about components interaction allows multidimensional annotation; one dimensional annotation includes identification of genes in genome and description of functionality; two dimensional annotation specifies the cellular components and their interactions; three dimensional annotation of genome includes description of intracellular arrangement of chromosome and other cellular components, while four dimensional genome annotation could include changes in genome sequences due to the evolution (Reed et al., 2006). Genome annotation is usually preformed using one of the bioinformatics tools, GLIMMER, GlimmerM and GENSCAN (those programs include gene finding algorithm) or

Taking in account central dogma of molecular biology developed by Francis Crick (transfer of sequence information between different biopolymers: RNA, DNA and proteins) there are three possible places of regulation of production of an active gene; first is the transcriptional regulation, second the translation regulation and the third post-translation or posttranscriptional regulation (Fig.1.). Regulation of gene expression is fundamental for the coordinate synthesis, assembly and localization of the macromolecular structures of cells

Regulation of gene expression at transcriptional level is evolutionary conserved mechanism in all cellular organisms. This process is mediated by physical interactions between transcription factors and *cis*-acting regulatory elements in promoter region of target genes (Janky et al., 2009). During transcription, mRNA is synthesized using mRNA polymerase. This process can be divided in four steps: (i) promoter recognition, (ii) chain initiation, (iii) mRNA chain elongation and (iii) chain termination and regulation can occur at each step. Protein synthesis occurs during the translation process; mRNA is "translated" into specific polypeptide according to rules of tri nucleotide genetic code. This step of protein biosynthesis can also be divided into three parts: (i) initiation, (ii) elongation and (iii) termination. Each of these phases requires a specific group of translocation factors (Day & Tuite, 1998).

BLAST, FASTA and HAMER (sequence-homology search tools) (Reed et al., 2006).

post-translational modifications and (vii) protein structural analysis.

total number of genes.

**2.1 Gene regulation** 

(Halbeisen et al., 2007).

has one or more activators and one or more inhibitors that are regulating the specific gene expression, depending on the situation in the cell and cell environment. The complex network of genes and there activators and/or inhibitors is defined as gene regulatory network. Gene regulatory networks can be very usefully for understanding the organisation within cells, because in gene regulatory networks information form the cell state and the outside environment are translated into correctly timed gene expression (Crombach & Hogeweg, 2008). Gene regulatory networks are usually described as network models where the dependencies between genes are presented by direct graph, in which nodes represent genes, proteins, enzymes or other chemical substances and edges led form a regulator to its target (edges represent transformation, eg. phosphorylation and dephosphorylation, or activation and deactivation)(Wilczynski & Furlog, 2010; Dilão & Muraro, 2010). Ideally, gene regulatory network display flow of information throughout embryogenesis (Hunman et al., 2009). To easily analyse those complex systems, mathematical models of gene regulatory networks have been developed. Mathematical models of gene regulatory networks include set of differential equations, graphical networks, stochastic functions and simulation models. Models can be used for making novel predictions and to plan future experiments.

In this chapter the theory of gene regulatory networks will be presented. The chapter will start with ideas how gene regulatory networks are constructed. There will be data on different types of gene regulatory networks and approaches for modeling those systems. This chapter will try to explain why is the modeling of complex regulatory networks important for genetic engineering and how can the mathematical analysis of gene regulatory networks be used for genetic engineering experiments planning and results interpretation.

## **2. Genes and genome**

The hereditary nature of every living organism is defined by genome. Genome is formed of long sequences of DNA that provide information necessary to construct organism (Lewin, 2004). So genome can be divided into series of DNA sequences called genes. Each gene represents single protein (there is relationship between the base sequences of a gene and the amino acid sequence of the polypeptide whose synthesis directs the gene) (Berg, 2001). Genome of living organism can contain from less than 500 genes (for mycoplasma) to more than 40 000 genes (for human genome) (Table 1).


Table 1. The genome size of some organisms (Lewin, 2004)

has one or more activators and one or more inhibitors that are regulating the specific gene expression, depending on the situation in the cell and cell environment. The complex network of genes and there activators and/or inhibitors is defined as gene regulatory network. Gene regulatory networks can be very usefully for understanding the organisation within cells, because in gene regulatory networks information form the cell state and the outside environment are translated into correctly timed gene expression (Crombach & Hogeweg, 2008). Gene regulatory networks are usually described as network models where the dependencies between genes are presented by direct graph, in which nodes represent genes, proteins, enzymes or other chemical substances and edges led form a regulator to its target (edges represent transformation, eg. phosphorylation and dephosphorylation, or activation and deactivation)(Wilczynski & Furlog, 2010; Dilão & Muraro, 2010). Ideally, gene regulatory network display flow of information throughout embryogenesis (Hunman et al., 2009). To easily analyse those complex systems, mathematical models of gene regulatory networks have been developed. Mathematical models of gene regulatory networks include set of differential equations, graphical networks, stochastic functions and simulation models. Models can be used for making novel predictions and to plan future experiments. In this chapter the theory of gene regulatory networks will be presented. The chapter will start with ideas how gene regulatory networks are constructed. There will be data on different types of gene regulatory networks and approaches for modeling those systems. This chapter will try to explain why is the modeling of complex regulatory networks important for genetic engineering and how can the mathematical analysis of gene regulatory networks be used for genetic engineering experiments planning and results interpretation.

The hereditary nature of every living organism is defined by genome. Genome is formed of long sequences of DNA that provide information necessary to construct organism (Lewin, 2004). So genome can be divided into series of DNA sequences called genes. Each gene represents single protein (there is relationship between the base sequences of a gene and the amino acid sequence of the polypeptide whose synthesis directs the gene) (Berg, 2001). Genome of living organism can contain from less than 500 genes (for mycoplasma) to more

> Phylum Species Genome (bp) Algae *Pyrenomas salina* 6.6 105 Mycoplasma *M. pneumoniae* 1.0 106 Bacterium *E. coli* 4.2 106 Yeast *S. cerevisiae* 1.3 107 Slime mold *D. discoideum* 5.4 107 Nematode *C. elegans* 8.0 107 Insect *D. melanogaster* 1.4 108 Bird *G. domesticus* 1.2 109 Amphibian *X. laevis* 3.1 109 Mammal *H. sapiens* 3.3 109

**2. Genes and genome** 

than 40 000 genes (for human genome) (Table 1).

Table 1. The genome size of some organisms (Lewin, 2004)

The number of genes in genome can be identified in several ways: (i) by defining open reading frames, (ii) by identifying all the mRNAs (transcriptome) or (iii) by identifying all the proteins (proteome). Due to the fact that some of the genes are presented in more then one copy or are related to one another, the number of different types of genes is less than total number of genes.

Over the past decade genome sequencing has generated large amount of new information. The main goal in sequencing is the identification of molecular and cellular function of all gene products. Interpretation of raw DNA sequences data includes identification and annotation of genes, proteins and metabolic and regulatory pathways (Médigue & Moszer, 2007). Accurate annotation of the human and genome of other organisms is essential for drug discovery (Rust et al., 2002). The mostly used annotation method is sequence homology recognition. According to Yakunin et al., 2004 apart sequence-based method, few others approaches can be used: (i) analysis of temporal, spatial and physiological proteins regulation, (ii) analysis of protein interactions, (iii) analysis of gene neighborhood, (iv) analysis of gene knockout phenotype, (v) analysis of the protein activities, (vi) analysis of post-translational modifications and (vii) protein structural analysis.

More information about components interaction allows multidimensional annotation; one dimensional annotation includes identification of genes in genome and description of functionality; two dimensional annotation specifies the cellular components and their interactions; three dimensional annotation of genome includes description of intracellular arrangement of chromosome and other cellular components, while four dimensional genome annotation could include changes in genome sequences due to the evolution (Reed et al., 2006). Genome annotation is usually preformed using one of the bioinformatics tools, GLIMMER, GlimmerM and GENSCAN (those programs include gene finding algorithm) or BLAST, FASTA and HAMER (sequence-homology search tools) (Reed et al., 2006).

## **2.1 Gene regulation**

Taking in account central dogma of molecular biology developed by Francis Crick (transfer of sequence information between different biopolymers: RNA, DNA and proteins) there are three possible places of regulation of production of an active gene; first is the transcriptional regulation, second the translation regulation and the third post-translation or posttranscriptional regulation (Fig.1.). Regulation of gene expression is fundamental for the coordinate synthesis, assembly and localization of the macromolecular structures of cells (Halbeisen et al., 2007).

Regulation of gene expression at transcriptional level is evolutionary conserved mechanism in all cellular organisms. This process is mediated by physical interactions between transcription factors and *cis*-acting regulatory elements in promoter region of target genes (Janky et al., 2009). During transcription, mRNA is synthesized using mRNA polymerase. This process can be divided in four steps: (i) promoter recognition, (ii) chain initiation, (iii) mRNA chain elongation and (iii) chain termination and regulation can occur at each step.

Protein synthesis occurs during the translation process; mRNA is "translated" into specific polypeptide according to rules of tri nucleotide genetic code. This step of protein biosynthesis can also be divided into three parts: (i) initiation, (ii) elongation and (iii) termination. Each of these phases requires a specific group of translocation factors (Day & Tuite, 1998).

Mathematical Modelling of Gene Regulatory Networks 117

important for clinical research. There are few hounded of described post-translation modification; the most common are phosphorylation, ubiquitination, glycosylation, *S*-

When talking about biochemical network they can be divided into three groups: (i) metabolic network-describing chemical transformations between metabolites, (ii) protein networks (signaling networks)-describing protein-protein interaction and (iii) gene networks- describing relationships between genes (Brazhnik et al., 2002, Schlitt & Brazma, 2005). Key differences between regulatory and metabolic networks are listed in the Table 2.

Network feature Metabolic networks Regulatory networks

Limited conversion of *cis*  regulatory sites between closely related species

Adjustable structure, because of the possibility

in the *cis* regulatory sites change binding specificity

Most subnetworks have not been well characterized even in microbial model

Quantitative models can be currently constructed only on a small scale; qualitative discrete network models can be used to study large

Possibly significant in determining both structural features of the network and the overall response of the network to a stimulus

that mutations

organisms

networks

Structure Hazard stochiometry Qualitative statements

conserved across species

Fixed structure in terms of the substrates that a particular enzymes can process

Fairly complete understanding

Quantitative constraint-based models can be constructed at

Relatively small because of the

high concentrations of metabolites involved in most

Table 2. Differences between regulatory and metabolic networks (Herrgård et al., 2004)

Gene regulatory networks regulate the expression of thousands of genes. It can be sad that gene regulatory networks are maps of the interactions between regulatory gene products and their *cis* regulatory elements (gene and gene products interact and form networks), as well between signaling ligand and their receptor. So, basic functional unit of gene regulatory network is promoter region of a gene or operon which contains *cis* regulatory binding site for transcription factors, The location of binding sites and affinity of transcription factors

of most subsystems in microbial organisms

the genome-scale

reactions

determinate the level of gene expression (Herrgård et al., 2004) (Fig. 2).

nitrosylation, proteolysis and methylation (Egorina et al., 2008).

Evolutionary conservation Enzyme sequences highly

**3. Gene regulatory networks** 

Malleability

Level of biochemical characterization

Modelling approaches

Role of noise

Fig. 1. Gene expression (http://csls-text.c.u-tokyo.ac.jp/active/04\_03.html)

Translation initiation includes events that lead to positioning of 80S ribosome at the start codon of mRNA. Translation rates are primarily regulated at initiation level involving large number of initiation factors (Macdonald, 2001). The amount of mRNA available for translation can be changed at different steps of RNA maturation. Two families of proteins (the RNA binding proteins and RNA helicases) determinate the fate of pre-mRNAs and mRNA by regulating steps from transcription to translation (Mazzucotell et al., 2008). Translation control is critical in regulating wide range of process in cells form development, cell differentiation and proliferation to regulation of metabolic pathways. It is also important for protection of cell from external effects (Garcia-Sanz et al., 1998).

Transcription and translation regulation mechanisms are till now described in literature quite detail, but there is still only few data of post-transcriptional and post-translational regulation mechanism. Due to the fact that large number of RNA molecules is being synthesis in the cell, the precise post-transcriptional regulation is necessary to control the activity and location of produced RNA molecules. This mechanism is controlled by RNAbinging proteins (Halbeisen et al., 2007). Post-transcriptional regulations of gene expression occur at the levels of pre-messenger RNA (mRNA) processing (capping, splicing, and polyadenylation), mRNA stability, and mRNA translation (Floris et al., 2009). The last level of gene expression control is the post-translational regulation. This step is responsible for controlling the levels of protein activity. Post-translation protein modifications are important for clinical research. There are few hounded of described post-translation modification; the most common are phosphorylation, ubiquitination, glycosylation, *S*nitrosylation, proteolysis and methylation (Egorina et al., 2008).

## **3. Gene regulatory networks**

116 Applied Biological Engineering – Principles and Practice

Fig. 1. Gene expression (http://csls-text.c.u-tokyo.ac.jp/active/04\_03.html)

for protection of cell from external effects (Garcia-Sanz et al., 1998).

Translation initiation includes events that lead to positioning of 80S ribosome at the start codon of mRNA. Translation rates are primarily regulated at initiation level involving large number of initiation factors (Macdonald, 2001). The amount of mRNA available for translation can be changed at different steps of RNA maturation. Two families of proteins (the RNA binding proteins and RNA helicases) determinate the fate of pre-mRNAs and mRNA by regulating steps from transcription to translation (Mazzucotell et al., 2008). Translation control is critical in regulating wide range of process in cells form development, cell differentiation and proliferation to regulation of metabolic pathways. It is also important

Transcription and translation regulation mechanisms are till now described in literature quite detail, but there is still only few data of post-transcriptional and post-translational regulation mechanism. Due to the fact that large number of RNA molecules is being synthesis in the cell, the precise post-transcriptional regulation is necessary to control the activity and location of produced RNA molecules. This mechanism is controlled by RNAbinging proteins (Halbeisen et al., 2007). Post-transcriptional regulations of gene expression occur at the levels of pre-messenger RNA (mRNA) processing (capping, splicing, and polyadenylation), mRNA stability, and mRNA translation (Floris et al., 2009). The last level of gene expression control is the post-translational regulation. This step is responsible for controlling the levels of protein activity. Post-translation protein modifications are When talking about biochemical network they can be divided into three groups: (i) metabolic network-describing chemical transformations between metabolites, (ii) protein networks (signaling networks)-describing protein-protein interaction and (iii) gene networks- describing relationships between genes (Brazhnik et al., 2002, Schlitt & Brazma, 2005). Key differences between regulatory and metabolic networks are listed in the Table 2.



Gene regulatory networks regulate the expression of thousands of genes. It can be sad that gene regulatory networks are maps of the interactions between regulatory gene products and their *cis* regulatory elements (gene and gene products interact and form networks), as well between signaling ligand and their receptor. So, basic functional unit of gene regulatory network is promoter region of a gene or operon which contains *cis* regulatory binding site for transcription factors, The location of binding sites and affinity of transcription factors determinate the level of gene expression (Herrgård et al., 2004) (Fig. 2).

Mathematical Modelling of Gene Regulatory Networks 119

As mentioned before, gene regulatory networks are becoming more and more usefully tool for analysis and understanding organization within cells and their dynamics (Crombach & Hogeweg, 2008). To better understand the complex process in gene regulatory networks, mathematical models of those systems have been developed. Mathematical models are very useful for predicting the effect of nonlinear interactions (Smolen et al., 2000) and can provide insight into systems understanding of regulation of processes in the cell (Zak et al., 2005). Gene regulatory networks are modelled as networks composed of nodes representing genes, proteins or metabolites and edges representing molecular interactions (proteinprotein, DNA-protein or relationships between genes) (Hecker et al., 2009). The biggest problem in a field of mathematical modelling of gene regulatory networks is still in development of model based on experimental data because it is very difficult to defining the quality of available experimental data. There are many approaches for defining gene regulatory networks identification; in the most general manner we can defer unstructured and structured approach (Zak et al., 2005). In unstructured modelling approach there is assumption that every gene regulates every other gene. Using additional domain knowledge it is possible to develop structured model. Subcellular structure, nuclear connectivity and dynamical model structure have to be taken into consideration when

Fig. 3. (a) Unstructured and (b) structured gene regulatory network modelling

**4. Mathematical modelling of gene regulatory network** 

developing structured model (Fig 3).

(Zak et al., 2005)

Gene regulatory maps display flow of regulatory information throughout embryogenesis (Hinman et al., 2009). Gene network analysis provides many important information:


Fig. 2. Genomic view of gene regulatory network. From genomic perspective transcriptional regulation can be presented as an interplay between *cis*-regulatory elements and different transcription factors (Janga & Collado-Vides, 2007)

The activity of functional genes is influenced by few factors: transcriptional factors and cofactor that effects transcription, by degradation of proteins and transcripts and by posttranslational modifications (Hecker et al., 2009). The idea of gene regulatory network is to describe dependence between molecules included in gene activity. Gene regulatory network is composed of nodes (representing genes proteins or metabolites) and edges (representing molecular interactions) (Hecker et al., 2009). Identification of gene regulatory networks is based on deterministic models of gene expression (Cinquemani et al., 2008).

The architecture of gene regulatory networks arise directly form DNA sequences of the genome and representation of gene regulatory networks must have specific emphasis on predicted DNA inputs and it has to be viewable at a number of different levels (Longabaugh et al., 2008). Identifying gene networks from large-scale dataset measurements is a difficult computational and experimental problem (Tegnér & Björkegren, 2006).

Gene regulatory maps display flow of regulatory information throughout embryogenesis

Fig. 2. Genomic view of gene regulatory network. From genomic perspective transcriptional regulation can be presented as an interplay between *cis*-regulatory elements and different

The activity of functional genes is influenced by few factors: transcriptional factors and cofactor that effects transcription, by degradation of proteins and transcripts and by posttranslational modifications (Hecker et al., 2009). The idea of gene regulatory network is to describe dependence between molecules included in gene activity. Gene regulatory network is composed of nodes (representing genes proteins or metabolites) and edges (representing molecular interactions) (Hecker et al., 2009). Identification of gene regulatory networks is

The architecture of gene regulatory networks arise directly form DNA sequences of the genome and representation of gene regulatory networks must have specific emphasis on predicted DNA inputs and it has to be viewable at a number of different levels (Longabaugh et al., 2008). Identifying gene networks from large-scale dataset measurements is a difficult

based on deterministic models of gene expression (Cinquemani et al., 2008).

computational and experimental problem (Tegnér & Björkegren, 2006).

(Hinman et al., 2009). Gene network analysis provides many important information:

1. gene network provides information to help annotate genome

3. it provides new idea to treat some diseases (Liu et al., 2006).

2. it helps to uncover the biochemical network in a cell

transcription factors (Janga & Collado-Vides, 2007)

#### **4. Mathematical modelling of gene regulatory network**

As mentioned before, gene regulatory networks are becoming more and more usefully tool for analysis and understanding organization within cells and their dynamics (Crombach & Hogeweg, 2008). To better understand the complex process in gene regulatory networks, mathematical models of those systems have been developed. Mathematical models are very useful for predicting the effect of nonlinear interactions (Smolen et al., 2000) and can provide insight into systems understanding of regulation of processes in the cell (Zak et al., 2005). Gene regulatory networks are modelled as networks composed of nodes representing genes, proteins or metabolites and edges representing molecular interactions (proteinprotein, DNA-protein or relationships between genes) (Hecker et al., 2009). The biggest problem in a field of mathematical modelling of gene regulatory networks is still in development of model based on experimental data because it is very difficult to defining the quality of available experimental data. There are many approaches for defining gene regulatory networks identification; in the most general manner we can defer unstructured and structured approach (Zak et al., 2005). In unstructured modelling approach there is assumption that every gene regulates every other gene. Using additional domain knowledge it is possible to develop structured model. Subcellular structure, nuclear connectivity and dynamical model structure have to be taken into consideration when developing structured model (Fig 3).

Fig. 3. (a) Unstructured and (b) structured gene regulatory network modelling (Zak et al., 2005)

Mathematical Modelling of Gene Regulatory Networks 121

1. clustering coefficients - for node *i* in a network with *ki* edges connecting it to the nearest

 1 2 *ii <sup>i</sup> kk*

were *n* represents the number of edges between nearest neighbours. *Ci* can have numerical values between 0 and 1. When *Ci*=0 node is linked to disconnected group,

2. network diameter – is defined as the smallest number of the links by which starting

Ciliberti et al., 2007 analysed relationship between robustness and network topology for millions of networks with different topologies. Results showed that significantly different network architecture can show the same gene expression patterns. It was also noticed that some networks are highly robust to gene expression noise and mutations whereas some are quite fragile. Crombach & Hogeweg, 2008 analysed the evolution of gene regulatory networks. Their results showed that interplay between long term evolution process and short term gene regulation dynamics leads to increase in efficiency of crating adapted

3. degree distribution – is probability *P(k)* that a node has *k* links (Lukashin et al., 2003).

*<sup>n</sup> <sup>C</sup>* (1)

neighbours, the clustering coefficient is defined with Eq. 1.

and when *Ci*=1 node is connected to interlinked group.

from one node another node can be reached

Fig. 5. Network growth model (Lukashin et al., 2003)

offspring.

Mathematical sciences can contribute to biology in field of models diversity. Different types of cell are developed as a consequence of the gene activity which is under control of gene regulatory network (Fig. 4) (Mochizuki, 2008).

Fig. 4. Example of gene regulatory network (Mochizuki, 2008)

When developing model two facts have too be taken into account: (i) gene expression levels are regulated by the combined action of multiple gene products, (ii) the number of measurements is relatively small compared to the number of measured genes and measures noise has to be taken into account (van Someren et al., 2002). According to Schlitt & Brazma, 2005 gene networks models can be divided into four groups according to increasing level of detail in the models: (i) part lists, (ii) topology models, (iii) control logic models, (iv) dynamic models.

All mentioned approaches face the same two problems which make the automatic discovery of gene networks form experimental data far form trivial (van Someren et al., 2002). The first is statistical robustness and the second biological interpretation of the results (how to differ regulation form co-expression and indirect regulation form direct regulation) (Lulli & Romauch, 2009). When talking about statistical robustness the focus is the fact that highdimensionality problem cusses the hypothetical models to be highly susceptible (number of microarray experiments is usually much smaller that number of genes included into network) (Chan et al., 2008).

## **4.1 Parts list**

The first step in developing gene regulatory network is construction of a part list of the components included into network (Hu et al., 2010). High-throughput genome sequencing project have made available complete genomic lists of many organism (Alm & Arkin, 2003). Those lists include genes, transcriptional factors, promoters, binding sites and many other molecules important for functioning of gene network (Schlitt & Brazma, 2007).

## **4.2 Topology models**

After defining the components of the gene networks, the next step of the modelling of the gene regulatory network is definition of the connections between nodes (definition of the edges). Development of network topology includes decision about genes are included into the networks, which acts as inhibitors or activator of transcription (Mendes et al., 2003). The different topology classes of networks (regular lattice, small-world, random networks…) are consequence of different ways how large sets of elements are connected (Gonçalves & Costa, 2008). Network growth model is present in Fig. 5. To quantitatively describe a network topology at minimum three metrics are employed:

Mathematical sciences can contribute to biology in field of models diversity. Different types of cell are developed as a consequence of the gene activity which is under control of gene

When developing model two facts have too be taken into account: (i) gene expression levels are regulated by the combined action of multiple gene products, (ii) the number of measurements is relatively small compared to the number of measured genes and measures noise has to be taken into account (van Someren et al., 2002). According to Schlitt & Brazma, 2005 gene networks models can be divided into four groups according to increasing level of detail in the models: (i) part lists, (ii) topology models, (iii) control logic models, (iv)

All mentioned approaches face the same two problems which make the automatic discovery of gene networks form experimental data far form trivial (van Someren et al., 2002). The first is statistical robustness and the second biological interpretation of the results (how to differ regulation form co-expression and indirect regulation form direct regulation) (Lulli & Romauch, 2009). When talking about statistical robustness the focus is the fact that highdimensionality problem cusses the hypothetical models to be highly susceptible (number of microarray experiments is usually much smaller that number of genes included into

The first step in developing gene regulatory network is construction of a part list of the components included into network (Hu et al., 2010). High-throughput genome sequencing project have made available complete genomic lists of many organism (Alm & Arkin, 2003). Those lists include genes, transcriptional factors, promoters, binding sites and many other

After defining the components of the gene networks, the next step of the modelling of the gene regulatory network is definition of the connections between nodes (definition of the edges). Development of network topology includes decision about genes are included into the networks, which acts as inhibitors or activator of transcription (Mendes et al., 2003). The different topology classes of networks (regular lattice, small-world, random networks…) are consequence of different ways how large sets of elements are connected (Gonçalves & Costa, 2008). Network growth model is present in Fig. 5. To quantitatively describe a network

molecules important for functioning of gene network (Schlitt & Brazma, 2007).

regulatory network (Fig. 4) (Mochizuki, 2008).

dynamic models.

**4.1 Parts list** 

network) (Chan et al., 2008).

**4.2 Topology models** 

topology at minimum three metrics are employed:

Fig. 4. Example of gene regulatory network (Mochizuki, 2008)

1. clustering coefficients - for node *i* in a network with *ki* edges connecting it to the nearest neighbours, the clustering coefficient is defined with Eq. 1.

$$C\_i = \frac{2n}{k\_i(k\_i - 1)}\tag{1}$$

were *n* represents the number of edges between nearest neighbours. *Ci* can have numerical values between 0 and 1. When *Ci*=0 node is linked to disconnected group, and when *Ci*=1 node is connected to interlinked group.


Fig. 5. Network growth model (Lukashin et al., 2003)

Ciliberti et al., 2007 analysed relationship between robustness and network topology for millions of networks with different topologies. Results showed that significantly different network architecture can show the same gene expression patterns. It was also noticed that some networks are highly robust to gene expression noise and mutations whereas some are quite fragile. Crombach & Hogeweg, 2008 analysed the evolution of gene regulatory networks. Their results showed that interplay between long term evolution process and short term gene regulation dynamics leads to increase in efficiency of crating adapted offspring.

Mathematical Modelling of Gene Regulatory Networks 123

Continuous models give more realistic description of the process, but development of those models requires large amounts of experimental data. As mentioned before in Boolean models at each time point the gene state depends on the state of the gene regulators at

Some modification of traditional Boolean gene regulatory network models can be found in literature. One of them is temporal Boolean network. The difference between those two network models is in the fact temporal Boolean network allows the state of gene at time *t+1* depends on state of genes at times *t*, *t-1*,….., *t-(T-1)*(Silvescu & Honavar, 2001). Another approach is propped by Shulevich et al, 2002; probabilistic Boolean network. Probabilistic Boolean network includes properties of Boolean networks (rule-based dependence between genes), but due to the probabilistic nature this approach is suitable for systematic study of

Petri net theory provides graphical notation with mathematical background. A Petri net is directed, bipartite and labelled graph which is build of four parts: (i) palces, denoted with circle representing biological compounds (metabolites), (ii) transitions, denoted with black rectangle, representing biochemical reactions between metabolites (iii) arcs, denoted with

As mentioned before, places represent resource of the system and can contain movable objects (tokens). Tokens represent quantitative unit of compounds. Transitions correspond to events that can change the state of the resources. Arcs (arcs label corresponds to stoichiometric number in reaction equation). Places represent resource of the system, and transitions correspond to events that can change the state of the resources. Arcs connect places to transitions (Chaouiya, 2007) and are allowed only between places and transitions

According to Steggles et al., 2006, it is possible to develop gene regulatory network model based on Petri net starting from Boolean network. The idea was to use logic minimization to extract Boolean terms representing gene network and then to translate this into Petri net structure; the resulting Petri net model is capable to correctly capture dynamic behaviour of

arrows and (iv) tokens denoted by black rectangle (Fig.7.) (Steggles et al., 2007).

and vice versa, never between places or between transitions (Koch et al., 2005).

Fig. 6. Boolean network of three entities (Steggles et al., 2007)

previous time step (Giacomantonio & Goodhill, 2010).

regulatory networks.

**4.4.2 Petri net models** 

gene networks.

## **4.3 Control logic models**

After defining the network topology, the next step in development of gene regulatory network is analysis of the rules of the interaction between the network elements (Schlitt and Brazma, 2007). Transcriptional-regulatory systems is based on the presence of transcription factor binding sites of genes which are responsible for receiving temporal regulatory input signals; sequential logic model (SML) can be used for description of trans-activation and temporal mRNA expression profiles (Yeo et al., 2007). SML technique can ensure detail insight into gene regulation and it can ensure systematically analysis of the dynamic transcriptional inputs.

## **4.4 Dynamic models**

The nodes in gene network population of genes, proteins and other regulatory molecules. There can be from few to few thousands of copies of those molecules in cell. Components of the gene regulatory networks can be changed in response to internal and external stimuli. It is important to include those interactions into network; this is possible using dynamic modelling approach. Dynamic modelling frameworks are usually classified along two axes: continuous versus discrete (describes the level of detail of node state) and deterministic versus stochastic (in view of uncertainties and variability of the transfer functions) (Albert, 2007). Dynamic models can also be divided into quantitative (base on system of ordinary differential equations) and qualitative models (piecewise linear differential system) (Chaouiya, 2007).

#### **4.4.1 Boolean models**

Boolean networks describe the state of genes with binary (ON/OFF) variables. Dynamic behaviour of each variable is governed by Boolean function (Albert, 2004). Although Boolean networks allow the analysis of the dynamics of the gene regulatory networks, they ignore the effect of genes at intermediate levels (Xu et al., 2007). Boolean networks have been intensely investigated as models for genetic control in cells. In those networks, each gene represents the node, and as mentioned before each node has two states ON (producing the protein) or OFF (there is no protein production). The biological basis for development of Boolean netwok as a model of gene regulatory network lies in the fact that during regulation of functional states the cell exhibits switch-like behaviour; this form of behaviour ensures the movement of cell from one state to another (Shmulevich et al., 2002). In the network there are links between nods (one node has impact on the other) (Pomerance et al., 2009). The Boolean networks have ability to contain very large number of nodes but are very crude in their approximation in biology (Karlsson & Hörnquist, 2007). In Boolean network form (Fig.6.), the genome is presented by set of binary variables, *g1,g2….gN*. The expression of each gene changes with time according to Eq.2.:

$$\mathbf{g}\_n(t+1) = \mathbf{F}\_n\left(\mathbf{g}\_{n\_1}(t), \mathbf{g}\_{n\_2}(t)...\mathbf{g}\_{n\_{k\_n}}(t)\right) \tag{2}$$

where *Fn* is Boolean function constructed according to the inhibition or activation nature of the regulators. According to Balleza et al, 2008 if *F(g1,g2)* is the function of two regulators *g1* and *g2* than function *F* can be in one of the following forms: *F*(1,1)=1, *F*(1,0)=1, *F*(0,1)=0 and *F*(0,0)=1. Regulatory phrase for *F*=1 is activator and for *F*=0 inhibitor.

After defining the network topology, the next step in development of gene regulatory network is analysis of the rules of the interaction between the network elements (Schlitt and Brazma, 2007). Transcriptional-regulatory systems is based on the presence of transcription factor binding sites of genes which are responsible for receiving temporal regulatory input signals; sequential logic model (SML) can be used for description of trans-activation and temporal mRNA expression profiles (Yeo et al., 2007). SML technique can ensure detail insight into gene regulation and it can ensure systematically analysis of the dynamic

The nodes in gene network population of genes, proteins and other regulatory molecules. There can be from few to few thousands of copies of those molecules in cell. Components of the gene regulatory networks can be changed in response to internal and external stimuli. It is important to include those interactions into network; this is possible using dynamic modelling approach. Dynamic modelling frameworks are usually classified along two axes: continuous versus discrete (describes the level of detail of node state) and deterministic versus stochastic (in view of uncertainties and variability of the transfer functions) (Albert, 2007). Dynamic models can also be divided into quantitative (base on system of ordinary differential equations) and qualitative models (piecewise linear differential system)

Boolean networks describe the state of genes with binary (ON/OFF) variables. Dynamic behaviour of each variable is governed by Boolean function (Albert, 2004). Although Boolean networks allow the analysis of the dynamics of the gene regulatory networks, they ignore the effect of genes at intermediate levels (Xu et al., 2007). Boolean networks have been intensely investigated as models for genetic control in cells. In those networks, each gene represents the node, and as mentioned before each node has two states ON (producing the protein) or OFF (there is no protein production). The biological basis for development of Boolean netwok as a model of gene regulatory network lies in the fact that during regulation of functional states the cell exhibits switch-like behaviour; this form of behaviour ensures the movement of cell from one state to another (Shmulevich et al., 2002). In the network there are links between nods (one node has impact on the other) (Pomerance et al., 2009). The Boolean networks have ability to contain very large number of nodes but are very crude in their approximation in biology (Karlsson & Hörnquist, 2007). In Boolean network form (Fig.6.), the genome is presented by set of binary variables, *g1,g2….gN*. The expression of each

where *Fn* is Boolean function constructed according to the inhibition or activation nature of the regulators. According to Balleza et al, 2008 if *F(g1,g2)* is the function of two regulators *g1* and *g2* than function *F* can be in one of the following forms: *F*(1,1)=1, *F*(1,0)=1, *F*(0,1)=0 and

*F*(0,0)=1. Regulatory phrase for *F*=1 is activator and for *F*=0 inhibitor.

( 1) 1 2 , .... *<sup>k</sup> <sup>n</sup> n nn n n <sup>g</sup> t F <sup>g</sup> <sup>t</sup> <sup>g</sup> <sup>t</sup> <sup>g</sup> <sup>t</sup>* (2)

**4.3 Control logic models** 

transcriptional inputs.

**4.4 Dynamic models** 

(Chaouiya, 2007).

**4.4.1 Boolean models** 

gene changes with time according to Eq.2.:

Fig. 6. Boolean network of three entities (Steggles et al., 2007)

Continuous models give more realistic description of the process, but development of those models requires large amounts of experimental data. As mentioned before in Boolean models at each time point the gene state depends on the state of the gene regulators at previous time step (Giacomantonio & Goodhill, 2010).

Some modification of traditional Boolean gene regulatory network models can be found in literature. One of them is temporal Boolean network. The difference between those two network models is in the fact temporal Boolean network allows the state of gene at time *t+1* depends on state of genes at times *t*, *t-1*,….., *t-(T-1)*(Silvescu & Honavar, 2001). Another approach is propped by Shulevich et al, 2002; probabilistic Boolean network. Probabilistic Boolean network includes properties of Boolean networks (rule-based dependence between genes), but due to the probabilistic nature this approach is suitable for systematic study of regulatory networks.

## **4.4.2 Petri net models**

Petri net theory provides graphical notation with mathematical background. A Petri net is directed, bipartite and labelled graph which is build of four parts: (i) palces, denoted with circle representing biological compounds (metabolites), (ii) transitions, denoted with black rectangle, representing biochemical reactions between metabolites (iii) arcs, denoted with arrows and (iv) tokens denoted by black rectangle (Fig.7.) (Steggles et al., 2007).

As mentioned before, places represent resource of the system and can contain movable objects (tokens). Tokens represent quantitative unit of compounds. Transitions correspond to events that can change the state of the resources. Arcs (arcs label corresponds to stoichiometric number in reaction equation). Places represent resource of the system, and transitions correspond to events that can change the state of the resources. Arcs connect places to transitions (Chaouiya, 2007) and are allowed only between places and transitions and vice versa, never between places or between transitions (Koch et al., 2005).

According to Steggles et al., 2006, it is possible to develop gene regulatory network model based on Petri net starting from Boolean network. The idea was to use logic minimization to extract Boolean terms representing gene network and then to translate this into Petri net structure; the resulting Petri net model is capable to correctly capture dynamic behaviour of gene networks.

Mathematical Modelling of Gene Regulatory Networks 125

concentration on protein concentration. According to Hecker et al., 2009 ordinary

1. linear differential equations can used for description of gene expression kinetics (Eq.6)

, 1

Gebert et al., 2007 used developed model of pecewise linear differential equation for description of interaction between genes in regulatory networks; variables of the model

Model was based on assumption that regulation between genes can be described using

, ,

 

(7)

 

(10)

(8)

(9)

 . <sup>1</sup> 1,1 1 1,1 1,1 1,3 3 1,3 1,3 1 1 *x khx m khx m x* , ,

> . <sup>2</sup> 2,1 1 2,1 2,1 2 2 *x khx m x* , ,

 . <sup>3</sup> 3,1,2 1 3,1 3,1 2 3,2 3,2 3 3 *x k hx m hx m x* ,, ,,

the relationships between internal state variables and observation variables.

 1 2 <sup>d</sup> , ,..., 1,2,... <sup>d</sup>

*i ni*

*i*

*t*

experimental data, it can be polynomial (Eq.11):

represents the degradation rate of mRNA and *k* are rate constants.

Wu et al., 2004 proposed method to model gene expression dynamic from measured time-course data including linear equations. Developed dynamic equations described

2. non-linear differential equations are used for describing complex dynamic behaviours. Comparing to linear models, identification of the non-linear differential equation model is computationally more intensive and it requires more data (Quian & Wang, 2007). The numerical representation of non-linear ODE model of gene regulatory network (Eq.10):

*<sup>x</sup> <sup>f</sup> xx x i N*

where *fi* represents the non-linear function which can be determinated from

*<sup>x</sup> w x bu*

*i j j i*

*<sup>i</sup> <sup>j</sup> f p* is usually non-linear and describes the dependence of mRNA

(5)

(6)

<sup>d</sup> <sup>i</sup> ( ) <sup>d</sup> *P i i ii <sup>p</sup> fr p <sup>t</sup>*

differential equations for description of gene regulatory network can be divided into:

*N i*

*j*

*t*

d d

were mRNA concentrations (Fig.8.).

Fig. 8. Model of gene regulation (Gebert et al., 2007)

piecewise linear differential equations (Eq 7-9).

the function ( ) *<sup>R</sup>*

were 

Fig. 7. Petri net modelling of different reactions (Chaouiya, 2007)

#### **4.4.3 Difference and differential equation models**

Using ordinary differential equations for representing gene regulatory networks concentrations of proteins, mRNAs and other molecules are presented as continuous time variables (Polynikis et al., 2009). Flexibility of ordinary deferential equations allows the description of complex relations between components of the net. Differential equations can describe complex dynamic behaviour like oscillations, cyclical patterns, multistationary and switch-like behaviour (Gebert et al., 2007). According to Hecker et al., 2009 the dynamic of gene regulatory networks can be described with (Eq.3.):

$$\frac{d\mathbf{x}}{dt} = f(\mathbf{x}, p, u, t) \tag{3}$$

were 1 ( ) ( ( )...... ( )) *<sup>n</sup> xt x t x t* represents gene expression vector of genes for 1 to n, *f* is function that describes the rate of change of variable *x*. *p* presents model parameter set and *u*  external perturbation signals. Transcription and translation can be model using ordinary differential equations (Eq. 4-5):

$$\frac{\text{d}\mathbf{r}\_i}{\text{d}t} = F\left(f\_i^{\mathbb{R}}\left(p\_1\right), f\_i^{\mathbb{R}}\left(p\_2\right)...f\_i^{\mathbb{R}}\left(p\_n\right)\right) - \gamma\_i r\_i \tag{4}$$

Fig. 7. Petri net modelling of different reactions (Chaouiya, 2007)

Using ordinary differential equations for representing gene regulatory networks concentrations of proteins, mRNAs and other molecules are presented as continuous time variables (Polynikis et al., 2009). Flexibility of ordinary deferential equations allows the description of complex relations between components of the net. Differential equations can describe complex dynamic behaviour like oscillations, cyclical patterns, multistationary and switch-like behaviour (Gebert et al., 2007). According to Hecker et al., 2009 the dynamic of

> <sup>d</sup> ( , , ,) <sup>d</sup> *<sup>x</sup> <sup>f</sup> xput <sup>t</sup>*

were 1 ( ) ( ( )...... ( )) *<sup>n</sup> xt x t x t* represents gene expression vector of genes for 1 to n, *f* is function that describes the rate of change of variable *x*. *p* presents model parameter set and *u*  external perturbation signals. Transcription and translation can be model using ordinary

> <sup>i</sup> 1 2 <sup>d</sup> , .... <sup>d</sup>

*RR R*

*i i i n ii <sup>r</sup> Ff p f p f p r <sup>t</sup>*

(3)

(4)

**4.4.3 Difference and differential equation models** 

gene regulatory networks can be described with (Eq.3.):

differential equations (Eq. 4-5):

$$\frac{\mathbf{d}p\_i}{\mathbf{d}t} = f\_i^P(r\_i) - \delta\_i p\_i \tag{5}$$

the function ( ) *<sup>R</sup> <sup>i</sup> <sup>j</sup> f p* is usually non-linear and describes the dependence of mRNA concentration on protein concentration. According to Hecker et al., 2009 ordinary differential equations for description of gene regulatory network can be divided into:

1. linear differential equations can used for description of gene expression kinetics (Eq.6)

$$\frac{\mathbf{dx}\_i}{\mathbf{dt}} = \sum\_{j=1}^{N} w\_{i,j} \mathbf{x}\_j + b\_i u \tag{6}$$

Gebert et al., 2007 used developed model of pecewise linear differential equation for description of interaction between genes in regulatory networks; variables of the model were mRNA concentrations (Fig.8.).

Model was based on assumption that regulation between genes can be described using piecewise linear differential equations (Eq 7-9).

$$\dot{\mathbf{x}}\_1 = k\_{1,1}h^+\left(\mathbf{x}\_{1'}\,\theta\_{1,1'}m\_{1,1}\right) + k\_{1,3}h^+\left(\mathbf{x}\_{3'}\,\theta\_{1,3'}m\_{1,3}\right) - \boldsymbol{\gamma}\_1\mathbf{x}\_1\tag{7}$$

$$\dot{\mathbf{x}}\_{2} = k\_{2,1} \mathbf{h}^{+} \left( \mathbf{x}\_{1}, \theta\_{2,1}, m\_{2,1} \right) - \boldsymbol{\gamma}\_{2} \mathbf{x}\_{2} \tag{8}$$

$$\dot{\mathbf{x}}\_{3} = k\_{3,1,2}h^{+}\left(\mathbf{x}\_{1}, \theta\_{3,1}, m\_{3,1}\right)h^{+}\left(\mathbf{x}\_{2}, \theta\_{3,2}, m\_{3,2}\right) - \gamma\_{3}\mathbf{x}\_{3} \tag{9}$$

were represents the degradation rate of mRNA and *k* are rate constants.

Wu et al., 2004 proposed method to model gene expression dynamic from measured time-course data including linear equations. Developed dynamic equations described the relationships between internal state variables and observation variables.

2. non-linear differential equations are used for describing complex dynamic behaviours. Comparing to linear models, identification of the non-linear differential equation model is computationally more intensive and it requires more data (Quian & Wang, 2007). The numerical representation of non-linear ODE model of gene regulatory network (Eq.10):

$$\frac{\text{d}x\_i}{\text{d}t} = f\_i(\mathbf{x}\_1, \mathbf{x}\_2, \dots, \mathbf{x}\_n) + \nu\_i \qquad i = 1, 2, \dots \\ N \tag{10}$$

where *fi* represents the non-linear function which can be determinated from experimental data, it can be polynomial (Eq.11):

Mathematical Modelling of Gene Regulatory Networks 127

where *x* represents the amount of molecules (state variable), *p(x,t)* probability distribution. Assuming that t→0, the equation for stochastic representation of gene regulatory network

> 

Methodology of finite state linear modelling (FSLM) was developed by Bramza & Schlitt, 2003; it combines discrete and continuous aspects of gene regulation in structured way. Model was developed on few assumptions: (i) gene activity is defined by state of transcription binding sites in promoter region, (ii) each binding site can be in one of the finite number of states, (iii) active gene produces substance with rate dependant on activity level, (iv) state of binding site depends on concentrations of transcription factors. The continuous parts of the model consist of the state of the proton concentrations. As mentioned before it also includes Boolean-type model gene regulation (each gene and each binding site can have only two sates; ON or OFF). Bramza & Schitt, 2003 used finite state

*<sup>j</sup> <sup>j</sup> p x t*

(13)

*j*

1 *, ,* 

*<sup>m</sup>*

*t p x t*

linear model for construction of biological network of λ-phage (Fig.9.)

Fig. 9. Gene network of λ-phage (Bramza & Schitt, 2003 )

is developed Eq. 13:

**4.4.5 Finite state linear models** 

$$f\_i = \sum\_{j=1}^{L\_i} \left[ \left( w\_{ij} + \mu\_{ij} \right) \Omega\_{ij} \left( \mathbf{x}\_1, \mathbf{x}\_2, \dots, \mathbf{x}\_n \right) \right] \qquad \mathbf{i} = \mathbf{1}, \mathbf{2}, \dots \mathbf{N} \tag{11}$$

where *Li* is the number of terms in *fi*, *wij* represent parameters that need to be estimated and *Ωij(x1, x2,…xN)* is the component of the nonlinear function.

Quian and Wang, 2007 developed gene regulatory network model including evolutionary algorithm and filtering approach; noise was modelled using nonlinear ordinary differential equations. Simulation showed the usage of proposed model on experimental data for microarray experiments.

Using set of ordinary differential equations for description of gene network, the inference of genetic networks is often defined as a function optimization problem to minimize the defences between gene expression levels obtained numerically and levels measured in experiments (Kimura et al., 2009). The problems that occurs when working with differential equation model are that those models include many parameters which have to be estimated form experimental data or obtained from literature. It also has to be taken into consideration that for complex differential equations analytical solution and analysis of the equations can be very complex.

#### **4.4.4 Stochastic modelling**

All cellular events depend on probabilistic collisions between molecules. Due to the fact that number of events occurring in the cells is not large and events are dependent, it is not possible to use deterministic rate equations for description of the gene network (gene expression is stochastic process (Paulsson, 2005). There are many important stochastic phenomena during the life time of the cell, like random fluctuations that initiate transcription, spontaneous jumps in mRNA or protein concentrations (Rosenfeld, 2007). Study of stochastic properties in genetic systems involves formulation of molecular noise, formulation of approximation of these representations and development of computational algorithms capable for describing complexity of network dynamics (El Samad, et al., 2005).

According to Rosenfeld, 2007 for mathematical description of stochastic dynamics of gene regulatory networks two approaches can be used:


Stochastic modelling approach is mathematically represented with Eq.12:

$$p\left(\mathbf{x}, t + \Delta t\right) = p\left(\mathbf{x}, t + \Delta t\right) \cdot \left(\mathbf{1} - \sum\_{j=1}^{m} \alpha\_j \Delta t\right) + \sum\_{j=1}^{m} \beta\_j \Delta t \tag{12}$$

where *x* represents the amount of molecules (state variable), *p(x,t)* probability distribution. Assuming that t→0, the equation for stochastic representation of gene regulatory network is developed Eq. 13:

$$\frac{\partial p(\mathbf{x},t)}{\partial t} = \sum\_{j=1}^{m} \left(\beta\_j - \alpha\_j p(\mathbf{x}, t)\right) \tag{13}$$

#### **4.4.5 Finite state linear models**

126 Applied Biological Engineering – Principles and Practice

*f w xx x i N*

where *Li* is the number of terms in *fi*, *wij* represent parameters that need to be estimated

Quian and Wang, 2007 developed gene regulatory network model including evolutionary algorithm and filtering approach; noise was modelled using nonlinear ordinary differential equations. Simulation showed the usage of proposed model on

Using set of ordinary differential equations for description of gene network, the inference of genetic networks is often defined as a function optimization problem to minimize the defences between gene expression levels obtained numerically and levels measured in experiments (Kimura et al., 2009). The problems that occurs when working with differential equation model are that those models include many parameters which have to be estimated form experimental data or obtained from literature. It also has to be taken into consideration that for complex differential equations analytical solution and analysis of the equations can

All cellular events depend on probabilistic collisions between molecules. Due to the fact that number of events occurring in the cells is not large and events are dependent, it is not possible to use deterministic rate equations for description of the gene network (gene expression is stochastic process (Paulsson, 2005). There are many important stochastic phenomena during the life time of the cell, like random fluctuations that initiate transcription, spontaneous jumps in mRNA or protein concentrations (Rosenfeld, 2007). Study of stochastic properties in genetic systems involves formulation of molecular noise, formulation of approximation of these representations and development of computational algorithms capable for describing complexity of network dynamics (El Samad, et al.,

According to Rosenfeld, 2007 for mathematical description of stochastic dynamics of gene

1. non-linear dynamics paradigm – treats the biochemical components included in gene expression regulation as continuous variables and describes their variations using non-

2. Markov process paradigm – due to the fact that some molecules included into gene expression regulation can occur in cell in very low concentrations they can not be treated as a continuous variables and their random fluctuations can be very high.

1 1

 *t t*

(12)

*m m j j j j*

 

Stochastic modelling approach is mathematically represented with Eq.12:

*p xt t p xt t*

, ,1

, ,..., 1,2,...

(11)

1 2

*i ij ij ij n*

and *Ωij(x1, x2,…xN)* is the component of the nonlinear function.

1

experimental data for microarray experiments.

regulatory networks two approaches can be used:

linear differential equations

be very complex.

2005).

**4.4.4 Stochastic modelling** 

*Li*

*j*

Methodology of finite state linear modelling (FSLM) was developed by Bramza & Schlitt, 2003; it combines discrete and continuous aspects of gene regulation in structured way. Model was developed on few assumptions: (i) gene activity is defined by state of transcription binding sites in promoter region, (ii) each binding site can be in one of the finite number of states, (iii) active gene produces substance with rate dependant on activity level, (iv) state of binding site depends on concentrations of transcription factors. The continuous parts of the model consist of the state of the proton concentrations. As mentioned before it also includes Boolean-type model gene regulation (each gene and each binding site can have only two sates; ON or OFF). Bramza & Schitt, 2003 used finite state linear model for construction of biological network of λ-phage (Fig.9.)

Fig. 9. Gene network of λ-phage (Bramza & Schitt, 2003 )

Mathematical Modelling of Gene Regulatory Networks 129

This work was supported by Ministry of Science, Education and Sport of Republic of Croatia

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**7. Acknowledgment** 

grant MZOŠ 0589.

**8. References** 

Ruklisa et al., 2005 used previously described FSLM model for testing some theoretical properties of the model: (i) what kind of network dynamic could be modelled using this framework, (ii) is it possible to describe chaotic network dynamics and some others. A series of experiments were performed to estimate the regularity of behaviour of random networks; networks were simulated in 10000 steps and results show that FSLM models can be suitable for describing biological reality.

## **4.4.6 Hybrid models**

Due to fact that boundaries between discreet and continuous model depend on the level of details included into the model there is an attempt to develop the models that could include both approaches (Schlitt & Bramza, 2007). Matsuno & Doi, 2000 proposed hybrid Petri net model for presentation of gene regulatory networks of λ-phage. Hybrid Petri net is an extension of Petri net that has continues and discrete elements and can be easily used for protein or mRNA concentration. Another approach to development of hybrid model is present by Crudu et al., 2009. They proposed unified framework for hybrid simplification of the Markov models of stochastic gene network dynamics. It was shown that those simplified models describe with good accuracy the stochastic properties of the gene networks and can be used for multi-scale biochemical systems.

## **5. Conclusion**

Gene expression can be regulated on few levels. Gene regulatory networks are defined as collections of DNA segments in cells which interact with each other. Construction of gene regulatory networks is first step in biological analysis. It is very import to understand and explain the dynamic of gene regulatory networks. To explain and understand those complex biochemical systems different mathematical models have been developed. Techniques of mathematical modelling defer in level of details. Each modelling technique has its advantages and disadvantages and that has to be taken into consideration when developing mathematical model, because proposed model has to provide good insight into gene regulation process and be useful for prediction of some possible mutations or any other change.

## **6. Future direction section**

When modelling gene regulatory networks the fact that model describes only some properties has to be taken into consideration. So there is always open question how real the developed model can be (Schlitt & Bramza, 2007). Using new molecular methods large amount of data can be collected ensuring the better insight into process in the cell. Including all this information in the model more detail model can be developed. When talking about mathematical modelling of gene regulatory networks the neural networks have been used lately for modelling (Lee & Yang, 2008; Xu et al., 2008). For example Knott et al., 2010 presented approach to model gene regulatory networks as non-liner system using artificial neural network. There is also idea in developing synthetic networks. All described approaches have one goal developing simple model which would describe the process in the cell; so the future direction of modelling of gene regulatory networks would be in funding the way how to reduce the complexly of biological systems and to preserve the model functionality.

## **7. Acknowledgment**

This work was supported by Ministry of Science, Education and Sport of Republic of Croatia grant MZOŠ 0589.

### **8. References**

128 Applied Biological Engineering – Principles and Practice

Ruklisa et al., 2005 used previously described FSLM model for testing some theoretical properties of the model: (i) what kind of network dynamic could be modelled using this framework, (ii) is it possible to describe chaotic network dynamics and some others. A series of experiments were performed to estimate the regularity of behaviour of random networks; networks were simulated in 10000 steps and results show that FSLM models can be suitable

Due to fact that boundaries between discreet and continuous model depend on the level of details included into the model there is an attempt to develop the models that could include both approaches (Schlitt & Bramza, 2007). Matsuno & Doi, 2000 proposed hybrid Petri net model for presentation of gene regulatory networks of λ-phage. Hybrid Petri net is an extension of Petri net that has continues and discrete elements and can be easily used for protein or mRNA concentration. Another approach to development of hybrid model is present by Crudu et al., 2009. They proposed unified framework for hybrid simplification of the Markov models of stochastic gene network dynamics. It was shown that those simplified models describe with good accuracy the stochastic properties of the gene networks and can

Gene expression can be regulated on few levels. Gene regulatory networks are defined as collections of DNA segments in cells which interact with each other. Construction of gene regulatory networks is first step in biological analysis. It is very import to understand and explain the dynamic of gene regulatory networks. To explain and understand those complex biochemical systems different mathematical models have been developed. Techniques of mathematical modelling defer in level of details. Each modelling technique has its advantages and disadvantages and that has to be taken into consideration when developing mathematical model, because proposed model has to provide good insight into gene regulation process and be useful for prediction of some possible mutations or any other

When modelling gene regulatory networks the fact that model describes only some properties has to be taken into consideration. So there is always open question how real the developed model can be (Schlitt & Bramza, 2007). Using new molecular methods large amount of data can be collected ensuring the better insight into process in the cell. Including all this information in the model more detail model can be developed. When talking about mathematical modelling of gene regulatory networks the neural networks have been used lately for modelling (Lee & Yang, 2008; Xu et al., 2008). For example Knott et al., 2010 presented approach to model gene regulatory networks as non-liner system using artificial neural network. There is also idea in developing synthetic networks. All described approaches have one goal developing simple model which would describe the process in the cell; so the future direction of modelling of gene regulatory networks would be in funding the way how to reduce the complexly of biological systems and to preserve the

for describing biological reality.

be used for multi-scale biochemical systems.

**4.4.6 Hybrid models** 

**5. Conclusion** 

change.

**6. Future direction section** 

model functionality.


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**6** 

 *Romania* 

**Modern Methods Used in the Complex** 

Nicolae Marius Roman1 and Stefan Gergely2

*2National Institute for Research and Development of Isotopic and Molecular Technologies, Cluj-Napoca,* 

*1Technical University, Cluj-Napoca,* 

**Analysis of the Phonocardiography Signal** 

Sometimes we need an accurate or approximate representation of a quantity in a different form; either the quantity is given by an analytical expression or by the finite set of values. Using transformations, we usually measure the similarity of a given function with an entire class of functions depending on one or more parameters (such as the frequency in the Fourier transform) which may change continuously or discretely. The wavelet representation is given in the spacefrequency domain, opposite to the Fourier analysis that gives only a frequency representation. Compact supports of wavelets provide a space, and their oscillatory nature provides a frequency representation of a transformed function. It is clear that such representation is essential for the non stationary signal. The wavelet representation of a function has the multiresolution property, which means that it is given on several resolution scales. Details defined on various refinement levels (fine meshes) are added to the rough approximation determined on a coarse mesh. The dimension of the data set that store information about the function is considerably decreased while the most important information is not lost. This is very important for a good compression that saves storage in a system memory. A data compression is fundamental for an efficient analyzing of a signal with an extremely high noise density and a large variety of shapes (Abbas

If a compression scheme is lossless it can be always recover the entire original message by uncompressing then a compressed message that has the same total entropy as the original,

Another problem that has to be solved during the filtering process is the so called boundary distortion. This appears at the end samples of the signal because there are left fewer samples than multiplying coefficients. The easiest way to resolve this issue is to introduce zeros at the end of the signal. This does not affect the entropy of the iteration even if the signal is not following the

Wavelet functions are localized both in frequency and in time domain by shifting and scaling function without a projection over the entire transformed signal. Another important aspect is that in terms of number of calculations which are necessary for the Fourier transform. The Fourier transform requires a number of *O(n·log2(n))* operations instead of

original pattern. All the filtering processes are done by using of the wavelet transform.

only *O(n)* mathematical operations for the wavelet transform.

**1. Introduction** 

K.Abbas & Rasha Bassam, 2009).

but in fewer bits.


## **Modern Methods Used in the Complex Analysis of the Phonocardiography Signal**

Nicolae Marius Roman1 and Stefan Gergely2

*1Technical University, Cluj-Napoca, 2National Institute for Research and Development of Isotopic and Molecular Technologies, Cluj-Napoca, Romania* 

## **1. Introduction**

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Boolean networks to Petri nets. *Lecture Notes in Computer Sciences*, Vol.42, (October

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Unconventional systems analysis problem in molecular biology: a case study in gene regulatory network modelling. *Computational and Chemical Engineering,* Vol.29, Sometimes we need an accurate or approximate representation of a quantity in a different form; either the quantity is given by an analytical expression or by the finite set of values. Using transformations, we usually measure the similarity of a given function with an entire class of functions depending on one or more parameters (such as the frequency in the Fourier transform) which may change continuously or discretely. The wavelet representation is given in the spacefrequency domain, opposite to the Fourier analysis that gives only a frequency representation. Compact supports of wavelets provide a space, and their oscillatory nature provides a frequency representation of a transformed function. It is clear that such representation is essential for the non stationary signal. The wavelet representation of a function has the multiresolution property, which means that it is given on several resolution scales. Details defined on various refinement levels (fine meshes) are added to the rough approximation determined on a coarse mesh. The dimension of the data set that store information about the function is considerably decreased while the most important information is not lost. This is very important for a good compression that saves storage in a system memory. A data compression is fundamental for an efficient analyzing of a signal with an extremely high noise density and a large variety of shapes (Abbas K.Abbas & Rasha Bassam, 2009).

If a compression scheme is lossless it can be always recover the entire original message by uncompressing then a compressed message that has the same total entropy as the original, but in fewer bits.

Another problem that has to be solved during the filtering process is the so called boundary distortion. This appears at the end samples of the signal because there are left fewer samples than multiplying coefficients. The easiest way to resolve this issue is to introduce zeros at the end of the signal. This does not affect the entropy of the iteration even if the signal is not following the original pattern. All the filtering processes are done by using of the wavelet transform.

Wavelet functions are localized both in frequency and in time domain by shifting and scaling function without a projection over the entire transformed signal. Another important aspect is that in terms of number of calculations which are necessary for the Fourier transform. The Fourier transform requires a number of *O(n·log2(n))* operations instead of only *O(n)* mathematical operations for the wavelet transform.

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 135

A key criterion in determining the type of wavelet function consists in evaluation the overall reconstruction error, for the given type of signals that will appear in the application. So the evaluation must be made for signal reconstruction at the extreme in terms of spectral content. We imposed this condition for the decomposition algorithm to use a minimum number of coefficients, to optimize the convolution calculation time. Therefore the evaluation of the reconstruction error is done by using the functions from the Matlab

After computing the wavelet function we tested the validity of the selection by taking on all detail components of reconstructed signal and computing the reconstruction error. The goal was to find a maximum error therefore the maximum sensitivity of the wavelet function to the given input signal. The tables are presenting the overall computed errors which must be the lowest possible and the component extraction error which must indicate the highest

These two conditions are met by the Daubeschies db2 function. It seemed that this function did answer very well to the PCG signal which is a strongly polynomial type due the massive presence of arbitrary heart murmur signals. Due to the Matlab convention the db2 wavelet function is mathematically defined by four coefficients which are computed by using the orthogonally conditions along with a specially imposed condition which gives the

The Daubeschies functions family plays an important role in signal analysis because it is most often used to break down signals into sub-band components. Therefore the use of Db4 function requires the computation of the scaling coefficients. The scaling equation for a wavelet function having four coefficients is given by equation (6): (Gergely et al. 2011)

*tc tc t c t c t* 01 2 3 2 21 22 23 (6)

*tc tc t c t c t* 01 2 3 2 21 22 23 (7)

 

 

Prof. Ingrid Daubeschies imposed a supplementary condition regarding the smoothness of

toolbox which are shown in figure 2 (Gergely S., 2011).

Fig. 2. Evaluation of the reconstruction error

sensitivity of the wavelet functions.

smoothness of the Daubeschies functions

And the equation for the wavelet function is:

the wavelet function which is given by equation 8:

 

#### **2. The fast wavelet transform**

The approximation at the m+1 scale is given by equation 1

$$S\_{m+1,n} = \bigcap\_{-\infty}^{\infty} \mathbf{x}\left(t\right) \Phi\_{m+1,n}\left(t\right) dt \tag{1}$$

by replacing 1 we get:

$$S\_{m+1,n} = \int\_{-\infty}^{\infty} x(t) \cdot \left[ \frac{1}{\sqrt{2}} \sum\_{k} c\_k \Phi\_{m,2n+k} \left( t \right) \right] dt \tag{2}$$

For a much better illustration, by rearranging the terms it yields:

$$S\_{m+1,n} = \frac{1}{\sqrt{2}} \sum\_{k} c\_k \left[ \int\_{-\infty}^{\omega} \mathbf{x}(t) \Phi\_{m,2n+k}(t) dt \right] \tag{3}$$

and finally the approximation coefficient *Sm,2n+k* for each k we get:

$$S\_{m+1,n} = \frac{1}{\sqrt{2}} \sum\_{k} c\_k S\_{m,2n+k} = \frac{1}{\sqrt{2}} \sum\_{k} c\_{k-2n} S\_{m,k} \tag{4}$$

In a similar manner we get the wavelet detail coefficients:

$$T\_{m+1,n} = \frac{1}{\sqrt{2}} \sum\_{k} b\_k S\_{m,2n+k} = \frac{1}{\sqrt{2}} \sum\_{k} b\_{k-2n} S\_{m,k} \tag{5}$$

As a result the equations 4 and 5 are forming the multi-resolution decomposition algorithm used in our paper.

#### **2.1 Choosing the optimal wavelet function for the analysis of PGC**

Every application which requires the using of a wavelet transform requires the adaptation or finding of a certain type of wavelet function. The first criterion is defined by the correlation factor between the wavelet function and the analyzed signal. Unfortunately the shape of the correlated wavelet function is capable to indicate only the family of wavelet functions but gives no indication regarding the number of the wavelet coefficients. To compute the necessary coefficient numbers, we used the wavelet toolbox of the Matlab program. The PCG signal is decomposed accordingly the algorithm shown in figure 1:

Fig. 1. Three level decomposition algorithm

A key criterion in determining the type of wavelet function consists in evaluation the overall reconstruction error, for the given type of signals that will appear in the application. So the evaluation must be made for signal reconstruction at the extreme in terms of spectral content. We imposed this condition for the decomposition algorithm to use a minimum number of coefficients, to optimize the convolution calculation time. Therefore the evaluation of the reconstruction error is done by using the functions from the Matlab toolbox which are shown in figure 2 (Gergely S., 2011).


Fig. 2. Evaluation of the reconstruction error

134 Applied Biological Engineering – Principles and Practice

*S x t t dt m n* 1, *m n* 1, 

1, ,2 <sup>1</sup> 2 *m n k m nk*

1, ,2

1, ,2 2 , 1 1 2 2 *m n km nk k n mk k k*

1, ,2 2 , 1 1 2 2 *m n km nk k n mk k k*

As a result the equations 4 and 5 are forming the multi-resolution decomposition algorithm

Every application which requires the using of a wavelet transform requires the adaptation or finding of a certain type of wavelet function. The first criterion is defined by the correlation factor between the wavelet function and the analyzed signal. Unfortunately the shape of the correlated wavelet function is capable to indicate only the family of wavelet functions but gives no indication regarding the number of the wavelet coefficients. To compute the necessary coefficient numbers, we used the wavelet toolbox of the Matlab program. The PCG signal is decomposed accordingly the algorithm shown in figure 1:

*S c x t t dt* 

2 *m n <sup>k</sup> m nk k*

1

For a much better illustration, by rearranging the terms it yields:

and finally the approximation coefficient *Sm,2n+k* for each k we get:

**2.1 Choosing the optimal wavelet function for the analysis of PGC** 

In a similar manner we get the wavelet detail coefficients:

Fig. 1. Three level decomposition algorithm

*k S x t c t dt*

(1)

(2)

(3)

*<sup>S</sup> c S c S* (4)

*<sup>T</sup> b S b S* (5)

**2. The fast wavelet transform** 

by replacing 1 we get:

used in our paper.

The approximation at the m+1 scale is given by equation 1

After computing the wavelet function we tested the validity of the selection by taking on all detail components of reconstructed signal and computing the reconstruction error. The goal was to find a maximum error therefore the maximum sensitivity of the wavelet function to the given input signal. The tables are presenting the overall computed errors which must be the lowest possible and the component extraction error which must indicate the highest sensitivity of the wavelet functions.

These two conditions are met by the Daubeschies db2 function. It seemed that this function did answer very well to the PCG signal which is a strongly polynomial type due the massive presence of arbitrary heart murmur signals. Due to the Matlab convention the db2 wavelet function is mathematically defined by four coefficients which are computed by using the orthogonally conditions along with a specially imposed condition which gives the smoothness of the Daubeschies functions

The Daubeschies functions family plays an important role in signal analysis because it is most often used to break down signals into sub-band components. Therefore the use of Db4 function requires the computation of the scaling coefficients. The scaling equation for a wavelet function having four coefficients is given by equation (6): (Gergely et al. 2011)

$$
\Phi(t) = c\_0 \Phi(2t) + c\_1 \Phi(2t - 1) + c\_2 \Phi(2t - 2) + c\_3 \Phi(2t - 3) \tag{6}
$$

And the equation for the wavelet function is:

$$
\psi\left(t\right) = c\_0 \nu\left(2t\right) - c\_1 \nu\left(2t - 1\right) + c\_2 \nu\left(2t - 2\right) - c\_3 \nu\left(2t - 3\right) \tag{7}
$$

Prof. Ingrid Daubeschies imposed a supplementary condition regarding the smoothness of the wavelet function which is given by equation 8:

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 137

Equations 9 and 10 are used to compute the partial multiresolution decomposition up to level seven, which is used in the characterization of the PCG signals. The wavelet transform is done by using *Daubeschies 4* coefficients along with signal decimation by two. Another benefit of using the wavelet transform is due the filtering effect which reduces the

A common situation which occurs in the analysis of the PCG signals is that the domains of signal frequency spectra are almost identical but the temporal distribution of spectral components is totally different. For this reason the frequency analysis requires a different approach to traditional methods. The main parameter that leads to differentiation of the two signals is the energy distribution in time domain, which is well evidenced by Parseval's

2 2

(12)

<sup>2</sup> [ ] [ ]

*x i MagX k N*

So the best approach is a non-stationary analysis of signal properties coupled with a timefrequency representation type. Wavelet representation is made in time-frequency domain opposed to Fourier analysis as only be effective in the frequency domain representation. The compact support offered by the wavelet transform allows the analysis by space and the oscillating character of a signal. This type of analysis is best suited for non-stationary signal type. Although apparently PCG signal is characterized by time periodicity of cardiac activity, the high frequency components of the signal spectrum are strongly marked by acoustic noise which is created by blood flow through vessels and cardiac valves. Wavelet representation of a function is characterized by multi-resolution property which means that it can be decomposed in several scales. By performing wavelet transform on a signal it results a considerably signal vector size decreases due to decimation by 2, at each level of transform. This is essential as a good signal compression to store transform in a low amount of available memory and having limited resources which is specific to the embedded type of microcomputers. The simulation software packages of the Matlab programming environment, offers a wide range of functions as a representation of time-frequency analysis but their export is generally possible only at the graphic level. The correct design of the time-frequency scalogram algorithm requires more detailed study of how the spectrum inversion occurs at the decimation by two of the wavelet high pass filter. Identifying the areas in which the frequency spectrum inversion occurs can be done by the representation of wavelet packet on several levels. In figure 4 it can be observed

The time-frequency scalogram decomposition is actually a total multi-resolution analysis, so that the representation of time-frequency scalogram requires the correct reordering of the resulted spectrum fields. So it can be seen how the spectrum fields results from filtering G (high pass), following the decimation by 2 produces spectral inversion. Given the above observations, in figure 4 we can see another interesting phenomenon in the last decomposition, where the order of occurrence of the frequency domains follows a pattern similar to the Gray code (A.Jensen & A. la Cour-Harbo, 2001). Spectral range as natural frequency ordering is done by interpreting the initial results of permutations that are written

in binary 000, 001, 011, 010, 110, 111, 101, 100 (the string of numbers marked in green).

1 2

*N N*

*i k*

0 0

bandwidth of the signal.

relation given in equation 12:

the inversion algorithm then takes place.

**2.2 The time-frequency representation of PCG signals** 

$$\sum\_{k=0}^{N\_k-1} \left(-\mathbf{1}\right)^k c\_k k^m = \mathbf{0} \tag{8}$$

For , 1,2,3,..., / 2 1 *m Zm N <sup>k</sup>* . This means that the wavelet function can suppress or show up parts of the signal which are polynomial structure up to /2 1 *Nk* grade, or better put out the signal parts that have a polynomial behavior. Finally by solving the system of equations shown in figure 3 it yields the solutions from table 1:


Table 1. Coefficients of the wavelet function

Fig. 3. Equations system for solving the Daubeschies 4 coefficients

Therefore in the case of Daubeschies multiresolution algorithm we get:

$$S\_{m+1,n} = \frac{1}{\sqrt{2}} \left( c\_0 S\_{m,2n} + c\_1 S\_{m,2n+1} + c\_2 S\_{m,2n+2} + c\_3 S\_{m,2n+3} \right) \tag{9}$$

By replacing with the computed coefficients, we get the final form:

$$S\_{m+1,n} = 0.483 \cdot S\_{m,2n} + 0.837 \cdot S\_{m,2n+1} + 0.224 \cdot S\_{m,2n+2} - 0.129 \cdot S\_{m,2n+3} \tag{10}$$

In the same manner by replacing <sup>1</sup> 1 *<sup>k</sup> k k Nk b c* and also the computed coefficients in equation 5, it yields:

$$T\_{m+1,n} = -0.129 \cdot S\_{m,2n} - 0.224 \cdot S\_{m,2n+1} + 0.837 \cdot S\_{m,2n+2} - 0.483 \cdot S\_{m,2n+3} \tag{11}$$

Equations 9 and 10 are used to compute the partial multiresolution decomposition up to level seven, which is used in the characterization of the PCG signals. The wavelet transform is done by using *Daubeschies 4* coefficients along with signal decimation by two. Another benefit of using the wavelet transform is due the filtering effect which reduces the bandwidth of the signal.

#### **2.2 The time-frequency representation of PCG signals**

136 Applied Biological Engineering – Principles and Practice

1 0

c0 c1 c2 c3

(8)

3 3 4 

1 3 4 


1 3 4 

0.6830

0.3170

3 3 4 

1.1830

*c k*

For , 1,2,3,..., / 2 1 *m Zm N <sup>k</sup>* . This means that the wavelet function can suppress or show up parts of the signal which are polynomial structure up to /2 1 *Nk* grade, or better put out the signal parts that have a polynomial behavior. Finally by solving the system of

> 3 3 4

1.1830

3 3 4 

0.3170

 1

*Nk <sup>k</sup> <sup>m</sup> k*

0

*k*

equations shown in figure 3 it yields the solutions from table 1:

1 3 4 

0.6830

1 3 4 


Fig. 3. Equations system for solving the Daubeschies 4 coefficients

By replacing with the computed coefficients, we get the final form:

1 2

In the same manner by replacing <sup>1</sup> 1 *<sup>k</sup>*

equation 5, it yields:

Therefore in the case of Daubeschies multiresolution algorithm we get:

1, 0 ,2 1 ,2 1 2 ,2 2 3 ,2 3

*k*

*S cS cS cS cS m n mn mn mn mn* (9)

*k Nk b c* and also the computed coefficients in

1, ,2 ,2 1 ,2 2 ,2 3 *S SS S S m n* 0.483 0.837 0.224 0.129 *m n m n m n m n* (10)

1, ,2 ,2 1 ,2 2 ,2 3 *T SS S S m n* 0.129 0.224 0.837 0.483 *m n m n m n m n* (11)

Table 1. Coefficients of the wavelet function

*t*

*t*

A common situation which occurs in the analysis of the PCG signals is that the domains of signal frequency spectra are almost identical but the temporal distribution of spectral components is totally different. For this reason the frequency analysis requires a different approach to traditional methods. The main parameter that leads to differentiation of the two signals is the energy distribution in time domain, which is well evidenced by Parseval's relation given in equation 12:

$$\sum\_{i=0}^{N-1} \mathbf{x}[i]^2 = \frac{2}{N} \sum\_{k=0}^{N/2} \text{MagX}[k]^2 \tag{12}$$

So the best approach is a non-stationary analysis of signal properties coupled with a timefrequency representation type. Wavelet representation is made in time-frequency domain opposed to Fourier analysis as only be effective in the frequency domain representation. The compact support offered by the wavelet transform allows the analysis by space and the oscillating character of a signal. This type of analysis is best suited for non-stationary signal type. Although apparently PCG signal is characterized by time periodicity of cardiac activity, the high frequency components of the signal spectrum are strongly marked by acoustic noise which is created by blood flow through vessels and cardiac valves. Wavelet representation of a function is characterized by multi-resolution property which means that it can be decomposed in several scales. By performing wavelet transform on a signal it results a considerably signal vector size decreases due to decimation by 2, at each level of transform. This is essential as a good signal compression to store transform in a low amount of available memory and having limited resources which is specific to the embedded type of microcomputers. The simulation software packages of the Matlab programming environment, offers a wide range of functions as a representation of time-frequency analysis but their export is generally possible only at the graphic level. The correct design of the time-frequency scalogram algorithm requires more detailed study of how the spectrum inversion occurs at the decimation by two of the wavelet high pass filter. Identifying the areas in which the frequency spectrum inversion occurs can be done by the representation of wavelet packet on several levels. In figure 4 it can be observed the inversion algorithm then takes place.

The time-frequency scalogram decomposition is actually a total multi-resolution analysis, so that the representation of time-frequency scalogram requires the correct reordering of the resulted spectrum fields. So it can be seen how the spectrum fields results from filtering G (high pass), following the decimation by 2 produces spectral inversion. Given the above observations, in figure 4 we can see another interesting phenomenon in the last decomposition, where the order of occurrence of the frequency domains follows a pattern similar to the Gray code (A.Jensen & A. la Cour-Harbo, 2001). Spectral range as natural frequency ordering is done by interpreting the initial results of permutations that are written in binary 000, 001, 011, 010, 110, 111, 101, 100 (the string of numbers marked in green).

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 139

dsPIC30F6012 microcontroller the overall computing time is approximately 0.96 seconds. The displaying of the scalogram requires the construction of a special algorithm which is capable to calculate the addresses allocated to each pixel. The address of the first pixel is programmed for the upper left corner. This reference address position is convenient for

In the case of the scalogram the standard display mode changes the addresses on the vertical axis by computing the interlaced Gray code addressing mode used to correct the spectral distribution. For a continuous representation throughout the full 62-800Hz spectral range, the algorithm displays only the spectral bands found in the decomposition of level 7. The displaying algorithm (Gergely et al.) of the time-frequency plane is shown in figure 5:

After the total decomposition the obtained frequency resolution is given by equation 13:

*dec <sup>f</sup> <sup>f</sup> Hz*

Adding a further level of decomposition, increases the frequency resolution by increasing the number of bands, but also it occurs a lower temporal resolution by reducing the number of samples. This is a consequence of the principle that states that a time-frequency representation has an intrinsic limitation, as the product in time and frequency resolution is

> 1 2

800 62 5.76 128

(13)

*t f* (14)

limited by Heisenberg's uncertainty principle which expresses the equation 14:

*nr INDEX*

*Band*

standard graphics display and alphanumeric character set implementation.

Fig. 5. Time-frequency plane algorithm

Where *t* and *f* are given by equations 15 and 16:

Fig. 4. (a) Wavelet packet order (b) natural order

An autonomous medical device witch is using a graphical color display, showing a timefrequency scalograme as a result of multiple wavelets transforms, is a very complex problem. To solve the implementation on a microcontroller, the specific problems associated with time-frequency representation have following steps:


The time-frequency plane is used to describe the way in which the signal energy is distributed along the signal. The time-frequency scalogram is actually a full decomposition when analyzing multi-resolution, so that proper representation requires reordering the domain of the resulted spectrum. Spectral areas ordering by following the natural frequency, is done by interpreting the initial permutations results which are written in binary 000, 001, 011, 010, 110, 111, 101, 100. The new frequency order follows a Gray code pattern. It may be noted that Gray property type permutations is changing a single bit to change from one value to another. The computation of the time-frequency plane requires reiterating the wavelet transform routines for 254 times. The samples numbers of the original signal are decreasing to half after each transformation. Therefore the total amounts of required operations are 32768\*7=229376 MAC instructions. At the level of the

An autonomous medical device witch is using a graphical color display, showing a timefrequency scalograme as a result of multiple wavelets transforms, is a very complex problem. To solve the implementation on a microcontroller, the specific problems associated

a. Correct scaling of the calculated results of multi-resolution wavelet transforms on both

c. Construction of time-frequency plane by allocating the appropriate memory addresses

d. Correction of the natural order of frequency representation. Due to decimation by 2 at each level of decomposition, the filtered frequency domain appears in the mirror.

f. Converting data from the memory allocated time-frequency representation to a bxp type file. We assigned this type of graphics file to the DEM128160 display. The graphic conversion program between bmp files and bxp files were done by using the graphics

The time-frequency plane is used to describe the way in which the signal energy is distributed along the signal. The time-frequency scalogram is actually a full decomposition when analyzing multi-resolution, so that proper representation requires reordering the domain of the resulted spectrum. Spectral areas ordering by following the natural frequency, is done by interpreting the initial permutations results which are written in binary 000, 001, 011, 010, 110, 111, 101, 100. The new frequency order follows a Gray code pattern. It may be noted that Gray property type permutations is changing a single bit to change from one value to another. The computation of the time-frequency plane requires reiterating the wavelet transform routines for 254 times. The samples numbers of the original signal are decreasing to half after each transformation. Therefore the total amounts of required operations are 32768\*7=229376 MAC instructions. At the level of the

Fig. 4. (a) Wavelet packet order (b) natural order

for each levels of decomposition.

library of the Embarcadero C + + program.

x, y coordinates.

with time-frequency representation have following steps:

b. Calculation of the samples power average coefficient scaling.

e. Setting the calculated energy values to the equivalent RGB colors.

dsPIC30F6012 microcontroller the overall computing time is approximately 0.96 seconds. The displaying of the scalogram requires the construction of a special algorithm which is capable to calculate the addresses allocated to each pixel. The address of the first pixel is programmed for the upper left corner. This reference address position is convenient for standard graphics display and alphanumeric character set implementation.

In the case of the scalogram the standard display mode changes the addresses on the vertical axis by computing the interlaced Gray code addressing mode used to correct the spectral distribution. For a continuous representation throughout the full 62-800Hz spectral range, the algorithm displays only the spectral bands found in the decomposition of level 7. The displaying algorithm (Gergely et al.) of the time-frequency plane is shown in figure 5:

Fig. 5. Time-frequency plane algorithm

After the total decomposition the obtained frequency resolution is given by equation 13:

$$
\Delta f = \frac{\Delta f\_{Band}}{nr \left[INDEN\_{dec}\right]} = \frac{800 - 62}{128} = 5.76 Hz \tag{13}
$$

Adding a further level of decomposition, increases the frequency resolution by increasing the number of bands, but also it occurs a lower temporal resolution by reducing the number of samples. This is a consequence of the principle that states that a time-frequency representation has an intrinsic limitation, as the product in time and frequency resolution is limited by Heisenberg's uncertainty principle which expresses the equation 14:

$$
\Delta t \cdot \Delta f > \frac{1}{2} \tag{14}
$$

Where *t* and *f* are given by equations 15 and 16:

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 141

Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. In the wavelet transform theory the Shannon entropy is the measure for a cost function as how much decomposition has to be made to attain a full decomposition. After the signal decomposition, the level iterations contain a specific narrow signature reflected in the information content in a specific frequency band. At the end of the decomposition the signal is characterized by a number of Shannon's entropy coefficients. The first step in the characterization of the PCG signals is to compute the multi-resolution decomposition of the signal by using of the wavelet transform. The level at which the decomposition stops is given by the optimization is the number of calculations and the content of information of on levels below a certain threshold where it no longer pays a further decomposition. The multi-resolution wavelet decomposition shown in figure 7 presents a PCG signal with pathology. These representations are the result of simulations made under the National Instruments - LabWindows CVI platform without using any embedded software packages for the wavelet

transform.

Fig. 7. Shannon entropy of PCG signal decomposition

on up to L levels and containing N samples for the original signal.

Equation 17 (Gergely S., 2011) represents the matrix of a PCG signal which is decomposed

$$
\Delta t = \sqrt{\frac{t^2 \left| \nu \left( t \right) \right|^2 dt}{\int \left| \nu \left( t \right) \right|^2 dt}} \tag{15}
$$

$$
\Delta f = \sqrt{\frac{\int \alpha^2 \left| \Psi \left( \alpha \right) \right|^2 d\alpha}{\int \left| \Psi \left( \alpha \right) \right|^2 d\alpha}} \tag{16}
$$

Where is the Fourier transform of base wavelet function 

In figure 6 it is showed a few time-frequency scalograms obtained by using of the multiresolution algorithm presented in figure 5.

Fig. 6. Time-frequency scalograms of the acquired PCG signals

#### **2.3 The Shannon multirate entropy in computing of the Euclidian distance of the PCG pathology**

In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits.

*t*

*f*

is the Fourier transform of base wavelet function

Fig. 6. Time-frequency scalograms of the acquired PCG signals

**2.3 The Shannon multirate entropy in computing of the Euclidian distance of the PCG** 

In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits.

Where

**pathology** 

resolution algorithm presented in figure 5.

 

2 *t t dt*

*t dt*

 

 

2 *d*

*d*

2 2

(15)

(16)

2 2

> 

In figure 6 it is showed a few time-frequency scalograms obtained by using of the multi-

Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. In the wavelet transform theory the Shannon entropy is the measure for a cost function as how much decomposition has to be made to attain a full decomposition. After the signal decomposition, the level iterations contain a specific narrow signature reflected in the information content in a specific frequency band. At the end of the decomposition the signal is characterized by a number of Shannon's entropy coefficients. The first step in the characterization of the PCG signals is to compute the multi-resolution decomposition of the signal by using of the wavelet transform. The level at which the decomposition stops is given by the optimization is the number of calculations and the content of information of on levels below a certain threshold where it no longer pays a further decomposition. The multi-resolution wavelet decomposition shown in figure 7 presents a PCG signal with pathology. These representations are the result of simulations made under the National Instruments - LabWindows CVI platform without using any embedded software packages for the wavelet transform.

Fig. 7. Shannon entropy of PCG signal decomposition

Equation 17 (Gergely S., 2011) represents the matrix of a PCG signal which is decomposed on up to L levels and containing N samples for the original signal.

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 143

The correlation algorithm is using only the approximation coefficients of the wavelet transform. So that the question is which decomposition level is to be used for the signal correlation algorithm? The envelope of the signal must contain as much as possible amount of samples to get a specific pathology characterization. The property of the multilevel wavelet transform is that, each computed approximation coefficients do contain both the approximation and detail coefficients of the next level. The envelope of the PCG signal is computed by using the third level of signal decomposition which is

After all the issue is to test the correlation between the acquired signal and all reference signals that are stored in the *SD* card. Our studies showed that the heart beat rate does not affect the overall spectral density of the *PCG* signal. The Shannon sampling theorem has been extended to allow for sampling times which are not uniformly spaced (Gergely S., 2011; Fliege N.J., 1994). Several slightly different versions of the non-uniform sampling theorem have arisen. The differences lie in the spaces of functions being considered and the different classes of sampling times which are permitted. The theorem essentially says that a band-limited signal *x*(*t*) is uniquely determined by knowledge of its samples *{an* = *x*(*tn*)*}* as long as the sampling times *{tn}* occur at a rate which is on average higher than the *Nyquist* rate. By compressing or expanding the signal the envelope remains shift able and also the resulted frequency variations are not important. The frequency content is previously analyzed by the using of the

**2.4 Correlation of the PCG signals** 

Fig. 8. Decomposition levels of the PCG signals

shown in figure 8:

$$\mathcal{W}\_{L}\left(N\right) = \begin{vmatrix} c\_{11} & c\_{12} & c\_{13} & c\_{14} & \dots & c\_{1N} \\ c\_{21} & c\_{22} & c\_{23} & \dots & c\_{2N} & 0 \\ c\_{31} & c\_{32} & \dots & c\_{3N} & 0 & 0 \\ c\_{41} & c\_{42} & \dots & c\_{4N} & 0 & 0 \\ & \dots & \dots & \dots & \dots & \dots \\ \dots & \dots & \dots & \dots & \dots & \dots \\ c\_{L,1} & c\_{L,2} & \dots & c\_{L,N-2} & 0 & 0 \end{vmatrix} \tag{17}$$

Such a signal can be represented and stored using only 14 coefficients by replacing each line in the matrix with 2 coefficients obtained by computing the Shannon entropy of each individual level of decomposition. These two coefficients are taken from the above figure. By simulation of the calculation algorithms directly in C language, it was significantly reduced the time required to implement the DSP programs. For this reason, the code generation for the DSP microcontroller was used in another C compiler but with the same source code optimized for a different level of precision. Quantization errors which are inherent in floating point calculations do not alter the results because all evaluations were made by identifying only the minimum values of Euclidian distance. The Euclidian distance is computed by using equation 18:

$$d\left(p\_{ij}, q\_{ij}\right) = \sqrt{\sum\_{i=1}^{m} \sum\_{j=1}^{n} \left(q\_{ij} - p\_{ij}\right)^2} \tag{18}$$

The signal coefficients are stored in the SD memory card in specific vectors (address) which represent the comparison reference for the recognizing process of the specific pathology. By using the Shannon entropy coefficients there is not necessary to store the entire pathology signals. These coefficients represent the compressed form of the pathology signals. The pathology signals have therefore specific spectral fingerprints which are used to compute the Euclidian distance between the stored reference vectors and the currently analyzed signal. By using the wavelet transform in the analyzing of *PCG* signals it is possible to compress and to preserve all time–frequency characteristics of the signals. On the other hand either time domain or frequency domain analysis does not fully describe the nature of non-stationary signal. A pathological *PCG* signal is dominated by the high frequency components along with the low frequency *S* type pulses. The statistical characterization method is usable only for a primary signal classification. A precise *PCG* signal characterization done with the intention of pathology recognizing, is possible only if a reference signal is in fact compared with the fully or partially acquired signal. The frequency content in the multilevel wavelet transform may well be evaluated by the information content of each level defined by the Shannon entropy which is presented in the following equation:

$$S = -\sum\_{i=0}^{N} \mathbf{x}\_i^2 \log \left(\mathbf{x}\_i^2\right) \tag{19}$$

The estimation of the signals envelope as a final characterization is a difficult task that involves intensive computing resources. Therefore the algorithm was designed to be implemented on a device using *DSP* engine for the signal processing.

#### **2.4 Correlation of the PCG signals**

142 Applied Biological Engineering – Principles and Practice

*ccc c*

31 32 <sup>3</sup> <sup>4</sup> 41 42 <sup>4</sup> <sup>8</sup>

*cc c*

*cc c*

,1 ,2 , 2

Such a signal can be represented and stored using only 14 coefficients by replacing each line in the matrix with 2 coefficients obtained by computing the Shannon entropy of each individual level of decomposition. These two coefficients are taken from the above figure. By simulation of the calculation algorithms directly in C language, it was significantly reduced the time required to implement the DSP programs. For this reason, the code generation for the DSP microcontroller was used in another C compiler but with the same source code optimized for a different level of precision. Quantization errors which are inherent in floating point calculations do not alter the results because all evaluations were made by identifying only the minimum values of Euclidian distance. The Euclidian distance

> <sup>2</sup> 1 1

The signal coefficients are stored in the SD memory card in specific vectors (address) which represent the comparison reference for the recognizing process of the specific pathology. By using the Shannon entropy coefficients there is not necessary to store the entire pathology signals. These coefficients represent the compressed form of the pathology signals. The pathology signals have therefore specific spectral fingerprints which are used to compute the Euclidian distance between the stored reference vectors and the currently analyzed signal. By using the wavelet transform in the analyzing of *PCG* signals it is possible to compress and to preserve all time–frequency characteristics of the signals. On the other hand either time domain or frequency domain analysis does not fully describe the nature of non-stationary signal. A pathological *PCG* signal is dominated by the high frequency components along with the low frequency *S* type pulses. The statistical characterization method is usable only for a primary signal classification. A precise *PCG* signal characterization done with the intention of pathology recognizing, is possible only if a reference signal is in fact compared with the fully or partially acquired signal. The frequency content in the multilevel wavelet transform may well be evaluated by the information content of each level defined by the Shannon entropy which is presented in the following

2 2

log

*i i*

0

The estimation of the signals envelope as a final characterization is a difficult task that involves intensive computing resources. Therefore the algorithm was designed to be

*i S xx* 

implemented on a device using *DSP* engine for the signal processing.

*N*

*m n ij ij ij ij i j dp q q p* 

,

*L L L N*

*cc c*

11 12 13 14 1 21 22 23 <sup>2</sup> <sup>2</sup>

*ccc c c*

... ... ... ... ... ...

... ... 0

*N*

(17)

*N*

(18)

(19)

... 0 0 ... 0 0

*N*

*N*

... *<sup>L</sup>* 0 0

*L*

is computed by using equation 18:

equation:

*W N*

The correlation algorithm is using only the approximation coefficients of the wavelet transform. So that the question is which decomposition level is to be used for the signal correlation algorithm? The envelope of the signal must contain as much as possible amount of samples to get a specific pathology characterization. The property of the multilevel wavelet transform is that, each computed approximation coefficients do contain both the approximation and detail coefficients of the next level. The envelope of the PCG signal is computed by using the third level of signal decomposition which is shown in figure 8:

Fig. 8. Decomposition levels of the PCG signals

After all the issue is to test the correlation between the acquired signal and all reference signals that are stored in the *SD* card. Our studies showed that the heart beat rate does not affect the overall spectral density of the *PCG* signal. The Shannon sampling theorem has been extended to allow for sampling times which are not uniformly spaced (Gergely S., 2011; Fliege N.J., 1994). Several slightly different versions of the non-uniform sampling theorem have arisen. The differences lie in the spaces of functions being considered and the different classes of sampling times which are permitted. The theorem essentially says that a band-limited signal *x*(*t*) is uniquely determined by knowledge of its samples *{an* = *x*(*tn*)*}* as long as the sampling times *{tn}* occur at a rate which is on average higher than the *Nyquist* rate. By compressing or expanding the signal the envelope remains shift able and also the resulted frequency variations are not important. The frequency content is previously analyzed by the using of the

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 145

After the computing of the autocorrelation the HBR parameter is obtained with the equation

The correct cross-correlation is complete after the re-sampling of the acquired signal in accordance to the reference signal *HBR*. After re-sampling, the signal is interpreted as having the same original sampling rate. The necessary re-sampling rate is given by the ratio between the HBR parameter of the analyzed signal and the HBR parameter of the reference:

*nW HBR beats*

algorithm has the drawback of using a lot of memory space in the systems memory.

*Sr x tn <sup>L</sup> <sup>R</sup> Rr x tn M*

Where L is the interpolation factor which means that between two consecutive signal samples there are inserted a number of L-1 zeros. M is the decimation factor which is always constantly equal with 100. Extensive simulations have proved that the algorithm is permissive to an RRAtio from 0.43 to 0.99. The reference signal is always converted to a HBR equal to 100 before it is stored in the pathology data base. As a consequence the above

The sensitive part of the overall algorithm is the interpolator used in the multirate sampling module. It turned out that the final correlation operation is obviously sensitive to the unmatched envelope. The issue is the lag over the real envelope of the computed values in case of a under filtering or a diminishing and distorted wave form in case of an over filtering. Therefore it was necessary to calculate the interpolation filter. The first step of using a linear interpolator has the ability of good low frequency attenuation but on the other hand the high frequency components of the envelope signal are slightly distorted. Finally

<sup>3</sup> <sup>60</sup> /min int

*Ratio*

*n index T*

*sampling*

(21)

(22)

Fig. 10. Auto-correlation of the third level decomposed PCG signal

21:

*Shannon* entropy which classifies the *PCG* signal at each wavelet decomposition level. The complex overall algorithm is shown in figure:

Fig. 9. PCG signal correlation algorithm

The above presented algorithm is capable to analyze the extremely complex structure of the PCG signal which is characterized by a signal envelope which is amplitude modulated and in the same time it is frequency modulated having specific and distributed "carrier" frequencies. The frequency band of the original PCG signal is limited extremely sharp by using a 512 coefficients FIR filter which follows the input anti-alias analog filter. The useful frequency band of the PCG signal is situated between 62-800 Hz.

The main difficulty in doing the correlation task is that, the acquired signal is never at the same *HBR* (Heart Beat Rate) like the reference signals; as a result the time shift will corrupt the peak value of the cross-correlation. All signal envelopes references are recorded at a known *HBR*, information which is stored in the file of each signal. In signal processing, auto-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or inner-product. It is commonly used to search a long duration signal for a shorter, known feature. The auto-correlation (Broersen Piet M.T., 2006). of the third level decomposition is done by using the equation:

$$R\_{\text{xx}}\left(j\right) = \sum\_{i} \mathbf{x}\_{i} \mathbf{x}\_{i-j} \tag{20}$$

The reason for which we have used the third level of decomposition instead of the original signal is because of the necessity to reduce the number of computation operations. By using the third level of decomposition, the overall computations are reduced by a factor of 64 due to the squaring of the samplings reduction which is at a factor of 8. The using of the crosscorrelation is the only practical method to extract a certain sequence from a noisy PCG signal which is dominated by the murmur of the heart (Abdallah et al.,1988).. The resulted auto-correlation is shown in figure 10:

*Shannon* entropy which classifies the *PCG* signal at each wavelet decomposition level. The

The above presented algorithm is capable to analyze the extremely complex structure of the PCG signal which is characterized by a signal envelope which is amplitude modulated and in the same time it is frequency modulated having specific and distributed "carrier" frequencies. The frequency band of the original PCG signal is limited extremely sharp by using a 512 coefficients FIR filter which follows the input anti-alias analog filter. The useful

The main difficulty in doing the correlation task is that, the acquired signal is never at the same *HBR* (Heart Beat Rate) like the reference signals; as a result the time shift will corrupt the peak value of the cross-correlation. All signal envelopes references are recorded at a known *HBR*, information which is stored in the file of each signal. In signal processing, auto-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or inner-product. It is commonly used to search a long duration signal for a shorter, known feature. The auto-correlation (Broersen Piet M.T.,

> *xx i i <sup>j</sup> i*

The reason for which we have used the third level of decomposition instead of the original signal is because of the necessity to reduce the number of computation operations. By using the third level of decomposition, the overall computations are reduced by a factor of 64 due to the squaring of the samplings reduction which is at a factor of 8. The using of the crosscorrelation is the only practical method to extract a certain sequence from a noisy PCG signal which is dominated by the murmur of the heart (Abdallah et al.,1988).. The resulted

*<sup>R</sup> <sup>j</sup> x x* (20)

complex overall algorithm is shown in figure:

Fig. 9. PCG signal correlation algorithm

auto-correlation is shown in figure 10:

frequency band of the PCG signal is situated between 62-800 Hz.

2006). of the third level decomposition is done by using the equation:

Fig. 10. Auto-correlation of the third level decomposed PCG signal

After the computing of the autocorrelation the HBR parameter is obtained with the equation 21:

$$HBR\left(\text{beats} \,/\,\text{min}\right) = \text{int}\left(\begin{array}{c} \mathbf{60} \cdot nW\_3\\ n\left[\text{index}\right] \cdot T\_{\text{sampling}} \end{array}\right) \tag{21}$$

The correct cross-correlation is complete after the re-sampling of the acquired signal in accordance to the reference signal *HBR*. After re-sampling, the signal is interpreted as having the same original sampling rate. The necessary re-sampling rate is given by the ratio between the HBR parameter of the analyzed signal and the HBR parameter of the reference:

$$\frac{\text{Str }\uparrow \ge (tn)}{\text{R }r \downarrow \ge (tn)} = \frac{L}{M} = R\_{Ratio} \tag{22}$$

Where L is the interpolation factor which means that between two consecutive signal samples there are inserted a number of L-1 zeros. M is the decimation factor which is always constantly equal with 100. Extensive simulations have proved that the algorithm is permissive to an RRAtio from 0.43 to 0.99. The reference signal is always converted to a HBR equal to 100 before it is stored in the pathology data base. As a consequence the above algorithm has the drawback of using a lot of memory space in the systems memory.

The sensitive part of the overall algorithm is the interpolator used in the multirate sampling module. It turned out that the final correlation operation is obviously sensitive to the unmatched envelope. The issue is the lag over the real envelope of the computed values in case of a under filtering or a diminishing and distorted wave form in case of an over filtering. Therefore it was necessary to calculate the interpolation filter. The first step of using a linear interpolator has the ability of good low frequency attenuation but on the other hand the high frequency components of the envelope signal are slightly distorted. Finally

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 147

*STOP PASS sampling*

> 3.3 *sampling*

> > 300

*aquired*

*HBR*

*ref*

*f f <sup>f</sup> <sup>f</sup>*

*N*

*Ratio*

these coefficients are stored in the program memory of the DSP microcontroller.

Fig. 12. Time compression of the PCG signal by using the third level of decomposition

*R*

The cutting frequency does not depend on the interpolation factor *L* and is given by:

2 *PASS STOP <sup>t</sup>*

It yields for *L* interpolation factor between 43 to 99 a number of 355 to 817 coefficients.

For the above mentioned RRatio interval we got a number of coefficients between 355 and 817. The result of the re-sampling process is shown in the figure 12. These values aren't large in comparison to the permanently used 512 coefficients in the overall band pass filter. All

The number of filtering coefficients is computed with equation 6.8

For HBR between 43 - 99

Where *HBRre*f =100

*h n hn w n <sup>w</sup> Ham* (26)

(27)

*f f <sup>f</sup> Hz* (29)

*<sup>f</sup>* (28)

*HBR* (30)

we have preferred a FIR filter. The usually used two filters for the re-sampling process is reduced to a single filter which is chosen by using equation 23; (Fliege N.J., 1994)

$$\theta\_c = \min\left(\frac{\pi}{L}, \frac{\pi}{M}\right) \tag{23}$$

At the third level of signal decomposition the new sampling rate is interpreted as 1000 Hz The frequency domain which must be covered by the filters is shown in figure 11:

Fig. 11. Frquency domain of the multirate sampling filter

Therefore the imposed conditions to the re-sampling filter are:


Below are presented the equations used to compute the interpolation filter:

The impulse response of the low pass filter is given by equation 24:

$$h(n) = \begin{cases} \frac{\Omega\_c}{\pi} & n = 0\\ \frac{\pi}{\sin\left(\Omega\_c n\right)} & \text{for } n \neq 0 \text{ , } -M \le n \le M\\ \frac{\sin\left(\Omega\_c n\right)}{n\pi} & \end{cases} \tag{24}$$

The filter coefficients are weighted with the Hamming window:

$$w\_{Ham}(n) = 0.54 + 0.46 \cos\left(\frac{n\pi}{M}\right) \text{ where } -M \le n \le M \tag{25}$$

$$h\_w(n) = h(n) \cdot w\_{Ham}(n) \tag{26}$$

The number of filtering coefficients is computed with equation 6.8

$$
\Delta f = \frac{f\_{\text{STOP}} - f\_{\text{PASS}}}{f\_{\text{sampling}}} \tag{27}
$$

$$N = \frac{3.3}{\Delta f\_{sampling}}\tag{28}$$

The cutting frequency does not depend on the interpolation factor *L* and is given by:

$$f\_t = \frac{f\_{pASS} + f\_{STOP}}{2} = 300Hz \tag{29}$$

For HBR between 43 - 99

146 Applied Biological Engineering – Principles and Practice

we have preferred a FIR filter. The usually used two filters for the re-sampling process is

min , *<sup>c</sup> L M* 

At the third level of signal decomposition the new sampling rate is interpreted as 1000 Hz

(23)

for 0 *n* , *M n M* (24)

where *<sup>M</sup> n M* (25)

reduced to a single filter which is chosen by using equation 23; (Fliege N.J., 1994)

The frequency domain which must be covered by the filters is shown in figure 11:

Fig. 11. Frquency domain of the multirate sampling filter

1. Pass band 0÷100Hz 2. First stop band 100÷500Hz 3. Second pass band 0÷100Hz 4. Second stop band 500Hz÷50KHz

5. Pass band ripple 0.02db 6. Stop band attenuation 53db 7. Used window: Hamming

Therefore the imposed conditions to the re-sampling filter are:

Below are presented the equations used to compute the interpolation filter:

0

*M* 

*c*

*n*

*n*

The impulse response of the low pass filter is given by equation 24:

The filter coefficients are weighted with the Hamming window:

*h n*

*w n*

sin

*Ham* 0.54 0.46cos *<sup>n</sup>*

 

*n*

*c*

$$R\_{Ratio} = \frac{H \text{BR}\_{aquried}}{H \text{BR}\_{ref}} \tag{30}$$

Where *HBRre*f =100

It yields for *L* interpolation factor between 43 to 99 a number of 355 to 817 coefficients.

For the above mentioned RRatio interval we got a number of coefficients between 355 and 817. The result of the re-sampling process is shown in the figure 12. These values aren't large in comparison to the permanently used 512 coefficients in the overall band pass filter. All these coefficients are stored in the program memory of the DSP microcontroller.

Fig. 12. Time compression of the PCG signal by using the third level of decomposition

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 149

2 2 0

 

(32)

> 

(33)

 

(34)

*s s*

*j t j t j t h t H e d je d e d*

1 1 0 /2 /2 0 1 cos /2 <sup>2</sup>

For a discrete signal the above result has to be adapted, therefore the final form is given by

 1 cos *sf h n <sup>n</sup> n*

*<sup>s</sup> ee e e*

<sup>202</sup>

*s s*

*s s j jt jt j*

*t t*

 

Fig. 14. (a) Impulse response of the Hilbert transform (b) using of a Blackman window

coefficients using the finite impulse response of the transform.

It is possible to use a signal envelope in the evaluation process of the PCG signal because the algorithm does not care about the frequency spectrum of the original signal. The frequency spectrum of the signal was previously evaluated in a probabilistic manner by the Shannon entropy. The Hilbert transform is software implemented by computing the filtering

Therefore the FIR coefficients are computed by replacing the n index in the above equation. Choosing an odd number of coefficients is an essential criterion because of the center tap of the signal phase condition. To improve the low frequency response of the Hilbert transform we used a supplementary Blackman window. The Hilbert transform implementation is

The impulse response of the Hilbert transform is shown in figure 14:

For *n and h n pentru n* 0, 0, 0 where

fs is the sampling rate in samples/second

n is the time domain index,

shown in figure 15:

equation 34:

1 11 2 22

#### **2.5 Computing of the PCG signals envelope**

Hilbert transform is a process which is capable to extract the precise envelope of a given signal. Generating a signal in the complex domain and out of phase by 90 degrees from the real signal provides a series of numerical processing such as quadrature modulation and demodulation of signals, and the implementation of automatic gain control systems. Time and frequency representation shows how the Hilbert transform cosine signal spectral component rotates with -j and the negative component by +j. An important property of the Hilbert transform is that it is a theoretical system with frequency response magnitude one and phase equal to 90 degrees for all frequencies. This means that a signal passing through a Hilbert system will be weighted by 2 the amplitude and phase will be modified by ¼ the period T. If a real signal xr(t) is modulated in amplitude, then the modulated signal envelope is that it contains the useful information. So the instantaneous envelope E(t) becomes:

$$E(t) = \left| \mathbf{x}\_c(t) \right| = \sqrt{\mathbf{x}\_r(t)^2 + \mathbf{x}\_i(t)^2} \tag{31}$$

The above equation is the envelope of the modulator signal and is used to calculate also the PCG signal envelope. Traditional signal demodulation of amplitude modulated signal consists of previously rectifying the signal by squaring and applying a smoothing low pass filter for the carrier frequency. This type of demodulation has been tested for PCG signal envelope but a comparison shows that the voltage ripple obtained by Hilbert transform is clearly in favor. The filter ripple for both methods is shown in figure 13:

Fig. 13. Voltage ripple (a) Squaring method (b) Hilbert transform

In terms of the number of calculations required, the Hilbert transform method is faster because it involves the using of a filter with a lower number of coefficients.

Implementation of Hilbert transform involves the calculating of the impulse response of a system considered linear. So that for arbitrary signal:

$$h(t) = \frac{1}{2\pi} \int\_{-a/2}^{a/2} H\left(o\right) e^{iat} do = \frac{1}{2\pi} \int\_{-a/2}^{0} je^{iat} do + \frac{1}{2\pi} \int\_{0}^{a/2} -e^{iat} do \tag{32}$$

$$\hat{\sigma} = \frac{1}{2\pi t} \left( e^{j0} - e^{-j\alpha\_s t/2} - e^{-j\alpha\_s t/2} + e^{j0} \right) = \frac{1}{\pi t} \left[ 1 - \cos(\alpha\_s / 2) \right] \tag{33}$$

For a discrete signal the above result has to be adapted, therefore the final form is given by equation 34:

$$h(n) = \frac{f\_s}{\pi n} \left[ 1 - \cos(\pi n) \right] \tag{34}$$

For *n and h n pentru n* 0, 0, 0 where

n is the time domain index,

148 Applied Biological Engineering – Principles and Practice

Hilbert transform is a process which is capable to extract the precise envelope of a given signal. Generating a signal in the complex domain and out of phase by 90 degrees from the real signal provides a series of numerical processing such as quadrature modulation and demodulation of signals, and the implementation of automatic gain control systems. Time and frequency representation shows how the Hilbert transform cosine signal spectral component rotates with -j and the negative component by +j. An important property of the Hilbert transform is that it is a theoretical system with frequency response magnitude one and phase equal to 90 degrees for all frequencies. This means that a signal passing through a Hilbert system will be weighted by 2 the amplitude and phase will be modified by ¼ the period T. If a real signal xr(t) is modulated in amplitude, then the modulated signal envelope is that it contains the useful information. So the instantaneous

The above equation is the envelope of the modulator signal and is used to calculate also the PCG signal envelope. Traditional signal demodulation of amplitude modulated signal consists of previously rectifying the signal by squaring and applying a smoothing low pass filter for the carrier frequency. This type of demodulation has been tested for PCG signal envelope but a comparison shows that the voltage ripple obtained by Hilbert transform is

In terms of the number of calculations required, the Hilbert transform method is faster

Implementation of Hilbert transform involves the calculating of the impulse response of a

clearly in favor. The filter ripple for both methods is shown in figure 13:

Fig. 13. Voltage ripple (a) Squaring method (b) Hilbert transform

system considered linear. So that for arbitrary signal:

because it involves the using of a filter with a lower number of coefficients.

2 2 *Et x t x t x t c ri* (31)

**2.5 Computing of the PCG signals envelope** 

envelope E(t) becomes:

fs is the sampling rate in samples/second

The impulse response of the Hilbert transform is shown in figure 14:

Fig. 14. (a) Impulse response of the Hilbert transform (b) using of a Blackman window

It is possible to use a signal envelope in the evaluation process of the PCG signal because the algorithm does not care about the frequency spectrum of the original signal. The frequency spectrum of the signal was previously evaluated in a probabilistic manner by the Shannon entropy. The Hilbert transform is software implemented by computing the filtering coefficients using the finite impulse response of the transform.

Therefore the FIR coefficients are computed by replacing the n index in the above equation. Choosing an odd number of coefficients is an essential criterion because of the center tap of the signal phase condition. To improve the low frequency response of the Hilbert transform we used a supplementary Blackman window. The Hilbert transform implementation is shown in figure 15:

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 151

analysis similar to pattern recognition located in an image (Andrew K.Chan & Steve J.Liu, 1998). Thus the points defined in terms of measured values X0Y are introducing a second dimension of the signal and can thus be interpreted as an image. Reducing the number of calculations required to scale the amplitude vector x[t] for a number of dots (pixels).This type of resulted image can be processed by using advanced image processing methods. On a closer analysis, there is an important feature which allows to limit one of the coordinates of the vector w[y][x]. It can be observed that both signals involved in the algorithm are scaled to the same number of values on the Y coordinate, which provides a significantly higher computing speed. This was imposed because the simple convolution of the reference signal with the analyzed signal in order to get the pathology correlation is not efficient. The solution to the problem was to convert the one dimensional signal vector to a twodimensional vector which at the end represents a graphical image of the PCG signal (Anke Meyer-Base, 2004). The conversion starts with the dividing of the sample amplitude to a given number of desired vertical pixels. If the value is in the computed domain it will be replaced by the value of 1, or if the value is outside of the domain it becomes zero. The

signal conversion process is shown in figure 17.

Fig. 17. Two-dimensional conversion of the PCG signal

processed by using conventional image processing algorithms.

are shown in figure 18:

By extending the method it is possible to give a different magnitude to different image segments by inserting different values instead of ones. As a result the image performs as a picture having a new z coordinate. The modified method makes possible the transformation from absolute pathology detection to a probable type of detection which is useful for primary pathology classification. This way the PCG signal image of the envelope is

The extraction of the PCG signal references is done using a custom designed program which is fully interactive and provides the necessary support for the archiving of the results. All extracted reference vectors are stored in the SD card of a hand held device. The amount of necessary memory to store a reference image does not exceed 2KB. Some reference images

Fig. 15. Software implementation of the Hilbert transforms

The results by using the Hilbert transform are shown in figure 16. It can be observed the almost perfect envelope of a signal having a complex frequency spectrum below the detected envelope. The Hilbert transform does not influence the peak value of the signal which is an important feature of the envelope extraction procedure.

Fig. 16. Envelope detection of the PCG signal

Due to the complex structure of the PCG signal which is characterized by the presence of a large number of distributed peak values, it was necessary to introduce supplementary information regarding the amplitude of the signal. During the researches we applied a new method to analyze the PCG signal by introducing an additional coordinate to the signal vector which is visible in picture 17. The idea is that we switched to two-dimensional

The results by using the Hilbert transform are shown in figure 16. It can be observed the almost perfect envelope of a signal having a complex frequency spectrum below the detected envelope. The Hilbert transform does not influence the peak value of the signal

Due to the complex structure of the PCG signal which is characterized by the presence of a large number of distributed peak values, it was necessary to introduce supplementary information regarding the amplitude of the signal. During the researches we applied a new method to analyze the PCG signal by introducing an additional coordinate to the signal vector which is visible in picture 17. The idea is that we switched to two-dimensional

Fig. 15. Software implementation of the Hilbert transforms

Fig. 16. Envelope detection of the PCG signal

which is an important feature of the envelope extraction procedure.

analysis similar to pattern recognition located in an image (Andrew K.Chan & Steve J.Liu, 1998). Thus the points defined in terms of measured values X0Y are introducing a second dimension of the signal and can thus be interpreted as an image. Reducing the number of calculations required to scale the amplitude vector x[t] for a number of dots (pixels).This type of resulted image can be processed by using advanced image processing methods. On a closer analysis, there is an important feature which allows to limit one of the coordinates of the vector w[y][x]. It can be observed that both signals involved in the algorithm are scaled to the same number of values on the Y coordinate, which provides a significantly higher computing speed. This was imposed because the simple convolution of the reference signal with the analyzed signal in order to get the pathology correlation is not efficient. The solution to the problem was to convert the one dimensional signal vector to a twodimensional vector which at the end represents a graphical image of the PCG signal (Anke Meyer-Base, 2004). The conversion starts with the dividing of the sample amplitude to a given number of desired vertical pixels. If the value is in the computed domain it will be replaced by the value of 1, or if the value is outside of the domain it becomes zero. The signal conversion process is shown in figure 17.

Fig. 17. Two-dimensional conversion of the PCG signal

By extending the method it is possible to give a different magnitude to different image segments by inserting different values instead of ones. As a result the image performs as a picture having a new z coordinate. The modified method makes possible the transformation from absolute pathology detection to a probable type of detection which is useful for primary pathology classification. This way the PCG signal image of the envelope is processed by using conventional image processing algorithms.

The extraction of the PCG signal references is done using a custom designed program which is fully interactive and provides the necessary support for the archiving of the results. All extracted reference vectors are stored in the SD card of a hand held device. The amount of necessary memory to store a reference image does not exceed 2KB. Some reference images are shown in figure 18:

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 153

without intensity parameter Z (pixel has value 1) and no interpolation therefore a minimum number of points. The lowest number of points (42) is contained by the reference of normal heart rhythm. Analogous to the procedure for the reference signal, it applies the same above procedure for the analyzed signal. As a pattern recognition method, we have used the computation of the Euclidian distance between the analyzed signal and the stored

The equipment's operating system (Gergely S., 2011) is programmed to handle internal data flow between its component microcontrollers, communication with the outside through the USB port and graphics system. An important component of the program management module for distributing data is between the two microcontrollers. The operating system was designed to allow on board test routines running for the speed performance evaluation of the development system. The hardware system connects to a PC via USB2 interface which is managed by its own program, designed specifically for this application. The host program was implemented in LabWindows CVI which is capable to load into RAM or SD card any routine to emulate the original data in the DSP microcontroller. The resulting data are then transmitted back to the PC for evaluation. This was required because between the programs which are running on your PC and development board are differences in the computing precision. While DSP microcontroller does run routines with the precision given by organizing the data in Q1.15 format, all written routines in LabWindows CVI for the initial simulation are in double precision. The hardware uses a dsPIC30F6012 microcontroller with built-in DSP unit and a PIC18F4550 microcontroller equipped with built-in USB (Gergely S., 2011; Axelson Jan,

The hardware set of elements which are entering in the composition of the DSP module are specialized for rapid calculation of the amount of products. This equation is fundamental in digital signal processing and mathematical point of view is based on the convolution operation. The development is designed so that it carries out all processes signal analysis

1

*i i*

(35)

*N*

*i S ab* 

0

Recursive FIR filter implementation can be done easily by using modulo addressing type programming which after computing the values; it provides the return address used for the filter coefficients. Hilbert transform calculation assumes a similar algorithm but to simplify modulo addressing type, due to the small amount of Hilbert coefficients the zero values are

The DSP microcontroller has two direct hardware implemented instructions to compute the Euclidian distance with or without accumulation (ED and EDAC). The minimum value for the distance measured to all references represents the match with the analyzed signal. The

**3. Construction of a PCG signal analyzer device** 

references.

2006) full speed mode.

using equation 35:

inserted in the looping list.

data stored on the SD card is downloaded via the USB.

Fig. 18. PCG signals reference images

Pathology reference images were extracted from the real signals and shows how easy it can be identified with the pathology of origin. The obtained signals does resemble with the well known EKG signals. All noises under the signals envelope were eliminated for a better pathology exploration. By computing the Euclidian distance in order to evaluate the correlation between these reference signals and the analyzed signals, finally we got a nearly perfect match which is shown in figure 19:

Fig. 19. Perfect correlations of two PCG signals

The construction of the above shown algorithm is achieved through a very simple calculation routine that consists only of a few lines of program. Reference signals were rescaled to 1Volt for a total of 50 points. The x axis number of points remains unchanged against the original signal and dynamically allocated between 100 and maximum 350 points. Under these conditions the reference image is represented in a matrix of 50x350 points. To test the recognition algorithm, the routine uses computer generated pixels of the image without intensity parameter Z (pixel has value 1) and no interpolation therefore a minimum number of points. The lowest number of points (42) is contained by the reference of normal heart rhythm. Analogous to the procedure for the reference signal, it applies the same above procedure for the analyzed signal. As a pattern recognition method, we have used the computation of the Euclidian distance between the analyzed signal and the stored references.

## **3. Construction of a PCG signal analyzer device**

152 Applied Biological Engineering – Principles and Practice

Pathology reference images were extracted from the real signals and shows how easy it can be identified with the pathology of origin. The obtained signals does resemble with the well known EKG signals. All noises under the signals envelope were eliminated for a better pathology exploration. By computing the Euclidian distance in order to evaluate the correlation between these reference signals and the analyzed signals, finally we got a nearly

The construction of the above shown algorithm is achieved through a very simple calculation routine that consists only of a few lines of program. Reference signals were rescaled to 1Volt for a total of 50 points. The x axis number of points remains unchanged against the original signal and dynamically allocated between 100 and maximum 350 points. Under these conditions the reference image is represented in a matrix of 50x350 points. To test the recognition algorithm, the routine uses computer generated pixels of the image

Fig. 18. PCG signals reference images

perfect match which is shown in figure 19:

Fig. 19. Perfect correlations of two PCG signals

The equipment's operating system (Gergely S., 2011) is programmed to handle internal data flow between its component microcontrollers, communication with the outside through the USB port and graphics system. An important component of the program management module for distributing data is between the two microcontrollers. The operating system was designed to allow on board test routines running for the speed performance evaluation of the development system. The hardware system connects to a PC via USB2 interface which is managed by its own program, designed specifically for this application. The host program was implemented in LabWindows CVI which is capable to load into RAM or SD card any routine to emulate the original data in the DSP microcontroller. The resulting data are then transmitted back to the PC for evaluation. This was required because between the programs which are running on your PC and development board are differences in the computing precision. While DSP microcontroller does run routines with the precision given by organizing the data in Q1.15 format, all written routines in LabWindows CVI for the initial simulation are in double precision. The hardware uses a dsPIC30F6012 microcontroller with built-in DSP unit and a PIC18F4550 microcontroller equipped with built-in USB (Gergely S., 2011; Axelson Jan, 2006) full speed mode.

The hardware set of elements which are entering in the composition of the DSP module are specialized for rapid calculation of the amount of products. This equation is fundamental in digital signal processing and mathematical point of view is based on the convolution operation. The development is designed so that it carries out all processes signal analysis using equation 35:

$$S = \sum\_{i=0}^{N-1} a\_i b\_i \tag{35}$$

Recursive FIR filter implementation can be done easily by using modulo addressing type programming which after computing the values; it provides the return address used for the filter coefficients. Hilbert transform calculation assumes a similar algorithm but to simplify modulo addressing type, due to the small amount of Hilbert coefficients the zero values are inserted in the looping list.

The DSP microcontroller has two direct hardware implemented instructions to compute the Euclidian distance with or without accumulation (ED and EDAC). The minimum value for the distance measured to all references represents the match with the analyzed signal. The data stored on the SD card is downloaded via the USB.

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 155

The above mentioned operating system is an ideal structure which makes possible a separate development of the DSP computing routines. At the end the final program structure can be embedded in one single DSP microcontroller. In that case the system requires an external USB hardware. All resulted data and graphics are displayed on a 1.8" color LCD. This 128x160 pixels display is sufficient for a small portable unit but if the user wishes all graphical data may be transferred to a host PC for a much better image resolution. The display uses a Himax HX8345-A controller which has to be programmed through the 18 bit parallel port. It turned out that the initial high color depth is useless in the application; therefore this was downgraded to 65536 color levels by reducing the bit number

of the parallel port. The hardware bus configuration is shown in figure 21:

Fig. 20. The structure of the operating system

Fig. 21. Configuration of the reallocated parallel port

The experiments were made using the internal 12 bit ADC converter. The final objective was to construct an algorithm capable of discriminate between certain pathological situations. The measured frequency band of the phonocardiography signal is between 62Hz to 800Hz. The chosen sampling frequency is a standard 8 KHz. As a result the sampling frequency is much higher than the required Nyquist criterion. This way the aliases are pushed far from the used frequency band. The over-sampling is the best way to design a low order anti-alias analog filter for the input. After the acquisition process the signal is normalized to an amplitude of ±1V or in other words is converted to the Q15 binary signed fraction representation which means 0x7FFF (32767) to 0x8000 (-32768). This way any multiplying with the normalized filtering coefficients does not exceed the value of 1. Obviously because the ADC has only 12 bits the over range risk is less likely.

During the acquisition of the PCG signal the samples are previously filtered with a 512 taps FIR band pass filter to cut under 60db the low frequency noises generated by the patient moving along with the operators hand moving. The presence of the FIR filter is crucial due to the necessity of a band limited signal required by the wavelet transform. The DSP engine is well suitable for the fast computing of the required convolution between the acquired signal and the filtering coefficients. This is a similar process to any FIR or IIR filter which is a familiar in digital signal processing (Emmanuel C. Ifeachor & Barrie W. Jervis, 2002). The wavelet filter uses the hardware implemented MAC (Multiply Accumulate) instruction. Usually by design the FIR filter coefficients are symmetrical, having one or two middle values identical. In the case of the wavelet filter a special attention requires the correct order of indexing the filtered signal coefficients, because of the non-symmetrical coefficient values. In case of a wrong order or array flipping, the process of the convolution ends with a crosscorrelation with unexpected output values. This is happening because the two DSP processes are mathematically related. Thus the memory address of the hardware DSP circular buffer of the coefficient data memory space has to be initiated properly. The wavelet filtering process starts with the saving of the stored data to a SD memory card, card preferable FAT formatted for direct file writing-reading. Each filtering iteration is done first for the approximation coefficients and secondly for the detail coefficients. After the iteration is done the sample number is half of the original signal or the previous approximation coefficients. The results are stored back to the memory card and this way the DSP processes may possibly be tested through the systems USB connectivity by an external PC. The overall necessary processing time for a scale index equal with 7 but only on the wavelet tree is equal to 12.5s, including al the read and write time to the SD memory card. In case of using a large static RAM instead of a SD memory card the overall time goes down to 25ms. The system is equipped with a color LCD display therefore is capable of displaying the signals coefficient scalogram in a complex time-frequency representation. The Daubeschies 4 coefficients are used in a similar manner to compute the wavelet transforms, but the circular buffer is addressed in a way that the resulted signal coefficients are decimated by two.

For a much shorter name using, the two microcontrollers are called "north" and "south". These two units are controlled by an operating system which is embedded in the south microcontroller. The south microcontroller is slower but it has the USB communication module. This module makes possible the firmware update via the USB port or a fast data exchange between the device and the host PC program. The structure of the operating system is presented in figure 20:

Fig. 20. The structure of the operating system

The experiments were made using the internal 12 bit ADC converter. The final objective was to construct an algorithm capable of discriminate between certain pathological situations. The measured frequency band of the phonocardiography signal is between 62Hz to 800Hz. The chosen sampling frequency is a standard 8 KHz. As a result the sampling frequency is much higher than the required Nyquist criterion. This way the aliases are pushed far from the used frequency band. The over-sampling is the best way to design a low order anti-alias analog filter for the input. After the acquisition process the signal is normalized to an amplitude of ±1V or in other words is converted to the Q15 binary signed fraction representation which means 0x7FFF (32767) to 0x8000 (-32768). This way any multiplying with the normalized filtering coefficients does not exceed the value of 1. Obviously because

During the acquisition of the PCG signal the samples are previously filtered with a 512 taps FIR band pass filter to cut under 60db the low frequency noises generated by the patient moving along with the operators hand moving. The presence of the FIR filter is crucial due to the necessity of a band limited signal required by the wavelet transform. The DSP engine is well suitable for the fast computing of the required convolution between the acquired signal and the filtering coefficients. This is a similar process to any FIR or IIR filter which is a familiar in digital signal processing (Emmanuel C. Ifeachor & Barrie W. Jervis, 2002). The wavelet filter uses the hardware implemented MAC (Multiply Accumulate) instruction. Usually by design the FIR filter coefficients are symmetrical, having one or two middle values identical. In the case of the wavelet filter a special attention requires the correct order of indexing the filtered signal coefficients, because of the non-symmetrical coefficient values. In case of a wrong order or array flipping, the process of the convolution ends with a crosscorrelation with unexpected output values. This is happening because the two DSP processes are mathematically related. Thus the memory address of the hardware DSP circular buffer of the coefficient data memory space has to be initiated properly. The wavelet filtering process starts with the saving of the stored data to a SD memory card, card preferable FAT formatted for direct file writing-reading. Each filtering iteration is done first for the approximation coefficients and secondly for the detail coefficients. After the iteration is done the sample number is half of the original signal or the previous approximation coefficients. The results are stored back to the memory card and this way the DSP processes may possibly be tested through the systems USB connectivity by an external PC. The overall necessary processing time for a scale index equal with 7 but only on the wavelet tree is equal to 12.5s, including al the read and write time to the SD memory card. In case of using a large static RAM instead of a SD memory card the overall time goes down to 25ms. The system is equipped with a color LCD display therefore is capable of displaying the signals coefficient scalogram in a complex time-frequency representation. The Daubeschies 4 coefficients are used in a similar manner to compute the wavelet transforms, but the circular buffer is

addressed in a way that the resulted signal coefficients are decimated by two.

system is presented in figure 20:

For a much shorter name using, the two microcontrollers are called "north" and "south". These two units are controlled by an operating system which is embedded in the south microcontroller. The south microcontroller is slower but it has the USB communication module. This module makes possible the firmware update via the USB port or a fast data exchange between the device and the host PC program. The structure of the operating

the ADC has only 12 bits the over range risk is less likely.

The above mentioned operating system is an ideal structure which makes possible a separate development of the DSP computing routines. At the end the final program structure can be embedded in one single DSP microcontroller. In that case the system requires an external USB hardware. All resulted data and graphics are displayed on a 1.8" color LCD. This 128x160 pixels display is sufficient for a small portable unit but if the user wishes all graphical data may be transferred to a host PC for a much better image resolution. The display uses a Himax HX8345-A controller which has to be programmed through the 18 bit parallel port. It turned out that the initial high color depth is useless in the application; therefore this was downgraded to 65536 color levels by reducing the bit number of the parallel port. The hardware bus configuration is shown in figure 21:

Fig. 21. Configuration of the reallocated parallel port

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 157

of a parallel transmission protocol instead of the SPI transmission. Of course this mode of transmission does increase complexity of the designed hardware. NORDSEL signal selects DSP microcontroller which answers after interruption by turning on SSW that generates parallel port command words transfer by activating RS. If the sent command to the DSP is to acquire an acquisition, than it can communicate directly to RAM. After transmission, the DSP microcontroller sends an interrupt to the south POE2 confirmation signal. The answer will be change south direction by activating the DSP to send other commands. Data transfer between the south microcontroller and the RAM memory is done indirectly by DSP

Data obtained during the execution of signal processing routines and all graphical elements are stored on a SD memory card or MMC card. In this way the available system memory is practically unlimited given the fact that the 32-bit addressing way allows access to 4GB of memory. The memory card can have access to FAT16 or as access to physical memory sectors. Because the FAT protocol is a copyright of Microsoft Corporation, yet we preferred to access the SD card memory as physical memory. Of course in this way, only the host PC can access the card by using a proprietary memory structure. The advantage of this mode of operation is having a full control of stored data without the possibility of unauthorized copying of the content. Bringing the SD card in active state and data transferring to memory is done according to a predetermined by the manufacturer protocol, which includes a series of command words. Also the speed of accessing the SPI communication protocol is critically dependent on the state in which the SD card is accessed. A series of data related to memory capacity, internal organization and memory speed are programmed in a sometimes inaccessible memory area, which is equivalent to hard disks MBR. The organization by predefined memory sector structure is similar to a hard disk. The major difference from a hard disk access speed is very limited on some models. The Best SD cards reach a speed of 20MB/sec but the slower may be under 250Kb/sec. For this reason the SD memory card is the slowest element in the operating system which was taking into account at the design of software routines. The SD card memory of the designed prototype is organized as shown in

microcontroller.

figure 23:

Fig. 23. Data structure of the SD card memory

For data displaying it was built a custom designed character set which is structured on 13xW pixels where the W parameter may vary from 4 to 8. By using a dynamically allocated character width, the displayed text does have a much realistic appearance. The device uses also some graphics which uses a BMP structure. The conversion of the images from 18 bit to 16 bit RGB565, required the design of a auxiliary conversion program which makes also possible the transferring of the raw bmp pictures to the SD card of the device. For intermediary data storage the device is using a 4Mb static RAM addressed in a 16 bit structure. The memory can be addressed by both microcontrollers but the data flow is managed by the south master microcontroller. In order to avoid bus conflicts the system uses two buffered data transceivers. The south microcontroller can address the RAM only indirectly because of the 19 bit port which is generated by the DSP north microcontroller. The structure of how the RAM is accessed is shown in figure 22:

Fig. 22. RAM accessing protocol

As it can be seen in the above picture, the DSP microcontroller may well access RAM directly, but entering into this routine is subject to the interrupt generated by the master microcontroller. Meaning the data is controlled by setting the direction of the data access switches SSW and NSW. For optimal control of data flow and to avoid transfer conflicts, the master microcontroller will set that directly or indirectly the access to RAM, by the DSP microcontroller through SW-NSW. To increase the transmission speed we preferred the use

For data displaying it was built a custom designed character set which is structured on 13xW pixels where the W parameter may vary from 4 to 8. By using a dynamically allocated character width, the displayed text does have a much realistic appearance. The device uses also some graphics which uses a BMP structure. The conversion of the images from 18 bit to 16 bit RGB565, required the design of a auxiliary conversion program which makes also possible the transferring of the raw bmp pictures to the SD card of the device. For intermediary data storage the device is using a 4Mb static RAM addressed in a 16 bit structure. The memory can be addressed by both microcontrollers but the data flow is managed by the south master microcontroller. In order to avoid bus conflicts the system uses two buffered data transceivers. The south microcontroller can address the RAM only indirectly because of the 19 bit port which is generated by the DSP north microcontroller.

As it can be seen in the above picture, the DSP microcontroller may well access RAM directly, but entering into this routine is subject to the interrupt generated by the master microcontroller. Meaning the data is controlled by setting the direction of the data access switches SSW and NSW. For optimal control of data flow and to avoid transfer conflicts, the master microcontroller will set that directly or indirectly the access to RAM, by the DSP microcontroller through SW-NSW. To increase the transmission speed we preferred the use

The structure of how the RAM is accessed is shown in figure 22:

Fig. 22. RAM accessing protocol

of a parallel transmission protocol instead of the SPI transmission. Of course this mode of transmission does increase complexity of the designed hardware. NORDSEL signal selects DSP microcontroller which answers after interruption by turning on SSW that generates parallel port command words transfer by activating RS. If the sent command to the DSP is to acquire an acquisition, than it can communicate directly to RAM. After transmission, the DSP microcontroller sends an interrupt to the south POE2 confirmation signal. The answer will be change south direction by activating the DSP to send other commands. Data transfer between the south microcontroller and the RAM memory is done indirectly by DSP microcontroller.

Data obtained during the execution of signal processing routines and all graphical elements are stored on a SD memory card or MMC card. In this way the available system memory is practically unlimited given the fact that the 32-bit addressing way allows access to 4GB of memory. The memory card can have access to FAT16 or as access to physical memory sectors. Because the FAT protocol is a copyright of Microsoft Corporation, yet we preferred to access the SD card memory as physical memory. Of course in this way, only the host PC can access the card by using a proprietary memory structure. The advantage of this mode of operation is having a full control of stored data without the possibility of unauthorized copying of the content. Bringing the SD card in active state and data transferring to memory is done according to a predetermined by the manufacturer protocol, which includes a series of command words. Also the speed of accessing the SPI communication protocol is critically dependent on the state in which the SD card is accessed. A series of data related to memory capacity, internal organization and memory speed are programmed in a sometimes inaccessible memory area, which is equivalent to hard disks MBR. The organization by predefined memory sector structure is similar to a hard disk. The major difference from a hard disk access speed is very limited on some models. The Best SD cards reach a speed of 20MB/sec but the slower may be under 250Kb/sec. For this reason the SD memory card is the slowest element in the operating system which was taking into account at the design of software routines. The SD card memory of the designed prototype is organized as shown in figure 23:

Fig. 23. Data structure of the SD card memory

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 159

The preconditioning of the PCG signal is completed by using a 6th order Sallen-Key filter which has to cut all unwanted frequency harmonics below 72db at the half of the sampling frequency. That way the 12bit analog-digital converter is acquiring a clean non-aliased signal. The frequency response of the combined anti-alias and FIR filter is presented in figure 26. It can be observed the outstandingly sharp, band-pass characteristic of the overall

Fig. 25. Hardware structure of the PCG signal analyzer

Fig. 26. Frequency response of the signal preconditioning module

filter.

SPI interface is based on a different protocol, not using the native mode of communication used by the SD card. This interface allows the use in advantageous terms on a SD card SPI port type that is found as a peripheral module in all modern microcontrollers. The communication protocol of an SD card consists of two types of data. Initialization and normal operation involves sending a first set of codes in the form of control bytes followed by receiving a response. That way the established communication type between a SD card and a host microcontroller becomes bidirectional. The control data packet which is transmitted between the SD card and microcontroller has a fixed length of 6 bytes as shown in figure 24.

Fig. 24. Data packets in SPI transmission mode

After sending a control packet to the card, the microcontroller will receive a response R1, R2 or R3; because data transfer is ensured by generating a clock signal, the host must always send a false 0xFF byte type to keep the communication channel active. The allocated response time after sending a command packet (NCR) of the SD card has a length of 0-8 bytes. Ultimately the CRC field is optional to check the validity of data and becomes critical only when using high-speed transmission between host and SD card. To ensure compatibility with SD cards having limited capacity, the application design does not use CRC field because the transmission rate was reduced to a rate of 250Kb. Normally, this rate of transmission can use a minimum speed 400Kb. The necessary condition for the activation of the SD card is to exceed the power supply voltage value of 2 volts then that CS and DI is set to high level for at least 170 SCLK transmitted clock periods. Immediately after activating the card, it can receive native commands. After activating the card it will receive automatically a soft reset. This sets the SPI port system clock to 100 KHz and it is send CMD0 with CS at low level for entry into reset mode. After entry into SPI mode the host will switch off the SD card verification CRC. After acceptance of commands CMD0 the card goes in idle mode. Switching to Idle mode takes up to 400ms while the card is not accessible to the host microcontroller.

The hardware of the device is divided in two parts which are separated by the independent microcontrollers. The DSP microcontroller uses an 80MHz clock frequency which makes possible a real time FIR filtering of the input signal by using of 512 coefficients in about 18μs for every sample. Obviously, that the FIR filtering is used following the anti-alias filtering of the input signal. The supplementary FIR filtering is necessary to avoid the occurrence of frequency artifacts during the wavelet filtering. The hardware structure of the device is shown in figure 25:

SPI interface is based on a different protocol, not using the native mode of communication used by the SD card. This interface allows the use in advantageous terms on a SD card SPI port type that is found as a peripheral module in all modern microcontrollers. The communication protocol of an SD card consists of two types of data. Initialization and normal operation involves sending a first set of codes in the form of control bytes followed by receiving a response. That way the established communication type between a SD card and a host microcontroller becomes bidirectional. The control data packet which is transmitted between the SD card and microcontroller has a fixed length of 6 bytes as shown

After sending a control packet to the card, the microcontroller will receive a response R1, R2 or R3; because data transfer is ensured by generating a clock signal, the host must always send a false 0xFF byte type to keep the communication channel active. The allocated response time after sending a command packet (NCR) of the SD card has a length of 0-8 bytes. Ultimately the CRC field is optional to check the validity of data and becomes critical only when using high-speed transmission between host and SD card. To ensure compatibility with SD cards having limited capacity, the application design does not use CRC field because the transmission rate was reduced to a rate of 250Kb. Normally, this rate of transmission can use a minimum speed 400Kb. The necessary condition for the activation of the SD card is to exceed the power supply voltage value of 2 volts then that CS and DI is set to high level for at least 170 SCLK transmitted clock periods. Immediately after activating the card, it can receive native commands. After activating the card it will receive automatically a soft reset. This sets the SPI port system clock to 100 KHz and it is send CMD0 with CS at low level for entry into reset mode. After entry into SPI mode the host will switch off the SD card verification CRC. After acceptance of commands CMD0 the card goes in idle mode. Switching to Idle mode takes up to 400ms while the card is not accessible to

The hardware of the device is divided in two parts which are separated by the independent microcontrollers. The DSP microcontroller uses an 80MHz clock frequency which makes possible a real time FIR filtering of the input signal by using of 512 coefficients in about 18μs for every sample. Obviously, that the FIR filtering is used following the anti-alias filtering of the input signal. The supplementary FIR filtering is necessary to avoid the occurrence of frequency artifacts during the wavelet filtering. The hardware structure of the device is

in figure 24.

Fig. 24. Data packets in SPI transmission mode

the host microcontroller.

shown in figure 25:

Fig. 25. Hardware structure of the PCG signal analyzer

The preconditioning of the PCG signal is completed by using a 6th order Sallen-Key filter which has to cut all unwanted frequency harmonics below 72db at the half of the sampling frequency. That way the 12bit analog-digital converter is acquiring a clean non-aliased signal. The frequency response of the combined anti-alias and FIR filter is presented in figure 26. It can be observed the outstandingly sharp, band-pass characteristic of the overall filter.

Fig. 26. Frequency response of the signal preconditioning module

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 161

direct compilation of C language into machine code. This was imposed primarily by the lack of a compiler able to handle directly the microcontroller DSP module, which imposed direct writing routines in assembly language DSP. The immediate consequence was increasing difficulty in debugging programs. So we preferred the original C language debugging even if this greatly increases processing time. At this moment the system is capable to compute autonomously the time-frequency scalogram and the Shannon entropy of the acquired PCG signal. Currently we are working at the implementation of the correlation algorithm which requires first of all, the construction of a pathology data base. The displayed results of a

time-frequency scalogram are shown in figure 28:

Fig. 28. Time-frequency scalogram of the "Aortic stenosis" pathology

only by the memory capacity of the hosting microcontroller.

customizable.

The "System Settings" menu includes setting of the sampling frequency. Changing the sampling rate requires the recalculation of the input anti-alias filter and the use of another board for the analog circuit. The operating menu can be reconfigured easily by changing the menu text in each command line of which belongs to a menu page. The programming menu is made so that it can implement a large number of pages of which limitation is imposed

By rewriting part of the operating system it can be designed a menu option which automatically is loaded from the SD card, depending on the application. In conclusion the same operating system can manage multiple applications which are completely

The device is equipped also with a digital-analog converter which converts in real time the acquired and filtered signal into sound through a headphone amplifier. Therefore the device is capable to offer to the physician the possibility of standard auscultation along with recording and storing the data.

The input FIR filter can be chosen to obtain the emulated "Bell", "Diaphragm" or "Bandpass" characteristics of a standard stethoscope. The working device is shown in figure 27:

Fig. 27. The working prototype of the PCG signal analyser

The device uses a friendly menu equiped with sufficient graphical elements. This feature is important because it helps the medical staff for a quick use of the device without the need of a instruction manual by using a clear explanatory demo.

For the same purpose the interface uses a keyboard of only three keys which meaning are automatically configured. After boot-up the system displays a waiting image, the time (RTC) and the voltage of the power supply. For the moment by selecting the main menu, the system displays the working menu which makes possible the selection of the implemented program routines.

In order to testing the desired program routines, the operating system allows the independent data downloading from a host PC. Flashing of the menu can be made for any desired application by changing text messages from the operating system program. At this stage until the final release point of the processing algorithms, the DSP microcontroller executes routines calculation in external assistance of the computer.

The activation of selected computer routine transfers in RAM and SD card data to be processed. After selecting the routine, the operating system checks if USB is listed by the computer. If the USB connection is active operating system commands from the computer expects. The first calculation routines were programmed in DSP microcontroller through

The device is equipped also with a digital-analog converter which converts in real time the acquired and filtered signal into sound through a headphone amplifier. Therefore the device is capable to offer to the physician the possibility of standard auscultation along with

The input FIR filter can be chosen to obtain the emulated "Bell", "Diaphragm" or "Bandpass" characteristics of a standard stethoscope. The working device is shown in figure 27:

The device uses a friendly menu equiped with sufficient graphical elements. This feature is important because it helps the medical staff for a quick use of the device without the need of

For the same purpose the interface uses a keyboard of only three keys which meaning are automatically configured. After boot-up the system displays a waiting image, the time (RTC) and the voltage of the power supply. For the moment by selecting the main menu, the system displays the working menu which makes possible the selection of the implemented

In order to testing the desired program routines, the operating system allows the independent data downloading from a host PC. Flashing of the menu can be made for any desired application by changing text messages from the operating system program. At this stage until the final release point of the processing algorithms, the DSP microcontroller

The activation of selected computer routine transfers in RAM and SD card data to be processed. After selecting the routine, the operating system checks if USB is listed by the computer. If the USB connection is active operating system commands from the computer expects. The first calculation routines were programmed in DSP microcontroller through

recording and storing the data.

Fig. 27. The working prototype of the PCG signal analyser

a instruction manual by using a clear explanatory demo.

executes routines calculation in external assistance of the computer.

program routines.

direct compilation of C language into machine code. This was imposed primarily by the lack of a compiler able to handle directly the microcontroller DSP module, which imposed direct writing routines in assembly language DSP. The immediate consequence was increasing difficulty in debugging programs. So we preferred the original C language debugging even if this greatly increases processing time. At this moment the system is capable to compute autonomously the time-frequency scalogram and the Shannon entropy of the acquired PCG signal. Currently we are working at the implementation of the correlation algorithm which requires first of all, the construction of a pathology data base. The displayed results of a time-frequency scalogram are shown in figure 28:

Fig. 28. Time-frequency scalogram of the "Aortic stenosis" pathology

The "System Settings" menu includes setting of the sampling frequency. Changing the sampling rate requires the recalculation of the input anti-alias filter and the use of another board for the analog circuit. The operating menu can be reconfigured easily by changing the menu text in each command line of which belongs to a menu page. The programming menu is made so that it can implement a large number of pages of which limitation is imposed only by the memory capacity of the hosting microcontroller.

By rewriting part of the operating system it can be designed a menu option which automatically is loaded from the SD card, depending on the application. In conclusion the same operating system can manage multiple applications which are completely customizable.

Modern Methods Used in the Complex Analysis of the Phonocardiography Signal 163

volts and an integrated memory of 320KB/16biţi. The move to Texas Instruments microprocessors is supported also by an additional argument; the TI components do have accreditation for standard medical use. Development of electronic equipment is linked to building a database of reference PCG signal images for a large variety of pathologies. The cross-correlation algorithm is although under construction but the proved interest for this device among the cardiologists, makes us confident for the utility of the newly designed

We wish to thank in this way Mr. Robert Owen, responsible for the European academic program initiated by the Texas Instruments company for the donation of development

A. Jensen & A. la Cour-Harbo (2001). *Ripples in mathematics, The discrete wavelet transform*,

Abbas K.Abbas & Rasha Bassam (2009). *Phonocardiography signal processing*, MCP, ISBN:

Abdallah et al. (1988). *Arterial stenosis murmurs: an analysis of flow and pressure fields*, Journal

Addison S. Paul (2002). *The illustrated wavelet transform handbook*, IOP, ISBN: 0-7503-0692-0 Andreas Antoniu (2006). *Digital signal processing: signals systems and filters*, McGraw-Hill,

Anke Meyer-Base (2004). *Pattern recognition for medical imaging*, Elsevier, ISBN:0-12-493290-8

Bachman George, Lawrenc Narici & Edward Beckenstein (2000) *Fourier and wavelet analysis*,

Broersen Piet M.T. (2006). *Automatic Autocorrelation and Spectral Analysis*, Springer, ISBN-10:

Emmanuel C. Ifeachor & Barrie W. Jervis (2002). *Digital signal processing; A practical approach* 

Fliege N.J. (1994). *Multirate digital signal processing; multirate systems, filter banks, wavelets*,

Gergely S, Roman M.N. & Ciupa R.V. (2011). *Portable PCG signal analyzer*, International Conference on Advancements of Medicine and Health Care through Technology IFMBE Proceedings, Volume 36, Part 2, 140-143, DOI: 10.1007/978-3-642-22586-4\_29 Gergely S, Roman M.N., Fort C. (2011). *Multirate sampling in PCG signal correlation*,

Gergely S., M.N. Roman & R.V.Ciupa (2011). *Wavelet transform using DSP microcontroller*, 5th

International Conference on Advancements of Medicine and Health Care through Technology IFMBE Proceedings,Volume 36, Part 3, 198-201, DOI: 10.1007/978-3-

European IFMBE Conference, IFMBE Proceedings 37, pp. 117–120, Budapest, ISBN

systems which are necessary to continue the research on this project.

Andrew K.Chan & Steve J.Liu (1998). *Wavelet toolware*, ISBN 0121745953

Bu-Chin (2008). *Radar image processing*, Wiley&Sons, ISBN: 978-0-470-18092-1

Axelson Jan (2006). *USB Mass storage*, ISBN-13: 978-1-931448-05-5

Springer, ISBN: 3-540-41662-5

Acoust. Soc Am. 83(1): 318-34

Springer, ISBN:0-387-98899-8

*sec.ed*., ISBN 0201-59619-9

978-3-642-23507-8, ISSN 1680-0737

ISBN: 0-471-93976-5

642-22586-4\_43

9781598299762

ISBN: 0-07-145424-1

1-84628-328-0

features.

**6. Acknowledgements** 

**7. References** 

## **4. Conclusion**

Smart use of digital processing tools helps in a new approach as concerning the classical cardiac auscultation, the innovative techniques with the ultimate goal of improvement in prevention and cardiology care. Early identification of cardiac pathologies is closely related to the physician's capacity to perceive and correctly interpret the heart sounds. By using a medical electronic device for PCG signal analysis, it can be increased the rate to identify heart abnormalities, compared with classical method of auscultation. The absolute novelty of the work consists of providing a series of original algorithms that can be used to accurately identify cardiac pathologies. This opens a new road in the PCG signal analysis said to be almost unapproachable. So far, most noninvasive type tests are extracted from the ECG signal. Transformation of PCG signal into a signal with a precise and predictable envelope classified after a pattern archive, together with a known spectral behavior makes possible a full characterization of cardiac pathology obviously within the limits set by a cardiologist professional.

Algorithms presented in this paper refer to those which can be implemented immediately in embedded analysis software. Development of new algorithms for analysis is directly linked to the hardware capabilities of the systems that are to implement, therefore the project started to show weakness when we decided to implement the convolution algorithm of the computed PCG images. The immediate problem that arose was insufficient RAM for the large number of two-dimensional vectors which had to be temporarily stored. Temporary solution was to transfer the algorithm towards the development system by computing the interpolation routine segments with intermediate storage of data on SD memory card. High memory access time of the SD card increases the calculation times to impractical values. So at this moment, the prototype system is capable at this development stage only for the Shannon entropy calculations which are necessary for the display of signal's time-frequency scalogram. The introduction of the additional intelligent decision-making algorithms to the operating system presented in the paper can be a powerful tool for characterization of cardiac pathologies by acquiring the PCG signal. Although this new medical imaging device suffers from a low spatial and temporal resolution; it could be proved to be a good choice for low-cost and mobility strategy in cardiac imaging, rather than the expensive ultrasound imaging devices. The classical auscultation technique benefits from a great quality improvement by using a device which is capable to offer a time-frequency representation.

## **5. Future directions**

The expected research direction is to be guided to improve the image quality on a larger display and increase the number of wavelet decomposing levels to avoid the necessary interpolations used in present. In terms of hardware we can go two ways of solving the lack of resources. The first way is redesigning part of the current development system to increase the RAM capacity, or alternatively to satisfy also the condition of low energy demand which consist of a total redesign by migrating to the Texas Instruments microprocessors. The change of the microprocessor version implies full rewrite of the operating system. TMS320C5000 series microprocessors are low cost with fixed-point DSP capabilities and having a very low consumption in terms of supply using a voltage of 1.8 volts and an integrated memory of 320KB/16biţi. The move to Texas Instruments microprocessors is supported also by an additional argument; the TI components do have accreditation for standard medical use. Development of electronic equipment is linked to building a database of reference PCG signal images for a large variety of pathologies. The cross-correlation algorithm is although under construction but the proved interest for this device among the cardiologists, makes us confident for the utility of the newly designed features.

## **6. Acknowledgements**

We wish to thank in this way Mr. Robert Owen, responsible for the European academic program initiated by the Texas Instruments company for the donation of development systems which are necessary to continue the research on this project.

## **7. References**

162 Applied Biological Engineering – Principles and Practice

Smart use of digital processing tools helps in a new approach as concerning the classical cardiac auscultation, the innovative techniques with the ultimate goal of improvement in prevention and cardiology care. Early identification of cardiac pathologies is closely related to the physician's capacity to perceive and correctly interpret the heart sounds. By using a medical electronic device for PCG signal analysis, it can be increased the rate to identify heart abnormalities, compared with classical method of auscultation. The absolute novelty of the work consists of providing a series of original algorithms that can be used to accurately identify cardiac pathologies. This opens a new road in the PCG signal analysis said to be almost unapproachable. So far, most noninvasive type tests are extracted from the ECG signal. Transformation of PCG signal into a signal with a precise and predictable envelope classified after a pattern archive, together with a known spectral behavior makes possible a full characterization of cardiac pathology obviously within the limits set by a

Algorithms presented in this paper refer to those which can be implemented immediately in embedded analysis software. Development of new algorithms for analysis is directly linked to the hardware capabilities of the systems that are to implement, therefore the project started to show weakness when we decided to implement the convolution algorithm of the computed PCG images. The immediate problem that arose was insufficient RAM for the large number of two-dimensional vectors which had to be temporarily stored. Temporary solution was to transfer the algorithm towards the development system by computing the interpolation routine segments with intermediate storage of data on SD memory card. High memory access time of the SD card increases the calculation times to impractical values. So at this moment, the prototype system is capable at this development stage only for the Shannon entropy calculations which are necessary for the display of signal's time-frequency scalogram. The introduction of the additional intelligent decision-making algorithms to the operating system presented in the paper can be a powerful tool for characterization of cardiac pathologies by acquiring the PCG signal. Although this new medical imaging device suffers from a low spatial and temporal resolution; it could be proved to be a good choice for low-cost and mobility strategy in cardiac imaging, rather than the expensive ultrasound imaging devices. The classical auscultation technique benefits from a great quality improvement by using a

The expected research direction is to be guided to improve the image quality on a larger display and increase the number of wavelet decomposing levels to avoid the necessary interpolations used in present. In terms of hardware we can go two ways of solving the lack of resources. The first way is redesigning part of the current development system to increase the RAM capacity, or alternatively to satisfy also the condition of low energy demand which consist of a total redesign by migrating to the Texas Instruments microprocessors. The change of the microprocessor version implies full rewrite of the operating system. TMS320C5000 series microprocessors are low cost with fixed-point DSP capabilities and having a very low consumption in terms of supply using a voltage of 1.8

device which is capable to offer a time-frequency representation.

**4. Conclusion** 

cardiologist professional.

**5. Future directions** 


**Osteocytes Characterization Using Synchrotron Radiation** 

*1Charité Universitätsmedizin Berlin* 

*3Zuse Institute Berlin, ZIB* 

*Germany* 

**CT and Finite Element Analysis** 

*2Federal Institute for Materials Research and Testing, BAM* 

Zully Ritter1, Andreas Staude2, Steffen Prohaska3 and Dieter Felsenberg1

Since a correlation between osteocyte number and their morphology with bone aging or its response to pharmacological treatment appears to exist, a methodology to characterize osteocytes from bone biopsies becomes important. In this chapter, the usage of synchrotron measurements, algorithms for image analysis (Amira, ZIB), and the finite element method using parallelized computational resources for topological analysis of osteocytes is explained and discussed. Different routines normally applied for material characterization of network-like structures (skeletonization) have been adapted to visualize osteocytes along bone cement lines at high resolution (2.174 µm). The different steps concerning to counting osteocytes and analyzing the mechanical behavior of bones are illustrated with an example. The methods were developed to answer some scientific questions such as: Does bone osteocyte distribution, number and volume differ between healthy and osteoporotic bone? How much does the osteocytes' morphology and topology contribute to load transmission capacity in bones? Which parameters are useful to characterize bones and their changes due to aging? Which strategies can be used to maintain a balance of osteocyte number and

Usage of the combined methodologies from CT up to numerical analysis (fem) are presented in this chapter in an easy, feasible and repeatable way allowing osteocytes characterization, whose topology is an indicator of bone adaption under different mechanical or pharmacological conditions. The interdisciplinary work between Charité Universitätsmedizin Berlin (Center for Muscle and Bone Research), BAM (federal Institute for Materials Research and Testing) and Zuse Institute Berlin (ZIB) was essential for quantifying and characterizing osteocytes at different age stages. The required techniques, advantages and disadvantages of

Osteocytes are differentiated bone cells from osteoblasts, which are embedded into osteons and connected in between by means of their processes. There is evidence that osteocytes are

the combined methods as well as the expected results are discussed in the chapter.

connectivity in order to balance for minimizing bone aging effects?

**1. Introduction** 

**1.1 Scientific background** 

Gergely S. PhD. Thesis (2011). *Research and implementation of medical electronic equipment, to use in cardiology*, Technical University of Cluj-Napoca, Romania **7** 

## **Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis**

Zully Ritter1, Andreas Staude2, Steffen Prohaska3 and Dieter Felsenberg1 *1Charité Universitätsmedizin Berlin 2Federal Institute for Materials Research and Testing, BAM 3Zuse Institute Berlin, ZIB Germany* 

## **1. Introduction**

164 Applied Biological Engineering – Principles and Practice

Gergely S. PhD. Thesis (2011). *Research and implementation of medical electronic equipment, to* 

Since a correlation between osteocyte number and their morphology with bone aging or its response to pharmacological treatment appears to exist, a methodology to characterize osteocytes from bone biopsies becomes important. In this chapter, the usage of synchrotron measurements, algorithms for image analysis (Amira, ZIB), and the finite element method using parallelized computational resources for topological analysis of osteocytes is explained and discussed. Different routines normally applied for material characterization of network-like structures (skeletonization) have been adapted to visualize osteocytes along bone cement lines at high resolution (2.174 µm). The different steps concerning to counting osteocytes and analyzing the mechanical behavior of bones are illustrated with an example.

The methods were developed to answer some scientific questions such as: Does bone osteocyte distribution, number and volume differ between healthy and osteoporotic bone? How much does the osteocytes' morphology and topology contribute to load transmission capacity in bones? Which parameters are useful to characterize bones and their changes due to aging? Which strategies can be used to maintain a balance of osteocyte number and connectivity in order to balance for minimizing bone aging effects?

Usage of the combined methodologies from CT up to numerical analysis (fem) are presented in this chapter in an easy, feasible and repeatable way allowing osteocytes characterization, whose topology is an indicator of bone adaption under different mechanical or pharmacological conditions. The interdisciplinary work between Charité Universitätsmedizin Berlin (Center for Muscle and Bone Research), BAM (federal Institute for Materials Research and Testing) and Zuse Institute Berlin (ZIB) was essential for quantifying and characterizing osteocytes at different age stages. The required techniques, advantages and disadvantages of the combined methods as well as the expected results are discussed in the chapter.

### **1.1 Scientific background**

Osteocytes are differentiated bone cells from osteoblasts, which are embedded into osteons and connected in between by means of their processes. There is evidence that osteocytes are

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 167

coefficients with those from phantom measurements of materials of known density values. Cortical bone density and trabecular bone density can thus be determined. After segmentation structural bone parameters such as BV/TV and cortical thickness are calculated. There are additional structural and geometrical parameters (e.g. trabecular thickness, trabecular separation, cortical porosity) that are derived from mathematical relations of the density parameters combined with the geometrical contours or bone

Osteoporosis implies a fracture risk whose asymptomatic development is not seriously considered by the affected population. CT-techniques allow analysis of bone structure, geometry and density in time (*in vivo*) or its detailed analysis in nanometer scales by analysis of *in vitro* CT measurements. Actually clinical CTs possess a resolution of 150 µm. Some indicators calculated after reconstruction and evaluation of bones are widely accepted to show bone adaption and to estimate its fracture risk. Such parameters are however normally given as a mean value over the measured volume. Although these parameters are a good indicator of bone morphology, in some cases they are insufficient to show how bone is responding under a pharmacological treatment or newly adapted conditions. Osteocytes are not only directly responsible for starting bone remodeling regions, but their number, sizes and distribution in comparable bone volumes shows how bone has changed by a disease or by medication that alter bone mineralization such as strontium ranelate or bisphosphonates. We have concentrated on developing a methodology for osteocytes characterization using available commercial platforms and adapted algorithms. Radiological and tridimensional visualization allows understanding how a pathological condition or an alteration of the normal bone conditions is related to the osteocytes morphology and their

Evidences of osteocytes (monkeys) ultrastructural changes under microgravity (Rodionova

Maintenance of subject specific cell mechanosensitivity for prevention of osteoporosis

Osteonal geometry reconstruction and BMU activity analysis by using SR-CT (osteocytes are

Specific location of osteon type structures correlate with its mechanical environment

It appears that osteocytes are physiologically adapted to "sense" its mechanical

Visualizing osteocytes canaliculi network (limited VOI) able to show 2 osteocytes (lacunae)

Osteon diameter is related with the strain environment distribution (van Oers *et al.* 2008)

Tensile strains regulate stem cell osteogenesis (Kearney *et al.* 2010)

Osteocytes apoptosis induce angiogenesis (Cheung *et al.* 2011)

environment by means of its primary cilium (Whitfield 2003)

aligned around osteon cavities) (Cooper *et al.* 2011)

(external loads) (Beraudi *et al.* 2010)

segmentation.

distribution.

*et al.* 2002)

**2. Related work** 

(Mulvihill *et al.* 2008)

(Schneider *et al.* 2011)

not only responsible for sensing mechanical stimuli but also for transmitting the amplified signal to the bone surface (You *et al.* 2001; Cowin 2002; Whitfield 2003; Han *et al.* 2004; Anderson *et al.* 2008; Jacobs *et al.* 2010; Cheung *et al.* 2011). In normal conditions, the sensed mechanical stimulus is transduced in biochemical and bioelectrical signals captured for the osteoblast and osteoclast thus starting bone formation and bone resorption activities. At a macro level, the bone geometry and density is continuously adapted to guarantee bone mechanical functionality under physiological loads. It is known that bone adaption follows the Wolf's and Roux's rules for allowing maximal strength by optimized bone mass.

A misbalance in this process (osteocytes-mechanosignal transmission-osteoblastic and osteoclastic activities) will generate changes in the bone geometry and density distribution such as observed in bone diseases. In the elderly, a misbalance between an accelerated osteoclastic activity and an incapacity of osteoblasts to form new bone results in a progressive reduction of the trabecular bone structures, an increment in the cortical porosity and a reduction of the cortical thickness. At a micro-level, bone is a composite material formed by hydroxylapatite and collagen. Other alterations in the signal pathway from osteocytes to osteoblasts and/or osteoclasts are related with induced changes in the hydroxylapatite crystals by increased secretion of Ca. Thereby the hydroxylapatite crystal number increases and the collagen content decrease and a glass-like bone structure is formed (osteogenesis imperfecta) (Boyde *et al.* 1999; Roschger *et al.* 2008; Dong *et al.* 2010). Similarly, an overproduction of collagen fibrils results in a hyper elastic bone material with a gummy-like mechanical behavior (osteomalacia) (Feng *et al.* 2006). In all cases, osteocytes generated signals appear to be associated with these bone diseases. Osteoporosis is one of the most frequent bone diseases affecting the elderly population, whose number will probably sharply increase in the future, thus we will concentrate firstly in the analysis and comparison of osteocytes from osteoporotic in comparison with healthy bone biopsies. The method explained here is of course applicable independently of the bone biopsies or disease type, including bone samples after pharmacological interventions.

As the signal coming from the osteocytes will stimulate both bone formation and bone resorption, many pharmacological interventions try to effect the receptors for these signals: osteoblast and osteoclast, more than acting directly on the osteocytes. Additionally, it is known that bone resorption velocities are in general higher as required for bone formation (Huiskes 2000; Liu 2001; Nabavi *et al.* 2001; Huang *et al.* 2010). The pharmacy industry develops therefore principally antiresorptive drugs, which will reduce or inhibit osteoclastogenesis. The most used antiresorptive drugs are bisphosphonates, estrogen receptor modulators (SERMs), calcitonin, parathyroid hormone (PTH), cathepsin K inhibitors, Denosumab and strontium ranelate. This last drug might not only have an antiresorptive effect but is also able to stimulate osteoblastic activities. However, it is not clear how much the hydroxylapatite crystal is morphologically changed by replacement of Ca atoms through Sr atoms. Thus it is unclear how much the densitometric measurements are affected. Osteocytes characterization from bone biopsies of patient treated with strontium ranelate will help to illustrate how osteocytes (and consequently osteoblastic and osteoclastic activities) are affected after alteration of the hydroxylapatite bone crystal.

Bone adaption or its pathological changes in time are nowadays monitored by densitometric and *in vivo* CT or similar radiological measurements. After measurement evaluation, the density bone distribution is calculated by comparison of measured absorptiometry coefficients with those from phantom measurements of materials of known density values. Cortical bone density and trabecular bone density can thus be determined. After segmentation structural bone parameters such as BV/TV and cortical thickness are calculated. There are additional structural and geometrical parameters (e.g. trabecular thickness, trabecular separation, cortical porosity) that are derived from mathematical relations of the density parameters combined with the geometrical contours or bone segmentation.

Osteoporosis implies a fracture risk whose asymptomatic development is not seriously considered by the affected population. CT-techniques allow analysis of bone structure, geometry and density in time (*in vivo*) or its detailed analysis in nanometer scales by analysis of *in vitro* CT measurements. Actually clinical CTs possess a resolution of 150 µm.

Some indicators calculated after reconstruction and evaluation of bones are widely accepted to show bone adaption and to estimate its fracture risk. Such parameters are however normally given as a mean value over the measured volume. Although these parameters are a good indicator of bone morphology, in some cases they are insufficient to show how bone is responding under a pharmacological treatment or newly adapted conditions. Osteocytes are not only directly responsible for starting bone remodeling regions, but their number, sizes and distribution in comparable bone volumes shows how bone has changed by a disease or by medication that alter bone mineralization such as strontium ranelate or bisphosphonates. We have concentrated on developing a methodology for osteocytes characterization using available commercial platforms and adapted algorithms. Radiological and tridimensional visualization allows understanding how a pathological condition or an alteration of the normal bone conditions is related to the osteocytes morphology and their distribution.

## **2. Related work**

166 Applied Biological Engineering – Principles and Practice

not only responsible for sensing mechanical stimuli but also for transmitting the amplified signal to the bone surface (You *et al.* 2001; Cowin 2002; Whitfield 2003; Han *et al.* 2004; Anderson *et al.* 2008; Jacobs *et al.* 2010; Cheung *et al.* 2011). In normal conditions, the sensed mechanical stimulus is transduced in biochemical and bioelectrical signals captured for the osteoblast and osteoclast thus starting bone formation and bone resorption activities. At a macro level, the bone geometry and density is continuously adapted to guarantee bone mechanical functionality under physiological loads. It is known that bone adaption follows

A misbalance in this process (osteocytes-mechanosignal transmission-osteoblastic and osteoclastic activities) will generate changes in the bone geometry and density distribution such as observed in bone diseases. In the elderly, a misbalance between an accelerated osteoclastic activity and an incapacity of osteoblasts to form new bone results in a progressive reduction of the trabecular bone structures, an increment in the cortical porosity and a reduction of the cortical thickness. At a micro-level, bone is a composite material formed by hydroxylapatite and collagen. Other alterations in the signal pathway from osteocytes to osteoblasts and/or osteoclasts are related with induced changes in the hydroxylapatite crystals by increased secretion of Ca. Thereby the hydroxylapatite crystal number increases and the collagen content decrease and a glass-like bone structure is formed (osteogenesis imperfecta) (Boyde *et al.* 1999; Roschger *et al.* 2008; Dong *et al.* 2010). Similarly, an overproduction of collagen fibrils results in a hyper elastic bone material with a gummy-like mechanical behavior (osteomalacia) (Feng *et al.* 2006). In all cases, osteocytes generated signals appear to be associated with these bone diseases. Osteoporosis is one of the most frequent bone diseases affecting the elderly population, whose number will probably sharply increase in the future, thus we will concentrate firstly in the analysis and comparison of osteocytes from osteoporotic in comparison with healthy bone biopsies. The method explained here is of course applicable independently of the bone biopsies or disease

As the signal coming from the osteocytes will stimulate both bone formation and bone resorption, many pharmacological interventions try to effect the receptors for these signals: osteoblast and osteoclast, more than acting directly on the osteocytes. Additionally, it is known that bone resorption velocities are in general higher as required for bone formation (Huiskes 2000; Liu 2001; Nabavi *et al.* 2001; Huang *et al.* 2010). The pharmacy industry develops therefore principally antiresorptive drugs, which will reduce or inhibit osteoclastogenesis. The most used antiresorptive drugs are bisphosphonates, estrogen receptor modulators (SERMs), calcitonin, parathyroid hormone (PTH), cathepsin K inhibitors, Denosumab and strontium ranelate. This last drug might not only have an antiresorptive effect but is also able to stimulate osteoblastic activities. However, it is not clear how much the hydroxylapatite crystal is morphologically changed by replacement of Ca atoms through Sr atoms. Thus it is unclear how much the densitometric measurements are affected. Osteocytes characterization from bone biopsies of patient treated with strontium ranelate will help to illustrate how osteocytes (and consequently osteoblastic and osteoclastic activities) are affected after alteration of the hydroxylapatite bone crystal.

Bone adaption or its pathological changes in time are nowadays monitored by densitometric and *in vivo* CT or similar radiological measurements. After measurement evaluation, the density bone distribution is calculated by comparison of measured absorptiometry

the Wolf's and Roux's rules for allowing maximal strength by optimized bone mass.

type, including bone samples after pharmacological interventions.

Evidences of osteocytes (monkeys) ultrastructural changes under microgravity (Rodionova *et al.* 2002)

Tensile strains regulate stem cell osteogenesis (Kearney *et al.* 2010)

Maintenance of subject specific cell mechanosensitivity for prevention of osteoporosis (Mulvihill *et al.* 2008)

Osteon diameter is related with the strain environment distribution (van Oers *et al.* 2008)

Osteocytes apoptosis induce angiogenesis (Cheung *et al.* 2011)

Osteonal geometry reconstruction and BMU activity analysis by using SR-CT (osteocytes are aligned around osteon cavities) (Cooper *et al.* 2011)

Specific location of osteon type structures correlate with its mechanical environment (external loads) (Beraudi *et al.* 2010)

It appears that osteocytes are physiologically adapted to "sense" its mechanical environment by means of its primary cilium (Whitfield 2003)

Visualizing osteocytes canaliculi network (limited VOI) able to show 2 osteocytes (lacunae) (Schneider *et al.* 2011)

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 169

In our example study an analysis of the jaw was performed. For comparison and results interpretation, the regions of interest selected for study need to be biomechanically comparable. In our case, bone samples were extracted from region 36. For analysis of osteocytes morphological changes after prostheses implantation, it is recommendable not only to compare biopsies from the same regions of healthy subjects but with biopsies taken from the contralateral bone side of the same subject. The implantation of prostheses implies drastic induced changes in the mechanical bone environment, thus significant differences on osteocytes morphology could be erroneously measured by comparing with healthy subjects. On the other hand, considering that bone biopsies are an invasive procedure, an alternative would be to extract the biopsies at least one year after implantation, time in which bone adaption velocity achieves normal balanced levels again. After extraction, bone samples

were maintained under routinely used conditions of constant -20°C temperature.

**3.2.2 Task 2: Laboratory µCT measurements** *in vitro* **(minimal resolution: 20 µm)** 

measurement, averaged, and used for correcting the projections.

**3.2.3 Task 3: 3D reconstructions** 

Since osteocytes characterization is basically performed by means of SR-CT measurements, a highly specialized technique, it is recommendable to pre-select the best biopsies that could show typical patterns for the bone disease or bone topic under study. We recommend, therefore, a previous image analysis using a typical CT laboratory such as outlined in task 2.

SR-CT is a specialized CT measurement, which is time consuming and requires knowledge and good planning. Therefore, to obtain better results, the regions to be analyzed with this technique need to be firstly pre-selected after analysis and comparison of the bone structure and density parameters coming from, for example, laboratory CT measurements. In most of the cases, biopsies have typical dimensions of 2 mm in diameter and 10 mm in length. Conebeam CTs with a resolution between 15 and 20 µm will be sufficient to determine bone structure and density. A high-energy X-Ray source will allow good contrast and reduced noise, thus improving measurement quality. For our study, we used 20 µm and a cone beam CT using 100 kV and 30 µAmpere. Flat and dark exposures were taken before and after the

After projection filtering, maximal and minimal values of the gray values corresponding to the attenuation coefficients of the bone are obtained. In general it is not recommendable to perform additional Gauss filtering to reduce the noise. This will results in loosing important information concerning the bone trabecular structure. Instead, a good segmentation is preferred. Analysis of the histograms of the gray value distribution from in the best case a random selection including 50% of the samples from each group or at least one sample from each group under study (here osteoporotic vs. healthy bone) allows the determination of the threshold values required for segmentation. The valleys formed between each peak-value in the histograms indicate the appropriate threshold values to be used. Advanced image analysis software such as Amira (ZIB) possesses tools (e.g. magic wand) for improving the segmented bone/material regions. This threshold needs to remain constant until finalizing the study, since calculation of bone structure, geometrical and density parameters depend on it. The BV/TV is the most accurately determinable structure parameter. Using the contours at the

**3.2 Detailed methodology description 3.2.1 Task 1: Bone biopsies extraction** 

It appears that osteocytes networks mimic the orientation of the surrounding extracellular bone matrix(Kerschnitzki *et al.* 2011)

## **3. Methodology**

Osteocytes characterization has been made possible by combining radiological, image and numerical analysis. We have employed: laboratory micro-CT and Synchrotron radiation CT (SR-CT) (Rack *et al.* 2008) for radiological *in vitro* measurements, Amira (ZIB) (Stalling 2005) for image analysis and the finite element method (Abaqus) for estimating and comparing compressive stiffness from healthy and osteoporotic bone biopsies after SR-CT measurements. Additional algorithms were implemented in Matlab. Before describing the method in detail general considerations for sample preparation will be discussed.

#### **3.1 General considerations**

The first step is the bone sample preparation. Bone samples are normally fixed in methyl methacrylate or in ethanol for tissue conservation. In our study, the biopsies were maintained fixed in 70% ethanol and 30% water for allowing posterior histological analysis (e.g. von Kossa staining) when required. If subsequent analyses are not planned, biopsies embedded in methyl methacrylate guarantee CT measurements free from movement artifacts. Some studies have shown that derived bone structural analysis from biopsies first fixed in ethanol with those after methyl methacrylate do not present significant differences (Perilli *et al.* 2007). An ethanol fixation allows adapting the container to the requirements of the CT acquisition. In case of using an ethanol fixation, the samples should be acclimated to the ambient room temperature previous to SR-CT measurements, in order to avoid micromovements during the measurement.

The method from CT measurement up to FE Analysis includes the following steps:


## **3.2 Detailed methodology description**

168 Applied Biological Engineering – Principles and Practice

It appears that osteocytes networks mimic the orientation of the surrounding extracellular

Osteocytes characterization has been made possible by combining radiological, image and numerical analysis. We have employed: laboratory micro-CT and Synchrotron radiation CT (SR-CT) (Rack *et al.* 2008) for radiological *in vitro* measurements, Amira (ZIB) (Stalling 2005) for image analysis and the finite element method (Abaqus) for estimating and comparing compressive stiffness from healthy and osteoporotic bone biopsies after SR-CT measurements. Additional algorithms were implemented in Matlab. Before describing the

The first step is the bone sample preparation. Bone samples are normally fixed in methyl methacrylate or in ethanol for tissue conservation. In our study, the biopsies were maintained fixed in 70% ethanol and 30% water for allowing posterior histological analysis (e.g. von Kossa staining) when required. If subsequent analyses are not planned, biopsies embedded in methyl methacrylate guarantee CT measurements free from movement artifacts. Some studies have shown that derived bone structural analysis from biopsies first fixed in ethanol with those after methyl methacrylate do not present significant differences (Perilli *et al.* 2007). An ethanol fixation allows adapting the container to the requirements of the CT acquisition. In case of using an ethanol fixation, the samples should be acclimated to the ambient room temperature previous to SR-CT measurements, in order to avoid micro-

method in detail general considerations for sample preparation will be discussed.

The method from CT measurement up to FE Analysis includes the following steps:

Task 4: Standard bone structure and density parameters calculation (e.g. BT/TV,

Task 5: Selecting bone biopsies for SR-CT (based on compared parameters in task 5 (e.g.

Task 9: Analysis of osteocytes topology (number and volume) by adapting skeletonization

Task 11: Finite element mesh generation (script in Matlab interface Amira-Abaqus (for

Task 12: FEA and generation of comparative histograms from mechanical parameters (von

Task 2: Laboratory µCT measurements *in vitro* (minimal resolution: 20 µm)

Trabecular Number (Tb.N), Trabecular Separation (Tb.Sp))

Task 6: Preparation of tailored bone containers for SR-CT measurements

bone matrix(Kerschnitzki *et al.* 2011)

**3.1 General considerations** 

movements during the measurement.

Task 3: 3D projections reconstruction

Task 7: Repeating Task 3 to Task 5

techniques

samples with a BV/TV variation > 60%)

Task 10: Comparison of obtained results in Task 9

Task 13: Comparison of obtained results in Task 12

Amira version previous to 2010)

Mises, minimum principal strains)

Task 8: Image analysis including 3D stereoscopy (Amira)

Task 1: Bone biopsies extraction

**3. Methodology** 

## **3.2.1 Task 1: Bone biopsies extraction**

In our example study an analysis of the jaw was performed. For comparison and results interpretation, the regions of interest selected for study need to be biomechanically comparable. In our case, bone samples were extracted from region 36. For analysis of osteocytes morphological changes after prostheses implantation, it is recommendable not only to compare biopsies from the same regions of healthy subjects but with biopsies taken from the contralateral bone side of the same subject. The implantation of prostheses implies drastic induced changes in the mechanical bone environment, thus significant differences on osteocytes morphology could be erroneously measured by comparing with healthy subjects. On the other hand, considering that bone biopsies are an invasive procedure, an alternative would be to extract the biopsies at least one year after implantation, time in which bone adaption velocity achieves normal balanced levels again. After extraction, bone samples were maintained under routinely used conditions of constant -20°C temperature.

Since osteocytes characterization is basically performed by means of SR-CT measurements, a highly specialized technique, it is recommendable to pre-select the best biopsies that could show typical patterns for the bone disease or bone topic under study. We recommend, therefore, a previous image analysis using a typical CT laboratory such as outlined in task 2.

## **3.2.2 Task 2: Laboratory µCT measurements** *in vitro* **(minimal resolution: 20 µm)**

SR-CT is a specialized CT measurement, which is time consuming and requires knowledge and good planning. Therefore, to obtain better results, the regions to be analyzed with this technique need to be firstly pre-selected after analysis and comparison of the bone structure and density parameters coming from, for example, laboratory CT measurements. In most of the cases, biopsies have typical dimensions of 2 mm in diameter and 10 mm in length. Conebeam CTs with a resolution between 15 and 20 µm will be sufficient to determine bone structure and density. A high-energy X-Ray source will allow good contrast and reduced noise, thus improving measurement quality. For our study, we used 20 µm and a cone beam CT using 100 kV and 30 µAmpere. Flat and dark exposures were taken before and after the measurement, averaged, and used for correcting the projections.

## **3.2.3 Task 3: 3D reconstructions**

After projection filtering, maximal and minimal values of the gray values corresponding to the attenuation coefficients of the bone are obtained. In general it is not recommendable to perform additional Gauss filtering to reduce the noise. This will results in loosing important information concerning the bone trabecular structure. Instead, a good segmentation is preferred. Analysis of the histograms of the gray value distribution from in the best case a random selection including 50% of the samples from each group or at least one sample from each group under study (here osteoporotic vs. healthy bone) allows the determination of the threshold values required for segmentation. The valleys formed between each peak-value in the histograms indicate the appropriate threshold values to be used. Advanced image analysis software such as Amira (ZIB) possesses tools (e.g. magic wand) for improving the segmented bone/material regions. This threshold needs to remain constant until finalizing the study, since calculation of bone structure, geometrical and density parameters depend on it. The BV/TV is the most accurately determinable structure parameter. Using the contours at the

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 171

For each data set the rotational axis can numerically determined. From this, the tilt angle and displacement are calculated for eliminating double contours, also allowing correction of each slice separately. An important aspect is to control the existence of ring artifacts, which in the case of our data is mainly caused by damages of and pollutions of the scintillator. If the location of the defect region is known, the attenuation coefficient corresponding to the region can be averaged from the neighbors and corrected computationally during the reconstruction process. The flatfield corrected projection data are filtered with a 3x3 median filter and reconstructed using a standard filtered back-projection algorithm with only a ramp filter. Thus the spatial resolution is degraded less than when using a smoothing filter

After segmentation and assignment of gray value ranges to each specific material, here bone and osteocytes, the first characterization parameter related to osteocytes characterization, that is their localization, will be obtained. For analysis of osteocytes trajectories, it is highly recommendable to use 3D stereoscopic views of the generated osteocyte surfaces embedded on the bone tissue. 3D-stereoscopy allows a detailed description of the trajectory especially in the trabecular bone volumes, in which the classical circular lamellae around the osteons are not visualized. By superposition of the orthoslices and using a minor contrast canal on the reconstructed volume, the osteocytes trajectories and patterns can clearly be identified;

(e.g. Shepp-Logan) and the high frequency noise is suppressed sufficiently.

in this form, their relation to the cement lines location becomes understandable.

volume and total volume (bone)/tissue (osteocytes) volume are determinate.

*Osteocytes number calculation*. The osteocytes number can be calculated after skeletonization (Fouard *et al.* 2006) of the segmented biopsy, in which only the osteocytes

**3.2.9 Task 9 - 10: Analysis of osteocytes topology (number and volume) by adapting** 

Once the projections from the SR-CT measurements containing the gray values have been reconstructed for each stack, this will be positioned and merged to obtain the total CTbiopsy measurement. A review of the orthoslices can be made for checking ring artifacts. For segmentation in Amira, a "label voxel" tool can be used for supplying the limit threshold values of the gray scales to separate each material type, or grade of mineralization in the bone label. In our study, the different grades of mineralization on the bone volume were not segmented separately. Air/Exterior, bone, osteons and osteocytes were segmented. As osteons canals, osteocytes (lacunae) and the exterior/air regions will have similar attenuation coefficients, making it difficult to determine an appropriate threshold value for osteocytes segmentation, it will be simple and semiautomatic to enable the options "voxel accuracy" and "bubbles" in Amira (ZIB) using the "label-voxel" toolbox. Thus the osteons will be segmented (separated using the magic wand). This tool causes all connected voxels with same material properties to be selected, separating osteons from osteocytes. The remaining bubble voxels could be adjudicated to "osteocyte" material. Optimal results depend on the grade of contrast and reduced noise of the original CT measurement. As mentioned above, at this scale, it is not recommendable to use Gauss filters or similar. Instead a good segmentation could be used. After segmentation, the number of the voxels for each material region (bone, osteons and osteocytes) and its total volume is determined (material statistics in Amira). Thus the relations total volume (biopsy volume)/tissue (bone)

**3.2.8 Task 8: Image analysis including 3D stereoscopy** 

**skeletonization techniques** 

perimeter in each transversal segmented projection and filling the total area inside, the total volume containing the biopsy will be determined (BV). After determination of the bone volume from the segmented region, the tissue volume (TV) value will be determined. Thus the BV/TV ratio can be calculated. Once the BV/TV has been calculated for all biopsy samples and after comparison between the groups under study, it is recommendable to select biopsies with a difference larger than 60% in the BV/TV ratio between groups (here healthy vs. osteoporotic bone biopsies from the same jaw region (e.g. for our sample 36).

In a similar way as described above, 3D segmentation after SR-CT measurements can be performed.

#### **3.2.4 Task 4: Standard bone structure and density parameters calculation (e.g. BT/TV, Trabecular Number (Tb.N), Trabecular Separation (Tb.Sp))**

Commercial CTs scanners are able to perform an automatic evaluation of BV/TV and other structural and geometrical parameters. The most relevant structural bone parameters are Tb.N, Tb.Sp, cortical thickness (Ct.Th.), cortical perimeter (Ct.Pt), and from the density parameters group, cortical (Dcomp) and trabecular density (Dtrab). Frequently other parameters are reported (e.g. density at the center of the bone section: Dmeta, or immediately near to the cortical bone (Dinn) but these are mathematically derived from the Dcomp und Dtrab in combination with their geometrical location. In similar form, series of structural parameters can be mathematically obtained from BV/TV in combination with superimposed geometrical forms (e.g. spheres or ellipses). A linear relation of the measured attenuation coefficient distribution to the bone volume allows assignment of density values for each voxel.

#### **3.2.5 Task 5: Selecting bone biopsies for SR-CT (based on compared parameters in task 5 (e.g. samples with a BV/TV variation > 60%)**

As explained above, the BV/TV ratio is easy to calculate, without employment of external software. A non-automatic calculation allows following the process and to improve segmentation if required. The BV/TV will be calculated from standard laboratory CTmeasurements (at least 20 µm). After that and for synchrotron radiation measurements, specimens with a difference of 60% in the BV/TV value between groups (e.g. osteoporotic vs. healthy) will be chosen for osteocytes morphology characterization.

## **3.2.6 Task 6: Preparation of tailored bone containers for SR-CT measurements**

Containers with dimensions as close as possible to the biopsy dimension need to be selected. In our study, the containers were tailored +10% of the biopsy diameter. At such scales, it is recommendable first to fill the container partially with the ethanol solution (if applicable) to avoid air bubbles formation under the biopsy, to introduce the bone sample, and to continue up to complete filling. High temperature variations need to be avoided for suppressing possible additional movement artifacts.

#### **3.2.7 Task 7: Repeating Task 3 to Task 5 (from SR-CT-measurements up to 3D volume reconstruction)**

For SR-CT measurements with a pixel size of 2.174 µm of the total biopsy (height ca. 1 cm), two stacks each one with 2500 slices are required. Due to the high variability of the beam, flat exposures are collected every 100 projections.

For each data set the rotational axis can numerically determined. From this, the tilt angle and displacement are calculated for eliminating double contours, also allowing correction of each slice separately. An important aspect is to control the existence of ring artifacts, which in the case of our data is mainly caused by damages of and pollutions of the scintillator. If the location of the defect region is known, the attenuation coefficient corresponding to the region can be averaged from the neighbors and corrected computationally during the reconstruction process. The flatfield corrected projection data are filtered with a 3x3 median filter and reconstructed using a standard filtered back-projection algorithm with only a ramp filter. Thus the spatial resolution is degraded less than when using a smoothing filter (e.g. Shepp-Logan) and the high frequency noise is suppressed sufficiently.

#### **3.2.8 Task 8: Image analysis including 3D stereoscopy**

170 Applied Biological Engineering – Principles and Practice

perimeter in each transversal segmented projection and filling the total area inside, the total volume containing the biopsy will be determined (BV). After determination of the bone volume from the segmented region, the tissue volume (TV) value will be determined. Thus the BV/TV ratio can be calculated. Once the BV/TV has been calculated for all biopsy samples and after comparison between the groups under study, it is recommendable to select biopsies with a difference larger than 60% in the BV/TV ratio between groups (here healthy vs.

In a similar way as described above, 3D segmentation after SR-CT measurements can be

**3.2.4 Task 4: Standard bone structure and density parameters calculation (e.g. BT/TV,** 

Commercial CTs scanners are able to perform an automatic evaluation of BV/TV and other structural and geometrical parameters. The most relevant structural bone parameters are Tb.N, Tb.Sp, cortical thickness (Ct.Th.), cortical perimeter (Ct.Pt), and from the density parameters group, cortical (Dcomp) and trabecular density (Dtrab). Frequently other parameters are reported (e.g. density at the center of the bone section: Dmeta, or immediately near to the cortical bone (Dinn) but these are mathematically derived from the Dcomp und Dtrab in combination with their geometrical location. In similar form, series of structural parameters can be mathematically obtained from BV/TV in combination with superimposed geometrical forms (e.g. spheres or ellipses). A linear relation of the measured attenuation coefficient

distribution to the bone volume allows assignment of density values for each voxel.

vs. healthy) will be chosen for osteocytes morphology characterization.

**3.2.6 Task 6: Preparation of tailored bone containers for SR-CT measurements** 

**3.2.5 Task 5: Selecting bone biopsies for SR-CT (based on compared parameters in** 

As explained above, the BV/TV ratio is easy to calculate, without employment of external software. A non-automatic calculation allows following the process and to improve segmentation if required. The BV/TV will be calculated from standard laboratory CTmeasurements (at least 20 µm). After that and for synchrotron radiation measurements, specimens with a difference of 60% in the BV/TV value between groups (e.g. osteoporotic

Containers with dimensions as close as possible to the biopsy dimension need to be selected. In our study, the containers were tailored +10% of the biopsy diameter. At such scales, it is recommendable first to fill the container partially with the ethanol solution (if applicable) to avoid air bubbles formation under the biopsy, to introduce the bone sample, and to continue up to complete filling. High temperature variations need to be avoided for suppressing

**3.2.7 Task 7: Repeating Task 3 to Task 5 (from SR-CT-measurements up to 3D volume** 

For SR-CT measurements with a pixel size of 2.174 µm of the total biopsy (height ca. 1 cm), two stacks each one with 2500 slices are required. Due to the high variability of the beam,

osteoporotic bone biopsies from the same jaw region (e.g. for our sample 36).

**Trabecular Number (Tb.N), Trabecular Separation (Tb.Sp))** 

**task 5 (e.g. samples with a BV/TV variation > 60%)** 

possible additional movement artifacts.

flat exposures are collected every 100 projections.

**reconstruction)** 

performed.

After segmentation and assignment of gray value ranges to each specific material, here bone and osteocytes, the first characterization parameter related to osteocytes characterization, that is their localization, will be obtained. For analysis of osteocytes trajectories, it is highly recommendable to use 3D stereoscopic views of the generated osteocyte surfaces embedded on the bone tissue. 3D-stereoscopy allows a detailed description of the trajectory especially in the trabecular bone volumes, in which the classical circular lamellae around the osteons are not visualized. By superposition of the orthoslices and using a minor contrast canal on the reconstructed volume, the osteocytes trajectories and patterns can clearly be identified; in this form, their relation to the cement lines location becomes understandable.

#### **3.2.9 Task 9 - 10: Analysis of osteocytes topology (number and volume) by adapting skeletonization techniques**

Once the projections from the SR-CT measurements containing the gray values have been reconstructed for each stack, this will be positioned and merged to obtain the total CTbiopsy measurement. A review of the orthoslices can be made for checking ring artifacts. For segmentation in Amira, a "label voxel" tool can be used for supplying the limit threshold values of the gray scales to separate each material type, or grade of mineralization in the bone label. In our study, the different grades of mineralization on the bone volume were not segmented separately. Air/Exterior, bone, osteons and osteocytes were segmented. As osteons canals, osteocytes (lacunae) and the exterior/air regions will have similar attenuation coefficients, making it difficult to determine an appropriate threshold value for osteocytes segmentation, it will be simple and semiautomatic to enable the options "voxel accuracy" and "bubbles" in Amira (ZIB) using the "label-voxel" toolbox. Thus the osteons will be segmented (separated using the magic wand). This tool causes all connected voxels with same material properties to be selected, separating osteons from osteocytes. The remaining bubble voxels could be adjudicated to "osteocyte" material. Optimal results depend on the grade of contrast and reduced noise of the original CT measurement. As mentioned above, at this scale, it is not recommendable to use Gauss filters or similar. Instead a good segmentation could be used. After segmentation, the number of the voxels for each material region (bone, osteons and osteocytes) and its total volume is determined (material statistics in Amira). Thus the relations total volume (biopsy volume)/tissue (bone) volume and total volume (bone)/tissue (osteocytes) volume are determinate.

*Osteocytes number calculation*. The osteocytes number can be calculated after skeletonization (Fouard *et al.* 2006) of the segmented biopsy, in which only the osteocytes

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 173

Traditionally, the power of the finite element analysis is to show zones of high stress or strains concentration, which are indicators of regions susceptible to mechanical failure, thus allowing redesigning by re-dimensioning or improving the strength or mechanical properties of the materials. For the analysis of biological tissues, it is not only important to visualize these zones of high stresses but to compare the effect of pharmacological interventions on the bone or the effect of artificial implants and to quantify these effects on bone tissues even at short times. Histogram distributions of stress and strains in pre-defined thresholds are used for this. Explicitly in the case of osteocytes, the zones of stress concentration were visualized and histograms were elaborated for analysis and comparison of the effect of the size, number and location on bone strength for osteoporotic and healthy biopsies of the jaw. For histograms, interpretation of the translational displacement and the picks of the histograms were analyzed. Translational displacement differences between groups (osteoporotic vs. healthy bone biopsies) are indicator of the compressive bone stiffness. If the histogram curve tends to be localized to the left (Y axis), a high percentage of finite elements possesses low stress values, thus indicating that the bone are more mechanically stable. On the other hand, the differences of the height of the histogram (Gauss distribution) are an indicator of stress concentration, thus under same mechanical boundary conditions, a sample experiencing highest magnitudes of stresses (highest pick) is less able to resist and to transmit external acting physiological loads, which imply highest damage tendency under physiological load (bad mechanical bone quality). The histogram generation and their comparisons can be performed by writing a simple Matlab subroutine or amongst

Biopsies from osteoporotic and healthy bones were analyzed. The results from each of the

No special techniques were employed for bone biopsy extraction and no post-traumatic

In an initial step, 20 healthy and 20 osteoporotic bone biopsies were scanned using an isotropic resolution of 20 µm. Three-dimensional volume reconstructions and image analyses performed using Amira (ZIB) are shown in the Fig. 1. A voxel based density distribution color map (red-orange: from low to middle density values and from yellow to white: highest density values) was used to identify new bone from old one, as well as the differently mineralized bone regions. After analysis of the histogram distributions of the gray values obtained from the CT-measurements (segmentation), the BV/TV ratios were calculated using the procedure explained above. Exemplarily, the calculated values are reported at the bottom of the figures 1 and 2. As observed, the highest calculated BV/TV differences were registered for the biopsy fr2 (from the healthy group at the center in Fig. 1) with a BV/TV= 0.3426 and for the biopsy fr7 (from the osteoporotic group at the right in Fig. 2), thus these two biopsies were selected for

**4.2 Task 2 - 6: Laboratory µCT measurements and 3D reconstruction** *in vitro*

**3.2.12 Task 13: Comparison of obtained results in Task 12** 

others using the Python programming language.

**4. Practical example (results)** 

task described above will be presented.

**4.1 Task 1: Bone biopsies extraction** 

events were registered.

are kept. Thus, the other materials should be selected and deleted only for this step (of course after saving the original Amira mesh containing all material regions). A skeleton is a schematic representation of a solid after extraction of geometrical and topological simplified shape features, thus facilitating its analysis on the extracted schema. In biomechanics this tool is commonly used for analysis of the nerve or the circular systems (e.g. diameter and length distribution of the vessel is obtained). The distant transformation map concept introduced by H. Blum calculates the closest boundary (vertices) for each point in the represented object. In the case of the osteocytes, this results in a center point inside the surface (bubble) at each osteocyte (Fig. 9). For large osteocytes, a two vertices joined by one line will be generated. Looking at the skeletonization results, the total number of vertices and lines corresponding to the segmented osteocytes are reported. The osteocytes number (N) is calculated subtracting the number of vertices (v) from the number of lines (l). This simple method was tested and validated by automatic counting compared with a manual counting of osteocytes in a reduce volume of the biopsy.

### **3.2.10 Task 11: Finite element mesh generation**

After segmentation and previous to osteocytes counting procedure, a surface for each material is obtained. For mesh generation the semi-automatic tool from Amira ("tetragen") was employed. The triangular surface is then converted to solid tetrahedrons. Requisite for successful 3D meshing are that the triangulated surface fills the criterions of nonintersection, surface closeness, aspect ratio and non-wrong conserved orientation. Once the surface is ready, the tetrahedral mesh is automatically generated using an advancing front algorithm implemented in Amira. Prior to mesh generation, it is recommendable to check the number of expected finite elements. If the represented geometry is not affected, improvements in the mesh generation could be allowed. Finally, the mesh topology (coordinates and elements connectivity) can be written in an ASCII format, readable for the most common FE solvers (Abaqus, Ansys, etc.).

#### **3.2.11 Task 12: FEA and generation of comparative histograms from mechanical parameters (von Mises, minimum principal strains)**

In our study, the mesh topology was imported in Abaqus. Using Abaqus-CAE the boundary conditions, material properties and mechanical material behavior will be imposed in the solid model of the bone volume with the osteocytes. A compression test was simulated by encastring the nodes (all six degrees of freedom = 0) at the basis of the mesh and a distributed load on the top of the model. For comparison with other studies, the material properties were taken from literature (Boutroy *et al.* 2008; Rincon-Kohli *et al.* 2009; Varga *et al.* 2011; Vilayphiou *et al.* 2011). The materials were modeled to be isotropic and homogeneous and to possess a linear elastic behavior. The Abaqus solver was used to calculate the strain and strength tensors. After analysis, reports (ASCII format) containing the magnitude of each mechanical parameter amount others (e.g. minimum principal strains and von Mises stress distribution) were exported for post-processing analysis. The magnitudes were averaged at the centroid of each element. Lists containing the element number and corresponding strength/strain values were represented in histograms in preselected thresholds. Logarithms representations of such distributions will conduce to wrong results interpretation. Thus, a natural scale of percental number of elements at each interval is preferred.

## **3.2.12 Task 13: Comparison of obtained results in Task 12**

172 Applied Biological Engineering – Principles and Practice

are kept. Thus, the other materials should be selected and deleted only for this step (of course after saving the original Amira mesh containing all material regions). A skeleton is a schematic representation of a solid after extraction of geometrical and topological simplified shape features, thus facilitating its analysis on the extracted schema. In biomechanics this tool is commonly used for analysis of the nerve or the circular systems (e.g. diameter and length distribution of the vessel is obtained). The distant transformation map concept introduced by H. Blum calculates the closest boundary (vertices) for each point in the represented object. In the case of the osteocytes, this results in a center point inside the surface (bubble) at each osteocyte (Fig. 9). For large osteocytes, a two vertices joined by one line will be generated. Looking at the skeletonization results, the total number of vertices and lines corresponding to the segmented osteocytes are reported. The osteocytes number (N) is calculated subtracting the number of vertices (v) from the number of lines (l). This simple method was tested and validated by automatic counting compared with a manual

After segmentation and previous to osteocytes counting procedure, a surface for each material is obtained. For mesh generation the semi-automatic tool from Amira ("tetragen") was employed. The triangular surface is then converted to solid tetrahedrons. Requisite for successful 3D meshing are that the triangulated surface fills the criterions of nonintersection, surface closeness, aspect ratio and non-wrong conserved orientation. Once the surface is ready, the tetrahedral mesh is automatically generated using an advancing front algorithm implemented in Amira. Prior to mesh generation, it is recommendable to check the number of expected finite elements. If the represented geometry is not affected, improvements in the mesh generation could be allowed. Finally, the mesh topology (coordinates and elements connectivity) can be written in an ASCII format, readable for the

**3.2.11 Task 12: FEA and generation of comparative histograms from mechanical** 

In our study, the mesh topology was imported in Abaqus. Using Abaqus-CAE the boundary conditions, material properties and mechanical material behavior will be imposed in the solid model of the bone volume with the osteocytes. A compression test was simulated by encastring the nodes (all six degrees of freedom = 0) at the basis of the mesh and a distributed load on the top of the model. For comparison with other studies, the material properties were taken from literature (Boutroy *et al.* 2008; Rincon-Kohli *et al.* 2009; Varga *et al.* 2011; Vilayphiou *et al.* 2011). The materials were modeled to be isotropic and homogeneous and to possess a linear elastic behavior. The Abaqus solver was used to calculate the strain and strength tensors. After analysis, reports (ASCII format) containing the magnitude of each mechanical parameter amount others (e.g. minimum principal strains and von Mises stress distribution) were exported for post-processing analysis. The magnitudes were averaged at the centroid of each element. Lists containing the element number and corresponding strength/strain values were represented in histograms in preselected thresholds. Logarithms representations of such distributions will conduce to wrong results interpretation. Thus, a natural scale of percental number of elements at each interval

counting of osteocytes in a reduce volume of the biopsy.

**3.2.10 Task 11: Finite element mesh generation** 

most common FE solvers (Abaqus, Ansys, etc.).

is preferred.

**parameters (von Mises, minimum principal strains)** 

Traditionally, the power of the finite element analysis is to show zones of high stress or strains concentration, which are indicators of regions susceptible to mechanical failure, thus allowing redesigning by re-dimensioning or improving the strength or mechanical properties of the materials. For the analysis of biological tissues, it is not only important to visualize these zones of high stresses but to compare the effect of pharmacological interventions on the bone or the effect of artificial implants and to quantify these effects on bone tissues even at short times. Histogram distributions of stress and strains in pre-defined thresholds are used for this. Explicitly in the case of osteocytes, the zones of stress concentration were visualized and histograms were elaborated for analysis and comparison of the effect of the size, number and location on bone strength for osteoporotic and healthy biopsies of the jaw. For histograms, interpretation of the translational displacement and the picks of the histograms were analyzed. Translational displacement differences between groups (osteoporotic vs. healthy bone biopsies) are indicator of the compressive bone stiffness. If the histogram curve tends to be localized to the left (Y axis), a high percentage of finite elements possesses low stress values, thus indicating that the bone are more mechanically stable. On the other hand, the differences of the height of the histogram (Gauss distribution) are an indicator of stress concentration, thus under same mechanical boundary conditions, a sample experiencing highest magnitudes of stresses (highest pick) is less able to resist and to transmit external acting physiological loads, which imply highest damage tendency under physiological load (bad mechanical bone quality). The histogram generation and their comparisons can be performed by writing a simple Matlab subroutine or amongst others using the Python programming language.

## **4. Practical example (results)**

Biopsies from osteoporotic and healthy bones were analyzed. The results from each of the task described above will be presented.

## **4.1 Task 1: Bone biopsies extraction**

No special techniques were employed for bone biopsy extraction and no post-traumatic events were registered.

## **4.2 Task 2 - 6: Laboratory µCT measurements and 3D reconstruction** *in vitro*

In an initial step, 20 healthy and 20 osteoporotic bone biopsies were scanned using an isotropic resolution of 20 µm. Three-dimensional volume reconstructions and image analyses performed using Amira (ZIB) are shown in the Fig. 1. A voxel based density distribution color map (red-orange: from low to middle density values and from yellow to white: highest density values) was used to identify new bone from old one, as well as the differently mineralized bone regions. After analysis of the histogram distributions of the gray values obtained from the CT-measurements (segmentation), the BV/TV ratios were calculated using the procedure explained above. Exemplarily, the calculated values are reported at the bottom of the figures 1 and 2. As observed, the highest calculated BV/TV differences were registered for the biopsy fr2 (from the healthy group at the center in Fig. 1) with a BV/TV= 0.3426 and for the biopsy fr7 (from the osteoporotic group at the right in Fig. 2), thus these two biopsies were selected for

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 175

BSch-M4, fr4\_20 BH5, fr5\_20 KG7, **fr7\_20** 

BV/TV = 0.2203 BV/TV = 0.237 **BT/TV=0.1791** 

Fig. 2. Osteoporotic bone biopsies from the jaw: 3D reconstructions and BV/TV determination after µCT laboratory measurements (20 µm isotropic resolution).

SR-CT measurements to find out if the number of osteocytes, their volume, and their distribution along the cement lines are correlated with aging.

BV/TV= 0.33 **BV/TV= 0.3426** BV/TV= 0.256

Fig. 1. Healthy bone biopsies from the jaw: 3D reconstructions and BV/TV determination after µCT laboratory measurements (20 µm isotropic resolution).

## **4.3 Task 8: SR-CT image analysis including 3D stereoscopy**

#### **4.3.1 Task 8.1: Image analysis**

As explained above, after SR-CT measurements (ca. 5000 slices @2.174 µm isotropic resolution), the volumes were visualized using Amira (ZIB) as shown in the Figure 3. It appears that the osteocytes are more frequent in the healthy biopsy and that they are shorter compared with the osteoporotic one. Outside of osteons the osteocytes are localized along the cement lines. Additionally they seem to be more frequent in the high mineralized regions (more lightening voxels) as shown in the selected axial and orthogonal slices of the Fig. 3. In the Fig. 4, a view of the 3D volume reconstructions (osteoporotic and healthy) and a detail from the osteoporotic bone biopsy (fr7) through a slice using an inverse color map shows that near the bone surface osteocytes are minor in number and the bone appears to be less mineralized. Confirming the initial observations, osteocytes are mainly localized along to the cement lines and are less spaced inside the highly mineralized regions. Osteocytes distribution (red) embedded in the bone matrix for the healthy bone biopsy (section) are shown in the Fig. 5.

BSch-M4, fr4\_20 BH5, fr5\_20 KG7, **fr7\_20** 

174 Applied Biological Engineering – Principles and Practice

SR-CT measurements to find out if the number of osteocytes, their volume, and their

TF1, fr9\_20 TF2, **fr2\_20** RC3, fr3\_20

BV/TV= 0.33 **BV/TV= 0.3426** BV/TV= 0.256 Fig. 1. Healthy bone biopsies from the jaw: 3D reconstructions and BV/TV determination

As explained above, after SR-CT measurements (ca. 5000 slices @2.174 µm isotropic resolution), the volumes were visualized using Amira (ZIB) as shown in the Figure 3. It appears that the osteocytes are more frequent in the healthy biopsy and that they are shorter compared with the osteoporotic one. Outside of osteons the osteocytes are localized along the cement lines. Additionally they seem to be more frequent in the high mineralized regions (more lightening voxels) as shown in the selected axial and orthogonal slices of the Fig. 3. In the Fig. 4, a view of the 3D volume reconstructions (osteoporotic and healthy) and a detail from the osteoporotic bone biopsy (fr7) through a slice using an inverse color map shows that near the bone surface osteocytes are minor in number and the bone appears to be less mineralized. Confirming the initial observations, osteocytes are mainly localized along to the cement lines and are less spaced inside the highly mineralized regions. Osteocytes distribution (red) embedded in the bone matrix for the healthy bone biopsy (section) are

after µCT laboratory measurements (20 µm isotropic resolution).

**4.3 Task 8: SR-CT image analysis including 3D stereoscopy** 

**4.3.1 Task 8.1: Image analysis** 

shown in the Fig. 5.

distribution along the cement lines are correlated with aging.

Fig. 2. Osteoporotic bone biopsies from the jaw: 3D reconstructions and BV/TV determination after µCT laboratory measurements (20 µm isotropic resolution).

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 177

Fig. 4. 3D Reconstruction of a healthy (left) and an osteoporotic (right) bone biopsy after SR-CT measurements (2.174 µm). In slice (inverse color map) different mineralized regions and

osteocytes are shown (bottom: detail).

Fig. 3. Axial and orthogonal cuts showing the different grades of mineralization and osteocytes location for a healthy (fr2) and an osteoporotic (fr7) bone biopsy of the jaw region36 after SR-CT measurements @ 2.174 µm (BESSY).

## **4.3.2 Task 8.2: 3D stereoscopy (Amira ZIB)**

Due to the high resolution of the scans, especially for the healthy biopsies in which a large number of osteocytes were visualized, it can be difficult to follow the osteocytes trajectory after surface rendering. We found that using stereoscopic views of the segmented and subsequently rendered volumes of osteocytes facilitates understanding osteocytes morphology. It appears that osteocytes presented an elliptical-like surface and that its major radius is mainly aligned with the longitudinal axis of the biopsies, which represents, in the case of the analyzed regions, the loading axis. Stereoscopic views are essential to understanding how osteocytes are really distributed inside the bone volume (exemplary shown for the osteoporotic bone biopsy; osteocytes colored in yellow (Fig. 6)), and their trajectory is clearly identifiable (Fig. 7).

Fig. 3. Axial and orthogonal cuts showing the different grades of mineralization and osteocytes location for a healthy (fr2) and an osteoporotic (fr7) bone biopsy of the jaw

Due to the high resolution of the scans, especially for the healthy biopsies in which a large number of osteocytes were visualized, it can be difficult to follow the osteocytes trajectory after surface rendering. We found that using stereoscopic views of the segmented and subsequently rendered volumes of osteocytes facilitates understanding osteocytes morphology. It appears that osteocytes presented an elliptical-like surface and that its major radius is mainly aligned with the longitudinal axis of the biopsies, which represents, in the case of the analyzed regions, the loading axis. Stereoscopic views are essential to understanding how osteocytes are really distributed inside the bone volume (exemplary shown for the osteoporotic bone biopsy; osteocytes colored in yellow (Fig. 6)), and their

region36 after SR-CT measurements @ 2.174 µm (BESSY).

**4.3.2 Task 8.2: 3D stereoscopy (Amira ZIB)** 

trajectory is clearly identifiable (Fig. 7).

Fig. 4. 3D Reconstruction of a healthy (left) and an osteoporotic (right) bone biopsy after SR-CT measurements (2.174 µm). In slice (inverse color map) different mineralized regions and osteocytes are shown (bottom: detail).

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 179

In both samples the osteocytes were localized mainly on the low mineralized regions (qualitatively) or enlarge of the cement lines as show exemplary in a cut of the projections

The size of the osteocytes was higher in the osteoporotic biopsies. After qualitatively analysis the center points representing each osteocyte were quantified and compared as

Fig. 6. Example of a stereoscopic 3D view for the osteoporotic biopsy section showing the

osteocytes in yellow aligned in the load direction.

from the healthy bone biopsy (Fig. 8).

show in the next section.

Fig. 5. 3D Volume rendering of a healthy bone biopsy (section) after SR-CT measurements @2.174 µm (BESSY), showing osteocytes (in red) embedded in the bone matrix (Amira ZIB, bottom: cut).

Fig. 5. 3D Volume rendering of a healthy bone biopsy (section) after SR-CT measurements @2.174 µm (BESSY), showing osteocytes (in red) embedded in the bone matrix (Amira ZIB,

bottom: cut).

In both samples the osteocytes were localized mainly on the low mineralized regions (qualitatively) or enlarge of the cement lines as show exemplary in a cut of the projections from the healthy bone biopsy (Fig. 8).

The size of the osteocytes was higher in the osteoporotic biopsies. After qualitatively analysis the center points representing each osteocyte were quantified and compared as show in the next section.

Fig. 6. Example of a stereoscopic 3D view for the osteoporotic biopsy section showing the osteocytes in yellow aligned in the load direction.

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 181

Fig. 8. Stereoscopic view of the projection from the healthy bone biopsy showing the osteocytes aligned along to the cement lines (SR-CT measurements @2.174 µm).

additionally quantified, compared, and shown in Figs. 11 and 12 respectively.

Fig. 9. Osteocytes numbers is calculated by counting the center points inside of each

osteocyte surface. Right: osteoporotic and left: healthy bone sample.

After using the skeletonization tool from the voxel topology as described in 4.2.9, the osteocyte number was determined, which was larger in a healthy bone biopsy. To confirm these findings two additional biopsies from the jaw with identical regions, one from an osteoporotic and one from a healthy bone, were analyzed following the same protocol. After comparing osteocytes number quantification (Fig. 10), it was found that osteoporotic bone could have up to of 85.4% (mean comparisons) less osteocytes in the jaw in the same region (36). As healthy bone possesses higher bone mass, the osteocytes number related to the analyzed bone volume (identical biopsy section) as well as the osteocytes volume related to the bone volume were

**4.4 Task 9 - 10: Analysis of osteocytes topology** 

Fig. 7. Stereoscopic view of osteocytes path distribution in a healthy (top) and an osteoporotic (bottom) bone biopsy section.

Fig. 8. Stereoscopic view of the projection from the healthy bone biopsy showing the osteocytes aligned along to the cement lines (SR-CT measurements @2.174 µm).

### **4.4 Task 9 - 10: Analysis of osteocytes topology**

180 Applied Biological Engineering – Principles and Practice

Fig. 7. Stereoscopic view of osteocytes path distribution in a healthy (top) and an

osteoporotic (bottom) bone biopsy section.

After using the skeletonization tool from the voxel topology as described in 4.2.9, the osteocyte number was determined, which was larger in a healthy bone biopsy. To confirm these findings two additional biopsies from the jaw with identical regions, one from an osteoporotic and one from a healthy bone, were analyzed following the same protocol. After comparing osteocytes number quantification (Fig. 10), it was found that osteoporotic bone could have up to of 85.4% (mean comparisons) less osteocytes in the jaw in the same region (36). As healthy bone possesses higher bone mass, the osteocytes number related to the analyzed bone volume (identical biopsy section) as well as the osteocytes volume related to the bone volume were additionally quantified, compared, and shown in Figs. 11 and 12 respectively.

Fig. 9. Osteocytes numbers is calculated by counting the center points inside of each osteocyte surface. Right: osteoporotic and left: healthy bone sample.

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 183

Due to the high computational costs, only a section from the healthy and bone biopsies from equivalent anatomical regions were analyzed. After meshing following the protocol described in 4.2.10, boundary conditions and material properties were imposed in the FE

Fig. 13. FEM from a bone biopsy (left) and a zoomed section (right) with a cutting plane showing the projection in a false color map and the meshed osteocytes inside in red.

For osteocytes an elastic Young modulus of 1% of the elastic modulus of bone was given. Due to the fact that with the used resolution it was not possible to visualize the canaliculi, non-hydrostatic properties were chosen for the osteocytes. Thus for the same reason and in order to keep simplicity, the bone was not modeled as biphasic but as homogenous, isotropic and linear elastic. To compare with other studies, in which *in vivo* analysis of human µFE-models has been analyzed, material properties and boundary conditions (load magnitude and application) were taken from literature. Thus, an E-modulus of 17 GPa, a Poisson ratio () of 0.3 and 1.7 GPa and = 0.45 for bone and osteocytes were used respectively. As explained above the differently mineralized regions were not segmented and consequently meshed together. Similarly for comparison with other analyses, a compression load of 1000 N was applied ramp-like and linear in the step. The step has a total time of 100 seconds, and reports of the results were set to be printed each 25 seconds. This allows visualization of the first regions that achieve maximal stress and strains tensors (Fig. 15). After analysis of the results, under the same conditions the load transmission capacity in the osteoporotic bone was reduced up to approx. 23% compared with the healthy biopsy after interpreting von Mises stress and minimum principal strain distribution. It appears that the size of osteocytes is more important than their number. Of course these findings need to be confirmed by analyzing more bone samples not only for the same region but other anatomical regions from healthy subjects and osteoporotic

**4.5 Task 11 - 13: Finite element analysis** 

models (Fig. 13 and 14).

patients.

Fig. 11. BV/TV relations.

Fig. 12. Osteocytes number related to the bone volume.

## **4.5 Task 11 - 13: Finite element analysis**

182 Applied Biological Engineering – Principles and Practice

Fig. 10. Osteocytes number for healthy and osteoporotic bone biopsies of the jaw (section).

Fig. 11. BV/TV relations.

Fig. 12. Osteocytes number related to the bone volume.

Due to the high computational costs, only a section from the healthy and bone biopsies from equivalent anatomical regions were analyzed. After meshing following the protocol described in 4.2.10, boundary conditions and material properties were imposed in the FE models (Fig. 13 and 14).

Fig. 13. FEM from a bone biopsy (left) and a zoomed section (right) with a cutting plane showing the projection in a false color map and the meshed osteocytes inside in red.

For osteocytes an elastic Young modulus of 1% of the elastic modulus of bone was given. Due to the fact that with the used resolution it was not possible to visualize the canaliculi, non-hydrostatic properties were chosen for the osteocytes. Thus for the same reason and in order to keep simplicity, the bone was not modeled as biphasic but as homogenous, isotropic and linear elastic. To compare with other studies, in which *in vivo* analysis of human µFE-models has been analyzed, material properties and boundary conditions (load magnitude and application) were taken from literature. Thus, an E-modulus of 17 GPa, a Poisson ratio () of 0.3 and 1.7 GPa and = 0.45 for bone and osteocytes were used respectively. As explained above the differently mineralized regions were not segmented and consequently meshed together. Similarly for comparison with other analyses, a compression load of 1000 N was applied ramp-like and linear in the step. The step has a total time of 100 seconds, and reports of the results were set to be printed each 25 seconds. This allows visualization of the first regions that achieve maximal stress and strains tensors (Fig. 15). After analysis of the results, under the same conditions the load transmission capacity in the osteoporotic bone was reduced up to approx. 23% compared with the healthy biopsy after interpreting von Mises stress and minimum principal strain distribution. It appears that the size of osteocytes is more important than their number. Of course these findings need to be confirmed by analyzing more bone samples not only for the same region but other anatomical regions from healthy subjects and osteoporotic patients.

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 185

CT-Techniques and image analysis already allow bone structure, geometry and density evaluation over time (*in vivo*) or its detailed analysis at the nanometer scale (*in vitro*). However, it appears to be more challenging to describe how bones respond to pharmacological treatment or new mechanical conditions. Considering that osteocytes are not only directly responsible for starting bone remodeling regions, but that their number, size and distribution in comparable bone volumes shows how bone changed due to diseases or medications (e.g. as strontium ranelate or bisphosphonates, which alter bone mineralization), we have therefore developed a methodology for osteocytes characterization. For the first time, the complete method from laboratory CT (using a standard resolution of 20 µm), SR-CT (voxel size 2.174 µm) up to their finite element

Considering the actual developments in software and hardware, it has become possible not only to measure and reconstruct the bone biopsies using both 20 µm (laboratory CT) but also for the first time the total volume biopsy (2.2 mm diameter and 1cm length) using 2.174 µm isotropic resolution. It was important to visualize osteocytes distribution in their whole length and to verify the positioning of the osteocytes inside the total bone volume of the biopsy. The evaluation of bone biopsies (e.g. intact vs. unhealthy such as shown in this chapter, or after pharmacological treatments) will be a relevant and in the future important

Once the relation between osteocytes and bone healthiness is understood, the methods described in this chapter will be used for the design of technologies to intervene in the mechanobiological process directed for the osteocytes. Patient specific pharmacological

The method described here uses commercially available computational software and hardware and can easily be reproduced for visualization of the osteocytes lacunae and their processes distribution (to visualize this last a higher SR-CT resolution will be needed). In general, healthy bone matrix or its alterations due to genetics, aging or reduction in the bone

In the future, the analysis of environment conditions and necessities of each patient will be carried out. After SR-CT measurements, its analysis requires advanced computational tools. Although the method described here is easy and reliable, it will not be readily available for all interested parties. Biopsies are an invasive technique. Maybe in the future and due to the continuous development in CTs technologies, reduced volume of bone samples will be sufficient for analysis but conserving the requirements of sufficient bone mass with a considerable number of osteocytes that allows comparisons and understanding bone diseases or bone response after usage of designed pharmacological interventions. However it remains speculative to suppose a minimal bone volume size to understand how osteocytes are acting. For future studies, it could be interesting for better understanding of osteocytes'

**5. Specific scientific relevance and innovative aspects of osteocytes** 

**characterization** 

analysis was carried out.

indicator for bone quality evaluation.

**6. Potential users of the methodology and results** 

interventions or training conditions will be designed for it.

mechanical stimuli could be studied and analyzed using this method.

Fig. 14. Detail (through-view) of the FE-Mesh of the bone and osteocytes embedded in the bone matrix.

Fig. 15. von Mises stress distribution for a bone section and selected osteocytes with high stress values.

Fig. 14. Detail (through-view) of the FE-Mesh of the bone and osteocytes embedded in the

Fig. 15. von Mises stress distribution for a bone section and selected osteocytes with high

bone matrix.

stress values.

## **5. Specific scientific relevance and innovative aspects of osteocytes characterization**

CT-Techniques and image analysis already allow bone structure, geometry and density evaluation over time (*in vivo*) or its detailed analysis at the nanometer scale (*in vitro*). However, it appears to be more challenging to describe how bones respond to pharmacological treatment or new mechanical conditions. Considering that osteocytes are not only directly responsible for starting bone remodeling regions, but that their number, size and distribution in comparable bone volumes shows how bone changed due to diseases or medications (e.g. as strontium ranelate or bisphosphonates, which alter bone mineralization), we have therefore developed a methodology for osteocytes characterization. For the first time, the complete method from laboratory CT (using a standard resolution of 20 µm), SR-CT (voxel size 2.174 µm) up to their finite element analysis was carried out.

Considering the actual developments in software and hardware, it has become possible not only to measure and reconstruct the bone biopsies using both 20 µm (laboratory CT) but also for the first time the total volume biopsy (2.2 mm diameter and 1cm length) using 2.174 µm isotropic resolution. It was important to visualize osteocytes distribution in their whole length and to verify the positioning of the osteocytes inside the total bone volume of the biopsy. The evaluation of bone biopsies (e.g. intact vs. unhealthy such as shown in this chapter, or after pharmacological treatments) will be a relevant and in the future important indicator for bone quality evaluation.

## **6. Potential users of the methodology and results**

Once the relation between osteocytes and bone healthiness is understood, the methods described in this chapter will be used for the design of technologies to intervene in the mechanobiological process directed for the osteocytes. Patient specific pharmacological interventions or training conditions will be designed for it.

The method described here uses commercially available computational software and hardware and can easily be reproduced for visualization of the osteocytes lacunae and their processes distribution (to visualize this last a higher SR-CT resolution will be needed). In general, healthy bone matrix or its alterations due to genetics, aging or reduction in the bone mechanical stimuli could be studied and analyzed using this method.

In the future, the analysis of environment conditions and necessities of each patient will be carried out. After SR-CT measurements, its analysis requires advanced computational tools. Although the method described here is easy and reliable, it will not be readily available for all interested parties. Biopsies are an invasive technique. Maybe in the future and due to the continuous development in CTs technologies, reduced volume of bone samples will be sufficient for analysis but conserving the requirements of sufficient bone mass with a considerable number of osteocytes that allows comparisons and understanding bone diseases or bone response after usage of designed pharmacological interventions. However it remains speculative to suppose a minimal bone volume size to understand how osteocytes are acting. For future studies, it could be interesting for better understanding of osteocytes'

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 187

Our findings showed a clear alignment of the osteocytes along the cement lines. Interestingly at the regions near the bone surface with reduced mineralization grade osteocytes were mainly aligned along the close to high mineralized region. Apparently, not only osteocytes number is reduced with aging but their size increases and become sparely

Automatic tetrahedron mesh generation using the "tetragen" tool from Amira worked adequately for meshing the biopsies with a resolution of 20 µm, but meshing biopsies with osteocytes embedded on the bone matrix from the SR-CT samples consumes an enormous amount of time, due to necessary adjustments for avoiding intersections and conserving

It is important to consider that this study has been initiated in 2008 (first scans with 20 µm) and remains an on-going study for performing the rest of SR-CT measurements, and for quantifying osteocytes/grade of mineralization. It was given importance to visualize osteocytes (lacunae) in the complete bone volume biopsy, and although the method has been established, new questions occurred: How is the grade of connectivity between osteocytes? Are there changes in the number and direction of the osteocytes dendrites for the osteoporotic and healthy bone biopsies? Is it possible that osteocytes for the osteoporotic bone samples are large but that all osteocytes possesses more or less the same number of processes (canaliculi), such that the number of canaliculi will become an specific characteristic of this bone cells? Or will due to aging a general mal-functioning of the osteocytes occur, such that only a reduced number of processes will be expected? In this last case, the pathway of the mechanical stimuli to osteoblastic and osteoclastic bone cell will be interrupted, and bone formation will never be initiated for regions with unconnected osteocytes and new bone will not be formed, similarly bone resorption required for

To finalize with such speculations, new measurements of the same 4 biopsies measured at BESSY with 2.174 µm (results report in this chapter) have been performed using a resolution of approx. 0.2 µm. We expect to see the canaliculi network, to perform 3D volume visualization and their quantitative analysis, following the established protocol presented

Additionally and since in osteoporotic bones osteocytes size appears to be larger as for healthy, additional analysis on the sample group included in this study will be performed for confirming or neglecting this finding. If the initial finding is true, it could be important to analyze if the grade of mineralization and number, size and distribution of osteocytes are related. SR-CT is able to show different degrees of mineralization. These analyses will be then realized at short time by including additional steps using the skeletonization tool after segmentation of the different mineralized regions in Amira, allowing their quantification

There are some reports about the morphology and connectivity between osteocytes. However it is not clear how they are distributed in relation to the different grades of

distributed in comparison with the healthy bone samples from the human mandible.

**8. Conclusion and future direction** 

initiating bone repair will be stopped.

**8.1 Future direction** 

and comparison.

here.

model closeness.

morphology and their role on bone behavior to analyze bone samples from regions with high turn-over metabolic process, thus to analyze osteocytes morphology and their interconnectivity. We propose the methodology described here as standard method, hence comparison between results from different studies will provide valuable knowledge on osteocytes nature.

## **7. Discussion**

## **7.1 On the method**

Considering that non necrotic bone tissue was present in the biopsies, it is assumed that in each osteocyte lacunae resides a living, active osteocyte with identical and normal functionality. Thus, the comparison of osteocytes morphology from bone samples, as e.g. osteoporotic and healthy analyzed and reported here, are valid providing information about relations between bone mechanics response and osteocytes morphology.

An obvious requirement is the measurement quality. For laboratory CT measurements, it is not critical because after reconstruction, it is possible to repeat the measurement in an adequate time. But, at least for the synchrotron measurements at BESSY, it was critical to repeat a SR-CT measurement, due to considerable time requirements for measuring and projections reconstruction and an inflexible time schedule. Thus, the selection of the biopsies and their preparations are not trivial at all.

One of the principal advantages of CT is its non-destructive nature, implying that measurements not only at different CT resolutions of the same samples and regions are possible, but it can also be combined with other techniques (e.g. atomic force microscope for studying the interaction with proteins). After comparisons of measured parameters at different scales, quantitative relations between density, bone structural parameters and number of osteocytes can be derived.

Combined CT techniques for measurement and reconstruction, image analysis and the finite element method are adequate to study and analyze osteocytes morphology and their relation with bone stiffness.

## **7.2 On the findings**

As confirmed in this study the relation BV/TV is a good indicator of the bone quality. Considering that as observed in the laboratory µCT measurements (20 healthy and 20 osteoporotic bone biopsies) and observed in detail in the SR-CT measurements, in most cases the highest mineralized regions are localized at the center of each geometrical bone structure. Thus the possible effects on the ratios determination due to partial volume effects are counterbalanced independently from the scale used for scanning (of course for 20 µm and less).

After analysis of the first two biopsies selected for SR-CT measurements, the number of osteocytes for the healthy bone biopsy was clearly larger than for the osteoporotic bone sample, as expected, and although a major number of biopsies need to be analyzed this finding was confirmed after measurements of two additional samples. But an interesting fact was that osteocytes size appears to be smaller in the healthy bone biopsies.

## **8. Conclusion and future direction**

186 Applied Biological Engineering – Principles and Practice

morphology and their role on bone behavior to analyze bone samples from regions with high turn-over metabolic process, thus to analyze osteocytes morphology and their interconnectivity. We propose the methodology described here as standard method, hence comparison between results from different studies will provide valuable knowledge on

Considering that non necrotic bone tissue was present in the biopsies, it is assumed that in each osteocyte lacunae resides a living, active osteocyte with identical and normal functionality. Thus, the comparison of osteocytes morphology from bone samples, as e.g. osteoporotic and healthy analyzed and reported here, are valid providing information about

An obvious requirement is the measurement quality. For laboratory CT measurements, it is not critical because after reconstruction, it is possible to repeat the measurement in an adequate time. But, at least for the synchrotron measurements at BESSY, it was critical to repeat a SR-CT measurement, due to considerable time requirements for measuring and projections reconstruction and an inflexible time schedule. Thus, the selection of the biopsies

One of the principal advantages of CT is its non-destructive nature, implying that measurements not only at different CT resolutions of the same samples and regions are possible, but it can also be combined with other techniques (e.g. atomic force microscope for studying the interaction with proteins). After comparisons of measured parameters at different scales, quantitative relations between density, bone structural parameters and

Combined CT techniques for measurement and reconstruction, image analysis and the finite element method are adequate to study and analyze osteocytes morphology and their

As confirmed in this study the relation BV/TV is a good indicator of the bone quality. Considering that as observed in the laboratory µCT measurements (20 healthy and 20 osteoporotic bone biopsies) and observed in detail in the SR-CT measurements, in most cases the highest mineralized regions are localized at the center of each geometrical bone structure. Thus the possible effects on the ratios determination due to partial volume effects are counterbalanced independently from the scale used for scanning (of course for 20 µm

After analysis of the first two biopsies selected for SR-CT measurements, the number of osteocytes for the healthy bone biopsy was clearly larger than for the osteoporotic bone sample, as expected, and although a major number of biopsies need to be analyzed this finding was confirmed after measurements of two additional samples. But an interesting

fact was that osteocytes size appears to be smaller in the healthy bone biopsies.

relations between bone mechanics response and osteocytes morphology.

and their preparations are not trivial at all.

number of osteocytes can be derived.

relation with bone stiffness.

**7.2 On the findings** 

and less).

osteocytes nature.

**7. Discussion 7.1 On the method**  Our findings showed a clear alignment of the osteocytes along the cement lines. Interestingly at the regions near the bone surface with reduced mineralization grade osteocytes were mainly aligned along the close to high mineralized region. Apparently, not only osteocytes number is reduced with aging but their size increases and become sparely distributed in comparison with the healthy bone samples from the human mandible.

Automatic tetrahedron mesh generation using the "tetragen" tool from Amira worked adequately for meshing the biopsies with a resolution of 20 µm, but meshing biopsies with osteocytes embedded on the bone matrix from the SR-CT samples consumes an enormous amount of time, due to necessary adjustments for avoiding intersections and conserving model closeness.

It is important to consider that this study has been initiated in 2008 (first scans with 20 µm) and remains an on-going study for performing the rest of SR-CT measurements, and for quantifying osteocytes/grade of mineralization. It was given importance to visualize osteocytes (lacunae) in the complete bone volume biopsy, and although the method has been established, new questions occurred: How is the grade of connectivity between osteocytes? Are there changes in the number and direction of the osteocytes dendrites for the osteoporotic and healthy bone biopsies? Is it possible that osteocytes for the osteoporotic bone samples are large but that all osteocytes possesses more or less the same number of processes (canaliculi), such that the number of canaliculi will become an specific characteristic of this bone cells? Or will due to aging a general mal-functioning of the osteocytes occur, such that only a reduced number of processes will be expected? In this last case, the pathway of the mechanical stimuli to osteoblastic and osteoclastic bone cell will be interrupted, and bone formation will never be initiated for regions with unconnected osteocytes and new bone will not be formed, similarly bone resorption required for initiating bone repair will be stopped.

## **8.1 Future direction**

To finalize with such speculations, new measurements of the same 4 biopsies measured at BESSY with 2.174 µm (results report in this chapter) have been performed using a resolution of approx. 0.2 µm. We expect to see the canaliculi network, to perform 3D volume visualization and their quantitative analysis, following the established protocol presented here.

Additionally and since in osteoporotic bones osteocytes size appears to be larger as for healthy, additional analysis on the sample group included in this study will be performed for confirming or neglecting this finding. If the initial finding is true, it could be important to analyze if the grade of mineralization and number, size and distribution of osteocytes are related. SR-CT is able to show different degrees of mineralization. These analyses will be then realized at short time by including additional steps using the skeletonization tool after segmentation of the different mineralized regions in Amira, allowing their quantification and comparison.

There are some reports about the morphology and connectivity between osteocytes. However it is not clear how they are distributed in relation to the different grades of

Osteocytes Characterization Using Synchrotron Radiation CT and Finite Element Analysis 189

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## **9. Acknowledgments**

Only the interaction and team work between different disciplines, and groups has allowed visualization and analysis using good established tools such as the finite element method and to incorporate new developments from Amira and the BAM procedures for measurements and reconstructions.

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P. D. Finite element analysis based on in vivo HR-pQCT images of the distal radius is associated with wrist fracture in postmenopausal women. *J Bone Miner Res*

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apoptosis is mechanically regulated and induces angiogenesis in vitro. *J Orthop Res*

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S., Rios, H., Drezner, M. K., Quarles, L. D., Bonewald, L. F. and White, K. E. Loss of DMP1 causes rickets and osteomalacia and identifies a role for osteocytes in

point.

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*Interact* Vol.2,(3), 2002, pp:256-60.

**9. Acknowledgments** 

**10. References** 


**8** 

*Silver Spring, MD* 

*USA* 

**Specific Absorption Rate** 

**Analysis of Heterogeneous Head** 

Leonardo M. Angelone1,2 and Giorgio Bonmassar2

*1Division of Physics, Office of Science and Engineering Laboratories,* 

**Models with EEG Electrodes/Leads at 7T MRI** 

*Center for Devices and Radiological Health, U.S. Food and Drug Administration,* 

*2Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA* 

In this chapter we explore the use of anatomically accurate head models for radio frequency (RF) dosimetry and design of electroencephalography (EEG) electrode and leads. The study is conducted at 300 MHz, which is the frequency used to elicit the proton-based Magnetic Resonance Imaging (MRI) signal at 7 Tesla (7T). The use of electrically heterogeneous vs. homogeneous numerical models is explored in terms of investigation of antenna-effect for EEG leads. While the results in the homogeneous model can be validated with direct measurements in phantoms, the experimental validation of numerical simulations with electrically heterogeneous head models would require the use of a multi-structure physical phantom, much more cumbersome and expensive to build. This study aimed to evaluate whether the use of a more complex heterogeneous head model would provide additional information when looking at energy absorbed by a human head wearing EEG

MRI-based high-resolution homogeneous and heterogeneous head models were implemented for this study. The electromagnetic (EM) interactions between EEG electrodes/leads on the human head and the incident RF field used to elicit the MRI signal were investigated in terms of electromagnetic field, induced currents in the leads, and specific absorption rate (SAR) in a

Non-significant differences in whole-head SAR (i.e. less than 5%) and a 30% difference in peak-10g-averaged SAR values were observed with the homogeneous vs. heterogeneous models. The difference for peak-1g-averaged SAR estimated with the homogeneous vs. heterogeneous model was up to 100%. The presence of an insulating layer between EEG electrode and skin resulted in a change of 10% of peak-10g-averaged SAR and 280% for peak 1g-averaged SAR. Results of this study suggest that a homogeneous model could be used to estimate the changes on whole-head and 10g-averaged SAR due to the antenna effect of EEG leads at 7 T MRI. Precise modeling of the electrically conductive interface between electrode

human head. Both perfectly conductive and resistive EEG leads were studied.

**1. Introduction** 

electrodes/leads and exposed to a 300 MHz RF field.

and head surface is also fundamental.


## **Specific Absorption Rate Analysis of Heterogeneous Head Models with EEG Electrodes/Leads at 7T MRI**

Leonardo M. Angelone1,2 and Giorgio Bonmassar2 *1Division of Physics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD 2Athinoula A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Harvard Medical School, Charlestown, MA USA* 

## **1. Introduction**

190 Applied Biological Engineering – Principles and Practice

Stalling, D., Westerhoff, M., and Hege, H.-C. (2005). Amira: a highly interactive system for

van Oers, R. F., Ruimerman, R., van Rietbergen, B., Hilbers, P. A. and Huiskes, R. Relating

Varga, P., Pahr, D. H., Baumbach, S. and Zysset, P. K. HR-pQCT based FE analysis of the

Vilayphiou, N., Boutroy, S., Szulc, P., Van Rietbergen, B., Munoz, F., Delmas, P. D. and

You, L., Cowin, S. C., Schaffler, M. B. and Weinbaum, S. A model for strain amplification in

images and fragility fractures at all sites in men. *J Bone Miner Res*, 2011. Whitfield, J. F. Primary cilium--is it an osteocyte's strain-sensing flowmeter? *J Cell Biochem*

osteon diameter to strain. *Bone* Vol.43,(3), 2008, pp:476-82.

Christopher R., Elsevier: 749-767.

Vol.89,(2), 2003, pp:233-7.

in vitro. *Bone* Vol.47,(5), 2011, pp:982-8.

*Biomech* Vol.34,(11), 2001, pp:1375-86.

visual data analysis. *The Visualization Handbook*. C. D. Hansen, and Johnson,

most distal radius section provides an improved prediction of Colles' fracture load

Chapurlat, R. Finite element analysis performed on radius and tibia HR-pQCT

the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix. *J* 

In this chapter we explore the use of anatomically accurate head models for radio frequency (RF) dosimetry and design of electroencephalography (EEG) electrode and leads. The study is conducted at 300 MHz, which is the frequency used to elicit the proton-based Magnetic Resonance Imaging (MRI) signal at 7 Tesla (7T). The use of electrically heterogeneous vs. homogeneous numerical models is explored in terms of investigation of antenna-effect for EEG leads. While the results in the homogeneous model can be validated with direct measurements in phantoms, the experimental validation of numerical simulations with electrically heterogeneous head models would require the use of a multi-structure physical phantom, much more cumbersome and expensive to build. This study aimed to evaluate whether the use of a more complex heterogeneous head model would provide additional information when looking at energy absorbed by a human head wearing EEG electrodes/leads and exposed to a 300 MHz RF field.

MRI-based high-resolution homogeneous and heterogeneous head models were implemented for this study. The electromagnetic (EM) interactions between EEG electrodes/leads on the human head and the incident RF field used to elicit the MRI signal were investigated in terms of electromagnetic field, induced currents in the leads, and specific absorption rate (SAR) in a human head. Both perfectly conductive and resistive EEG leads were studied.

Non-significant differences in whole-head SAR (i.e. less than 5%) and a 30% difference in peak-10g-averaged SAR values were observed with the homogeneous vs. heterogeneous models. The difference for peak-1g-averaged SAR estimated with the homogeneous vs. heterogeneous model was up to 100%. The presence of an insulating layer between EEG electrode and skin resulted in a change of 10% of peak-10g-averaged SAR and 280% for peak 1g-averaged SAR. Results of this study suggest that a homogeneous model could be used to estimate the changes on whole-head and 10g-averaged SAR due to the antenna effect of EEG leads at 7 T MRI. Precise modeling of the electrically conductive interface between electrode and head surface is also fundamental.

Specific Absorption Rate Analysis

changes of SAR in the head.

of Heterogeneous Head Models with EEG Electrodes/Leads at 7T MRI 193

("quasi-static approximation") [Bottomley 1978]. Consequently, previous studies evaluating RF heating for EEG leads and MRI systems up to 1.5T have mainly focused on faradayinduced eddy currents [Lemieux 1997]. Based on these studies, some solutions have been proposed to overcome the issue of the induced currents along EEG leads, such as twisted pair configuration [Godlman 2002], or the use of current-limiting resistors [Lemieux 1997]. At high field MRI (3 T or higher) however, this approximation is no longer valid (e.g., RF wavelength at 300 MHz/7T in empty space is 1m) and a full-wave characterization of the incident RF field [Ibrahim 2007] is necessary. The full-wave model requires the analysis of the complete Maxwell equations; given the complexity of the geometries considered, numerical solutions have been implemented [Collins 2005, Gandhi 1999, Jin 1997, Kainz 2003, Trakic 2007, Van der Berg 2007]. Among the different algorithms used, the Finite

Difference Time Domain [Kunz 1993, Taflove 2005] is often the method of choice.

The "antenna-effect" defines the physical phenomenon for which a conductive lead immersed in an EM field scatters the incident field, becoming a transmitting-antenna [Balanis 2005]. This mechanism creates two different issues: 1) a mismatch of conductivity at the interface between a lead and the skin, with charge accumulation ("capacitive" effect) and enhancement of electric field in the area underneath the electrode [Guy 1975]; 2) a perturbation of the EM field compared to the one generated by the RF coil only, with related

The currents induced along the EEG leads in an RF field depend on the geometry of the leads, the characteristics of the incident EM field, and the material properties of the lead. The efficiency of the leads as antennas, hence their effect into the incident EM field, is higher for lead dimensions comparable with the wavelength of the incident field. Given the typical length of EEG leads (~50-100 cm) the EM fields generated by rapid gradient switching have wavelengths too long to generate a significant antenna behavior for the EEG leads [Dempsey 2001]. Conversely, the antenna effect of the leads will be significant at the RF frequencies used for imaging. The RF current induced in the leads depend on the relative position of the leads with respect to the incident RF field, being maximal with leads parallel

Given the geometrical complexity of the problem considered, computational EM can help to further understand the interaction between variably-resistive EEG leads and the human body. Whole-body averaged, partial body, and whole-head averaged SAR [IEC 2002, FDA 2003] are the values of reference used in the MRI systems to control the maximum RF transmitted power allowed during an MRI examination. A spatial resolution of 2×2×2.5mm3 to model the human head is considered accurate when evaluating whole-head SAR in MRI [Collins 2003]. However, in the specific case of a human head with conductive leads during MRI, the interactions between leads and the RF-field are expected to generate local peaks of electric field and SAR near the electrodes [Guy 1975]. In this case, the use of the whole-head SAR as an exclusive dosimetric parameter for safety profile is inaccurate and the estimation of local 1g- or 10g-averaged SAR is more appropriate [Angelone 2010, Nitz 2005]. In this study, the hypothesis that 2×2×2.5mm3 is sufficient for SAR computation was rejected, and a MRI-based head model with 1×1×1mm3 isotropic spatial resolution was implemented [Angelone 2008, Makris 2008]. A similar model has been used to study the effect of purely metallic EEG leads [Angelone 2004], to evaluate the use of high resistive leads with numerical simulations on a homogeneous model [MRI 2006], and to evaluate the effect of EEG electrodes/leads in the human head exposed to RF sources of mobile-phone [Angelone

to the RF field and null with the leads perpendicular to the RF field [Balanis 2005].

Simultaneous EEG and MRI/fMRI recordings are frequently performed in clinical research as they provide fundamental information on the physiological and hemodynamic activity of the brain [Allen 2000, Benar 2003, Comi 2005, Kobayashi 2005, Liebenthal 2003, Matsuda 2002, Mirsattari 2004, Mulert 2005, Purdon 2009]. While clinical application for this technology (e.g. epilepsy) are mainly limited to MRI fields up to 1.5 T [Stern 2006], the possibility of increased spatial resolution and signal to noise ratio for brain structural and functional information drives an increasing number of research groups toward the use of high field MRI, namely 3T [Goldman 2000, Iannetti 2005, Purdon 2009, Scarff 2004] and even 7T [Mullinger 2008, Vasios 2006].

EEG recordings at high-field MRI present several technological challenges, including signal and safety issues. The EEG electrodes/leads can affect the MRI signal [Bonmassar 2001], and the MRI can add noise into the EEG signal [Allen 2000, Lemieux 1997]. The safety issues present are intrinsic to high-field MRI [Ibrahim 2007] as well as due to interaction between static, gradient and RF field with EEG electrodes and leads on the human head [Schenk 2000, Shellock 2011].

Safety issues for simultaneous EEG and high-field MRI recordings are typically categorized as: force and torque on device due to static and spatial gradient fields [Schenk 2000], peripheral nerve stimulation due to gradient-switching [Shellock 2011], and potential issues due to induced currents and related adverse thermal effects associated with energy dissipation inside the head [IEC 2002, FDA 2003].Because of the low magnetic permeability of the human body [Polk 1986], RF heating from magnetic energy dissipated inside the human head is typically disregarded and only the electric component of the incident field is considered when calculating RF heating. The electric energy fed into the RF coil of the MRI systems is partly radiated into the empty space and partly dissipated with the EEG leads and the head. If the energy dissipated inside the head is not properly balanced by the thermoregulatory system, potential adverse thermal effects can occur [Adair 1986]. The quantity used to quantify the amount of power dissipated in the human body is the SAR, measured in W/kg [NCRP 1981].

A full evaluation of RF-induced heating requires the calculation of electric field in each point of the volume of interest. The electric coupling can be analyzed in terms of both a) Faradayinduced non-conservative coupling and b) conservative capacitive coupling:

$$
\vec{E} = -j\alpha \vec{A} - \nabla V \tag{1}
$$

Faraday's induced currents ("eddy currents"), represented by the non-conservative term of eq. (1) *j A* , are generated by coupling between the MRI gradient and/or RF field and conductive loops within EEG leads, inside the human head, and/or between EEG leads and human head [Dempsey 2001]. Capacitive coupling - represented by the conservative term of eq. (1) *V* , occurs when the dimensions of the load (i.e., head with leads) are comparable with the incident wavelength, and the time-varying electric component is "picked up" by the load, acting as scattering antennas [Armenean 2004, Balanis 2005, Dempsey 2001, Yeung 2002]. Hence, there is a difference of potential ( *V* in eq. 1) due to charge accumulation that contributes to the conservative component of the electric field.

For MRI fields up to 1.5 T the EM wavelength (e.g., 4.7m in empty space at 64 MHz/1.5T) is much longer than dimensions of the head and the capacitive coupling can be disregarded

Simultaneous EEG and MRI/fMRI recordings are frequently performed in clinical research as they provide fundamental information on the physiological and hemodynamic activity of the brain [Allen 2000, Benar 2003, Comi 2005, Kobayashi 2005, Liebenthal 2003, Matsuda 2002, Mirsattari 2004, Mulert 2005, Purdon 2009]. While clinical application for this technology (e.g. epilepsy) are mainly limited to MRI fields up to 1.5 T [Stern 2006], the possibility of increased spatial resolution and signal to noise ratio for brain structural and functional information drives an increasing number of research groups toward the use of high field MRI, namely 3T [Goldman 2000, Iannetti 2005, Purdon 2009, Scarff 2004] and even

EEG recordings at high-field MRI present several technological challenges, including signal and safety issues. The EEG electrodes/leads can affect the MRI signal [Bonmassar 2001], and the MRI can add noise into the EEG signal [Allen 2000, Lemieux 1997]. The safety issues present are intrinsic to high-field MRI [Ibrahim 2007] as well as due to interaction between static, gradient and RF field with EEG electrodes and leads on the human head [Schenk

Safety issues for simultaneous EEG and high-field MRI recordings are typically categorized as: force and torque on device due to static and spatial gradient fields [Schenk 2000], peripheral nerve stimulation due to gradient-switching [Shellock 2011], and potential issues due to induced currents and related adverse thermal effects associated with energy dissipation inside the head [IEC 2002, FDA 2003].Because of the low magnetic permeability of the human body [Polk 1986], RF heating from magnetic energy dissipated inside the human head is typically disregarded and only the electric component of the incident field is considered when calculating RF heating. The electric energy fed into the RF coil of the MRI systems is partly radiated into the empty space and partly dissipated with the EEG leads and the head. If the energy dissipated inside the head is not properly balanced by the thermoregulatory system, potential adverse thermal effects can occur [Adair 1986]. The quantity used to quantify the amount of power dissipated in the human body is the SAR,

A full evaluation of RF-induced heating requires the calculation of electric field in each point of the volume of interest. The electric coupling can be analyzed in terms of both a) Faraday-

> *E jA V*

Faraday's induced currents ("eddy currents"), represented by the non-conservative term of

conductive loops within EEG leads, inside the human head, and/or between EEG leads and human head [Dempsey 2001]. Capacitive coupling - represented by the conservative term of eq. (1) *V* , occurs when the dimensions of the load (i.e., head with leads) are comparable with the incident wavelength, and the time-varying electric component is "picked up" by the load, acting as scattering antennas [Armenean 2004, Balanis 2005, Dempsey 2001, Yeung 2002]. Hence, there is a difference of potential ( *V* in eq. 1) due to charge accumulation that

For MRI fields up to 1.5 T the EM wavelength (e.g., 4.7m in empty space at 64 MHz/1.5T) is much longer than dimensions of the head and the capacitive coupling can be disregarded

, are generated by coupling between the MRI gradient and/or RF field and

(1)

induced non-conservative coupling and b) conservative capacitive coupling:

contributes to the conservative component of the electric field.

7T [Mullinger 2008, Vasios 2006].

measured in W/kg [NCRP 1981].

eq. (1) *j A*

2000, Shellock 2011].

("quasi-static approximation") [Bottomley 1978]. Consequently, previous studies evaluating RF heating for EEG leads and MRI systems up to 1.5T have mainly focused on faradayinduced eddy currents [Lemieux 1997]. Based on these studies, some solutions have been proposed to overcome the issue of the induced currents along EEG leads, such as twisted pair configuration [Godlman 2002], or the use of current-limiting resistors [Lemieux 1997].

At high field MRI (3 T or higher) however, this approximation is no longer valid (e.g., RF wavelength at 300 MHz/7T in empty space is 1m) and a full-wave characterization of the incident RF field [Ibrahim 2007] is necessary. The full-wave model requires the analysis of the complete Maxwell equations; given the complexity of the geometries considered, numerical solutions have been implemented [Collins 2005, Gandhi 1999, Jin 1997, Kainz 2003, Trakic 2007, Van der Berg 2007]. Among the different algorithms used, the Finite Difference Time Domain [Kunz 1993, Taflove 2005] is often the method of choice.

The "antenna-effect" defines the physical phenomenon for which a conductive lead immersed in an EM field scatters the incident field, becoming a transmitting-antenna [Balanis 2005]. This mechanism creates two different issues: 1) a mismatch of conductivity at the interface between a lead and the skin, with charge accumulation ("capacitive" effect) and enhancement of electric field in the area underneath the electrode [Guy 1975]; 2) a perturbation of the EM field compared to the one generated by the RF coil only, with related changes of SAR in the head.

The currents induced along the EEG leads in an RF field depend on the geometry of the leads, the characteristics of the incident EM field, and the material properties of the lead. The efficiency of the leads as antennas, hence their effect into the incident EM field, is higher for lead dimensions comparable with the wavelength of the incident field. Given the typical length of EEG leads (~50-100 cm) the EM fields generated by rapid gradient switching have wavelengths too long to generate a significant antenna behavior for the EEG leads [Dempsey 2001]. Conversely, the antenna effect of the leads will be significant at the RF frequencies used for imaging. The RF current induced in the leads depend on the relative position of the leads with respect to the incident RF field, being maximal with leads parallel to the RF field and null with the leads perpendicular to the RF field [Balanis 2005].

Given the geometrical complexity of the problem considered, computational EM can help to further understand the interaction between variably-resistive EEG leads and the human body. Whole-body averaged, partial body, and whole-head averaged SAR [IEC 2002, FDA 2003] are the values of reference used in the MRI systems to control the maximum RF transmitted power allowed during an MRI examination. A spatial resolution of 2×2×2.5mm3 to model the human head is considered accurate when evaluating whole-head SAR in MRI [Collins 2003]. However, in the specific case of a human head with conductive leads during MRI, the interactions between leads and the RF-field are expected to generate local peaks of electric field and SAR near the electrodes [Guy 1975]. In this case, the use of the whole-head SAR as an exclusive dosimetric parameter for safety profile is inaccurate and the estimation of local 1g- or 10g-averaged SAR is more appropriate [Angelone 2010, Nitz 2005]. In this study, the hypothesis that 2×2×2.5mm3 is sufficient for SAR computation was rejected, and a MRI-based head model with 1×1×1mm3 isotropic spatial resolution was implemented [Angelone 2008, Makris 2008]. A similar model has been used to study the effect of purely metallic EEG leads [Angelone 2004], to evaluate the use of high resistive leads with numerical simulations on a homogeneous model [MRI 2006], and to evaluate the effect of EEG electrodes/leads in the human head exposed to RF sources of mobile-phone [Angelone

Specific Absorption Rate Analysis

**Anatomical Structures**

(d) [FCC website] based on [Gabriel 1996].

**NON-BRAIN**

**BRAIN**

of Heterogeneous Head Models with EEG Electrodes/Leads at 7T MRI 195

**Grey Matter** 1030(a) 0.69 60.00 **White Matter** 1030(a) 0.41 43.77 **Cerebro Spinal Fluid** 1010(a) 2.22 72.73 **Adipose** 920(a) 0.07 11.74 **Air (Resp./Diges./Sinus)** 1.3(b) 0.00 1.00 **Bone (Facial)** 1850(b) 0.08 13.43 **Connective Tissue** 1100(a) 0.55 46.77 **Cornea** 1076(c) 1.15 61.37 **Diploe / Bone Marrow** 1080(b) 0.21 23.16

**Density (kg/m<sup>3</sup> )**

**Dura** 1030(a) 0.80 47.95 **Ear / Pinna** 1100(a) 0.55 46.77 **Eye Humor (Aqueous)** 1010(a,c) 1.51 69.01 **Eye Humor (Vitreous)** 1010(a,c) 1.51 69.01 **Eye Lens** 1100(c) 0.64 48.95 **Epidermis/Dermis** 1100(a) 0.64 49.82 **Inner Table** 1850(b) 0.08 13.43 **Muscle** 1040(d) 0.79 58.97 **Nasal-Structures** 1100(a) 0.55 46.77 **Nerve** 1040(a) 0.41 36.90 **Orbital Fat** 920(a) 0.07 11.74 **Outer Table** 1850(b) 0.08 13.43 **Retina/Choroid/Sclera** 1170(a) 0.97 58.90 **Spinal Cord** 1040(a) 0.41 36.90 **Soft Tissue** 1100(a) 0.55 46.77 **Subcutaneous Tissue** 1100(a) 0.55 46.77 **Subcutaneous Fat** 920(a) 0.07 11.74 **Teeth** 1850(b) 0.08 13.43 **Tongue** 1040(d) 0.79 58.97

Table 1. Anatomical structures and electrical properties of high-resolution heterogeneous head model at 300 MHz. The electrical properties were constant for all the anatomical structures in the homogeneous model. (a) [Li 2006]; (b) [Collins 2004], (c) [DeMarco 2003],

*Classification of anatomical structures at radio-frequency by their electrical properties -* The classification of anatomical structures in terms of electrical properties is necessary to precisely compute the EM field and SAR in the human head during an MRI experiment. The electrical properties of anatomical structures, such as electrical conductivity and permittivity, vary depending on their structural composition. Specifically, the electrical

 **(S/m) <sup>r</sup> (S/m) <sup>r</sup>**

**Density (kg/m<sup>3</sup> )**

**Heterogeneous Homogeneous**

**300 MHz (d)**

**300 MHz (d)**

1040 0.80 59

2010]. In this chapter we investigate the effect of using electrically heterogeneous vs. homogeneous human head models.

## **2. Methods**

*Numerical head model: Anatomical segmentation and classification at radio-frequency by electrical properties. MRI data -* One healthy 37-year-old, right-handed adult male volunteer participated in this study. Informed consent was obtained in accordance with Massachusetts General Hospital policies. High-resolution anatomical MRI data were acquired with a quadrature birdcage transmit/receive head coil on a 1.5 T scanner (General Electric, Milwaukee, WI). Data were collected with a T1-weighted 3D-SPGR sequence (TR/TE = 24/8 ms) with 124 slices, 1.3 mm thick (matrix size 256×192, FOV 256 mm). The volume data was resampled to isotropic voxels with dimensions of 1x1x1 mm3. Segmentation was then applied to this dataset volume.

Fig. 1. High resolution head model with 32 electrodes/leads and RF coil. The 3D view shows the head model with EEG leads centered in a 16-wire RF coil.

*Anatomical segmentation -* Twenty-five non-brain anatomical structures (**Figure 1**) were manually segmented from the MRI data by an expert anatomist [Makris 2008]. Three brain structures (Cerebro Spinal Fluid, Grey and White matter) were additionally segmented with an automatic segmentation algorithm [Dale 1999, Segonne 2004] and coregistered with the non-brain structures. The final head model consisted of a total of 28 anatomical structures (**Table 1**). The total number of Yee cells [Yee 1966] was 4,642,730. The head dimensions were 170 mm in width, 217 mm in depth, and 238 mm in height.

2010]. In this chapter we investigate the effect of using electrically heterogeneous vs.

*Numerical head model: Anatomical segmentation and classification at radio-frequency by electrical properties. MRI data -* One healthy 37-year-old, right-handed adult male volunteer participated in this study. Informed consent was obtained in accordance with Massachusetts General Hospital policies. High-resolution anatomical MRI data were acquired with a quadrature birdcage transmit/receive head coil on a 1.5 T scanner (General Electric, Milwaukee, WI). Data were collected with a T1-weighted 3D-SPGR sequence (TR/TE = 24/8 ms) with 124 slices, 1.3 mm thick (matrix size 256×192, FOV 256 mm). The volume data was resampled to isotropic voxels with dimensions of 1x1x1 mm3. Segmentation was then

Fig. 1. High resolution head model with 32 electrodes/leads and RF coil. The 3D view

*Anatomical segmentation -* Twenty-five non-brain anatomical structures (**Figure 1**) were manually segmented from the MRI data by an expert anatomist [Makris 2008]. Three brain structures (Cerebro Spinal Fluid, Grey and White matter) were additionally segmented with an automatic segmentation algorithm [Dale 1999, Segonne 2004] and coregistered with the non-brain structures. The final head model consisted of a total of 28 anatomical structures (**Table 1**). The total number of Yee cells [Yee 1966] was 4,642,730. The head dimensions were

shows the head model with EEG leads centered in a 16-wire RF coil.

170 mm in width, 217 mm in depth, and 238 mm in height.

homogeneous human head models.

applied to this dataset volume.

**2. Methods** 


Table 1. Anatomical structures and electrical properties of high-resolution heterogeneous head model at 300 MHz. The electrical properties were constant for all the anatomical structures in the homogeneous model. (a) [Li 2006]; (b) [Collins 2004], (c) [DeMarco 2003], (d) [FCC website] based on [Gabriel 1996].

*Classification of anatomical structures at radio-frequency by their electrical properties -* The classification of anatomical structures in terms of electrical properties is necessary to precisely compute the EM field and SAR in the human head during an MRI experiment. The electrical properties of anatomical structures, such as electrical conductivity and permittivity, vary depending on their structural composition. Specifically, the electrical

Specific Absorption Rate Analysis

Tissue", "Connective Tissue", and "Soft tissue") [Makris 2008].

relative permittivity r

adjacent generators.

FDA 2003].

**3. Results** 

**Figure 4** the electric field *E*

of Heterogeneous Head Models with EEG Electrodes/Leads at 7T MRI 197

properties of muscle at 300 MHz [FCC Website]. For the heterogeneous model, each anatomical structure was assigned more specific electrical properties, based on the data of the comprehensive study by Gabriel et al. [Gabriel 1996a, 1996b, 1996c] (**Table 1**). The values of mass density were derived from literature [Collins 2004, DeMarco 2003, Gabriel 1996, FCC website, Li 2006]. An average value of conductivity and permittivity was assigned to the anatomical structures without a direct equivalence in the database (i.e., "Subcutaneous

*Numerical Model of EEG electrodes and Leads -* The layout of thirty-two EEG electrodes on a 2D mask was designed using Circuit Maker (Altium Inc, San Diego, CA) and imported into Matlab (Mathworks, Natick, MA). The mask was co-registered with the axial slice of largest diameter on the head model. The EEG electrodes and leads of the mask were projected and placed on the surface of the head model ("epidermis" tissue, see **Figure 1**) [Angelone 2006]. The EEG electrodes were modeled as small cylinders (radius: 7 mm, thickness: 3 mm) and were positioned in direct contact with the skin as for the expanded 10-20 montage [Regan

bundled above the Cz electrode [Regan 1989],oriented vertically, and curved downward as shown in **Figure 1**. The complete model (i.e., head with 32 EEG electrodes/leads) was then imported into the XFDTD software (Remcomi Inc., State College, PA). EEG leads were shortened on one side, to simulate the short circuit created by the low-pass filter in the input stage of the EEG recording system [Purdon 2008], and connected on the other side to the head surface.

*Numerical Model of RF Coil -* The RF source was based on a volume RF coil [Jin 1997, Collins 2001]. The coil was modeled with 16 perfect electrically conductive rods of 295 mm in length and disposed around the head with circular symmetry (diameter 260mm) (**Figure 1**). The RF source was simulated as a circular excitation driving the current generators placed on the centers of the rods with 1A peak-to-peak amplitude and a 22.5o phase-shift between any two

*FDTD simulations -* Numerical simulations were performed using commercially available software XFDTD, based on the Finite-Difference-Time-Domain (FDTD) algorithm. Numerical simulations were performed at a frequency of 300 MHz. A total of seven perfectly matching layers were used for boundary conditions [Berenger 1994]. The total volume, including the free space around the model, was 297353303 mm3; the time step used to meet the Courant condition for numerical stability [Taflove 2005] was 1.92 ps, and the total number of time steps was 25,000. Simulations provided the magnitude of electromagnetic field and induced currents for each voxel, as well as whole-head averaged SAR, 1g- and 10 g-averaged SAR [IEC 2002,

*Model without EEG electrodes/leads -* **Figure 3** shows the magnetic flux density *B*

heterogeneous head model. The load of the head on the RF coil (i.e. the impedance seen by each of the 16 sources) was similar (± 10%) in both models, in line with physical RF coil

and induced currents *<sup>J</sup>*

1040 kg /m , corresponding to the average

/ 1.67 10

*el leads copper <sup>m</sup>* ), and were

  0.8 S /m ,

, and

computed with homogeneous and

properties were assigned to all the anatomical structures, i.e., conductivity tot

1989]. The leads were modeled as metallic leads ( <sup>8</sup>

 59 , and density <sup>3</sup> d 

properties of the models used in this study were considered as [Vorst 2006]: a) linear with electric field, b) isotropic, c) dispersive, and d) heterogeneous in space. Under these conditions, complex permittivity (ε\*) is defined as:

$$\begin{split} \varepsilon^\* \left( \boldsymbol{\alpha} \right) &= \varepsilon\_r \left( \boldsymbol{\alpha} \right) - j \varepsilon^\* \left( \boldsymbol{\alpha} \right) \\ &= \varepsilon\_r \left( \boldsymbol{\alpha} \right) - j \frac{\sigma\_{\mathrm{hit}} \left( \boldsymbol{\alpha} \right)}{\alpha \varepsilon\_0} = \varepsilon\_r \left( \boldsymbol{\alpha} \right) - j \left( \frac{\sigma\_i \left( \boldsymbol{\alpha} \right)}{\alpha \varepsilon\_0} + \varepsilon\_d \left( \boldsymbol{\alpha} \right) \right) \end{split} \tag{2}$$

where <sup>r</sup> is the frequency-dependent relative permittivity of the material, ε0 is the permittivity of free space (equal to 8.854·10-12 F m−1), ω is the angular frequency of the field (ω = 2πf, with *f* frequency in Hz); ''() is the frequency-dependent loss factor, with tot the total conductivity, that includes a frequency-independent ionic conductivity ( <sup>i</sup> ) and the frequency-dependent losses due to dielectric polarization ( <sup>d</sup> ). The frequency used in this study was 300 MHz which is approximately the RF frequency needed to elicit proton MRI signal at 7 T.

In the EEG leads, typically built with metals or non-biological materials, the loss component is due to free electrons only:

$$
\varepsilon''(\boldsymbol{\phi}) = \frac{\sigma\_{\text{byl}}(\boldsymbol{\phi})}{\alpha \varepsilon\_0} = \frac{\sigma\_i(\boldsymbol{\phi})}{\alpha \varepsilon\_0} \tag{3}
$$

Fig. 2. Biophysical properties for homogeneous and heterogeneous model at 300 MHz. The high-spatial resolution of the model allowed distinguishing contiguous structures with different electrical properties, such as bone-marrow vs. outer table, skin vs. fat.

The anatomical classification, mass density and electrical properties at 300 MHz are shown in **Table 1** and mapped in **Figure 2**. Two different electrical models - a homogeneous and a heterogeneous one - were implemented. For the homogeneous case, the same physical properties were assigned to all the anatomical structures, i.e., conductivity tot 0.8 S /m , relative permittivity r 59 , and density <sup>3</sup> d 1040 kg /m , corresponding to the average properties of muscle at 300 MHz [FCC Website]. For the heterogeneous model, each anatomical structure was assigned more specific electrical properties, based on the data of the comprehensive study by Gabriel et al. [Gabriel 1996a, 1996b, 1996c] (**Table 1**). The values of mass density were derived from literature [Collins 2004, DeMarco 2003, Gabriel 1996, FCC website, Li 2006]. An average value of conductivity and permittivity was assigned to the anatomical structures without a direct equivalence in the database (i.e., "Subcutaneous Tissue", "Connective Tissue", and "Soft tissue") [Makris 2008].

*Numerical Model of EEG electrodes and Leads -* The layout of thirty-two EEG electrodes on a 2D mask was designed using Circuit Maker (Altium Inc, San Diego, CA) and imported into Matlab (Mathworks, Natick, MA). The mask was co-registered with the axial slice of largest diameter on the head model. The EEG electrodes and leads of the mask were projected and placed on the surface of the head model ("epidermis" tissue, see **Figure 1**) [Angelone 2006]. The EEG electrodes were modeled as small cylinders (radius: 7 mm, thickness: 3 mm) and were positioned in direct contact with the skin as for the expanded 10-20 montage [Regan 1989]. The leads were modeled as metallic leads ( <sup>8</sup> / 1.67 10 *el leads copper <sup>m</sup>* ), and were bundled above the Cz electrode [Regan 1989],oriented vertically, and curved downward as shown in **Figure 1**. The complete model (i.e., head with 32 EEG electrodes/leads) was then imported into the XFDTD software (Remcomi Inc., State College, PA). EEG leads were shortened on one side, to simulate the short circuit created by the low-pass filter in the input stage of the EEG recording system [Purdon 2008], and connected on the other side to the head surface.

*Numerical Model of RF Coil -* The RF source was based on a volume RF coil [Jin 1997, Collins 2001]. The coil was modeled with 16 perfect electrically conductive rods of 295 mm in length and disposed around the head with circular symmetry (diameter 260mm) (**Figure 1**). The RF source was simulated as a circular excitation driving the current generators placed on the centers of the rods with 1A peak-to-peak amplitude and a 22.5o phase-shift between any two adjacent generators.

*FDTD simulations -* Numerical simulations were performed using commercially available software XFDTD, based on the Finite-Difference-Time-Domain (FDTD) algorithm. Numerical simulations were performed at a frequency of 300 MHz. A total of seven perfectly matching layers were used for boundary conditions [Berenger 1994]. The total volume, including the free space around the model, was 297353303 mm3; the time step used to meet the Courant condition for numerical stability [Taflove 2005] was 1.92 ps, and the total number of time steps was 25,000. Simulations provided the magnitude of electromagnetic field and induced currents for each voxel, as well as whole-head averaged SAR, 1g- and 10 g-averaged SAR [IEC 2002, FDA 2003].

## **3. Results**

196 Applied Biological Engineering – Principles and Practice

properties of the models used in this study were considered as [Vorst 2006]: a) linear with electric field, b) isotropic, c) dispersive, and d) heterogeneous in space. Under these

> 0 0

is the frequency-dependent relative permittivity of the material, ε0 is the

 

 <sup>d</sup>    (2)

 tot the

) and the

 <sup>i</sup> 

). The frequency used in this

(3)

*tot i r rd*

 

*j j*

permittivity of free space (equal to 8.854·10-12 F m−1), ω is the angular frequency of the field

study was 300 MHz which is approximately the RF frequency needed to elicit proton MRI

In the EEG leads, typically built with metals or non-biological materials, the loss component

Fig. 2. Biophysical properties for homogeneous and heterogeneous model at 300 MHz. The high-spatial resolution of the model allowed distinguishing contiguous structures with

The anatomical classification, mass density and electrical properties at 300 MHz are shown in **Table 1** and mapped in **Figure 2**. Two different electrical models - a homogeneous and a heterogeneous one - were implemented. For the homogeneous case, the same physical

different electrical properties, such as bone-marrow vs. outer table, skin vs. fat.

 *tot i* 

0 0

 

conditions, complex permittivity (ε\*) is defined as:

where

 <sup>r</sup> 

signal at 7 T.

is due to free electrons only:

*j*

 

 

(ω = 2πf, with *f* frequency in Hz); ''() is the frequency-dependent loss factor, with

total conductivity, that includes a frequency-independent ionic conductivity (

 

*r*

 

 

frequency-dependent losses due to dielectric polarization (

*Model without EEG electrodes/leads -* **Figure 3** shows the magnetic flux density *B* , and **Figure 4** the electric field *E* and induced currents *<sup>J</sup>* computed with homogeneous and heterogeneous head model. The load of the head on the RF coil (i.e. the impedance seen by each of the 16 sources) was similar (± 10%) in both models, in line with physical RF coil

Specific Absorption Rate Analysis

Fig. 4. Amplitude of electric field *E*

of Heterogeneous Head Models with EEG Electrodes/Leads at 7T MRI 199

and induced currents *<sup>J</sup>*

and heterogeneous head model, without ("Noelec") and with EEG electrodes/leads.

computed with homogeneous

tuning on the bench with anatomically accurate phantoms or human head [Ibrahim 2005]. The characteristic Central Brightening Effect at 7T [Collins 2005] was present in both models. The superposition of electromagnetic fields determined a complex pattern of electric field inside the head and local peaks of electric field at the boundaries between skin and air as well as inside the head. The effect of the tissue conductivity focused the currents in the most conductive structures (e.g., Cerebro Spinal Fluid and eye region).

Fig. 3. Amplitude of magnetic flux density *B* computed with homogeneous and heterogeneous head model without ("Noelec") and with EEG electrodes/leads. The characteristic Central Brightening Effect at 7T [ Collins 2005] was present in both models.

*Head plus metallic leads -* **Figure 4** shows the effect of metallic leads with the head. The superposition of the electric field radiated from the RF coil and field scattered by the leads resulted in an increase of the field near the leads and on the skin, and in a reduction of the field at the center of the head ("shielding effect of the EEG leads") [Hamblin 2007]. There was a peak of induced currents on the skin, near the leads. Because of the EEG-leads acting as antennas, the coil load and the magnetic field inside the head were different compared to the control case of no leads.

tuning on the bench with anatomically accurate phantoms or human head [Ibrahim 2005]. The characteristic Central Brightening Effect at 7T [Collins 2005] was present in both models. The superposition of electromagnetic fields determined a complex pattern of electric field inside the head and local peaks of electric field at the boundaries between skin and air as well as inside the head. The effect of the tissue conductivity focused the currents

computed with homogeneous and

in the most conductive structures (e.g., Cerebro Spinal Fluid and eye region).

Fig. 3. Amplitude of magnetic flux density *B*

compared to the control case of no leads.

models.

heterogeneous head model without ("Noelec") and with EEG electrodes/leads. The characteristic Central Brightening Effect at 7T [ Collins 2005] was present in both

*Head plus metallic leads -* **Figure 4** shows the effect of metallic leads with the head. The superposition of the electric field radiated from the RF coil and field scattered by the leads resulted in an increase of the field near the leads and on the skin, and in a reduction of the field at the center of the head ("shielding effect of the EEG leads") [Hamblin 2007]. There was a peak of induced currents on the skin, near the leads. Because of the EEG-leads acting as antennas, the coil load and the magnetic field inside the head were different

Fig. 4. Amplitude of electric field *E* and induced currents *<sup>J</sup>* computed with homogeneous and heterogeneous head model, without ("Noelec") and with EEG electrodes/leads.

Specific Absorption Rate Analysis

of Heterogeneous Head Models with EEG Electrodes/Leads at 7T MRI 201

Fig. 5. Specific Absorption Rate (SAR) computed with an electrically homogeneous (top) and

electrically heterogeneous (bottom head) model. Sagittal and coronal maps for SAR

unaveraged, 1g-averaged and 10g-averaged SAR are shown.

*SAR -* The whole-head SAR computed with the two models (with/without leads) was similar (i.e., 3% difference, see **Table 2**). No significant difference (<5%) in wholehead SAR was observed for the case with perfectly conductive EEG leads. The heterogeneity of the structures and the local differences of electrical properties affected the 1g-averaged SAR, with up to two-fold difference for the peak 1g-averaged SAR (**Figure 5**) in the control case without leads (1stvs. 3rd column, **Table 2**), and a 30% difference with EEG leads (2ndvs. 4th column, **Table 2**). Smaller differences with homogeneous vs. heterogeneous model were observed in the computation of 10-g averaged SAR, with a 15% difference without leads and 20% difference with EEG leads (**Table 2**).


Table 2. Results for simulations with homogeneous and heterogeneous model, without and with copper EEG leads.

## **4. Discussion**

While the results in the homogeneous model can be validated with direct measurements in phantoms, the validation of numerical simulations with heterogeneous head models require a multi-structure phantom, which would be much more cumbersome and expensive to build. This study aimed to evaluate whether the use of a more complex heterogeneous model would provide additional information when looking at SAR changes due to EEG electrodes/leads in a human head exposed to a 300 MHz RF field.

For this purpose, the study was based on a high-resolution head model segmented by an expert anatomist from MRI data of an adult healthy subject (**Figure 1**). In the control-case of a head model without EEG electrodes/leads, thei EM field was slightly asymmetric [Amjas 2005, Sled 1998]. The EM fields and induced currents were also different between the homogeneous and heterogeneous models [Amjad 2005].

*SAR -* The whole-head SAR computed with the two models (with/without leads) was similar (i.e., 3% difference, see **Table 2**). No significant difference (<5%) in wholehead SAR was observed for the case with perfectly conductive EEG leads. The heterogeneity of the structures and the local differences of electrical properties affected the 1g-averaged SAR, with up to two-fold difference for the peak 1g-averaged SAR (**Figure 5**) in the control case without leads (1stvs. 3rd column, **Table 2**), and a 30% difference with EEG leads (2ndvs. 4th column, **Table 2**). Smaller differences with homogeneous vs. heterogeneous model were observed in the computation of 10-g averaged SAR, with a 15% difference without leads and 20% difference with EEG leads

Table 2. Results for simulations with homogeneous and heterogeneous model, without and

56%

1.8

0.32

0.09

1.37

33.9

3.3

2.1

52%

1.1 0.48

0.10

0.29

4.1

1.05

0.09 0.40

51% 1.9

38.8

4.5 3.6

**noelec 32elec-copper noelec 32elec-copper** 

**Homogeneous Heterogeneus**

0.33

0.10

2.3 0.92

2.1 1.4 2.4 1.8

47%

While the results in the homogeneous model can be validated with direct measurements in phantoms, the validation of numerical simulations with heterogeneous head models require a multi-structure phantom, which would be much more cumbersome and expensive to build. This study aimed to evaluate whether the use of a more complex heterogeneous model would provide additional information when looking at SAR changes due to EEG

For this purpose, the study was based on a high-resolution head model segmented by an expert anatomist from MRI data of an adult healthy subject (**Figure 1**). In the control-case of a head model without EEG electrodes/leads, thei EM field was slightly asymmetric [Amjas 2005, Sled 1998]. The EM fields and induced currents were also different between the

electrodes/leads in a human head exposed to a 300 MHz RF field.

homogeneous and heterogeneous models [Amjad 2005].

(**Table 2**).

with copper EEG leads.

Max SAR [W/kg]

Peak 1g avg. SAR [W/kg]

Peak 10g avg. SAR [W/kg] Whole Head [W/kg] Input power [W]

Efficiency

Radiated power [W]

Power dissipated in head[W] 2.0

**300 MHz**

**4. Discussion** 

Fig. 5. Specific Absorption Rate (SAR) computed with an electrically homogeneous (top) and electrically heterogeneous (bottom head) model. Sagittal and coronal maps for SAR unaveraged, 1g-averaged and 10g-averaged SAR are shown.

Specific Absorption Rate Analysis

with perfectly insulating material (

change in computed 1g-averaged SAR.

measurements with corresponding physical models.

[Hamblin 2007] and the frequency considered [Angelone 2004].

of Heterogeneous Head Models with EEG Electrodes/Leads at 7T MRI 203

*SAR estimation with homogeneous and heterogeneous model-* No significant differences were observed for whole-head SAR computed with or without EEG leads for both the homogeneous and heterogeneous models, suggesting that whole-head SAR may be an excessively smoothing parameter for RF dosimetry with EEG leads. The small difference in peak SAR estimated with homogeneous or heterogeneous model for the case with metallic EEG leads was likely due to the specific location of the peak SAR (i.e., few mm underneath the electrodes); the volume of interest in the heterogeneous model included only two structures, epidermis and subcutaneous tissue, with electrical properties similar to the one used for the homogeneous model. On the other hand, because of the spatially-limited characteristics of SAR changes it is important to properly model the variably-conductive interfaces between EEG electrodes, epidermis, and subcutaneous tissues, both in terms of anatomical structures and electrical properties. As a further test, we have compared the results obtained with the homogeneous model with metallic leads with a model where the external layer (i.e., the epidermis) was substituted

not affected by the dramatic change in conductivity at the interface, but there was a 280%

The use of a heterogeneous head model may allow for improved SAR computation and visualization for heterogeneous structures with different electrical properties, such as skin, fat, muscle or bone marrow (**Figure 2**). However, the use of an anatomically finegrained head model may add potential errors when modeling the internal structures of the head [Gajsek 2002]. Due to the difficulties in matching exactly all the anatomical definitions to existing literature, some of the anatomical structures were assigned the same electrical properties; 16 different electrical properties were used to characterize the anatomical structures (**Figure 2**). Further work may be performed to improve the electrical characterization of the numerical head model and to validate using direct

*Effect of geometry -* This study focused on evaluating the effect of head electrical heterogeneity as well as lead resistivity on SAR. The geometrical model was constant with respect to other physical variables (**Figure 1**) which may affect SAR: number of electrodes, length and orientation of the leads, position of the head inside the RF coil, and RF source geometry, as well as size and shape of the head model. In clinical applications, these variables will be affected by various external constraints, such as length of the imager used for the MRI recording, position of EEG system inside the MRI room, and geometry of RF coil used to obtain the best Signal to Noise Ratio (SNR). For example, EEG leads may be connected to a pre-amplifier placed either on the back of the imager (EEG leads from the top of the head oriented farther away from the head) or in the front of the scanner (EEG leads placed along the head and exiting from the neck down); in this case the minimal physical length of the leads will depend on the placement of the pre-amplifier. We have modeled 32 electrodes and leads, a configuration currently used in many laboratories for EEG-MRI recordings. The results of this study cannot be directly extrapolated to different number of electrodes, because the presence of more leads may increase the interaction with the EM field, with resulting SAR in the head that could be higher or lower, depending on the geometry, the shielding effect of the EEG leads

0 / *S m* ). Whole-head and 10g-averaged SAR were

Fig. 6. 3D view of SAR (W/Kg) with copper leads on epidermis and bone structures (outer table, inner table, bone, teeth). The high-resolution of the model allowed for precise anatomical definition of thin structures, such the epidermis, where the contact with copper EEG leads induces local electric field and SAR enhancement. Max SAR = 10 W/kg. Values normalized to 1 W of Input Power.

Fig. 6. 3D view of SAR (W/Kg) with copper leads on epidermis and bone structures (outer table, inner table, bone, teeth). The high-resolution of the model allowed for precise anatomical definition of thin structures, such the epidermis, where the contact with copper

EEG leads induces local electric field and SAR enhancement. Max SAR = 10 W/kg.

Values normalized to 1 W of Input Power.

*SAR estimation with homogeneous and heterogeneous model-* No significant differences were observed for whole-head SAR computed with or without EEG leads for both the homogeneous and heterogeneous models, suggesting that whole-head SAR may be an excessively smoothing parameter for RF dosimetry with EEG leads. The small difference in peak SAR estimated with homogeneous or heterogeneous model for the case with metallic EEG leads was likely due to the specific location of the peak SAR (i.e., few mm underneath the electrodes); the volume of interest in the heterogeneous model included only two structures, epidermis and subcutaneous tissue, with electrical properties similar to the one used for the homogeneous model. On the other hand, because of the spatially-limited characteristics of SAR changes it is important to properly model the variably-conductive interfaces between EEG electrodes, epidermis, and subcutaneous tissues, both in terms of anatomical structures and electrical properties. As a further test, we have compared the results obtained with the homogeneous model with metallic leads with a model where the external layer (i.e., the epidermis) was substituted with perfectly insulating material ( 0 / *S m* ). Whole-head and 10g-averaged SAR were not affected by the dramatic change in conductivity at the interface, but there was a 280% change in computed 1g-averaged SAR.

The use of a heterogeneous head model may allow for improved SAR computation and visualization for heterogeneous structures with different electrical properties, such as skin, fat, muscle or bone marrow (**Figure 2**). However, the use of an anatomically finegrained head model may add potential errors when modeling the internal structures of the head [Gajsek 2002]. Due to the difficulties in matching exactly all the anatomical definitions to existing literature, some of the anatomical structures were assigned the same electrical properties; 16 different electrical properties were used to characterize the anatomical structures (**Figure 2**). Further work may be performed to improve the electrical characterization of the numerical head model and to validate using direct measurements with corresponding physical models.

*Effect of geometry -* This study focused on evaluating the effect of head electrical heterogeneity as well as lead resistivity on SAR. The geometrical model was constant with respect to other physical variables (**Figure 1**) which may affect SAR: number of electrodes, length and orientation of the leads, position of the head inside the RF coil, and RF source geometry, as well as size and shape of the head model. In clinical applications, these variables will be affected by various external constraints, such as length of the imager used for the MRI recording, position of EEG system inside the MRI room, and geometry of RF coil used to obtain the best Signal to Noise Ratio (SNR). For example, EEG leads may be connected to a pre-amplifier placed either on the back of the imager (EEG leads from the top of the head oriented farther away from the head) or in the front of the scanner (EEG leads placed along the head and exiting from the neck down); in this case the minimal physical length of the leads will depend on the placement of the pre-amplifier. We have modeled 32 electrodes and leads, a configuration currently used in many laboratories for EEG-MRI recordings. The results of this study cannot be directly extrapolated to different number of electrodes, because the presence of more leads may increase the interaction with the EM field, with resulting SAR in the head that could be higher or lower, depending on the geometry, the shielding effect of the EEG leads [Hamblin 2007] and the frequency considered [Angelone 2004].

Specific Absorption Rate Analysis

Institute (R21EY020961-01) (GB).

p. 4185-4187.

xvii, 1117 p.

114(3): p. 569-80.

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Magn Reson Imaging, 1986. 4(4): p. 321-33.

Computational Physics, 1994. 114: p. 185-200.

**7. References** 

**6. Acknowledgments** 

of Heterogeneous Head Models with EEG Electrodes/Leads at 7T MRI 205

We would like to thank Dr. Nikos Makris, Jonathan Kaiser, and the Center for Morphometric Analysis at Massachusetts General Hospital for their help for this study. We also would like to thank Drs. CK Chou, Bu Sik Park, and Jana Delfino for the useful insights. The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services. This research was carried out in whole or in part at the Athinoula A. Martinos Center for Biomedical Imaging at the Massachusetts General Hospital, using resources provided by the *Center for Functional Neuroimaging Technologies, P41RR14075,* a P41 Regional Resource supported by the Biomedical Technology Program of the National Center for Research Resources (NCRR), National Institutes of Health. This work was also supported in part by the National Institute of Biomedical Imaging and Bioengineering (R01EB006385) (GB), and by the National Eye

Adair E.R., and Berglund L.G. On the thermoregulatory consequences of NMR imaging.

Allen P.J., Josephs O., and Turner R. A method for removing imaging artifact from continuous EEG recorded during functional MRI. Neuroimage, 2000. 12(2): p. 230-9. Amjad A., Kamondetdacha R., Kildishev A., Park S.M., and Nyenhuis J. Power deposition

Angelone L.M., Potthast A., Segonne F., Iwaki S., Belliveau J., and Bonmassar G. Metallic

Angelone L.M., Vasios C.E., Wiggins G., Purdon P.L., and Bonmassar G. On the effect of

Armenean C., Perrin E., Armenean M., Beuf O., Pilleul F., and Saint-Jalmes H. RF-induced

influence of diameter and length. Magn Reson Med, 2004. 52(5): p. 1200-6. Balanis, C.A., Antenna theory : analysis and design. 3rd ed. 2005, Hoboken, NJ: John Wiley.

Benar C., Aghakhani Y., Wang Y., Izenberg A., Al-Asmi A., Dubeau F., and Gotman J.

Berenger J.P. A perfectly matched layer for the absorption of electromagnetic waves.

Bonmassar G., Hadjikhani N., Ives J.R., Hinton D., and Belliveau J.W. Influence of EEG electrodes on the BOLD fMRI signal. Hum Brain Mapp, 2001. 14(2): p. 108-15. Bottomley P.A. and Andrew E.R. RF magnetic field penetration, phase shift and power

simulation studies. Bioelectromagnetics, 2004. 25(4): p. 285-295.

measurement studies. Magn Reson Imaging, 2006. 24(6): p. 801-12

inside a phantom for testing of MRI heating. IEEE Trans on Magnetics, 2005. 41(10):

electrodes and leads in simultaneous EEG-MRI: specific absorption rate (SAR)

resistive EEG electrodes and leads during 7 T MRI: simulation and temperature

temperature elevation along metallic wires in clinical magnetic resonance imaging:

Quality of EEG in simultaneous EEG-fMRI for epilepsy. Clin Neurophysiol, 2003.

dissipation in biological tissue: Implications for NMR imaging. Phys. Med. Biol.,

*Antenna effect -* The typical length of EEG leads is in the order of ~ 50-100cm, which is comparable with the wavelength of the RF field at 300 MHz (i.e., 1 m in empty space). The interactions of the EEG leads and RF coils will induce changes in the EM field inside the head (i.e., "shielding effect" of the EEG leads) [Hamblin 2007] and local SAR enhancement at the interface between electrodes and skin [Armenean 2004, Yeung 2002]. Low resistivity EEG leads ( min 0.0001 *lead m* ) behave as lossless antenna [Balanis 2005] and will have maximum induced currents along the leads. The high discontinuity of resistivity between lead and surrounding medium ( <sup>8</sup> 1 .67 10 *lead <sup>m</sup>* vs. 1 1 .56 *skin skin m* for the skin/epidermis, **Table 1**) determines an electric field enhancement at the interface between leads and head surface (i.e., epidermis). This observation is in line with theoretical models [Guy 1975] and physical evidence of reports of burns due to "antenna-effect" of leads [Dempsey 2001].

## **5. Conclusions**

The aim of this study was to investigate the possible effect of using complex heterogeneous head models when investigating SAR in a human head wearing EEG electrodes/leads while exposed to RF field of high-field MRI. MRI-based high-resolution homogeneous and heterogeneous head models with 32 EEG electrodes/leads were implemented. Electromagnetic simulations based on FDTD algorithm were performed. Non-significant differences in whole-head SAR (i.e. less than 5%) and a 30% difference in peak 10g-averaged SAR values were observed with the homogeneous vs. heterogeneous models. The presence of an insulating layer between EEG electrode and skin resulted in a three-fold change in computed 1g-averaged SAR. Results of this study suggest that when whole-head, 10gaveraged, and 1g-averaged SAR in a human head wearing EEG electrodes/leads are computed with a homogeneous rather than electrically heterogeneous model this can result in a difference of up to 30%. In all cases, a precise modeling of the electrically conductive interface between electrode and head surface is fundamental to avoid a significant underestimation of the local SAR.

*Future directions –* The systematic analysis presented in this chapter improved the scientific understanding of the complex interactions between radiofrequency electromagnetic field and a human head with EEG leads. Such a numerical framework can be used to support the design and development of novel leads for multimodal recording at ultra high-field MRI. Future work may be directed toward investigating the effect of the specific head model used, in terms of inter-subject variability and in the presence of anatomical pathologies. Moreover, further improvement of the electrical model, namely the electrical properties associated with each anatomical structure, can be obtained by taking advantage of MRIbased direct measurements, i.e., electrical properties tomography (EPT). Finally, while the specific absorption rate is the current parameter used for RF dosimetry, the use of temperature is a more biologically significant quantity, and future work may be directed toward a better evaluation of the changes in temperature – rather than only SAR – in the body. The experimental validation with properly matching geometries between numerical and physical models will most likely be the final fundamental step toward a complete dosimetric evaluation.

## **6. Acknowledgments**

204 Applied Biological Engineering – Principles and Practice

*Antenna effect -* The typical length of EEG leads is in the order of ~ 50-100cm, which is comparable with the wavelength of the RF field at 300 MHz (i.e., 1 m in empty space). The interactions of the EEG leads and RF coils will induce changes in the EM field inside the head (i.e., "shielding effect" of the EEG leads) [Hamblin 2007] and local SAR enhancement at the interface between electrodes and skin [Armenean 2004, Yeung 2002]. Low resistivity

have maximum induced currents along the leads. The high discontinuity of resistivity

the skin/epidermis, **Table 1**) determines an electric field enhancement at the interface between leads and head surface (i.e., epidermis). This observation is in line with theoretical models [Guy 1975] and physical evidence of reports of burns due to "antenna-effect" of

The aim of this study was to investigate the possible effect of using complex heterogeneous head models when investigating SAR in a human head wearing EEG electrodes/leads while exposed to RF field of high-field MRI. MRI-based high-resolution homogeneous and heterogeneous head models with 32 EEG electrodes/leads were implemented. Electromagnetic simulations based on FDTD algorithm were performed. Non-significant differences in whole-head SAR (i.e. less than 5%) and a 30% difference in peak 10g-averaged SAR values were observed with the homogeneous vs. heterogeneous models. The presence of an insulating layer between EEG electrode and skin resulted in a three-fold change in computed 1g-averaged SAR. Results of this study suggest that when whole-head, 10gaveraged, and 1g-averaged SAR in a human head wearing EEG electrodes/leads are computed with a homogeneous rather than electrically heterogeneous model this can result in a difference of up to 30%. In all cases, a precise modeling of the electrically conductive interface between electrode and head surface is fundamental to avoid a significant

*Future directions –* The systematic analysis presented in this chapter improved the scientific understanding of the complex interactions between radiofrequency electromagnetic field and a human head with EEG leads. Such a numerical framework can be used to support the design and development of novel leads for multimodal recording at ultra high-field MRI. Future work may be directed toward investigating the effect of the specific head model used, in terms of inter-subject variability and in the presence of anatomical pathologies. Moreover, further improvement of the electrical model, namely the electrical properties associated with each anatomical structure, can be obtained by taking advantage of MRIbased direct measurements, i.e., electrical properties tomography (EPT). Finally, while the specific absorption rate is the current parameter used for RF dosimetry, the use of temperature is a more biologically significant quantity, and future work may be directed toward a better evaluation of the changes in temperature – rather than only SAR – in the body. The experimental validation with properly matching geometries between numerical and physical models will most likely be the final fundamental step toward a complete

*m* ) behave as lossless antenna [Balanis 2005] and will

*lead <sup>m</sup>* vs. 1 1 .56 

 *skin skin* 

*m* for

EEG leads ( min 0.0001 *lead* 

underestimation of the local SAR.

dosimetric evaluation.

leads [Dempsey 2001].

**5. Conclusions** 

between lead and surrounding medium ( <sup>8</sup> 1 .67 10

We would like to thank Dr. Nikos Makris, Jonathan Kaiser, and the Center for Morphometric Analysis at Massachusetts General Hospital for their help for this study. We also would like to thank Drs. CK Chou, Bu Sik Park, and Jana Delfino for the useful insights.

The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services. This research was carried out in whole or in part at the Athinoula A. Martinos Center for Biomedical Imaging at the Massachusetts General Hospital, using resources provided by the *Center for Functional Neuroimaging Technologies, P41RR14075,* a P41 Regional Resource supported by the Biomedical Technology Program of the National Center for Research Resources (NCRR), National Institutes of Health. This work was also supported in part by the National Institute of Biomedical Imaging and Bioengineering (R01EB006385) (GB), and by the National Eye Institute (R21EY020961-01) (GB).

## **7. References**


Specific Absorption Rate Analysis

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**9** 

*1,2The Netherlands* 

*3Bulgaria* 

**Simulating Idiopathic Parkinson's** 

Tjitske Heida1, Jan Stegenga1, Marcel Lourens2,

**Disease by** *In Vitro* **and Computational Models** 

Hil Meijer2, Stephan van Gils2, Nikolai Lazarov3 and Enrico Marani1

*2Department of Applied Analysis and Mathematical Physics, University of Twente* 

The motor disorder of Parkinson's disease (PD) results from injury of the basal ganglia (BG). Understanding of the pathophysiology came late, especially with regard to the involvement of the substantia nigra. The description of 'shaking palsy' or 'paralysis agitans' (Parkinson, 1817) did not bring forward the recognition of its pathological origin. Lewy (1912, 1913) put emphasis on the globus pallidus and putamen. Von Economo's emphasis (1917) on the substantia nigra (SN) in encephalitis lethargica, with analogous clinical appearance, prompted others to pay attention to this nucleus. Tetriakoff (1919) was the first to describe SN involvement in paralysis agitans. Hassler (1937, 1938, 1939), by studying the normal cytoarchitecture of the SN, discovered a differential damage in the pars compacta using the collection of Cecile and Oscar Vogt. Moreover, he described the damage in the locus coeruleus. It was Friede, already in 1953 (1953, 1966), using histochemical techniques, who proposed a relation with catecholaminergic systems. Although the SN-catecholamine doctrine was regularly scrutinized in the early days of catecholamine research (see e.g.

Parkinson's disease is nowadays subdivided in idiopathic Parkinson's disease and Parkinson plus syndromes (see Usunoff et al., 2002). Parkinson plus syndromes counts for 15% of all Parkinsonism, although in large autopsy series the percentage augmented to 20- 25% (Hughes et al., 1992), thus leaving idiopathic Parkinson's disease as the most frequently occurring form (Jellinger, 1987). Nevertheless contested (see e.g. Gibb, 1988; Kingsburry et al., 1999), the suggestion that the vulnerability of SN neurons is related to the neuromelanin/tyrosine hydroxylase content is favored in idiopathic Parkinsonism (Hirsch et al. 1988). Idiopathic Parkinson's disease is characterized by neuromelanin-containing cell

Mettler, 1964), it has not been overthrown up till now.

**1.2 Idiopathic Parkinson's disease** 

**1. Introduction 1.1 Short history**  *1Department of Biomedical Signals and Systems, University of Twente* 

*3Department of Anatomy and Histology, Medical University Sofia* 


## **Simulating Idiopathic Parkinson's Disease by** *In Vitro* **and Computational Models**

Tjitske Heida1, Jan Stegenga1, Marcel Lourens2, Hil Meijer2, Stephan van Gils2, Nikolai Lazarov3 and Enrico Marani1

*1Department of Biomedical Signals and Systems, University of Twente 2Department of Applied Analysis and Mathematical Physics, University of Twente 3Department of Anatomy and Histology, Medical University Sofia 1,2The Netherlands 3Bulgaria* 

## **1. Introduction**

208 Applied Biological Engineering – Principles and Practice

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Simultaneous 3-T fMRI and high-density recording of human auditory evoked

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EEG/(f)MRI measurements at 7 Tesla using a new EEG cap ("InkCap").

Equations in Isotropic Media. IEEE Transactions on Antennas and Propagation,

depends on the phase distribution of the transmit field. Magn Reson Med, 2002.

#### **1.1 Short history**

The motor disorder of Parkinson's disease (PD) results from injury of the basal ganglia (BG). Understanding of the pathophysiology came late, especially with regard to the involvement of the substantia nigra. The description of 'shaking palsy' or 'paralysis agitans' (Parkinson, 1817) did not bring forward the recognition of its pathological origin. Lewy (1912, 1913) put emphasis on the globus pallidus and putamen. Von Economo's emphasis (1917) on the substantia nigra (SN) in encephalitis lethargica, with analogous clinical appearance, prompted others to pay attention to this nucleus. Tetriakoff (1919) was the first to describe SN involvement in paralysis agitans. Hassler (1937, 1938, 1939), by studying the normal cytoarchitecture of the SN, discovered a differential damage in the pars compacta using the collection of Cecile and Oscar Vogt. Moreover, he described the damage in the locus coeruleus. It was Friede, already in 1953 (1953, 1966), using histochemical techniques, who proposed a relation with catecholaminergic systems. Although the SN-catecholamine doctrine was regularly scrutinized in the early days of catecholamine research (see e.g. Mettler, 1964), it has not been overthrown up till now.

### **1.2 Idiopathic Parkinson's disease**

Parkinson's disease is nowadays subdivided in idiopathic Parkinson's disease and Parkinson plus syndromes (see Usunoff et al., 2002). Parkinson plus syndromes counts for 15% of all Parkinsonism, although in large autopsy series the percentage augmented to 20- 25% (Hughes et al., 1992), thus leaving idiopathic Parkinson's disease as the most frequently occurring form (Jellinger, 1987). Nevertheless contested (see e.g. Gibb, 1988; Kingsburry et al., 1999), the suggestion that the vulnerability of SN neurons is related to the neuromelanin/tyrosine hydroxylase content is favored in idiopathic Parkinsonism (Hirsch et al. 1988). Idiopathic Parkinson's disease is characterized by neuromelanin-containing cell

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 211

circuit. Then we will concentrate on rat SN and STN experimental results as obtained in our group. On the one hand anatomical data of the afferent and efferent connections of the SN and STN are presented, while on the other hand electrophysiological data of the neuronal activity patterns as observed in dissociated STN cell cultures and brain slices is discussed. Finally, a selection of computational models developed in our Applied Analysis and Mathematical Physics, and Biomedical Signals and Systems groups, related to different aspects of idiopathic Parkinson's disease are summarized. One of the aims of these computational models is to understand the mechanism of DBS. This review relies also on earlier publications, congress abstracts and presented posters (Cagnan et al., 2009; Heida et al., 2008, 2009, 2010a,b,c,d; Lourens et al., 2009, 2011; Marani et al., 2008, 2010; Meijer et al.,

**2. Which connections are involved in idiopathic Parkinson's disease? 2.1 Classic connectivity diagram of the corticothalamic-basal ganglia network** 

on the BG output nuclei, and thus on the thalamic targets of these nuclei.

extended overview).

The major pathways within the basal ganglia-thalamocortical circuit, which are known to be involved in the execution of voluntary movement, are illustrated in Figure 1 (see Gerfen & Wilson, 1996; and Groenewegen & Van Dongen, 2008). Albin et al. (1989) and De Long (1990) first proposed these pathways through the basal ganglia (BG). Two major connections link the BG input nucleus (striatum) to the output nuclei (globus pallidus interna (GPi)/substantia nigra pars reticulata (SNr)), namely the 'direct' and 'indirect' pathways. The critical balance between these two pathways determines normal motor behavior. The BG output nuclei have a high rate of spontaneous discharge, and thus exert a tonic, GABAmediated, inhibitory effect on their target nuclei in the thalamus. The inhibitory outflow is differentially modulated by the direct and indirect pathways, which have opposing effects

The 'direct' pathway arises from inhibitory striatal efferents that contain both GABA and substance P and projects directly to the output nuclei. It is transiently activated by increased phasic excitatory input from the SNc (substantia nigra pars compacta) to the striatum. Activation of the direct pathway briefly suppresses the tonically active inhibitory neurons of the output nuclei, disinhibiting the thalamus, and thus increasing thalamocortical activity. The 'indirect' pathway begins with inhibitory striatal efferents that contain both GABA and enkephalin. These striatal neurons project to the GPe (globus pallidus externus). The GPe projects to the STN, via a purely GABAergic pathway, which finally projects to the output nuclei via an excitatory, glutamatergic projection. There is also a direct projection from the GPe to the output nuclei. The indirect pathway is phasically activated by decreased inhibitory input from the SNc to the striatum, causing an increase in striatal output along its pathway. Normally the high spontaneous discharge rate of GPe neurons exerts a tonic inhibitory influence on the STN. Activation of the 'indirect' pathway tends to suppress the activity of GPe neurons, disinhibiting the STN, and increasing the excitatory drive on the output nuclei. The decreased GPe activity also directly disinhibits the output nuclei. The resulting increase in activity of the output nuclei inhibits the thalamus further, decreasing thalamocortical activity. Activation of the direct pathway thus *facilitates* movement, whereas activation of the indirect pathway *inhibits* movement (see McIntyre and Hahn, 2010, for an

in press; Moroney et al., 2008; Stegenga et al., 2009, 2010a,b,c).

loss and by the presence of Lewy inclusion bodies in surviving neurons in the SN and other areas (for an overview see Usunoff et al., 2002). "Lewy bodies in the SN are considered the pathological hallmark of Parkinson's disease, which means that if they cannot be found, the diagnosis is not Parkinson's disease" (Usunoff et al., 2002). The conclusion that idiopathic Parkinson's disease involves degeneration of pigmented neurons of the brain stem is inevitable (Greenfield & Bosanquet, 1953). This conclusion is also based on the distribution of Lewy bodies in other brainstem areas. However, within the human SN not all subareas degenerate (for an overview see Usunoff et al., 2002). Since topography is present in the human SN, circuits of these sparse unharmed areas do survive.

#### **1.3 Models of idiopathic Parkinson's disease**

Animal research profoundly increased by the detection of MPTP. In 1982, a young male, age 29, in northern California, used a new synthetic heroin, which brought him and his also addicted brother and several others, profound and unremitting Parkinsonism (Langston et al. 1999). In this case Meperidine (Demerol, Pethidine) was used. MPPP, the 'Designer heroin' (1-methyl-4-phenyl-4-propionoxypiperidine) contained not only MPPP but also 2.5 to 2.9% of MPTP (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine) by weight, a byproduct in the synthesis of MPPP. Biotransformation produces from MPTP the 1-methyl-4 phenylpyridinium ion (MPP+), which is taken up by the dopamine transporter of the SN neurons, where it blocks the mitochondrial respiratory chain (see Langston et al., 1999 and references herein). An experimental monkey model was developed (see Vitale et al., 2009, for ethical criticism on this monkey model). MPTP was quickly shown experimentally to selectively destroy nerve cells in the SN after systemic administration. The resulting striatal dopamine depletion explained most, if not all of the clinical features of Parkinson's disease (for an extensive summary see Langston et al., 1983; Langston et al., 1999, and a report of an earlier case by Davis et al., 1979). MPTP works in dogs, cats and pigs, but is less effective in rats and guinea pigs, while the MPTP effect is strain dependent in mice. The overview of monkey MPTP results (Israel and Bergman, 2008) shows that these studies demonstrated the importance of the inactivation of the STN, inducing Parkinson symptoms and that the onset of synchronized bursts and high frequency oscillations interfered with normal function of the spatio-temporal function of the basal ganglia.

"However, although an experimental animal model is present and enormous efforts have been carried out to detect the cause of Parkinsonism, what initiates the disease is still unknown. Moreover, human studies have an ethical drawback and a case as described above is seldom found in literature. Therefore, experimental results from animals, often not possible to translate to the human situation, especially rat and mouse results, is what scientists have to relay on. Consequently model studies, using systemic, neuroanatomically developed, models, are of the utmost importance in the study of Parkinson's disease and are significant in their contribution to the understanding of Deep Brain Stimulation (DBS), nowadays mainly carried out in the subthalamic nucleus (STN)" (Heida et al., 2008; see also Toulouse & Sullivan, 2008).

It is, therefore, the gathering and the correct transformation of experimental animal results into newly developed PD models that determine the success of such a model in the contribution to the understanding of idiopathic Parkinson's disease. This review paper will first give an overview of the (classic) connection scheme of the basal ganglia-corticothalamic

loss and by the presence of Lewy inclusion bodies in surviving neurons in the SN and other areas (for an overview see Usunoff et al., 2002). "Lewy bodies in the SN are considered the pathological hallmark of Parkinson's disease, which means that if they cannot be found, the diagnosis is not Parkinson's disease" (Usunoff et al., 2002). The conclusion that idiopathic Parkinson's disease involves degeneration of pigmented neurons of the brain stem is inevitable (Greenfield & Bosanquet, 1953). This conclusion is also based on the distribution of Lewy bodies in other brainstem areas. However, within the human SN not all subareas degenerate (for an overview see Usunoff et al., 2002). Since topography is present in the

Animal research profoundly increased by the detection of MPTP. In 1982, a young male, age 29, in northern California, used a new synthetic heroin, which brought him and his also addicted brother and several others, profound and unremitting Parkinsonism (Langston et al. 1999). In this case Meperidine (Demerol, Pethidine) was used. MPPP, the 'Designer heroin' (1-methyl-4-phenyl-4-propionoxypiperidine) contained not only MPPP but also 2.5 to 2.9% of MPTP (1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine) by weight, a byproduct in the synthesis of MPPP. Biotransformation produces from MPTP the 1-methyl-4 phenylpyridinium ion (MPP+), which is taken up by the dopamine transporter of the SN neurons, where it blocks the mitochondrial respiratory chain (see Langston et al., 1999 and references herein). An experimental monkey model was developed (see Vitale et al., 2009, for ethical criticism on this monkey model). MPTP was quickly shown experimentally to selectively destroy nerve cells in the SN after systemic administration. The resulting striatal dopamine depletion explained most, if not all of the clinical features of Parkinson's disease (for an extensive summary see Langston et al., 1983; Langston et al., 1999, and a report of an earlier case by Davis et al., 1979). MPTP works in dogs, cats and pigs, but is less effective in rats and guinea pigs, while the MPTP effect is strain dependent in mice. The overview of monkey MPTP results (Israel and Bergman, 2008) shows that these studies demonstrated the importance of the inactivation of the STN, inducing Parkinson symptoms and that the onset of synchronized bursts and high frequency oscillations interfered with normal function of

"However, although an experimental animal model is present and enormous efforts have been carried out to detect the cause of Parkinsonism, what initiates the disease is still unknown. Moreover, human studies have an ethical drawback and a case as described above is seldom found in literature. Therefore, experimental results from animals, often not possible to translate to the human situation, especially rat and mouse results, is what scientists have to relay on. Consequently model studies, using systemic, neuroanatomically developed, models, are of the utmost importance in the study of Parkinson's disease and are significant in their contribution to the understanding of Deep Brain Stimulation (DBS), nowadays mainly carried out in the subthalamic nucleus (STN)" (Heida et al., 2008; see also

It is, therefore, the gathering and the correct transformation of experimental animal results into newly developed PD models that determine the success of such a model in the contribution to the understanding of idiopathic Parkinson's disease. This review paper will first give an overview of the (classic) connection scheme of the basal ganglia-corticothalamic

human SN, circuits of these sparse unharmed areas do survive.

**1.3 Models of idiopathic Parkinson's disease** 

the spatio-temporal function of the basal ganglia.

Toulouse & Sullivan, 2008).

circuit. Then we will concentrate on rat SN and STN experimental results as obtained in our group. On the one hand anatomical data of the afferent and efferent connections of the SN and STN are presented, while on the other hand electrophysiological data of the neuronal activity patterns as observed in dissociated STN cell cultures and brain slices is discussed. Finally, a selection of computational models developed in our Applied Analysis and Mathematical Physics, and Biomedical Signals and Systems groups, related to different aspects of idiopathic Parkinson's disease are summarized. One of the aims of these computational models is to understand the mechanism of DBS. This review relies also on earlier publications, congress abstracts and presented posters (Cagnan et al., 2009; Heida et al., 2008, 2009, 2010a,b,c,d; Lourens et al., 2009, 2011; Marani et al., 2008, 2010; Meijer et al., in press; Moroney et al., 2008; Stegenga et al., 2009, 2010a,b,c).

## **2. Which connections are involved in idiopathic Parkinson's disease?**

## **2.1 Classic connectivity diagram of the corticothalamic-basal ganglia network**

The major pathways within the basal ganglia-thalamocortical circuit, which are known to be involved in the execution of voluntary movement, are illustrated in Figure 1 (see Gerfen & Wilson, 1996; and Groenewegen & Van Dongen, 2008). Albin et al. (1989) and De Long (1990) first proposed these pathways through the basal ganglia (BG). Two major connections link the BG input nucleus (striatum) to the output nuclei (globus pallidus interna (GPi)/substantia nigra pars reticulata (SNr)), namely the 'direct' and 'indirect' pathways. The critical balance between these two pathways determines normal motor behavior. The BG output nuclei have a high rate of spontaneous discharge, and thus exert a tonic, GABAmediated, inhibitory effect on their target nuclei in the thalamus. The inhibitory outflow is differentially modulated by the direct and indirect pathways, which have opposing effects on the BG output nuclei, and thus on the thalamic targets of these nuclei.

The 'direct' pathway arises from inhibitory striatal efferents that contain both GABA and substance P and projects directly to the output nuclei. It is transiently activated by increased phasic excitatory input from the SNc (substantia nigra pars compacta) to the striatum. Activation of the direct pathway briefly suppresses the tonically active inhibitory neurons of the output nuclei, disinhibiting the thalamus, and thus increasing thalamocortical activity. The 'indirect' pathway begins with inhibitory striatal efferents that contain both GABA and enkephalin. These striatal neurons project to the GPe (globus pallidus externus). The GPe projects to the STN, via a purely GABAergic pathway, which finally projects to the output nuclei via an excitatory, glutamatergic projection. There is also a direct projection from the GPe to the output nuclei. The indirect pathway is phasically activated by decreased inhibitory input from the SNc to the striatum, causing an increase in striatal output along its pathway. Normally the high spontaneous discharge rate of GPe neurons exerts a tonic inhibitory influence on the STN. Activation of the 'indirect' pathway tends to suppress the activity of GPe neurons, disinhibiting the STN, and increasing the excitatory drive on the output nuclei. The decreased GPe activity also directly disinhibits the output nuclei. The resulting increase in activity of the output nuclei inhibits the thalamus further, decreasing thalamocortical activity. Activation of the direct pathway thus *facilitates* movement, whereas activation of the indirect pathway *inhibits* movement (see McIntyre and Hahn, 2010, for an extended overview).

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 213

pathway and an increase in transmission through the indirect pathway, causing an

The depletion of striatal dopamine changes neuronal firing rates in basal ganglia nuclei. Increased firing rates are found in the striatum, GPi and STN and a minimally decreased discharge in the GPe. A summary of tonic firing rates of BG nuclei in the normal and parkinsonian situation can be found in Heida et al. (2008). However, the pattern of discharge of basal ganglia neurons is thought to be equally as important as the rate of discharge in the execution of smooth movements. Several alterations in the discharge pattern have been observed in neurons of the BG in PD subjects. These alterations include a tendency of neurons to discharge in bursts, increased correlation and synchronisation of discharge between neighbouring neurons, rhythmic and oscillatory behaviour (Brown, 2003). Coherence between STN and GPi activity has been confirmed at tremor frequencies (3-10 Hz) (Brown et al., 2001). These oscillatory patterns are projected to GPi's thalamic projection site, the nucleus ventralis anterior thalami, and the cortex. In addition, STN and GPi demonstrate a tendency to synchronization at 11-30 Hz, which is likely to be driven from the motor areas of the cortex (Brown, 2003). In this circuit, the thalamus is in a key position as it receives the convergent afferent input from the GPi, the cortex, and the peripheral system, which it then projects back

Gait is related to the pedunculopontine nucleus (Piallat et al., 2009), and therefore this nucleus plays an important role in gait and balance disorders that are common in Parkinson's disease. Topographically a pars compacta and a pars dissipatus of the PPN is discerned (Jacobsohn, 1909; Olszewski and Baxter, 1954). The pars dissipatus is supposed to contain glutamatergic neurons. Both parts contain cholinergic neurons. In humans the pars compacta exists of 90% cholinergic cells and the pars dissipatus of 25-75% (Mesulam et al., 1989). It should be noted, that intra-striatal pathways and PPN connections towards the SNc are mainly cholinergic. Cholinergic systems are also degenerated in Parkinson's disease. Nevertheless, next to a dopamine receptor balance a dopamine-acetylcholine balance also plays a role and "a cholinergic overactivity has been used to explain the improvement of some motor signs such as tremor, reported after muscarinic receptor blockade" (Calabresi et al., 2006), although a more cooperative role is supported for acetylcholine and dopamine in human cognitive performance. Cholinergic drugs do also have an improving effect on

Physiological studies subdivided PPN neurons in three types (I, II and III) identified on the basis of their electrophysiological membrane properties obtained by intracellular recording. Type I neurons are characterized by low threshold calcium spikes (LTS), which give rise to a burst of fast action potentials after the offset of a hyperpolarizing current. The neurons also fire bursts of spikes when a depolarized stimulus is given during hyperpolarization. According to Takakusaki and Kitai (1997) Type I neurons are glutamatergic. Type II neurons do not burst. Instead they fire single action potentials with large after-hyperpolarizations in response to injections of depolarizing current. This type is thus suited to generate a relatively slow tonic repetitive firing pattern. About 50% of Type II neurons are cholinergic. Type III neurons miss characteristics of Type I and Type II PPN neurons, thus lacking lowthreshold spikes. The PPN neuron receives pallidal information, gathers information from the STN-SN network with strong SN influence, also from the cortex, from the limbic system

imbalance between the two pathways.

to the cortex, including motor areas (Smith et al., 1998).

**2.2 Pedunculopontine and cholinergic connections** 

cognitive behavior in Parkinson's patients (Calabresi et al., 2006).

The cortico-STN-GPi 'hyperdirect' pathway (Nambu et al., 2000, 2002; Nambu, 2005; Brown, 2003; BarGad et al., 2003; Squire et al., 2003) conveys powerful excitatory effects from the motor-related cortical areas to the globus pallidus, bypassing the striatum. The hyperdirect pathway is therefore an alternative direct cortical link to the BG, possibly as important to motor control as the direct pathway, which is typically considered to be the main cortical relay in the BG.

Fig. 1. Connection diagram of the basal ganglia-thalamocortical motor circuit. The relative connection strengths are indicated for Left: the normal healthy brain, and Right: the parkinsonian brain. Blue lines indicate inhibitory pathways; red lines indicate excitatory pathways. GPi: globus pallidus internus; GPe: globus pallidus externus; SNc: substantia nigra pars compacta; SNr: substantia nigra pars reticulata; STN: subthalamic nucleus; GABA: gamma amino butyric acid.

Nigrostriatal dopamine projections exert contrasting effects on the direct and indirect pathways (see Figure 1). Striatal neurons projecting in the direct pathway have D1 dopamine type receptors (D1 and D5) which cause excitatory post-synaptic potentials, thereby producing a net excitatory effect on striatal neurons of the direct pathway. Those projecting in the indirect pathway have D2 type receptors (D2, D3 and D4), which cause inhibitory post-synaptic potentials, thereby producing a net inhibitory effect on striatal neurons of the indirect pathway. The facilitation of transmission along the direct pathway and suppression of transmission along the indirect pathway leads to the same effect – reducing inhibition of the thalamocortical neurons and thus facilitating movements initiated in the cortex. Thus, the overall influence of dopamine within the striatum may be to reinforce the activation of the particular basal ganglia-thalamocortical circuit which has been initiated by the cortex (Gerfen, 1992; Gerfen & Wilson, 1996; see also Hurley & Jenner, 2006). Due to the differential effects of dopamine on the D1 and D2 dopamine receptors of the striatum, a loss of striatal dopamine results in a reduction in transmission through the direct

The cortico-STN-GPi 'hyperdirect' pathway (Nambu et al., 2000, 2002; Nambu, 2005; Brown, 2003; BarGad et al., 2003; Squire et al., 2003) conveys powerful excitatory effects from the motor-related cortical areas to the globus pallidus, bypassing the striatum. The hyperdirect pathway is therefore an alternative direct cortical link to the BG, possibly as important to motor control as the direct pathway, which is typically considered to be the main cortical

 Fig. 1. Connection diagram of the basal ganglia-thalamocortical motor circuit. The relative connection strengths are indicated for Left: the normal healthy brain, and Right: the parkinsonian brain. Blue lines indicate inhibitory pathways; red lines indicate excitatory pathways. GPi: globus pallidus internus; GPe: globus pallidus externus; SNc: substantia nigra pars compacta; SNr: substantia nigra pars reticulata; STN: subthalamic nucleus;

Nigrostriatal dopamine projections exert contrasting effects on the direct and indirect pathways (see Figure 1). Striatal neurons projecting in the direct pathway have D1 dopamine type receptors (D1 and D5) which cause excitatory post-synaptic potentials, thereby producing a net excitatory effect on striatal neurons of the direct pathway. Those projecting in the indirect pathway have D2 type receptors (D2, D3 and D4), which cause inhibitory post-synaptic potentials, thereby producing a net inhibitory effect on striatal neurons of the indirect pathway. The facilitation of transmission along the direct pathway and suppression of transmission along the indirect pathway leads to the same effect – reducing inhibition of the thalamocortical neurons and thus facilitating movements initiated in the cortex. Thus, the overall influence of dopamine within the striatum may be to reinforce the activation of the particular basal ganglia-thalamocortical circuit which has been initiated by the cortex (Gerfen, 1992; Gerfen & Wilson, 1996; see also Hurley & Jenner, 2006). Due to the differential effects of dopamine on the D1 and D2 dopamine receptors of the striatum, a loss of striatal dopamine results in a reduction in transmission through the direct

relay in the BG.

GABA: gamma amino butyric acid.

pathway and an increase in transmission through the indirect pathway, causing an imbalance between the two pathways.

The depletion of striatal dopamine changes neuronal firing rates in basal ganglia nuclei. Increased firing rates are found in the striatum, GPi and STN and a minimally decreased discharge in the GPe. A summary of tonic firing rates of BG nuclei in the normal and parkinsonian situation can be found in Heida et al. (2008). However, the pattern of discharge of basal ganglia neurons is thought to be equally as important as the rate of discharge in the execution of smooth movements. Several alterations in the discharge pattern have been observed in neurons of the BG in PD subjects. These alterations include a tendency of neurons to discharge in bursts, increased correlation and synchronisation of discharge between neighbouring neurons, rhythmic and oscillatory behaviour (Brown, 2003). Coherence between STN and GPi activity has been confirmed at tremor frequencies (3-10 Hz) (Brown et al., 2001). These oscillatory patterns are projected to GPi's thalamic projection site, the nucleus ventralis anterior thalami, and the cortex. In addition, STN and GPi demonstrate a tendency to synchronization at 11-30 Hz, which is likely to be driven from the motor areas of the cortex (Brown, 2003). In this circuit, the thalamus is in a key position as it receives the convergent afferent input from the GPi, the cortex, and the peripheral system, which it then projects back to the cortex, including motor areas (Smith et al., 1998).

#### **2.2 Pedunculopontine and cholinergic connections**

Gait is related to the pedunculopontine nucleus (Piallat et al., 2009), and therefore this nucleus plays an important role in gait and balance disorders that are common in Parkinson's disease. Topographically a pars compacta and a pars dissipatus of the PPN is discerned (Jacobsohn, 1909; Olszewski and Baxter, 1954). The pars dissipatus is supposed to contain glutamatergic neurons. Both parts contain cholinergic neurons. In humans the pars compacta exists of 90% cholinergic cells and the pars dissipatus of 25-75% (Mesulam et al., 1989). It should be noted, that intra-striatal pathways and PPN connections towards the SNc are mainly cholinergic. Cholinergic systems are also degenerated in Parkinson's disease. Nevertheless, next to a dopamine receptor balance a dopamine-acetylcholine balance also plays a role and "a cholinergic overactivity has been used to explain the improvement of some motor signs such as tremor, reported after muscarinic receptor blockade" (Calabresi et al., 2006), although a more cooperative role is supported for acetylcholine and dopamine in human cognitive performance. Cholinergic drugs do also have an improving effect on cognitive behavior in Parkinson's patients (Calabresi et al., 2006).

Physiological studies subdivided PPN neurons in three types (I, II and III) identified on the basis of their electrophysiological membrane properties obtained by intracellular recording. Type I neurons are characterized by low threshold calcium spikes (LTS), which give rise to a burst of fast action potentials after the offset of a hyperpolarizing current. The neurons also fire bursts of spikes when a depolarized stimulus is given during hyperpolarization. According to Takakusaki and Kitai (1997) Type I neurons are glutamatergic. Type II neurons do not burst. Instead they fire single action potentials with large after-hyperpolarizations in response to injections of depolarizing current. This type is thus suited to generate a relatively slow tonic repetitive firing pattern. About 50% of Type II neurons are cholinergic. Type III neurons miss characteristics of Type I and Type II PPN neurons, thus lacking lowthreshold spikes. The PPN neuron receives pallidal information, gathers information from the STN-SN network with strong SN influence, also from the cortex, from the limbic system

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 215

connections are not treated in this review). All thalamic connections are SN efferent, except for the parafascicular thalamic nucleus. The afferent SN connections of this nucleus are ipsilateral. All efferents of the SN to the other thalamic nuclei are also ipsilateral, with the exception of the connections to medial dorsal-, ventral medial- and central lateral thalamic nucleus, which are both ipsi- and contralateral, like those of the pedunculopontine nuclei and superior and inferior colliculus connections. Ipsi- and contralateral afferents to the SN are found for the hypothalamus, laterodorsal tegmental nucleus and the parabrachial nuclei. All other connections, including cortex, caudate-putamen and pallidum connections are afferent and/or efferent and always ipsilateral. It means that SN influence is mainly ipsilateral and only a few pathways can also steer the contralateral side of certain thalamic nuclei, lateral habenular nucleus, superior and inferior colliculus, periaquaductal gray, and

**Afferents to substantia nigra Efferents from substantia nigra**  SNr SNc SNl SNr SNc SNl ipsi con ipsi con ipsi con ipsi con ipsi con ipsi con

x x x Cortex x x x x x x Caudate-Putamen x x x

x x Amygdala x x

thalamic nucleus <sup>x</sup>

Parafascicular

thalamic nucleus <sup>x</sup>

thalamic nucleus <sup>x</sup>

Lateral habenular

Dorsal lateral geniculate nucleus

thalamic nucleus x x x

thalamic nucleus x x x

thalamic nucleus x x

thalamic nucleus x x

thalamic nucleus x x

nucleus x x

x x x

x x Pallidum x x x x Accumbens x Hippocampus x

Lateral dorsal

Medial dorsal

Ventral medial

Central medial

Central lateral

Paracentral

Lateral posterior

x x x

x x x

the pedunculopontine nucleus (see Table I and Marani et al., 2008).

and hypothalamus, from the cerebellum and from the brainstem and can transmit it towards nearly all nuclei of the thalamus (both the cholinergic and non-cholinergic ones), and weakly towards the cortex and basal ganglia (Usunoff et al., 2003).

PPN plays a role in the control of muscle tone by means of its excitatory projections to the muscle tone inhibitory system in the brainstem. The PPN is also thought to produce the main influence on the parafascicular thalamic nucleus in cases of SN degeneration; the parafascicular nucleus being involved in motor control (Yan et al., 2008). In Parkinson's disease the increased inhibitory basal ganglia output, together with a decrease in cortical excitation of the PPN, may increase the level of muscle tone causing rigidity (Takusaki et al., 2004).

## **2.3 Subthalamic nucleus connections**

The STN projection neurons are glutamatergic, excitatory, and heavily innervated by widely branching axons of the substantia nigra (SN), the internal pallidal segment (GPi), followed by the external pallidal segment (GPe) and the pedunculopontine tegmental nucleus (PPN). The most well-known afferent connections of the STN arise in the GPe. The STN is also innervated by glutamatergic corticosubthalamic axons. A substantial, bilateral cholinergic/glutamatergic projection arises in the PPN, while the thalamic centromedianparafascicular complex also innervates the STN (see Table I). Finally, serotoninergic fibers from the raphe nuclei terminate profusely within the STN. The nigrosubthalamic connection was demonstrated by axonal transport techniques, and transmitter immunocytochemistry. The nigrosubthalamic connection arises from the dopaminergic (DA) neurons of the SN pars compacta (SNc). In addition, a moderate projection was described from the parvalbumin immunoreactive, presumably GABAergic neurons of the SN pars reticulata (SNr) to the STN. The nigrosubthalamic connection has always been described as ipsilateral, but rat tracer studies now oppose this view (see below and Marani et al., 2008). STN-pallidal fibers arborize more widely and terminate on more proximal neuronal elements of the pallidum than striato-pallidal fibers. Thus, the striatal and STN inputs to GPi form a pattern of fast, widespread, divergent excitation from the STN, and a slower, focused, convergent inhibition from the striatum (Squire et al., 2003). Furthermore, cortico-STN neurons and cortico-striatal neurons belong to distinct populations. Thus, signals through the hyperdirect pathway may broadly inhibit motor programs; then signals through the direct pathway may adjust the selected motor program according to the situation (the 'center-surround' model of Nambu, 2005). STN neurons can discharge continuously and repetitively at low frequencies (10-30 Hz) and can fire with bursts of high frequency spikes. STN neurons are physiologically subdivided in non-plateau neurons (neurons that react with low threshold spikes) and plateau generating neurons (those that can react with bursts, low threshold spikes or plateau potentials). The neuron has to be in a hyperpolarized state, for depolarizing or hyperpolarizing current pulses to induce plateau behavior (Beurrier et al., 1999). The tonic discharges are sodium-dependent, while its hyperpolarizing phases are calcium dependent. Bursts are calcium-dependent phenomena.

## **3. Rat experimental results: Anatomy and electrophysiology**

#### **3.1 Anatomy: Outline of SN connections in the rat**

The afferent and efferent connections of the rat SN, studied with degenerative and tracer techniques, are restricted to the cortex, brainstem and cerebellum (the cerebellum and its

and hypothalamus, from the cerebellum and from the brainstem and can transmit it towards nearly all nuclei of the thalamus (both the cholinergic and non-cholinergic ones), and

PPN plays a role in the control of muscle tone by means of its excitatory projections to the muscle tone inhibitory system in the brainstem. The PPN is also thought to produce the main influence on the parafascicular thalamic nucleus in cases of SN degeneration; the parafascicular nucleus being involved in motor control (Yan et al., 2008). In Parkinson's disease the increased inhibitory basal ganglia output, together with a decrease in cortical excitation of the PPN, may

The STN projection neurons are glutamatergic, excitatory, and heavily innervated by widely branching axons of the substantia nigra (SN), the internal pallidal segment (GPi), followed by the external pallidal segment (GPe) and the pedunculopontine tegmental nucleus (PPN). The most well-known afferent connections of the STN arise in the GPe. The STN is also innervated by glutamatergic corticosubthalamic axons. A substantial, bilateral cholinergic/glutamatergic projection arises in the PPN, while the thalamic centromedianparafascicular complex also innervates the STN (see Table I). Finally, serotoninergic fibers from the raphe nuclei terminate profusely within the STN. The nigrosubthalamic connection was demonstrated by axonal transport techniques, and transmitter immunocytochemistry. The nigrosubthalamic connection arises from the dopaminergic (DA) neurons of the SN pars compacta (SNc). In addition, a moderate projection was described from the parvalbumin immunoreactive, presumably GABAergic neurons of the SN pars reticulata (SNr) to the STN. The nigrosubthalamic connection has always been described as ipsilateral, but rat tracer studies now oppose this view (see below and Marani et al., 2008). STN-pallidal fibers arborize more widely and terminate on more proximal neuronal elements of the pallidum than striato-pallidal fibers. Thus, the striatal and STN inputs to GPi form a pattern of fast, widespread, divergent excitation from the STN, and a slower, focused, convergent inhibition from the striatum (Squire et al., 2003). Furthermore, cortico-STN neurons and cortico-striatal neurons belong to distinct populations. Thus, signals through the hyperdirect pathway may broadly inhibit motor programs; then signals through the direct pathway may adjust the selected motor program according to the situation (the 'center-surround' model of Nambu, 2005). STN neurons can discharge continuously and repetitively at low frequencies (10-30 Hz) and can fire with bursts of high frequency spikes. STN neurons are physiologically subdivided in non-plateau neurons (neurons that react with low threshold spikes) and plateau generating neurons (those that can react with bursts, low threshold spikes or plateau potentials). The neuron has to be in a hyperpolarized state, for depolarizing or hyperpolarizing current pulses to induce plateau behavior (Beurrier et al., 1999). The tonic discharges are sodium-dependent, while its hyperpolarizing phases are

weakly towards the cortex and basal ganglia (Usunoff et al., 2003).

increase the level of muscle tone causing rigidity (Takusaki et al., 2004).

calcium dependent. Bursts are calcium-dependent phenomena.

**3.1 Anatomy: Outline of SN connections in the rat** 

**3. Rat experimental results: Anatomy and electrophysiology** 

The afferent and efferent connections of the rat SN, studied with degenerative and tracer techniques, are restricted to the cortex, brainstem and cerebellum (the cerebellum and its

**2.3 Subthalamic nucleus connections** 

connections are not treated in this review). All thalamic connections are SN efferent, except for the parafascicular thalamic nucleus. The afferent SN connections of this nucleus are ipsilateral. All efferents of the SN to the other thalamic nuclei are also ipsilateral, with the exception of the connections to medial dorsal-, ventral medial- and central lateral thalamic nucleus, which are both ipsi- and contralateral, like those of the pedunculopontine nuclei and superior and inferior colliculus connections. Ipsi- and contralateral afferents to the SN are found for the hypothalamus, laterodorsal tegmental nucleus and the parabrachial nuclei. All other connections, including cortex, caudate-putamen and pallidum connections are afferent and/or efferent and always ipsilateral. It means that SN influence is mainly ipsilateral and only a few pathways can also steer the contralateral side of certain thalamic nuclei, lateral habenular nucleus, superior and inferior colliculus, periaquaductal gray, and the pedunculopontine nucleus (see Table I and Marani et al., 2008).


Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 217

between SNr and the cerebral peduncle. Reaching the caudal pole of the STN, the labeled axons pierce into the nucleus through its lateral wedge, but also into its ventral border and enter also from the medially running bundle, dorsal to the STN. Within the STN, especially in the lateral half of the nucleus, along with passing fibers oriented mediolaterally, a large amount of terminal labeling is present. In the medial part of the STN mainly discrete bursts of labeled endings are noted. Midline crossing of SN axons occurs at several places. The most substantial component of crossed axons runs in the mesencephalic tegmentum ventral to the periaqueductal gray (PAG). Such bundles are found through the entire rostrocaudal extent of the mesencephalon. Some fibers in the rostral mesencephalon in fact come into the STN through its dorsal border. The midline is also crossed in the commissure of the superior colliculus and in the posterior commissure. The efferent SN axons cross the midline (crossed nigro-thalamic axons) rostral to the SN, and the last component of crossing axons runs in the supraoptic decussation, immediately above the optic tract. Some of these axons take a dorsomedial course towards the contralateral STN. In the contralateral STN a lower amount of labeled axons are noted. Nevertheless, they form very distinct mediolaterally extended patches. Most of these discrete fields of terminal labeling are in the central and lateral

These results provide data for the existence of a substantial nigrosubthalamic connection in the rat, which emits also a moderate component to the contralateral STN (Figure 2). Ipsilaterally the efferent SN axons terminate in large, profuse terminal fields, whilst contralaterally they terminate in discrete, sharply circumscribed patches. Although the crossed nigrosubthalamic connection is moderate, exactly by its topical distribution, its 'point to point' connection is especially evident. The medial SNc projects to the contralateral medial STN, and the lateral SNc also projects mainly to the lateral half of the contralateral

Fig. 2. Ipsilateral and contralateral nigro-subthalamic connections. SN: substantia nigra; STN: subthalamic nucleus; C: SN pars compacta; R: SN pars reticulata; c: caudal; r: rostral.

portions of the STN, but also medially some terminal 'whorls' are seen.

STN (see Marani et al., 2008).


Table 1. Overview of afferent and efferent connections of the SN. SNr: substantia nigra pars reticularis; SNc: substantia nigra pars compacta; SNl: substantia nigra pars lateralis; ispi: ipsilateral; con: contralateral; x: existing connection.

### **3.1.1 Nigro-subthalamic connections in the rat**

The outline of the nigro-subthalamic connections is shown by large injection sites with the anterograde BDA (biotinylated dextran amine) tracer that was injected into the lateral SNr (reticulata) and SNc (compacta). The axons running towards the brainstem and the mounting axons to the forebrain take at first a medial way towards the prerubral area. Few nigro-thalamic axons course dorsally towards the tegmentum. Most of the axons directed to the brainstem and forebrain progress immediately dorsal to SN, and some axons pass lateromedially of the SNc. Few axons bend ventromedially and travel along the border

SNr SNc SNl SNr SNc SNl ipsi con ipsi con ipsi con ipsi con ipsi con ipsi con

Subthalamic

nucleus

gray

Laterodorsal tegmental nucleus <sup>x</sup>

Parabrachial

Parvocellular pontine reticular nucleus

 x Cerebellum x x x Table 1. Overview of afferent and efferent connections of the SN. SNr: substantia nigra pars

The outline of the nigro-subthalamic connections is shown by large injection sites with the anterograde BDA (biotinylated dextran amine) tracer that was injected into the lateral SNr (reticulata) and SNc (compacta). The axons running towards the brainstem and the mounting axons to the forebrain take at first a medial way towards the prerubral area. Few nigro-thalamic axons course dorsally towards the tegmentum. Most of the axons directed to the brainstem and forebrain progress immediately dorsal to SN, and some axons pass lateromedially of the SNc. Few axons bend ventromedially and travel along the border

reticularis; SNc: substantia nigra pars compacta; SNl: substantia nigra pars lateralis;

nucleus <sup>x</sup>

reticular nucleus x x

tegmental nucleus x x x

nuclei x x

Locus coeruleus x x x

x x

x x x x x x Hypothalamus x x x

nucleus <sup>x</sup>

Inferior colliculus x x

x x

colliculus x x

Zona incerta x

 Red nucleus x x x Entopeduncular

x x Raphe dorsalis x

x x Pedunculopontine

Superior

Periaqueductal

Cuneiform

Mesencephalic

ispi: ipsilateral; con: contralateral; x: existing connection.

**3.1.1 Nigro-subthalamic connections in the rat** 

x x x x x x

x x x x x x

x x x

between SNr and the cerebral peduncle. Reaching the caudal pole of the STN, the labeled axons pierce into the nucleus through its lateral wedge, but also into its ventral border and enter also from the medially running bundle, dorsal to the STN. Within the STN, especially in the lateral half of the nucleus, along with passing fibers oriented mediolaterally, a large amount of terminal labeling is present. In the medial part of the STN mainly discrete bursts of labeled endings are noted. Midline crossing of SN axons occurs at several places. The most substantial component of crossed axons runs in the mesencephalic tegmentum ventral to the periaqueductal gray (PAG). Such bundles are found through the entire rostrocaudal extent of the mesencephalon. Some fibers in the rostral mesencephalon in fact come into the STN through its dorsal border. The midline is also crossed in the commissure of the superior colliculus and in the posterior commissure. The efferent SN axons cross the midline (crossed nigro-thalamic axons) rostral to the SN, and the last component of crossing axons runs in the supraoptic decussation, immediately above the optic tract. Some of these axons take a dorsomedial course towards the contralateral STN. In the contralateral STN a lower amount of labeled axons are noted. Nevertheless, they form very distinct mediolaterally extended patches. Most of these discrete fields of terminal labeling are in the central and lateral portions of the STN, but also medially some terminal 'whorls' are seen.

These results provide data for the existence of a substantial nigrosubthalamic connection in the rat, which emits also a moderate component to the contralateral STN (Figure 2). Ipsilaterally the efferent SN axons terminate in large, profuse terminal fields, whilst contralaterally they terminate in discrete, sharply circumscribed patches. Although the crossed nigrosubthalamic connection is moderate, exactly by its topical distribution, its 'point to point' connection is especially evident. The medial SNc projects to the contralateral medial STN, and the lateral SNc also projects mainly to the lateral half of the contralateral STN (see Marani et al., 2008).

Fig. 2. Ipsilateral and contralateral nigro-subthalamic connections. SN: substantia nigra; STN: subthalamic nucleus; C: SN pars compacta; R: SN pars reticulata; c: caudal; r: rostral.

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 219

Selective injections into the medial SNc and lateral SNc produced labeled axons that were followed exclusively to the ipsilateral Me5c while the contralateral Me5c and Me5r on both sides displayed few labeled fibers (Figure 3). Terminal labeling was present in an extensive network in the ipsilateral Me5c, diminishing slightly from medial to lateral. Most of the terminal labeling surrounded the pseudo-unipolar mesencephalic trigeminal neurons. Some perikarya clearly displayed terminal and passing boutons covering their cell exterior. Throughout the neuropil of Me5c a meshwork of fine labeled fibers with varicosities was also present after injection into the lateral SNc. Single pseudo-unipolar neurons containing boutons en passant and boutons termineaux clearly visible on their surface were noted. The terminal labeling extended medially to the Me5c, to include the area of smaller cells in the locus coeruleus. A minute injection focus selectively infiltrated the SNl. In the Me5 area only few varicose fibers and their terminals reached the ipsilateral Me5c, while the rostral portion of this nucleus showed a slightly larger number of labeled fibers. In this case, no

The results of this study provide strong evidence that the SN also directly innervates the proprioceptive trigeminal neurons and thus, both the motor and sensory neurons controlling jaw muscles involved in mastication. Since pseudo-unipolar mesencephalic trigeminal nucleus neurons send axons to the pontine and spinal trigeminal nuclei, it appears that the entire trigeminal nuclear complex (see Usunoff et al., 1997) is profoundly influenced by the SN. Therefore, it can be inferred that inputs from SN possibly modify, modulate or interact with outputs from all these nuclei to control the masticatory behavior

We describe two approaches which can be followed to investigate the neuronal properties and network activity patterns *in-vitro*. Both use multi-electrode arrays (MEA's, Figure 4) to measure the extracellular membrane potential of neurons located close to the MEA's 60 electrodes. The first method we describe makes use of acute slices of rat brain, in which some of the structure remains intact but which can only be used for a short time (less than 8 hours). The second is to put neurons from a particular area in culture on top of the MEA,

Fig. 4. View from above on a MEA (Ayanda Biosystems) used in slice research. The round culture chamber has an inner diameter of 2.4 mm. The 60 electrodes are spaced 200 µm apart in an 8 by 8 grid (the inset shows the electrodes covered by a slice). The electrodes are

conically shaped, with the tips protruding 50-70 μm from the glass surface.

anterograde terminal labeling was observed in Me5 contralaterally.

**3.2 Electrophysiology: Rat brain slices and dissociated STN cell cultures** 

which loses all spatial structure, but can be used for months.

(see Marani et al., 2010).

## **3.1.2 Nigro-trigeminal connections in the rat**

It is generally accepted that also in the rat, the SN is involved in oral movements and orofacial dyskinesias. Until now, is has been believed that the SN influences the trigeminal motoneurons via a multisynaptic pathway (see Usunoff et al., 1997; Lazarov, 2002). Histopathological changes in this rat model's substantia nigra have been demonstrated in tardive dyskinesias (Andreassen et al., 2003). Direct stimulation by STN DBS improves orofacial dyskinesia in a rat model (Creed et al., 2010). Therefore, a renewed interest in the rat nigro-trigeminal pathway arose.

Specifically, the large BDA injection in the lateral SNc and parts of the adjacent SNr and SNl (lateral) resulted in anterograde labeling throughout the Me5 (mesencephalic trigeminal nucleus, see Usunoff et al., 1997) with a strong ipsilateral predominance, but contralateral labeling was also present. The results for SNc are summarized in Figure 3. Surrounding the injection site many intensely labeled neurons were present. Terminal labeling was observed among the perikarya of pseudo-unipolar neurons in the ipsilateral Me5c (caudal). At this sectional plane, virtually all pseudo-unipolar neurons were at least partially surrounded by varicose fibers, contacting their cell surface. The intensity of anterograde labeling in the Me5r (rostral) decreased almost bilaterally. Moderate terminal labeling was present around but not on pseudo-unipolar neuronal somata, both in the caudal and rostral Me5, on the contralateral side.

Fig. 3. Overview of the injection sites of three transversal slices of the SNc. The column at the right schematically shows the ipsi- and contralateral labeling in Me5, which is subdivided in a head and three tail areas. Anterograde labeling and injections (summed throughout the nucleus) are indicated in a map of the SN, with SNc, SNr and SNl, and Me5. Darker gray levels indicate a higher intensity of the labeling in Me5.

It is generally accepted that also in the rat, the SN is involved in oral movements and orofacial dyskinesias. Until now, is has been believed that the SN influences the trigeminal motoneurons via a multisynaptic pathway (see Usunoff et al., 1997; Lazarov, 2002). Histopathological changes in this rat model's substantia nigra have been demonstrated in tardive dyskinesias (Andreassen et al., 2003). Direct stimulation by STN DBS improves orofacial dyskinesia in a rat model (Creed et al., 2010). Therefore, a renewed interest in the rat

Specifically, the large BDA injection in the lateral SNc and parts of the adjacent SNr and SNl (lateral) resulted in anterograde labeling throughout the Me5 (mesencephalic trigeminal nucleus, see Usunoff et al., 1997) with a strong ipsilateral predominance, but contralateral labeling was also present. The results for SNc are summarized in Figure 3. Surrounding the injection site many intensely labeled neurons were present. Terminal labeling was observed among the perikarya of pseudo-unipolar neurons in the ipsilateral Me5c (caudal). At this sectional plane, virtually all pseudo-unipolar neurons were at least partially surrounded by varicose fibers, contacting their cell surface. The intensity of anterograde labeling in the Me5r (rostral) decreased almost bilaterally. Moderate terminal labeling was present around but not on pseudo-unipolar neuronal somata, both in the caudal and rostral Me5, on the

Fig. 3. Overview of the injection sites of three transversal slices of the SNc. The column at the right schematically shows the ipsi- and contralateral labeling in Me5, which is subdivided in a head and three tail areas. Anterograde labeling and injections (summed throughout the nucleus) are indicated in a map of the SN, with SNc, SNr and SNl, and Me5.

Darker gray levels indicate a higher intensity of the labeling in Me5.

**3.1.2 Nigro-trigeminal connections in the rat** 

nigro-trigeminal pathway arose.

contralateral side.

Selective injections into the medial SNc and lateral SNc produced labeled axons that were followed exclusively to the ipsilateral Me5c while the contralateral Me5c and Me5r on both sides displayed few labeled fibers (Figure 3). Terminal labeling was present in an extensive network in the ipsilateral Me5c, diminishing slightly from medial to lateral. Most of the terminal labeling surrounded the pseudo-unipolar mesencephalic trigeminal neurons. Some perikarya clearly displayed terminal and passing boutons covering their cell exterior. Throughout the neuropil of Me5c a meshwork of fine labeled fibers with varicosities was also present after injection into the lateral SNc. Single pseudo-unipolar neurons containing boutons en passant and boutons termineaux clearly visible on their surface were noted. The terminal labeling extended medially to the Me5c, to include the area of smaller cells in the locus coeruleus. A minute injection focus selectively infiltrated the SNl. In the Me5 area only few varicose fibers and their terminals reached the ipsilateral Me5c, while the rostral portion of this nucleus showed a slightly larger number of labeled fibers. In this case, no anterograde terminal labeling was observed in Me5 contralaterally.

The results of this study provide strong evidence that the SN also directly innervates the proprioceptive trigeminal neurons and thus, both the motor and sensory neurons controlling jaw muscles involved in mastication. Since pseudo-unipolar mesencephalic trigeminal nucleus neurons send axons to the pontine and spinal trigeminal nuclei, it appears that the entire trigeminal nuclear complex (see Usunoff et al., 1997) is profoundly influenced by the SN. Therefore, it can be inferred that inputs from SN possibly modify, modulate or interact with outputs from all these nuclei to control the masticatory behavior (see Marani et al., 2010).

## **3.2 Electrophysiology: Rat brain slices and dissociated STN cell cultures**

We describe two approaches which can be followed to investigate the neuronal properties and network activity patterns *in-vitro*. Both use multi-electrode arrays (MEA's, Figure 4) to measure the extracellular membrane potential of neurons located close to the MEA's 60 electrodes. The first method we describe makes use of acute slices of rat brain, in which some of the structure remains intact but which can only be used for a short time (less than 8 hours). The second is to put neurons from a particular area in culture on top of the MEA, which loses all spatial structure, but can be used for months.

Fig. 4. View from above on a MEA (Ayanda Biosystems) used in slice research. The round culture chamber has an inner diameter of 2.4 mm. The 60 electrodes are spaced 200 µm apart in an 8 by 8 grid (the inset shows the electrodes covered by a slice). The electrodes are conically shaped, with the tips protruding 50-70 μm from the glass surface.

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 221

Fig. 6. Localization of activity in horizontal slices of STN (-8.1 mm from Bregma, figure 187

The addition of dopamine to acute slice preparations shows its effect on the firing rate and patterns of STN neurons, but also on SN neurons, depending on the placing of the MEA. Increasing concentrations of dopamine added to slices shows an increase in the spontaneous activity of the STN neurons, while a decrease of the spontaneous activity in SN was noted for a short period, before the increase started. Based on an analogous approach as done for intra-nuclear connections, mapping of extra-nuclear connections is also possible, here


STN electrodes SNR electrodes Remaining active electrodes Inactive electrodes

Fig. 7. Response of neurons located in STN and SN to dopamine application. Left: mean firing rate of 12 electrodes located in STN (blue) and 9 electrodes located in SN (green). The dopamine concentration was increased from 0 to 64 μM in steps of 16 μM (shaded gray background). Right: corresponding figure (188, Paxinos & Watson, 2007) with the position of

in Paxinos & Watson, 2007) classified according to mean frequency and spike train properties. STN neurons predominantly displayed low mean firing frequencies (<4 Hz)

while spike trains were generally 'bursty'.

between STN and SN (Figure 7).

STN electrodes SNR electrodes

the MEA electrodes included.

Mean firing frequency per electrode

 (Hz)

<sup>0</sup> <sup>100</sup> <sup>200</sup> <sup>300</sup> <sup>400</sup> <sup>500</sup> <sup>600</sup> <sup>700</sup> <sup>800</sup> <sup>900</sup> <sup>6</sup>

0 16 32 48 64 Dopamine concentration (μM)

Time (seconds)

Horizontal slices of the STN-containing midbrain produced from rats, aged between 16-52 days, were placed such that the electrode matrix of the MEA was underneath the STN. Signals of spontaneous STN activity recorded in continuously perfused and carboxygenated artificial cerebro-spinal fluid (ACSF) were amplified, bandpass filtered (10 Hz-10 kHz) and digitized using a measurement system of MCS (MultiChannelSystems GmbH, Reutlingen, Germany). After software filtering (50-350 Hz), threshold crossings exceeding 5 times standard deviation were stored. Results show average firing rates of four neurons firing at mean frequencies of 0.1, 0.1, 0.06 and 1.2 Hz, respectively (Figure 5). In this example, the most active fourth neuron is the only neuron localized within (the motor cortex innervated area of) the STN. Neurons 2 and 4 were classified as 'bursty', neuron 1 was termed 'random' and neuron 3 was labeled 'regular' (for definitions of random, regular and bursty see Kaneoke and Vitek, 1996). On further inspection, many spikes were part of *doublets* (two spikes in close succession), while bursts of longer duration were rare. Such bursting STN activity was noted in many rat slices and the method used was able to discriminate several spiking patterns (Figure 6). Here, properties of random, regular and bursty spikes were allocated to the electrodes with their position within STN. Network connections may be detected by cross correlation analysis of spontaneous activity (Le Feber et al., 2007) or poststimulus histograms (see Stegenga et al., 2010b). Moreover, the extranuclear network can also be studied (Figure 7, right panel).

Fig. 5. Action potential waveforms and spike train analysis of 4 simultaneously recorded neurons in a horizontal slice of the rat brain including STN. Left: aligned action potential waveforms. Middle: spike trains of the 4 neurons. Right: density histograms of the spike trains, i.e. the number of occurrences that an interval of 1 s contained a certain number of spikes . The histograms were compared to a Poisson distribution for classification. Neuron 1: 'random'; neuron 3: 'regular'; neuron 2 and 4: 'bursty'.

Horizontal slices of the STN-containing midbrain produced from rats, aged between 16-52 days, were placed such that the electrode matrix of the MEA was underneath the STN. Signals of spontaneous STN activity recorded in continuously perfused and carboxygenated artificial cerebro-spinal fluid (ACSF) were amplified, bandpass filtered (10 Hz-10 kHz) and digitized using a measurement system of MCS (MultiChannelSystems GmbH, Reutlingen, Germany). After software filtering (50-350 Hz), threshold crossings exceeding 5 times standard deviation were stored. Results show average firing rates of four neurons firing at mean frequencies of 0.1, 0.1, 0.06 and 1.2 Hz, respectively (Figure 5). In this example, the most active fourth neuron is the only neuron localized within (the motor cortex innervated area of) the STN. Neurons 2 and 4 were classified as 'bursty', neuron 1 was termed 'random' and neuron 3 was labeled 'regular' (for definitions of random, regular and bursty see Kaneoke and Vitek, 1996). On further inspection, many spikes were part of *doublets* (two spikes in close succession), while bursts of longer duration were rare. Such bursting STN activity was noted in many rat slices and the method used was able to discriminate several spiking patterns (Figure 6). Here, properties of random, regular and bursty spikes were allocated to the electrodes with their position within STN. Network connections may be detected by cross correlation analysis of spontaneous activity (Le Feber et al., 2007) or poststimulus histograms (see Stegenga et al., 2010b). Moreover, the extranuclear network can

Fig. 5. Action potential waveforms and spike train analysis of 4 simultaneously recorded neurons in a horizontal slice of the rat brain including STN. Left: aligned action potential waveforms. Middle: spike trains of the 4 neurons. Right: density histograms of the spike trains, i.e. the number of occurrences that an interval of 1 s contained a certain number of spikes . The histograms were compared to a Poisson distribution for classification.

Neuron 1: 'random'; neuron 3: 'regular'; neuron 2 and 4: 'bursty'.

also be studied (Figure 7, right panel).

Fig. 6. Localization of activity in horizontal slices of STN (-8.1 mm from Bregma, figure 187 in Paxinos & Watson, 2007) classified according to mean frequency and spike train properties. STN neurons predominantly displayed low mean firing frequencies (<4 Hz) while spike trains were generally 'bursty'.

The addition of dopamine to acute slice preparations shows its effect on the firing rate and patterns of STN neurons, but also on SN neurons, depending on the placing of the MEA. Increasing concentrations of dopamine added to slices shows an increase in the spontaneous activity of the STN neurons, while a decrease of the spontaneous activity in SN was noted for a short period, before the increase started. Based on an analogous approach as done for intra-nuclear connections, mapping of extra-nuclear connections is also possible, here between STN and SN (Figure 7).

Fig. 7. Response of neurons located in STN and SN to dopamine application. Left: mean firing rate of 12 electrodes located in STN (blue) and 9 electrodes located in SN (green). The dopamine concentration was increased from 0 to 64 μM in steps of 16 μM (shaded gray background). Right: corresponding figure (188, Paxinos & Watson, 2007) with the position of the MEA electrodes included.

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 223

The total spike activity after the entire period of 1.5 hours (the period starting at the moment the first 10 μM was added till the moment ACh was washed out) was reduced by almost 25%. If synchronized bursting activity was present in the cultures, this activity was not reduced by addition of ACh. This suggests that cholinergic PPN input in the STN has a decreasing effect on the spontaneous activity of the STN. Loss of cholinergic input, on its

It should be noted that the symptoms of Parkinson's disease are a result of alterations in the network activity of the motor cortex, the thalamus and the basal ganglia. The alterations ultimately originate from a shortage of dopamine as a consequence of degeneration of (a.o.) the dopaminergic cells in the substantia nigra pars compacta. However, compensatory mechanisms effectively combat the effect of dopamine-shortage until roughly 80% of dopaminergic SNc cells have died. At any stage, we study not only the disease, but also the mechanisms nature uses to combat its effects (and maintain function). To model the disease and possible interventions (L-DOPA; DBS), fundamental research about the

Experiments with acute slices can provide us with detailed data, but only with respect to one moment in time and only by damaging a large part of the network that is involved in PD. The short-term effect of chemicals (drugs) and electrical stimulation (DBS) can be studied in tremendous detail and may lead to a better understanding of particularly the latter (and ultimately to better interventions). The progress made in MEA technology and slice preparation allows even more complex systems to be studied. For mice and rats, the maximum thickness of slices (~400 um) is enough to preserve much of the connectivity of the basal ganglia. The preservation of connections between distant nuclei (motor cortex, thalamus, substantia nigra) may well be possible, even though they may not be within a single slice. For now, these techniques allow us to check the models that have been created to study basal ganglia (dys)function such as the reciprocal coupling between STN and globus pallidus, which is claimed to result in bursting activity at low concentrations of dopamine. We can also test whether there is feedback from STN to the SN, thus ameliorating the effect of shortage of dopamine, but possibly speeding up PD progression (Blandini et al., 2000). We have already observed a marked increase in firing rate in both STN and SN with rising dopamine concentration. We expect that compensatory mechanisms (i.e. adaptation) will counter large changes in firing rate on the longer term, possibly by changing the firing patterns (i.e. neuronal and synaptic properties). Medication by L-DOPA may have the same effect in PD patients; enabling neurons to fire in patterns that, at least, do not interfere with normal function. The question of which patterns do not interfere with normal function, may be answered by simulating DBS in-vitro, since the

For longitudinal studies, cultures of dissociated neurons, or even (non-dissociated) cocultures can be used. Even though these will create networks that differ from those in the intact brain, they can be used to study basic mechanisms and how they evolve over longer periods of time. Here, more fundamental questions about neuronal adaptation to various inputs and chemical additions can be answered. From cultures of cortical neurons we know that basic properties of these networks (e.g. percentage of excitatory/inhibitory connections) develop in a similar way compared to in-vivo counterparts. This even allows the study of

turn, increases STN spontaneous activity (see Heida et al., 2008).

electrophysiology of all of the involved nuclei is needed.

effects of DBS are visible almost instantly.

age-related effects.

The rat neuroanatomical studies show a refined connection pattern between SN, Me5 and STN, which is new and hardly incorporated into models. Moreover rat dissociated STN neurons in culture and rat horizontal brain slices, containing the STN, provide the possibility to study artificial and original STN networks (in part), respectively. Herewith the mechanisms underlying bursting and oscillation of the rat STN neurons can be investigated, since the reaction of whole intranuclear, but also extranuclear networks can be studied together with single neuron reactions on artificial modulation of activity or by ablation of connections or by adding agonists and antagonists of neurotransmitters or receptors.

#### **3.2.1 Mimicking the cholinergic PPN-STN connection in dissociated cultures**

The pedunculopontine nucleus (PPN) is used as a new therapeutic target for DBS in patients suffering from Parkinson's disease with severe gait and postural impairment (Plaha & Gill, 2005). DBS of the PPN is only effective, if carried out at low frequencies (~20 Hz), while STN-DBS requires high frequencies (~130 Hz) to be successful. This is hardly comprehended. The projections from the PPN are reciprocal both towards the SN and the STN (see Usunoff, 2003). This nucleus contains cholinergic neurons (mainly Ch5 in the rat), that project onto the STN. There exists a direct relation between the severity of Parkinson's disease and the loss of cholinergic neurons in the PPN (Rinne et al., 2008), which provided the incentive to look into cholinergic effects on STN neurons.

To this end, rat STN areas from one day old rat pups were dissociated and cultured on the coated glass surface of a MEA similar to the example shown in Figure 4, in chemically defined, serum free, medium. Acetylcholine (ACh) was added in steps of 10 μM and extracelluar action potential activity of a maximum of 60 neurons was recorded. Addition of ACh reduced the spontaneous activity immediately and substantially for 50-100 seconds (Figure 8).

Fig. 8. Normalized spike activity in dissociated STN cultures after administration of ACh. Each red striped line marks the time at which the concentration ACh was increased by 10 μM. At the last line ACh was washed out. The action-potential activity of all recorded neurons was averaged and binned in 20 s bins. The green dots show the average activity for the different concentrations of ACh.

The rat neuroanatomical studies show a refined connection pattern between SN, Me5 and STN, which is new and hardly incorporated into models. Moreover rat dissociated STN neurons in culture and rat horizontal brain slices, containing the STN, provide the possibility to study artificial and original STN networks (in part), respectively. Herewith the mechanisms underlying bursting and oscillation of the rat STN neurons can be investigated, since the reaction of whole intranuclear, but also extranuclear networks can be studied together with single neuron reactions on artificial modulation of activity or by ablation of

connections or by adding agonists and antagonists of neurotransmitters or receptors.

The pedunculopontine nucleus (PPN) is used as a new therapeutic target for DBS in patients suffering from Parkinson's disease with severe gait and postural impairment (Plaha & Gill, 2005). DBS of the PPN is only effective, if carried out at low frequencies (~20 Hz), while STN-DBS requires high frequencies (~130 Hz) to be successful. This is hardly comprehended. The projections from the PPN are reciprocal both towards the SN and the STN (see Usunoff, 2003). This nucleus contains cholinergic neurons (mainly Ch5 in the rat), that project onto the STN. There exists a direct relation between the severity of Parkinson's disease and the loss of cholinergic neurons in the PPN (Rinne et al., 2008), which provided

To this end, rat STN areas from one day old rat pups were dissociated and cultured on the coated glass surface of a MEA similar to the example shown in Figure 4, in chemically defined, serum free, medium. Acetylcholine (ACh) was added in steps of 10 μM and extracelluar action potential activity of a maximum of 60 neurons was recorded. Addition of ACh reduced the spontaneous activity immediately and substantially for 50-100 seconds (Figure 8).

Fig. 8. Normalized spike activity in dissociated STN cultures after administration of ACh. Each red striped line marks the time at which the concentration ACh was increased by 10 μM. At the last line ACh was washed out. The action-potential activity of all recorded neurons was averaged and binned in 20 s bins. The green dots show the average activity for

**3.2.1 Mimicking the cholinergic PPN-STN connection in dissociated cultures** 

the incentive to look into cholinergic effects on STN neurons.

the different concentrations of ACh.

The total spike activity after the entire period of 1.5 hours (the period starting at the moment the first 10 μM was added till the moment ACh was washed out) was reduced by almost 25%. If synchronized bursting activity was present in the cultures, this activity was not reduced by addition of ACh. This suggests that cholinergic PPN input in the STN has a decreasing effect on the spontaneous activity of the STN. Loss of cholinergic input, on its turn, increases STN spontaneous activity (see Heida et al., 2008).

It should be noted that the symptoms of Parkinson's disease are a result of alterations in the network activity of the motor cortex, the thalamus and the basal ganglia. The alterations ultimately originate from a shortage of dopamine as a consequence of degeneration of (a.o.) the dopaminergic cells in the substantia nigra pars compacta. However, compensatory mechanisms effectively combat the effect of dopamine-shortage until roughly 80% of dopaminergic SNc cells have died. At any stage, we study not only the disease, but also the mechanisms nature uses to combat its effects (and maintain function). To model the disease and possible interventions (L-DOPA; DBS), fundamental research about the electrophysiology of all of the involved nuclei is needed.

Experiments with acute slices can provide us with detailed data, but only with respect to one moment in time and only by damaging a large part of the network that is involved in PD. The short-term effect of chemicals (drugs) and electrical stimulation (DBS) can be studied in tremendous detail and may lead to a better understanding of particularly the latter (and ultimately to better interventions). The progress made in MEA technology and slice preparation allows even more complex systems to be studied. For mice and rats, the maximum thickness of slices (~400 um) is enough to preserve much of the connectivity of the basal ganglia. The preservation of connections between distant nuclei (motor cortex, thalamus, substantia nigra) may well be possible, even though they may not be within a single slice. For now, these techniques allow us to check the models that have been created to study basal ganglia (dys)function such as the reciprocal coupling between STN and globus pallidus, which is claimed to result in bursting activity at low concentrations of dopamine. We can also test whether there is feedback from STN to the SN, thus ameliorating the effect of shortage of dopamine, but possibly speeding up PD progression (Blandini et al., 2000). We have already observed a marked increase in firing rate in both STN and SN with rising dopamine concentration. We expect that compensatory mechanisms (i.e. adaptation) will counter large changes in firing rate on the longer term, possibly by changing the firing patterns (i.e. neuronal and synaptic properties). Medication by L-DOPA may have the same effect in PD patients; enabling neurons to fire in patterns that, at least, do not interfere with normal function. The question of which patterns do not interfere with normal function, may be answered by simulating DBS in-vitro, since the effects of DBS are visible almost instantly.

For longitudinal studies, cultures of dissociated neurons, or even (non-dissociated) cocultures can be used. Even though these will create networks that differ from those in the intact brain, they can be used to study basic mechanisms and how they evolve over longer periods of time. Here, more fundamental questions about neuronal adaptation to various inputs and chemical additions can be answered. From cultures of cortical neurons we know that basic properties of these networks (e.g. percentage of excitatory/inhibitory connections) develop in a similar way compared to in-vivo counterparts. This even allows the study of age-related effects.

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 225

Fig. 9. Top: The model synaptic input reflects the burstiness of the activity of the measured GPi neuron. Bottom: The thalamic relay cell exhibits post-inhibitory rebound action potentials, i.e., during the pause after the GPi burst an action potential is generated.

Fig. 10. The effect of overwriting the pathological GPi input by increasing DBS amplitude. The upper traces represent the membrane voltage (V) of the TC cell. The precise timing of the excitatory input (mean rate 16.5 Hz) is displayed beneath each voltage trace. Top: If the stimulation amplitude is too weak, rebounds and an incorrect signal relay occur. Middle: With moderate DBS amplitude, rebounds are quenched and relay is correct. Bottom: With

high DBS amplitude, relay of sensory information is impaired.

## **4. Computational models of PD and DBS treatment**

Computational studies are useful in investigating how pathological conditions and DBS induced activity may find their way through the basal ganglia-thalamocortical circuit. Highfrequency stimulation leads to somatic inhibition of neurons that are close to the electrical field while simultaneously afferent and efferent axons may be excited. Both cellular and network effects may contribute to the overall clinical effects of DBS. McIntyre and Hahn (2010) claim that: "changes in the underlying dynamics of the stimulated brain networks may represent the core mechanisms of DBS and that those basic dynamical changes can be achieved via activation, inhibition, or lesion". Stimulation does not necessarily has to restore the network to a pre-pathological/normal state, but should allow improvement in Parkinson's symptoms.

Normally a parametric approach based on investigations of the biological system and network or molecular/channel characteristics, is preferred. Since not all systems are studied in detail, a non-parametric based model may be used, in which only input and output are considered, leaving the system a black box. Due to the extreme data gathering on Parkinson's disease non-parametric approaches are uncommon and the models brought forward can be classified as parametric. Here we will concentrate on the models for the thalamocortical relay neuron and the PPN neuron, thus directing towards an efferent thalamo-projecting model and an efferent spinal-projecting model.

## **4.1 Model of the thalamic relay neuron**

The output of the basal ganglia network is directed towards the thalamic nuclei (Figure 1), which influences the motor cortex and its output is relayed via the pyramidal tract towards the secondary motor neurons. In two recent studies we have investigated how DBS can affect the functioning of the thalamus as a relay station (Cagnan et al., 2009; Meijer et al., 2011). Although this is a simplication, it is presumed that this relay should retransmit incoming information from cortex and sensory systems back to cortex. This extends earlier work by Rubin and Terman who showed that the mechanism of DBS may be regularizing the output of thalamus (Rubin & Terman, 2004). They demonstrated that under pathological conditions STN-GPe networks can show a pacemaker rhythm at tremor frequency (Terman et al., 2002). These phasic signals from basal ganglia may impair the transmission of thalamocortical information. When replacing the pathological oscillations by regular DBS input thalamocortical relay may be restored (Rubin & Terman, 2004; Guo et al., 2008).

We started to model a simpler situation by first focussing on rest tremor. A GPi-spike train obtained from a human PD patient during DBS surgery with characteristic patterns of rest tremor was used to generate GPi input to the thalamus. Without relay of cortical input (rest situation), the thalamic model response consisted of rebounds at the same tremor frequency (Figure 9).

By including excitatory input the combined effects of relay, PD and DBS could be examined. The pathological input was partially replaced by DBS pulses reflecting a limited volume of tissue being activated by the stimulation. For DBS there are two common targets: STN and GPi.

Computational studies are useful in investigating how pathological conditions and DBS induced activity may find their way through the basal ganglia-thalamocortical circuit. Highfrequency stimulation leads to somatic inhibition of neurons that are close to the electrical field while simultaneously afferent and efferent axons may be excited. Both cellular and network effects may contribute to the overall clinical effects of DBS. McIntyre and Hahn (2010) claim that: "changes in the underlying dynamics of the stimulated brain networks may represent the core mechanisms of DBS and that those basic dynamical changes can be achieved via activation, inhibition, or lesion". Stimulation does not necessarily has to restore the network to a pre-pathological/normal state, but should allow improvement in

Normally a parametric approach based on investigations of the biological system and network or molecular/channel characteristics, is preferred. Since not all systems are studied in detail, a non-parametric based model may be used, in which only input and output are considered, leaving the system a black box. Due to the extreme data gathering on Parkinson's disease non-parametric approaches are uncommon and the models brought forward can be classified as parametric. Here we will concentrate on the models for the thalamocortical relay neuron and the PPN neuron, thus directing towards an efferent

The output of the basal ganglia network is directed towards the thalamic nuclei (Figure 1), which influences the motor cortex and its output is relayed via the pyramidal tract towards the secondary motor neurons. In two recent studies we have investigated how DBS can affect the functioning of the thalamus as a relay station (Cagnan et al., 2009; Meijer et al., 2011). Although this is a simplication, it is presumed that this relay should retransmit incoming information from cortex and sensory systems back to cortex. This extends earlier work by Rubin and Terman who showed that the mechanism of DBS may be regularizing the output of thalamus (Rubin & Terman, 2004). They demonstrated that under pathological conditions STN-GPe networks can show a pacemaker rhythm at tremor frequency (Terman et al., 2002). These phasic signals from basal ganglia may impair the transmission of thalamocortical information. When replacing the pathological oscillations by regular DBS input thalamocortical relay may be restored (Rubin & Terman,

We started to model a simpler situation by first focussing on rest tremor. A GPi-spike train obtained from a human PD patient during DBS surgery with characteristic patterns of rest tremor was used to generate GPi input to the thalamus. Without relay of cortical input (rest situation), the thalamic model response consisted of rebounds at the same tremor frequency

By including excitatory input the combined effects of relay, PD and DBS could be examined. The pathological input was partially replaced by DBS pulses reflecting a limited volume of tissue being activated by the stimulation. For DBS there are two common targets: STN and GPi.

**4. Computational models of PD and DBS treatment** 

thalamo-projecting model and an efferent spinal-projecting model.

**4.1 Model of the thalamic relay neuron** 

Parkinson's symptoms.

2004; Guo et al., 2008).

(Figure 9).

Fig. 9. Top: The model synaptic input reflects the burstiness of the activity of the measured GPi neuron. Bottom: The thalamic relay cell exhibits post-inhibitory rebound action potentials, i.e., during the pause after the GPi burst an action potential is generated.

Fig. 10. The effect of overwriting the pathological GPi input by increasing DBS amplitude. The upper traces represent the membrane voltage (V) of the TC cell. The precise timing of the excitatory input (mean rate 16.5 Hz) is displayed beneath each voltage trace. Top: If the stimulation amplitude is too weak, rebounds and an incorrect signal relay occur. Middle: With moderate DBS amplitude, rebounds are quenched and relay is correct. Bottom: With high DBS amplitude, relay of sensory information is impaired.

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 227

addition, we investigated the effect of DBS in PPN and STN on the behaviour of the PPNbasal ganglia network and on the relay property of the PPN cell. DBS is modeled as a train of positive current pulses, injected directly into the target cells. PPN-DBS is applied with high amplitude (100 μA cm-2) at 40 Hz and STN-DBS is applied at 130 Hz with an amplitude of 400 μA cm-2; both stimuli have a pulse width of 0.15 ms. For the relay property it turns out that combined high-frequency stimulation of STN and low frequency stimulation of PPN hardly improves the effect of exclusive STN stimulation. PPN-DBS eliminates the pathological firing pattern of STN and GPe cells, whereas STN-DBS and combined STN- and PPN-DBS eliminate the pathological firing pattern only from STN cells, see Figure 11.

In general there is a wide gap between experimental animal results, especially with respect to neuroanatomical data, and computational modeling. In order to be able to investigate the anatomical and functional properties of afferent and efferent connections between the different nuclei of the basal ganglia, similar studies need to be performed as described for the substantia nigra. These studies, though very time-consuming, are essential to decide which pathways play important roles in normal functioning and therefore need to be included in modeling studies. In addition, it should be known what neuroanatomical changes take place resulting from the neurodegeneration associated with Parkinson's disease and how they affect network behavior. For instance, the direct effects of DBS on motor control are of interest, but since DBS has a low threshold to side effects, additional non-motor pathways are expected to be involved. Including these pathways in network models may shed light on the extent and effect of stimulation. Similarly, as PPN stimulation may have a beneficial influence on gait and balance, different pathways are important

The classic diagram of the basal ganglia as presented in Figure 1 not only leaves out a number of connections that are discussed in this review, it also is based on average firing rates while currently it is known that firing patterns change under parkinsonian conditions. The irregular firing characteristics within the nuclei of the basal ganglia are transformed into a more synchronous and bursting activity pattern. Functionality of neuronal networks is dependent of neurotransmitters and their receptors, together with the channels present in the cell membrane. Studies on the properties and localization of the receptors and channels are therefore a prerequisite for adequate modeling. However, the enormous amount of receptors and channel types, and their variability in distribution makes it virtually impossible to describe neuronal function for all basal ganglia nuclei (see e.g. the eloquent

Dissociated neural cultures as well as brain slices positioned on multi electrode arrays open the possibility to study basal ganglia nuclear functional action and interaction, i.e. the overall result of all cell membrane activities of a neuron or group of neurons. By the addition of neurotransmitters, their agonists or antagonists, PD basal ganglia activity can be mimicked in-vitro. It is expected that this alternative route of studying PD will bring up the most needed extra information to support fine-tuning of neuron and neuronal network models and will as a consequence incorporate the more subtle connections nowadays

regarding the different motor symptoms of Parkinson's disease.

studies on GABA in the basal ganglia; Tepper et al., 2007).

described in neuroanatomical studies.

**5. Discussion** 

Stimulation of the STN may recruit efferent fibers that excite GPi. In both cases it is therefore plausible that DBS leads to additional downstream GPi output. At the thalamus, the input from the basal ganglia comes from the GPi and is therefore inhibitory. A key property of thalamic relay cells is their low-threshold T-type calcium current. When the thalamic relay cell is inhibited long enough, it fires rebound action potentials (Janssen & Llinàs, 1984). The effect of such phasic pathological inhibition is that the thalamic output activity does not reflect the original input. This stems from two sources of errors. Long periods of inhibition diminish the responsiveness of the TC cell and rebound spikes are mixed with successful relays.

In the model we found that this extra inhibition can jam the transmission of pathological oscillations around the loop. Additionally we investigated the frequency dependence of this therapeutic regime and showed that in the model it persists to frequencies as low as 60 Hz, although the plateau starts at 100 Hz. In Cagnan et al. (2009) we considered a similar setup but considered the frequency content of the output. In particular, we showed that DBS can diminish the power at pathological frequencies in the spectrum of the thalamic output. Finally, we also found that if the frequency of the relay input is sufficiently high, and the variance low enough, this can also block the transmission of pathological low-frequency oscillations. This may be interpreted as a suppression of rest tremor.

## **4.2 Model of the PPN neuron**

Due to its location in the brainstem and its function in locomotion and postural control, the pedunculopontine nucleus (PPN) has been suggested as a target for DBS to improve gait and postural instability. The glutamatergic PPN neurons are reciprocally connected with the basal ganglia and these neurons provide the descending PPN output to the spinal cord. Therefore, PPN has a pivot role in regulation of the basal ganglia and spinal cord, and providing indirect pathway for the basal ganglia to regulate the initiation of gait (Pahapill & Lozano, 2000; Hamani et al., 2007).

In Lourens et al. (2011) we have developed a computational conductance based model for the glutamatergic PPN type I to investigate the response of the PPN cell to various basal ganglia inputs. The specific characteristics of PPN currents are described by Takakusaki and Kitai (1997). A persistent sodium current is responsible for subthreshold membrane oscillations in PPN type I neurons, which underlies spontaneous repetitive firing. Moreover the LTS property is mediated by the T-type calcium current. The model is based on neurophysiological data of the thalamocortical relay neuron, and the pre-Bötzinger neuron. The PPN Type I is modelled as a single compartment model using the Hodgkin-Huxley formalism, except for the calcium current which is described by the Goldman-Hodgkin-Katz ion current equation. We used the basal ganglia model as proposed by Rubin and Terman (2004) to generate input to the PPN type I model. Moreover, we include the projection from the PPN back to the basal ganglia.

The model of an isolated type I PPN neuron shows the experimental behaviour as described in literature (Takakusaki & Kitai, 1997). The PPN neuron model shows spontaneous firing at 8 Hz, and bursting behaviour after the release of a hyperpolarizing input. In the network model, including 8 cells of STN, GPe and GPi and 1 PPN cell, we found that under PD conditions the firing rate of the PPN cell decreases and its firing pattern regularizes. In addition, we investigated the effect of DBS in PPN and STN on the behaviour of the PPNbasal ganglia network and on the relay property of the PPN cell. DBS is modeled as a train of positive current pulses, injected directly into the target cells. PPN-DBS is applied with high amplitude (100 μA cm-2) at 40 Hz and STN-DBS is applied at 130 Hz with an amplitude of 400 μA cm-2; both stimuli have a pulse width of 0.15 ms. For the relay property it turns out that combined high-frequency stimulation of STN and low frequency stimulation of PPN hardly improves the effect of exclusive STN stimulation. PPN-DBS eliminates the pathological firing pattern of STN and GPe cells, whereas STN-DBS and combined STN- and PPN-DBS eliminate the pathological firing pattern only from STN cells, see Figure 11.

## **5. Discussion**

226 Applied Biological Engineering – Principles and Practice

Stimulation of the STN may recruit efferent fibers that excite GPi. In both cases it is therefore plausible that DBS leads to additional downstream GPi output. At the thalamus, the input from the basal ganglia comes from the GPi and is therefore inhibitory. A key property of thalamic relay cells is their low-threshold T-type calcium current. When the thalamic relay cell is inhibited long enough, it fires rebound action potentials (Janssen & Llinàs, 1984). The effect of such phasic pathological inhibition is that the thalamic output activity does not reflect the original input. This stems from two sources of errors. Long periods of inhibition diminish the responsiveness of the TC cell and rebound spikes are mixed with successful

In the model we found that this extra inhibition can jam the transmission of pathological oscillations around the loop. Additionally we investigated the frequency dependence of this therapeutic regime and showed that in the model it persists to frequencies as low as 60 Hz, although the plateau starts at 100 Hz. In Cagnan et al. (2009) we considered a similar setup but considered the frequency content of the output. In particular, we showed that DBS can diminish the power at pathological frequencies in the spectrum of the thalamic output. Finally, we also found that if the frequency of the relay input is sufficiently high, and the variance low enough, this can also block the transmission of pathological low-frequency

Due to its location in the brainstem and its function in locomotion and postural control, the pedunculopontine nucleus (PPN) has been suggested as a target for DBS to improve gait and postural instability. The glutamatergic PPN neurons are reciprocally connected with the basal ganglia and these neurons provide the descending PPN output to the spinal cord. Therefore, PPN has a pivot role in regulation of the basal ganglia and spinal cord, and providing indirect pathway for the basal ganglia to regulate the initiation of gait (Pahapill &

In Lourens et al. (2011) we have developed a computational conductance based model for the glutamatergic PPN type I to investigate the response of the PPN cell to various basal ganglia inputs. The specific characteristics of PPN currents are described by Takakusaki and Kitai (1997). A persistent sodium current is responsible for subthreshold membrane oscillations in PPN type I neurons, which underlies spontaneous repetitive firing. Moreover the LTS property is mediated by the T-type calcium current. The model is based on neurophysiological data of the thalamocortical relay neuron, and the pre-Bötzinger neuron. The PPN Type I is modelled as a single compartment model using the Hodgkin-Huxley formalism, except for the calcium current which is described by the Goldman-Hodgkin-Katz ion current equation. We used the basal ganglia model as proposed by Rubin and Terman (2004) to generate input to the PPN type I model. Moreover, we include the projection from

The model of an isolated type I PPN neuron shows the experimental behaviour as described in literature (Takakusaki & Kitai, 1997). The PPN neuron model shows spontaneous firing at 8 Hz, and bursting behaviour after the release of a hyperpolarizing input. In the network model, including 8 cells of STN, GPe and GPi and 1 PPN cell, we found that under PD conditions the firing rate of the PPN cell decreases and its firing pattern regularizes. In

oscillations. This may be interpreted as a suppression of rest tremor.

relays.

**4.2 Model of the PPN neuron** 

Lozano, 2000; Hamani et al., 2007).

the PPN back to the basal ganglia.

In general there is a wide gap between experimental animal results, especially with respect to neuroanatomical data, and computational modeling. In order to be able to investigate the anatomical and functional properties of afferent and efferent connections between the different nuclei of the basal ganglia, similar studies need to be performed as described for the substantia nigra. These studies, though very time-consuming, are essential to decide which pathways play important roles in normal functioning and therefore need to be included in modeling studies. In addition, it should be known what neuroanatomical changes take place resulting from the neurodegeneration associated with Parkinson's disease and how they affect network behavior. For instance, the direct effects of DBS on motor control are of interest, but since DBS has a low threshold to side effects, additional non-motor pathways are expected to be involved. Including these pathways in network models may shed light on the extent and effect of stimulation. Similarly, as PPN stimulation may have a beneficial influence on gait and balance, different pathways are important regarding the different motor symptoms of Parkinson's disease.

The classic diagram of the basal ganglia as presented in Figure 1 not only leaves out a number of connections that are discussed in this review, it also is based on average firing rates while currently it is known that firing patterns change under parkinsonian conditions. The irregular firing characteristics within the nuclei of the basal ganglia are transformed into a more synchronous and bursting activity pattern. Functionality of neuronal networks is dependent of neurotransmitters and their receptors, together with the channels present in the cell membrane. Studies on the properties and localization of the receptors and channels are therefore a prerequisite for adequate modeling. However, the enormous amount of receptors and channel types, and their variability in distribution makes it virtually impossible to describe neuronal function for all basal ganglia nuclei (see e.g. the eloquent studies on GABA in the basal ganglia; Tepper et al., 2007).

Dissociated neural cultures as well as brain slices positioned on multi electrode arrays open the possibility to study basal ganglia nuclear functional action and interaction, i.e. the overall result of all cell membrane activities of a neuron or group of neurons. By the addition of neurotransmitters, their agonists or antagonists, PD basal ganglia activity can be mimicked in-vitro. It is expected that this alternative route of studying PD will bring up the most needed extra information to support fine-tuning of neuron and neuronal network models and will as a consequence incorporate the more subtle connections nowadays described in neuroanatomical studies.

Simulating Idiopathic Parkinson's Disease by *In Vitro* and Computational Models 229

"Despite numerous diverse- and at times frankly bizarre- etiologic speculations over a considerable period of time, the cause or causes of Parkinson's disease remain unknown" (Stern, 1996). This statement still holds and therefore the efforts in Parkinson´s research are focused on investigating ´what goes wrong in the parkinsonian brain, and how can we reverse this pathological behaviour´. Medication and deep brain stimulation are meant to restore direct causes of the disease symptoms: compensating the loss of dopamine, and desynchronizing the pathological oscillations, respectively. A lot of attention is drawn to the basal ganglia and the causes and effects of its dysfunction. Individual neuronal receptor studies on basal ganglia or SNc cells hardly can give the overall outcome of the typical neuronal dysfunction. Dissociated neuronal cultures and brain slices presumably will be

Due to the neuronal plasticity of the brain, several mechanisms are involved in functional compensation for the progressive loss of dopamine. PD symptoms do not become clinically manifest until neuronal death exceeds a critical threshold: about 70–80% of striatal nerve terminals and 50–60% of SNc dopamine neurons (Bezard et al., 2003). While initially it was suggested that the preclinical state reflected the ability of the affected neuronal system to actively compensate for the loss of dopamine (Bezard et al., 2003), we now know that compensatory mechanisms outside that basal ganglia exist. Although the basal ganglia may be in a parkinsonian state, these mechanisms may prevent the appearance of symptoms. The overactivation of lateral premotor areas as found from PET and fMRI studies may express compensation processes (Samuel et al. 1997; Berardelli et al. 2001; Bezard et al., 2003). The cerebellothalamocortical circuit is proposed to play an important role in these processes since the cerebellum has strong connections with the lateral premotor areas. It is concerned with externally triggered movement, which may explain the beneficial effect PD patients experience from external cues in guiding movements. In contrast, the cerebellothalamic circuit was also hypothesized to play a role in tremor generation (Helmich et al., 2011). A prerequisite for the development of novel therapeutic methods in-vitro and computational models of Parkinson's disease is to include those circuits that are involved in compensating

for the parkinsonian symptoms, based on cellular and connective studies.

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Albin, R.L., Aldrige, J.W. & Young AB et al. (1989) The functional anatomy of basal ganglia

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**6. Future direction** 

more successful.

**7. References** 

439-473

B)

Fig. 11. Effect of PPN-DBS and STN-DBS on the activity of GPe and STN cells. Stimulation starts at 1 s and 4 s, as indicated by the arrows. With STN-DBS stimulation clusters remain and the time period of the clusters gets longer in GPe, while STN cells are locked to the STN-DBS frequency. Addition of PPN-DBS shows no change (A). With only PPN-DBS (B) the STN and GPe clusters are disrupted after some transients.

Essential in modeling is to formulate reduced models that still capture essential properties of the dynamics but are able to include even these subtle connections. Models need verification by experiments to demonstrate that the model has reality value. With the increasing amount of in-vitro and in-vivo experimental data computational models may become applicable in human research and health care problems. The therapeutic stimulation parameters for DBS (polarity, pulse amplitude, pulse width, frequency) will in the near future rely more on the predictions made by model simulations (Cutsuridis et al., 2011).

## **6. Future direction**

228 Applied Biological Engineering – Principles and Practice

A)

B) Fig. 11. Effect of PPN-DBS and STN-DBS on the activity of GPe and STN cells. Stimulation starts at 1 s and 4 s, as indicated by the arrows. With STN-DBS stimulation clusters remain and the time period of the clusters gets longer in GPe, while STN cells are locked to the STN-DBS frequency. Addition of PPN-DBS shows no change (A). With only PPN-DBS (B)

Essential in modeling is to formulate reduced models that still capture essential properties of the dynamics but are able to include even these subtle connections. Models need verification by experiments to demonstrate that the model has reality value. With the increasing amount of in-vitro and in-vivo experimental data computational models may become applicable in human research and health care problems. The therapeutic stimulation parameters for DBS (polarity, pulse amplitude, pulse width, frequency) will in the near future rely more on the predictions made by model simulations (Cutsuridis et al., 2011).

the STN and GPe clusters are disrupted after some transients.

"Despite numerous diverse- and at times frankly bizarre- etiologic speculations over a considerable period of time, the cause or causes of Parkinson's disease remain unknown" (Stern, 1996). This statement still holds and therefore the efforts in Parkinson´s research are focused on investigating ´what goes wrong in the parkinsonian brain, and how can we reverse this pathological behaviour´. Medication and deep brain stimulation are meant to restore direct causes of the disease symptoms: compensating the loss of dopamine, and desynchronizing the pathological oscillations, respectively. A lot of attention is drawn to the basal ganglia and the causes and effects of its dysfunction. Individual neuronal receptor studies on basal ganglia or SNc cells hardly can give the overall outcome of the typical neuronal dysfunction. Dissociated neuronal cultures and brain slices presumably will be more successful.

Due to the neuronal plasticity of the brain, several mechanisms are involved in functional compensation for the progressive loss of dopamine. PD symptoms do not become clinically manifest until neuronal death exceeds a critical threshold: about 70–80% of striatal nerve terminals and 50–60% of SNc dopamine neurons (Bezard et al., 2003). While initially it was suggested that the preclinical state reflected the ability of the affected neuronal system to actively compensate for the loss of dopamine (Bezard et al., 2003), we now know that compensatory mechanisms outside that basal ganglia exist. Although the basal ganglia may be in a parkinsonian state, these mechanisms may prevent the appearance of symptoms. The overactivation of lateral premotor areas as found from PET and fMRI studies may express compensation processes (Samuel et al. 1997; Berardelli et al. 2001; Bezard et al., 2003). The cerebellothalamocortical circuit is proposed to play an important role in these processes since the cerebellum has strong connections with the lateral premotor areas. It is concerned with externally triggered movement, which may explain the beneficial effect PD patients experience from external cues in guiding movements. In contrast, the cerebellothalamic circuit was also hypothesized to play a role in tremor generation (Helmich et al., 2011). A prerequisite for the development of novel therapeutic methods in-vitro and computational models of Parkinson's disease is to include those circuits that are involved in compensating for the parkinsonian symptoms, based on cellular and connective studies.

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**10** 

*Ireland* 

*Dublin City University* 

**Vascular Stent Design Optimisation** 

**Using Numerical Modelling Techniques** 

Since their first introduction in 1985 by Palmaz et al. (1985), balloon-mounted vascular stents have revolutionised the treatment of atherosclerosis, and in particular coronary artery disease. Vascular stents were developed to restore blood flow in stenosed arteries of the body, thereby preventing ischemia and myocardial infarction in peripheral and coronary arteries, respectively. A modification to these first stents by Schatz et al. (1987) led to the development of the first commercially successful stent, the Palmaz–Schatz stent. This redesign of the very first stent led the way in a new era of vascular medical device design, with a vast range of new stent designs, materials and adjunct drug therapies subsequently emerging at an ever increasing pace. Now over 25 years on, stents have undeniably become the gold standard in the non invasive treatment of atherosclerosis with 3 million implanted worldwide each year (van Beusekom & Serruys, 2010). To-date, vascular stents have been developed using an extensive range of high grade metals, from tantalum and titanium to the more common medical grade stainless steel, and more recently high yield strength materials such as cobalt chromium and platinum chromium alloys have also been used (Lally et al., 2006; Gopinath et al., 2007**;** Huibregtse et al., 2011). Self-expanding stents have been developed from shape memory alloys for peripheral anatomies to eliminate the need for expansion using angioplasty balloons (Gopinath et al., 2007**).** Biodegradable stents have been developed to allow for removal of the stent following successful revascularisation, whilst stents have also been developed to incorporate complementary drug, gene and radiation therapies and even pre-seeded with endothelial cells to lower thrombosis and encourage re-endothelialisation (Serruys et al., 2006; Sharif et al., 2004; Kay et al., 2001; Van der Giessen 1988; Dichek et al., 1989).While many of these new stent designs have offered improvements on their predecessors, no single design has successfully incorporated all of the characteristics of the ideal stent and one significant limitation in the long-term success of

In-stent restenosis, which ultimately results in re-occlusion of a stented artery, is effectively an over-zealous wound healing response. It has been identified to comprise mainly of neointimal growth, composed principally of proliferating smooth muscle cells (SMC) and extracellular matrix (Lowe et al., 2002). Stent induced injury to the vessel wall is believed to be a determining factor in the onset and progression of in-stent restenosis (Hoffmann & G. S. Mintz, 2000) and consequently there is increasing evidence that stent design influences restenosis. While the biocompatibility of the metal or surface coating may affect long-term

**1. Introduction** 

stents still remains, namely in-stent restenosis.

Houman Zahedmanesh, Paul A. Cahill and Caitríona Lally

Yan, W., Zang, Q.J., Liu, J., Wang, T., Wang, S., Liu, X., Chen, L. & Gui, Z.H. (2008) The neural activity of the parafascicular nucleus is conversely regulated by nigrostriatal pathway and pedunculopontine nucleus in rat. *Brain Res* 1240, pp. 204-212

## **Vascular Stent Design Optimisation Using Numerical Modelling Techniques**

Houman Zahedmanesh, Paul A. Cahill and Caitríona Lally *Dublin City University Ireland* 

## **1. Introduction**

236 Applied Biological Engineering – Principles and Practice

Yan, W., Zang, Q.J., Liu, J., Wang, T., Wang, S., Liu, X., Chen, L. & Gui, Z.H. (2008) The

pathway and pedunculopontine nucleus in rat. *Brain Res* 1240, pp. 204-212

neural activity of the parafascicular nucleus is conversely regulated by nigrostriatal

Since their first introduction in 1985 by Palmaz et al. (1985), balloon-mounted vascular stents have revolutionised the treatment of atherosclerosis, and in particular coronary artery disease. Vascular stents were developed to restore blood flow in stenosed arteries of the body, thereby preventing ischemia and myocardial infarction in peripheral and coronary arteries, respectively. A modification to these first stents by Schatz et al. (1987) led to the development of the first commercially successful stent, the Palmaz–Schatz stent. This redesign of the very first stent led the way in a new era of vascular medical device design, with a vast range of new stent designs, materials and adjunct drug therapies subsequently emerging at an ever increasing pace. Now over 25 years on, stents have undeniably become the gold standard in the non invasive treatment of atherosclerosis with 3 million implanted worldwide each year (van Beusekom & Serruys, 2010). To-date, vascular stents have been developed using an extensive range of high grade metals, from tantalum and titanium to the more common medical grade stainless steel, and more recently high yield strength materials such as cobalt chromium and platinum chromium alloys have also been used (Lally et al., 2006; Gopinath et al., 2007**;** Huibregtse et al., 2011). Self-expanding stents have been developed from shape memory alloys for peripheral anatomies to eliminate the need for expansion using angioplasty balloons (Gopinath et al., 2007**).** Biodegradable stents have been developed to allow for removal of the stent following successful revascularisation, whilst stents have also been developed to incorporate complementary drug, gene and radiation therapies and even pre-seeded with endothelial cells to lower thrombosis and encourage re-endothelialisation (Serruys et al., 2006; Sharif et al., 2004; Kay et al., 2001; Van der Giessen 1988; Dichek et al., 1989).While many of these new stent designs have offered improvements on their predecessors, no single design has successfully incorporated all of the characteristics of the ideal stent and one significant limitation in the long-term success of stents still remains, namely in-stent restenosis.

In-stent restenosis, which ultimately results in re-occlusion of a stented artery, is effectively an over-zealous wound healing response. It has been identified to comprise mainly of neointimal growth, composed principally of proliferating smooth muscle cells (SMC) and extracellular matrix (Lowe et al., 2002). Stent induced injury to the vessel wall is believed to be a determining factor in the onset and progression of in-stent restenosis (Hoffmann & G. S. Mintz, 2000) and consequently there is increasing evidence that stent design influences restenosis. While the biocompatibility of the metal or surface coating may affect long-term

Vascular Stent Design Optimisation Using Numerical Modelling Techniques 239

**A** 

**B** 

**C** 

**E** 

**D** 

Fig. 1. Development of in-stent restenosis following stent deployment. (A) normal artery (B) de-endothelialisation and injury of the media (C) modulation of medial VSMC phenotype and their migration and proliferation towards the lumen (D) development of in-stent restenosis (E) re-endothelialisation and differentiation of VSMC back to the quiescent phenotype. (EC) endothelial cells, (IEL), internal elastic lamina, (s VSMC) synthetic vascular smooth muscle cell,

(c VSMC) contractile vascular smooth muscle cell, (EEL), external elastic lamina.

healing in stented vessels, studies have shown that stent geometry designed to optimize expansion and lower recoil is a prerequisite for favourable clinical outcomes (McLean & Eigler 2002). Strut thickness also appears to be an important risk factor, but changing one parameter, such as strut thickness, requires altering other design characteristics, thus altering the overall stent design (McLean & Eigler 2002). Computational models of stent deployment, such as finite element (FE) models, are a very cost effective means of optimising stent designs and can be used to carry out parameterisation studies, whereby the influence of alterations in several stent parameters on the overall stent performance are systematically investigated (Bedoya et al., 2006). Materials changes can be analysed quickly and effectively using numerical modelling techniques such that even the influence that material degradation has on the scaffolding offered by a biodegradable stent can be assessed (Grogan et al., 2011).

FE models of stent expansion enable quantification of the stress-strain field in stents and the vessel wall following stent deployment and therefore provide insights into the various aspects of stent design that are critical in terms of arterial injury (Lally et al., 2005; Holzapfel et al., 2005a). More importantly, however, numerical modelling also provides a means to model the biological response to an implant using mechanobiological models whereby the mechanical environment may be used to dictate the growth and remodelling of vascular cells (Boyle et al., 2011; Zahedmanesh & Lally, 2011). With the emergence of Drug Eluting Stents (DES) and gene delivery stents, however, comes a need to include not only the growth and remodelling of the vessel wall but also the temporal and spatial distribution of such therapeutic agents and their influence on cell growth. Mechanobiological models offer the possibility of including such factors and therefore have the potential to enable future stent designs to be developed such that they combine the best features of conventional bare metal stent designs with the modifications required to facilitate biodegradation or optimum multi-agent drug or gene elution for a variety of vascular applications.

## **2. The mechanism of in-stent restenosis**

Following stent deployment, a healing biological response initiates within the arterial wall which can ultimately lead to renarrowing of the vessel due to excessive migration and proliferation of medial vascular smooth muscle cells (VSMC) towards the vessel lumen. This biological response known as in-stent restenosis consists of four main phases, namely (i) thrombosis (ii) inflammation (iii) proliferation and (iv) remodelling (Edelman et al*.,* 1998). Biomechanical factors which are dictated by the mechanical design of stents have been found to play a key role in all of the aforementioned phases in the development of in-stent restenosis.

During the expansion of the stent, high stresses induced by the stent cause injury to the artery which leads to thrombosis formation in the arterial wall and a cascade of inflammatory events. Close correlation has been observed between the degree of inflammation and neo-intimal thickness which suggests that inflammation caused by the arterial injury plays a central role in the formation of in-stent restenosis (Wieneke et al*.,* 1999; Welt et al*.,* 2002; Mitra et al*.,* 2006). After stent deployment, vessel injury by the stent struts leads to the activation of thrombocytes and the formation of mural thrombus at the injury site. These thrombocytes produce mitogenic factors which contribute to dedifferentiation of medial VSMC, which are in a quiescent and contractile phenotype in the uninjured artery, to a synthetic phenotype. This change of phenotype is followed by a chemotactic migration and proliferation of dedifferentiated medial VSMC towards the lumen and lesion formation, see Figure 1.

healing in stented vessels, studies have shown that stent geometry designed to optimize expansion and lower recoil is a prerequisite for favourable clinical outcomes (McLean & Eigler 2002). Strut thickness also appears to be an important risk factor, but changing one parameter, such as strut thickness, requires altering other design characteristics, thus altering the overall stent design (McLean & Eigler 2002). Computational models of stent deployment, such as finite element (FE) models, are a very cost effective means of optimising stent designs and can be used to carry out parameterisation studies, whereby the influence of alterations in several stent parameters on the overall stent performance are systematically investigated (Bedoya et al., 2006). Materials changes can be analysed quickly and effectively using numerical modelling techniques such that even the influence that material degradation has on the scaffolding offered by a biodegradable stent can be assessed

FE models of stent expansion enable quantification of the stress-strain field in stents and the vessel wall following stent deployment and therefore provide insights into the various aspects of stent design that are critical in terms of arterial injury (Lally et al., 2005; Holzapfel et al., 2005a). More importantly, however, numerical modelling also provides a means to model the biological response to an implant using mechanobiological models whereby the mechanical environment may be used to dictate the growth and remodelling of vascular cells (Boyle et al., 2011; Zahedmanesh & Lally, 2011). With the emergence of Drug Eluting Stents (DES) and gene delivery stents, however, comes a need to include not only the growth and remodelling of the vessel wall but also the temporal and spatial distribution of such therapeutic agents and their influence on cell growth. Mechanobiological models offer the possibility of including such factors and therefore have the potential to enable future stent designs to be developed such that they combine the best features of conventional bare metal stent designs with the modifications required to facilitate biodegradation or optimum

Following stent deployment, a healing biological response initiates within the arterial wall which can ultimately lead to renarrowing of the vessel due to excessive migration and proliferation of medial vascular smooth muscle cells (VSMC) towards the vessel lumen. This biological response known as in-stent restenosis consists of four main phases, namely (i) thrombosis (ii) inflammation (iii) proliferation and (iv) remodelling (Edelman et al*.,* 1998). Biomechanical factors which are dictated by the mechanical design of stents have been found to play a key role in all of the aforementioned phases in the development of in-stent restenosis. During the expansion of the stent, high stresses induced by the stent cause injury to the artery which leads to thrombosis formation in the arterial wall and a cascade of inflammatory events. Close correlation has been observed between the degree of inflammation and neo-intimal thickness which suggests that inflammation caused by the arterial injury plays a central role in the formation of in-stent restenosis (Wieneke et al*.,* 1999; Welt et al*.,* 2002; Mitra et al*.,* 2006). After stent deployment, vessel injury by the stent struts leads to the activation of thrombocytes and the formation of mural thrombus at the injury site. These thrombocytes produce mitogenic factors which contribute to dedifferentiation of medial VSMC, which are in a quiescent and contractile phenotype in the uninjured artery, to a synthetic phenotype. This change of phenotype is followed by a chemotactic migration and proliferation of dedifferentiated medial VSMC towards the lumen and lesion formation, see Figure 1.

multi-agent drug or gene elution for a variety of vascular applications.

**2. The mechanism of in-stent restenosis** 

(Grogan et al., 2011).

Fig. 1. Development of in-stent restenosis following stent deployment. (A) normal artery (B) de-endothelialisation and injury of the media (C) modulation of medial VSMC phenotype and their migration and proliferation towards the lumen (D) development of in-stent restenosis (E) re-endothelialisation and differentiation of VSMC back to the quiescent phenotype. (EC) endothelial cells, (IEL), internal elastic lamina, (s VSMC) synthetic vascular smooth muscle cell, (c VSMC) contractile vascular smooth muscle cell, (EEL), external elastic lamina.

Vascular Stent Design Optimisation Using Numerical Modelling Techniques 241

VSMC resumed a contractile phenotype as the neointima reached its final size with development of a complete basement membrane. Based on these observations Thyberg et al., (1997) suggested that laminin and other basement membrane components promote differentiation of VSMC towards a quiescent and contractile phenotype whereas their degradation leads into VSMC dedifferentiation and activation. Consistently, several studies have shown the role of collagen type IV, a major component of ECM representing 50% of all basement membrane proteins, in promoting restoration of VSMC to a contractile and quiescent phenotype (Hirose et al., 1999; Aguilera et al., 2003). In addition, exposing VSMC to mechanical loading has been shown to upregulate matrix metalloproteinase (MMP) synthesis by VSMC and mechanical injury upregulates MMP-2 production which is a major proteinase of the basement membrane (James et al.; 1993; Bendeck et al. 1994; Southgate et al., 1996; George et al., 1997) and so does mechanical stretch (Asanoma et al., 2002; Grote et al., 2003). By degrading ECM, MMPs are therefore key regulators of the onset and progression of in-stent restenosis, since they can regulate VSMC phenotype and

Finally, it should be noted that the origin of VSMC that accumulate in the neointima in vascular diseases such as in-stent restenosis remains controversial. These cells are a highly heterogeneous cell population with different characteristics and markers, and distinct phenotypes in physiological and pathological conditions. Although, early research on the pathophysiology of in stent-restenosis presents evidence indicating that these cells originate in the host artery (Edelman et al*.,* 1998), several more recent studies have reported a role for bone marrow-derived progenitor cells in vascular maintenance and repair. Moreover, bone marrow-derived smooth muscle progenitor cells have been detected in human atherosclerotic tissue as well as in *in vivo* mouse models of vascular disease. However, it is not clear whether smooth muscle progenitor cells can be regarded as a 'friend' or 'foe' in neointima formation (van Oostrom er al., 2009). The relationship of circulating progenitor cells during stent deployment to the subsequent development of in-stent restenosis has also been evaluated. Bone-marrow- and neural-crest-derived cells, the most dendritic cells, have been found to be consistently present in in-stent restenosis, whilst α-smooth muscle actin positive cells constitute the largest intimal cell pool (Skowasch et al., 2003). Patients with restenosis also have higher numbers of subpopulations of endothelial progenitor cells incorporated into endothelial cells when compared with controls (Pelliccia et al., 2010). Cleary the role of intimal cells and progenitor cells in in-stent restenosis remains to be further elucidated and numerical modelling, and in particular mechanobiological

consequently their behaviour i.e. migration and proliferation.

modelling, may provide insights in this area.

**3.1 Stress/strain analyses of stenting** 

**3. Numerical modelling as a means to reduce stent induced injury** 

In addition to being cost effective, computational models often offer the only solution to address some of the important challenges influencing stent design, such as the estimation of stresses induced in the vessel wall and therefore the degree of vascular injury. Several different computational models of stent deployment have been developed in recent years. These models have improved our knowledge on the mechanics of stent-artery interaction (Migliavacca et al., 2002; Wang et al., 2006; Zahedmanesh et al*.,* 2010) and the influence of several different variables of stent geometry such as the influence of stent strut thickness

The cytokines produced by the inflammatory cells not only serve as mitogens for VSMC but also upregulate synthesis of extracellular matrix by the synthetic VSMC (Wieneke et al*.,* 1999; Babapulle and Eisenberg, 2002; Welt et al*.,* 2002; Mitra et al*.,* 2006).

In addition to the stresses induced within the arterial wall and the resulting mechanical injury, flow field perturbations due to stent implantation have also been found to influence the degree to which thrombocytes are recruited and their adhesion to the arterial wall. Specifically, it has been shown that a higher degree of thrombocyte aggregation occurs in locations where the flow field is directed toward the arterial wall rather than away from the wall (Duraiswamy et al*.,* 2005). In addition, stagnant flow patterns adjacent to stent struts, particularly low shear stress, has been found to trigger the recruited inflammatory cells into their activated states (Kroll et al*.,* 1996; Moazzam et al*.,* 1997).

The altered solid mechanical environment following stent deployment also governs the inflammatory and remodelling response. The stent induced lesions are invaded by VSMC with mainly a synthetic phenotype. These cells produce extracellular matrix (ECM) components such as collagen, elastin and proteoglycans which constitute the neointimal tissue and the process usually takes up to 6 months, after which further luminal loss is minimal (Wieneke et al*.,* 1999, Sousa et al*.,* 2005). Intimal hyperplasia is found to be present at increasing thicknesses following injury and lacerations to the internal elastic lamina (IEL), the media, external elastic lamina (EEL) and adventitia (Wieneke et al*.,* 1999; Lowe et al*.,* 2002). An experimental study carried out in pigs identified the degree of injury caused by the implantation of a stent as an independent determinant for estimating the thickness of restenotic growth (Schwartz & Holmes 1994). Consistently, Gunn defined an Injury Score system that determined the degree of injury according to the angle of the IEL at the point of strut contact, the rupture of the IEL or, for extreme cases, rupture of EEL. Gunn applied this scoring system to categorize injury arising from the deployment of a stent in a porcine model (Gunn et al., 2002). The degree of vessel injury is therefore a major determining factor for in-stent restenosis and consequently a key design consideration for stents. In the context of stent optimisation using numerical modelling techniques, the design objective must therefore be to minimise the stress level in the arterial wall following stent deployment (Lally et al., 2005, Holzapfel et al., 2005a).

Several factors are involved in the modulation of VSMC phenotype from a quiescent to synthetic phenotype, including endothelial damage and denudation during stent deployment which is followed by adhesion of thrombocytes which express mitogenic chemokines and result in the chemotactic migration and proliferation of VSMC towards the lumen. Nevertheless, mitogens are not the only factor involved in the phenotypic modulation and activation of medial VSMC. For example, exogenously added fibroblast growth factor (FGF) increases VSMC proliferation in injured arteries, whereas it does not influence VSMC proliferation in uninjured arteries (Lindner & Reidy, 1991; Reidy & Lindner 1991). This observation suggests that other changes related to injury within the vessel may also be involved in the regulation of VSMC activation. In this context, the extracellular matrix (ECM) changes following vessel injury seem to be key regulators of VSMC phenotype and activation. Thyberg et al. (1997) showed that the medial VSMC in injured rat carotid arteries with a synthetic phenotype were enclosed by an incomplete basement membrane compared to normal arteries. These cells were found to migrate into the intima via holes in the internal elastic lamina and to form the neointimal tissue. Ultimately the

The cytokines produced by the inflammatory cells not only serve as mitogens for VSMC but also upregulate synthesis of extracellular matrix by the synthetic VSMC (Wieneke et al*.,* 1999;

In addition to the stresses induced within the arterial wall and the resulting mechanical injury, flow field perturbations due to stent implantation have also been found to influence the degree to which thrombocytes are recruited and their adhesion to the arterial wall. Specifically, it has been shown that a higher degree of thrombocyte aggregation occurs in locations where the flow field is directed toward the arterial wall rather than away from the wall (Duraiswamy et al*.,* 2005). In addition, stagnant flow patterns adjacent to stent struts, particularly low shear stress, has been found to trigger the recruited inflammatory cells into

The altered solid mechanical environment following stent deployment also governs the inflammatory and remodelling response. The stent induced lesions are invaded by VSMC with mainly a synthetic phenotype. These cells produce extracellular matrix (ECM) components such as collagen, elastin and proteoglycans which constitute the neointimal tissue and the process usually takes up to 6 months, after which further luminal loss is minimal (Wieneke et al*.,* 1999, Sousa et al*.,* 2005). Intimal hyperplasia is found to be present at increasing thicknesses following injury and lacerations to the internal elastic lamina (IEL), the media, external elastic lamina (EEL) and adventitia (Wieneke et al*.,* 1999; Lowe et al*.,* 2002). An experimental study carried out in pigs identified the degree of injury caused by the implantation of a stent as an independent determinant for estimating the thickness of restenotic growth (Schwartz & Holmes 1994). Consistently, Gunn defined an Injury Score system that determined the degree of injury according to the angle of the IEL at the point of strut contact, the rupture of the IEL or, for extreme cases, rupture of EEL. Gunn applied this scoring system to categorize injury arising from the deployment of a stent in a porcine model (Gunn et al., 2002). The degree of vessel injury is therefore a major determining factor for in-stent restenosis and consequently a key design consideration for stents. In the context of stent optimisation using numerical modelling techniques, the design objective must therefore be to minimise the stress level in the arterial wall following stent deployment

Several factors are involved in the modulation of VSMC phenotype from a quiescent to synthetic phenotype, including endothelial damage and denudation during stent deployment which is followed by adhesion of thrombocytes which express mitogenic chemokines and result in the chemotactic migration and proliferation of VSMC towards the lumen. Nevertheless, mitogens are not the only factor involved in the phenotypic modulation and activation of medial VSMC. For example, exogenously added fibroblast growth factor (FGF) increases VSMC proliferation in injured arteries, whereas it does not influence VSMC proliferation in uninjured arteries (Lindner & Reidy, 1991; Reidy & Lindner 1991). This observation suggests that other changes related to injury within the vessel may also be involved in the regulation of VSMC activation. In this context, the extracellular matrix (ECM) changes following vessel injury seem to be key regulators of VSMC phenotype and activation. Thyberg et al. (1997) showed that the medial VSMC in injured rat carotid arteries with a synthetic phenotype were enclosed by an incomplete basement membrane compared to normal arteries. These cells were found to migrate into the intima via holes in the internal elastic lamina and to form the neointimal tissue. Ultimately the

Babapulle and Eisenberg, 2002; Welt et al*.,* 2002; Mitra et al*.,* 2006).

their activated states (Kroll et al*.,* 1996; Moazzam et al*.,* 1997).

(Lally et al., 2005, Holzapfel et al., 2005a).

VSMC resumed a contractile phenotype as the neointima reached its final size with development of a complete basement membrane. Based on these observations Thyberg et al., (1997) suggested that laminin and other basement membrane components promote differentiation of VSMC towards a quiescent and contractile phenotype whereas their degradation leads into VSMC dedifferentiation and activation. Consistently, several studies have shown the role of collagen type IV, a major component of ECM representing 50% of all basement membrane proteins, in promoting restoration of VSMC to a contractile and quiescent phenotype (Hirose et al., 1999; Aguilera et al., 2003). In addition, exposing VSMC to mechanical loading has been shown to upregulate matrix metalloproteinase (MMP) synthesis by VSMC and mechanical injury upregulates MMP-2 production which is a major proteinase of the basement membrane (James et al.; 1993; Bendeck et al. 1994; Southgate et al., 1996; George et al., 1997) and so does mechanical stretch (Asanoma et al., 2002; Grote et al., 2003). By degrading ECM, MMPs are therefore key regulators of the onset and progression of in-stent restenosis, since they can regulate VSMC phenotype and consequently their behaviour i.e. migration and proliferation.

Finally, it should be noted that the origin of VSMC that accumulate in the neointima in vascular diseases such as in-stent restenosis remains controversial. These cells are a highly heterogeneous cell population with different characteristics and markers, and distinct phenotypes in physiological and pathological conditions. Although, early research on the pathophysiology of in stent-restenosis presents evidence indicating that these cells originate in the host artery (Edelman et al*.,* 1998), several more recent studies have reported a role for bone marrow-derived progenitor cells in vascular maintenance and repair. Moreover, bone marrow-derived smooth muscle progenitor cells have been detected in human atherosclerotic tissue as well as in *in vivo* mouse models of vascular disease. However, it is not clear whether smooth muscle progenitor cells can be regarded as a 'friend' or 'foe' in neointima formation (van Oostrom er al., 2009). The relationship of circulating progenitor cells during stent deployment to the subsequent development of in-stent restenosis has also been evaluated. Bone-marrow- and neural-crest-derived cells, the most dendritic cells, have been found to be consistently present in in-stent restenosis, whilst α-smooth muscle actin positive cells constitute the largest intimal cell pool (Skowasch et al., 2003). Patients with restenosis also have higher numbers of subpopulations of endothelial progenitor cells incorporated into endothelial cells when compared with controls (Pelliccia et al., 2010). Cleary the role of intimal cells and progenitor cells in in-stent restenosis remains to be further elucidated and numerical modelling, and in particular mechanobiological modelling, may provide insights in this area.

## **3. Numerical modelling as a means to reduce stent induced injury**

#### **3.1 Stress/strain analyses of stenting**

In addition to being cost effective, computational models often offer the only solution to address some of the important challenges influencing stent design, such as the estimation of stresses induced in the vessel wall and therefore the degree of vascular injury. Several different computational models of stent deployment have been developed in recent years. These models have improved our knowledge on the mechanics of stent-artery interaction (Migliavacca et al., 2002; Wang et al., 2006; Zahedmanesh et al*.,* 2010) and the influence of several different variables of stent geometry such as the influence of stent strut thickness

Vascular Stent Design Optimisation Using Numerical Modelling Techniques 243

investigated the mechanical response of stents using FEM and have suggested different strategies for their simulation (Lee et al*.,* 1992, Rogers et al*.,* 1999, Auricchio et al*.,* 2001, Prendergast et al*.,* 2003, Holzapfel et al*.,* 2005a, Lally et al*.,* 2005, Migliavacca et al*.,* 2002, 2005, 2007, Wang et al*.,* 2006, Gijsen et al*.,* 2008). Given the difficulties involved in construction of the model geometry and the complex contact problem involved in the interaction of a balloon, stent and artery, many simplified methods have been used to model the complex mechanics of stent deployment. Balloons used for stent deployment are initially in a folded configuration. As the balloon unfolds it appears highly compliant, however, as its unfolded shape is reached the balloon becomes highly noncompliant. This complex procedure of balloon unfolding is difficult and very computationally expensive to model. Four main strategies have been used in the literature for numerically modelling balloon expansion of stents which include, (i) direct application of a uniform pressure to the stent luminal surface (Dumoulin & Cochelin 2000; Migliavacca et al*.,* 2005; De Beule et al*.,* 2006; Early et al*.,* 2008), (ii) a rigid cylinder expanded by application of radial displacement (Hall & Kasper, 2006; Takashima et al*.,* 2007; Wu et al*.,* 2007), (iii) stent deployment using a folded balloon model (De Beule et al*.,* 2008; Gervaso et al*.,* 2008; Mortier et al., 2010) and (iiii) pressurisation of simple elastic cylinders with hyperelastic material properties neglecting

In a recent study using FE simulation Zahedmanesh et al. (2010) presented a method to create a folded balloon model and utilised the method to numerically model the accurate deployment of a stent in a realistic geometry of an atherosclerotic human coronary artery. Stent deployment is commonly modelled by applying an increasing pressure to the stent, thereby neglecting the balloon and reducing the computational cost and complicated contact between the balloon, stent and artery. This method was compared to the realistic balloon expansion simulation to fully elucidate the limitations of this more simplified procedure. The results illustrated that inclusion of a realistic balloon model is essential for accurate modelling of stent deformation and stent stresses. An alternative balloon simulation procedure was also presented however, which overcame many of the limitations of the applied pressure approach by using elements which restrained the stent as the desired diameter was achieved (Zahedmanesh et al., 2010). This study showed that direct application of pressure to the stent inner surface may be used as an optimal modelling strategy to estimate the stresses in the vessel wall using these restraining elements and hence offer a very efficient alternative approach to numerically modelling stent deployment within complex arterial geometries.

The aforementioned advances in computational modelling when applied to the analysis of the mechanical interaction between stents and the vessel wall provide a robust and efficient tool for stent design optimisation. The models can quantitatively assess the risk of vessel injury by different stents in the early design phase and hence minimise in-stent restenosis in

The global biological response of vessels to the biomechanical perturbation caused by stent implantation emerges at the tissue level as excessive luminal ingrowth. However, the tissue level response stems from the dynamic changes which occur in the micro-environment of cells deep at the cell level. Cellular behaviours such as differentiation, proliferation, migration, protein and chemokine synthesis and cell death are influenced by the changes in

the balloon folds (Ju et al*.,* 2008; Kiousis et al*.,* 2009).

**3.2 Mechanobiological models and stenting** 

the longer term.

(Timmins et al., 2007; Zahedmanesh & Lally 2009), plaque composition (Pericevic et al., 2009) and bending in stented peripheral arteries (Early et al., 2009). Balloon expandable stents and self expandable stents have been compared in terms of the level of stresses they induce within the arterial wall and hence the risk of arterial injury using finite element (FE) models (Migliavacca et al., 2004) whilst a number of studies have also been dedicated to investigating hemodynamic related factors in stent design and performance (Wentzel et al., 2000; Wentzel et al., 2001; LaDisa et al., 2006; Duraiswamy et al., 2007; Pant et al., 2010).

One important advantage of computational models of stent deployment over *in-vivo* studies is that they enable the influence of the mechanical parameters of interest to be studied in isolation. Due to the several complex and intertwined biological, chemical and mechanical factors involved *in-vivo*, it is often difficult to associate the outcome of an *in-vivo* trial with one specific mechanical factor. A good example of this is the influence of stent strut thickness on in-stent restenosis. In recent years, several clinical trials have identified stent strut thickness as an independent predictor of restenosis (Kastrati et al*.,* 2001; Briguori et al*.,* 2002; Pache et al*.,* 2003). A clear conclusion from the many clinical studies on stent strut thickness is that stents with thinner struts have a lower restenosis rate, consequently, most of the current generation of stents are produced with thinner struts using high strength materials such as cobalt–chromium alloys (Morton et al*.,* 2004). The ISAR-STEREO clinical trial focussed on the influence of stent strut thickness and compared the restenosis outcome for two stents with the same design but different strut thickness (Kastrati et al*.,* 2001). Although the study highlights the importance of stent strut thickness, it does not clearly elucidate the role and significance of the mechanism by which stent strut thickness could lead to the higher restenosis rate.

From a mechanical perspective the effect of stent strut thickness can be twofold: (i) from a solid mechanical viewpoint strut thickness would influence the stresses induced in the artery during stent deployment and recoil, and (ii) from a hemodynamic viewpoint strut thickness could influence blood flow perturbations. *In-vitro* studies cannot address each of these factors in isolation whilst *in vivo* several biological factors are also involved, such as the higher metal surface exposed to blood flow in thicker strut stents to which platelets can adhere and produce mitogenic growth factors. In contrast, computational models enable each different parameter involved in such a complex process to be studied in isolation. For instance, Duraiswamy et al*.,* (2007) studied the influence of stent strut thickness from a hemodynamics perspective and quantitatively showed that thicker stent struts lead to significantly larger recirculation zones and altered shear stress patterns in the vicinity of struts which can contribute to restenosis. In this context, to further elucidate the influence of stent strut thickness on the vessel wall stresses Zahedmanesh & Lally developed FE simulations of stent deployment procedures and showed that stents with thicker struts induce higher chronic stresses within the vessel wall and also pose a higher risk of injury in the vessel during expansion (Zahedmanesh & Lally 2009). Together, these results elucidate the role of the mechanical environment in the lower restenosis rates observed when using thin strut stents compared to thick strut stents as reported by such clinical trials as the ISAR-STEREO, (Kastrati et al., 2001).

Stent strut thickness is just one of the many factors involved in stent design and the use of finite element method (FEM) is not limited to this factor. FEM can be utilised to study a wide range of design parameters in order to reduce arterial injury. Several studies have

(Timmins et al., 2007; Zahedmanesh & Lally 2009), plaque composition (Pericevic et al., 2009) and bending in stented peripheral arteries (Early et al., 2009). Balloon expandable stents and self expandable stents have been compared in terms of the level of stresses they induce within the arterial wall and hence the risk of arterial injury using finite element (FE) models (Migliavacca et al., 2004) whilst a number of studies have also been dedicated to investigating hemodynamic related factors in stent design and performance (Wentzel et al., 2000; Wentzel et al., 2001; LaDisa et al., 2006; Duraiswamy et al., 2007; Pant et al., 2010).

One important advantage of computational models of stent deployment over *in-vivo* studies is that they enable the influence of the mechanical parameters of interest to be studied in isolation. Due to the several complex and intertwined biological, chemical and mechanical factors involved *in-vivo*, it is often difficult to associate the outcome of an *in-vivo* trial with one specific mechanical factor. A good example of this is the influence of stent strut thickness on in-stent restenosis. In recent years, several clinical trials have identified stent strut thickness as an independent predictor of restenosis (Kastrati et al*.,* 2001; Briguori et al*.,* 2002; Pache et al*.,* 2003). A clear conclusion from the many clinical studies on stent strut thickness is that stents with thinner struts have a lower restenosis rate, consequently, most of the current generation of stents are produced with thinner struts using high strength materials such as cobalt–chromium alloys (Morton et al*.,* 2004). The ISAR-STEREO clinical trial focussed on the influence of stent strut thickness and compared the restenosis outcome for two stents with the same design but different strut thickness (Kastrati et al*.,* 2001). Although the study highlights the importance of stent strut thickness, it does not clearly elucidate the role and significance of the mechanism by which stent strut thickness could

From a mechanical perspective the effect of stent strut thickness can be twofold: (i) from a solid mechanical viewpoint strut thickness would influence the stresses induced in the artery during stent deployment and recoil, and (ii) from a hemodynamic viewpoint strut thickness could influence blood flow perturbations. *In-vitro* studies cannot address each of these factors in isolation whilst *in vivo* several biological factors are also involved, such as the higher metal surface exposed to blood flow in thicker strut stents to which platelets can adhere and produce mitogenic growth factors. In contrast, computational models enable each different parameter involved in such a complex process to be studied in isolation. For instance, Duraiswamy et al*.,* (2007) studied the influence of stent strut thickness from a hemodynamics perspective and quantitatively showed that thicker stent struts lead to significantly larger recirculation zones and altered shear stress patterns in the vicinity of struts which can contribute to restenosis. In this context, to further elucidate the influence of stent strut thickness on the vessel wall stresses Zahedmanesh & Lally developed FE simulations of stent deployment procedures and showed that stents with thicker struts induce higher chronic stresses within the vessel wall and also pose a higher risk of injury in the vessel during expansion (Zahedmanesh & Lally 2009). Together, these results elucidate the role of the mechanical environment in the lower restenosis rates observed when using thin strut stents compared to thick strut stents as reported by such clinical trials as the ISAR-

Stent strut thickness is just one of the many factors involved in stent design and the use of finite element method (FEM) is not limited to this factor. FEM can be utilised to study a wide range of design parameters in order to reduce arterial injury. Several studies have

lead to the higher restenosis rate.

STEREO, (Kastrati et al., 2001).

investigated the mechanical response of stents using FEM and have suggested different strategies for their simulation (Lee et al*.,* 1992, Rogers et al*.,* 1999, Auricchio et al*.,* 2001, Prendergast et al*.,* 2003, Holzapfel et al*.,* 2005a, Lally et al*.,* 2005, Migliavacca et al*.,* 2002, 2005, 2007, Wang et al*.,* 2006, Gijsen et al*.,* 2008). Given the difficulties involved in construction of the model geometry and the complex contact problem involved in the interaction of a balloon, stent and artery, many simplified methods have been used to model the complex mechanics of stent deployment. Balloons used for stent deployment are initially in a folded configuration. As the balloon unfolds it appears highly compliant, however, as its unfolded shape is reached the balloon becomes highly noncompliant. This complex procedure of balloon unfolding is difficult and very computationally expensive to model. Four main strategies have been used in the literature for numerically modelling balloon expansion of stents which include, (i) direct application of a uniform pressure to the stent luminal surface (Dumoulin & Cochelin 2000; Migliavacca et al*.,* 2005; De Beule et al*.,* 2006; Early et al*.,* 2008), (ii) a rigid cylinder expanded by application of radial displacement (Hall & Kasper, 2006; Takashima et al*.,* 2007; Wu et al*.,* 2007), (iii) stent deployment using a folded balloon model (De Beule et al*.,* 2008; Gervaso et al*.,* 2008; Mortier et al., 2010) and (iiii) pressurisation of simple elastic cylinders with hyperelastic material properties neglecting the balloon folds (Ju et al*.,* 2008; Kiousis et al*.,* 2009).

In a recent study using FE simulation Zahedmanesh et al. (2010) presented a method to create a folded balloon model and utilised the method to numerically model the accurate deployment of a stent in a realistic geometry of an atherosclerotic human coronary artery. Stent deployment is commonly modelled by applying an increasing pressure to the stent, thereby neglecting the balloon and reducing the computational cost and complicated contact between the balloon, stent and artery. This method was compared to the realistic balloon expansion simulation to fully elucidate the limitations of this more simplified procedure. The results illustrated that inclusion of a realistic balloon model is essential for accurate modelling of stent deformation and stent stresses. An alternative balloon simulation procedure was also presented however, which overcame many of the limitations of the applied pressure approach by using elements which restrained the stent as the desired diameter was achieved (Zahedmanesh et al., 2010). This study showed that direct application of pressure to the stent inner surface may be used as an optimal modelling strategy to estimate the stresses in the vessel wall using these restraining elements and hence offer a very efficient alternative approach to numerically modelling stent deployment within complex arterial geometries.

The aforementioned advances in computational modelling when applied to the analysis of the mechanical interaction between stents and the vessel wall provide a robust and efficient tool for stent design optimisation. The models can quantitatively assess the risk of vessel injury by different stents in the early design phase and hence minimise in-stent restenosis in the longer term.

#### **3.2 Mechanobiological models and stenting**

The global biological response of vessels to the biomechanical perturbation caused by stent implantation emerges at the tissue level as excessive luminal ingrowth. However, the tissue level response stems from the dynamic changes which occur in the micro-environment of cells deep at the cell level. Cellular behaviours such as differentiation, proliferation, migration, protein and chemokine synthesis and cell death are influenced by the changes in

Vascular Stent Design Optimisation Using Numerical Modelling Techniques 245

dedifferentiation and activation of medial VSMC. Here, a novel mechanistic model is presented which quantitatively captures the processes involved in the degradation and activation of VSMC following stent implantation. The model enables quantitative investigation of the role of stent induced stresses, ECM degradation by MMPs and the subsequent response of VSMC. It can therefore provide insight into the mechanisms involved in the development of in-stent restenosis and it can also be used as a robust and efficient tool to improve the mechanical behaviour of stents in the design cycle. A significant novelty of the presented model is the combination of the FEM with a lattice free ABM which

A mechanobiological modelling framework was developed which comprises of two main coupled modules, (i) a module based on FEM that quantifies von Mises stress to determine the level of arterial damage due to stent deployment and (ii) a biological modelling module based on a lattice free ABM that simulates the key responses of VSMC growth, i.e. migration, proliferation, and ECM degradation and synthesis, in the arterial wall in

response to the stent induced damage quantified using the FE analysis, see Figure 2.

Fig. 2. Overall schematic of the mechanobiological model of in-stent restenosis

holds significant advantages over the lattice based CA models.

**4.2 Materials and methods**

**4.2.1 Model overview**

the micro-environmental factors such as extracellular matrix, chemicals, and forces and combine to result in complex responses at the tissue level. This intrinsic multi-scale behaviour of biological systems necessitates a multi scale modelling approach. Therefore, multiscale approaches utilising discrete methods such as cellular automata (CA) (Masselot & Chopard 1998, Ilachinski 2001) and agent based models (ABM) (Wooldridge 2002; Walker et al*.,* 2004) have recently received particular attention for modelling in-stent restenosis.

One prominent example is the multiscale modelling platform developed within the COAST (complex automata simulation technique) project (www.complex-automata.org) which is funded by the European Commision (Evans et al., 2008). The project takes a multiscale and discrete approach towards modelling in-stent restenosis where the growth response of VSMC within the arterial wall is modelled based on the value of wall shear stress (WSS) due to blood flow, the stress level experienced by VSMC within the arterial wall and the concentration of the anti-proliferative drugs diffused from drug eluting stents (Caiazzo et al*.,* 2009). Their model has also been applied to investigate the influence of stent strut size and shape where their simulation results suggest that the growth of the restenotic lesion is strongly dependent on the stent strut cross-sectional profile consistent with the outcome of clinical and animal models (Tahir et al*.,* 2011).

In addition to the approach adopted by the COAST project which is mainly based on discrete methods, a hybrid approach can also be adopted by combining continuum methods such as FEM and discrete methods. FEM is particularly advantageous given that it has proved to be a robust method for quantification of arterial stresses and has been successfully utilised for patient specific modelling of stent-artery interaction (Zahedmanesh et al., 2010, Gijsen et al., 2008). As an example, Boyle et al., (2010) used FE simulations of stent deployment to quantify damage within a stented artery and subsequently used a CA approach to simulate the biological response of the artery to this stent induced damage quantified by the FE model (Boyle et al*.,* 2010, Boyle et al., 2011).

Although the differences between CA and ABM are marginal, the main difference is that a lattice needs to be defined for CA while ABM can be lattice free, meaning that cells can be at any location in the computational domain. This location is usually determined by solving either kinematic or dynamic equations of motion for each individual cell. Hence ABM can yield more realistic results given that no restriction is imposed on the location of the cells in comparison to CA where the cells can only move through certain predefined lattice points and results can therefore be highly dependent on the lattice structure and lattice point density. As a result, a hybrid model utilising ABM, as opposed to CA, and FEM can potentially provide greater simulation capabilities and produce more realistic results. Therefore, a novel hybrid model to simulate in-stent restenosis, using coupled ABM and FEM, will now be presented by the authors. This novel approach has recently been applied to model vascularisation in tissue engineered blood vessels (Zahedmanesh et al*.,* 2011) and is adapted and applied here to model in-stent restenosis.

## **4. A multi-scale mechanobiological model of in-stent restenosis using coupled agent based models and the finite element method**

#### **4.1 Model background**

As previously discussed, changes occurring within the arterial wall, particularly ECM changes and degradation of basement membrane around VSMC, play a key role in the dedifferentiation and activation of medial VSMC. Here, a novel mechanistic model is presented which quantitatively captures the processes involved in the degradation and activation of VSMC following stent implantation. The model enables quantitative investigation of the role of stent induced stresses, ECM degradation by MMPs and the subsequent response of VSMC. It can therefore provide insight into the mechanisms involved in the development of in-stent restenosis and it can also be used as a robust and efficient tool to improve the mechanical behaviour of stents in the design cycle. A significant novelty of the presented model is the combination of the FEM with a lattice free ABM which holds significant advantages over the lattice based CA models.

## **4.2 Materials and methods**

## **4.2.1 Model overview**

244 Applied Biological Engineering – Principles and Practice

the micro-environmental factors such as extracellular matrix, chemicals, and forces and combine to result in complex responses at the tissue level. This intrinsic multi-scale behaviour of biological systems necessitates a multi scale modelling approach. Therefore, multiscale approaches utilising discrete methods such as cellular automata (CA) (Masselot & Chopard 1998, Ilachinski 2001) and agent based models (ABM) (Wooldridge 2002; Walker et al*.,* 2004) have recently received particular attention for modelling in-stent restenosis.

One prominent example is the multiscale modelling platform developed within the COAST (complex automata simulation technique) project (www.complex-automata.org) which is funded by the European Commision (Evans et al., 2008). The project takes a multiscale and discrete approach towards modelling in-stent restenosis where the growth response of VSMC within the arterial wall is modelled based on the value of wall shear stress (WSS) due to blood flow, the stress level experienced by VSMC within the arterial wall and the concentration of the anti-proliferative drugs diffused from drug eluting stents (Caiazzo et al*.,* 2009). Their model has also been applied to investigate the influence of stent strut size and shape where their simulation results suggest that the growth of the restenotic lesion is strongly dependent on the stent strut cross-sectional profile consistent with the outcome of

In addition to the approach adopted by the COAST project which is mainly based on discrete methods, a hybrid approach can also be adopted by combining continuum methods such as FEM and discrete methods. FEM is particularly advantageous given that it has proved to be a robust method for quantification of arterial stresses and has been successfully utilised for patient specific modelling of stent-artery interaction (Zahedmanesh et al., 2010, Gijsen et al., 2008). As an example, Boyle et al., (2010) used FE simulations of stent deployment to quantify damage within a stented artery and subsequently used a CA approach to simulate the biological response of the artery to this stent induced damage

Although the differences between CA and ABM are marginal, the main difference is that a lattice needs to be defined for CA while ABM can be lattice free, meaning that cells can be at any location in the computational domain. This location is usually determined by solving either kinematic or dynamic equations of motion for each individual cell. Hence ABM can yield more realistic results given that no restriction is imposed on the location of the cells in comparison to CA where the cells can only move through certain predefined lattice points and results can therefore be highly dependent on the lattice structure and lattice point density. As a result, a hybrid model utilising ABM, as opposed to CA, and FEM can potentially provide greater simulation capabilities and produce more realistic results. Therefore, a novel hybrid model to simulate in-stent restenosis, using coupled ABM and FEM, will now be presented by the authors. This novel approach has recently been applied to model vascularisation in tissue engineered blood vessels (Zahedmanesh et al*.,* 2011) and

**4. A multi-scale mechanobiological model of in-stent restenosis using** 

As previously discussed, changes occurring within the arterial wall, particularly ECM changes and degradation of basement membrane around VSMC, play a key role in the

**coupled agent based models and the finite element method** 

clinical and animal models (Tahir et al*.,* 2011).

quantified by the FE model (Boyle et al*.,* 2010, Boyle et al., 2011).

is adapted and applied here to model in-stent restenosis.

**4.1 Model background** 

A mechanobiological modelling framework was developed which comprises of two main coupled modules, (i) a module based on FEM that quantifies von Mises stress to determine the level of arterial damage due to stent deployment and (ii) a biological modelling module based on a lattice free ABM that simulates the key responses of VSMC growth, i.e. migration, proliferation, and ECM degradation and synthesis, in the arterial wall in response to the stent induced damage quantified using the FE analysis, see Figure 2.

Fig. 2. Overall schematic of the mechanobiological model of in-stent restenosis

Vascular Stent Design Optimisation Using Numerical Modelling Techniques 247

As a first approach, damage/injury level within the stented artery was quantified with a continuous linear range of 0 to 1. A value of 1 was assigned for the damage in the elements where von Mises stresses exceeded 150kPa. This is a simplified assumption which represents a very first approach to modelling damage accumulation within the artery. This value was chosen given that the intimal layer in human coronary arteries has been reported to have an ultimate tensile strength of 394±223 kPa in the circumferential direction whilst the human medial layer has an ultimate tensile strength of 446±194kPa (Holzapfel et al., 2005b). Therefore, 150kPa represents the lowest value of ultimate tensile strength of these tissues before failure, i.e. one standard deviation below the mean for intimal tissue, and it is therefore deemed a suitable stress level for maximal injury. The authors are currently developing a more sophisticated damage model which will provide a more accurate measure of damage accumulation by defining damage as a continuous function of stent induced stress rather than simply using a threshold stress value. It should be noted that the ABM-FE model presented here can incorporate any range of damage models, with damage accumulation calibrated against clinical or experimental data, such as that proposed by

An agent based model of an artery was constructed with VSMC randomly distributed throughout the artery domain. Following the FE analysis the values of the arterial damage at each element of the FE model were exported to the ABM module where the response of VSMC to damage was modelled similar to the approach previously outlined in

The damage induced in the vessel wall due to high stresses upregulates MMP synthesis by VSMC which consequently causes degradation of the ECM. Initially VSMC are in a quiescent and contractile phenotype, degradation of ECM modulates their differentiation toward a synthetic phenotype at the site of damage which ultimately triggers their migration and proliferation, i.e. cells are only allowed to migrate and proliferate when their ECM is degraded to lower than half of the value of ECM in the healthy arteries which for collagen is a value of approximately 3.1×10-4 μg/cell (Hahn et al., 2007). In the meantime ECM cleavage and degradation due to MMP upregulation reduces the value of the initially accumulated damage, and hence functions as a negative feedback mechanism leading to recession of the neointimal growth rate. In addition, the proliferating VSMC synthesise ECM and gradually switch back to the contractile phenotype once their value of ECM reaches normal values, see Figure 1. A summary of the relevant parameters used in the ABM and

**Parameter Value Reference** 

(Kim et al., 2009; Okuno et al., 2002)

1981)

0.0006 ) <sup>=</sup> 6hour (pg/cell) MMP(

where dmg is damage value with a range of 0 to 1.

degradation rate 50 pg collagen/pg MMP/hour (Welgus et al., 1980,

by VSMC ( 16.3 dmg) 1+3462 <sup>e</sup>

**4.2.3 Damage/injury quantification** 

Boyle et al, 2011.

**4.2.4 Agent based model**

Zahedmanesh et al., (2011).

their values is provided in Table 2.

MMP synthesis

ECM

The simulation starts in the FE module where the value of the initial stent induced damage is quantified and is transferred to the ABM where the growth of VSMC is simulated. A customwritten routine was developed using python programming language to enable communication between the FE software Abaqus (Simulia, Providence, RI, USA) and the agent-based modelling framework BREVE (www.Spiderland.org). The ABM was programmed using the STEVE language specific to the BREVE agent-based modelling framework.

## **4.2.2 Finite element model**

An axisymmetric hyperelastic FE model of an artery was developed and the influence of stent struts was modelled by application of a radial displacement of 1mm to the luminal surface of the artery where the stent strut contacts the artery, see Figure 3. A pressure of 120 mmHg was applied to the luminal surface to take the systolic arterial blood pressure into account while the two ends of the artery were longitudinally tethered. The model is composed of 3,040 equilateral rectangular axisymmetric elements (Abaqus type CAX4RH). The artery geometry was modelled as 8mm long with a thickness of 0.673mm and a luminal diameter of 4.18mm and was discretised by 190 elements longitudinally and 16 elements radially. This mesh density was chosen based on mesh sensitivity studies.

Fig. 3. Axisymmetric representation of the model

The following Ogden hyperelastic equation was used to model the stress-strain response of the artery (Ogden, 1972).

$$\overline{\mathbf{U}} = \sum\_{i=1}^{3} \frac{2\mu\_i}{\mathbf{u}\_i^2} (\lambda\_1^{-\alpha\_i} + \lambda\_2^{-\alpha\_i} + \lambda\_3^{-\alpha\_i} - 3) \tag{1}$$

Where, U� is the deviatoric strain energy density, λi denotes the deviatoric principle stretches and μi and αi are the hyperelastic constants, see table 1.


Table 1. Coefficients of the Ogden hyperelastic constitutive models (Zahedmanesh & Lally 2009, Zahedmanesh et al., 2011)

## **4.2.3 Damage/injury quantification**

246 Applied Biological Engineering – Principles and Practice

The simulation starts in the FE module where the value of the initial stent induced damage is quantified and is transferred to the ABM where the growth of VSMC is simulated. A customwritten routine was developed using python programming language to enable communication between the FE software Abaqus (Simulia, Providence, RI, USA) and the agent-based modelling framework BREVE (www.Spiderland.org). The ABM was programmed using the STEVE

An axisymmetric hyperelastic FE model of an artery was developed and the influence of stent struts was modelled by application of a radial displacement of 1mm to the luminal surface of the artery where the stent strut contacts the artery, see Figure 3. A pressure of 120 mmHg was applied to the luminal surface to take the systolic arterial blood pressure into account while the two ends of the artery were longitudinally tethered. The model is composed of 3,040 equilateral rectangular axisymmetric elements (Abaqus type CAX4RH). The artery geometry was modelled as 8mm long with a thickness of 0.673mm and a luminal diameter of 4.18mm and was discretised by 190 elements longitudinally and 16 elements

The following Ogden hyperelastic equation was used to model the stress-strain response of

<sup>2</sup><sup>μ</sup> U (<sup>λ</sup> λ λ 3)

Where, U� is the deviatoric strain energy density, λi denotes the deviatoric principle stretches

�� (Pa) -1,231,144.96 �� (Pa) 785,118.59 �� (Pa) 453,616.46 �� 16.59 �� 16.65 �� 16.50 Table 1. Coefficients of the Ogden hyperelastic constitutive models (Zahedmanesh & Lally

iii

(1)

i ααα 2 123

language specific to the BREVE agent-based modelling framework.

radially. This mesh density was chosen based on mesh sensitivity studies.

3

i 1 i

α

Hyperelastic constants Value

Fig. 3. Axisymmetric representation of the model

and μi and αi are the hyperelastic constants, see table 1.

**4.2.2 Finite element model** 

the artery (Ogden, 1972).

2009, Zahedmanesh et al., 2011)

As a first approach, damage/injury level within the stented artery was quantified with a continuous linear range of 0 to 1. A value of 1 was assigned for the damage in the elements where von Mises stresses exceeded 150kPa. This is a simplified assumption which represents a very first approach to modelling damage accumulation within the artery. This value was chosen given that the intimal layer in human coronary arteries has been reported to have an ultimate tensile strength of 394±223 kPa in the circumferential direction whilst the human medial layer has an ultimate tensile strength of 446±194kPa (Holzapfel et al., 2005b). Therefore, 150kPa represents the lowest value of ultimate tensile strength of these tissues before failure, i.e. one standard deviation below the mean for intimal tissue, and it is therefore deemed a suitable stress level for maximal injury. The authors are currently developing a more sophisticated damage model which will provide a more accurate measure of damage accumulation by defining damage as a continuous function of stent induced stress rather than simply using a threshold stress value. It should be noted that the ABM-FE model presented here can incorporate any range of damage models, with damage accumulation calibrated against clinical or experimental data, such as that proposed by Boyle et al, 2011.

## **4.2.4 Agent based model**

An agent based model of an artery was constructed with VSMC randomly distributed throughout the artery domain. Following the FE analysis the values of the arterial damage at each element of the FE model were exported to the ABM module where the response of VSMC to damage was modelled similar to the approach previously outlined in Zahedmanesh et al., (2011).

The damage induced in the vessel wall due to high stresses upregulates MMP synthesis by VSMC which consequently causes degradation of the ECM. Initially VSMC are in a quiescent and contractile phenotype, degradation of ECM modulates their differentiation toward a synthetic phenotype at the site of damage which ultimately triggers their migration and proliferation, i.e. cells are only allowed to migrate and proliferate when their ECM is degraded to lower than half of the value of ECM in the healthy arteries which for collagen is a value of approximately 3.1×10-4 μg/cell (Hahn et al., 2007). In the meantime ECM cleavage and degradation due to MMP upregulation reduces the value of the initially accumulated damage, and hence functions as a negative feedback mechanism leading to recession of the neointimal growth rate. In addition, the proliferating VSMC synthesise ECM and gradually switch back to the contractile phenotype once their value of ECM reaches normal values, see Figure 1. A summary of the relevant parameters used in the ABM and their values is provided in Table 2.


Vascular Stent Design Optimisation Using Numerical Modelling Techniques 249

A significant area in the vicinity of stent strut showed stresses higher than the threshold stress value for damage and hence a damage value of 1 was automatically assigned to the associated elements. This damage was fully removed following two weeks due to

Fig. 5. Distribution of von Mises stresses (Pa) in the arterial wall following stent

Fig. 6. Damage accumulation in the artery following stent deployment and its reduction due

**Day 0** 

**Day 7** 

**Day 14** 

Following stent deployment, neointimal growth started due to degradation of ECM by MMPs which were upregulated due to the damage accumulation. Neointimal growth reached its maximum following 35 days when the stenosis size reached steady state, see

The alteration in the ECM distribution and value with time post stent deployment is shown in Figure 7 where ECM is initially degraded due to the damage accumulation and upregulation of MMPs. With the removal of damage and recession of the inflammation, new ECM is synthesised by VSMC, reaching the normal values of ECM in the healthy arteries

upregulation of MMPs, see Figure 6.

deployment.

to the healing response.

Figures 4 & 7.

following 100 days.


Table 2. Parameters used in the ABM module and their values.

## **4.3 Results**

The mechanobiological model captured the characteristic S-shaped neointimal growth response of arteries to stent deployment previously reported in *in-vivo* studies (Schwartz et al., 1996), see Figure 4. The growth curve comprised a dramatic increase in VSMC number shortly after stent deployment and a plateau region following stabilisation of the healing response. The value of arterial von Mises stresses due to stent deployment was quantified showing high stress concentrations where the stent strut contacted the artery, see Figure 5.

Fig. 4. Increase in the VSMC count in the model due to in-stent restenosis.

Set to ensure damage will be fully remove in 15 days

constraint)

(Kim et al. 1988; Schlumberger et al., 1991; Absood et al., 2004)

2011)

2011)

0.001 mm/hr (Zahedmanesh et al.,

**Parameter Value Reference** 

MMP Removal 0.0001pg MMP/element/hour (Mass balance

synthetic VSMC 35 hours (Zahedmanesh et al.,

The mechanobiological model captured the characteristic S-shaped neointimal growth response of arteries to stent deployment previously reported in *in-vivo* studies (Schwartz et al., 1996), see Figure 4. The growth curve comprised a dramatic increase in VSMC number shortly after stent deployment and a plateau region following stabilisation of the healing response. The value of arterial von Mises stresses due to stent deployment was quantified showing high stress concentrations where the stent strut contacted the artery, see Figure 5.

by MMPs 0.1/ pg MMP/hour

by VSMC 0.00899 pg collagen/hour/cell

Table 2. Parameters used in the ABM module and their values.

Fig. 4. Increase in the VSMC count in the model due to in-stent restenosis.

0 5 10 15 20 25

**Weeks**

0

100

200

300

**Increase in cell number**

400

500

600

Damage removal

ECM synthesis

Doubling time of

Maximum VSMC migration Speed:

**4.3 Results** 

A significant area in the vicinity of stent strut showed stresses higher than the threshold stress value for damage and hence a damage value of 1 was automatically assigned to the associated elements. This damage was fully removed following two weeks due to upregulation of MMPs, see Figure 6.

Fig. 5. Distribution of von Mises stresses (Pa) in the arterial wall following stent deployment.

Fig. 6. Damage accumulation in the artery following stent deployment and its reduction due to the healing response.

Following stent deployment, neointimal growth started due to degradation of ECM by MMPs which were upregulated due to the damage accumulation. Neointimal growth reached its maximum following 35 days when the stenosis size reached steady state, see Figures 4 & 7.

The alteration in the ECM distribution and value with time post stent deployment is shown in Figure 7 where ECM is initially degraded due to the damage accumulation and upregulation of MMPs. With the removal of damage and recession of the inflammation, new ECM is synthesised by VSMC, reaching the normal values of ECM in the healthy arteries following 100 days.

Vascular Stent Design Optimisation Using Numerical Modelling Techniques 251

significant within ECM and specifically collagen matrix which is the most abundant ECM constituent, making up more than 50% of the basement membrane (Monaco et al., 200). This hypothesis is also supported by comparison to *in-vivo* studies on injured arteries, where it has been shown that VSMC with synthetic phenotype in the injured arteries are encapsulated by an incomplete basement membrane (Thyberg et al., 1997). Whether this observed disruption of the basement membrane is caused by direct mechanical injury or it is due to the increased matrix degradation, it is clear from such *in-vivo* findings that ECM, and specifically the basement membrane, plays a key role in regulation of VSMC phenotype as

The presented model provides a quantitative evaluation of the ECM alterations occurring within the arterial wall following stent deployment and the resulting neointimal growth. In addition the multiscale mechanobiological model provides a platform for understanding the processes underlying the development of in-stent restenosis. The platform enables new hypotheses on the mechanisms of in-stent restenosis to be tested quantitatively and hence helps to generate key knowledge and insights into the pathophysiology of in-stent restenosis. Knowledge creation is a particular advantage of this modelling framework given that ABMs enable a fully mechanistic approach towards modelling the mechanisms involved in the development of in-stent restenosis. This strength of ABM also facilitates direct translation and incorporation of *in-vitro* and clinical data into the *in-silico* models of in-stent restenosis in a manner which is comprehensible for scientists from diverse backgrounds, such as biologists, clinicians and engineers. As such, ABMs facilitate communication and integration of investigators with diverse backgrounds for a more thorough analysis and understanding of biomedial challenges, which is a crucial requirement for today's multidisciplinary research in the biomedical field. In addition, combining the lattice free ABMs with FE simulations of stent deployment gives a new dimension to the ongoing research on modelling in-stent restenosis by integrating the proven capabilities of FEM in capturing the mechanics of stent-artery interaction with the added value of ABM for mechanistic modelling of the biological response of cells within

This model clearly has the potential to be used as a robust and efficient tool in the design phase of stents and can be developed further to include additional cell populations such as endothelial cells, the influence of various growth factors, and even drug or gene elution

Whilst stent optimisation studies have advanced considerably in the last 20 years by using numerical modelling techniques, the future of such studies lies in their ability to assess the biological response of the artery to the deployed stent along with the mechanical environment changes induced by the stent. The real power of these models will only be fully realised when inter-patient variability can be incorporated into the models, thereby generating similar data to clinical trials where the probability of stent success in a large population is determined rather than simply one clinical outcome. This can be achieved using patient-specific geometry and material properties in numerical models of stents and such data can currently be obtained from non-invasive medical imaging techniques (Creane et al., 2010). Variations in patient growth responses, and even genetic information can be

the main mechanism underlying the development of intimal hyperplasia.

arteries.

from the stent or stent degradation.

**5. Future directions**

Fig. 7. The development of neointimal tissue with time, (left) alterations of ECM due to degradation and also synthesis by activated VSMC, (right) VSMC growth and distribution.

#### **4.4 Conclusion**

Although in a relatively early stage of development, the mechanobiological model presented here successfully captures the key characteristics of the arterial response to stent deployment, specifically the neointimal growth. *In-vivo* studies on the development of intimal hyperplasia in patients due to vascular injury report an exponential increase in the number of neointimal VSMC with a peak in the proliferation rate occurring about two weeks post injury, followed by a reduction in the cell proliferation rate (Schwartz et al., 1996). This characteristic growth response is captured by the mechanobiological model where the cells initially increase at exponential rate followed by a cessation in the cell proliferation and lesion size, see Figure 4 & 7. Nevertheless, this response also depends on the intensity of the mechanical damage and hence it is necessary to further study how different stent designs and deployment parameters influence the development of in-stent restenosis. In this context, when the extent of vascular injury increases, causing laceration to the external elastic lamina and adventitia, the neointimal thickness significantly increases and could necessitate repeat surgical intervention (Wieneke et al., 1999). In addition, endothelial denudation and disruption is observed following stent deployment which has implications for in-stent restenosis given that endothelial cells synthesise nitric oxide which is directly implicated in inducing and maintaining the contractile and quiescent phenotype in VSMC (Lemson et al., 2000). It is therefore also necessary to study the influence of reendothelialisation following stent deployment and this will be addressed with further development of the model and inclusion of endothelial cells.

The presented model is based on the hypothesis that damage accumulation occurs within the ECM, given that ECM components bear the most significant part of the mechanical load. Clearly therefore, it is feasible to hypothesise that mechanical damage accumulation is most significant within ECM and specifically collagen matrix which is the most abundant ECM constituent, making up more than 50% of the basement membrane (Monaco et al., 200). This hypothesis is also supported by comparison to *in-vivo* studies on injured arteries, where it has been shown that VSMC with synthetic phenotype in the injured arteries are encapsulated by an incomplete basement membrane (Thyberg et al., 1997). Whether this observed disruption of the basement membrane is caused by direct mechanical injury or it is due to the increased matrix degradation, it is clear from such *in-vivo* findings that ECM, and specifically the basement membrane, plays a key role in regulation of VSMC phenotype as the main mechanism underlying the development of intimal hyperplasia.

The presented model provides a quantitative evaluation of the ECM alterations occurring within the arterial wall following stent deployment and the resulting neointimal growth. In addition the multiscale mechanobiological model provides a platform for understanding the processes underlying the development of in-stent restenosis. The platform enables new hypotheses on the mechanisms of in-stent restenosis to be tested quantitatively and hence helps to generate key knowledge and insights into the pathophysiology of in-stent restenosis. Knowledge creation is a particular advantage of this modelling framework given that ABMs enable a fully mechanistic approach towards modelling the mechanisms involved in the development of in-stent restenosis. This strength of ABM also facilitates direct translation and incorporation of *in-vitro* and clinical data into the *in-silico* models of in-stent restenosis in a manner which is comprehensible for scientists from diverse backgrounds, such as biologists, clinicians and engineers. As such, ABMs facilitate communication and integration of investigators with diverse backgrounds for a more thorough analysis and understanding of biomedial challenges, which is a crucial requirement for today's multidisciplinary research in the biomedical field. In addition, combining the lattice free ABMs with FE simulations of stent deployment gives a new dimension to the ongoing research on modelling in-stent restenosis by integrating the proven capabilities of FEM in capturing the mechanics of stent-artery interaction with the added value of ABM for mechanistic modelling of the biological response of cells within arteries.

This model clearly has the potential to be used as a robust and efficient tool in the design phase of stents and can be developed further to include additional cell populations such as endothelial cells, the influence of various growth factors, and even drug or gene elution from the stent or stent degradation.

## **5. Future directions**

250 Applied Biological Engineering – Principles and Practice

Fig. 7. The development of neointimal tissue with time, (left) alterations of ECM due to degradation and also synthesis by activated VSMC, (right) VSMC growth and distribution.

Although in a relatively early stage of development, the mechanobiological model presented here successfully captures the key characteristics of the arterial response to stent deployment, specifically the neointimal growth. *In-vivo* studies on the development of intimal hyperplasia in patients due to vascular injury report an exponential increase in the number of neointimal VSMC with a peak in the proliferation rate occurring about two weeks post injury, followed by a reduction in the cell proliferation rate (Schwartz et al., 1996). This characteristic growth response is captured by the mechanobiological model where the cells initially increase at exponential rate followed by a cessation in the cell proliferation and lesion size, see Figure 4 & 7. Nevertheless, this response also depends on the intensity of the mechanical damage and hence it is necessary to further study how different stent designs and deployment parameters influence the development of in-stent restenosis. In this context, when the extent of vascular injury increases, causing laceration to the external elastic lamina and adventitia, the neointimal thickness significantly increases and could necessitate repeat surgical intervention (Wieneke et al., 1999). In addition, endothelial denudation and disruption is observed following stent deployment which has implications for in-stent restenosis given that endothelial cells synthesise nitric oxide which is directly implicated in inducing and maintaining the contractile and quiescent phenotype in VSMC (Lemson et al., 2000). It is therefore also necessary to study the influence of reendothelialisation following stent deployment and this will be addressed with further

The presented model is based on the hypothesis that damage accumulation occurs within the ECM, given that ECM components bear the most significant part of the mechanical load. Clearly therefore, it is feasible to hypothesise that mechanical damage accumulation is most

development of the model and inclusion of endothelial cells.

**4.4 Conclusion** 

Whilst stent optimisation studies have advanced considerably in the last 20 years by using numerical modelling techniques, the future of such studies lies in their ability to assess the biological response of the artery to the deployed stent along with the mechanical environment changes induced by the stent. The real power of these models will only be fully realised when inter-patient variability can be incorporated into the models, thereby generating similar data to clinical trials where the probability of stent success in a large population is determined rather than simply one clinical outcome. This can be achieved using patient-specific geometry and material properties in numerical models of stents and such data can currently be obtained from non-invasive medical imaging techniques (Creane et al., 2010). Variations in patient growth responses, and even genetic information can be

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## **6. Acknowledgments**

Funding was provided by Irish Research Council for Science Engineering and Technology (IRCSET) under Embark Initiative postgraduate scholarship and Research Frontiers Grant SFI (08/RFP/ENM1378)

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**Part 2** 

**Biomechanical Engineering** 

**Methods and Applications** 


## **Part 2**

**Biomechanical Engineering Methods and Applications** 

258 Applied Biological Engineering – Principles and Practice

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**11** 

*Japan* 

**Functional Significance of Force Fluctuation** 

*1Department of Sports Science, Faculty of Sports Science, Kyushu Kyoritsu University* 

Human movement is the result of the joint torque or muscle force generated by the contraction of multiple muscles. The force generated during voluntary muscle contraction is not constant, but fluctuates as observed through the variability in movement. The normalised force fluctuation (measured according to the standard deviation (SD) of force) during isometric contractions is referred to as 'steadiness', which influences functional human movement (Carville et al., 2007; Kornatz et al., 2005; Marmon et al., 2011; Salonikidis et al., 2009). For example, Salonikidis et al. (2009) and Kornatz et al. (2005) report that greater fluctuation during voluntary muscle contraction can influence functional human movement in the upper limbs. With regard to the lower limbs, Carville et al. (2007) report that the elderly who tend to fall exhibit less steady knee extension than do both the young and the elderly who do not tend to fall. However, the relationship between force fluctuations in lower limb muscles and human movements for daily activities remains unclear. The ability to control posture during quiet standing is one of the fundamental activities of daily living. Furthermore, the muscle activities of lower limb muscles are important for postural stability during quiet standing. Therefore, this chapter focuses on the relationship between force steadiness in lower limb muscles and

Some studies demonstrate that the asymmetry of muscle function between the 2 legs may influence human movement. For example, Skelton et al. (2002) report that although 'fallers' (20 women living at home, aged >65 years with a history of falls in the past year) and 'nonfallers' (15 age-matched women with no history of falls) have asymmetric lower limb power, the fallers exhibit significantly greater asymmetry. Furthermore, the relationship between the asymmetry of leg strength and walking speed in 1,205 healthy women aged 30–89 years old has been reported (Oshita et al., 2009). Walking speed is fastest when the asymmetries of knee extension and flexion strength are below 5%, as shown in Fig. 1. However, if the asymmetry of one of the parameters (i.e. knee extension or flexion) is more than 10%, walking speed is still reduced. Furthermore, the walking speed is slowest when the asymmetries of knee extension and flexion strength are more than 10% (Fig. 1). Moreover, the asymmetry of leg strength does not affect the walking speed of subjects with higher leg

**1. Introduction** 

postural stability during quiet standing.

**1.1 Asymmetry of muscle function in leg muscles** 

*2Graduate School of Human Development and Environment, Kobe University* 

**During Voluntary Muscle Contraction** 

Kazushige Oshita1,2 and Sumio Yano2

## **Functional Significance of Force Fluctuation During Voluntary Muscle Contraction**

Kazushige Oshita1,2 and Sumio Yano2

*1Department of Sports Science, Faculty of Sports Science, Kyushu Kyoritsu University 2Graduate School of Human Development and Environment, Kobe University Japan* 

## **1. Introduction**

Human movement is the result of the joint torque or muscle force generated by the contraction of multiple muscles. The force generated during voluntary muscle contraction is not constant, but fluctuates as observed through the variability in movement. The normalised force fluctuation (measured according to the standard deviation (SD) of force) during isometric contractions is referred to as 'steadiness', which influences functional human movement (Carville et al., 2007; Kornatz et al., 2005; Marmon et al., 2011; Salonikidis et al., 2009). For example, Salonikidis et al. (2009) and Kornatz et al. (2005) report that greater fluctuation during voluntary muscle contraction can influence functional human movement in the upper limbs. With regard to the lower limbs, Carville et al. (2007) report that the elderly who tend to fall exhibit less steady knee extension than do both the young and the elderly who do not tend to fall. However, the relationship between force fluctuations in lower limb muscles and human movements for daily activities remains unclear. The ability to control posture during quiet standing is one of the fundamental activities of daily living. Furthermore, the muscle activities of lower limb muscles are important for postural stability during quiet standing. Therefore, this chapter focuses on the relationship between force steadiness in lower limb muscles and postural stability during quiet standing.

## **1.1 Asymmetry of muscle function in leg muscles**

Some studies demonstrate that the asymmetry of muscle function between the 2 legs may influence human movement. For example, Skelton et al. (2002) report that although 'fallers' (20 women living at home, aged >65 years with a history of falls in the past year) and 'nonfallers' (15 age-matched women with no history of falls) have asymmetric lower limb power, the fallers exhibit significantly greater asymmetry. Furthermore, the relationship between the asymmetry of leg strength and walking speed in 1,205 healthy women aged 30–89 years old has been reported (Oshita et al., 2009). Walking speed is fastest when the asymmetries of knee extension and flexion strength are below 5%, as shown in Fig. 1. However, if the asymmetry of one of the parameters (i.e. knee extension or flexion) is more than 10%, walking speed is still reduced. Furthermore, the walking speed is slowest when the asymmetries of knee extension and flexion strength are more than 10% (Fig. 1). Moreover, the asymmetry of leg strength does not affect the walking speed of subjects with higher leg strength (Fig. 2). However, in subjects with low leg strength, walking speed decreases with increasing asymmetry of leg strength.

\*; *P* < 0.05

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 263

Although these previous studies suggest that the asymmetry of leg strength might affect the human movement regarding postural stability, the intensity of most daily activities is not maximal, but is thought to be less than approximately 20% of maximum voluntary contraction (MVC) (Sawai et al., 2004). These studies lead us to hypothesise that asymmetry in muscle function at less than 20% MVC is an important factor for postural stability. Thus, in section 3, we introduce the asymmetry of force fluctuations during isometric contraction

Based on the dynamics of human quiet standing, numerous studies (i.e. analyses using electromyograms or the model of a single-joint inverted pendulum rotating around the ankle joint) show that the plantar flexor muscles play a significant role in stabilising the body during quiet standing. For example, the activities of the plantar flexors during bipedal quiet stance are coherent with both spontaneous body swaying (Gatev et al., 1999; Masani et al., 2003) and mechanically induced body swaying (Fitzpatrick et al., 1996). Although many factors (e.g. proprioception, control of upper body motion, etc.) are related to postural stability during quiet standing, the plantar flexors (i.e. the soleus muscle) are the most activated muscles in the entire body during quiet standing (Ohnishi et al., 2005; Sawai et al., 2004). These studies lead us to hypothesise that quiet standing is associated with force fluctuation in the plantar flexors. If force fluctuation in the plantar flexors is one of the most important factors for postural stability during quiet standing, the amplitude of force fluctuation will indicate a relationship between ability and posture stability. In section 4, we discuss the relationship between force

in lower limb muscles during low-intensity muscle contraction.

steadiness of the plantar flexors and the postural sway during quiet standing.

**1.3 Practice reduces force fluctuation and improves human movement** 

neuron firing rate, and motor unit synchronisation (Ohmori et al., 2010).

In order to increase muscle strength in healthy adults, the American College of Sports Medicine (1998) recommends strength training at least 2–3 times per week. Further, 1 day of exercise per week may not develop into habitual exercise; for example, the definition of habitual exercise according to a national health and nutrition survey is least 2 sessions of exercise per week (Ministry of Health, Labour, and Welfare of Japan, 2011). Although this training frequency is generally recommended for strength training, it might be not necessarily realistic for people aiming to maintain their health or who are unable to devote a considerable amount of time to strength training alone (Ohmori et al., 2010). However, previous studies involving relatively low-frequency strength or functional training (1 session per week or per 2 weeks) demonstrate increases in muscle strength in both normal young adults (Hayashi and Miyamoto, 2009; Ohmori et al., 2010) as well as in normal and functionally limited older adults (Oshita et al., 2008; Sato et al., 2007). The improvement in strength brought about by such lowfrequency training is attributed to several neural factors such as motor learning, adjustment of motor function, acquisition of skills, excitability of alpha-motor neurons, increased motor

In order to reduce force fluctuations in healthy adults, strength training and/or steadiness practice can be used during voluntary contraction of the distal muscles of the upper and lower limbs. Keen et al. (1994) report that in young adults, 4 weeks of strength training of the first dorsal interosseous muscle using a heavy load (80% of maximum) reduces the force fluctuations measured during isometric contraction at 50% MVC. Similarly, steady

**1.2 Plantar flexor muscles during quiet standing** 

Fig. 1. Relationship between walking speed and asymmetry of leg strength

\*; *P* < 0.05

Fig. 2. Relationship between walking speed and leg strength and asymmetry of leg strength

Although these previous studies suggest that the asymmetry of leg strength might affect the human movement regarding postural stability, the intensity of most daily activities is not maximal, but is thought to be less than approximately 20% of maximum voluntary contraction (MVC) (Sawai et al., 2004). These studies lead us to hypothesise that asymmetry in muscle function at less than 20% MVC is an important factor for postural stability. Thus, in section 3, we introduce the asymmetry of force fluctuations during isometric contraction in lower limb muscles during low-intensity muscle contraction.

#### **1.2 Plantar flexor muscles during quiet standing**

262 Applied Biological Engineering – Principles and Practice

strength (Fig. 2). However, in subjects with low leg strength, walking speed decreases with

Fig. 1. Relationship between walking speed and asymmetry of leg strength

Fig. 2. Relationship between walking speed and leg strength and asymmetry of leg strength

\*; *P* < 0.05

\*; *P* < 0.05

increasing asymmetry of leg strength.

Based on the dynamics of human quiet standing, numerous studies (i.e. analyses using electromyograms or the model of a single-joint inverted pendulum rotating around the ankle joint) show that the plantar flexor muscles play a significant role in stabilising the body during quiet standing. For example, the activities of the plantar flexors during bipedal quiet stance are coherent with both spontaneous body swaying (Gatev et al., 1999; Masani et al., 2003) and mechanically induced body swaying (Fitzpatrick et al., 1996). Although many factors (e.g. proprioception, control of upper body motion, etc.) are related to postural stability during quiet standing, the plantar flexors (i.e. the soleus muscle) are the most activated muscles in the entire body during quiet standing (Ohnishi et al., 2005; Sawai et al., 2004). These studies lead us to hypothesise that quiet standing is associated with force fluctuation in the plantar flexors. If force fluctuation in the plantar flexors is one of the most important factors for postural stability during quiet standing, the amplitude of force fluctuation will indicate a relationship between ability and posture stability. In section 4, we discuss the relationship between force steadiness of the plantar flexors and the postural sway during quiet standing.

## **1.3 Practice reduces force fluctuation and improves human movement**

In order to increase muscle strength in healthy adults, the American College of Sports Medicine (1998) recommends strength training at least 2–3 times per week. Further, 1 day of exercise per week may not develop into habitual exercise; for example, the definition of habitual exercise according to a national health and nutrition survey is least 2 sessions of exercise per week (Ministry of Health, Labour, and Welfare of Japan, 2011). Although this training frequency is generally recommended for strength training, it might be not necessarily realistic for people aiming to maintain their health or who are unable to devote a considerable amount of time to strength training alone (Ohmori et al., 2010). However, previous studies involving relatively low-frequency strength or functional training (1 session per week or per 2 weeks) demonstrate increases in muscle strength in both normal young adults (Hayashi and Miyamoto, 2009; Ohmori et al., 2010) as well as in normal and functionally limited older adults (Oshita et al., 2008; Sato et al., 2007). The improvement in strength brought about by such lowfrequency training is attributed to several neural factors such as motor learning, adjustment of motor function, acquisition of skills, excitability of alpha-motor neurons, increased motor neuron firing rate, and motor unit synchronisation (Ohmori et al., 2010).

In order to reduce force fluctuations in healthy adults, strength training and/or steadiness practice can be used during voluntary contraction of the distal muscles of the upper and lower limbs. Keen et al. (1994) report that in young adults, 4 weeks of strength training of the first dorsal interosseous muscle using a heavy load (80% of maximum) reduces the force fluctuations measured during isometric contraction at 50% MVC. Similarly, steady

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 265

Each participant performed an isometric unilateral knee extension exercise with each leg while in a seated position, with the hip and knee joints both flexed at 90° (full extension = 0°). Throughout the experiment, the participant's upper body was firmly fixed to a chair with a seat belt. The force of the isometric contraction of the knee extensor muscles was measured by a load cell (LTZ-100KA, Kyowa, Tokyo, Japan) attached to the ankle just above the malleolus by a strap. The amount of force produced and the target were displayed on a computer screen (14.1 inches) positioned 1 m away at the level of the participant's eyes to

Each participant performed MVC for a period of 5 s with encouragement from the investigators. Participants performed 3 trials with subsequent trials performed if the difference in the peak force of 2 MVCs was >5%. Participants were allowed to reject any effort that they did not consider 'maximal'. The trial with the highest peak force was chosen for analysis.

On the basis of the MVC measurements, the participants performed a steady isometric contraction task for 15-20 s at levels corresponding to 10%, 20%, or 30% of the MVC; there was an approximately 30-min rest period between MVC measurement and these tasks. The force signals were obtained by a sensor interface with a 12-bit analogue-to-digital converter at a sampling frequency of 1 kHz (PCD-300A, Kyowa, Tokyo, Japan) and stored on the hard disk of a computer for future analysis. Data were collected for 1 trial with each target, and the order of the target forces was randomised for each participant. There was a rest period of >1 min between trials, and between-trial rest periods of up to 5 min were also allowed at

Each participant was instructed to remove all footwear and maintain quiet standing for 30- 40 s on a platform (Fig. 4). The subjects had their arms alongside their body and their feet were kept parallel with the centres of the heels 15 cm apart. To assess the trajectory of the centre of mass displacement (CoMdis) during quiet standing the horizontal position of a lumbar point at L3 was measured by a laser displacement sensor (ANR 1251, SUNX, Japan). The present study focused on anteroposterior CoMdis, because the force produced by the plantar flexor muscles mainly contributes to the body sway in this particular axis (Masani et al., 2003). The signals were acquired at a sampling frequency of 100 Hz with a 16-bit analogue-to-digital converter (AI-1608AY, CONTEC, Japan) and stored on the hard disk of a

The data were processed with SPCANA waveform analysis software (version 4.71, Japan) and Microsoft Excel. For the stored force signals, the data for an 8-s period in the middle portion of the collected data (15-20 s) were selected for analysing individual trials because there was no systematic change in fluctuations within trials. After low-pass filtering (<100 Hz), the SD of the force was calculated to evaluate the amplitude of force fluctuation.

provide visual feedback.

subject's request.

**2.2 Muscle strength test (MVC measurement)** 

**2.4 Postural sway during quiet standing** 

computer for future analysis.

**2.5 Data analysis** 

**2.3 Force-matching (steady isometric contraction) task** 

contractions or force-tracking tasks also reduce force fluctuations. For example, 2 weeks of practicing a steadiness task with a light load (10% of maximum) on the index finger reduces force fluctuations and the discharge rate variability of single motor units in the hand muscles of older adults (Kornatz et al., 2005); similar effects are observed in young adults. Patten and Kamen (2000) report that the ability to match force trajectory in the dorsiflexor muscles improves after 2 weeks of isometric force modulation training. However, the effect of low-frequency steadiness practice (1 day of practice per week) on force fluctuations during isometric contraction is currently unknown. Furthermore, if the force fluctuations in the plantar flexor muscles are associated with postural stability, force steadiness practice should improve postural stability during quiet standing. Thus, in section 5, we discuss the effects of low-frequency steadiness practice in the plantar flexor muscles on force fluctuations during isometric contraction and postural stability during quiet standing.

#### **2. Method**

#### **2.1 Experimental setup**

Here, we describe the design used for the plantar flexion exercise. Each participant performed a static unilateral plantar flexion exercise (Fig. 3). Participants were instructed to remove all footwear and sit on an insulated straight-backed chair. An additional strap was used to secure the thigh of the leg to the chair. Force was measured with a load cell (LPR-A-S10, Kyowa, Tokyo, Japan) positioned between a metal base plate and the foot. The foot was secured with a strap at the foot lever plate. The strain gauge transducer was aligned between the 2 plates near the distal part of the foot. The exact position of the entire device was carefully adjusted such that the knee was fully extended with the ankle joint angle at 90°. The amount of force produced and the target were displayed on a computer screen (14.1 inches) positioned 1 m away at the level of the participant's eyes to provide visual feedback.

The following paragraph outlines the design used for the knee extension exercise (Fig. 3).

Fig. 3. Schematic drawing of the setup used for the isometric plantar flexion (left) and knee extension (right)

Each participant performed an isometric unilateral knee extension exercise with each leg while in a seated position, with the hip and knee joints both flexed at 90° (full extension = 0°). Throughout the experiment, the participant's upper body was firmly fixed to a chair with a seat belt. The force of the isometric contraction of the knee extensor muscles was measured by a load cell (LTZ-100KA, Kyowa, Tokyo, Japan) attached to the ankle just above the malleolus by a strap. The amount of force produced and the target were displayed on a computer screen (14.1 inches) positioned 1 m away at the level of the participant's eyes to provide visual feedback.

## **2.2 Muscle strength test (MVC measurement)**

264 Applied Biological Engineering – Principles and Practice

contractions or force-tracking tasks also reduce force fluctuations. For example, 2 weeks of practicing a steadiness task with a light load (10% of maximum) on the index finger reduces force fluctuations and the discharge rate variability of single motor units in the hand muscles of older adults (Kornatz et al., 2005); similar effects are observed in young adults. Patten and Kamen (2000) report that the ability to match force trajectory in the dorsiflexor muscles improves after 2 weeks of isometric force modulation training. However, the effect of low-frequency steadiness practice (1 day of practice per week) on force fluctuations during isometric contraction is currently unknown. Furthermore, if the force fluctuations in the plantar flexor muscles are associated with postural stability, force steadiness practice should improve postural stability during quiet standing. Thus, in section 5, we discuss the effects of low-frequency steadiness practice in the plantar flexor muscles on force fluctuations during isometric contraction and postural stability during quiet standing.

Here, we describe the design used for the plantar flexion exercise. Each participant performed a static unilateral plantar flexion exercise (Fig. 3). Participants were instructed to remove all footwear and sit on an insulated straight-backed chair. An additional strap was used to secure the thigh of the leg to the chair. Force was measured with a load cell (LPR-A-S10, Kyowa, Tokyo, Japan) positioned between a metal base plate and the foot. The foot was secured with a strap at the foot lever plate. The strain gauge transducer was aligned between the 2 plates near the distal part of the foot. The exact position of the entire device was carefully adjusted such that the knee was fully extended with the ankle joint angle at 90°. The amount of force produced and the target were displayed on a computer screen (14.1 inches) positioned 1 m away at the level of the participant's eyes to provide visual feedback. The following paragraph outlines the design used for the knee extension exercise (Fig. 3).

 Fig. 3. Schematic drawing of the setup used for the isometric plantar flexion (left) and knee

**2. Method** 

extension (right)

**2.1 Experimental setup** 

Each participant performed MVC for a period of 5 s with encouragement from the investigators. Participants performed 3 trials with subsequent trials performed if the difference in the peak force of 2 MVCs was >5%. Participants were allowed to reject any effort that they did not consider 'maximal'. The trial with the highest peak force was chosen for analysis.

## **2.3 Force-matching (steady isometric contraction) task**

On the basis of the MVC measurements, the participants performed a steady isometric contraction task for 15-20 s at levels corresponding to 10%, 20%, or 30% of the MVC; there was an approximately 30-min rest period between MVC measurement and these tasks. The force signals were obtained by a sensor interface with a 12-bit analogue-to-digital converter at a sampling frequency of 1 kHz (PCD-300A, Kyowa, Tokyo, Japan) and stored on the hard disk of a computer for future analysis. Data were collected for 1 trial with each target, and the order of the target forces was randomised for each participant. There was a rest period of >1 min between trials, and between-trial rest periods of up to 5 min were also allowed at subject's request.

#### **2.4 Postural sway during quiet standing**

Each participant was instructed to remove all footwear and maintain quiet standing for 30- 40 s on a platform (Fig. 4). The subjects had their arms alongside their body and their feet were kept parallel with the centres of the heels 15 cm apart. To assess the trajectory of the centre of mass displacement (CoMdis) during quiet standing the horizontal position of a lumbar point at L3 was measured by a laser displacement sensor (ANR 1251, SUNX, Japan). The present study focused on anteroposterior CoMdis, because the force produced by the plantar flexor muscles mainly contributes to the body sway in this particular axis (Masani et al., 2003). The signals were acquired at a sampling frequency of 100 Hz with a 16-bit analogue-to-digital converter (AI-1608AY, CONTEC, Japan) and stored on the hard disk of a computer for future analysis.

## **2.5 Data analysis**

The data were processed with SPCANA waveform analysis software (version 4.71, Japan) and Microsoft Excel. For the stored force signals, the data for an 8-s period in the middle portion of the collected data (15-20 s) were selected for analysing individual trials because there was no systematic change in fluctuations within trials. After low-pass filtering (<100 Hz), the SD of the force was calculated to evaluate the amplitude of force fluctuation.

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 267

Fig. 5. Representative force fluctuations during isometric knee extension (A) and means and

Adam et al. (1998) report significantly greater fluctuation in the non-preferred hand than in the preferred hand during a 30% MVC isometric abduction task in the index finger; furthermore, the discharge rate variability during task is greater in the non-preferred hand than in the preferred hand. One of the important factors in the asymmetry differences in the upper limb is their daily preferential use. However, our results indicate that no asymmetry in force fluctuation was observed during steady isometric knee extension at 10 or 20% MVC. Furthermore, figure 5 and 6 show mechanomyogram signals in vastus lateralis during the steady isometric knee extension task. These results indicate that no asymmetry differences in the mechanical characteristics in the active muscle were observed. In contrast to the upper limb, the role of limb preference in lower limbs is not clear. For example, if a person kicks a ball with their preferred limb, the other limb is often required to support the entire body weight. Therefore, it is unclear which limb is stronger: the limb preferred for daily use or the other limb regularly supporting the body weight over many years. However, our results are consistent with those of Semmler and Nordstrom (1995) who report that no asymmetry of force fluctuation or discharge variability is observed during isometric index finger abduction. The difference in the results of Adam et al. (1998) and Semmler and Nordstrom (1995) is thought to be due to differences in contraction intensity. Although the asymmetry of force fluctuation is observed during 30% MVC (Adam et al., 1998), it is not observed during <10% (Semmler and Nordstrom, 1995), 10%, or 20% MVC (Fig. 5). The force fluctuations observed during isometric contraction are correlated with the discharge rate variability, which is thought to be a major determinant of force fluctuations (Mottram et al., 2005; Tracy et al., 2005). Thus, no asymmetry of force fluctuations might be observed during low-intensity contraction because the variability in the discharge rate is too small. Furthermore, the present results indicate asymmetry of mechanomyogram signals in the

standard errors of the means (B) (Oshita and Yano, 2010a)

Fig. 4. Schematic drawing of the setup used for the measurement of postural sway

For the CoMdis signals, the data for a 20-s period in the middle portion of the collected data (30-40 s) were selected for analysing individual trials. The velocity of CoMdis (CoMvel) was calculated by numerically differentiating CoMdis as a function of time. This is because the velocity of body sway (i.e. the centre of pressure displacement or CoMdis) in the anteroposterior axis is the most sensitive parameter capable of distinguishing not only children and young adults from seniors, but also middle-aged subjects from seniors (Abrahamova and Hlavacka, 2008; Prieto et al. 1996; Masani et al., 2007). Furthermore, the SD of CoMvel was calculated to assess postural sway during quiet standing.

## **3. Asymmetry of force fluctuation in leg muscles**

## **3.1 Proximal part (Knee extension)**

In this section, we discuss the asymmetry of force fluctuations during isometric knee extension (Oshita and Yano, 2010a). Data were obtained from 12 healthy men (age, 21 ± 1 years). Each participant performed the steady isometric knee extension task for 15 s at levels corresponding to 10% or 20% MVC. Force fluctuations were compared between the stronger and weaker MVC limbs. In all subjects, the right limb was stronger. The MVCs of the stronger and weaker limbs were 688.0 ± 49.6 and 625.8 ± 43.1 N, respectively. Figure 5 shows the force fluctuations during the steady isometric knee extension task. Force fluctuation was significantly greater in the 20% MVC task than in the 10% MVC task in both limbs. However, no significant differences in force fluctuations during the 10% and 20% MVC tasks were observed between the stronger and weaker limbs. Thus, although force fluctuation increased with contraction intensity, no asymmetry of force fluctuation was observed during low-intensity steady isometric knee extension.

Fig. 4. Schematic drawing of the setup used for the measurement of postural sway

SD of CoMvel was calculated to assess postural sway during quiet standing.

**3. Asymmetry of force fluctuation in leg muscles** 

observed during low-intensity steady isometric knee extension.

**3.1 Proximal part (Knee extension)** 

For the CoMdis signals, the data for a 20-s period in the middle portion of the collected data (30-40 s) were selected for analysing individual trials. The velocity of CoMdis (CoMvel) was calculated by numerically differentiating CoMdis as a function of time. This is because the velocity of body sway (i.e. the centre of pressure displacement or CoMdis) in the anteroposterior axis is the most sensitive parameter capable of distinguishing not only children and young adults from seniors, but also middle-aged subjects from seniors (Abrahamova and Hlavacka, 2008; Prieto et al. 1996; Masani et al., 2007). Furthermore, the

In this section, we discuss the asymmetry of force fluctuations during isometric knee extension (Oshita and Yano, 2010a). Data were obtained from 12 healthy men (age, 21 ± 1 years). Each participant performed the steady isometric knee extension task for 15 s at levels corresponding to 10% or 20% MVC. Force fluctuations were compared between the stronger and weaker MVC limbs. In all subjects, the right limb was stronger. The MVCs of the stronger and weaker limbs were 688.0 ± 49.6 and 625.8 ± 43.1 N, respectively. Figure 5 shows the force fluctuations during the steady isometric knee extension task. Force fluctuation was significantly greater in the 20% MVC task than in the 10% MVC task in both limbs. However, no significant differences in force fluctuations during the 10% and 20% MVC tasks were observed between the stronger and weaker limbs. Thus, although force fluctuation increased with contraction intensity, no asymmetry of force fluctuation was

Fig. 5. Representative force fluctuations during isometric knee extension (A) and means and standard errors of the means (B) (Oshita and Yano, 2010a)

Adam et al. (1998) report significantly greater fluctuation in the non-preferred hand than in the preferred hand during a 30% MVC isometric abduction task in the index finger; furthermore, the discharge rate variability during task is greater in the non-preferred hand than in the preferred hand. One of the important factors in the asymmetry differences in the upper limb is their daily preferential use. However, our results indicate that no asymmetry in force fluctuation was observed during steady isometric knee extension at 10 or 20% MVC.

Furthermore, figure 5 and 6 show mechanomyogram signals in vastus lateralis during the steady isometric knee extension task. These results indicate that no asymmetry differences in the mechanical characteristics in the active muscle were observed. In contrast to the upper limb, the role of limb preference in lower limbs is not clear. For example, if a person kicks a ball with their preferred limb, the other limb is often required to support the entire body weight. Therefore, it is unclear which limb is stronger: the limb preferred for daily use or the other limb regularly supporting the body weight over many years. However, our results are consistent with those of Semmler and Nordstrom (1995) who report that no asymmetry of force fluctuation or discharge variability is observed during isometric index finger abduction. The difference in the results of Adam et al. (1998) and Semmler and Nordstrom (1995) is thought to be due to differences in contraction intensity. Although the asymmetry of force fluctuation is observed during 30% MVC (Adam et al., 1998), it is not observed during <10% (Semmler and Nordstrom, 1995), 10%, or 20% MVC (Fig. 5). The force fluctuations observed during isometric contraction are correlated with the discharge rate variability, which is thought to be a major determinant of force fluctuations (Mottram et al., 2005; Tracy et al., 2005). Thus, no asymmetry of force fluctuations might be observed during low-intensity contraction because the variability in the discharge rate is too small. Furthermore, the present results indicate asymmetry of mechanomyogram signals in the

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 269

In section 3.1, we found that force fluctuations during isometric knee extension at 10% and 20% MVC were not significantly different between the 2 legs. However, Adam et al. (1998) reported a significantly greater fluctuation for the non-preferred than the preferred hand during a 30% MVC isometric abduction task with the index finger. The different results obtained by Adam, et al. (1998) and Semmler and Nordstrom (1995) are thought to reflect the difference in intensity of contraction. If the asymmetry of force fluctuations is influenced by intensity of contraction, asymmetry of force fluctuation in the lower limbs which was not observed below 20% MVC might be observed above 30% MVC. Furthermore, although the intensity of most daily activities is below 20% MVC, some activities of high intensity are required in daily life (e.g., climbing stairs or walking up or down a slope) or sports activities. Apparently, although Oshita and Yano (2010a) reported the asymmetry of force fluctuation in leg muscle at low intensity, the asymmetry of force fluctuation in the leg muscles at moderate intensity remains unclear. In this section, we discuss the asymmetry of force fluctuation during

isometric knee extension at low and moderate intensities (Oshita and Yano, 2011a).

Data were obtained from 11 healthy men (age, 21 ± 1 years). Each participant performed the steady isometric knee extension task for 15 s at levels corresponding to 20% or 30% MVC. Figure 10 shows the force fluctuations during the steady isometric knee extension task. Although force fluctuation was not statistically significantly different between the 2 legs during the 20% MVC task, it was statistically significantly higher in the left leg than in the right leg during the 30% MVC task (Fig. 8). These results indicate asymmetry of force fluctuation during isometric knee extension was observed in the moderate intensity task (30% MVC) but not in the low intensity task (20% MVC). In the section 3.1, we reported the force fluctuations during isometric knee extension at low intensities (10% and 20% MVC) were not significantly different between the 2 legs (Oshita and Yano; 2010a). In the upper limbs, Semmler and Nordstrom (1995) also reported the force fluctuation during isometric abduction of the index finger at below 10% MVC was not statistically significantly different between the 2 hands. These previous data are consistent with the present result; force fluctuation during isometric knee extension at low intensity (20% MVC) was not statistically significantly different between the 2 legs. However, Adam et al. (1998) reported a statistically significantly greater fluctuation for the non-preferred than for the preferred hand during a task with 30% MVC isometric abduction of the index finger. They suggested the different results of Adam et al. (1998) and Semmler and Nordstrom (1995) were influenced by the difference in the intensity of contraction. In the current study, force fluctuation during knee extension which was not different between the 2 legs at low intensity (20% MVC) was statistically significantly different between the legs at moderate intensity (30% MVC). Therefore, the present results were consistent with the suggestion of Adam et al. (1998) that the asymmetry of force fluctuation in lower limbs was also

Several researchers have suggested that a major determinant of the force fluctuation is the variability in motor-unit discharge rate (Mottram et al., 2005; Tracy et al., 2005), viz., the positive association of force fluctuation with variability of the discharge rate during isometric contraction (Mottram, et al., 2005; Tracy, et al., 2005). Although the present study did not measure the activities of motor units directly, the firing rate of the motor unit in active muscle (i.e. vastus lateralis) was evaluated using an mechanomyogram. Further, there was a statistically significant association between the 2 legs' mean power frequency of

**3.2 Effect of contraction intensity** 

influenced by the contraction intensity.

active muscle. These results suggest that no asymmetry of force fluctuations during lowintensity isometric knee extension is observed, because there are no differences regarding mechanical characteristics in the active muscle between stronger and weaker legs.

Fig. 6. Representative amplitude of mechanomyogram signal during isometric knee extension (A) and means and standard errors of the means (B) (Oshita and Yano, 2010a)

Fig. 7. Representative mean power frequency of mechanomyogram signals during isometric knee extension (A) and means and standard errors of the means (B) (Oshita and Yano, 2010a)

#### **3.2 Effect of contraction intensity**

268 Applied Biological Engineering – Principles and Practice

active muscle. These results suggest that no asymmetry of force fluctuations during lowintensity isometric knee extension is observed, because there are no differences regarding

mechanical characteristics in the active muscle between stronger and weaker legs.

Fig. 6. Representative amplitude of mechanomyogram signal during isometric knee extension (A) and means and standard errors of the means (B) (Oshita and Yano, 2010a)

Fig. 7. Representative mean power frequency of mechanomyogram signals during isometric knee extension (A) and means and standard errors of the means (B) (Oshita and Yano, 2010a) In section 3.1, we found that force fluctuations during isometric knee extension at 10% and 20% MVC were not significantly different between the 2 legs. However, Adam et al. (1998) reported a significantly greater fluctuation for the non-preferred than the preferred hand during a 30% MVC isometric abduction task with the index finger. The different results obtained by Adam, et al. (1998) and Semmler and Nordstrom (1995) are thought to reflect the difference in intensity of contraction. If the asymmetry of force fluctuations is influenced by intensity of contraction, asymmetry of force fluctuation in the lower limbs which was not observed below 20% MVC might be observed above 30% MVC. Furthermore, although the intensity of most daily activities is below 20% MVC, some activities of high intensity are required in daily life (e.g., climbing stairs or walking up or down a slope) or sports activities. Apparently, although Oshita and Yano (2010a) reported the asymmetry of force fluctuation in leg muscle at low intensity, the asymmetry of force fluctuation in the leg muscles at moderate intensity remains unclear. In this section, we discuss the asymmetry of force fluctuation during isometric knee extension at low and moderate intensities (Oshita and Yano, 2011a).

Data were obtained from 11 healthy men (age, 21 ± 1 years). Each participant performed the steady isometric knee extension task for 15 s at levels corresponding to 20% or 30% MVC. Figure 10 shows the force fluctuations during the steady isometric knee extension task. Although force fluctuation was not statistically significantly different between the 2 legs during the 20% MVC task, it was statistically significantly higher in the left leg than in the right leg during the 30% MVC task (Fig. 8). These results indicate asymmetry of force fluctuation during isometric knee extension was observed in the moderate intensity task (30% MVC) but not in the low intensity task (20% MVC). In the section 3.1, we reported the force fluctuations during isometric knee extension at low intensities (10% and 20% MVC) were not significantly different between the 2 legs (Oshita and Yano; 2010a). In the upper limbs, Semmler and Nordstrom (1995) also reported the force fluctuation during isometric abduction of the index finger at below 10% MVC was not statistically significantly different between the 2 hands. These previous data are consistent with the present result; force fluctuation during isometric knee extension at low intensity (20% MVC) was not statistically significantly different between the 2 legs. However, Adam et al. (1998) reported a statistically significantly greater fluctuation for the non-preferred than for the preferred hand during a task with 30% MVC isometric abduction of the index finger. They suggested the different results of Adam et al. (1998) and Semmler and Nordstrom (1995) were influenced by the difference in the intensity of contraction. In the current study, force fluctuation during knee extension which was not different between the 2 legs at low intensity (20% MVC) was statistically significantly different between the legs at moderate intensity (30% MVC). Therefore, the present results were consistent with the suggestion of Adam et al. (1998) that the asymmetry of force fluctuation in lower limbs was also influenced by the contraction intensity.

Several researchers have suggested that a major determinant of the force fluctuation is the variability in motor-unit discharge rate (Mottram et al., 2005; Tracy et al., 2005), viz., the positive association of force fluctuation with variability of the discharge rate during isometric contraction (Mottram, et al., 2005; Tracy, et al., 2005). Although the present study did not measure the activities of motor units directly, the firing rate of the motor unit in active muscle (i.e. vastus lateralis) was evaluated using an mechanomyogram. Further, there was a statistically significant association between the 2 legs' mean power frequency of

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 271

Force fluctuation may influence functional performance of controlling finger or limb movements in daily life. Although the intensity of most daily activities is below 20% MVC, some activities of high intensity are required in daily life or sports activities. Asymmetry of force fluctuation might be important in these motions. Most importantly, although the intensity of most daily activities is below 20% MVC for individuals with normal or high muscle strength, it would be of higher intensity for those with lower muscle strength. Asymmetry of force fluctuation during voluntary contractions of high intensity might affect

Although the force fluctuations were not significantly different between the 2 legs during low-intensity isometric knee extension, the asymmetry of force fluctuations in the plantar flexor muscles is currently unknown. The apparent biomechanical differences between limb segments are reflected in the distinct control of proximal versus distal joints. There are different control loops for distal and proximal muscles in the cerebellum and reflex pathways (Kurata and Tanji, 1986; Nisky et al., 2010). According to previous studies (Lemon and Griffiths, 2005; Davidson and Buford, 2006; Nisky et al., 2010), humans are more accurate in control and perception of the position of endpoint of the limb. Opposite gradients in maximum controllable force and resolution of force control were reported; that is, proximal joints are more successful than distal joints in the control of force (Hamilton et al., 2004; Nisky et al., 2010). Thus, a significant difference in the force fluctuations between the 2 legs might be observed in the plantar flexor muscles. In this section, we discuss the asymmetry of force fluctuations during isometric plantar flexion (Oshita and Yano, 2010b).

Fig. 10. Representative force fluctuations during isometric plantar flexion (A) and means

and standard errors of the mean (B) (Oshita and Yano, 2010b)

normal daily activities of individuals with low muscle strength.

**3.3 Distal part (Plantar flexion)** 

mechanomyogram signal during the 20% MVC task but not during the 30% MVC task (Fig. 9), so individuals who had higher (or lower) mean power frequency of mechanomyogram signal in the right leg's active muscle also tended to have higher (or lower) mean power frequency in the left leg during isometric knee extension at low intensity (20% MVC). In contrast, mean power frequency of mechanomyogram signal during the moderate intensity (30% MVC) task was uneven between the 2 legs. Thus, the asymmetry of the firing rates of the motor units in active muscle during isometric knee extension is associated with intensity of the contraction.

Fig. 8. Representative force fluctuations during isometric knee extension (A) and means and standard errors of the means (B) (Oshita and Yano, 2011a)

Fig. 9. Relationships regarding mean power frequency of mechanomyogram signal during isometric knee extension at 20% (left) and 30% (rihgt) MVC between the right and left legs (Oshita and Yano, 2011a)

Force fluctuation may influence functional performance of controlling finger or limb movements in daily life. Although the intensity of most daily activities is below 20% MVC, some activities of high intensity are required in daily life or sports activities. Asymmetry of force fluctuation might be important in these motions. Most importantly, although the intensity of most daily activities is below 20% MVC for individuals with normal or high muscle strength, it would be of higher intensity for those with lower muscle strength. Asymmetry of force fluctuation during voluntary contractions of high intensity might affect normal daily activities of individuals with low muscle strength.

#### **3.3 Distal part (Plantar flexion)**

270 Applied Biological Engineering – Principles and Practice

mechanomyogram signal during the 20% MVC task but not during the 30% MVC task (Fig. 9), so individuals who had higher (or lower) mean power frequency of mechanomyogram signal in the right leg's active muscle also tended to have higher (or lower) mean power frequency in the left leg during isometric knee extension at low intensity (20% MVC). In contrast, mean power frequency of mechanomyogram signal during the moderate intensity (30% MVC) task was uneven between the 2 legs. Thus, the asymmetry of the firing rates of the motor units in active muscle during isometric knee extension is associated with intensity

Fig. 8. Representative force fluctuations during isometric knee extension (A) and means and

Fig. 9. Relationships regarding mean power frequency of mechanomyogram signal during isometric knee extension at 20% (left) and 30% (rihgt) MVC between the right and left legs

standard errors of the means (B) (Oshita and Yano, 2011a)

(Oshita and Yano, 2011a)

of the contraction.

Although the force fluctuations were not significantly different between the 2 legs during low-intensity isometric knee extension, the asymmetry of force fluctuations in the plantar flexor muscles is currently unknown. The apparent biomechanical differences between limb segments are reflected in the distinct control of proximal versus distal joints. There are different control loops for distal and proximal muscles in the cerebellum and reflex pathways (Kurata and Tanji, 1986; Nisky et al., 2010). According to previous studies (Lemon and Griffiths, 2005; Davidson and Buford, 2006; Nisky et al., 2010), humans are more accurate in control and perception of the position of endpoint of the limb. Opposite gradients in maximum controllable force and resolution of force control were reported; that is, proximal joints are more successful than distal joints in the control of force (Hamilton et al., 2004; Nisky et al., 2010). Thus, a significant difference in the force fluctuations between the 2 legs might be observed in the plantar flexor muscles. In this section, we discuss the asymmetry of force fluctuations during isometric plantar flexion (Oshita and Yano, 2010b).

Fig. 10. Representative force fluctuations during isometric plantar flexion (A) and means and standard errors of the mean (B) (Oshita and Yano, 2010b)

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 273

in submitting). Data were obtained from 12 healthy men (age, 21 ± 1 years). Each participant performed the isometric unilateral plantar flexion exercise with their preferred leg. The relationship between force fluctuation during isometric plantar flexion and postural sway during quiet standing was evaluated using linear regression analysis. Figure 12 shows the relationship between postural sway during quiet standing and force fluctuation in plantar flexion. Although postural sway was significantly associated with force fluctuation at 10% MVC, it was not significantly associated with that at 20% MVC. These results suggest that the strategy of motor output in the plantar flexor muscles during low-intensity contraction is different between 10% and 20% MVC; moreover, the fluctuation in motor output in the plantar flexor muscles at 10% MVC was associated with postural sway during quiet

Fig. 12. Relationship between postural sway and force fluctuation during plantar flexion at

Numerous studies show that the plantar flexor muscles play a significant role in stabilising the body during quiet standing (Masani et al., 2003; Morasso and Schieppati, 1999). Furthermore, we observed a relationship between postural stability during quiet standing and force fluctuations during low-intensity isometric plantar flexion exercise. Therefore, individuals who have greater difficulty controlling plantar flexion force during isometric contraction tend to have greater difficulty controlling their standing posture. We revealed that plantar flexor force fluctuation is associated with postural sway during quiet standing in young adults. These results indicate that the force steadiness in plantar flexor muscles is important for postural stability during quiet standing; this is somewhat consistent with the results of previous studies. Oshita and Yano (2010c) report that force fluctuation during plantar flexion at 20% MVC is associated with postural stability during single-leg quiet standing. Although they report that postural stability is associated with force fluctuation at 20% MVC, the present results show a significant positive correlation between postural sway and force fluctuation at 10% MVC. The discrepancy between these results is thought to be due to the difference in the state of quiet standing. Oshita and Yano (2010c) report that force fluctuation is associated with postural stability during single-leg quiet standing. The activity level of the plantar flexor muscles is approximately 15–20% of MVC during single-leg standing (Sawai et al., 2004); however, it is approximately 10% of MVC during bipedal

standing in young adults.

10% (left) and 20% (right) MVC

Data were obtained from 12 healthy men (age, 21 ± 1 years). Each participant performed the steady isometric plantar flexion task for 20 s at levels corresponding to 10% and 20% MVC. Force fluctuations in the plantar flexors were compared between the stronger (right) and weaker (left) MVC limbs. In all subjects, the right limb was the stronger limb. Figure 10 shows force fluctuations during the steady isometric plantar flexion task. Force fluctuation was significantly greater in the 20% MVC task than in the 10% MVC task in both limbs. However, no significant differences in force fluctuations in both the 10% and 20% MVC tasks were observed between the right and left limbs. Furthermore, the force fluctuation was significantly associated between the 2 legs (Fig. 11). In addition, the participants who had greater (or smaller) force fluctuations in the right limb also had greater (or smaller) fluctuations in the left limb. Although force fluctuation increased with contraction intensity, no asymmetry of force fluctuation was observed during low-intensity steady isometric plantar flexion.

Fig. 11. Relationships regarding force fluctuation during force-matching tasks between the right and left legs (Oshita and Yano, 2010b)

Although there are different control loops for distal and proximal muscles in the cerebellum and reflex pathways, force fluctuations in the plantar flexor muscles were not significantly different between the 2 legs. The present study focuses on investigating the asymmetry of force fluctuations during low-intensity isometric contraction in lower limb muscles. Therefore, the underlying mechanisms of the asymmetry of force fluctuation remain unclear. Future studies are required to determine muscle activity in the antagonist muscle and/or neuromuscular properties (e.g. electromyography, motor unit activity, etc.) in order to clarify the mechanisms of the effects of practice like those reported here.

#### **4. Steadiness in plantar flexion and postural sway**

If force fluctuation in the plantar flexors is an important factor for postural stability during quiet standing, the amplitude of force fluctuation will indicate a relationship between ability and postural stability. Thus, in this section, we discuss the relationship between the force steadiness of the plantar flexors and postural sway during quiet standing (Oshita and Yano,

Data were obtained from 12 healthy men (age, 21 ± 1 years). Each participant performed the steady isometric plantar flexion task for 20 s at levels corresponding to 10% and 20% MVC. Force fluctuations in the plantar flexors were compared between the stronger (right) and weaker (left) MVC limbs. In all subjects, the right limb was the stronger limb. Figure 10 shows force fluctuations during the steady isometric plantar flexion task. Force fluctuation was significantly greater in the 20% MVC task than in the 10% MVC task in both limbs. However, no significant differences in force fluctuations in both the 10% and 20% MVC tasks were observed between the right and left limbs. Furthermore, the force fluctuation was significantly associated between the 2 legs (Fig. 11). In addition, the participants who had greater (or smaller) force fluctuations in the right limb also had greater (or smaller) fluctuations in the left limb. Although force fluctuation increased with contraction intensity, no asymmetry of force fluctuation was observed during low-intensity steady isometric

Fig. 11. Relationships regarding force fluctuation during force-matching tasks between the

Although there are different control loops for distal and proximal muscles in the cerebellum and reflex pathways, force fluctuations in the plantar flexor muscles were not significantly different between the 2 legs. The present study focuses on investigating the asymmetry of force fluctuations during low-intensity isometric contraction in lower limb muscles. Therefore, the underlying mechanisms of the asymmetry of force fluctuation remain unclear. Future studies are required to determine muscle activity in the antagonist muscle and/or neuromuscular properties (e.g. electromyography, motor unit activity, etc.) in order

If force fluctuation in the plantar flexors is an important factor for postural stability during quiet standing, the amplitude of force fluctuation will indicate a relationship between ability and postural stability. Thus, in this section, we discuss the relationship between the force steadiness of the plantar flexors and postural sway during quiet standing (Oshita and Yano,

to clarify the mechanisms of the effects of practice like those reported here.

**4. Steadiness in plantar flexion and postural sway** 

right and left legs (Oshita and Yano, 2010b)

plantar flexion.

in submitting). Data were obtained from 12 healthy men (age, 21 ± 1 years). Each participant performed the isometric unilateral plantar flexion exercise with their preferred leg. The relationship between force fluctuation during isometric plantar flexion and postural sway during quiet standing was evaluated using linear regression analysis. Figure 12 shows the relationship between postural sway during quiet standing and force fluctuation in plantar flexion. Although postural sway was significantly associated with force fluctuation at 10% MVC, it was not significantly associated with that at 20% MVC. These results suggest that the strategy of motor output in the plantar flexor muscles during low-intensity contraction is different between 10% and 20% MVC; moreover, the fluctuation in motor output in the plantar flexor muscles at 10% MVC was associated with postural sway during quiet standing in young adults.

Fig. 12. Relationship between postural sway and force fluctuation during plantar flexion at 10% (left) and 20% (right) MVC

Numerous studies show that the plantar flexor muscles play a significant role in stabilising the body during quiet standing (Masani et al., 2003; Morasso and Schieppati, 1999). Furthermore, we observed a relationship between postural stability during quiet standing and force fluctuations during low-intensity isometric plantar flexion exercise. Therefore, individuals who have greater difficulty controlling plantar flexion force during isometric contraction tend to have greater difficulty controlling their standing posture. We revealed that plantar flexor force fluctuation is associated with postural sway during quiet standing in young adults. These results indicate that the force steadiness in plantar flexor muscles is important for postural stability during quiet standing; this is somewhat consistent with the results of previous studies. Oshita and Yano (2010c) report that force fluctuation during plantar flexion at 20% MVC is associated with postural stability during single-leg quiet standing. Although they report that postural stability is associated with force fluctuation at 20% MVC, the present results show a significant positive correlation between postural sway and force fluctuation at 10% MVC. The discrepancy between these results is thought to be due to the difference in the state of quiet standing. Oshita and Yano (2010c) report that force fluctuation is associated with postural stability during single-leg quiet standing. The activity level of the plantar flexor muscles is approximately 15–20% of MVC during single-leg standing (Sawai et al., 2004); however, it is approximately 10% of MVC during bipedal

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 275

Another possibility is that Ia afferent function has the capacity to modulate force fluctuations and postural stability. Ia afferent inputs contribute to force fluctuations in the low-frequency range. Yoshitake et al. (2004) report force fluctuations in the plantar flexor muscles at <2 Hz during low-level contractions (<10% MVC) after prolonged Achilles tendon vibration, a factor known to influence Ia afferent function. Oshita and Yano (2011b) found a reduction in force fluctuation in the frequency range of <2 Hz after force steadiness practice (Fig. 13). Furthermore, postural stability during quiet standing is also influenced by the efficacy of Ia afferent function as reflected by the amplitude of the H-reflex (Tokuno et al., 2007; Tokuno et al., 2008). Thus, force fluctuations might be associated with postural sway as a result of the contribution of Ia afferent function. Future studies are required to determine muscle activity in the antagonist muscle and/or neuromuscular properties (e.g. electromyography, motor unit activity, etc.) in order to clarify the mechanisms of practice

In summary, the present results indicate that the significant correlation between postural stability during quiet standing and force fluctuation during plantar flexion is found only at the corresponding contraction intensities for the plantar flexor muscles in young adults. Furthermore, the present results suggest that the neural strategies for plantar flexor muscles during quiet standing are similar to those controlling the plantar flexor force in young adults.

In section 4, we found a significant correlation between postural stability during quiet standing and force fluctuation in plantar flexion. If the force fluctuation in the plantar flexor muscles is reduced by steadiness practice, postural sway during quiet standing would also be reduced. This is because the results presented in section 4 suggest that the neural strategies employed by the plantar flexor muscles during quiet standing are similar to those controlling plantar flexion forces in young adults. Thus, in this section, we discuss the effects of steadiness practice in the plantar flexor muscles on force fluctuation during isometric contraction and postural sway during quiet standing (Oshita and Yano, 2011c).

Data were obtained from 21 healthy men (age, 21 ± 1 years). Participants were randomly assigned to a practice group (n = 14) and a non-exercising control group (n = 7). Practice groups were divided according to the frequency of practice: for 4 weeks, 7 participants practiced once a week while the other 7 practiced twice a week. Participants performed a strength test, force-matching tasks, and a postural stability test before and 4 weeks after the practice program. Strength was assessed by measuring MVC force. Force-matching tasks were performed to maintain isometric contraction. Steady contraction practice was performed as an isometric plantar flexion exercise under conditions identical to those in the experimental session. All practice was performed in the laboratory under supervision with emphasis on performing steady contractions. Practice consisted of 5 sets of practice per session. Verbal encouragement was provided during the sessions. The practice session consisted of the steady contraction task that lasted for 60 s (30 s at 10% and 20% MVC each)

Although MVC values were not significantly different before and after the practice period in the practice group, force fluctuation was significantly lower. Although the practice itself reduced force fluctuation, the frequency of practice did not have an effect (Table 1). Furthermore, there was no statistically significant interaction between practice intervention

**5. Steadiness practice reduces force fluctuation and postural sway** 

effects like those reported here.

followed by a 30-s rest period.

standing (Ohnishi et al., 2005; Sawai, et al., 2004). Further, we suggest that the significant correlation between postural stability during quiet standing and the plantar flexor force fluctuation is found only at the corresponding contraction intensities for plantar flexor muscles. Therefore, the present results suggest that the neural strategies for plantar flexor muscles during quiet standing are similar to the strategies for controlling plantar flexor force in young adults.

Although the neural strategies at work in the plantar flexor muscles during quiet standing and those controlling plantar flexion forces are similar, the underlying mechanisms of the effects of steadiness practice on postural stability remain unclear. One possibility is that influence of the co-activation of the antagonist muscle (i.e. tibialis anterior) during both a force-matching task and quiet standing. Benjuya et al. (2004) report that subjects with a large postural sway (i.e. elderly adults) exhibit greater co-activation of the tibialis anterior during quiet standing. During the force steadiness tasks in finger muscles, fluctuations can be produced by alternating activation of the agonist and antagonist muscles (Vallbo and Wessberg, 1993). However, some studies (Burnett et al., 2000; Tracy and Enoka, 2002) report conflicting results in that the co-activation of antagonist muscles does not seem to have a major effect on force fluctuations. Thus, it remains unclear whether co-activation influences force fluctuation and postural stability.

\**P* < 0.05

Fig. 13. Power spectral analysis of force fluctuation before and after steadiness practice (Oshita and Yano, 2011b)

standing (Ohnishi et al., 2005; Sawai, et al., 2004). Further, we suggest that the significant correlation between postural stability during quiet standing and the plantar flexor force fluctuation is found only at the corresponding contraction intensities for plantar flexor muscles. Therefore, the present results suggest that the neural strategies for plantar flexor muscles during quiet standing are similar to the strategies for controlling plantar flexor

Although the neural strategies at work in the plantar flexor muscles during quiet standing and those controlling plantar flexion forces are similar, the underlying mechanisms of the effects of steadiness practice on postural stability remain unclear. One possibility is that influence of the co-activation of the antagonist muscle (i.e. tibialis anterior) during both a force-matching task and quiet standing. Benjuya et al. (2004) report that subjects with a large postural sway (i.e. elderly adults) exhibit greater co-activation of the tibialis anterior during quiet standing. During the force steadiness tasks in finger muscles, fluctuations can be produced by alternating activation of the agonist and antagonist muscles (Vallbo and Wessberg, 1993). However, some studies (Burnett et al., 2000; Tracy and Enoka, 2002) report conflicting results in that the co-activation of antagonist muscles does not seem to have a major effect on force fluctuations. Thus, it remains unclear whether co-activation influences

Fig. 13. Power spectral analysis of force fluctuation before and after steadiness practice

\**P* < 0.05

force in young adults.

force fluctuation and postural stability.

(Oshita and Yano, 2011b)

Another possibility is that Ia afferent function has the capacity to modulate force fluctuations and postural stability. Ia afferent inputs contribute to force fluctuations in the low-frequency range. Yoshitake et al. (2004) report force fluctuations in the plantar flexor muscles at <2 Hz during low-level contractions (<10% MVC) after prolonged Achilles tendon vibration, a factor known to influence Ia afferent function. Oshita and Yano (2011b) found a reduction in force fluctuation in the frequency range of <2 Hz after force steadiness practice (Fig. 13). Furthermore, postural stability during quiet standing is also influenced by the efficacy of Ia afferent function as reflected by the amplitude of the H-reflex (Tokuno et al., 2007; Tokuno et al., 2008). Thus, force fluctuations might be associated with postural sway as a result of the contribution of Ia afferent function. Future studies are required to determine muscle activity in the antagonist muscle and/or neuromuscular properties (e.g. electromyography, motor unit activity, etc.) in order to clarify the mechanisms of practice effects like those reported here.

In summary, the present results indicate that the significant correlation between postural stability during quiet standing and force fluctuation during plantar flexion is found only at the corresponding contraction intensities for the plantar flexor muscles in young adults. Furthermore, the present results suggest that the neural strategies for plantar flexor muscles during quiet standing are similar to those controlling the plantar flexor force in young adults.

## **5. Steadiness practice reduces force fluctuation and postural sway**

In section 4, we found a significant correlation between postural stability during quiet standing and force fluctuation in plantar flexion. If the force fluctuation in the plantar flexor muscles is reduced by steadiness practice, postural sway during quiet standing would also be reduced. This is because the results presented in section 4 suggest that the neural strategies employed by the plantar flexor muscles during quiet standing are similar to those controlling plantar flexion forces in young adults. Thus, in this section, we discuss the effects of steadiness practice in the plantar flexor muscles on force fluctuation during isometric contraction and postural sway during quiet standing (Oshita and Yano, 2011c).

Data were obtained from 21 healthy men (age, 21 ± 1 years). Participants were randomly assigned to a practice group (n = 14) and a non-exercising control group (n = 7). Practice groups were divided according to the frequency of practice: for 4 weeks, 7 participants practiced once a week while the other 7 practiced twice a week. Participants performed a strength test, force-matching tasks, and a postural stability test before and 4 weeks after the practice program. Strength was assessed by measuring MVC force. Force-matching tasks were performed to maintain isometric contraction. Steady contraction practice was performed as an isometric plantar flexion exercise under conditions identical to those in the experimental session. All practice was performed in the laboratory under supervision with emphasis on performing steady contractions. Practice consisted of 5 sets of practice per session. Verbal encouragement was provided during the sessions. The practice session consisted of the steady contraction task that lasted for 60 s (30 s at 10% and 20% MVC each) followed by a 30-s rest period.

Although MVC values were not significantly different before and after the practice period in the practice group, force fluctuation was significantly lower. Although the practice itself reduced force fluctuation, the frequency of practice did not have an effect (Table 1). Furthermore, there was no statistically significant interaction between practice intervention

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 277

muscles during quiet standing and those controlling plantar flexion forces in young adults

Figure 14 shows the relationship between pre-practice postural sway and changes in steadiness. Linear regression analysis revealed a significant relationship between prepractice postural sway and the change in postural sway due to steadiness practice. This result indicates that subjects exhibiting relatively large pre-practice postural sway also exhibit greater reductions in postural sway following force steadiness practice in the plantar flexor muscles. Thus, the effects of practice on postural stability are dependent on prepractice postural stability. This finding is also consistent with the findings of other reports demonstrating that improvements in steadiness are more frequent in subjects with low initial steadiness levels (Manini et al., 2005; Tracy et al., 2004); this strengthens the notion

Fig. 14. Relationship between baseline postural sway and changes in postural sway (Oshita

As indicated in section 4, multiple factors influence the relationship between force steadiness and postural stability. Although we focused on whether force steadiness practice in the plantar flexor muscles improves postural stability during quiet standing, we demonstrated the functional significance of force fluctuations during voluntary contraction. From the perspective of exercise prescription, the results reported in this section also suggest that even low-frequency, (once a week) low-intensity (within 20% MVC) steadiness

This chapter discussed the relationship between force steadiness in lower limb muscles and postural stability during quiet standing. Although previous studies suggest that the

practice is an effective method for improving human movement.

that the effectiveness of training is dependent on the initial level of steadiness.

are similar.

and Yano, 2011c)

**6. Conclusion** 

and frequency (Table 1). These results indicate that force fluctuation is reduced by lowintensity force steadiness practice but does not change the MVC. Moreover, no effect of practice frequency (one or two time per week) was observed between groups.

Strength and steadiness practice reduce force fluctuation during the voluntary contraction of the distal muscles of the upper and lower limbs. Keen et al. (1994) found that 4 weeks of strength practice with the first dorsal interosseous muscle with a heavy load (80% of maximum) in 10 young adults (aged 18–27 years) reduced force fluctuation during isometric contraction at 50% MVC. Patten and Kamen (2000) report that the ability of 6 young adults (aged 18–22 years) to match a force trajectory requiring force modulation up to 60% MVC in the dorsiflexor muscles improved after 2 weeks of isometric force modulation training.


Table 1. Changes in muscle strength and force fluctuation due to steadiness practice in the practice group (Oshita and Yano, 2011c)

These previous findings corroborate those of the present study. Both the existing literature and present results indicate that strength and steadiness training interventions consistently reduce fluctuations during the low-to-moderate-intensity contractions of the distal muscles of the upper and lower limbs. Furthermore, even though the frequency of practice was relatively low (once a week), it was sufficient to reduce the force fluctuation in the present study.

We also showed that steadiness practice in the plantar flexor muscles reduces the postural sway during quiet standing. In a study involving the upper limbs, Ranganathan et al. (2001) found that skilled finger movement practice improves both the steadiness of the hand muscle and Purdue pegboard test scores. Kornatz et al. (2005) also found that steadiness practice in hand muscles improves the steadiness of the hand muscles and Purdue pegboard test scores. The results of these previous studies led us to hypothesise that steadiness practice in the plantar flexor muscles decreases the force fluctuations of the plantar flexor muscles and improves postural stability. The results of the present study demonstrate that steadiness practice in the plantar flexor muscles reduces postural sway during quiet standing. Therefore, this suggests that the neural strategies employed by the plantar flexor muscles during quiet standing and those controlling plantar flexion forces in young adults are similar.

Figure 14 shows the relationship between pre-practice postural sway and changes in steadiness. Linear regression analysis revealed a significant relationship between prepractice postural sway and the change in postural sway due to steadiness practice. This result indicates that subjects exhibiting relatively large pre-practice postural sway also exhibit greater reductions in postural sway following force steadiness practice in the plantar flexor muscles. Thus, the effects of practice on postural stability are dependent on prepractice postural stability. This finding is also consistent with the findings of other reports demonstrating that improvements in steadiness are more frequent in subjects with low initial steadiness levels (Manini et al., 2005; Tracy et al., 2004); this strengthens the notion that the effectiveness of training is dependent on the initial level of steadiness.

Fig. 14. Relationship between baseline postural sway and changes in postural sway (Oshita and Yano, 2011c)

As indicated in section 4, multiple factors influence the relationship between force steadiness and postural stability. Although we focused on whether force steadiness practice in the plantar flexor muscles improves postural stability during quiet standing, we demonstrated the functional significance of force fluctuations during voluntary contraction. From the perspective of exercise prescription, the results reported in this section also suggest that even low-frequency, (once a week) low-intensity (within 20% MVC) steadiness practice is an effective method for improving human movement.

#### **6. Conclusion**

276 Applied Biological Engineering – Principles and Practice

and frequency (Table 1). These results indicate that force fluctuation is reduced by lowintensity force steadiness practice but does not change the MVC. Moreover, no effect of

Strength and steadiness practice reduce force fluctuation during the voluntary contraction of the distal muscles of the upper and lower limbs. Keen et al. (1994) found that 4 weeks of strength practice with the first dorsal interosseous muscle with a heavy load (80% of maximum) in 10 young adults (aged 18–27 years) reduced force fluctuation during isometric contraction at 50% MVC. Patten and Kamen (2000) report that the ability of 6 young adults (aged 18–22 years) to match a force trajectory requiring force modulation up to 60% MVC in the dorsiflexor muscles improved after 2 weeks of isometric force

Table 1. Changes in muscle strength and force fluctuation due to steadiness practice in the

These previous findings corroborate those of the present study. Both the existing literature and present results indicate that strength and steadiness training interventions consistently reduce fluctuations during the low-to-moderate-intensity contractions of the distal muscles of the upper and lower limbs. Furthermore, even though the frequency of practice was relatively low (once a week), it was sufficient to reduce the force fluctuation

We also showed that steadiness practice in the plantar flexor muscles reduces the postural sway during quiet standing. In a study involving the upper limbs, Ranganathan et al. (2001) found that skilled finger movement practice improves both the steadiness of the hand muscle and Purdue pegboard test scores. Kornatz et al. (2005) also found that steadiness practice in hand muscles improves the steadiness of the hand muscles and Purdue pegboard test scores. The results of these previous studies led us to hypothesise that steadiness practice in the plantar flexor muscles decreases the force fluctuations of the plantar flexor muscles and improves postural stability. The results of the present study demonstrate that steadiness practice in the plantar flexor muscles reduces postural sway during quiet standing. Therefore, this suggests that the neural strategies employed by the plantar flexor

practice frequency (one or two time per week) was observed between groups.

modulation training.

practice group (Oshita and Yano, 2011c)

in the present study.

This chapter discussed the relationship between force steadiness in lower limb muscles and postural stability during quiet standing. Although previous studies suggest that the

Functional Significance of Force Fluctuation During Voluntary Muscle Contraction 279

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asymmetry of leg muscle functions might affect the human movements (Skelton et al., 2002; Oshita et al., 2009), no significant differences in force steadiness during isometric knee extension or plantar flexion were observed between the 2 legs as shown in section 3. In section 4, a significant correlation between postural stability during quiet standing and force fluctuation during plantar flexion was found only at the corresponding contraction intensities of the plantar flexor muscles in young adults. Furthermore, in section 5, we found that steadiness practice in plantar flexor muscles improves postural stability during quiet standing and that the effects of practice are dependent on pre-practice postural stability. These results will provide useful information to design a training program for postural stability. Usually, the goal of many training programs is improvement of postural stability by an increase in muscle strength (Anderson and Behm, 2005; Holviala et al., 2006). Certainly, strength of the main working muscles to support self body weight is thought to be the most important factor for postural stability. However, MVC in the plantar flexor did not relate with posture sway in our report (Oshita and Yano, 2010c). Further, Kouzaki et al. (2007) reported that postural sway during bipedal quiet standing increases following bed rest despite maintenance of the muscle volume of the main working muscle for human postural standing by strength training. These results indicate that not only muscle strength but also force steadiness is an important factor for postural stability. From the perspective of exercise prescription, the results described in section 5 also suggest that even low-frequency (once a week), low-intensity (within 20% MVC) steadiness practice is an effective method for improving human movement. Therefore, this chapter demonstrates the functional significance of force fluctuations in lower limb muscles.

## **7. Future direction**

So far we have focused on clarifying the relations between postural stability and force steadiness in healthy young men. Regarding the force steadiness, the following investigations are also required:


In particular, unsteady movement or large variability in force output in elderly adults (Galganski, et al., 1993) might lead to difficulties in the performance of daily activities (Kornatz, et al., 2005). By examining the relations between force steadiness and human movement in multiple generations, the findings would more clarify the functional significance of force steadiness and might lead to an understanding of the physiological mechanisms of deteriorations in movement in elderly adult or individuals with neurological disorders.

## **8. Acknowledgment**

These works were supported by following grants

KAKENHI (Grant-in-Aid-for JSPS Fellows (21-2787)) KAKENHI (Grant-in-Aid for Scientific Research "B" (20300235))

#### **9. References**

278 Applied Biological Engineering – Principles and Practice

asymmetry of leg muscle functions might affect the human movements (Skelton et al., 2002; Oshita et al., 2009), no significant differences in force steadiness during isometric knee extension or plantar flexion were observed between the 2 legs as shown in section 3. In section 4, a significant correlation between postural stability during quiet standing and force fluctuation during plantar flexion was found only at the corresponding contraction intensities of the plantar flexor muscles in young adults. Furthermore, in section 5, we found that steadiness practice in plantar flexor muscles improves postural stability during quiet standing and that the effects of practice are dependent on pre-practice postural stability. These results will provide useful information to design a training program for postural stability. Usually, the goal of many training programs is improvement of postural stability by an increase in muscle strength (Anderson and Behm, 2005; Holviala et al., 2006). Certainly, strength of the main working muscles to support self body weight is thought to be the most important factor for postural stability. However, MVC in the plantar flexor did not relate with posture sway in our report (Oshita and Yano, 2010c). Further, Kouzaki et al. (2007) reported that postural sway during bipedal quiet standing increases following bed rest despite maintenance of the muscle volume of the main working muscle for human postural standing by strength training. These results indicate that not only muscle strength but also force steadiness is an important factor for postural stability. From the perspective of exercise prescription, the results described in section 5 also suggest that even low-frequency (once a week), low-intensity (within 20% MVC) steadiness practice is an effective method for improving human movement. Therefore, this chapter demonstrates the functional

So far we have focused on clarifying the relations between postural stability and force steadiness in healthy young men. Regarding the force steadiness, the following

To clarify the relationship between force steadiness and various human movements

To measure the force steadiness in multiple generations and, possibly, in individuals

In particular, unsteady movement or large variability in force output in elderly adults (Galganski, et al., 1993) might lead to difficulties in the performance of daily activities (Kornatz, et al., 2005). By examining the relations between force steadiness and human movement in multiple generations, the findings would more clarify the functional significance of force steadiness and might lead to an understanding of the physiological mechanisms of deteriorations in movement in elderly adult or individuals with neurological

(i.e., walking, to go up (down) stairs, dynamic postural stability, and so on)

significance of force fluctuations in lower limb muscles.

**7. Future direction** 

disorders.

**8. Acknowledgment** 

investigations are also required:

with neurological disorders.

These works were supported by following grants

KAKENHI (Grant-in-Aid-for JSPS Fellows (21-2787))

KAKENHI (Grant-in-Aid for Scientific Research "B" (20300235))


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steadiness with hand muscles in older adults. *Medicine & Science in Sports &* 

body sway velocity information in controlling ankle extensor activities during quiet

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*nutrition survey 2008*. Ministry of health, labour and welfare of Japan, Tokyo, 6 [in

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Y. & Yanagimoto, Y. (2008). Effects of the low frequency self weight bearing training on the elderly residing in or visiting geriatric health care facilities or special nursing homes. *Journal of Training Science for Exercise and Sport*. Vol.20, No.2,


**12** 

*Slovenia* 

**The Influence of Different Elbow Angles on the Twitch Response of the Biceps Brachii Muscle** 

**Between Intermittent Electrical Stimulations** 

*1Department of Biology, Biotechnical Faculty, University of Ljubljana, Ljubljana,* 

Srdjan Djordjevič1,3, Sašo Tomažič2,

*2Department of Telecommunications,* 

*University of Primorska, Koper,* 

Gregor Zupančič1, Rado Pišot3 and Raja Dahmane4

*Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, 3Institute for Kinesiology Research, Science and Research Center of Koper,* 

*4Medical Faculty, Institute of Anatomy, University of Ljubljana, Ljubljana,* 

Prolonged or repeated contractions of skeletal muscles lead to impaired muscle action or to a decrease in force-generating ability. This phenomenon is due to fatigue. Fatigue may be caused by factors/processes within the muscle cells (peripheral fatigue) or by diminished activation from the central nervous system (central fatigue). When observing a muscle twitch, decreases in contraction amplitude, decreases in contraction speed, and prolonged

There are several mechanisms involved in muscle fatigue. The variation of responsible mechanisms has been termed the task dependency of muscle fatigue (Enoka, 2002; Mottram,

The use of different protocols of electrical stimulation can characterize the variety of the task dependency of muscle fatigue. Two examples of the task dependency of fatigue are the phenomena known as low-frequency fatigue (LFF), first described by Edwards et al. (1977), and high-frequency fatigue (HFF), described by Bigland-Ritchie et al. (1979), Jones (1979)

Another possible variable in muscle response could be initial muscle tension/length. Muscle tension can influence the muscle activation pattern and the amplitude of muscle contraction. Two other phenomena also show relation between length of muscle and muscle contraction properties during electrical stimulation "the catchlike property" (Lee et al., 1999; Binder-

The level of fatigue depends on muscle length, in which the contractile response is measured. Using the human tibialis anterior muscle, Sacco et al. (1994) observed that, when

Macleod and Ketlar, 2005) and "twitch potentiation" (Raissier, 2000; Place, 2005).

**1. Introduction** 

2005a; 2005b; Baudry, 2010).

and Jones, et al. (1986).

relaxation phases are the main indicators of fatigue.


## **The Influence of Different Elbow Angles on the Twitch Response of the Biceps Brachii Muscle Between Intermittent Electrical Stimulations**

Srdjan Djordjevič1,3, Sašo Tomažič2, Gregor Zupančič1, Rado Pišot3 and Raja Dahmane4 *1Department of Biology, Biotechnical Faculty, University of Ljubljana, Ljubljana, 2Department of Telecommunications, Faculty of Electrical Engineering, University of Ljubljana, Ljubljana, 3Institute for Kinesiology Research, Science and Research Center of Koper, University of Primorska, Koper, 4Medical Faculty, Institute of Anatomy, University of Ljubljana, Ljubljana, Slovenia* 

## **1. Introduction**

282 Applied Biological Engineering – Principles and Practice

Tokuno, C.D.; Carpenter, M.G.; Thorstensson, A.; Garland, S.J. & Cresswell, A.G. (2007).

Tokuno, C.D.; Garland, S.J.; Carpenter, M.G.; Thorstensson, A. & Cresswell, A.G. (2008).

Tracy, B.L. & Enoka, R.M. (2002). Older adults are less steady during submaximal isometric

Tracy, B.L.; Byrnes, W.C. & Enoka, R.M. (2004). Strength training reduces force fluctuations

Tracy, B.L.; Maluf, K.S.; Stephenson, J.L.; Hunter, S.K. & Enoka, R.M. (2005). Variability of

Vallbo, A.B. & Wessberg, J. (1993). Organization of motor output in slow finger movements

Yoshitake, Y.; Shinohara, M.; Kouzaki, M. & Fukunaga, T. (2004). Fluctuations in plantar

*Physiologica*. Vol.191, No.3, 229-236

No.3, 1004-1012

*of Applied Physiology.* Vol.104, No.5, 1359-1365

*Joural of Applied Physiology*. Vol.96, No.4, 1530-1540

adults. *Muscle & Nerve*. Vol.32, No.4, 533-540

in man. *Journal of Physiology*. Vol.469, 673-691

*Physiology*. Vol.97, No.6, 2090-2097

Control of the triceps surae during the postural sway of quiet standing. *Acta* 

Sway-dependent modulation of the triceps surae H-reflex during standing. *Journal* 

contractions with the knee extensor muscles. *Journal of Applied Physiology*. Vol.92,

during anisometric contractions of the quadriceps femoris muscles in old adults.

motor unit discharge and force fluctuations across a range of muscle forces in older

flexion force are reduced after prolonged tendon vibration. *Journal of Applied* 

Prolonged or repeated contractions of skeletal muscles lead to impaired muscle action or to a decrease in force-generating ability. This phenomenon is due to fatigue. Fatigue may be caused by factors/processes within the muscle cells (peripheral fatigue) or by diminished activation from the central nervous system (central fatigue). When observing a muscle twitch, decreases in contraction amplitude, decreases in contraction speed, and prolonged relaxation phases are the main indicators of fatigue.

There are several mechanisms involved in muscle fatigue. The variation of responsible mechanisms has been termed the task dependency of muscle fatigue (Enoka, 2002; Mottram, 2005a; 2005b; Baudry, 2010).

The use of different protocols of electrical stimulation can characterize the variety of the task dependency of muscle fatigue. Two examples of the task dependency of fatigue are the phenomena known as low-frequency fatigue (LFF), first described by Edwards et al. (1977), and high-frequency fatigue (HFF), described by Bigland-Ritchie et al. (1979), Jones (1979) and Jones, et al. (1986).

Another possible variable in muscle response could be initial muscle tension/length. Muscle tension can influence the muscle activation pattern and the amplitude of muscle contraction. Two other phenomena also show relation between length of muscle and muscle contraction properties during electrical stimulation "the catchlike property" (Lee et al., 1999; Binder-Macleod and Ketlar, 2005) and "twitch potentiation" (Raissier, 2000; Place, 2005).

The level of fatigue depends on muscle length, in which the contractile response is measured. Using the human tibialis anterior muscle, Sacco et al. (1994) observed that, when

The Influence of Different Elbow Angles

head of the radius.

50% relaxation (tr).

directly onto the skin.

on the Twitch Response of the Biceps Brachii Muscle Between Intermittent Electrical Stimulations 285

anatomically, according to Delagi et al. (1975). Maximal muscle amplitude/response was used as an additional criterion for the optimal sensor position. For the BB, the sensor location was at the midpoint of the line between the lateral head of the clavicle and the

Muscle contraction was elicited by single-twitch electrical stimuli. Two self-adhesive electrodes were placed symmetrically around the TMG sensor. The anode was placed distally and the cathode proximally, 20-50 mm from the measuring point. Bipolar ES consisted of a single DC pulse of 1 ms in duration. A typical TMG record with parameters and definitions is shown in Figure 1. The measured parameters are shown in Figure 2. These parameters were the maximal amplitude of the signal (Dm), the delay time from the stimulation to 10% of the maximal contraction (td), the time of contraction from 10% to 90% of the maximal contraction (tc), the time of sustained contraction from 50% contraction to 50% of the relaxation (ts) and the relaxation time from 10% relaxation to

Fig. 1. Experimental setup used to evoke and measure the biceps brachii (BB) isometric twitch contraction responses. The TMG sensor measures muscle radial displacement during twitch contractions induced by short electrical stimuli. The stimulating electrodes are placed

the muscle was fatigued at short muscle lengths, the decline in force was more pronounced than when the muscle was fatigued at optimal length. Although this result was confirmed by Gauthier (1993), other researchers (Fitch et al. 1985; McKenzie et al. 1987; Lee et al., 2007) have observed reduced fatigue in short muscle lengths.

In our preliminary study (unpublished data), we observed the influence of different elbow angles on muscle twitch parameters, measured with the tensiomyography (TMG) method on the biceps brachii (BB) muscle during short-acting electrical stimulation (ES). We observed a shorter contraction time in pre-stretched muscles (long muscles, elbow angle 5°) compared to relaxed muscles (short muscles, elbow angle 60°). The question that arose was whether this observation was an isolated phenomenon or whether similar changes would also occur in different circumstances.

Therefore, the present study explored the twitch-to-twitch effect of an intermittent stimulation protocol at variable muscle lengths (different elbow angles) on the muscle twitch response of the human BB muscle.

Our working hypothesis was that the changes in muscle response to intermittent electrical stimulation would be dissimilar at different elbow angles.

## **2. Materials and methods**

#### **2.1 Subjects**

Nine healthy, sedentary subjects (6 men, 4 left-handed) ranging from 25 to 45 years old (mean of 32.7 ± 8), with no history of muscle or joint problems, participated in this study. All subjects were informed of the purpose and procedures of the study and gave written, informed consent for their participation.

The local ethics committee approved the tensiomyographical measurements.

## **2.2 Measurements**

The contractile properties of the BB muscles on the left and right side were measured with the TMG method, which is classified as a mechanomyographical (MMG) method based on the 1995 convention (CIBA Foundation Symposium, 1995). TMG is based on a displacement sensor detecting muscle belly enlargement in the radial direction. TMG was invented in 1997 (Valencic et al. 1997) and has since become more established (Dahmane et al. 2001; 2005; 2006; Zagar and Krizaj, 2005; Tous-Fajardo, 2010; García-Manso, 2011).

For the measurements, an inductive sensor, incorporating a spring with a coefficient of 0.17 N/mm, was used. It provided an initial pressure of approximately 1.5 x 10-2 N/mm2 on the tip area of 1.13 mm2. The responses of the BB muscles on the right and left sides were compared.

The measured subject sat in a measuring chair. The measured arm was fastened to the frame with two bands to achieve isometric conditions during the measurement. In all of our experiments, isometric conditions were applied within physiological limits. Our referential definition for isometric contraction was "the total length of the muscle tendon complex remains constant." The sensor location for each muscle was determined

the muscle was fatigued at short muscle lengths, the decline in force was more pronounced than when the muscle was fatigued at optimal length. Although this result was confirmed by Gauthier (1993), other researchers (Fitch et al. 1985; McKenzie et al. 1987; Lee et al., 2007)

In our preliminary study (unpublished data), we observed the influence of different elbow angles on muscle twitch parameters, measured with the tensiomyography (TMG) method on the biceps brachii (BB) muscle during short-acting electrical stimulation (ES). We observed a shorter contraction time in pre-stretched muscles (long muscles, elbow angle 5°) compared to relaxed muscles (short muscles, elbow angle 60°). The question that arose was whether this observation was an isolated phenomenon or whether similar changes would

Therefore, the present study explored the twitch-to-twitch effect of an intermittent stimulation protocol at variable muscle lengths (different elbow angles) on the muscle

Our working hypothesis was that the changes in muscle response to intermittent electrical

Nine healthy, sedentary subjects (6 men, 4 left-handed) ranging from 25 to 45 years old (mean of 32.7 ± 8), with no history of muscle or joint problems, participated in this study. All subjects were informed of the purpose and procedures of the study and gave written,

The contractile properties of the BB muscles on the left and right side were measured with the TMG method, which is classified as a mechanomyographical (MMG) method based on the 1995 convention (CIBA Foundation Symposium, 1995). TMG is based on a displacement sensor detecting muscle belly enlargement in the radial direction. TMG was invented in 1997 (Valencic et al. 1997) and has since become more established (Dahmane et al. 2001;

For the measurements, an inductive sensor, incorporating a spring with a coefficient of 0.17 N/mm, was used. It provided an initial pressure of approximately 1.5 x 10-2 N/mm2 on the tip area of 1.13 mm2. The responses of the BB muscles on the right and left sides were

The measured subject sat in a measuring chair. The measured arm was fastened to the frame with two bands to achieve isometric conditions during the measurement. In all of our experiments, isometric conditions were applied within physiological limits. Our referential definition for isometric contraction was "the total length of the muscle tendon complex remains constant." The sensor location for each muscle was determined

The local ethics committee approved the tensiomyographical measurements.

2005; 2006; Zagar and Krizaj, 2005; Tous-Fajardo, 2010; García-Manso, 2011).

have observed reduced fatigue in short muscle lengths.

stimulation would be dissimilar at different elbow angles.

also occur in different circumstances.

**2. Materials and methods** 

**2.1 Subjects** 

**2.2 Measurements** 

compared.

twitch response of the human BB muscle.

informed consent for their participation.

anatomically, according to Delagi et al. (1975). Maximal muscle amplitude/response was used as an additional criterion for the optimal sensor position. For the BB, the sensor location was at the midpoint of the line between the lateral head of the clavicle and the head of the radius.

Muscle contraction was elicited by single-twitch electrical stimuli. Two self-adhesive electrodes were placed symmetrically around the TMG sensor. The anode was placed distally and the cathode proximally, 20-50 mm from the measuring point. Bipolar ES consisted of a single DC pulse of 1 ms in duration. A typical TMG record with parameters and definitions is shown in Figure 1. The measured parameters are shown in Figure 2. These parameters were the maximal amplitude of the signal (Dm), the delay time from the stimulation to 10% of the maximal contraction (td), the time of contraction from 10% to 90% of the maximal contraction (tc), the time of sustained contraction from 50% contraction to 50% of the relaxation (ts) and the relaxation time from 10% relaxation to 50% relaxation (tr).

Fig. 1. Experimental setup used to evoke and measure the biceps brachii (BB) isometric twitch contraction responses. The TMG sensor measures muscle radial displacement during twitch contractions induced by short electrical stimuli. The stimulating electrodes are placed directly onto the skin.

The Influence of Different Elbow Angles

on the Twitch Response of the Biceps Brachii Muscle Between Intermittent Electrical Stimulations 287

Fig. 3. Fatigue-inducing stimulation protocol: ISP = intermittent electrical stimulation

Fig. 4. (a) Muscle twitches between the first 18 s of ISP60, assessed on human BB.

The ISP was repeated six times so that the whole stimulation lasted 90 s, which amounted to a total of 180 100-ms stimulation bouts. IBT was repeated five times. The entire protocol was flanked by two basic twitch stimuli (a single 1-ms impulse), one 3 s before and the other 3 s

protocol; IBT = in between twitch; TS = basic twitch stimulus.

after the end of the protocol.

Fig. 2. (a) The parameters that were measured with the TMG signal: Dm – maximum amplitude (displacement), td – initial delay time, tc – contraction time, ts – sustained contraction time and tr – half relaxation time.

#### **2.3 Measurement protocols**

Throughout the stimulation protocol, muscle activity was monitored with the TMG sensor. The stimulus intensity was set at 66% of a supramaximal twitch that was determined for a single 1-ms electrical impulse, before proceeding with the ES protocol for each muscle.

The electrical intermittent stimulation protocol (ISP) (Figure 3) consisted of 30 100-ms stimulation bouts (100 Hz, 0.1-ms impulse width) with 400-ms pauses between bouts, followed by a 1000-ms pause and an in-between twitch bout (IBT; also 100 Hz, 0.1-ms impulse width; Figures 3 and 4b), followed by a 900-ms pause. The protocol was repeated six times so that the whole stimulation lasted 90 s, which amounted to a total of 180 100-ms stimulation bouts. The entire protocol was flanked by two basic twitch stimuli (TS, single 1 ms impulse), one 3 s before and the other 3 s after end of the protocol.

The data were later read into Matlab (MathWorks, Natick, Massachusetts, USA) and analyzed with that software.

Measurements were performed on the biceps brachii muscles of both arms. On the left arm, the elbow angle was fixed at 5° (intermittent protocol of electrical stimulation at 5° [ISP5]), while the right arm was fixed at 60° (intermittent protocol of electrical stimulation at 60° [ISP60]). The reason for using the BB muscles of both arms was that the recovery from and/or the influence of a certain type of electrical stimulation can be quite prolonged. In severe cases, it may take as long as a few days to achieve full recovery (Jones et al. 1996).

Fig. 2. (a) The parameters that were measured with the TMG signal: Dm – maximum amplitude (displacement), td – initial delay time, tc – contraction time, ts – sustained

Throughout the stimulation protocol, muscle activity was monitored with the TMG sensor. The stimulus intensity was set at 66% of a supramaximal twitch that was determined for a single 1-ms electrical impulse, before proceeding with the ES protocol

The electrical intermittent stimulation protocol (ISP) (Figure 3) consisted of 30 100-ms stimulation bouts (100 Hz, 0.1-ms impulse width) with 400-ms pauses between bouts, followed by a 1000-ms pause and an in-between twitch bout (IBT; also 100 Hz, 0.1-ms impulse width; Figures 3 and 4b), followed by a 900-ms pause. The protocol was repeated six times so that the whole stimulation lasted 90 s, which amounted to a total of 180 100-ms stimulation bouts. The entire protocol was flanked by two basic twitch stimuli (TS, single 1-

The data were later read into Matlab (MathWorks, Natick, Massachusetts, USA) and

Measurements were performed on the biceps brachii muscles of both arms. On the left arm, the elbow angle was fixed at 5° (intermittent protocol of electrical stimulation at 5° [ISP5]), while the right arm was fixed at 60° (intermittent protocol of electrical stimulation at 60° [ISP60]). The reason for using the BB muscles of both arms was that the recovery from and/or the influence of a certain type of electrical stimulation can be quite prolonged. In severe cases, it may take as long as a few days to achieve full recovery

ms impulse), one 3 s before and the other 3 s after end of the protocol.

contraction time and tr – half relaxation time.

**2.3 Measurement protocols** 

analyzed with that software.

(Jones et al. 1996).

for each muscle.

Fig. 3. Fatigue-inducing stimulation protocol: ISP = intermittent electrical stimulation protocol; IBT = in between twitch; TS = basic twitch stimulus.

The ISP was repeated six times so that the whole stimulation lasted 90 s, which amounted to a total of 180 100-ms stimulation bouts. IBT was repeated five times. The entire protocol was flanked by two basic twitch stimuli (a single 1-ms impulse), one 3 s before and the other 3 s after the end of the protocol.

Fig. 4. (a) Muscle twitches between the first 18 s of ISP60, assessed on human BB.

The Influence of Different Elbow Angles

significant differences in tc or Dm.

there were no significant differences in tc, td, ts, tr or Dm.

found with the ISP60 protocol in Dm only (p<0.05).

the two elbow angles (indicated on the figure).

short muscles.

to contractions (ISP twitches), during both the ISP5 and ISP60 protocols.

on the Twitch Response of the Biceps Brachii Muscle Between Intermittent Electrical Stimulations 289

In the basic twitch responses before and after the ISP60 protocol (Figure 6a and Table 1),

In the ISP5 (Figure 6b) protocol, there were significant changes in td, ts, and tr and no

The IBTs had different dynamics of changes compared to those observed in twitches similar

From all the observed parameters in the IBTs during the ISP5 protocol, we found statistically significant differences in Dm only (p<0.05). The same pattern of response/changes was

Fig. 5. The time course of the decline of maximal displacement amplitudes, normalized to the initial amplitude, during the 90 s of the stimulation protocol. ISP5 - open triangles ± SE; ISP60 - black circles ± SE. There was a statistically significant difference (p<0.001) between

Table 1. Results of basic twitch response measurements before and after the ISP in long and

Fig. 4. (b) A detail with two types of twitches: IBT and ISP twitches.

## **2.4 Statistical Analysis**

Paired-samples t-tests were used to compare differences in the changes in contraction parameters td, tc, ts, tr, and Dm as well as the differences between the two protocols (ISP5 and ISP60). Paired t-tests have greater power than unpaired tests when the paired units are similar with respect to "noise factors" that are independent of membership. Paired t-test was used to reduce the effects of confounding factors in our study. Significance for all tests was set at P < 0.05.

## **3. Results**

A typical muscle response to ISP measured with the TMG sensor is shown in Figure 4a (first 18 s of 90-s intermittent stimulation with an extended or flexed elbow). An evident decrease in the contraction amplitude was observed during both ISPs at 15 to 20 s (Figure 5). There was a statistically significant change in responses during both protocols.

With the ISP5 protocol, we observed a significantly faster decrease in effective contraction amplitudes and, at the same time, a greater difference in amplitude decreases at the end of stimulation, compared to the ISP60 protocol (Figure 5). After 60 s of the ISP60 protocol, the ISP twitch amplitude was statistically unchanged.

The results of basic twitch response measurements before and after the ISP in long and short muscles are shown in Table 1.

The differences between time parameters (tc, td, ts, and tr in long [5°] and short [60°] muscles) before the ISP were statistically significant, as shown in Figure 6c and Table 1. The difference between Dm in long (5°) and short (60°) muscles before the ISP was also statistically significant. For example, tc was statistically shorter (tc ISP60=26.3±1.1 and tc ISP5=24.4±2.7, p<0.05) and Dm was smaller in long muscles (Dm ISP60=15.1±4.1, Dm ISP5=8.4±2.1, p<0.001)

Paired-samples t-tests were used to compare differences in the changes in contraction parameters td, tc, ts, tr, and Dm as well as the differences between the two protocols (ISP5 and ISP60). Paired t-tests have greater power than unpaired tests when the paired units are similar with respect to "noise factors" that are independent of membership. Paired t-test was used to reduce the effects of confounding factors in our study. Significance for all tests was

A typical muscle response to ISP measured with the TMG sensor is shown in Figure 4a (first 18 s of 90-s intermittent stimulation with an extended or flexed elbow). An evident decrease in the contraction amplitude was observed during both ISPs at 15 to 20 s (Figure 5). There

With the ISP5 protocol, we observed a significantly faster decrease in effective contraction amplitudes and, at the same time, a greater difference in amplitude decreases at the end of stimulation, compared to the ISP60 protocol (Figure 5). After 60 s of the ISP60 protocol, the

The results of basic twitch response measurements before and after the ISP in long and short

The differences between time parameters (tc, td, ts, and tr in long [5°] and short [60°] muscles) before the ISP were statistically significant, as shown in Figure 6c and Table 1. The difference between Dm in long (5°) and short (60°) muscles before the ISP was also statistically significant. For example, tc was statistically shorter (tc ISP60=26.3±1.1 and tc ISP5=24.4±2.7, p<0.05) and Dm was smaller in long muscles (Dm ISP60=15.1±4.1, Dm

Fig. 4. (b) A detail with two types of twitches: IBT and ISP twitches.

was a statistically significant change in responses during both protocols.

ISP twitch amplitude was statistically unchanged.

muscles are shown in Table 1.

ISP5=8.4±2.1, p<0.001)

**2.4 Statistical Analysis** 

set at P < 0.05.

**3. Results** 

In the basic twitch responses before and after the ISP60 protocol (Figure 6a and Table 1), there were no significant differences in tc, td, ts, tr or Dm.

In the ISP5 (Figure 6b) protocol, there were significant changes in td, ts, and tr and no significant differences in tc or Dm.

The IBTs had different dynamics of changes compared to those observed in twitches similar to contractions (ISP twitches), during both the ISP5 and ISP60 protocols.

From all the observed parameters in the IBTs during the ISP5 protocol, we found statistically significant differences in Dm only (p<0.05). The same pattern of response/changes was found with the ISP60 protocol in Dm only (p<0.05).

Fig. 5. The time course of the decline of maximal displacement amplitudes, normalized to the initial amplitude, during the 90 s of the stimulation protocol. ISP5 - open triangles ± SE; ISP60 - black circles ± SE. There was a statistically significant difference (p<0.001) between the two elbow angles (indicated on the figure).


Table 1. Results of basic twitch response measurements before and after the ISP in long and short muscles.

The Influence of Different Elbow Angles

**4. Discussion** 

on the Twitch Response of the Biceps Brachii Muscle Between Intermittent Electrical Stimulations 291

Fig. 6. (c) Twitch responses of the BB in the long muscle (elbow angle 5°) and short muscle (elbow angle 60°). The differences between tc and Dm in the long (5°) and short (60°) muscles were statistically significant (tc [60°] = 26.3±1.1, tc [5°] = 24.4±2.7, p<0.05)

TMG has been used in previous studies in which linear correlations were found between tc and the percentage of type I muscle fibers (Dahmane et al. 2001) and between relative axial

The initial muscle length (length at the beginning of a contraction) is an extremely important modulator of muscle action. It has been established previously that several skeletal muscle physiological parameters depend on initial muscle length. Examples include the production of force/tension (Rassier et al. 1999), changes in motor unit activity (Ballantyne et al. 1993; Van Zuylen et al. 1988; Kennedy 2001), Ca2+ sensitivity (Stephenson, 1984) and the development of fatigue (Sacco et al., 1994; Fitch et al., 1987; Gauthier et al., 2000; McKenzie

All the cited authors studying the development of fatigue (except Fitch et al. 1987; McKenzie et al. 1987) showed that shortened muscles fatigue more quickly than extended muscles. At first glance, our data were not consistent with most of these studies; however, these studies are difficult to compare, as different measuring approaches were used as well as different muscle groups and stimulation protocols. These differences may explain the inconsistency

In all previously mentioned studies, tetanic-type electrical stimulation was applied to induce fatigue. For example, in the study by Sacco et al. (1994), a fatigue protocol consisting of 6 15-s tetanic stimulations at 30 Hz (on the tibialis anterior) was applied. Rassier (2000) used a muscle fatigue protocol of nine tetanic contractions (50 Hz, 5 s in duration), with 5-s

force and muscle belly radial displacement (Djordjevic et al. 2005).

et al. 1987; Rassier, 2000, Lee et al., 2007).

of the obtained results.

The dynamics (direction and size of changes) of IBT response during the ISP were not significantly different when comparing the ISP60 and ISP5 protocols.

Fig. 6. (a) Twitch responses of the BB before and after ISP60. No statistically significant changes for any of the measured parameters were observed.

Fig. 6. (b) Twitch responses of the BB before and after ISP5. Statistically significant differences were observed for tr and Dm (p<0.05).

Fig. 6. (c) Twitch responses of the BB in the long muscle (elbow angle 5°) and short muscle (elbow angle 60°). The differences between tc and Dm in the long (5°) and short (60°) muscles were statistically significant (tc [60°] = 26.3±1.1, tc [5°] = 24.4±2.7, p<0.05)

## **4. Discussion**

290 Applied Biological Engineering – Principles and Practice

The dynamics (direction and size of changes) of IBT response during the ISP were not

Fig. 6. (a) Twitch responses of the BB before and after ISP60. No statistically significant

Fig. 6. (b) Twitch responses of the BB before and after ISP5. Statistically significant

differences were observed for tr and Dm (p<0.05).

changes for any of the measured parameters were observed.

significantly different when comparing the ISP60 and ISP5 protocols.

TMG has been used in previous studies in which linear correlations were found between tc and the percentage of type I muscle fibers (Dahmane et al. 2001) and between relative axial force and muscle belly radial displacement (Djordjevic et al. 2005).

The initial muscle length (length at the beginning of a contraction) is an extremely important modulator of muscle action. It has been established previously that several skeletal muscle physiological parameters depend on initial muscle length. Examples include the production of force/tension (Rassier et al. 1999), changes in motor unit activity (Ballantyne et al. 1993; Van Zuylen et al. 1988; Kennedy 2001), Ca2+ sensitivity (Stephenson, 1984) and the development of fatigue (Sacco et al., 1994; Fitch et al., 1987; Gauthier et al., 2000; McKenzie et al. 1987; Rassier, 2000, Lee et al., 2007).

All the cited authors studying the development of fatigue (except Fitch et al. 1987; McKenzie et al. 1987) showed that shortened muscles fatigue more quickly than extended muscles. At first glance, our data were not consistent with most of these studies; however, these studies are difficult to compare, as different measuring approaches were used as well as different muscle groups and stimulation protocols. These differences may explain the inconsistency of the obtained results.

In all previously mentioned studies, tetanic-type electrical stimulation was applied to induce fatigue. For example, in the study by Sacco et al. (1994), a fatigue protocol consisting of 6 15-s tetanic stimulations at 30 Hz (on the tibialis anterior) was applied. Rassier (2000) used a muscle fatigue protocol of nine tetanic contractions (50 Hz, 5 s in duration), with 5-s

The Influence of Different Elbow Angles

on the Twitch Response of the Biceps Brachii Muscle Between Intermittent Electrical Stimulations 293

more precise (statistically significant) detection of changes occurring during the fatigue

Fig. 7. The IBTs before (a and b) and after the ISP protocol (c and d) were measured at two different lengths of the BB muscle (elbow angle 5 and 60°). Shorter contraction time and faster fatigue (decline of contraction amplitude) were observed in the long muscle (elbow angle 5°). A statistically significant difference in fatigue development during the ISP was

displacement achieved a steady state; however, this finding was not observed during ISP5. The influence of muscle length was reflected in muscle contractions and twitch conditions

The crucial question that we wanted to answer in this study was whether the shorter contraction times at smaller angles (longer muscle) were related to changed muscle activation patterns (motor unit recruitment order) or whether there were other mechanisms involved. Hence, we expected the fatigue process to be more pronounced if faster twitch fibers were recruteited during contraction. Although this finding would not have been definite proof, it would have indicated that such a hypothesis could not be rejected. The results confirmed our working hypothesis. They showed a higher fatigue rate and a different time course in long muscles using the same ISP protocol. If we accept that the shorter tc in long muscles means a greater percentage recruitment of fast twitch fibers, then a faster and more pronounced onset of fatigue during the ISP5 protocol seems to be a logical

Prolonged or repeated contractions of skeletal muscles lead to impaired muscle action or to a decrease in force-generating ability. The present study explores the twitch-to-twitch effect of an intermittent stimulation protocol at variable muscle lengths (different elbow angles) on

observed after 10 s for the two elbow angles (e). During ISP60, after 50 s, the BB

and during fatigue conditions produced by the ISP.

**5. Conclusion and future directions** 

consequence.

process. A summary of important results/differences is shown in Figure 7.

intervals between contractions, on the quadricep muscle. Gauthier et al. (1993) used tetanic stimulation (train duration = 500 ms, duty cycle = 0.25) decreasing from 100 to 50 Hz with a 250-s duration on the rat diaphragm. In Fitch and McComas's (1993) study, the fatiguing procedure consisted of either indirect tetanic stimulation at 20 Hz or maximal voluntary contractions; each procedure lasted 90 s. Here, the observed muscle was the human ankle dorsal flexor muscle.

An important factor that may be responsible for the effects of stimulation is the recruitment order because this factor would affect the dynamics of fatigue. In our study, we used an intermittent type of transcutaneous electrical stimulation. Bursts of 100 Hz for 100 ms were given twice per second with two types of rest intervals (400 ms in between each pulse train and 1000 ms every 30 stimuli; Figure 3b), which was different from any of the previously published protocols. Our idea was to simulate the moderate cyclic activity of the muscles during fast walking, jogging or cycling. In this type of muscle activity, it is important that there is no overlapping of the contraction and the relaxation phases during fatigue development. Using the intermittent type ES, we wanted to avoid the effects of HFF, which can produce very dramatic losses of force/amplitude of contraction, and it is questionable whether HFF is a "normal" (physiological) fatigue mechanism (Jones 1996).

We believe that twitch intermittent-type ES has similar recruitment patterns to those found during voluntary action. A few studies have supported our contention that the recruitment order due to transcutaneous ES-induced contractions is non-selective (normal recruitment order versus reverse recruitment order) (Adams et al. 1993; Bickel et al. 2003; Binder-Macleod et al. 1995; Dahmane et al. 2005; Feiereisen et al. 1997; Knaflitz et al.1990; Slade et al. 2003).

Nevertheless, with the ISP5 protocol, we observed an almost immediate drop in the twitch amplitude (Figure 3c), while with the ISP60 protocol, a decrease occurred after 10-20 s. This last observation could be attributed to a usual HFF response (Jones 1996). In the time frame of 10-20 s, the difference between the two protocols was most evident. After 60 s with the ISP60 protocol, the twitch amplitude was unchanged, while the twitch amplitude with the ISP5 protocol continued to decrease (Figures 5 and 7).

A statistically significant difference was observed between the two protocols regarding the twitch response of the biceps brachii, while the differences in basic twitches before and after the ISP were not significant, except for td, ts, and tr when comparing the ISP5 and ISP60 protocols.

This finding can be explained by the different electrical stimuli and by the delay (1 s) at the end of the stimulation protocols before the 1-ms twitch. The reasoning for incorporating the 1-s delay into the protocol following the ISP, as opposed to the normal 400-ms delay between twitches, was to prevent the possibility of twitch fusion. The stimulation protocol is depicted in Figure 4b.

This study showed that the high data acquisition rate during the ISP resulted in a better assessment of the temporal components of the fatigue process. It also revealed that twitch measurements every 15 s (IBT) did not alone show statistically significant differences between the ISP protocols (it is true that the conditions were slightly different: 1000 ms versus 400 ms rest between 100 ms stimulus durations). The applied procedure and the recording method enabled a higher sampling rate (180 ISP twitches versus 7 IBTs), which resulted in a much more precise (statistically significant) detection of changes occurring during the fatigue process. A summary of important results/differences is shown in Figure 7.

Fig. 7. The IBTs before (a and b) and after the ISP protocol (c and d) were measured at two different lengths of the BB muscle (elbow angle 5 and 60°). Shorter contraction time and faster fatigue (decline of contraction amplitude) were observed in the long muscle (elbow angle 5°). A statistically significant difference in fatigue development during the ISP was observed after 10 s for the two elbow angles (e). During ISP60, after 50 s, the BB displacement achieved a steady state; however, this finding was not observed during ISP5. The influence of muscle length was reflected in muscle contractions and twitch conditions and during fatigue conditions produced by the ISP.

The crucial question that we wanted to answer in this study was whether the shorter contraction times at smaller angles (longer muscle) were related to changed muscle activation patterns (motor unit recruitment order) or whether there were other mechanisms involved. Hence, we expected the fatigue process to be more pronounced if faster twitch fibers were recruteited during contraction. Although this finding would not have been definite proof, it would have indicated that such a hypothesis could not be rejected. The results confirmed our working hypothesis. They showed a higher fatigue rate and a different time course in long muscles using the same ISP protocol. If we accept that the shorter tc in long muscles means a greater percentage recruitment of fast twitch fibers, then a faster and more pronounced onset of fatigue during the ISP5 protocol seems to be a logical consequence.

## **5. Conclusion and future directions**

292 Applied Biological Engineering – Principles and Practice

intervals between contractions, on the quadricep muscle. Gauthier et al. (1993) used tetanic stimulation (train duration = 500 ms, duty cycle = 0.25) decreasing from 100 to 50 Hz with a 250-s duration on the rat diaphragm. In Fitch and McComas's (1993) study, the fatiguing procedure consisted of either indirect tetanic stimulation at 20 Hz or maximal voluntary contractions; each procedure lasted 90 s. Here, the observed muscle was the human ankle

An important factor that may be responsible for the effects of stimulation is the recruitment order because this factor would affect the dynamics of fatigue. In our study, we used an intermittent type of transcutaneous electrical stimulation. Bursts of 100 Hz for 100 ms were given twice per second with two types of rest intervals (400 ms in between each pulse train and 1000 ms every 30 stimuli; Figure 3b), which was different from any of the previously published protocols. Our idea was to simulate the moderate cyclic activity of the muscles during fast walking, jogging or cycling. In this type of muscle activity, it is important that there is no overlapping of the contraction and the relaxation phases during fatigue development. Using the intermittent type ES, we wanted to avoid the effects of HFF, which can produce very dramatic losses of force/amplitude of contraction, and it is questionable

We believe that twitch intermittent-type ES has similar recruitment patterns to those found during voluntary action. A few studies have supported our contention that the recruitment order due to transcutaneous ES-induced contractions is non-selective (normal recruitment order versus reverse recruitment order) (Adams et al. 1993; Bickel et al. 2003; Binder-Macleod et al. 1995; Dahmane et al. 2005; Feiereisen et al. 1997; Knaflitz et al.1990; Slade et

Nevertheless, with the ISP5 protocol, we observed an almost immediate drop in the twitch amplitude (Figure 3c), while with the ISP60 protocol, a decrease occurred after 10-20 s. This last observation could be attributed to a usual HFF response (Jones 1996). In the time frame of 10-20 s, the difference between the two protocols was most evident. After 60 s with the ISP60 protocol, the twitch amplitude was unchanged, while the twitch amplitude with the

A statistically significant difference was observed between the two protocols regarding the twitch response of the biceps brachii, while the differences in basic twitches before and after the ISP were not significant, except for td, ts, and tr when comparing the ISP5 and ISP60

This finding can be explained by the different electrical stimuli and by the delay (1 s) at the end of the stimulation protocols before the 1-ms twitch. The reasoning for incorporating the 1-s delay into the protocol following the ISP, as opposed to the normal 400-ms delay between twitches, was to prevent the possibility of twitch fusion. The stimulation protocol is

This study showed that the high data acquisition rate during the ISP resulted in a better assessment of the temporal components of the fatigue process. It also revealed that twitch measurements every 15 s (IBT) did not alone show statistically significant differences between the ISP protocols (it is true that the conditions were slightly different: 1000 ms versus 400 ms rest between 100 ms stimulus durations). The applied procedure and the recording method enabled a higher sampling rate (180 ISP twitches versus 7 IBTs), which resulted in a much

whether HFF is a "normal" (physiological) fatigue mechanism (Jones 1996).

ISP5 protocol continued to decrease (Figures 5 and 7).

dorsal flexor muscle.

al. 2003).

protocols.

depicted in Figure 4b.

Prolonged or repeated contractions of skeletal muscles lead to impaired muscle action or to a decrease in force-generating ability. The present study explores the twitch-to-twitch effect of an intermittent stimulation protocol at variable muscle lengths (different elbow angles) on

The Influence of Different Elbow Angles

Res 114, 117-123.

[proceedings]. J Physiol 295, 90P-91P.

362, 205-213.

265-270.

Neurol 64, 401-413.

Biol Lett 7, 367-369.

Muscle Nerve 36, 789–797.

J Neurophysiol 94(4), 2878-87.

on the Twitch Response of the Biceps Brachii Muscle Between Intermittent Electrical Stimulations 295

[16] Feiereisen, P., Duchateau, J., Hainaut, K., 1997. Motor unit recruitment order during

[17] Fitch, S., McComas, A., 1985. Influence of human muscle length on fatigue. J Physiol

[18] García-Manso, J.M., Rodríguez-Ruiz, D., Rodríguez-Matoso, D., De Saa, Y., Sarmiento,

[19] Gauthier, A.P., Faltus, R.E., Macklem, P.T., Bellemare, F. 1993. Effects of fatigue on the length-tetanic force relationship of the rat diaphragm. J Appl Physiol 74, 326-332. [20] Jones, D.A., 1979. Change in excitation threshold as a cause of muscular fatigue

[21] Jones, D.A., 1996. High-and low-frequency fatigue revisited. Acta Physiol Scand 156,

[22] Jones, D.A., Bigland-Ritchie, B., Edwards, R.H., 1979. Excitation frequency and muscle

[23] Kennedy, P.M., Cresswell, A.G., 2001. The effect of muscle length on motor-unit recruitment during isometric plantar flexion in humans. Exp Brain Res 137, 58-64. [24] Kersevan, K., Valencic, V., Djordjevic, S., Simunic, B. 2002. The muscle adaptation

[25] Knaflitz, M., Merletti, R., De Luca, C.J., 1990. Inference of motor unit recruitment order in voluntary and electrically elicited contractions. J Appl Physiol 68, 1657-1667. [26] Lee, S.C., Gerdom, M.L., Binder-Macleod, S.A., 1999. Effects of length on the catchlike property of human quadriceps femoris muscle. Phys Ther 79(8), 738-48. [27] Lee, S.C., Braim, A., Becker, C.N., Prosser, L.A., Tokay, A.M., Binder Macleod, S.A.,

[28] McKenzie, D.K., Gandevia, S.C., 1987. Influence of muscle length on human inspiratory and limb muscle endurance. Respir Physiol 67, 171-182. [29] Mottram, C.J., Christou, E-A., Meyer, F.G., Enoka, R.M., 2005. Frequency modulation

[30] Mottram, C.J., Jakobi, J.M., Semmler, J.G., Enoka, R.M., 2005. Motor-unit activity differs with load type during a fatiguing contraction. J Neurophysiol, 93(3), 1381-92. [31] Place, N., Mafuletti, N.A., Ballay, Y., Lepers, R., 2005. Twitch potentiation is greater

[32] Rassier, D.E., 2000. The effects of length on fatigue and twitch potentiation in human

[33] Rassier, D.E., MacIntosh, B.R., Herzog, W., 1999. Length dependence of active force

[34] Sacco, P., McIntyre, D.B., Jones, D.A., 1994. Effects of length and stimulation frequency on fatigue of the human tibialis anterior muscle. J Appl Physiol 77, 1148-1154.

quadriceps muscle length. J Appl Physiol, 98, 429–436.

production in skeletal muscle. J Appl Physiol 86, 1445-1457.

skeletal muscle. Clin Physiol 20, 474-482.

fatigue: mechanical responses during voluntary and stimulated contractions. Exp

process as a result of pathological changes or specific training procedures. Cell Mol

2007. Diminished fatigue at reduced muscle length in human skeletal muscle.

of motor unit discharge has task-dependent effects on fluctuations in motor output.

after a fatiguing submaximal isometric contraction performed at short vs. long

triathlon using tensiomyography (TMG). J Sports Sci 29(6), 619-25

voluntary and electrically induced contractions in the tibialis anterior. Exp Brain

S., Quiroga, M., 2011. Assessment of muscle fatigue after an ultra-endurance

the muscle twitch response of the human biceps brachii muscle. Results showed a higher fatigue rate and a different time course in long muscles compared to short muscle using the same ISP protocol. For a better understanding of the detected changes and underlying processes, further research, in combination with other methods (EMG …) and conditions, e.g., normalize(load) cyclic voluntary muscle activation is required.

#### **6. References**


the muscle twitch response of the human biceps brachii muscle. Results showed a higher fatigue rate and a different time course in long muscles compared to short muscle using the same ISP protocol. For a better understanding of the detected changes and underlying processes, further research, in combination with other methods (EMG …) and conditions,

[1] Adams, G.R., Harris, R.T., Woodard, D., Dudley, G.A., 1993. Mapping of electrical

[2] Ballantyne, B.T., Kukulka, C.G., Soderberg, G.L., 1993. Motor unit recruitment in human

[3] Baudry, S., Maerz, A.H., Gould, J-R-, Enoka, R.M., 2011. Task- and time-dependent

[4] Bickel, C.S., Slade, J.M., Warren, G.L., Dudley, G.A., 2003. Fatigability and variablefrequency train stimulation of human skeletal muscles. Phys Ther 83, 366-373. [5] Bigland-Ritchie, B., Jones, D.A., Woods, J.J., 1979. Excitation frequency and muscle

[6] Binder-Macleod, S.A., Halden, E.E., Jungles, K.A., 1995. Effects of stimulation intensity

[7] Binder-Macleod, S.A., Kesar, T., 2005. Catchlike property of skeletal muscle: recent

[8] Burger, H., Valencic, V., Marincek, C., Kogovsek, N., 1996. Properties of musculus gluteus maximus in above-knee amputees. Clin Biomech (Bristol, Avon) 11, 35-38. [9] Dahmane, R., Valenčič, V., Knez, N., Eržen, I., 2001. Evaluation of the ability to make

[10] Dahmane, R., Djordjevic, S., Simunic, B., Valencic, V., 2005. Spatial fiber type

[11] Dahmane R, Djordjevic S, Smerdu V (2006) Adaptive potential of human biceps

[14] Djordjevič, S., Simunič. B., 2005. Comparison between parameters of axial force and

[15] Edwards, R.H., Hill, D.K., Jones, D.A., Merton, P.A., 1977. Fatigue of long duration in

mechanomyographical methods. Med Biol Eng Comput 44, 999-1006. [12] *Delagi, E.F., Perotto, A., Iazzetti, J., Morrison, D., 1975. Anatomic guide for the electromyographer: the limbs. In: Thomas, C.C. (Eds). Springfield, Illinois, pp. 35-43.* [13] Delitto, A., Brown, M., Strube, M.J., Rose, S.J., Lehman, R.C. 1989. Electrical stimulation

findings and clinical implications. Muscle Nerve 31(6):681-93.

medial gastrocnemius muscle during combined knee flexion and plantar flexion

modulation of Ia presynaptic inhibition during fatiguing contractions performed

fatigue: electrical responses during human voluntary and stimulated contractions.

on the physiological responses of human motor units. Med Sci Sports Exerc 27(4),

non-invasive estimation of muscle contractile properties on the basis of the muscle

distribution in normal human muscle. Histochemical and tensiomyographical

femoris muscle demonstrated by histochemical, immunohistochemical and

of quadriceps femoris in an elite weight lifter: a single subject experiment. Int J

muscle radial displacement during isometric twitch contraction In Proceedings of

e.g., normalize(load) cyclic voluntary muscle activation is required.

stimulation using. MRI. J Appl Physiol 74, 532-537.

isometric contractions. Exp Brain Res 93, 492-498.

by humans. J Neurophysiol, 106(1), 265-73.

belly response. Med Biol Eng Comp 38, 51-56.

the European College of Sport Science, Beograd.

human skeletal muscle after exercise. J Physiol 272, 769-778.

evaluation. J Biomech 38, 2451-2459.

Sports Med 10, 187-191.

Exp Neurol 64, 414-427.

556-565.

**6. References** 


**13** 

*Japan* 

**Experimental Examination** 

**Osteoarthritis of the Knee** 

**on the Effects and Adaptation Condition** 

**of the Fibula Excision Method Using** 

Nobutaka Maezaki, Tsutomu Ezumi and Masashi Hachiya *Shibaura Institute of Technology, Yokohama Minami Kyousai Hospital* 

The knee joint is a joint where arthropathy occurs frequently. Osteoarthritis of the Knee (: Knee OA) is the most important typical joint disease. In the medical orthopedics field, 900 thousand people regularly go to the hospital annually, of which the frequency of senior citizens is high. Conditions of deformations, such those of the cartilage between the knee joints, wearing out are common. Among Japanese people, pain is common on the inside of the knee. Depending upon the advancement of Knee OA, there are times when walking becomes difficult. The diagnosis of Knee OA generally measures leg alignment. Especially FTA, which measures the angle of the femur and the tibia that form the knee joint, provides a guide for the decisive deformation type and operation invasive quantity through measuring fixed quantities. In FTA measurement, a normal knee shows 172°~176°, inside contravariant shape knee arthropathy (O leg) is above 180°, and outside contravariant shape knee arthropathy (X leg) is below 170°. From previous reports of Knee OA types, among Japanese people, inside contravariant shape knee arthropathy (O leg) is common, and among Europeans and Americans, outside contravariant shape knee arthropathy (X leg) is common. When a mechanical factor related to the cause is common, therapeutic reform of the mechanical state becomes the main purpose. Implementation of operations, such as High tibial osteotomy (: HTO), total knee arthroplasty and (: TKA), in addition to minimally invasive surgery (: MIS), is sometimes necessary depending upon

Fig.1 shows the Osteoarthritis knee method and fibula excision method. The operation considers for four conditions: (1) The skin it is a little ardently, (2) the damage to the soft section organization is only a little, (3) the bleeding quantity is small, and (4) the bone excision is only a little. Operation requires that all above conditions be satisfied. Along with these four conditions, for the patient there are five: (1) operation time is short, (2) after operating, the pain is light, (3) the operation marks must be small and clean, (4) recovery is quick, and (5) economic burden is light. Presently, there is a fibula excision method for one

**1. Introduction** 

the condition.

**the Stress Freezing Method on the** 


## **Experimental Examination on the Effects and Adaptation Condition of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee**

Nobutaka Maezaki, Tsutomu Ezumi and Masashi Hachiya *Shibaura Institute of Technology, Yokohama Minami Kyousai Hospital Japan* 

#### **1. Introduction**

296 Applied Biological Engineering – Principles and Practice

[35] Slade, J.M., Bickel, C.S., Warren, G.L., Dudley, G.A., 2003. Variable frequency trains

[36] Stephenson, D.G., Wendt, I.R. 1984. Length dependence of changes in sarcoplasmic

[37] Tous-Fajardo, J., Moras, G., Rodríguez-Jiménez, S., Usach, R., Doutres, D.M.,

[38] Valencic, V., Knez, N., 1997. Measuring of skeletal muscles' dynamic properties. Artif

[39] Van Zuylen, E.J., Gielen, C.C., Denier van der Gon, J.J., 1988. Coordination and

[40] Zagar, T., Krizaj, D. 2005. Validation of an accelerometer for determination of muscle

belly radial displacement. Med Biol Eng Comput. 43,78-84.

92.

761-6.

Organs 21, 240-242.

Neurophysiol 60, 1523-1548.

J Muscle Res Cell Motil 5, 243-272.

enhance torque independent of stimulation amplitude. Acta Physiol Scand 177, 87-

calcium concentration and myofibrillar calcium sensitivity in striated muscle fibres.

Maffiuletti, N.A., 2010. Inter-rater reliability of muscle contractile property measurements using non-invasive tensiomyography. J Electromyogr Kinesiol 20(4),

inhomogeneous activation of human arm muscles during isometric torques. J

The knee joint is a joint where arthropathy occurs frequently. Osteoarthritis of the Knee (: Knee OA) is the most important typical joint disease. In the medical orthopedics field, 900 thousand people regularly go to the hospital annually, of which the frequency of senior citizens is high. Conditions of deformations, such those of the cartilage between the knee joints, wearing out are common. Among Japanese people, pain is common on the inside of the knee. Depending upon the advancement of Knee OA, there are times when walking becomes difficult. The diagnosis of Knee OA generally measures leg alignment. Especially FTA, which measures the angle of the femur and the tibia that form the knee joint, provides a guide for the decisive deformation type and operation invasive quantity through measuring fixed quantities. In FTA measurement, a normal knee shows 172°~176°, inside contravariant shape knee arthropathy (O leg) is above 180°, and outside contravariant shape knee arthropathy (X leg) is below 170°. From previous reports of Knee OA types, among Japanese people, inside contravariant shape knee arthropathy (O leg) is common, and among Europeans and Americans, outside contravariant shape knee arthropathy (X leg) is common. When a mechanical factor related to the cause is common, therapeutic reform of the mechanical state becomes the main purpose. Implementation of operations, such as High tibial osteotomy (: HTO), total knee arthroplasty and (: TKA), in addition to minimally invasive surgery (: MIS), is sometimes necessary depending upon the condition.

Fig.1 shows the Osteoarthritis knee method and fibula excision method. The operation considers for four conditions: (1) The skin it is a little ardently, (2) the damage to the soft section organization is only a little, (3) the bleeding quantity is small, and (4) the bone excision is only a little. Operation requires that all above conditions be satisfied. Along with these four conditions, for the patient there are five: (1) operation time is short, (2) after operating, the pain is light, (3) the operation marks must be small and clean, (4) recovery is quick, and (5) economic burden is light. Presently, there is a fibula excision method for one

Experimental Examination on the Effects and Adaptation Condition

**2.1 FTA, Mikulicz line** 

(X leg) is common.

Fig. 2. FTA and Mikulicz line

an imbalance of muscular strength or becoming fat).

**2. FTA, Mikulicz lineand and osteoarthritis of the knee** 

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 299

In the knee joint, the inside type (O leg) or outer part type (X leg) in the guide, are used for making a decision. An example is shown in Fig.2 of two Tsugas of FTA and the Mikulicz line. FTA is the angle which consists of the extended shaft direction of the femur and the tibia seen from the front. As for FTA of a normal knee, the range is 173° to approximately 176°. The inside type (O leg) for FTA is above 180°, and the outer part type (X leg) for FTA is below 170°. It is something which the Mikulicz line, the line which ties the thigh antique center and the foot joint center, displays for the leg load line in the standing position. Specifically, this is the line condition of the legs under the arrangement state of the pelvis, femur, tibia and ankle. A normal knee passes by the fog and outside from the center of the knee. As for an O leg, from the center of the knee it passes on the inside. In this research, FTA was utilized, and the leg alignment was decided. Among reports of Knee OA types, in Japanese people, the inside contravariant shape Osteoarthritis of the knee (O leg) is common, and among Europeans and Americans the outside contravariant shape Knee OA

Osteoarthritis of the knee is classified from appearance and inspection results; inside contravariant shape Knee OA (O leg) and the outside contravariant shape knee arthropathy (X leg). As dangerous factors of emergence there exists: history of external wounds, arthritis, age and obesity as four characteristic items for which Knee OA risk is increased. The emergence ratio becomes high from around 40 years old, and the frequency which emerges in senior citizens is high. As for the male to female ratio of patients, male : female = 1: 4. As a cause, mechanical factors are pointed out (e.g., stress concentrated inside the knee such as

operation technique of MIS. The object of this operation technique system is inside contravariant shape knee arthropathy (O leg). Especially, from the present condition where a large majority of patients are senior citizens, an optimum operation technique system will have the lowest physical strength burden on the patient. In this technique system, the fibula is revised so that the alignment of the legs reaches the normal position. However, the remedy guidelines of deformation characteristic arthropathy are being investigated presently in the Japanese medical orthopedics field. Especially, the occasion where engineering new technology is introduced in the future, reports regarding physicians on site, where engineering knowledge and experience influence the result, are many in number. For example, the excision quantity, detection angle, etc, of specifications and the bone positions of the affected parts examination and operation invasive quantity decisions, etc, are made at the time of planning before the operation.

In this research, the fibula excision method, which is an MIS was examined. This experiment dealt with the knee joint of a normal state and Osteoarthritis of the Knee before the operation and after the operation. The experiment supposed one foot standing and concerned the resultant stress state. Grasp of the mechanical state is important in operation, so this is useful as a mechanical guide at the time of planning before operation. In addition, mechanical examination of this operation system which can lighten physical strength burden with aging patients as a quite urgent characteristic is high.

Therefore, the remaining state of FTA and the meniscus, which are diagnostic guides of Osteoarthritis of the knee, influence the results of clearing for operation. A hybrid experiment used the 3-dimensional stress freezing method and a pressure gauge to examine the effectiveness and application condition of the fibula excision method.

Fig. 1. Osteoarthritis of knee method and fibula excision method

## **2. FTA, Mikulicz lineand and osteoarthritis of the knee**

## **2.1 FTA, Mikulicz line**

298 Applied Biological Engineering – Principles and Practice

operation technique of MIS. The object of this operation technique system is inside contravariant shape knee arthropathy (O leg). Especially, from the present condition where a large majority of patients are senior citizens, an optimum operation technique system will have the lowest physical strength burden on the patient. In this technique system, the fibula is revised so that the alignment of the legs reaches the normal position. However, the remedy guidelines of deformation characteristic arthropathy are being investigated presently in the Japanese medical orthopedics field. Especially, the occasion where engineering new technology is introduced in the future, reports regarding physicians on site, where engineering knowledge and experience influence the result, are many in number. For example, the excision quantity, detection angle, etc, of specifications and the bone positions of the affected parts examination and operation invasive quantity decisions, etc,

In this research, the fibula excision method, which is an MIS was examined. This experiment dealt with the knee joint of a normal state and Osteoarthritis of the Knee before the operation and after the operation. The experiment supposed one foot standing and concerned the resultant stress state. Grasp of the mechanical state is important in operation, so this is useful as a mechanical guide at the time of planning before operation. In addition, mechanical examination of this operation system which can lighten physical strength

Therefore, the remaining state of FTA and the meniscus, which are diagnostic guides of Osteoarthritis of the knee, influence the results of clearing for operation. A hybrid experiment used the 3-dimensional stress freezing method and a pressure gauge to examine

(a) Osteoarthritis of knee method (b) Fibula excision

Fig. 1. Osteoarthritis of knee method and fibula excision method

are made at the time of planning before the operation.

burden with aging patients as a quite urgent characteristic is high.

the effectiveness and application condition of the fibula excision method.

In the knee joint, the inside type (O leg) or outer part type (X leg) in the guide, are used for making a decision. An example is shown in Fig.2 of two Tsugas of FTA and the Mikulicz line. FTA is the angle which consists of the extended shaft direction of the femur and the tibia seen from the front. As for FTA of a normal knee, the range is 173° to approximately 176°. The inside type (O leg) for FTA is above 180°, and the outer part type (X leg) for FTA is below 170°. It is something which the Mikulicz line, the line which ties the thigh antique center and the foot joint center, displays for the leg load line in the standing position. Specifically, this is the line condition of the legs under the arrangement state of the pelvis, femur, tibia and ankle. A normal knee passes by the fog and outside from the center of the knee. As for an O leg, from the center of the knee it passes on the inside. In this research, FTA was utilized, and the leg alignment was decided. Among reports of Knee OA types, in Japanese people, the inside contravariant shape Osteoarthritis of the knee (O leg) is common, and among Europeans and Americans the outside contravariant shape Knee OA (X leg) is common.

Fig. 2. FTA and Mikulicz line

Osteoarthritis of the knee is classified from appearance and inspection results; inside contravariant shape Knee OA (O leg) and the outside contravariant shape knee arthropathy (X leg). As dangerous factors of emergence there exists: history of external wounds, arthritis, age and obesity as four characteristic items for which Knee OA risk is increased. The emergence ratio becomes high from around 40 years old, and the frequency which emerges in senior citizens is high. As for the male to female ratio of patients, male : female = 1: 4. As a cause, mechanical factors are pointed out (e.g., stress concentrated inside the knee such as an imbalance of muscular strength or becoming fat).

Experimental Examination on the Effects and Adaptation Condition

Fig. 3. Circular polariscope

(2) the stress state can be known.

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 301

Fringe order and the relationship of principal stress which occurs becomes (1).

 *N t* 

**3.2 Material error of relation between experimental model and actual model** 

relief with extension of 0.0125 have been reported as representing 95% or more.

sensitivity, and σ1 and σ2 are the principal stresses inside the slices.

epoxy resin concerning the quantitative error of the bone.

1 2 *N t* ( ) 

Here, for the N fringe order, t is the thickness of sliced specimen, α is the photoelastic

In addition, with respect to free boundaries, the σ1 each of σ2 becomes 0. Therefore, through

The epoxy resin of the photoelastic material used as the test material is an isotropic homogeneous body, but the organism bone (sponge bone and fine bone, from marrow constitution) is an anisotropic heterogeneous body. Due to this, error occurs in the comparison analysis of the material and the heterogeneous material of which Young's modulus, *E*, is homogeneous. Depending on this, examination becomes necessary by use of

Concerning this, Nishida allotted the epoxy resin of Young's modulus, *E*, which differs by layer, and a bend experiment which imitated the bone was performed. The design of the experiment is shown in Fig.4. As a result of the experiment, the error of Young's modulus, *E*, was calculated to be 10% when the experiment was performed on a solid monolayer structure. As the quantitative error is small, quantitative reproducibility can be expected. In addition, for the dynamic quality of the bone, due to a characteristic difference and personal equation, for the femur of an adult male 30~50 years of age, an average tension of 137.30MPa, an elastic limit of 100.82Mpa, and a recovery factor of the distortion due to stress

As for the bone, to think of the body as being composed of photoelastic material and use a photoelastic experiment is favorable. This method, which is a powerful experimental analysis method in stress distribution visualization of the whole bone, was adopted on the basis of these reports. In addition, mechanical characteristics of the silicon rubber which was

(1)

[MPa] (2)

## **3. Photoelastic theory, experimental model and actual model by epoxy resin**

## **3.1 Photoelastic theory**

The similarity rule is generally utilized for model production and analysis method. Production and an experiment must consider and satisfy the following conditions. (1) The experimental model and actual model from examination and supposition must be within the limit of elasticity, (2) Similarity of experimental model and actual model, (3) agreement of load point, load distribution and similarity, (4) similarity to Poisson's ratio *ν*. Then, when all conditions are satisfied, even with high polymer materials such as the epoxy resin, which was used for the experiment, the stress distribution of actual model of steel, alloy and concrete, etc, agrees. In addition, experimental values which can match the stress values of the actual model by conversion are possible.

However, like this experiment in the case of 3 dimensional photoelasticity, there are times when it does not agree to these under heating. It is necessary to know the characteristics and coping methods of the materials.

(1) the experimental model and examination within the elastic limit of the apparatus are supposed, and (2) the experimental model and similarity of the apparatus, are faults for the stress freezing process with respect to the relationship which utilizes the elastic body of the rubber condition, whereby the elastic coefficient is vitrified because it becomes 1/100, and deformation is easy to become large. In addition, the size of the model differs before the stress freezing and after the freezing, with error due to change in size being easy to occur. There is a deformation revision method as the expedient which removes these faults. This method, expecting the deformation quantity of the specimen beforehand, produces a model of the form which it revises, and stress freezing it is the method for the occasion of making a specified size. With this method, the error which originates in the deformation of geometric form can be made rather small.

As for the photoelastic experiment, other experimental stress analyses inside it are not possible for a single form to discover the pattern of analysis and entire stress distribution of stress simply. On the other hand, an experimental value which utilizes these features has recently become necessary, with experimental stress analysis it is the most effective method.

In addition, the numerical analysis with FEM has become easy, but the experimental data from which photoelasticity in the verification for supporting numerical analysis is of importance.

When analyzing the stress distribution of three dimensional structures, a stress freezing process which utilizes the characteristics of the epoxy resin is generally used, where the epoxy resin reaching a temperature above approximately 120 °C causes a second order transition, and the condition becomes rubber elastic. The load is loaded above this temperature. It makes the temperature fall to approximately room temperature. A distortion state occurs in the rubber elastic range under freezing. As for this distortion removing the load, it continues under freezing. In order to measure this distortion, the model after the stress freezing is sliced into approximately 5mm wide slices. The photoelastic device shown in Fig.3 was used. As for the distortion, which became an isochromatic fringe pattern depending upon the polarized light. Fig.3 shows the construction of the photoelastic device where S is the illuminant, L and L2 are the field lenses, P is the polarizer, A is the analyzer, and Q1 and Q2 are the quarter undulation plates.

Fig. 3. Circular polariscope

**3. Photoelastic theory, experimental model and actual model by epoxy resin** 

The similarity rule is generally utilized for model production and analysis method. Production and an experiment must consider and satisfy the following conditions. (1) The experimental model and actual model from examination and supposition must be within the limit of elasticity, (2) Similarity of experimental model and actual model, (3) agreement of load point, load distribution and similarity, (4) similarity to Poisson's ratio *ν*. Then, when all conditions are satisfied, even with high polymer materials such as the epoxy resin, which was used for the experiment, the stress distribution of actual model of steel, alloy and concrete, etc, agrees. In addition, experimental values which can match the stress values of

However, like this experiment in the case of 3 dimensional photoelasticity, there are times when it does not agree to these under heating. It is necessary to know the characteristics and

(1) the experimental model and examination within the elastic limit of the apparatus are supposed, and (2) the experimental model and similarity of the apparatus, are faults for the stress freezing process with respect to the relationship which utilizes the elastic body of the rubber condition, whereby the elastic coefficient is vitrified because it becomes 1/100, and deformation is easy to become large. In addition, the size of the model differs before the stress freezing and after the freezing, with error due to change in size being easy to occur. There is a deformation revision method as the expedient which removes these faults. This method, expecting the deformation quantity of the specimen beforehand, produces a model of the form which it revises, and stress freezing it is the method for the occasion of making a specified size. With this method, the error which originates in the deformation of geometric

As for the photoelastic experiment, other experimental stress analyses inside it are not possible for a single form to discover the pattern of analysis and entire stress distribution of stress simply. On the other hand, an experimental value which utilizes these features has recently become necessary, with experimental stress analysis it is the most effective method. In addition, the numerical analysis with FEM has become easy, but the experimental data from which photoelasticity in the verification for supporting numerical analysis is of

When analyzing the stress distribution of three dimensional structures, a stress freezing process which utilizes the characteristics of the epoxy resin is generally used, where the epoxy resin reaching a temperature above approximately 120 °C causes a second order transition, and the condition becomes rubber elastic. The load is loaded above this temperature. It makes the temperature fall to approximately room temperature. A distortion state occurs in the rubber elastic range under freezing. As for this distortion removing the load, it continues under freezing. In order to measure this distortion, the model after the stress freezing is sliced into approximately 5mm wide slices. The photoelastic device shown in Fig.3 was used. As for the distortion, which became an isochromatic fringe pattern depending upon the polarized light. Fig.3 shows the construction of the photoelastic device where S is the illuminant, L and L2 are the field lenses, P is the polarizer, A is the analyzer,

**3.1 Photoelastic theory** 

the actual model by conversion are possible.

coping methods of the materials.

form can be made rather small.

and Q1 and Q2 are the quarter undulation plates.

importance.

Fringe order and the relationship of principal stress which occurs becomes (1).

$$N = \operatorname{at}(\sigma\_1 - \sigma\_2) \tag{1}$$

Here, for the N fringe order, t is the thickness of sliced specimen, α is the photoelastic sensitivity, and σ1 and σ2 are the principal stresses inside the slices.

In addition, with respect to free boundaries, the σ1 each of σ2 becomes 0. Therefore, through (2) the stress state can be known.

$$
\sigma = \text{N/at} \text{[MPa]} \tag{2}
$$

## **3.2 Material error of relation between experimental model and actual model**

The epoxy resin of the photoelastic material used as the test material is an isotropic homogeneous body, but the organism bone (sponge bone and fine bone, from marrow constitution) is an anisotropic heterogeneous body. Due to this, error occurs in the comparison analysis of the material and the heterogeneous material of which Young's modulus, *E*, is homogeneous. Depending on this, examination becomes necessary by use of epoxy resin concerning the quantitative error of the bone.

Concerning this, Nishida allotted the epoxy resin of Young's modulus, *E*, which differs by layer, and a bend experiment which imitated the bone was performed. The design of the experiment is shown in Fig.4. As a result of the experiment, the error of Young's modulus, *E*, was calculated to be 10% when the experiment was performed on a solid monolayer structure. As the quantitative error is small, quantitative reproducibility can be expected. In addition, for the dynamic quality of the bone, due to a characteristic difference and personal equation, for the femur of an adult male 30~50 years of age, an average tension of 137.30MPa, an elastic limit of 100.82Mpa, and a recovery factor of the distortion due to stress relief with extension of 0.0125 have been reported as representing 95% or more.

As for the bone, to think of the body as being composed of photoelastic material and use a photoelastic experiment is favorable. This method, which is a powerful experimental analysis method in stress distribution visualization of the whole bone, was adopted on the basis of these reports. In addition, mechanical characteristics of the silicon rubber which was

Experimental Examination on the Effects and Adaptation Condition

**3.3.2 Experimental method** 

shown in Fig. 7 (b) and (c).

Fig. 5. Model specimen

Fig. 6. Load device

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 303

In this research, the skeletal structure of the knee joint was reproduced, making use of a specimen model of the framework which forms the left side of the knee joint, including the femur, tibia and fibula. The framework for reappearance consisted of the knee joint of the femoral model and the fibula combined with the tibia model. In order for more accurate vertical load to be imposed, the muscular part was produced using silicon as the jig. In the case of stress freezing, 107.8N was loaded as a freezing load. In reappearance of joint cartilage, clay for ceramic art with a hardness of HS29 (Sculpey III American poly- form the corp.) was used.

After the stress freezing ended, for the standing position state, especially when the FTA was maintained, slices of a 5mm thickness were made. Slices were made from the front of the knee, with the inside as a standard. The slice direction is shown in Fig. 7 (a), and a slice is

The specimen model is shown in Fig. 5, and the load device is shown in Fig. 6.

used in this experiment showed a hardness of JIS A43, a tensile strength of 2.2MPa, and a growth rate of 170%.

## **3.3 Experimental summary**

## **3.3.1 Test material and test pieces**

In this research, experimental analysis which used three-dimensional stress freezing was performed. A specimen model of the framework which forms the left side of the knee joint ,including the femur, tibia and fibula, was produced using actual equipment and material, making use of the medical organism skeletal model,. The test material selected was an epoxy resin (mixed weight ratio; ARALDITE B CT200: HARDENER HT901=100: 30). The normal temperature (25°C) and high temperature (128°C) against mechanical quality are shown in Table 1.

Organism bone is generally formed by marrow, etc, which does not bear stress from the fine adrenal cortex section and the porous spongin section, and furthermore, shows rigidity. Therefore, it is not possible to handle the homogeneous body, and in addition, the modulus anisotropy of elasticity and strength regarding the same adrenal cortex section must be considered. However, the aforementioned has reproducibility concerns, and error in this research is due to the layer system, so a 3 dimensional photoelastic experimental model was produced as a solid structure.


Table 1. Properties of the epoxy resin

## **3.3.2 Experimental method**

302 Applied Biological Engineering – Principles and Practice

used in this experiment showed a hardness of JIS A43, a tensile strength of 2.2MPa, and a

(a) homogeneous (b) unhomogeneous

In this research, experimental analysis which used three-dimensional stress freezing was performed. A specimen model of the framework which forms the left side of the knee joint ,including the femur, tibia and fibula, was produced using actual equipment and material, making use of the medical organism skeletal model,. The test material selected was an epoxy resin (mixed weight ratio; ARALDITE B CT200: HARDENER HT901=100: 30). The normal temperature (25°C) and high temperature (128°C) against mechanical quality are shown in

Organism bone is generally formed by marrow, etc, which does not bear stress from the fine adrenal cortex section and the porous spongin section, and furthermore, shows rigidity. Therefore, it is not possible to handle the homogeneous body, and in addition, the modulus anisotropy of elasticity and strength regarding the same adrenal cortex section must be considered. However, the aforementioned has reproducibility concerns, and error in this research is due to the layer system, so a 3 dimensional photoelastic experimental model was

growth rate of 170%.

Fig. 4. Difference between experiment and model

**3.3 Experimental summary** 

produced as a solid structure.

Table 1. Properties of the epoxy resin

Table 1.

**3.3.1 Test material and test pieces** 

In this research, the skeletal structure of the knee joint was reproduced, making use of a specimen model of the framework which forms the left side of the knee joint, including the femur, tibia and fibula. The framework for reappearance consisted of the knee joint of the femoral model and the fibula combined with the tibia model. In order for more accurate vertical load to be imposed, the muscular part was produced using silicon as the jig. In the case of stress freezing, 107.8N was loaded as a freezing load. In reappearance of joint cartilage, clay for ceramic art with a hardness of HS29 (Sculpey III American poly- form the corp.) was used. The specimen model is shown in Fig. 5, and the load device is shown in Fig. 6.

After the stress freezing ended, for the standing position state, especially when the FTA was maintained, slices of a 5mm thickness were made. Slices were made from the front of the knee, with the inside as a standard. The slice direction is shown in Fig. 7 (a), and a slice is shown in Fig. 7 (b) and (c).

Fig. 5. Model specimen

Fig. 6. Load device

Experimental Examination on the Effects and Adaptation Condition

as shown in (6).

calculated by (10).

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 305

Generally, for a three dimensional photoelastic experiment, if Poisson's ratio, ν, is almost identical to the experimental result and analogy is for conversion to the apparatus such that:

In the three dimensional problem, it designates the ratio of the length of the model as *Lratio*,

*ex ratio*

*ex ratio*

*Experimental load <sup>W</sup> <sup>W</sup>*

*ex ex ex ratio a aa W L W L*

For conversion to the stress ratio σ*ratio*=1, knowing a more accurate stress value is desirable, so it is necessary to consider the experimental load well. In addition, after drawing up a stress distribution chart, because the experimental load is computed from Fringe Order, the experimental stress value, σ*ex*, of the actual bone stress value, σ*a*, can be

*ex ex a ex*

**4.2 Experiment value and the calculation method which uses Young's modulus** *E* **of** 

The stress value of the actual bone is able to be calculated by the experimental value and the proportional system which uses Young's modulus, *E*. If the actual bone and the experimental model are similar figures, the same stress distribution is given regardless of material. However, when Young's modulus differs, conversion is necessary for the obtained

*a a W L W L*

*Experimental size <sup>L</sup> <sup>L</sup>*

where the area ratio, *Aratio*, and specific volume, *Vratio*, are given by (7),

 

**the experimental model and Young's modulus** *E* **of the actual bone** 

experimental value to give the stress value of the actual bone.

and the load ratio, *Wratio*, given by (8) becomes similar,

so that the stress ratio, σ*ratio*, (9) can be given by:

*a*

*a*

2

2

*Actual size L* (6)

2 3 , *A LV L ratio ratio ratio ratio* (7)

*Actual load W* (8)

(9)

(10)

 *ex a* 

 *a ex K* 

*a a ex ex <sup>W</sup> <sup>K</sup>*

2

(4)

(5)

*W L*

Fig. 7. Model slice

## **4. Relation experimental results converted to actual model**

As for stress distribution, if the apparatus and the figure are similar, the distribution is the same regardless of material. However, as it is a model experiment, when Young's modulus, *E*, differs, conversion of the obtained experimental value and the stress value of the apparatus are necessary. Therefore, a photoelastic material of which the Young's modulus, *E*, of the apparatus was known was inspected.

Concerning this, a system for the conversion of the stress value obtained from the experiment to the stress value of the actual bone is plural, and was implemented into the program conversion. Here, subscript experiment values: *ex* is the value of the actual bone: *a*.

#### **4.1 Experimental value for the calculation method regarding the stress value of the actual bone**

As an outline, the case of a plane surface stress state is written. The ratio, *L*, of length of the actual model and the experimental model is expressed by (3).

$$L = \frac{\text{Actual size}}{\text{Experimental size}}\tag{3}$$

The relation of (4) gives the length ratio, *L*, of the error ratio and load, *W*, of the respective stress value, σ, for the model. Depending on this, the stress value for the error ratio, *K*, of the actual model and the experimental model becomes (5).

$$K = \frac{\sigma\_a}{\sigma\_{ex}} = \frac{\mathcal{W}\_a}{\mathcal{W}\_{ex}L^2} \tag{4}$$

$$
\sigma\_{\rm at} = \mathbf{K} \cdot \sigma\_{\rm ex} \tag{5}
$$

Generally, for a three dimensional photoelastic experiment, if Poisson's ratio, ν, is almost identical to the experimental result and analogy is for conversion to the apparatus such that:

$$\nu\_{\alpha} \equiv \nu\_{a}$$

In the three dimensional problem, it designates the ratio of the length of the model as *Lratio*, as shown in (6).

$$L\_{ratio} = \frac{\text{Experimental size}}{\text{Actual size}} = \frac{L\_{cx}}{L\_a} \tag{6}$$

where the area ratio, *Aratio*, and specific volume, *Vratio*, are given by (7),

$$A\_{\text{ratio}} = \mathbf{L}\_{\text{ratio}}^2 \; V\_{\text{ratio}} = \mathbf{L}\_{\text{ratio}}^3 \tag{7}$$

and the load ratio, *Wratio*, given by (8) becomes similar,

$$\mathcal{W}\_{\text{ratio}} = \frac{\text{Experimental load}}{\text{Actual load}} = \frac{\mathcal{W}\_{\text{ex}}}{\mathcal{W}\_a} \tag{8}$$

so that the stress ratio, σ*ratio*, (9) can be given by:

304 Applied Biological Engineering – Principles and Practice

(a) Slice position

 (a) Slice of femur (b) Slice of tibia

As for stress distribution, if the apparatus and the figure are similar, the distribution is the same regardless of material. However, as it is a model experiment, when Young's modulus, *E*, differs, conversion of the obtained experimental value and the stress value of the apparatus are necessary. Therefore, a photoelastic material of which the Young's modulus,

Concerning this, a system for the conversion of the stress value obtained from the experiment to the stress value of the actual bone is plural, and was implemented into the program conversion. Here, subscript experiment values: *ex* is the value of the actual bone: *a*.

**4.1 Experimental value for the calculation method regarding the stress value of the** 

*Actual size <sup>L</sup>*

As an outline, the case of a plane surface stress state is written. The ratio, *L*, of length of the

The relation of (4) gives the length ratio, *L*, of the error ratio and load, *W*, of the respective stress value, σ, for the model. Depending on this, the stress value for the error ratio, *K*, of the

*Experimental size* (3)

**4. Relation experimental results converted to actual model** 

actual model and the experimental model is expressed by (3).

actual model and the experimental model becomes (5).

*E*, of the apparatus was known was inspected.

Fig. 7. Model slice

**actual bone** 

$$
\sigma\_{ratio} = \frac{\sigma\_{cx}}{\sigma\_a} = \frac{\mathcal{W}\_{cx}}{\mathcal{W}\_a} \left(\frac{L\_{ex}}{L\_a}\right)^2 \tag{9}
$$

For conversion to the stress ratio σ*ratio*=1, knowing a more accurate stress value is desirable, so it is necessary to consider the experimental load well. In addition, after drawing up a stress distribution chart, because the experimental load is computed from Fringe Order, the experimental stress value, σ*ex*, of the actual bone stress value, σ*a*, can be calculated by (10).

$$
\sigma\_a = \sigma\_{ex} \frac{\mathcal{W}\_{ex}}{\mathcal{W}\_a} \left(\frac{L\_{ex}}{L\_a}\right)^2 \tag{10}
$$

#### **4.2 Experiment value and the calculation method which uses Young's modulus** *E* **of the experimental model and Young's modulus** *E* **of the actual bone**

The stress value of the actual bone is able to be calculated by the experimental value and the proportional system which uses Young's modulus, *E*. If the actual bone and the experimental model are similar figures, the same stress distribution is given regardless of material. However, when Young's modulus differs, conversion is necessary for the obtained experimental value to give the stress value of the actual bone.

Experimental Examination on the Effects and Adaptation Condition

the outside is thicker than on the inside of the knee joint.

expanding the contact surface area.

Table 4. Parameter of Types

Table 5. Properties of silicone rubber and polyurethane resin

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 307

In Fig. 8 and Fig. 9, Types I and II show almost similar stress distribution states. From the fact that the state of the alignment of the normal knee of FTA 176° was reproduced, a normal contact state of the femur, tibia and fibula was established. It was achieved when the meniscus was approximately 60% moisture, much like a sponge which contains water. In addition, there are dynamic functional characteristics of stability for the joint which are quite important for load support, absorption and joint impact load regarding lubrication. For example, in absorbing approximately 20% of the loads which operate the knee joint at the time of knee joint extension, it is thought that it transmits approximately 50%. In addition, it has an influence on the dispersion of the load where the meniscus direction on

On the one hand, in Fig. 9, Type III can be seen to differ from Type I and II for stress distribution state. In the femur there was a centralization of stress in the contact section, and in the tibia influence in the frame work section was also observed. From this, the meniscus which is between the knee joint not only dispersed the stress of the contact section of the knee joint , but concerning the frame work section, it was found that it plays an important role in bone transmission, e.g., the centralization of stress is eased. A dynamic concentration of stress became a centralized load because it in fact occurred due to a centralized load, and regarding the knee joint, it was found to be in a state where deformation is promoted. In addition, the deformation characteristic of knee OA was the formation of bone spikes, however, it is understood that they were formed due to excessive stress. Type III of the stress distribution state and the stress value reached a higher degree to ease the excess stress, and it is presumed that the location of the bone spike was formed for the purpose of

Therefore, for the photoelastic material which is used it is necessary to know the Young's modulus, *E*, of the actual bone which we would like to inspect. Table 3 shows the mechanical characteristics of the femur and tibia. The mechanical characteristics of the epoxy resin are shown in Table 3. For the stress freezing process, Young's modulus, *E*, of the epoxy resin at the time (freezing) of high temperature was used. Therefore, Young's modulus, *E*=13.62[MPa].


Table 2. Mechanical properties of mechanical characteristics of femur and tibia


Table 3. Mechanical properties of the epoxy resin

Proportional system (11) can be converted into formula (12), which substitutes the known Young's modulus, *E*, and experiment stress value, σ*ex*, respectively, and gives the stress value of the actual bone, σ*a*.

$$
\sigma\_{\text{max}\,ex} : E\_{\text{ex}} = \sigma\_{\text{max}\,a} : E\_a \tag{11}
$$

$$
\sigma\_{\text{max}\,a} = \frac{\sigma\_{\text{max}\,ex} \cdot E\_{ex}}{E\_a} \tag{12}
$$

#### **5. Importance of the meniscus**

The importance of the meniscus was considered in this experiment. Types I-III were set and compared. The FTA was set at 176°, that of the normal knee, and the meniscus was reproduced using the two materials of silicon rubber and polyurethane resin. In the same way, the meniscus completely wore through, and the femur and the tibia and fibula reached a state where they contacted directly. The laboratory conditions are shown in Table 4, and the experimental parameters are shown in Table 5.

Examples of a photoelastic stripe photograph and a stress distribution chart (principal stress difference at a point of contact) of the femur are shown in Fig. 8. That of the tibia is shown in Fig. 9.

In Fig. 8 and Fig. 9, Types I and II show almost similar stress distribution states. From the fact that the state of the alignment of the normal knee of FTA 176° was reproduced, a normal contact state of the femur, tibia and fibula was established. It was achieved when the meniscus was approximately 60% moisture, much like a sponge which contains water. In addition, there are dynamic functional characteristics of stability for the joint which are quite important for load support, absorption and joint impact load regarding lubrication. For example, in absorbing approximately 20% of the loads which operate the knee joint at the time of knee joint extension, it is thought that it transmits approximately 50%. In addition, it has an influence on the dispersion of the load where the meniscus direction on the outside is thicker than on the inside of the knee joint.

On the one hand, in Fig. 9, Type III can be seen to differ from Type I and II for stress distribution state. In the femur there was a centralization of stress in the contact section, and in the tibia influence in the frame work section was also observed. From this, the meniscus which is between the knee joint not only dispersed the stress of the contact section of the knee joint , but concerning the frame work section, it was found that it plays an important role in bone transmission, e.g., the centralization of stress is eased. A dynamic concentration of stress became a centralized load because it in fact occurred due to a centralized load, and regarding the knee joint, it was found to be in a state where deformation is promoted. In addition, the deformation characteristic of knee OA was the formation of bone spikes, however, it is understood that they were formed due to excessive stress. Type III of the stress distribution state and the stress value reached a higher degree to ease the excess stress, and it is presumed that the location of the bone spike was formed for the purpose of expanding the contact surface area.


Table 4. Parameter of Types

306 Applied Biological Engineering – Principles and Practice

Therefore, for the photoelastic material which is used it is necessary to know the Young's modulus, *E*, of the actual bone which we would like to inspect. Table 3 shows the mechanical characteristics of the femur and tibia. The mechanical characteristics of the epoxy resin are shown in Table 3. For the stress freezing process, Young's modulus, *E*, of the epoxy resin at the time (freezing) of high temperature was used. Therefore, Young's

Table 2. Mechanical properties of mechanical characteristics of femur and tibia

Proportional system (11) can be converted into formula (12), which substitutes the known Young's modulus, *E*, and experiment stress value, σ*ex*, respectively, and gives the stress

max max : :

The importance of the meniscus was considered in this experiment. Types I-III were set and compared. The FTA was set at 176°, that of the normal knee, and the meniscus was reproduced using the two materials of silicon rubber and polyurethane resin. In the same way, the meniscus completely wore through, and the femur and the tibia and fibula reached a state where they contacted directly. The laboratory conditions are shown in Table 4, and

Examples of a photoelastic stripe photograph and a stress distribution chart (principal stress difference at a point of contact) of the femur are shown in Fig. 8. That of the tibia is shown in

 *ex ex a a E E* 

max

*ex ex*

*E*

*a*

*E*

(11)

(12)

max

*a*

Table 3. Mechanical properties of the epoxy resin

value of the actual bone, σ*a*.

**5. Importance of the meniscus** 

Fig. 9.

the experimental parameters are shown in Table 5.

modulus, *E*=13.62[MPa].


Table 5. Properties of silicone rubber and polyurethane resin

Experimental Examination on the Effects and Adaptation Condition

section of the fibula was excised in Types D and E.

Table 6. Parameter of Types A)E

**(FTA176º/extensive meniscus remains)** 

**-A ~ E type results-**

11.

advance.

a normal knee joint is stable.

Table 3.

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 309

In this experiment, concerning the stress rate, a comparison and examination of a meniscus and the inside of a contravariant shape knee arthropathy (O leg) was done after using the fibula excision method. At that time, the remaining state of the FTA and the meniscus were considered when the laboratory conditions were decided, as shown in

Furthermore, the fibula excision method reproduced a state where a 10mm frame work

**7. Examination of the effectiveness of the fibula excision method** 

The isochromatic fringe pattern and stress distribution chart of an example of Type A are shown in Fig. 10 (a) the femur, and (b) the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed stress points, the σmax, and the slice No. are given on the horizontal axis in Fig.

In the femur of a Type A normal knee, regarding Fig. 10, an almost equal stress distribution was shown on the inside and outside. Regarding Fig. 10 (b) of the tibia, on the tibia side, the stress was higher on the inside than on the outside. As for the FTA of 176°, it is thought that this kind of distribution was shown because some of it was transferred to the outer part type (X leg). Regarding Fig. 11, for a normal knee joint, the load was easily imposed on the outside, and the difference of stress which occurred inside and outside was small. Therefore, it was stabilized dynamically. Especially, when the emergence of Knee OA is considered, concentration of stress is difficult to obtain, and wear of the meniscus is thought to not

As for the result, in a healthy knee, for stress to be distributed outside, it must agree with the assumed idea in the orthopedics field that a nearly equal stress distribution is desirable (sharing a load 40 percent inside and 60 percent outside). As the stress value is low overall and the range is wide, the load which falls on the knee joint is efficiently dispersed, making

**7.1 Mechanical state of a normal knee joint of Type A: Normal knee** 

Fig. 8. Isochromatic fringe pattern (Femur)

Fig. 9. Isochromatic fringe pattern (Tibia)

## **6. Examination of the effectiveness of the fibula excision method - Experimental parameter -**

In this research, the fibula excision method was examined. The experiment dealt with the knee joint of a normal state, Osteoarthritis of the Knee before and after operation and supposed one foot standing and was concerned with stress state. The state of FTA and remaining meniscus, which are a diagnostic guide of the Osteoarthritis of the knee. In this research examines the influence which these give to an Osteoarthritis of the Knee and operation.

In this experiment, concerning the stress rate, a comparison and examination of a meniscus and the inside of a contravariant shape knee arthropathy (O leg) was done after using the fibula excision method. At that time, the remaining state of the FTA and the meniscus were considered when the laboratory conditions were decided, as shown in Table 3.

Furthermore, the fibula excision method reproduced a state where a 10mm frame work section of the fibula was excised in Types D and E.


Table 6. Parameter of Types A)E

308 Applied Biological Engineering – Principles and Practice

Fig. 8. Isochromatic fringe pattern (Femur)

Fig. 9. Isochromatic fringe pattern (Tibia)

**- Experimental parameter -** 

operation.

**6. Examination of the effectiveness of the fibula excision method** 

In this research, the fibula excision method was examined. The experiment dealt with the knee joint of a normal state, Osteoarthritis of the Knee before and after operation and supposed one foot standing and was concerned with stress state. The state of FTA and remaining meniscus, which are a diagnostic guide of the Osteoarthritis of the knee. In this research examines the influence which these give to an Osteoarthritis of the Knee and

## **7. Examination of the effectiveness of the fibula excision method -A ~ E type results-**

## **7.1 Mechanical state of a normal knee joint of Type A: Normal knee (FTA176º/extensive meniscus remains)**

The isochromatic fringe pattern and stress distribution chart of an example of Type A are shown in Fig. 10 (a) the femur, and (b) the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed stress points, the σmax, and the slice No. are given on the horizontal axis in Fig. 11.

In the femur of a Type A normal knee, regarding Fig. 10, an almost equal stress distribution was shown on the inside and outside. Regarding Fig. 10 (b) of the tibia, on the tibia side, the stress was higher on the inside than on the outside. As for the FTA of 176°, it is thought that this kind of distribution was shown because some of it was transferred to the outer part type (X leg). Regarding Fig. 11, for a normal knee joint, the load was easily imposed on the outside, and the difference of stress which occurred inside and outside was small. Therefore, it was stabilized dynamically. Especially, when the emergence of Knee OA is considered, concentration of stress is difficult to obtain, and wear of the meniscus is thought to not advance.

As for the result, in a healthy knee, for stress to be distributed outside, it must agree with the assumed idea in the orthopedics field that a nearly equal stress distribution is desirable (sharing a load 40 percent inside and 60 percent outside). As the stress value is low overall and the range is wide, the load which falls on the knee joint is efficiently dispersed, making a normal knee joint is stable.

Experimental Examination on the Effects and Adaptation Condition

Fig. 12. Isochromatic fringe pattern of Type B

Fig. 13. Isochromatic fringe pattern of Type B

**remains)** 

**7.3 Type C: Seriousness osteoarthritis of the knee (FTA186°/ on ly outside meniscus** 

The isochromatic fringe pattern and stress distribution chart of an example of Type C are shown in Fig. 14, the femur, and Fig. 15, the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed

stress points, the σmax , and the slice No. are given on the horizontal axis in Fig. 15.

outside.

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 311

From the graph in Fig. 13, in the femur, as for stress inside and outside, they were almost the same as in the tibia stress outside. We assumed that in an O leg high stress occurs inside, but, from the result, the cartilage remains even with the O leg, and with the point which only a dead load is loaded, it does not mean that stress is distributed to the inside and

Fig. 11. Stress distribution of Type A

#### **7.2 Contravariant shape knee arthropathy among minor Type B: Osteoarthritis of the knee (FTA186 º/ extensive meniscus remains)**

The isochromatic fringe pattern and stress distribution chart of an example of Type B are shown in Fig. 12 (a) the femur, and (b) the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed stress points, the σmax, and the slice No. are given on the horizontal axis in Fig. 13.

In Fig. 12 (b), the tibia, the stress distribution inside the peak of the tibia is narrower than that of Type A. The meniscus extensively remained, but the FTA was 186°. It is thought that 60% of the stress was distributed outside the knee. When walking where impacts occur over time, like the of ascent or descent of a stairway, it is expected that high stress occurs inside the knee. If during this the FTA is not normal, the meniscus cannot disperse the load equally, it is presumed that the change in FTA is strongly related to the wear and deformation of the meniscus.

From the graph in Fig. 13, in the femur, as for stress inside and outside, they were almost the same as in the tibia stress outside. We assumed that in an O leg high stress occurs inside, but, from the result, the cartilage remains even with the O leg, and with the point which only a dead load is loaded, it does not mean that stress is distributed to the inside and outside.

310 Applied Biological Engineering – Principles and Practice

**7.2 Contravariant shape knee arthropathy among minor Type B: Osteoarthritis of the** 

The isochromatic fringe pattern and stress distribution chart of an example of Type B are shown in Fig. 12 (a) the femur, and (b) the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed

In Fig. 12 (b), the tibia, the stress distribution inside the peak of the tibia is narrower than that of Type A. The meniscus extensively remained, but the FTA was 186°. It is thought that 60% of the stress was distributed outside the knee. When walking where impacts occur over time, like the of ascent or descent of a stairway, it is expected that high stress occurs inside the knee. If during this the FTA is not normal, the meniscus cannot disperse the load equally, it is presumed that the change in FTA is strongly related to the wear and

stress points, the σmax, and the slice No. are given on the horizontal axis in Fig. 13.

Fig. 10. Isochromatic fringe pattern of Type A

Fig. 11. Stress distribution of Type A

deformation of the meniscus.

**knee (FTA186 º/ extensive meniscus remains)** 

Fig. 13. Isochromatic fringe pattern of Type B

#### **7.3 Type C: Seriousness osteoarthritis of the knee (FTA186°/ on ly outside meniscus remains)**

The isochromatic fringe pattern and stress distribution chart of an example of Type C are shown in Fig. 14, the femur, and Fig. 15, the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed stress points, the σmax , and the slice No. are given on the horizontal axis in Fig. 15.

Experimental Examination on the Effects and Adaptation Condition

Fig. 15. Isochromatic fringe pattern of Type C (Tibia)

**7.4 Type D: After the operation of the fibula excision method for minor OA** 

The isochromatic fringe pattern and stress distribution chart of an example of Type C are shown in Fig. 17, the femur, and Fig. 18, the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed stress points, the σmax, and the slice No. are given on the horizontal axis in Fig.

From Figs. 17 and 18, for Type D the stress was distributed equally inside and outside the knee. From Fig. 19, the stress value and stress distribution state were similar to the normal knee (Type A), and were mechanically stability. Correction of FTA was indicated by removal of a fibula. Therefore, the mild OA knee became mechanically stable by the fibula excision method, achieving a mechanical position equal to the normal knee. Depending on the case, the fibula excision method effectiveness is suggested in cases of

Fig. 16. Stress distribution of Type C

19.

minor OA knees.

**(FTA176 º/ meniscus extensive remains)** 

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 313

Concentration of stress of higher-order was verified for Type C from Figs. 14 and 15, which show inside the knee where the meniscus disappeared. As for this, the load dispersion role of the meniscus was not fulfilled, and it is thought that the stress was concentrated.

In the tibia in Fig. 16, concentration of stress of higher-order was verified originally in the condylar between bulging sections which existed on the center of the tibia, which did not cause direct contact. This is related to the occurrence of bone spikes which are a feature of Knee OA. These contact states have been expressed as two peaks, one of which is on the left side in the graph. When the meniscus wears, the bones collide, are damaged, and when bending and stretching, the motion causes pain. In the inside contravariant shape knee OA, the result is exemplified by the pain, which agrees with the opinion within the orthopedics field that spikes occur in the condylar between bulging section of the tibia.

Depending, in order for the bone not to contact, it is necessary to perform a remedy which revises FTA and excises the bone spike. The stress which occurs in the knee joint from the abovementioned conditions of Knee OA differs. The stress which occurs in the knee joint from the abovementioned conditions of OA also differs. Especially, as the cartilage wear causes concentration of stress, contact in the condylar between bulging sections occurs, and it is important to prevent wear of the meniscus. FTA is related to the wear of the meniscus, and it is thought that the revision of FTA is connected to preventive methods.

Fig. 14. Isochromatic fringe pattern of Type C (Femur)

Fig. 16. Stress distribution of Type C

Concentration of stress of higher-order was verified for Type C from Figs. 14 and 15, which show inside the knee where the meniscus disappeared. As for this, the load dispersion role of the meniscus was not fulfilled, and it is thought that the stress was

In the tibia in Fig. 16, concentration of stress of higher-order was verified originally in the condylar between bulging sections which existed on the center of the tibia, which did not cause direct contact. This is related to the occurrence of bone spikes which are a feature of Knee OA. These contact states have been expressed as two peaks, one of which is on the left side in the graph. When the meniscus wears, the bones collide, are damaged, and when bending and stretching, the motion causes pain. In the inside contravariant shape knee OA, the result is exemplified by the pain, which agrees with the opinion within the orthopedics field that spikes occur in the condylar between bulging section of

Depending, in order for the bone not to contact, it is necessary to perform a remedy which revises FTA and excises the bone spike. The stress which occurs in the knee joint from the abovementioned conditions of Knee OA differs. The stress which occurs in the knee joint from the abovementioned conditions of OA also differs. Especially, as the cartilage wear causes concentration of stress, contact in the condylar between bulging sections occurs, and it is important to prevent wear of the meniscus. FTA is related to the wear of the meniscus, and it is thought that the revision of FTA is connected to preventive

concentrated.

the tibia.

methods.

Fig. 14. Isochromatic fringe pattern of Type C (Femur)

## **7.4 Type D: After the operation of the fibula excision method for minor OA (FTA176 º/ meniscus extensive remains)**

The isochromatic fringe pattern and stress distribution chart of an example of Type C are shown in Fig. 17, the femur, and Fig. 18, the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed stress points, the σmax, and the slice No. are given on the horizontal axis in Fig. 19.

From Figs. 17 and 18, for Type D the stress was distributed equally inside and outside the knee. From Fig. 19, the stress value and stress distribution state were similar to the normal knee (Type A), and were mechanically stability. Correction of FTA was indicated by removal of a fibula. Therefore, the mild OA knee became mechanically stable by the fibula excision method, achieving a mechanical position equal to the normal knee. Depending on the case, the fibula excision method effectiveness is suggested in cases of minor OA knees.

Experimental Examination on the Effects and Adaptation Condition

**of the knee (FTA176°/ only outside meniscus remains )** 

cannot be anticipated for Severe Knee OA.

Fig. 20. Isochromatic fringe pattern of Type E

Fig. 21.

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 315

**7.5 Type E: After the operation of the fibula excision method for severe osteoarthritis** 

The isochromatic fringe pattern and stress distribution chart of an example of Type D are shown in Fig. 20 (a), the femur, and (b), the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed stress points, the σmax, and the slice No. are given on the horizontal axis in

From Fig. 20 (a), the femur, and (b), the tibia, high order stress concentration was confirmed inside the knee for Type E. In addition, there was concentration of stress on the femur and the tibia. As for this stress distribution state was similar to Type C before the fibula excising, and there was no improvement. However, from Fig. 21, the stress regarding the contact of the condylar between bulging sections of the tibia was not verified to show improvement. From these, there is no improvement in minor Knee OA (Type D) in the contravariant shape knee arthropathy among serious illnesses. Only for the pain of the intercondylar eminence part was the effectiveness observed. However, remarkable improvement for Mild Knee OA

From the above, the fibula excision method is effective as a minor contravariant shape knee arthropathy remedy. In serious Knee OA, the revision of FTA was not obtained at a level of sufficient effect. In serious contravariant shape knee arthropathy, remedy by high tibial osteotomy (: HTO) and similar procedures are presumed to remedy FTA properly. In addition, in performing revision of FTA by the fibula excision method, it was found that the

curative effect differs depending upon the state of the remaining meniscus.

Fig. 18. Isochromatic fringe pattern of Type D (Tibia)

Fig. 19. Stress distribution of Type D

Fig. 17. Isochromatic fringe pattern of Type D (Femur)

Fig. 18. Isochromatic fringe pattern of Type D (Tibia)

Fig. 19. Stress distribution of Type D

#### **7.5 Type E: After the operation of the fibula excision method for severe osteoarthritis of the knee (FTA176°/ only outside meniscus remains )**

The isochromatic fringe pattern and stress distribution chart of an example of Type D are shown in Fig. 20 (a), the femur, and (b), the tibia. As for the scale, the upper is the fringe order (: F.O.) and the lower is the stress value (: S.O [kPa]). On the vertical axis are the most compressed stress points, the σmax, and the slice No. are given on the horizontal axis in Fig. 21.

From Fig. 20 (a), the femur, and (b), the tibia, high order stress concentration was confirmed inside the knee for Type E. In addition, there was concentration of stress on the femur and the tibia. As for this stress distribution state was similar to Type C before the fibula excising, and there was no improvement. However, from Fig. 21, the stress regarding the contact of the condylar between bulging sections of the tibia was not verified to show improvement. From these, there is no improvement in minor Knee OA (Type D) in the contravariant shape knee arthropathy among serious illnesses. Only for the pain of the intercondylar eminence part was the effectiveness observed. However, remarkable improvement for Mild Knee OA cannot be anticipated for Severe Knee OA.

From the above, the fibula excision method is effective as a minor contravariant shape knee arthropathy remedy. In serious Knee OA, the revision of FTA was not obtained at a level of sufficient effect. In serious contravariant shape knee arthropathy, remedy by high tibial osteotomy (: HTO) and similar procedures are presumed to remedy FTA properly. In addition, in performing revision of FTA by the fibula excision method, it was found that the curative effect differs depending upon the state of the remaining meniscus.

Fig. 20. Isochromatic fringe pattern of Type E

Experimental Examination on the Effects and Adaptation Condition

above photoelastic stress freezing method.

Fig. 23. Pressure distribution of no excision

the knee joint was stabilized became wide.

Fig. 24. Pressure distribution of fibula excision

**8.3 Examination of FTA and the adaptation condition** 

**8.2 Examination after the fibula excision method** 

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 317

From Fig. 23, in the healthy knee joint, when FTA was small, (X leg tendency), a small high pressure occurred outside. As FTA (O leg tendency) became larger, it decreased the pressure outside and pressure inside increased. As for pressure inside and outside becoming equal, it was verified that it is at approximately FTA 178°. Optimum FTA, at which the knee joint is stabilized, is therefore approximately 178°. Also, this result was similar to the result in the

From Fig. 24, after the fibula excision method, it can be seen that when FTA was small, (X leg tendency) pressure was increased outside, and when FTA was large, (O leg tendency) pressure increased inside. Pressure inside and outside became equal near the FTA 173°~183°, a wide range compared to before the fibula excision method. As for this, FTA was revised by the fibula excision method, and it is thought that the range of FTA at which

The pressures inside and outside the knee were added, and the overall pressure was calculated. The percentage pressure on the inside and the outside were calculated. A result for a normal knee joint is indicated in Fig 25, and that after the fibula excision method is indicated in Fig 26. The vertical axis ratio is the pressure (%), and on the horizontal axis FTA

Fig. 21. Stress distribution of Type E

## **8. Examination about the adaptation condition of the fibula excision method**

In this research, other than the photoelastic stress freezing method, pressure of the knee joint was measured by a small-sized pressure sensor. The advantage of using a pressure gauge is that it can obtain results continually. (Segmented type small-sized pressure sensor with a thickness of 2mm and a diameter of 6mm :Kyouwa dengyou \* PSM) In this experiment, FTA was changed gradually, and the influence on the knee joint was observed. As for the test-piece, a similar epoxy resin model to that used for stress freezing method was used. Similarly, the amount of remaining meniscus was considered. Similar load equipment and loads 9.8N, which is 1/11 at the time of the stress freezing method from the special quality of the pressure sensor, was used. The pressure sensor was installed in the occurrence position of the principal stress max from the result of the stress freezing method. In Fig. 22 the pressure sensor position and pressure gauge are shown.

Fig. 22. Pressure sensor position and pressure gauge

## **8.1 Examination of normal knee joint**

Fig. 23 shows the results of the experiment on a normal knee joint. Fig. 26 shows the results after the fibula excision method. In the graph, the vertical axis represents the pressure value, and on the horizontal axis FTA is shown. The solid line indicates inside the knee joint, and the broken line shows the pressure outside.

From Fig. 23, in the healthy knee joint, when FTA was small, (X leg tendency), a small high pressure occurred outside. As FTA (O leg tendency) became larger, it decreased the pressure outside and pressure inside increased. As for pressure inside and outside becoming equal, it was verified that it is at approximately FTA 178°. Optimum FTA, at which the knee joint is stabilized, is therefore approximately 178°. Also, this result was similar to the result in the above photoelastic stress freezing method.

Fig. 23. Pressure distribution of no excision

316 Applied Biological Engineering – Principles and Practice

**8. Examination about the adaptation condition of the fibula excision method**  In this research, other than the photoelastic stress freezing method, pressure of the knee joint was measured by a small-sized pressure sensor. The advantage of using a pressure gauge is that it can obtain results continually. (Segmented type small-sized pressure sensor with a thickness of 2mm and a diameter of 6mm :Kyouwa dengyou \* PSM) In this experiment, FTA was changed gradually, and the influence on the knee joint was observed. As for the test-piece, a similar epoxy resin model to that used for stress freezing method was used. Similarly, the amount of remaining meniscus was considered. Similar load equipment and loads 9.8N, which is 1/11 at the time of the stress freezing method from the special quality of the pressure sensor, was used. The pressure sensor was installed in the occurrence position of the principal stress max from the result of the stress freezing method. In Fig. 22

Fig. 23 shows the results of the experiment on a normal knee joint. Fig. 26 shows the results after the fibula excision method. In the graph, the vertical axis represents the pressure value, and on the horizontal axis FTA is shown. The solid line indicates inside the knee joint, and

Fig. 21. Stress distribution of Type E

the pressure sensor position and pressure gauge are shown.

Fig. 22. Pressure sensor position and pressure gauge

**8.1 Examination of normal knee joint** 

the broken line shows the pressure outside.

## **8.2 Examination after the fibula excision method**

From Fig. 24, after the fibula excision method, it can be seen that when FTA was small, (X leg tendency) pressure was increased outside, and when FTA was large, (O leg tendency) pressure increased inside. Pressure inside and outside became equal near the FTA 173°~183°, a wide range compared to before the fibula excision method. As for this, FTA was revised by the fibula excision method, and it is thought that the range of FTA at which the knee joint was stabilized became wide.

Fig. 24. Pressure distribution of fibula excision

#### **8.3 Examination of FTA and the adaptation condition**

The pressures inside and outside the knee were added, and the overall pressure was calculated. The percentage pressure on the inside and the outside were calculated. A result for a normal knee joint is indicated in Fig 25, and that after the fibula excision method is indicated in Fig 26. The vertical axis ratio is the pressure (%), and on the horizontal axis FTA

Experimental Examination on the Effects and Adaptation Condition

conditions of the fibula excision method.

meniscus.

**10. Future direction** 

and the artificial joint.

Japan

**11. References** 

As a result, the knowledge below was obtained:

contravariant shape knee arthropathy (X leg).

of the Fibula Excision Method Using the Stress Freezing Method on the Osteoarthritis of the Knee 319

Experimental conditions of 5 types of experimental hybrids, A-E, used the 3-dimensional stress freezing method and pressure gauge to examine the effectiveness and application

1. The fibula excision method showed validity for Mild inside type Osteoarthritis of the

2. Doing the revision of FTA, the curative effect of the fibula excision method differs depending upon disease condition. The effect is related in the remaining state of the

3. As for the fibula excision method, it is suggested to be suited for the remedy of outside

The photoelastic experiment the analysis of principal stress and singular point is possible too. This analysis is the major feature which only photoelastic experiment is possible. This research utilizes this feature and would like to use in remedy and development of the bone

Asano S., Ezumi T. and Hachiya M. (2004). *A Study on The Characteristics of The Dynamics of* 

Fischer K. J. & Jacobs, C, R. & Levenston, M, E. & Carter, D, R. (1998). Annals of biomedical

*Remodeling Simulations,*Vol. 25,No.2 (08.1997). pp.261-268, ISSN0090-6964 Fujiki, H. & Ishikawa, H. & Yshuda, K. (1999). The Japan Society Of Mechanical Engineers,

Hachiya,M. & Huji,H. &Yamada, K. (1999). Joint Surgery. *The method of Salter's Innominate* 

Ikeda,K. & Shimazu,H. (2000). *Bio Physical Properties / Medical Mechanical Engineering*,Gakken Medical Shujunsha (Shujunsha), ISBN978-4879622259, Tokyo, Japan Isekame,F. & Suenaga,M. &Mizushima,I. (1975). Clinical Orthopedic Surgery. *The* 

Kawai,H. & Morisaki, N. (1985). *Orthopedics Traumatology*. (The 4th edition), Bunkodo,

Koshino, T. (1992). Orthopedic. *Etiology, Diagnosis and Treatments for Osteoarthritis of the Knee,* 

collection A, Vol65, No.629, (01.1999), pp.187-193, ISSN03875008

Hayashi, K.(2000). Biomechanics, Coronasha, ISBN978-4381100818, Tokyo, Japan Ikada,Y. (1994) . *Bio Material Engineering*+ISBN978-4782880012, Tokyo, Japan

*Hip,* Vol.18, No.2, (02.1999), pp.229-235, ISSN0286-5394

pp.303-313, ISSN05570433

ISBN9784830627019, Tokyo, Japan

NO.43, (10.1992), pp.1629-1638,ISSN0030-5901

Distractive Inspection, Vol53, No.9, (09. 2004), pp566-571,ISSN0367-5866 Burstein, A, H. & Wright,M,T. M. &Kurosawa,H. &Yamanoi, T.&Yamakoshi,K.(1997).

*Osteoarthritis Treatment Using Photoelastic Method*, Journal of Japanese Non

*Fandamentals of Orthopedics Biomechanics*+Nankoudou, ISBN978-4524216215, Tokyo,

engineering. *Observations of Convergence and Uniqueness of Node-Based Bone* 

*Change and the influence of knee joint contact force by the total knee replacement*, Thesis

*Osteotomy and Pemberton's Pericapsular Osteotomy for the Residual Subluxation of the* 

*Circumference of the Occurrence of Osteoarthritis of the Knee,* Vol.10, No.4, (04.1975),

knee and is suitable for cases of FTA 186 ° and much remaining meniscus.

is shown. The percentage on the pressure inside the knee joint is given by a solid line, and the percentage of the pressure on the outside is shown as a broken line.

From Fig. 25, it can be seen that in the normal knee joint, the ratio of pressure inside and outside almost became equal at approximately FTA 178°, but, when FTA changed, that ratio changed suddenly. Especially, the FTA change in ratio was large within the range of 171°~181°. It is thought that 1° or 2° of change in FTA produces a great effect on the knee joint.

However, after the fibula excising, results in Fig. 26, the FTA ratio of pressure was almost 174°~183°, and remarkable reduction in pressure both inside and outside the knee could be seen. The knee joint was mechanically stabilized. In addition, it was found that the pressure which is loaded outside was lightened mechanically. Depending on this, it can be effective concerning the outside contravariant shape knee arthropathy (X leg).

Therefore, as for the fibula excision method, it is thought to be especially effective for adaptation concerning minor OA patients of FTA 174° ~ FTA 183°.

Fig. 25. Percentage of pressure in no excision

Fig. 26. Percentage of fibula excision

#### **9. Conclusion**

In this research, the fibula excision method was examined. The experiment dealt with the knee joint of a normal state, Osteoarthritis of the Knee before and after operation and supposed one foot standing and was concerned with stress state. The state of FTA and remaining meniscus, which are a diagnostic guide of the Osteoarthritis of the knee, clearly influenced the result of the operation.

Experimental conditions of 5 types of experimental hybrids, A-E, used the 3-dimensional stress freezing method and pressure gauge to examine the effectiveness and application conditions of the fibula excision method.

As a result, the knowledge below was obtained:


## **10. Future direction**

318 Applied Biological Engineering – Principles and Practice

is shown. The percentage on the pressure inside the knee joint is given by a solid line, and

From Fig. 25, it can be seen that in the normal knee joint, the ratio of pressure inside and outside almost became equal at approximately FTA 178°, but, when FTA changed, that ratio changed suddenly. Especially, the FTA change in ratio was large within the range of 171°~181°. It is thought that 1° or 2° of change in FTA produces a great effect on the knee joint. However, after the fibula excising, results in Fig. 26, the FTA ratio of pressure was almost 174°~183°, and remarkable reduction in pressure both inside and outside the knee could be seen. The knee joint was mechanically stabilized. In addition, it was found that the pressure which is loaded outside was lightened mechanically. Depending on this, it can be effective

Therefore, as for the fibula excision method, it is thought to be especially effective for

In this research, the fibula excision method was examined. The experiment dealt with the knee joint of a normal state, Osteoarthritis of the Knee before and after operation and supposed one foot standing and was concerned with stress state. The state of FTA and remaining meniscus, which are a diagnostic guide of the Osteoarthritis of the knee, clearly

the percentage of the pressure on the outside is shown as a broken line.

concerning the outside contravariant shape knee arthropathy (X leg).

adaptation concerning minor OA patients of FTA 174° ~ FTA 183°.

Fig. 25. Percentage of pressure in no excision

Fig. 26. Percentage of fibula excision

influenced the result of the operation.

**9. Conclusion** 

The photoelastic experiment the analysis of principal stress and singular point is possible too. This analysis is the major feature which only photoelastic experiment is possible. This research utilizes this feature and would like to use in remedy and development of the bone and the artificial joint.

## **11. References**


**14** 

*Canada* 

**Motor Unit Potential Train Validation and** 

*Department of Systems Design Engineering, University of Waterloo* 

Hossein Parsaei and Daniel W. Stashuk

**Its Application in EMG Signal Decomposition** 

Electromyographic (EMG) signal decomposition is the process of resolving an EMG signal into its constituent motor unit potential trains (MUPTs). The purpose of EMG signal decomposition is to provide an estimate of the firing pattern and motor unit potential (MUP) template of each active motor unit (MU) that contributed significant MUPs to the EMG signal. The extracted MU firing patterns, MUP templates, and their estimated feature values can assist with the diagnosis of neuromuscular disorders (Stalberg & Falck, 1997; Tröger & Dengler, 2000; Fuglsang-Frederiksen, 2006; Pino et al., 2008; Farkas et al., 2010), the understanding of motor control ( De Luca et al. 1982a, 1982b; Contessa et al.,2009), and the characterization of MU architecture (Lateva & McGill, 2001), but only if they are valid trains. Depending on the complexity of the signal being decomposed, the variability of MUP shapes and MU firing patterns, and the criteria and parameters used by the decomposition algorithm to merge or split the obtained MUPTs, several invalid MUPTs may be created.

An extracted MUPT is considered valid when it accurately represents the activity of a single MU and is contaminated by low numbers of false-classification errors (FCEs). Alternatively, an invalid MUPT either represents the activity of more than one MU (i.e., it is a merged

Unfortunately, the MUP template shapes and MU firing patterns of invalid MUPTs cannot be easily distinguished from those of valid trains. Often, the MUP template shape of an invalid train looks similar to that of a valid train; nevertheless, the train does not represent the MUPs of a single MU. As such, the variability of MUP shapes and possibly the MU firing pattern are greater for invalid trains compared to valid trains. If such inaccurate information is not detected and excluded from further analysis, it could improperly suggest an abnormal muscle when interpreted clinically or it may contribute to scientific misstatements. Consequently, the first and most critical step in the quantitative analysis of

Detecting invalid trains during decomposition can assist with improving the performance of these decomposition methods in terms of estimating the correct number of MUPTs constituting an EMG signal as well as reducing the number of missed-classification errors (MCEs) and FCEs in the extracted trains. At the end of each pass of assigning MUPs to detected MUPTs, invalid MUPTs are detected and then either have their FCEs corrected or are split into valid trains. Such corrections can help find the correct number of constituent

MUPT) or contains a high percentage of FCEs (i.e., it is a contaminated MUPT).

**1. Introduction** 

MUPTs is assessing their validity.


## **Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition**

Hossein Parsaei and Daniel W. Stashuk *Department of Systems Design Engineering, University of Waterloo Canada* 

## **1. Introduction**

320 Applied Biological Engineering – Principles and Practice

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Maezaki, N. & Ezumi T. & Hachiya M. (2010). The Japan Society of Mechanical Engineers,

Maezaki, N. & Ezumi T. & Hachiya M. (2008). The Japan Society of Mechanical Engineers,

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ISSN03875008

Electromyographic (EMG) signal decomposition is the process of resolving an EMG signal into its constituent motor unit potential trains (MUPTs). The purpose of EMG signal decomposition is to provide an estimate of the firing pattern and motor unit potential (MUP) template of each active motor unit (MU) that contributed significant MUPs to the EMG signal. The extracted MU firing patterns, MUP templates, and their estimated feature values can assist with the diagnosis of neuromuscular disorders (Stalberg & Falck, 1997; Tröger & Dengler, 2000; Fuglsang-Frederiksen, 2006; Pino et al., 2008; Farkas et al., 2010), the understanding of motor control ( De Luca et al. 1982a, 1982b; Contessa et al.,2009), and the characterization of MU architecture (Lateva & McGill, 2001), but only if they are valid trains. Depending on the complexity of the signal being decomposed, the variability of MUP shapes and MU firing patterns, and the criteria and parameters used by the decomposition algorithm to merge or split the obtained MUPTs, several invalid MUPTs may be created.

An extracted MUPT is considered valid when it accurately represents the activity of a single MU and is contaminated by low numbers of false-classification errors (FCEs). Alternatively, an invalid MUPT either represents the activity of more than one MU (i.e., it is a merged MUPT) or contains a high percentage of FCEs (i.e., it is a contaminated MUPT).

Unfortunately, the MUP template shapes and MU firing patterns of invalid MUPTs cannot be easily distinguished from those of valid trains. Often, the MUP template shape of an invalid train looks similar to that of a valid train; nevertheless, the train does not represent the MUPs of a single MU. As such, the variability of MUP shapes and possibly the MU firing pattern are greater for invalid trains compared to valid trains. If such inaccurate information is not detected and excluded from further analysis, it could improperly suggest an abnormal muscle when interpreted clinically or it may contribute to scientific misstatements. Consequently, the first and most critical step in the quantitative analysis of MUPTs is assessing their validity.

Detecting invalid trains during decomposition can assist with improving the performance of these decomposition methods in terms of estimating the correct number of MUPTs constituting an EMG signal as well as reducing the number of missed-classification errors (MCEs) and FCEs in the extracted trains. At the end of each pass of assigning MUPs to detected MUPTs, invalid MUPTs are detected and then either have their FCEs corrected or are split into valid trains. Such corrections can help find the correct number of constituent

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 323

are connected. Formally, a single α-motor neuron, its axon and the set of connected muscle fibres are called a MU (Basmajian & De Luca, 1985). The summation of the muscle fibre potentials created by the spatially and temporally dispersed depolarization and

During a muscle contraction, MUs fire repetitively to maintain the force of the muscle contraction. Consequently, each active MU generates a train of MUPs during a muscle contraction known as MUPT. A MUPT is mathematically described as (De Luca, 1979;

where M is the number of times that the *j*th motor unit fires, ji is the *i*th firing time of motor

Assuming *K* MUs were active during a muscle contraction, the detected EMG signal can be mathematically represented as (De Luca,1979; Basmajian & De Luca, 1985; Stashuk, 2001;

K

j 1 EMG(t) MUPT t n(t) 

where MUPTj(t) is the MUPT generated by the *j*th motor unit, and n(t) is background noise.

Fig.1 shows both an anatomical and physiological model for an EMG signal. In this figure, *h*i(*t*) is a filter with impulse response MUPi, and the impulses represent action potentials emerging from an - motor neuron to innervate the connected muscle fibers. As shown, an EMG signal is in fact the superposition of the MUPTs created by MUs active during a

The characteristics of a detected EMG signal depend on several factors such as the level of contraction, the shape and size of the electrode used, and the position and orientation of the electrode relative to the muscle fibres of the active MUs (De Luca, 1979; Basmajian & De Luca, 1985). In addition, the characteristics of an EMG signal detected from a contacting muscle are related to the anatomical and physiological features of the muscle and therefore to its age and state of health or fatigue(Stalberg & Falck, 1997; Tröger & Dengler, 2000; Fuglsang-Frederiksen, 2006; Pino et al., 2008; Farkas et al., 2010). Some parameters of EMG signals for normal and abnormal muscles are compared in Table 1. Consequently, analyzing EMG signals provides information that can be used clinically or for physiological investigation. The technique of detecting, evaluating, and analyzing EMG signals is known as electromyography. One useful technique in electromyography is EMG signal

EMG signal decomposition is the process of resolving a detected EMG signal into is constituent MUPTs. This process that is conceptually shown in Fig.2 is implemented by employing digital signal processing and pattern recognition techniques in four/five steps:

unit *j*, and MUPji(t) is the *i*th MUP generated by motor unit *j* during its *it*h firing.

 <sup>M</sup> j ji ji i 1 MUPT t MUP t- 

j

(1)

(2)

repolarization of all of the excited fibres of a single MU is known as MUP.

Basmajian & De Luca, 1985; Stashuk, 2001; Parsaei et al., 2010):

Parsaei et al., 2010):

decomposition.

**2.2 EMG signal decomposition** 

muscle contraction and background noise.

MUPTs, lead to better estimates of the MUP template and MU firing pattern statistics of each train, and also allow more MUPs to be correctly assigned to the obtained trains (i.e., reduce MCEs) during the next steps of decomposition. Consequently, MUPT validation can improve decomposition accuracy.

The majority of the existing MUPT validation methods are either time consuming or related to operator experience and skill (see Section 3). More importantly, they cannot be executed during automatic decomposition of EMG signals to assist with improving decomposition results. To overcome these issues, an automated system is presented to estimate the validity of MUPTs extracted from an EMG signal using a decomposition algorithm. The presented system to estimate the validity of a MUPT uses both its MU firing pattern information and its MUP shape information. MU firing pattern information is employed by a supervised classifier that determines MU firing pattern validity by assessing MU firing pattern consistency and MU firing pattern variability of the train under question. MUP shape information is used by a cluster validation–based algorithm that assesses the MUP shape consistency in the given train to determine its MUP shape validity. A train is considered valid based on a combination of its MU firing pattern and MUP shape validity. The MUP validation system can be used both during EMG signal decomposition and once the process is completed.

The effectiveness of using the developed MUPT validation systems and the MUPT editing methods during EMG signal decomposition was investigated by integrating these algorithms into a certainty–based EMG signal decomposition algorithm. During decomposition, invalid MUPTs are detected and then either have their FCEs corrected or are split into valid trains before decomposition continues. The minimum assignment threshold for each extracted MUPT is adjusted based on the estimated validity. With these modifications, the decomposition accuracy on average was improved 9% on average.

This chapter includes a brief review of the composition and decomposition of EMG signals, a discussion of MUPT validation concepts, a description of a system developed for automatic validation of MUPTs during EMG decomposition, and a discussion of a decomposition system that uses the proposed MUPT validation algorithm to merge or split MUPTs and to adjust the assignment threshold for each MUPT adaptively. Evaluation results using several simulated and real EMG signals and a discussion of the results will be presented at the last section.

## **2. EMG signal composition and decomposition**

To appreciate the concepts of EMG signal decomposition, it is crucial to be familiar with the composition of an EMG signal. This section presents the fundamentals of EMG signal composition followed by a discussion of EMG signal decomposition.

## **2.1 EMG signal composition**

An EMG signal is the sequence of voltages detected from a contracting muscle over time. The potentials are detected in the voltage field generated by the active muscle fibres of a contracting muscle. The muscle fibres of a muscle are organized into groups for the control of muscle force with each muscle fibre of a group being connected to an α-motor neuron. Each muscle fibre of a group is activated concurrently by the -motor neuron to which they

MUPTs, lead to better estimates of the MUP template and MU firing pattern statistics of each train, and also allow more MUPs to be correctly assigned to the obtained trains (i.e., reduce MCEs) during the next steps of decomposition. Consequently, MUPT validation can

The majority of the existing MUPT validation methods are either time consuming or related to operator experience and skill (see Section 3). More importantly, they cannot be executed during automatic decomposition of EMG signals to assist with improving decomposition results. To overcome these issues, an automated system is presented to estimate the validity of MUPTs extracted from an EMG signal using a decomposition algorithm. The presented system to estimate the validity of a MUPT uses both its MU firing pattern information and its MUP shape information. MU firing pattern information is employed by a supervised classifier that determines MU firing pattern validity by assessing MU firing pattern consistency and MU firing pattern variability of the train under question. MUP shape information is used by a cluster validation–based algorithm that assesses the MUP shape consistency in the given train to determine its MUP shape validity. A train is considered valid based on a combination of its MU firing pattern and MUP shape validity. The MUP validation system can be used both during EMG signal decomposition and once the process

The effectiveness of using the developed MUPT validation systems and the MUPT editing methods during EMG signal decomposition was investigated by integrating these algorithms into a certainty–based EMG signal decomposition algorithm. During decomposition, invalid MUPTs are detected and then either have their FCEs corrected or are split into valid trains before decomposition continues. The minimum assignment threshold for each extracted MUPT is adjusted based on the estimated validity. With these

This chapter includes a brief review of the composition and decomposition of EMG signals, a discussion of MUPT validation concepts, a description of a system developed for automatic validation of MUPTs during EMG decomposition, and a discussion of a decomposition system that uses the proposed MUPT validation algorithm to merge or split MUPTs and to adjust the assignment threshold for each MUPT adaptively. Evaluation results using several simulated and real EMG signals and a discussion of the results will be

To appreciate the concepts of EMG signal decomposition, it is crucial to be familiar with the composition of an EMG signal. This section presents the fundamentals of EMG signal

An EMG signal is the sequence of voltages detected from a contracting muscle over time. The potentials are detected in the voltage field generated by the active muscle fibres of a contracting muscle. The muscle fibres of a muscle are organized into groups for the control of muscle force with each muscle fibre of a group being connected to an α-motor neuron. Each muscle fibre of a group is activated concurrently by the -motor neuron to which they

modifications, the decomposition accuracy on average was improved 9% on average.

improve decomposition accuracy.

is completed.

presented at the last section.

**2.1 EMG signal composition** 

**2. EMG signal composition and decomposition** 

composition followed by a discussion of EMG signal decomposition.

are connected. Formally, a single α-motor neuron, its axon and the set of connected muscle fibres are called a MU (Basmajian & De Luca, 1985). The summation of the muscle fibre potentials created by the spatially and temporally dispersed depolarization and repolarization of all of the excited fibres of a single MU is known as MUP.

During a muscle contraction, MUs fire repetitively to maintain the force of the muscle contraction. Consequently, each active MU generates a train of MUPs during a muscle contraction known as MUPT. A MUPT is mathematically described as (De Luca, 1979; Basmajian & De Luca, 1985; Stashuk, 2001; Parsaei et al., 2010):

$$\mathbf{M}\mathbf{U}\mathbf{P}\mathbf{T}\_{\mathbf{j}}\left(\mathbf{t}\right) = \sum\_{i=1}^{M} \mathbf{M}\mathbf{U}\mathbf{P}\_{\mathbf{ji}}\left(\mathbf{t}\cdot\mathbf{\mathcal{S}}\_{\mathbf{ji}}\right) \tag{1}$$

where M is the number of times that the *j*th motor unit fires, ji is the *i*th firing time of motor unit *j*, and MUPji(t) is the *i*th MUP generated by motor unit *j* during its *it*h firing.

Assuming *K* MUs were active during a muscle contraction, the detected EMG signal can be mathematically represented as (De Luca,1979; Basmajian & De Luca, 1985; Stashuk, 2001; Parsaei et al., 2010):

$$\text{EMG(t)} = \sum\_{j=1}^{K} \text{MUPT}\_{j}(\mathbf{t}) + \mathbf{n(t)} \tag{2}$$

where MUPTj(t) is the MUPT generated by the *j*th motor unit, and n(t) is background noise.

Fig.1 shows both an anatomical and physiological model for an EMG signal. In this figure, *h*i(*t*) is a filter with impulse response MUPi, and the impulses represent action potentials emerging from an - motor neuron to innervate the connected muscle fibers. As shown, an EMG signal is in fact the superposition of the MUPTs created by MUs active during a muscle contraction and background noise.

The characteristics of a detected EMG signal depend on several factors such as the level of contraction, the shape and size of the electrode used, and the position and orientation of the electrode relative to the muscle fibres of the active MUs (De Luca, 1979; Basmajian & De Luca, 1985). In addition, the characteristics of an EMG signal detected from a contacting muscle are related to the anatomical and physiological features of the muscle and therefore to its age and state of health or fatigue(Stalberg & Falck, 1997; Tröger & Dengler, 2000; Fuglsang-Frederiksen, 2006; Pino et al., 2008; Farkas et al., 2010). Some parameters of EMG signals for normal and abnormal muscles are compared in Table 1. Consequently, analyzing EMG signals provides information that can be used clinically or for physiological investigation. The technique of detecting, evaluating, and analyzing EMG signals is known as electromyography. One useful technique in electromyography is EMG signal decomposition.

#### **2.2 EMG signal decomposition**

EMG signal decomposition is the process of resolving a detected EMG signal into is constituent MUPTs. This process that is conceptually shown in Fig.2 is implemented by employing digital signal processing and pattern recognition techniques in four/five steps:

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 325

Table 1. Some parameters of EMG signals for normal and abnormal muscles.

Fig. 2. A schematic representation of EMG signal decomposition (adapted from De Luca et

Once the decomposition process is completed, the prototypical MUP shape (MUP template) and MU firing pattern statistics for each extracted MUPT are estimated for future analysis (especially for quantitative electromyography). This provides information, regarding the temporal behaviour and morphological layout of the MUs that significantly contributed to the detected EMG signal, which can assist with the diagnosis of various neuromuscular diseases and the study of MU control, and lead to a better understanding of healthy, pathological, ageing or fatiguing neuromuscular systems ( De Luca et al., 1982a, 1982b; Stalberg & Falck, 1997; Tröger & Dengler, 2000; Stashuk, 2001; Fuglsang-Frederiksen, 2006; Calder et al., 2008; Farkas et al., 2010). However, this is achieved only when this information is valid. In fact, before using decomposition results and the MUP shape and MU firing pattern information for either clinical or research purposes the validity of the extracted

al. 2006; 1982a).

MUPTs needs to be confirmed.

signal preprocessing, signal segmentation and MUP detection, feature extraction, and then clustering and possibly supervised classification of detected MUPs (Stashuk, 2001; Parsaei et al., 2010).The first step is to remove background noise and low-frequency information from the detected EMG signal, to shorten the duration of MUPs and decrease MUP temporal overlap, and to sharpen the MUPs and increase discrimination between them. The second step is to section the signal into segments containing possible MUPs that were generated by active MUs that contributed significantly to the detected EMG signal. The detected MUPs are represented by a feature vector in the third steps and finally are sorted into MUPTs using clustering and/or supervised classification technniques. If a full or complete decomposition is required, superimposed MUPs (SMUPs) are resolved into their constituent MUPs in another step. For clinical use of EMG signal decomposition results, where only mean MU firing rate and MU firing rate variability are to be studied, resolving SMUPs is not essential ( Stashuk,1999,2001) because the desired MU firing parameters can be estimated from incomplete discharge patterns (Stashuk & Qu, 1996b; Stashuk, 1999). However, for detailed studies of MU control and muscle architecture, SMUPs must be resolved. A recent comprehensive review of the algorithms developed for the decomposition of indwelling EMG signals is provided by Parsaei et al. (2010).

Fig. 1. Anatomical and physiological model for an EMG signal (from Rasheed et al., 2010).

signal preprocessing, signal segmentation and MUP detection, feature extraction, and then clustering and possibly supervised classification of detected MUPs (Stashuk, 2001; Parsaei et al., 2010).The first step is to remove background noise and low-frequency information from the detected EMG signal, to shorten the duration of MUPs and decrease MUP temporal overlap, and to sharpen the MUPs and increase discrimination between them. The second step is to section the signal into segments containing possible MUPs that were generated by active MUs that contributed significantly to the detected EMG signal. The detected MUPs are represented by a feature vector in the third steps and finally are sorted into MUPTs using clustering and/or supervised classification technniques. If a full or complete decomposition is required, superimposed MUPs (SMUPs) are resolved into their constituent MUPs in another step. For clinical use of EMG signal decomposition results, where only mean MU firing rate and MU firing rate variability are to be studied, resolving SMUPs is not essential ( Stashuk,1999,2001) because the desired MU firing parameters can be estimated from incomplete discharge patterns (Stashuk & Qu, 1996b; Stashuk, 1999). However, for detailed studies of MU control and muscle architecture, SMUPs must be resolved. A recent comprehensive review of the algorithms developed for the decomposition of indwelling

Fig. 1. Anatomical and physiological model for an EMG signal (from Rasheed et al., 2010).

EMG signals is provided by Parsaei et al. (2010).

Table 1. Some parameters of EMG signals for normal and abnormal muscles.

Fig. 2. A schematic representation of EMG signal decomposition (adapted from De Luca et al. 2006; 1982a).

Once the decomposition process is completed, the prototypical MUP shape (MUP template) and MU firing pattern statistics for each extracted MUPT are estimated for future analysis (especially for quantitative electromyography). This provides information, regarding the temporal behaviour and morphological layout of the MUs that significantly contributed to the detected EMG signal, which can assist with the diagnosis of various neuromuscular diseases and the study of MU control, and lead to a better understanding of healthy, pathological, ageing or fatiguing neuromuscular systems ( De Luca et al., 1982a, 1982b; Stalberg & Falck, 1997; Tröger & Dengler, 2000; Stashuk, 2001; Fuglsang-Frederiksen, 2006; Calder et al., 2008; Farkas et al., 2010). However, this is achieved only when this information is valid. In fact, before using decomposition results and the MUP shape and MU firing pattern information for either clinical or research purposes the validity of the extracted MUPTs needs to be confirmed.

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 327

Fig. 3. Example of valid and invalid MUPTs. Column one shows the the shimmer plot of the MUPs assigned to each MUPT. Column two shows the IDI histogram and corresponding statistics for each extracted MUPT. Column three illustractes the discharge patterns and

Parsaei and his co-workers (Parsaei et al., 2011; Parsaei&Stashuk, 2011a) developed several methods for automatic validation of MUPTs extracted by a decomposition algorithm: a MU firing pattern based validation method, and a MUP shape based validation method. Across the sets of real and simulated data used for evaluating each of these two MUPT validation methods, the methods performed well in categorizing a train correctly. In addition these methods are fast enough to be used during the decomposition process. However, the accuracy of the firing pattern validity system in correctly classifying invalid trains decreases as the MCE rate (percentage of MCEs) in the MUPTs increases such that this accuracy was reduced to < 60% when the MCE rate was >80%. Likewise, the accuracy of the MUP-shape validation methods decreases as the separability between the trains used to create an invalid train decreases such that the methods failed to detect the majority ( >80%) of invalid trains composed of MUPTs with highly similar MUP templates. In this work, using both the MU firing pattern and MUP shape information of a MUPT to estimate its validity was explored with the hope of overcoming these two issues; the achievements of these efforts are presented in this chapter. The objective of developing such methods was to: 1) facilitate the use of intramuscular EMG signal decomposition results for clinical applications of

instantaneous firing rates for each MU.

## **3. MUPT validation**

In general, validating a MUPT is a process of determining whether a given MUPT accurately represents the activity of a single MU or not. The validity of a MUPT can be defined using two different criteria: MU firing pattern validity, and MUP shape validity.

MU firing pattern validity of a MUPT is determined by assessing its inter–discharge interval (IDI) histogram (density function) and the instantaneous firing rate of the corresponding MU versus time. The MU discharges corresponding to a valid MUPT occur at regular intervals and in general, have a Gaussian-shaped IDI histogram while for invalid MUPTs the IDIs have large variations and will not have a Gaussian-shaped IDI histogram. Even though some researchers have demonstrated that the IDI distribution of a MU may not actually be Gaussian (De Luca & Forrest,1973; Matthews, 1996), for MUPTs of MUs that are consistently recruited, the Gaussian density is an appropriate approximation (Clamann, 1969; McGill et al., 1985; McGill & Dorfman, 1985; Stashuk, 1999; Moritz et al., 2005; Rasheed et al., 2010;Parsaei et al.,2011). If an extracted MUPT represents the firing of a single MU and has suitably low percentage of FCEs (FCE rate), it has MU firing pattern validity. As an example, the first two MUPTs shown in Fig. 3 have MU firing pattern validity, but the third MUPT does not have firing pattern validity.

To determine MUP shape validity, a given train is assessed using the shapes of its MUPs. Assuming the MUPs generated by a single MU are homogeneous in shape, the MUPT under study can be assumed to have MUP-shape validity when its MUPs have consistent shapes. As an example, MUPTs shown in the first and third rows of Fig. 3 have MUP-shape validity; however, the MUPT given in the second row does not have MUP–shape validity.

Finally, a train can be considered valid based on a combination of its MU firing pattern and MUP shape validity. For example, the first MUPT shown in Fig. 3, which has both MU firing pattern and MUP shape validity, is considered valid, but the MUPTs shown in rows 2 and 3 will be labelled invalid because they do not have MUP–shape or MU firing pattern validity.

To date, MUPT validation is mainly conducted qualitatively by an expert operator. The MUP shape validity of a MUPT is assessed by an expert using raster/shimmer plots of its assigned MUPs ( Doherty & Stashuk,2003; Stashuk, 2001; Stashuk et al., 2004; Boe et al., 2005, Calder et al., 2008; Parsaei et al., 2010). MU firing pattern validity of a MUPT is determined by viewing and qualitative evaluation of its IDI histogram and the plots of the firing rate as a function of time. The accuracy of such qualitative MUPT evaluations, as with other methods that need operator supervision, depends on operator experience and skill. In addition, such evaluations are too time consuming to be practically completed in a busy clinical environment. More importantly, manual MUPT validation methods cannot assist with improving the performance of automatic EMG signal decomposition algorithms. To overcome these issues, methods need to be developed to automatically estimate the validity of a given MUPT.

McGill and Marateb (2010) developed a rigorous statistical method for assessing the validity of MUPTs extracted by decomposing an EMG signal. The evaluation results are encouraging, but due to the computational complexity of the procedures used in this method, the algorithm is only efficient for assessing the decomposition accuracy of 5–second–long, low-complexity signals composed of at most 6 MUPTs. In addition, full decomposition in required in this method. Therefore, this method cannot be used during decomposing or in a busy clinical environment.

In general, validating a MUPT is a process of determining whether a given MUPT accurately represents the activity of a single MU or not. The validity of a MUPT can be defined using

MU firing pattern validity of a MUPT is determined by assessing its inter–discharge interval (IDI) histogram (density function) and the instantaneous firing rate of the corresponding MU versus time. The MU discharges corresponding to a valid MUPT occur at regular intervals and in general, have a Gaussian-shaped IDI histogram while for invalid MUPTs the IDIs have large variations and will not have a Gaussian-shaped IDI histogram. Even though some researchers have demonstrated that the IDI distribution of a MU may not actually be Gaussian (De Luca & Forrest,1973; Matthews, 1996), for MUPTs of MUs that are consistently recruited, the Gaussian density is an appropriate approximation (Clamann, 1969; McGill et al., 1985; McGill & Dorfman, 1985; Stashuk, 1999; Moritz et al., 2005; Rasheed et al., 2010;Parsaei et al.,2011). If an extracted MUPT represents the firing of a single MU and has suitably low percentage of FCEs (FCE rate), it has MU firing pattern validity. As an example, the first two MUPTs shown in Fig. 3 have MU firing pattern validity, but the third

To determine MUP shape validity, a given train is assessed using the shapes of its MUPs. Assuming the MUPs generated by a single MU are homogeneous in shape, the MUPT under study can be assumed to have MUP-shape validity when its MUPs have consistent shapes. As an example, MUPTs shown in the first and third rows of Fig. 3 have MUP-shape validity;

Finally, a train can be considered valid based on a combination of its MU firing pattern and MUP shape validity. For example, the first MUPT shown in Fig. 3, which has both MU firing pattern and MUP shape validity, is considered valid, but the MUPTs shown in rows 2 and 3 will be labelled invalid because they do not have MUP–shape or MU firing pattern validity. To date, MUPT validation is mainly conducted qualitatively by an expert operator. The MUP shape validity of a MUPT is assessed by an expert using raster/shimmer plots of its assigned MUPs ( Doherty & Stashuk,2003; Stashuk, 2001; Stashuk et al., 2004; Boe et al., 2005, Calder et al., 2008; Parsaei et al., 2010). MU firing pattern validity of a MUPT is determined by viewing and qualitative evaluation of its IDI histogram and the plots of the firing rate as a function of time. The accuracy of such qualitative MUPT evaluations, as with other methods that need operator supervision, depends on operator experience and skill. In addition, such evaluations are too time consuming to be practically completed in a busy clinical environment. More importantly, manual MUPT validation methods cannot assist with improving the performance of automatic EMG signal decomposition algorithms. To overcome these issues, methods need to be developed to automatically estimate the validity

McGill and Marateb (2010) developed a rigorous statistical method for assessing the validity of MUPTs extracted by decomposing an EMG signal. The evaluation results are encouraging, but due to the computational complexity of the procedures used in this method, the algorithm is only efficient for assessing the decomposition accuracy of 5–second–long, low-complexity signals composed of at most 6 MUPTs. In addition, full decomposition in required in this method. Therefore, this method cannot be used during

however, the MUPT given in the second row does not have MUP–shape validity.

two different criteria: MU firing pattern validity, and MUP shape validity.

**3. MUPT validation** 

of a given MUPT.

MUPT does not have firing pattern validity.

decomposing or in a busy clinical environment.

Fig. 3. Example of valid and invalid MUPTs. Column one shows the the shimmer plot of the MUPs assigned to each MUPT. Column two shows the IDI histogram and corresponding statistics for each extracted MUPT. Column three illustractes the discharge patterns and instantaneous firing rates for each MU.

Parsaei and his co-workers (Parsaei et al., 2011; Parsaei&Stashuk, 2011a) developed several methods for automatic validation of MUPTs extracted by a decomposition algorithm: a MU firing pattern based validation method, and a MUP shape based validation method. Across the sets of real and simulated data used for evaluating each of these two MUPT validation methods, the methods performed well in categorizing a train correctly. In addition these methods are fast enough to be used during the decomposition process. However, the accuracy of the firing pattern validity system in correctly classifying invalid trains decreases as the MCE rate (percentage of MCEs) in the MUPTs increases such that this accuracy was reduced to < 60% when the MCE rate was >80%. Likewise, the accuracy of the MUP-shape validation methods decreases as the separability between the trains used to create an invalid train decreases such that the methods failed to detect the majority ( >80%) of invalid trains composed of MUPTs with highly similar MUP templates. In this work, using both the MU firing pattern and MUP shape information of a MUPT to estimate its validity was explored with the hope of overcoming these two issues; the achievements of these efforts are presented in this chapter. The objective of developing such methods was to: 1) facilitate the use of intramuscular EMG signal decomposition results for clinical applications of

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 329

The features used in this work are listed in Table 2; detailed definitions and calculation methods for these features are presented in (Parsaei et al., 2011; Parsaei, 2011). In short, the majority of these features are extracted from the IDI distribution of the given MUPT and target the left side of this distribution, where short IDIs (i.e., the errors of interest) are reflected. The identification rate targets the right side of the IDI distribution to measure the MCE rate in the MUPT. The firing rate mean consecutive difference measures the variation in the instantaneous firing rate over time. The instantaneous firing rate at each MUP occurrence in a MUPT is defined as the inverse of a local IDI that is obtained by applying a

normalized Hamming filter of length 11 to the IDIs of the train.

Fig. 5. The steps for the firing pattern validity classifier

LIDIR Lower IDI ratio

ID– rate Identification rate

**Feature Description**  CV Coefficient of variation CVL Lower coefficient of variation CVL/CVU The ratio of lower and upper CV PI Percentage of inconsistent IDIs

1stSCorr First coefficient of serial correlation

Skewness A measure of symmetry of the IDI histogram

FR–MCD Firing rate mean consecutive difference IDI–MCD IDI mean consecutive difference Table 2. Firing pattern features used for the firing pattern validity classifier.

quantitative electromyography by providing the overall validity of MUPTs and excluding or highlighting invalid MUPTs; 2) assist with improving the accuracy and completeness of decomposition results. Using the characteristics of the IDI distribution, MU firing patterns, and within train MUP shape variability of invalid MUPTs two methods based on a combination of feature extraction, cluster validation techniques and supervised classification algorithms were developed; details are presented in the following Section.

## **4. An automated system for estimating MUPT validity**

As discussed in the previous section and illustrated in Fig.3, the characteristics of IDI histograms, MU firing rates over time, and within-train MUP shape inconsistencies of invalid trains differ from those of valid trains. These facts motivate the development of an automated system to determine whether a given MUPT accurately represents the activity of a single MU (i.e., is valid) or not. With the developed MUPT validation method, a given train is considered valid if it has both MU firing pattern validity and MUP-shape validity; otherwise, the train is labelled invalid. MU firing pattern validity is estimated by a firing pattern validity classifier (FPVC) that uses a supervised classifier along with several features extracted from the IDI histo-gram and instantaneous firing rate of the MUPT. MUP–shape validity is determined by assessing the homogeneity of the wave shape of the MUPs of the given train using a MUP–shape validity system that is mainly based on a cluster validation technique. The overall procedure of the system is illustrated in Fig.4. Both the MU firing pattern system and MUP–shape validation system used are discussed below.

Fig. 4. The procedure of the developed MUPT validation system that estimates the validity of a MUPT by combining its MU firing pattern validity and MUP shape validity estimated using a supervised classifier and a cluster validation technique.

### **4.1 Firing pattern validity classifier**

The overall procedure of the developed FPVC is shown in Fig. 5. The goal of using the FPVC is to determine whether a MUPT accurately represents the firings of a single MU or not. This categorization is performed by a supervised classifier that uses nine features extracted from the IDI histograms and MU firing rates of the given MUPT.

quantitative electromyography by providing the overall validity of MUPTs and excluding or highlighting invalid MUPTs; 2) assist with improving the accuracy and completeness of decomposition results. Using the characteristics of the IDI distribution, MU firing patterns, and within train MUP shape variability of invalid MUPTs two methods based on a combination of feature extraction, cluster validation techniques and supervised classification

As discussed in the previous section and illustrated in Fig.3, the characteristics of IDI histograms, MU firing rates over time, and within-train MUP shape inconsistencies of invalid trains differ from those of valid trains. These facts motivate the development of an automated system to determine whether a given MUPT accurately represents the activity of a single MU (i.e., is valid) or not. With the developed MUPT validation method, a given train is considered valid if it has both MU firing pattern validity and MUP-shape validity; otherwise, the train is labelled invalid. MU firing pattern validity is estimated by a firing pattern validity classifier (FPVC) that uses a supervised classifier along with several features extracted from the IDI histo-gram and instantaneous firing rate of the MUPT. MUP–shape validity is determined by assessing the homogeneity of the wave shape of the MUPs of the given train using a MUP–shape validity system that is mainly based on a cluster validation technique. The overall procedure of the system is illustrated in Fig.4. Both the MU firing

algorithms were developed; details are presented in the following Section.

pattern system and MUP–shape validation system used are discussed below.

Fig. 4. The procedure of the developed MUPT validation system that estimates the validity of a MUPT by combining its MU firing pattern validity and MUP shape validity estimated

The overall procedure of the developed FPVC is shown in Fig. 5. The goal of using the FPVC is to determine whether a MUPT accurately represents the firings of a single MU or not. This categorization is performed by a supervised classifier that uses nine features extracted from

using a supervised classifier and a cluster validation technique.

the IDI histograms and MU firing rates of the given MUPT.

**4.1 Firing pattern validity classifier** 

**4. An automated system for estimating MUPT validity** 

The features used in this work are listed in Table 2; detailed definitions and calculation methods for these features are presented in (Parsaei et al., 2011; Parsaei, 2011). In short, the majority of these features are extracted from the IDI distribution of the given MUPT and target the left side of this distribution, where short IDIs (i.e., the errors of interest) are reflected. The identification rate targets the right side of the IDI distribution to measure the MCE rate in the MUPT. The firing rate mean consecutive difference measures the variation in the instantaneous firing rate over time. The instantaneous firing rate at each MUP occurrence in a MUPT is defined as the inverse of a local IDI that is obtained by applying a normalized Hamming filter of length 11 to the IDIs of the train.

Fig. 5. The steps for the firing pattern validity classifier


Table 2. Firing pattern features used for the firing pattern validity classifier.

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 331

For the Beal method (Gordon, 1999), the null hypothesis of a single cluster is rejected in

2 1 2 <sup>1</sup> 2/ 2 1

*W W <sup>W</sup> Bi <sup>F</sup> <sup>N</sup>*

*d*

where the value for Fcritical is obtained from an Fd,(N–2)d distribution at an level of

*critical*

(5)

(6)

2

For the DH method (Duda et al., 2000), the null hypothesis of one cluster is rejected if

*W*

*z*

*erf* .

filtered output for these time samples, *y*[n], are calculated as

where *L* is the skip factor and *TS* is the sampling interval.

a 1st-order LPD filter is preferred to a 2nd-order one.

2 1

<sup>8</sup> 2 1

*<sup>W</sup> <sup>d</sup> J z*

 

2

The effectiveness of Beal and DH methods in estimating the MUP–shape validity of a MUPT was investigated using some simulated MUPTs (see Section 6 for the description of the simulated data). For a given MUPT, each of its MUPs is represented using the 80 low-pass differencing (LPD) filtered data samples centred about its peak value (i.e., *d*=80) and then the MUP– shape validity of the given train was determined using one of these two methods. To split the given train into two clusters, the K-means

The LPD filtered samples were used instead of unfiltered samples because they discriminate between the MUPs generated by different MUs better than the raw. The 1st-order LPD filter (McGill et al., 1985) used is, in fact, a two-point central difference algorithm (Semmlow, 2004) that acts as a differentiator for the lower frequencies and as a low-pass filter for higher frequencies. Given that *x*[n], n=1,2, ..,80 are the discrete time samples of a MUP, the LPD

> [ ][ ] [ ] <sup>2</sup> *<sup>s</sup> xn L xn L*

It is worth pointing out that a 2nd-order LPD filter was also evaluated for filtering the MUPs, but the accuracy obtained for classifying valid MUPTs was drastically decreased compared to the accuracy obtained when the MUPs are filtered using a 1st-order LPD filter. Therefore,

(7)

*y n LT*

*d Nd*

<sup>2</sup> <sup>1</sup>

*N*

favor of multiple clusters if:

where z is given by 50 1 ( ) <sup>2</sup>

algorithm was used.

significance.

For supervised classification, a support vector machine (SVM) classifier (Vapnik, 1999), which uses a Gaussian radial basis function (Eq.3) as a kernel, was employed.

$$\mathbf{K}(\mathbf{x}, \mathbf{x}') = \exp(-\frac{\left\|\mathbf{x} - \mathbf{x}'\right\|^2}{2\sigma^2}) \tag{3}$$

where *x* is an input data point to a SVM, *x*' is the centre of the kernel and <sup>2</sup> is the width of the kernel specified a priori by the user. In training a SVM, in addition to <sup>2</sup> there is another parameter that has to be selected by the user, the cost parameter, C. This parameter, which is also known as the regularization parameter, controls the trade off between allowing training errors and the complexity of the machine. For the objectives of this work, <sup>2</sup> and C were determined experimentally using cross-validation.

#### **4.2 MUP –shape validity system**

Assuming the MUPs generated by a single MU are homogeneous in shape (but with possibly different degrees of variability across different MUs), the MUP–shape validity of a MUPT can be estimated by assessing the shape consistency of its MUPs. Overall, the process of EMG signal decomposition can be considered a clustering problem because neither the number of MUPTs (i.e., clusters) nor the labels of the MUPs are known in advance. During EMG signal decomposition, detected MUPs are clustered into groups called MUPTs. Therefore, the MUP–shape validation of a MUPT extracted by a decomposition algorithm can be considered a cluster validity problem and the decision to be made is whether the extracted MUPT represents one cluster in terms of the shapes of the assigned MUPs or not. For this purpose, in this work the Beal method (Gordon, 1999), and the Duda and Hart (DH) method (Duda et al., 2000), which are presented for estimating the numbers of clusters in a data set, were employed to develop two automated MUP–shape validation systems. Although numerous methods have been developed to estimate the number of groups in a dataset (Milligan & Cooper, 1985; Gordon, 1999), the majority of these methods cannot be used for assessing MUP–shape validity of a MUPT because of one of these two reasons: a) they cannot be used for testing one cluster versus multiple clusters in a dataset; b) they are computationally too expensive to be used for online validation of MUPTs and especially during EMG signal decomposition (Parsaei, 2011; Parsaei & Stashuk, 2011a).

For a data set consisting of *N* observations (patterns) each of which repented by *d* uncorrelated feature values, both the Beal and DH methods test the existence of clusters in the data set by comparing its within cluster dispersion (*W*1) to the resulting within cluster dispersion when it is partitioned into two clusters using a clustering algorithm (*W*2). The parameter *W*K (*k*=1,2)is usually given by

$$\mathbf{W}\_{\mathbf{K}} = \sum\_{\mathbf{i}=1}^{K} \sum\_{\mathbf{X} \in \mathcal{C}\_{\mathbf{i}}} (\mathbf{X} - \mathbf{m}\_{\mathbf{i}})(\mathbf{X} - \mathbf{m}\_{\mathbf{i}})^{\mathrm{T}} \tag{4}$$

where *X* is a vector of features representing each object of the given data set, *m*i is the sample mean of the *N*i objects assigned to cluster *C*i.

For the Beal method (Gordon, 1999), the null hypothesis of a single cluster is rejected in favor of multiple clusters if:

$$Bi = \frac{\left(\frac{\mathcal{W}\_2 - \mathcal{W}\_1}{\mathcal{W}\_2}\right)}{\left(\frac{\mathcal{N} - 1}{\mathcal{N} - 2}\right) 2^{2/d} - 1} > F\_{critical} \tag{5}$$

where the value for Fcritical is obtained from an Fd,(N–2)d distribution at an level of significance.

For the DH method (Duda et al., 2000), the null hypothesis of one cluster is rejected if

$$J = \frac{\left(-\frac{W\_2}{W\_1} + 1 - \frac{2}{\pi d}\right)}{\sqrt{2\left(1 - \frac{8}{\pi^2 d}\right)}} > z$$

where z is given by 50 1 ( ) <sup>2</sup> *z erf* .

330 Applied Biological Engineering – Principles and Practice

For supervised classification, a support vector machine (SVM) classifier (Vapnik, 1999),

x x' (x,x') exp( ) <sup>2</sup> 

where *x* is an input data point to a SVM, *x*' is the centre of the kernel and <sup>2</sup> is the width of the kernel specified a priori by the user. In training a SVM, in addition to <sup>2</sup> there is another parameter that has to be selected by the user, the cost parameter, C. This parameter, which is also known as the regularization parameter, controls the trade off between allowing training errors and the complexity of the machine. For the objectives of this work, <sup>2</sup> and C were

Assuming the MUPs generated by a single MU are homogeneous in shape (but with possibly different degrees of variability across different MUs), the MUP–shape validity of a MUPT can be estimated by assessing the shape consistency of its MUPs. Overall, the process of EMG signal decomposition can be considered a clustering problem because neither the number of MUPTs (i.e., clusters) nor the labels of the MUPs are known in advance. During EMG signal decomposition, detected MUPs are clustered into groups called MUPTs. Therefore, the MUP–shape validation of a MUPT extracted by a decomposition algorithm can be considered a cluster validity problem and the decision to be made is whether the extracted MUPT represents one cluster in terms of the shapes of the assigned MUPs or not. For this purpose, in this work the Beal method (Gordon, 1999), and the Duda and Hart (DH) method (Duda et al., 2000), which are presented for estimating the numbers of clusters in a data set, were employed to develop two automated MUP–shape validation systems. Although numerous methods have been developed to estimate the number of groups in a dataset (Milligan & Cooper, 1985; Gordon, 1999), the majority of these methods cannot be used for assessing MUP–shape validity of a MUPT because of one of these two reasons: a) they cannot be used for testing one cluster versus multiple clusters in a dataset; b) they are computationally too expensive to be used for online validation of MUPTs and especially during EMG signal

For a data set consisting of *N* observations (patterns) each of which repented by *d* uncorrelated feature values, both the Beal and DH methods test the existence of clusters in the data set by comparing its within cluster dispersion (*W*1) to the resulting within cluster dispersion when it is partitioned into two clusters using a clustering algorithm (*W*2). The

T

(4)

i

K i i

where *X* is a vector of features representing each object of the given data set, *m*i is the

W (X m )(X m )

K

i 1X C

2 2

(3)

which uses a Gaussian radial basis function (Eq.3) as a kernel, was employed.

determined experimentally using cross-validation.

decomposition (Parsaei, 2011; Parsaei & Stashuk, 2011a).

parameter *W*K (*k*=1,2)is usually given by

sample mean of the *N*i objects assigned to cluster *C*i.

**4.2 MUP –shape validity system** 

The effectiveness of Beal and DH methods in estimating the MUP–shape validity of a MUPT was investigated using some simulated MUPTs (see Section 6 for the description of the simulated data). For a given MUPT, each of its MUPs is represented using the 80 low-pass differencing (LPD) filtered data samples centred about its peak value (i.e., *d*=80) and then the MUP– shape validity of the given train was determined using one of these two methods. To split the given train into two clusters, the K-means algorithm was used.

The LPD filtered samples were used instead of unfiltered samples because they discriminate between the MUPs generated by different MUs better than the raw. The 1st-order LPD filter (McGill et al., 1985) used is, in fact, a two-point central difference algorithm (Semmlow, 2004) that acts as a differentiator for the lower frequencies and as a low-pass filter for higher frequencies. Given that *x*[n], n=1,2, ..,80 are the discrete time samples of a MUP, the LPD filtered output for these time samples, *y*[n], are calculated as

$$y[n] = \frac{\mathbf{x}[n+L] - \mathbf{x}[n-L]}{2LT\_s} \tag{7}$$

where *L* is the skip factor and *TS* is the sampling interval.

It is worth pointing out that a 2nd-order LPD filter was also evaluated for filtering the MUPs, but the accuracy obtained for classifying valid MUPTs was drastically decreased compared to the accuracy obtained when the MUPs are filtered using a 1st-order LPD filter. Therefore, a 1st-order LPD filter is preferred to a 2nd-order one.

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 333

(a) (b)

Given gap values and active parts are respectively estimated and identified for the MUPT under study, the sample corresponding to the maximum gap value in each active part is chosen as an effective feature. Consequently, the number of selected features will be equal to the number of active parts. Additional features, if required are selected based on their gap– values and also their intervals from the previous selected features. Each feature should have the maximum gap value among the remaining samples and also be at least eight samples

Fig. 7. The effect of preprocessing the MUPs of a MUPT. (a) raw MUPs , (b) LPD filterd

MUPs. Such a figure previously presented by McGill et al. (1985).

(i.e. 0.26 ms) before or after any selected features.

Fig. 6. An overview of the MUP–shape validation system.

Preliminary tests showed that when representing MUPs using LPD filtered time samples, neither the Beal method (Gordon, 1999) nor the DH method (Duda et al., 2000) (each with α =0.05) was accurate in correctly classifying valid trains. Their accuracy for classifying a valid train correctly was only 5% while that for an invalid train was 99%. The reason for the low accuracy for valid MUPTs were discovered to be: 1) the 80 LPD filtered time samples used as features are highly correlated; 2) the algorithms are sensitive to the inherent MUP shape variability in the valid MUPTs caused by jitter or jiggle (Stålberg & Sonoo, 1994); valid MUPTs with high jitter or jiggle are erroneously classified as invalid trains. To overcome these two issues, an adaptive method based on a combination of feature extraction techniques and the Beal orDH method was developed. An overview of the system is given in Fig. 6. A brief description of each step is given below, detailed discussion can be found elsewhere (Parsaei, 2011; Parsaei & Stashuk, 2011a).

#### **4.2.1 Prepossessing**

Preprocessing was completed to increase the signal-to-noise ratio (SNR) of the MUPs, sharpen MUPs, and ultimately enhance the discrimination between the MUPs created by two or more different MUs but mistakenly assigned to one MUPT. For this purposes, MUPs of a MUPT each of which represented using 80 time samples are filtered using a LPD filter (Eq. 7). Fig. 7 shows the effectiveness for a MUPT that consists of the MUPs of two MUs. As shown, LPD filtering increased the distinguishability of the MUPs and ultimately clarified that the given train is an invalid train.

### **4.2.2 Feature extraction**

The feature extraction step is to extract/select effective, uncorrelated, and discriminative features out of the 80 LPD filtered sample points used to represent the MUPs of a MUPT. These features can be extracted using principal component analysis (PCA), however due to computational complexity of the PCA, a PCA–based MUPT validation algorithm will be slow and ultimately will not be efficient to be used during EMG decomposition (Parsaei, 2011; Parsaei &Stashuk, 2011a). In this work a gap–based feature selection technique which is based on the way that a human would assess the validity of a MUPT using its MUP shimmer plot was employed for feature extraction. A human operator visually assesses the consistency of the shapes of the MUPs assigned to a MUPT by inspecting the existence of any gap or obvious differences between specific MUP time sample values. With the proposed gap–based feature selection, the regions in which the MUPs of a MUPT are significantly different are identified first and then the *m* samples for which the MUPs are significantly differ from each other are identified and used as the effective features representing the MUPs of the MUPT. Such regions that are called here "active parts" for the MUPT under study are determined by calculating gap values (GVs) for the train. Let *y*i[n] n=1,2,…,80 represent the 80 LPD filtered time samples of the *i*th MUP in the given MUPT. At each *n*, the largest adjacent change in the *N* sorted *y*i[n] values is GV[n]. An active part is a consecutive set of GV[n] values greater than the baseline noise. More details for estimating gap values for a MUPT are given in (Parsaei, 2011; Parsaei &Stashuk, 2011a).

Preliminary tests showed that when representing MUPs using LPD filtered time samples, neither the Beal method (Gordon, 1999) nor the DH method (Duda et al., 2000) (each with α =0.05) was accurate in correctly classifying valid trains. Their accuracy for classifying a valid train correctly was only 5% while that for an invalid train was 99%. The reason for the low accuracy for valid MUPTs were discovered to be: 1) the 80 LPD filtered time samples used as features are highly correlated; 2) the algorithms are sensitive to the inherent MUP shape variability in the valid MUPTs caused by jitter or jiggle (Stålberg & Sonoo, 1994); valid MUPTs with high jitter or jiggle are erroneously classified as invalid trains. To overcome these two issues, an adaptive method based on a combination of feature extraction techniques and the Beal orDH method was developed. An overview of the system is given in Fig. 6. A brief description of each step is given below, detailed discussion can be found

Preprocessing was completed to increase the signal-to-noise ratio (SNR) of the MUPs, sharpen MUPs, and ultimately enhance the discrimination between the MUPs created by two or more different MUs but mistakenly assigned to one MUPT. For this purposes, MUPs of a MUPT each of which represented using 80 time samples are filtered using a LPD filter (Eq. 7). Fig. 7 shows the effectiveness for a MUPT that consists of the MUPs of two MUs. As shown, LPD filtering increased the distinguishability of the MUPs and ultimately clarified

The feature extraction step is to extract/select effective, uncorrelated, and discriminative features out of the 80 LPD filtered sample points used to represent the MUPs of a MUPT. These features can be extracted using principal component analysis (PCA), however due to computational complexity of the PCA, a PCA–based MUPT validation algorithm will be slow and ultimately will not be efficient to be used during EMG decomposition (Parsaei, 2011; Parsaei &Stashuk, 2011a). In this work a gap–based feature selection technique which is based on the way that a human would assess the validity of a MUPT using its MUP shimmer plot was employed for feature extraction. A human operator visually assesses the consistency of the shapes of the MUPs assigned to a MUPT by inspecting the existence of any gap or obvious differences between specific MUP time sample values. With the proposed gap–based feature selection, the regions in which the MUPs of a MUPT are significantly different are identified first and then the *m* samples for which the MUPs are significantly differ from each other are identified and used as the effective features representing the MUPs of the MUPT. Such regions that are called here "active parts" for the MUPT under study are determined by calculating gap values (GVs) for the train. Let *y*i[n] n=1,2,…,80 represent the 80 LPD filtered time samples of the *i*th MUP in the given MUPT. At each *n*, the largest adjacent change in the *N* sorted *y*i[n] values is GV[n]. An active part is a consecutive set of GV[n] values greater than the baseline noise. More details for estimating gap values for a MUPT are given in (Parsaei,

elsewhere (Parsaei, 2011; Parsaei & Stashuk, 2011a).

**4.2.1 Prepossessing** 

**4.2.2 Feature extraction** 

2011; Parsaei &Stashuk, 2011a).

that the given train is an invalid train.

Fig. 6. An overview of the MUP–shape validation system.

Fig. 7. The effect of preprocessing the MUPs of a MUPT. (a) raw MUPs , (b) LPD filterd MUPs. Such a figure previously presented by McGill et al. (1985).

Given gap values and active parts are respectively estimated and identified for the MUPT under study, the sample corresponding to the maximum gap value in each active part is chosen as an effective feature. Consequently, the number of selected features will be equal to the number of active parts. Additional features, if required are selected based on their gap– values and also their intervals from the previous selected features. Each feature should have the maximum gap value among the remaining samples and also be at least eight samples (i.e. 0.26 ms) before or after any selected features.

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 335

signal decomposition algorithm used in the DQEMG (Stashuk, 1999). In the original certainty–based EMG signal decomposition, the detected MUPs are grouped into several MUPTs using a shape and temporal–based clustering (STBC) algorithm (Stashuk&Qu, 1996a) and a supervised certainty-based classifier (CBC). The STBC algorithm is a customized K-means clustering method that uses both MUP shape and MU firing pattern information to cluster MUPs. In the STBC, MUPTs are split or merged based on several heuristic criteria. Assuming the MUPTs provided by the STBC algorithm are valid, they are augmented by the CBC algorithm (Stashuk&Paoli, 1998) in which a MUP is assigned to the MUPT that has the greatest certainty value, if this value is greater than a certainty assignment threshold (CAT). Otherwise, the MUP is left unassigned. In the CBC algorithm, two MUPTs are merged if the resulting MUPT satisfies several predefined heuristic criteria but the MUPTs are not split nor assessed for splitting. The new decomposition system presented in this chapter employs the developed MUPT validation system —instead of those heuristic, user defined criteria—to merge or split MUPTs. The new system also adjusts the CAT value for each individual MUPT adaptively based its validity. The new decomposition program, which is called the validity–based EMG decomposition system, consists of four major steps: signal preprocessing, MUP detection, and clustering and

The signal preprocessing step is involved with filtering the signal to improve the SNR of the signal, decrease MUP temporal overlap, to accentuate the differences between MUPs created by different MUs, and to increase the separation between MUPs and the background noise. For this purpose, a 1st-order LPD filter (McGill et al., 1985) is employed. Fig.8 shows the effectiveness of LPD filtering an EMG signal. As shown, filtering flattens the signal baseline

MU detection identifies the position of the MUPs in a given EMG signal. The positions of suitable MUPs in the filtered signal are detected using a threshold crossing technique by which the prefilterd EMG signal is scanned and the peaks that satisfy several criteria (Stashuk, 1999) are detected and considered as the occurrence times of MUPs. In general, the amplitudes of detected MUPs are higher than the baseline noise. Fig. 8 illustrates the

For clustering and supervised classification, each detected MUP is represented using the 80 filtered data samples (i.e., 2.56 ms at 31250 Hz sampling rate), centered about its peak value

Detected MUPs are clustered to obtain the initial information required for supervised classification such as estimates of the number of MUPTs, their prototypical MUP shapes (or templates), and their MU firing pattern statistics. To extract such information, the MUPs detected in a specified portion (a 5 second interval with the highest number of detected MUPs) of the EMG signal are input to the STBC algorithm (Stashuk & Qu, 1996a) that

(i.e., about the position of maximum slope of the unfiltered MUP data).

supervised classification of the detected MUPs.

and makes the MUPs more narrow and recognizable.

segmentation procedure for an EMG signal.

**5.3 Clustering of the detected MUPs** 

**5.1 Signal preprocessing** 

**5.2 MUP detection** 

#### **4.2.3 Setting the parameter**

The objective of setting the value for parameter , that is the significance level for rejecting the null hypothesis of valid train, is to make the algorithm less likely to reject the MUP– shape validity of a given MUPT when its MUPs are very similar to each other, and more likely to reject this null hypothesis when the MUPs of a MUPT are less similar to each other. To achieve this, the value of parameter is set adaptively by first splitting a considered MUPT into two sub-trains using the K-means algorithm. The pseudo–correlation (PsC) between the MUP templates of the two sub-trains is then calculated as a measure of their similarity. Denoting S1 and S2 as the MUP templates of the two sub-trains, the PsC value between these templates is defined as (Florestal et al., 2006):

$$\text{PsC} = \max\left\{0, \frac{\sum\_{i=1}^{80} \left(S\_1[i] \, S\_2[i+t] - \left|S\_1[i] - S\_2[i+t]\right| \max\left\{S\_1[i], S\_2[i+t]\right\}\right)}{\sum\_{i=1}^{80} \max\left\{S\_1[i] \, S\_2[i+t]\right\}^2} \right\} \tag{8}$$

where S1[*i*] and S2[*i*] are the samples of the two templates S1 and S2, respectively. When calculating PsC, *t* ranges from -5 to +5 (corresponding to 0.32 ms) and the maximum value is selected.

Having a PsC value, the parameter α is defined as follows (Parsaei&Stashuk, 2011a):

$$\alpha = \begin{cases} 0.03 & \text{PsC} \ge 0.75 \\ 0.05 & 0.4 \le \text{PsC} < 0.75 \\ 0.1 & 0.3 \le \text{PsC} < 0.4 \\ 0.2 & \text{PsC} < 0.3 \end{cases} \tag{9}$$

#### **4.2.4 Estimating MUP–shape validity**

The MUP–shape validity which in this work is "1" when the shapes of the MUPs of a train are consistent and "0" vice versa is estimated using either Beal criterion or DH criterion as follows:


In the remaining of this Chapter, the MUP–shape validation system that is based on the Beal criterion (Gordon,1999) is called the SVB method and the one developed using the Duda and Hart criterion (Duda et al., 2000) is called SVDH method.

#### **5. Application of MUPT validation in EMG decomposition**

The hypothesis is that if invalid trains are detected and corrected during EMG decomposition, especially during the classification step, the decomposition accuracy will be improved. The effectiveness of using the developed MUPT validation system during EMG signal decomposition was studied by integrating this system into a certainty–based EMG signal decomposition algorithm used in the DQEMG (Stashuk, 1999). In the original certainty–based EMG signal decomposition, the detected MUPs are grouped into several MUPTs using a shape and temporal–based clustering (STBC) algorithm (Stashuk&Qu, 1996a) and a supervised certainty-based classifier (CBC). The STBC algorithm is a customized K-means clustering method that uses both MUP shape and MU firing pattern information to cluster MUPs. In the STBC, MUPTs are split or merged based on several heuristic criteria. Assuming the MUPTs provided by the STBC algorithm are valid, they are augmented by the CBC algorithm (Stashuk&Paoli, 1998) in which a MUP is assigned to the MUPT that has the greatest certainty value, if this value is greater than a certainty assignment threshold (CAT). Otherwise, the MUP is left unassigned. In the CBC algorithm, two MUPTs are merged if the resulting MUPT satisfies several predefined heuristic criteria but the MUPTs are not split nor assessed for splitting. The new decomposition system presented in this chapter employs the developed MUPT validation system —instead of those heuristic, user defined criteria—to merge or split MUPTs. The new system also adjusts the CAT value for each individual MUPT adaptively based its validity. The new decomposition program, which is called the validity–based EMG decomposition system, consists of four major steps: signal preprocessing, MUP detection, and clustering and supervised classification of the detected MUPs.

## **5.1 Signal preprocessing**

334 Applied Biological Engineering – Principles and Practice

The objective of setting the value for parameter , that is the significance level for rejecting the null hypothesis of valid train, is to make the algorithm less likely to reject the MUP– shape validity of a given MUPT when its MUPs are very similar to each other, and more likely to reject this null hypothesis when the MUPs of a MUPT are less similar to each other. To achieve this, the value of parameter is set adaptively by first splitting a considered MUPT into two sub-trains using the K-means algorithm. The pseudo–correlation (PsC) between the MUP templates of the two sub-trains is then calculated as a measure of their similarity. Denoting S1 and S2 as the MUP templates of the two sub-trains, the PsC value

*S iS i t S i S i t S iS i t*

]. [ ] [ ] [ ] max [ ], [ ]

<sup>80</sup> <sup>2</sup> 1 2

max [ ], [ ]

12 1 2 1 2

1

where S1[*i*] and S2[*i*] are the samples of the two templates S1 and S2, respectively. When calculating PsC, *t* ranges from -5 to +5 (corresponding to 0.32 ms) and the maximum value is

> 0.03 0.75 0.05 0.4 0.75 0.1 0.3 0.4 0.2 0.3

The MUP–shape validity which in this work is "1" when the shapes of the MUPs of a train are consistent and "0" vice versa is estimated using either Beal criterion or DH criterion as

a. Using the Beal criteria: If Bi <Fd,(N–2)d at an α level of significance, MUP–shape

The hypothesis is that if invalid trains are detected and corrected during EMG decomposition, especially during the classification step, the decomposition accuracy will be improved. The effectiveness of using the developed MUPT validation system during EMG signal decomposition was studied by integrating this system into a certainty–based EMG

b. Using DH method: If J<z, MUP–shape validity=1; otherwise MUP–shape validity=0. In the remaining of this Chapter, the MUP–shape validation system that is based on the Beal criterion (Gordon,1999) is called the SVB method and the one developed using the Duda

*PsC PsC PsC PsC*

*i*

Having a PsC value, the parameter α is defined as follows (Parsaei&Stashuk, 2011a):

(8)

(9)

*SiSi t*

**4.2.3 Setting the parameter** 

between these templates is defined as (Florestal et al., 2006):

[

80

1

*i*

PsC max 0,

**4.2.4 Estimating MUP–shape validity** 

validity=1; otherwise MUP–shape validity=0.

and Hart criterion (Duda et al., 2000) is called SVDH method.

**5. Application of MUPT validation in EMG decomposition** 

selected.

follows:

The signal preprocessing step is involved with filtering the signal to improve the SNR of the signal, decrease MUP temporal overlap, to accentuate the differences between MUPs created by different MUs, and to increase the separation between MUPs and the background noise. For this purpose, a 1st-order LPD filter (McGill et al., 1985) is employed. Fig.8 shows the effectiveness of LPD filtering an EMG signal. As shown, filtering flattens the signal baseline and makes the MUPs more narrow and recognizable.

## **5.2 MUP detection**

MU detection identifies the position of the MUPs in a given EMG signal. The positions of suitable MUPs in the filtered signal are detected using a threshold crossing technique by which the prefilterd EMG signal is scanned and the peaks that satisfy several criteria (Stashuk, 1999) are detected and considered as the occurrence times of MUPs. In general, the amplitudes of detected MUPs are higher than the baseline noise. Fig. 8 illustrates the segmentation procedure for an EMG signal.

For clustering and supervised classification, each detected MUP is represented using the 80 filtered data samples (i.e., 2.56 ms at 31250 Hz sampling rate), centered about its peak value (i.e., about the position of maximum slope of the unfiltered MUP data).

## **5.3 Clustering of the detected MUPs**

Detected MUPs are clustered to obtain the initial information required for supervised classification such as estimates of the number of MUPTs, their prototypical MUP shapes (or templates), and their MU firing pattern statistics. To extract such information, the MUPs detected in a specified portion (a 5 second interval with the highest number of detected MUPs) of the EMG signal are input to the STBC algorithm (Stashuk & Qu, 1996a) that

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 337

and represent the activity of a single MU that contributed detected MUPs to the given EMG signal. In this work, a new adaptive certainty-based classifier was developed for this purpose. The CCB (Stashuk & Paoli, 1998) is a supervised classifier that combines both MUP shape and MU firing pattern information to calculate the confidence of assigning a candidate MUP (let's say MUPj) to a MUPT. The certainties for assigning MUPj are evaluated for the two trains that have the most and the next most similar MUP templates found by calculating the Euclidian distance between MUPj and the MUP template of each MUPT. The certainties are calculated by combining MUP shape and MU firing pattern certainties. MUP shape certainty includes normalized absolute shape certainty (*C*ND) and relative shape certainty (*C*RD). The first represents the distance from MUPj to the template of a train, normalized by the energy of the template. The second represents the distance from MUPj to the most similar MUP template relative to the distance of MUPj to the next most similar MUP template. Firing pattern certainty, CFC, measures the consistency of the occurrence time of MUPj relative to the established MU firing pattern of a MUPT. Having the shape certainties and the firing pattern certainty, the overall certainties for assigning the MUPj to one of the two selected MUPTs are estimated by multiplying the shape and

; 1,2 *jj j j*

In order to accommodate non-stationarity in MUP shapes, the algorithm updates the MUP templates with each MUP assignment. The MUP templates are calculated using a moving average for which the weights are the certainties with which MUPs are assigned to the

threshold (0.6 in this work) the template of MUPT*i* (*Si*) is updated as (Stashuk & Paoli, 1998):

1

Once each classification pass through the set of detected MUPs is completed and before decomposition (the next pass) continues, the validity of each extracted MUPT is assessed using the system discussed in Section 4. Invalid trains are detected, corrected and have their CAT values adjusted. Merged MUPTs are split into valid trains using the K–means clustering algorithm; contaminated MUPTs have their FCEs corrected using an automated MUPT

To decrease the number of MCEs and FCEs in the MUPTs, the CAT value for each MUPT is adjusted based on its validity (i.e., an adaptive adjustment of the assignment threshold). For invalid MUPTs (either merged or contaminated), the CAT is increased by a step of 0.005 while the CAT of valid trains is decreased by 0.005. The CAT value of a MUPT is not

*j New i i j i j*

*C* 

*S a C*

*i*

value, if this value is greater than a *C*AT. Otherwise, the MUP is left unassigned.

*S*

MUPTs. If MUPj is assigned to MUPT*i* with certainty *C<sup>j</sup>*

decreased or increased below 0.005 or above 0.990, respectively.

*<sup>i</sup>* is the overall certainty of assigning MUPj to MUPT*i* which is one of the two closest

*i ND i RD i FC i CC C C i* (10)

*<sup>i</sup>* higher than the updating

(11)

*<sup>i</sup>* , MUPj is assigned to the MUPT that has the greatest certainty

firing pattern certainties as

MUPT to MUPj. Having*C<sup>j</sup>*

where aj is the feature vector of MUPj .

editing algorithm (Parsaei&Stashuk, 2011b).

where *C<sup>j</sup>*

groups the detected MUPs into several MUPTs using both firing time and shape information across multiple iterations. The initial estimate of the number of clusters (number of active MUs) is equal to the maximum number of MUPs and the initial cluster centers are the actual MUPs in the 30 ms interval within the selected 5 second interval. Having estimates for the number of clusters and their centers, each detected MUP is assigned to the closest cluster, if its distance to the core of the closest cluster is smaller than 0.25 times that of the second smallest distance from the candidate MUP and the cluster centers. In the STBC, a MUPT will be split into two trains if it includes a MU firing pattern inconsistency. Similar MUPTs are merged if their MUP templates are close and the firing pattern of the merged MUPT satisfies several criteria. The MUP assignment, cluster splitting, editing, and merging steps are repeated until the resulting MUPTs are stable. Details of the STBC algorithm can be found in (Stashuk & Qu, 1996a).

Fig. 8. The effectiveness of LPD filtering and the segmentation procedure for an EMG signal. A portion of the signal containing ten MUPs (top row). The LPD filtering results for this portion. Gray region shows the estimated level of baseline noise.

#### **5.4 Supervised classification of detected MUPs**

Having the initial information about possible MUPTs provided by the clustering step, the detected MUPs are assigned to MUPTs using a supervised classifier. The objective here is to assign each MUP to the MUPT for which the MUP's time of occurrence and shape are more consistent with respect to the MU firing times and MUP shapes of the selected MUPT, respectively, than to the other MUPTs. Each of the MUPTs should have low MCE and FCE rates

groups the detected MUPs into several MUPTs using both firing time and shape information across multiple iterations. The initial estimate of the number of clusters (number of active MUs) is equal to the maximum number of MUPs and the initial cluster centers are the actual MUPs in the 30 ms interval within the selected 5 second interval. Having estimates for the number of clusters and their centers, each detected MUP is assigned to the closest cluster, if its distance to the core of the closest cluster is smaller than 0.25 times that of the second smallest distance from the candidate MUP and the cluster centers. In the STBC, a MUPT will be split into two trains if it includes a MU firing pattern inconsistency. Similar MUPTs are merged if their MUP templates are close and the firing pattern of the merged MUPT satisfies several criteria. The MUP assignment, cluster splitting, editing, and merging steps are repeated until the resulting MUPTs are stable.

Fig. 8. The effectiveness of LPD filtering and the segmentation procedure for an EMG signal. A portion of the signal containing ten MUPs (top row). The LPD filtering results for this

Having the initial information about possible MUPTs provided by the clustering step, the detected MUPs are assigned to MUPTs using a supervised classifier. The objective here is to assign each MUP to the MUPT for which the MUP's time of occurrence and shape are more consistent with respect to the MU firing times and MUP shapes of the selected MUPT, respectively, than to the other MUPTs. Each of the MUPTs should have low MCE and FCE rates

portion. Gray region shows the estimated level of baseline noise.

**5.4 Supervised classification of detected MUPs** 

Details of the STBC algorithm can be found in (Stashuk & Qu, 1996a).

and represent the activity of a single MU that contributed detected MUPs to the given EMG signal. In this work, a new adaptive certainty-based classifier was developed for this purpose.

The CCB (Stashuk & Paoli, 1998) is a supervised classifier that combines both MUP shape and MU firing pattern information to calculate the confidence of assigning a candidate MUP (let's say MUPj) to a MUPT. The certainties for assigning MUPj are evaluated for the two trains that have the most and the next most similar MUP templates found by calculating the Euclidian distance between MUPj and the MUP template of each MUPT. The certainties are calculated by combining MUP shape and MU firing pattern certainties. MUP shape certainty includes normalized absolute shape certainty (*C*ND) and relative shape certainty (*C*RD). The first represents the distance from MUPj to the template of a train, normalized by the energy of the template. The second represents the distance from MUPj to the most similar MUP template relative to the distance of MUPj to the next most similar MUP template. Firing pattern certainty, CFC, measures the consistency of the occurrence time of MUPj relative to the established MU firing pattern of a MUPT. Having the shape certainties and the firing pattern certainty, the overall certainties for assigning the MUPj to one of the two selected MUPTs are estimated by multiplying the shape and firing pattern certainties as

$$\mathbf{C}\_{i}^{\dagger} = \mathbf{C}\_{\text{ND }i}^{\dagger} \times \mathbf{C}\_{\text{RD }i}^{\dagger} \times \mathbf{C}\_{\text{FC }i}^{\dagger}; i = \mathbf{1}, \mathbf{2} \tag{10}$$

where *C<sup>j</sup> <sup>i</sup>* is the overall certainty of assigning MUPj to MUPT*i* which is one of the two closest MUPT to MUPj. Having*C<sup>j</sup> <sup>i</sup>* , MUPj is assigned to the MUPT that has the greatest certainty value, if this value is greater than a *C*AT. Otherwise, the MUP is left unassigned.

In order to accommodate non-stationarity in MUP shapes, the algorithm updates the MUP templates with each MUP assignment. The MUP templates are calculated using a moving average for which the weights are the certainties with which MUPs are assigned to the MUPTs. If MUPj is assigned to MUPT*i* with certainty *C<sup>j</sup> <sup>i</sup>* higher than the updating threshold (0.6 in this work) the template of MUPT*i* (*Si*) is updated as (Stashuk & Paoli, 1998):

$$\mathbf{S}\_{i}^{New} = \frac{\mathbf{S}\_{i} + \mathbf{C}\_{i}^{j} \times \mathbf{a}\_{j}}{\mathbf{1} + \mathbf{C}\_{i}^{j}} \tag{11}$$

where aj is the feature vector of MUPj .

Once each classification pass through the set of detected MUPs is completed and before decomposition (the next pass) continues, the validity of each extracted MUPT is assessed using the system discussed in Section 4. Invalid trains are detected, corrected and have their CAT values adjusted. Merged MUPTs are split into valid trains using the K–means clustering algorithm; contaminated MUPTs have their FCEs corrected using an automated MUPT editing algorithm (Parsaei&Stashuk, 2011b).

To decrease the number of MCEs and FCEs in the MUPTs, the CAT value for each MUPT is adjusted based on its validity (i.e., an adaptive adjustment of the assignment threshold). For invalid MUPTs (either merged or contaminated), the CAT is increased by a step of 0.005 while the CAT of valid trains is decreased by 0.005. The CAT value of a MUPT is not decreased or increased below 0.005 or above 0.990, respectively.

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 339

Considering the reference MUPTs as the gold standard, the performance of the developed MUPT validation systems was evaluated in terms of correctly classifying valid and invalid trains. Three accuracy indices were defined for this purpose: accuracy for valid trains (AV), accuracy for invalid train (AIV), and total accuracy (AT). These three indices are given by:

Number of valid MUPTs correctly classified A % <sup>100</sup>

Number of invalid MUPTs correctly classified A % <sup>100</sup>

Number of MUPTs correctly classified A % <sup>100</sup>

For evaluating the performance of the developed MUPT validity–based EMG decomposition system, parts of the simulated and real EMG signals discussed in above were used. For each EMG signal used for this evaluation, the MU discharge patterns provided either by the EMG signal simulator used or by a human expert operator were used as

For real data, the real EMG signals provided by Nikolic (2001) were not considered in this evaluation because the true decomposition results for this data were not known. A group of the real EMG signals provided in (Florestal et al., 2009; McGill, n.d.) were employed for this evaluation. Of the MUs contributed to each EMG signal used only the discharge patterns of those MUs that were selected by the expert as accurately identified patterns and the amplitude of the slope of their MUP templates were >0.01V/S were considered as reference

Four indices as defined below were used for evaluation: assignment rate (Ar), accuracy (Ac), correct classification rate (CCr ), and error in finding the correct number of MUPTs (ENMUPTs).

Numberof MUPs assigned A % <sup>100</sup>

Numberof MUPs correctlyclassified A %= ×100

Numberof MUPs correctlyclassified CC % <sup>100</sup>

 ENMUPTs= Number of extracted MUPTs - Number of expected MUPTs (18) where the number of expected MUPTs equals to the number of MUPTs identified by the

Total number of valid MUPTs (12)

Total number of Invalid MUPTs (13)

Total number of MUPTs (14)

Numberof MUPs detected (15)

Total numberof MUPsclassified (16)

Total numberof MUPs detected (17)

V

IV

T

r

human expert or identified by the simulator as significant.

**6.2 Evaluating decomposition system** 

reference.

and used for evaluation.

c

r

In addition to splitting or editing invalid MUPTs, the chance of merging single MUPTs is evaluated. Pairs of MUPTs that have similar MUP templates (PsC ≥ 0.4) are merged if the resulting train is valid.

The MU firing pattern statistics of each MUPT are estimated using an error–filtered estimation algorithm that provides accurate estimates of these IDI statistics of a MUPT even when contaminated by a high MCE rate (Stashuk&Qu, 1996b). The MUP assignment and MUPT splitting, editing, and merging steps are repeated until either, the maximum number of iterations is exceeded or the MUPTs are stable. If trains are merged or split at least one more supervised classification pass will be completed.

## **6. Evaluation**

The performance of both the MUPT validation system and the new decomposition algorithm was evaluated using both simulated and real data. For this purpose, the simulated and real reference data described in (Parsaei&Stashuk, 2011a) were used.

The simulated data was generated using a physiologically–based EMG signal simulation algorithm [54]. Two hundred and sixty one, 30–second–long, EMG signals with different levels of intensity, ranging from 24 to 193 pulses per second (pps), with MUP jitter values ranging from 50 to 150*µ*s, with IDI variability (i.e., IDI–CV) ranging from 0.10 to 0.45, and with various myopathic or neurogenic degrees of involvement ranging from 0 to 50% were created.

The real data was comprised of three sets of EMG signals: single–channel EMG signals provided by Nikolic (2001); single–channel EMG signals provided by McGill (n.d.); and multi-channel (6 to 8) EMG signals provided by Florestal et al. (2009). In using the multi– channel EMG signals, the signals detected by each electrode were considered as singlechannel EMG signals. These three data sets allowed us to study the performance of the developed methods across signals detected using different electrodes and instruments.

#### **6.1 Evaluating MUPT validation system**

For evaluting MUPT validation system, the simulated EMG signals were decomposed using the DQEMG algorithms (Hamilton-Wright & Stashuk, 2005). The resulting MUPTs were assessed visually and classified as valid or invalid. Additional valid trains were generated by selecting valid MUPTs with greater than 100 MUPs and randomly splitting them into sub–trains of at least 50 MUPs. Additional invalid trains that are representative of invalid trains likely to be produced by a decomposition algorithm were generated by merging valid trains having similar MUP templates (PsC ≥ 0.5). In total 20,386 MUPTs (18,000 valid and 2386 invalid trains) were generated.

The same analysis as with the simulated data was completed using these signals. However, in analyzing the EMG signals provided by Florestal et al. (2009) and McGill (n.d.), the results of manual decomposition completed by an expert investigator were used. As with the simulated data, the valid trains in these three data sets were split into sub–trains of at least 50 MUPs and those valid trains having similar MUP templates were merged to generate invalid trains. Consequently, 14,632 MUPTs (13,024 valid and 1,608 invalid trains) were generated.

Considering the reference MUPTs as the gold standard, the performance of the developed MUPT validation systems was evaluated in terms of correctly classifying valid and invalid trains. Three accuracy indices were defined for this purpose: accuracy for valid trains (AV), accuracy for invalid train (AIV), and total accuracy (AT). These three indices are given by:

$$\mathbf{A\_V\%} = \frac{\text{Number of valid MUPPs correctly classified}}{\text{Total number of valid MUPTs}} \times 100\tag{12}$$

$$\mathbf{A\_{IV}\%} = \frac{\text{Number of invalid MUPPs correctly classified}}{\text{Total number of Invalid MUPPs}} \times 100\tag{13}$$

$$\mathbf{A\_T\%} = \frac{\text{Number of MUPTs correctly classified}}{\text{Total number of MUPTs}} \times 100\tag{14}$$

#### **6.2 Evaluating decomposition system**

338 Applied Biological Engineering – Principles and Practice

In addition to splitting or editing invalid MUPTs, the chance of merging single MUPTs is evaluated. Pairs of MUPTs that have similar MUP templates (PsC ≥ 0.4) are merged if the

The MU firing pattern statistics of each MUPT are estimated using an error–filtered estimation algorithm that provides accurate estimates of these IDI statistics of a MUPT even when contaminated by a high MCE rate (Stashuk&Qu, 1996b). The MUP assignment and MUPT splitting, editing, and merging steps are repeated until either, the maximum number of iterations is exceeded or the MUPTs are stable. If trains are merged or split at least one

The performance of both the MUPT validation system and the new decomposition algorithm was evaluated using both simulated and real data. For this purpose, the

The simulated data was generated using a physiologically–based EMG signal simulation algorithm [54]. Two hundred and sixty one, 30–second–long, EMG signals with different levels of intensity, ranging from 24 to 193 pulses per second (pps), with MUP jitter values ranging from 50 to 150*µ*s, with IDI variability (i.e., IDI–CV) ranging from 0.10 to 0.45, and with various myopathic or neurogenic degrees of involvement ranging from 0 to 50%

The real data was comprised of three sets of EMG signals: single–channel EMG signals provided by Nikolic (2001); single–channel EMG signals provided by McGill (n.d.); and multi-channel (6 to 8) EMG signals provided by Florestal et al. (2009). In using the multi– channel EMG signals, the signals detected by each electrode were considered as singlechannel EMG signals. These three data sets allowed us to study the performance of the developed methods across signals detected using different electrodes and instruments.

For evaluting MUPT validation system, the simulated EMG signals were decomposed using the DQEMG algorithms (Hamilton-Wright & Stashuk, 2005). The resulting MUPTs were assessed visually and classified as valid or invalid. Additional valid trains were generated by selecting valid MUPTs with greater than 100 MUPs and randomly splitting them into sub–trains of at least 50 MUPs. Additional invalid trains that are representative of invalid trains likely to be produced by a decomposition algorithm were generated by merging valid trains having similar MUP templates (PsC ≥ 0.5). In total 20,386 MUPTs (18,000 valid and

The same analysis as with the simulated data was completed using these signals. However, in analyzing the EMG signals provided by Florestal et al. (2009) and McGill (n.d.), the results of manual decomposition completed by an expert investigator were used. As with the simulated data, the valid trains in these three data sets were split into sub–trains of at least 50 MUPs and those valid trains having similar MUP templates were merged to generate invalid trains. Consequently, 14,632 MUPTs (13,024 valid and 1,608

simulated and real reference data described in (Parsaei&Stashuk, 2011a) were used.

resulting train is valid.

**6. Evaluation** 

were created.

more supervised classification pass will be completed.

**6.1 Evaluating MUPT validation system** 

2386 invalid trains) were generated.

invalid trains) were generated.

For evaluating the performance of the developed MUPT validity–based EMG decomposition system, parts of the simulated and real EMG signals discussed in above were used. For each EMG signal used for this evaluation, the MU discharge patterns provided either by the EMG signal simulator used or by a human expert operator were used as reference.

For real data, the real EMG signals provided by Nikolic (2001) were not considered in this evaluation because the true decomposition results for this data were not known. A group of the real EMG signals provided in (Florestal et al., 2009; McGill, n.d.) were employed for this evaluation. Of the MUs contributed to each EMG signal used only the discharge patterns of those MUs that were selected by the expert as accurately identified patterns and the amplitude of the slope of their MUP templates were >0.01V/S were considered as reference and used for evaluation.

Four indices as defined below were used for evaluation: assignment rate (Ar), accuracy (Ac), correct classification rate (CCr ), and error in finding the correct number of MUPTs (ENMUPTs).

$$\text{A}\_{\text{r}}\% = \frac{\text{Number of MUPs assigned}}{\text{Number of MUPs detected}} \times 100\tag{15}$$

$$\mathbf{A\_c \%} = \frac{\text{Number of MUS correctly classified}}{\text{Total number of MUS classified}} \times 100\tag{16}$$

$$\text{CC}\_{\text{r}}\% = \frac{\text{Number of MUsPs correctly classified}}{\text{Total number of MUsPs detected}} \times 100\tag{17}$$

$$\mathbf{E\_{NMUTs}} = \text{Number of extracted MLUTs - Number of expected MLUTs} \tag{18}$$

where the number of expected MUPTs equals to the number of MUPTs identified by the human expert or identified by the simulator as significant.

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 341

Fig. 9. AIV values for the studied MUPT validation methods versus the pseudo-correlation (PsC) between the templates of two valid MUPTs merged to generate an invalid train.

Fig. 10. AIV values for the studied MUPT validation algorithms versus the MCE rate in the

invalid trains. The MCE rate represents the sparsity of the MUPT.

## **7. Results and discussions**

## **7.1 MUPT validation system**

The calculated means and standard deviations for the three accuracy indices used to evaluate the developed MUPT validation methods are summarized in Table 3. The numbers were obtained by testing each method using both simulated and real data sets when each set is split into the ten different data subsets. In this table VB stands for the MUP validation system developed by combing the FPVC and SVB outputs using AND logic. Likewise, VDH stands for the MUP validation system developed by combing the FPVC and SVDH outputs using AND logic.

As shown in Table 3, the accuracy in detecting invalid trains (i.e., in terms of AIV) significantly improved when both MU firing pattern and MUP–shape information is employed for estimating the validity of a MUPT. However, the accuracy of both VB and VDH in correctly classifying valid MUPTs decreased compared to that of the FPVC, which only assesses the firing patterns of the MUPTs.

Figures 10 and 11 illustrate the advantage of using both MU firing pattern and MUP shape information for MUPT validation compared to using just MU firing pattern or MUP shape information.


Table 3. Mean and standard deviations for the accuracy of the different MUPT validation methods applied to both simulated and real data. In each column of the table, individual or groups of methods bolded and indicated by an '\*' had significantly better performance than the others as determined using analysis of variance, at a 5% significance level and the Tukey-Kramer honestly significant difference test for pair-wise comparison of the mean values.

Fig.10 presents AIV values versus the PsC between the templates of the two MUPTs selected for generating an invalid train for the methods studied. The PsC value represents a measure of the average similarity of the MUPs of the two trains selected to create an invalid train; high values of PsC indicate highly similar MUP templates. As shown, AIV values of the two MUP-shape validation methods (SVB and SVDH) decreases drastically as the PsC between the MUP templates of the constituent MUPTs increases; the methods failed to detect > 80% of invalid trains composed of two MUPTs with PsC > 0.8. On the other hand, the AIV values of both the VB and VDH methods were > 90% for most cases. For the worst case (high PsC), the accuracy of these two methods were > 80%, which is 57.6% higher than that of the SVB and SVDH methods. On average, the AIV was improved by a factor of 1.3.

The calculated means and standard deviations for the three accuracy indices used to evaluate the developed MUPT validation methods are summarized in Table 3. The numbers were obtained by testing each method using both simulated and real data sets when each set is split into the ten different data subsets. In this table VB stands for the MUP validation system developed by combing the FPVC and SVB outputs using AND logic. Likewise, VDH stands for the MUP validation system developed by combing the FPVC and SVDH outputs

As shown in Table 3, the accuracy in detecting invalid trains (i.e., in terms of AIV) significantly improved when both MU firing pattern and MUP–shape information is employed for estimating the validity of a MUPT. However, the accuracy of both VB and VDH in correctly classifying valid MUPTs decreased compared to that of the FPVC, which

Figures 10 and 11 illustrate the advantage of using both MU firing pattern and MUP shape information for MUPT validation compared to using just MU firing pattern or MUP shape

> **AT (%)**

Table 3. Mean and standard deviations for the accuracy of the different MUPT validation methods applied to both simulated and real data. In each column of the table, individual or groups of methods bolded and indicated by an '\*' had significantly better performance than the others as determined using analysis of variance, at a 5% significance level and the Tukey-Kramer honestly significant difference test for pair-wise comparison of the mean values.

Fig.10 presents AIV values versus the PsC between the templates of the two MUPTs selected for generating an invalid train for the methods studied. The PsC value represents a measure of the average similarity of the MUPs of the two trains selected to create an invalid train; high values of PsC indicate highly similar MUP templates. As shown, AIV values of the two MUP-shape validation methods (SVB and SVDH) decreases drastically as the PsC between the MUP templates of the constituent MUPTs increases; the methods failed to detect > 80% of invalid trains composed of two MUPTs with PsC > 0.8. On the other hand, the AIV values of both the VB and VDH methods were > 90% for most cases. For the worst case (high PsC), the accuracy of these two methods were > 80%, which is 57.6% higher than that of the SVB

and SVDH methods. On average, the AIV was improved by a factor of 1.3.

**FPVC 99.8±0.1\*** 95.9±0.7 **99.4±0.1 98.2±0.6\*** 96.2±1.4 **98.0±0.5\* SVB** 92.2±0.3 66.5±0.8 89.2±0.3 95.0±0.6 74.5±1.7 92.8±0.5 **SVDH** 93.8±0.3 73.9±1.0 91.5±0.3 96.7±0.3 80.4±1.2 94.9±0.5 **VB** 98.2±0.2 **98.6±0.3\*** 98.4±0.2 **98.0±0.6\* 99.1±0.3\* 98.3±0.3\* VDH** 93.7±0.7 **99.1±0.2\*** 96.4±0.5 95.2±0.7 **99.7±0.2\*** 94.4±0.3

**Simulated data Real data** 

**AV (%)**  **AIV (%)** 

**AT (%)** 

**7. Results and discussions 7.1 MUPT validation system** 

only assesses the firing patterns of the MUPTs.

**AIV (%)** 

using AND logic.

information.

**Method AV** 

**(%)** 

Fig. 9. AIV values for the studied MUPT validation methods versus the pseudo-correlation (PsC) between the templates of two valid MUPTs merged to generate an invalid train.

Fig. 10. AIV values for the studied MUPT validation algorithms versus the MCE rate in the invalid trains. The MCE rate represents the sparsity of the MUPT.

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 343

Overall, the validity–based decomposition system has significantly improved decomposition results in terms of all four performance indices (*p*<0.03); except for the real data that AC for both decomposition system was statistically equal. In addition, the validitybased system has lower STD for all performance measures (*p*<0.02), which shows that the system has better overall and less variable performance. The improvement in decomposition results (especially for CCr) increases as the complexity of the signal increases, such that for

**CCr** 

1 48.9 5 93.0 99.9 92.9 0 96.9 100.0 97.9 0 2 63.9 6 99.3 99.8 99.1 0 99.8 100.0 99.8 0 3 71.7 7 84.7 99.8 84.4 1 98.2 98.7 97.3 1 4 79.4 8 91.7 99.4 91.2 0 95.7 99.2 97.0 0 5 80.2 8 95.1 97.8 93.1 0 96.3 98.5 94.9 0 6 115.8 9 94.6 98.9 93.5 0 97.2 98.2 96.3 1 7 105.0 10 95.7 99.9 95.6 0 97.9 98.7 98.6 0 8 116.2 10 96.4 72.3 69.7 -3 98.8 96.4 97.2 0 9 112.4 11 82.7 97.0 80.2 4 92.0 96.4 86.7 1 10 114.3 11 86.6 98.8 85.6 1 93.8 97.2 93.1 0

**(%) ENMUPTs**

**Mean 92.0 96.4 88.5 0.9 96.7 98.3 95.0 0.3 STD 5.5 8.5 7.8 1.4 2.4 1.3 3.1 0.5** 

Table 5. The performnace of the validity-based decomposition system compared to that of the original decomposition algorithms of the DQEMG applied to the 10 real EMG signals.

Increases in MU firing pattern or MUP shape variability can decrease the performance of a decomposition system. Nonetheless, for the EMG signals with relatively high jitter or IDI– CV values studied (e.g., simulated EMG signal #10 which jitter value 100µs), the

Both DQEMG and the validity–based system are for decomposing intramuscular EMG signals mainly for clinical application; therefore, low amplitude MUPs, which are composed of low frequency components and created by MUs with no muscle fibers close to the electrode detection surface, are neither detected nor considered for clustering and supervised classification. If such MUPs were detected and then considered for clustering and supervised classification, the accuracies of both systems may not be as high as those presented in Tables 4 and 5. Finally, the accuracies of both DQEMG and the validity–based system for EMG signals contaminated by high levels of noise may be lower than the values

Finally, both DQEMG and the validity–based system assume the mean and standard deviation of the IDIs of the MUs that contributed to the signal being decomposed did not change during signal detection. Such assumptions are valid for EMG signals detected during short–term isometric contraction; however, these assumptions may not be realistic for signals detected during either force-varying or long contractions. Such limitations restrict the use of both DQEMG and the validity-based system for research applications where the decomposition of signals detected during non–isometric or long–term

improvement gained using the validity-based system was significant.

reported for the simulated and real EMG signals used in this work.

**Original DQEMG Validity–based system** 

**Ar**

**(%) Ac (%) CCr** 

**(%) ENMUPTs**

the last two signals in Table 4, the CCr values are improved by at least 13.4 %.

**Ac (%)**

**Signal Intensity (pps)**

**No. of MUPTs**

**Ar (%)**

Fig.11 demonstrates the advantages of using the VB and VDH algorithms (especially the VDH algorithm), which uses both MU firing pattern and MUP shape information in assessing the validity of a MUPT, over the FPVC that uses just MU firing pattern information. As shown, AIV for the FPVC decreases as the MCE rate in the trains increases such that the algorithm misclassified around 60% of the invalid trains having a MCE rate > 80%. One reason for the drop in AIV is that the accuracy with which the MU firing pattern statistics can be estimated and consequently the accuracy of the MU firing pattern features used decreases as a train becomes sparse (Parsaei et al. 2011). The VBDH method performed significantly better than the FPVC for invalid trains with MCE rate > 80%. The AIV values of the VBDH method for such invalid trains was 31% higher than the AIV of the FPVC, which is a significant improvement in detecting invalid trains especially during the early stages of an EMG signal decomposition.

Based on the results presented in Table 3 and Fig.11, the VDH method can be used in early stage of the decomposition when MCE rate >55%, as it is most accurate method in detecting highly–sparse invalid MUPTs. In the latter stage of the decomposition or for the MUPTs with MCE rate <55%, to avoid duplication of valid MUPT the other methods (VB or FPVC) that had higher AV values than the VDH can be used to assess the validity of the extracted MUPTs. Overall, it is recommended to use only the FPVC at the final stage of the decomposition or for trains with MCE rate <30%, because VB misclassified valid trains with high MUP shape variability and ultimately cause duplication of such trains (Parsaei; 2011).

## **7.2 EMG decomposition system**

Performance results for the validity–based decomposition system and that of the original decomposition algorithms of DQEMG for both simulated and real data are summarized in Tables 4 and 5, respectively. For each data set, the performance for each signal used along with the mean and standard deviation (STD) for the performance indices over all signals used is reported. Statistical comparison of the average values was conducted using paired t-tests (α= 0.05), while comparison of the STD values was conducted using F-tests (α= 0.05).


Table 4. The performnace of the validity-based decomposition system compared to that of the original decomposition algorithms of the DQEMG applied to the simulated data.

Fig.11 demonstrates the advantages of using the VB and VDH algorithms (especially the VDH algorithm), which uses both MU firing pattern and MUP shape information in assessing the validity of a MUPT, over the FPVC that uses just MU firing pattern information. As shown, AIV for the FPVC decreases as the MCE rate in the trains increases such that the algorithm misclassified around 60% of the invalid trains having a MCE rate > 80%. One reason for the drop in AIV is that the accuracy with which the MU firing pattern statistics can be estimated and consequently the accuracy of the MU firing pattern features used decreases as a train becomes sparse (Parsaei et al. 2011). The VBDH method performed significantly better than the FPVC for invalid trains with MCE rate > 80%. The AIV values of the VBDH method for such invalid trains was 31% higher than the AIV of the FPVC, which is a significant improvement in detecting

Based on the results presented in Table 3 and Fig.11, the VDH method can be used in early stage of the decomposition when MCE rate >55%, as it is most accurate method in detecting highly–sparse invalid MUPTs. In the latter stage of the decomposition or for the MUPTs with MCE rate <55%, to avoid duplication of valid MUPT the other methods (VB or FPVC) that had higher AV values than the VDH can be used to assess the validity of the extracted MUPTs. Overall, it is recommended to use only the FPVC at the final stage of the decomposition or for trains with MCE rate <30%, because VB misclassified valid trains with high MUP shape variability and ultimately cause duplication of such trains (Parsaei; 2011).

Performance results for the validity–based decomposition system and that of the original decomposition algorithms of DQEMG for both simulated and real data are summarized in Tables 4 and 5, respectively. For each data set, the performance for each signal used along with the mean and standard deviation (STD) for the performance indices over all signals used is reported. Statistical comparison of the average values was conducted using paired t-tests (α= 0.05), while comparison of the STD values was conducted using F-tests (α= 0.05).

**CCr** 

1 54.0 6 92.6 98.0 90.7 0 95.4 99.1 94.5 0 2 59.4 7 90.7 95.9 87.0 0 93.8 98.5 92.4 0 3 61.4 6 78.0 96.4 75.2 2 90.5 98 88.7 0 4 68.2 7 90.2 96.4 86.9 0 94.6 97.4 92.1 0 5 70.7 7 73.3 96.9 71.0 3 90.3 96.5 87.1 0 6 79.3 8 91.0 82.3 74.9 0 93.6 95.1 89.0 0 7 82.5 8 83.5 89.8 75.0 2 89.2 96.3 85.9 1 8 85.2 9 92.3 80.3 74.1 -1 93.2 96.9 90.3 0 9 91.7 7 80.5 85.8 69.0 1 85.8 96.2 82.5 1 10 97.5 10 87.6 84.8 74.3 1 91.8 95.8 87.9 0

**(%) ENMUPTs**

**Mean 86.0 90.7 77.8 1.0 91.8 97.0 89.1 0.2 STD 6.8 6.9 7.5 1.1 2.9 1.3 3.5 0.4** 

Table 4. The performnace of the validity-based decomposition system compared to that of the original decomposition algorithms of the DQEMG applied to the simulated data.

**Original DQEMG Validity–based system** 

**Ar (%)**

**Ac (%)** **CCr** 

**(%) ENMUPTs**

invalid trains especially during the early stages of an EMG signal decomposition.

**7.2 EMG decomposition system** 

**No. of MUPTs**

**Ar (%)**

**Ac (%)**

**Signal Intensity (pps)**

Overall, the validity–based decomposition system has significantly improved decomposition results in terms of all four performance indices (*p*<0.03); except for the real data that AC for both decomposition system was statistically equal. In addition, the validitybased system has lower STD for all performance measures (*p*<0.02), which shows that the system has better overall and less variable performance. The improvement in decomposition results (especially for CCr) increases as the complexity of the signal increases, such that for the last two signals in Table 4, the CCr values are improved by at least 13.4 %.


Table 5. The performnace of the validity-based decomposition system compared to that of the original decomposition algorithms of the DQEMG applied to the 10 real EMG signals.

Increases in MU firing pattern or MUP shape variability can decrease the performance of a decomposition system. Nonetheless, for the EMG signals with relatively high jitter or IDI– CV values studied (e.g., simulated EMG signal #10 which jitter value 100µs), the improvement gained using the validity-based system was significant.

Both DQEMG and the validity–based system are for decomposing intramuscular EMG signals mainly for clinical application; therefore, low amplitude MUPs, which are composed of low frequency components and created by MUs with no muscle fibers close to the electrode detection surface, are neither detected nor considered for clustering and supervised classification. If such MUPs were detected and then considered for clustering and supervised classification, the accuracies of both systems may not be as high as those presented in Tables 4 and 5. Finally, the accuracies of both DQEMG and the validity–based system for EMG signals contaminated by high levels of noise may be lower than the values reported for the simulated and real EMG signals used in this work.

Finally, both DQEMG and the validity–based system assume the mean and standard deviation of the IDIs of the MUs that contributed to the signal being decomposed did not change during signal detection. Such assumptions are valid for EMG signals detected during short–term isometric contraction; however, these assumptions may not be realistic for signals detected during either force-varying or long contractions. Such limitations restrict the use of both DQEMG and the validity-based system for research applications where the decomposition of signals detected during non–isometric or long–term

Motor Unit Potential Train Validation and Its Application in EMG Signal Decomposition 345

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## **8. Conclusions and future work**

Decomposition of an EMG signal may result in several invalid MUPTs that do not accurately represent the activity of a signal MU; such invalid MUPTs must be identified and then either corrected or excluded before extracted MUPTs are quantitatively analyzed. Characteristics of IDI histograms, MU firing rates over time and within-train MUP shape inconsistencies of MUPTs extracted during EMG decomposition can be used to estimate their validity. The existing qualitative MUPT validation methods, which typically need human operator supervision, are time consuming, related to operator experience and skill, and cannot assist with improving the performance of automatic EMG decomposition systems. To overcome these issues, in this chapter an automated MUPT validation system that estimate the validity of a MUPT is estimated using both its MU firing pattern and MUP shape information is presented.

Based on the results obtained, the developed methods with overall AT >91.5% performed well in classifying MUPTs extracted by a decomposition system. Nevertheless, the methods that use only shape or only firing pattern information did not perform as well as the ones that used both types of information, especially for invalid trains. Of the method studied, the VDH method is the most accurate method in classifying sparse invalid trains, but the FPVC and VB are more accurate than the VDH in classifying valid MUPTs. Therefore, using VDH when MCE rate of the train >55% and VB or FPVC when MCE rate < 55% and even FPVC when MCE rate < 30% in the optimum scheme of using the proposed validation methods.

Finally, it was revealed that using the proposed MUPT validation system during decomposition will improve the results in terms of finding the correct numbers of MUPTs that constitute a given signal as well as decreasing the MCE and FCE rates in the extracted trains. Overall, the decomposition accuracy for 20 EMG signals (10 simulated and 10 real) was improved by 9.0%. For these 20 signals, the validity–based decomposition system with average ENMUPTs 0.3 was better able to estimate the number of constituent MUPTs than the previous system, with average ENMUPTs of 0.9. The improvement gained using the validitybased system for dificult– to– decompose EMG signals was even higher. Such improvements, especially in ENMUPTs, along with the confidence that the extracted MUPTs will be valid encourage using the validity–based decomposition system for decomposing intramuscular EMG signals for clinical application.

Future work will address: a) further analysis of the developed decomposition system, especially using clinical EMG signals acquired from myopathic and neurogenic muscles; b) improving the performance of the developed MUPT validation system in terms of both accuracy and computational time.

## **9. Acknowledgment**

The authors would like to gratefully thank Dr. A. Ghodsi for his helpful discussion, on clustering and cluster validation methods, Dr. M. Nicolic, Dr. K.C. McGill, Dr. J.R. Florestal, Dr. P.A. Mathieu, Dr. Z. Lateva, and Dr. H.R. Marateb for sharing several EMG signals and the decomposition results of these signals. Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

#### **10. References**

344 Applied Biological Engineering – Principles and Practice

contractions are required. Nevertheless, DQEMG has been useful for the decomposition of intramuscular EMG signals acquired for clinical applications (Stashuk,1999; Doherty &

Decomposition of an EMG signal may result in several invalid MUPTs that do not accurately represent the activity of a signal MU; such invalid MUPTs must be identified and then either corrected or excluded before extracted MUPTs are quantitatively analyzed. Characteristics of IDI histograms, MU firing rates over time and within-train MUP shape inconsistencies of MUPTs extracted during EMG decomposition can be used to estimate their validity. The existing qualitative MUPT validation methods, which typically need human operator supervision, are time consuming, related to operator experience and skill, and cannot assist with improving the performance of automatic EMG decomposition systems. To overcome these issues, in this chapter an automated MUPT validation system that estimate the validity of a MUPT is estimated using both its MU firing pattern and MUP shape information is presented. Based on the results obtained, the developed methods with overall AT >91.5% performed well in classifying MUPTs extracted by a decomposition system. Nevertheless, the methods that use only shape or only firing pattern information did not perform as well as the ones that used both types of information, especially for invalid trains. Of the method studied, the VDH method is the most accurate method in classifying sparse invalid trains, but the FPVC and VB are more accurate than the VDH in classifying valid MUPTs. Therefore, using VDH when MCE rate of the train >55% and VB or FPVC when MCE rate < 55% and even FPVC when MCE rate < 30% in the optimum scheme of using the proposed validation methods. Finally, it was revealed that using the proposed MUPT validation system during decomposition will improve the results in terms of finding the correct numbers of MUPTs that constitute a given signal as well as decreasing the MCE and FCE rates in the extracted trains. Overall, the decomposition accuracy for 20 EMG signals (10 simulated and 10 real) was improved by 9.0%. For these 20 signals, the validity–based decomposition system with average ENMUPTs 0.3 was better able to estimate the number of constituent MUPTs than the previous system, with average ENMUPTs of 0.9. The improvement gained using the validitybased system for dificult– to– decompose EMG signals was even higher. Such improvements, especially in ENMUPTs, along with the confidence that the extracted MUPTs will be valid encourage using the validity–based decomposition system for decomposing

Future work will address: a) further analysis of the developed decomposition system, especially using clinical EMG signals acquired from myopathic and neurogenic muscles; b) improving the performance of the developed MUPT validation system in terms of both

The authors would like to gratefully thank Dr. A. Ghodsi for his helpful discussion, on clustering and cluster validation methods, Dr. M. Nicolic, Dr. K.C. McGill, Dr. J.R. Florestal, Dr. P.A. Mathieu, Dr. Z. Lateva, and Dr. H.R. Marateb for sharing several EMG signals and the decomposition results of these signals. Financial support from the Natural Sciences and

Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

Stashuk, 2003; Boe et al., 2005; Pino et al.,2008; Calder at al.,2008)

**8. Conclusions and future work** 

intramuscular EMG signals for clinical application.

accuracy and computational time.

**9. Acknowledgment** 


**0**

**15**

**of Femoral Head**

Ivo List<sup>1</sup> and Matej Daniel2

*Technical University in Prague*

*University of Ljubljana*

<sup>1</sup>*Slovenia* <sup>2</sup>*Czech Republic*

**Role of Biomechanical Parameters in Hip**

**Osteoarthritis and Avascular Necrosis**

Veronika Kralj - Igliˇc1, Drago Dolinar1, Matic Ivanovski1,

<sup>2</sup>*Laboratory of Biomechanics, Faculty of Mechanical Engineering,*

It is considered that living organisms are subject to physical laws. Forces and stresses importantly influence the development of tissues and cells. In order to manipulate physiological and patophysiological states of the organism, it is necessary to understand the underlying mechanisms. Experience has led to mechanical hypothesis stating that some diseases or disorders are a consequence of unfavorable load distribution which is expressed by biomechanical parameters (e.g. forces, stresses, load - bearing areas). Since 1993 we have considered contact stress in the hip joint. We took part in development of a mathematical model for determination of the contact hip stress distribution (Igliˇc (1993b); Ipavec (1999)) and in population studies which were performed to validate the model. Different diseases and disorders of the hip were considered by this model: hip dysplasia (Mavˇciˇc (2002; 2008); Pompe (2003; 2007)), slipped epiphysis of the femoral head (Zupanc (2008)), avascular necrosis of the femoral head (Daniel (2006); Dolinar (2003)), postoperative changes in hip geometry (Herman (2002); Kralj (2005); Vengust (2001)) and osteoarthritis of the hip (Reˇcnik (2007; 2009a;b)). The method HIPSTRESS was put forward consisting of mathematical model for resultant hip force (Igliˇc (1990; 1993a)), mathematical model for contact hip stress (Igliˇc (1993b); Ipavec (1999)) and the corresponding software. The models require as an input geometrical parameters of the hip and pelvis. These parameters can be assessed from images as for example from standard anteroposterior radiograms. As appropriate images are available from clinical practice and from the archives, prospective and retrospective studies of the development of different diseases can be performed. A thorough survey on resultant hip force and the corresponding

Albeit the HIPSTRESS method is of limited repeatability and accuracy, the population studies have shown that biomechanical parameters are useful in reaching better understanding of

**1. Introduction**

stress has recently been published (Daniel (2011)).

<sup>1</sup>*Laboratory of Clinical Biophysics, Faculty of Medicine,*


## **Role of Biomechanical Parameters in Hip Osteoarthritis and Avascular Necrosis of Femoral Head**

Veronika Kralj - Igliˇc1, Drago Dolinar1, Matic Ivanovski1, Ivo List<sup>1</sup> and Matej Daniel2 <sup>1</sup>*Laboratory of Clinical Biophysics, Faculty of Medicine, University of Ljubljana* <sup>2</sup>*Laboratory of Biomechanics, Faculty of Mechanical Engineering, Technical University in Prague* <sup>1</sup>*Slovenia* <sup>2</sup>*Czech Republic*

#### **1. Introduction**

346 Applied Biological Engineering – Principles and Practice

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firing patterns extracted by EMG signal decomposition. *Med Biol Eng Comput.*, vol.

sphincter Muscles using Quantitative Electromyography. *Clin Neurophysiol.*, vol.

ensembles for EMG signal decomposition based on classifier agreement. *IEEE Trans* 

potential, the "jiggle," at consecutive discharges. *Muscle Nerve*, vol. 17,no.10, pp.1135-1144.

It is considered that living organisms are subject to physical laws. Forces and stresses importantly influence the development of tissues and cells. In order to manipulate physiological and patophysiological states of the organism, it is necessary to understand the underlying mechanisms. Experience has led to mechanical hypothesis stating that some diseases or disorders are a consequence of unfavorable load distribution which is expressed by biomechanical parameters (e.g. forces, stresses, load - bearing areas). Since 1993 we have considered contact stress in the hip joint. We took part in development of a mathematical model for determination of the contact hip stress distribution (Igliˇc (1993b); Ipavec (1999)) and in population studies which were performed to validate the model. Different diseases and disorders of the hip were considered by this model: hip dysplasia (Mavˇciˇc (2002; 2008); Pompe (2003; 2007)), slipped epiphysis of the femoral head (Zupanc (2008)), avascular necrosis of the femoral head (Daniel (2006); Dolinar (2003)), postoperative changes in hip geometry (Herman (2002); Kralj (2005); Vengust (2001)) and osteoarthritis of the hip (Reˇcnik (2007; 2009a;b)). The method HIPSTRESS was put forward consisting of mathematical model for resultant hip force (Igliˇc (1990; 1993a)), mathematical model for contact hip stress (Igliˇc (1993b); Ipavec (1999)) and the corresponding software. The models require as an input geometrical parameters of the hip and pelvis. These parameters can be assessed from images as for example from standard anteroposterior radiograms. As appropriate images are available from clinical practice and from the archives, prospective and retrospective studies of the development of different diseases can be performed. A thorough survey on resultant hip force and the corresponding stress has recently been published (Daniel (2011)).

Albeit the HIPSTRESS method is of limited repeatability and accuracy, the population studies have shown that biomechanical parameters are useful in reaching better understanding of

P

*d* cos *γ* (1)

, so we can neglect the quadratic term in

*<sup>r</sup>*�). (3)

*<sup>r</sup>*�<sup>2</sup> − <sup>2</sup>*r*�*<sup>d</sup>* cos *<sup>γ</sup>* (2)

*r*� − *r* = *d* cos *γ*. (4)

*p* = *p*<sup>0</sup> cos *γ* (5)

*p*<sup>0</sup> cos *γ***dS** = **R**, (6)

*r* '

*d*

Fig. 1. Schematic presentation of the relative shift of the acetabular sphere and the femoral head sphere. A: before loading, the two spheres are concentric. B: after loading, the femoral

Role of Biomechanical Parameters in Hip Osteoarthritis and Avascular Necrosis of Femoral Head 349

<sup>2</sup> <sup>=</sup> *<sup>r</sup>*�<sup>2</sup> <sup>+</sup> *<sup>d</sup>*<sup>2</sup> <sup>−</sup> <sup>2</sup>*r*�

where *γ* (Fig. 1B) is the angle between the radius vector from the origin of the coordinate system at the centre of the articular sphere to the pole and the radius vector to the selected point on the articular surface while *r*, *r*� and *d* are the magnitudes of the vectors **r**, **r**� and **d**. It is considered that the deformation of the cartilage is very small i.e. that the distance of

<sup>√</sup><sup>1</sup> <sup>+</sup> *<sup>x</sup>* � <sup>1</sup> <sup>+</sup> *<sup>x</sup>*/2,

*d*

(1 − cos *γ*

As the normal stress at a particular point on the articular sphere (*p*) is taken proportional to

Considering the resultant hip force **R** to be known, it is connected to the hip stress distribution

where **dS** is the vector form of the area element pointing in the direction normal to the surface.

A B

head sphere penetrates towards the acetabular sphere.

penetration *d* is much smaller than distances *r* and *r*�

strain in the cartilage, it can be written as (Brinckmann (1981))

The integration is performed over the load - bearing area.

where the proportionality constant *p*<sup>0</sup> is the value of stress at the pole.

*r*

*r* = 

*r* = *r*�

The deformation and the strain of the cartilage are proportional to the difference *r*� − *r*,

It follows from trigonometric relations that

and use the approximation for small *x*,

Eq.(1),

by

*r*

T

mechanisms taking place in different diseases and in predicting the outcome of the treatment, on the level of populations. In particular, the results indicated that long lasting elevated contact stress is connected to degeneration of the hip articular cartilage and development of hip osteoarthritis (Dolinar (2003); Kralj (2005); Mavˇciˇc (2002; 2008); Pompe (2003); Reˇcnik (2007; 2009a;b)).

The physical content of the model for hip stress used in these studies is simple and clear. The model states that the resultant hip force is distributed over the load - bearing area according to the corresponding normal stress in the cartilage which is subject to Hooke's law. The equations that must be solved to obtain the relevant forces, stresses and load - bearing area are transparent while the solution of the problem is almost analytical. Moreover, a user friendly software HIPSTRESS was developed which by fast determination of biomechanical parameters of the hip and pelvis enables analyses of large populations of hips.

However, due to space limitations in journals, the full derivation of the model equations was not encouraged in our previously published papers. Presenting only the final short and elegant equation for determination of stress parameters may lead the readers to think that the model itself is also simple. To elucidate the derivation and the model assumptions, we present in the first part of this work a detailed derivation of the model for contact hip stress distribution within the HIPSTRESS method, and indicate the connection between an unfavorable stress distribution and osteoarthritis development. In the second part, we present new results indicating the contact hip stress distribution as an etiological factor in avascular necrosis of the femoral head.

## **2. Determination of hip stress distribution by mathematical model**

The femoral head is represented by a fraction of a sphere (the femoral head sphere) and the acetabulum is represented by a half of a spherical shell (the acetabular sphere). An articular spherical surface is imagined. This spherical surface is an abstract object rather than a physical one and extends beyond the load - bearing area. The load - bearing area is however a part of the articular spherical surface.

The shear stresses in the hip joint are neglected because of the small value of the frictional coefficient corresponding to forces acting in the hip joint (Eberhardt (1991); Lipshitz (1979); McCutchen (1962)) so that only the normal stress is considered. We refer to the normal stress as to the contact hip stress.

When the hip is unloaded, the femoral head sphere and the acetabular sphere are concentric (Fig.1A). Upon loading the femoral head moves towards the acetabulum thereby squeezing the cartilage in between (Fig.1B). The femoral head sphere and the acetabular sphere are no longer concentric and the surfaces are shifted with respect to each other. The point on the articular sphere corresponding to the closest approach of the femoral head sphere and the acetabular sphere is called the stress pole (denoted by P in Fig.1B).

The radius vector from the centre of the femoral head sphere to the selected point at the acetabular sphere after the loading is denoted by **r**, the respective radius vector before the loading is denoted by **r** and the penetration of the centre of the femoral head is denoted by **d**. The coordinate system is rotated so that the side view plane is defined by the three vectors.

Fig. 1. Schematic presentation of the relative shift of the acetabular sphere and the femoral head sphere. A: before loading, the two spheres are concentric. B: after loading, the femoral head sphere penetrates towards the acetabular sphere.

It follows from trigonometric relations that

2 Will-be-set-by-IN-TECH

mechanisms taking place in different diseases and in predicting the outcome of the treatment, on the level of populations. In particular, the results indicated that long lasting elevated contact stress is connected to degeneration of the hip articular cartilage and development of hip osteoarthritis (Dolinar (2003); Kralj (2005); Mavˇciˇc (2002; 2008); Pompe (2003); Reˇcnik

The physical content of the model for hip stress used in these studies is simple and clear. The model states that the resultant hip force is distributed over the load - bearing area according to the corresponding normal stress in the cartilage which is subject to Hooke's law. The equations that must be solved to obtain the relevant forces, stresses and load - bearing area are transparent while the solution of the problem is almost analytical. Moreover, a user friendly software HIPSTRESS was developed which by fast determination of biomechanical

However, due to space limitations in journals, the full derivation of the model equations was not encouraged in our previously published papers. Presenting only the final short and elegant equation for determination of stress parameters may lead the readers to think that the model itself is also simple. To elucidate the derivation and the model assumptions, we present in the first part of this work a detailed derivation of the model for contact hip stress distribution within the HIPSTRESS method, and indicate the connection between an unfavorable stress distribution and osteoarthritis development. In the second part, we present new results indicating the contact hip stress distribution as an etiological factor in avascular

The femoral head is represented by a fraction of a sphere (the femoral head sphere) and the acetabulum is represented by a half of a spherical shell (the acetabular sphere). An articular spherical surface is imagined. This spherical surface is an abstract object rather than a physical one and extends beyond the load - bearing area. The load - bearing area is however a part of

The shear stresses in the hip joint are neglected because of the small value of the frictional coefficient corresponding to forces acting in the hip joint (Eberhardt (1991); Lipshitz (1979); McCutchen (1962)) so that only the normal stress is considered. We refer to the normal stress

When the hip is unloaded, the femoral head sphere and the acetabular sphere are concentric (Fig.1A). Upon loading the femoral head moves towards the acetabulum thereby squeezing the cartilage in between (Fig.1B). The femoral head sphere and the acetabular sphere are no longer concentric and the surfaces are shifted with respect to each other. The point on the articular sphere corresponding to the closest approach of the femoral head sphere and the

The radius vector from the centre of the femoral head sphere to the selected point at the acetabular sphere after the loading is denoted by **r**, the respective radius vector before the loading is denoted by **r** and the penetration of the centre of the femoral head is denoted by **d**. The coordinate system is rotated so that the side view plane is defined by the three vectors.

parameters of the hip and pelvis enables analyses of large populations of hips.

**2. Determination of hip stress distribution by mathematical model**

acetabular sphere is called the stress pole (denoted by P in Fig.1B).

(2007; 2009a;b)).

necrosis of the femoral head.

the articular spherical surface.

as to the contact hip stress.

$$r^2 = r'^2 + d^2 - 2r'd\cos\gamma \tag{1}$$

where *γ* (Fig. 1B) is the angle between the radius vector from the origin of the coordinate system at the centre of the articular sphere to the pole and the radius vector to the selected point on the articular surface while *r*, *r*� and *d* are the magnitudes of the vectors **r**, **r**� and **d**. It is considered that the deformation of the cartilage is very small i.e. that the distance of penetration *d* is much smaller than distances *r* and *r*� , so we can neglect the quadratic term in Eq.(1),

$$r = \sqrt{r'^2 - 2r'd\cos\gamma} \tag{2}$$

and use the approximation for small *x*, <sup>√</sup><sup>1</sup> <sup>+</sup> *<sup>x</sup>* � <sup>1</sup> <sup>+</sup> *<sup>x</sup>*/2,

$$r = r'(1 - \cos \gamma \frac{d}{r'}).\tag{3}$$

The deformation and the strain of the cartilage are proportional to the difference *r*� − *r*,

$$r' - r = d\cos\gamma.\tag{4}$$

As the normal stress at a particular point on the articular sphere (*p*) is taken proportional to strain in the cartilage, it can be written as (Brinckmann (1981))

$$p = p\_0 \cos \gamma \tag{5}$$

where the proportionality constant *p*<sup>0</sup> is the value of stress at the pole.

Considering the resultant hip force **R** to be known, it is connected to the hip stress distribution by

$$\int p\_0 \cos \gamma \mathbf{d} \mathbf{S} = \mathbf{R}\_\prime \tag{6}$$

where **dS** is the vector form of the area element pointing in the direction normal to the surface. The integration is performed over the load - bearing area.

and

and

while Φ˜ = 0 so that

It follows from Eqs.(15) and (16)– (19) that in the rotated system

*Rx* = *p*0*r*<sup>2</sup>

*Ry* = *p*0*r*<sup>2</sup>

*Rz* = *p*0*r*

2 

This condition includes points which are for *π*/2 away from the stress pole.

Using expressions (5), (6), (10) and (20), the components of the vector equation for the resultant

Role of Biomechanical Parameters in Hip Osteoarthritis and Avascular Necrosis of Femoral Head 351

cos<sup>3</sup> *ϕ*d*ϕ*

cos<sup>2</sup> *ϕ* sin *ϕ*d*ϕ*

cos<sup>3</sup> *ϕ*d*ϕ*

In order to calculate the coordinates of the pole Θ and Φ and the value of stress at the pole *p*<sup>0</sup> we must solve the above system of equations. For this we must define the boundaries of the

We take for simplicity that the lateral border of the load - bearing area is defined by the lateral rim of the acetabulum. Neglecting the detailed anatomy of the border and taking that the rim presents a part of a circle on the sphere with the centre at the centre of the sphere, the rim is described by an intersection of the articular sphere and a plane passing through the center of the sphere. The plane is inclined by an angle *ϑ*<sup>L</sup> with respect to the vertical axis. The coordinate system is then rotated for an angle −Φ so that the lateral border is symmetric with respect to the frontal plane through the centre of the articular sphere. Stress represents loading only if it is positive. Therefore the medial border of the load - bearing area is defined

Consider a hip with the lateral coverage *ϑ*<sup>L</sup> and the pole of stress (given by angles Θ and Φ) located laterally with respect to the sagittal plane through the centre of the femoral head. The coordinate system is rotated for angles −Θ and −Φ, so in the rotated system, the lateral border is at *ϑ* = *ϑ*<sup>L</sup> − Θ. As the pole is at the top of the rotated system, the medial border in the rotated system is at *ϑ* = −*π*/2. Parameter *ϕ* is bounded within the interval [−*π*/2,*π*/2].

**2.1 Contact hip stress in relation to resultant hip force**

hip force in the rotated system are expressed as

load - bearing area within the articular surface.

at points on the articular sphere where stress vanishes,

sin Θ˜ = 0, (17)

cos Φ˜ = 1, (18)

sin Φ˜ = 0. (19)

cos *ϑ* sin *ϑ*d*ϑ*, (21)

cos *ϑ*d*ϑ*, (22)

cos2 *ϑ*d*ϑ*. (23)

cos *γ* = 0. (24)

cos *γ* = cos *ϕ* cos *ϑ*. (20)

The coordinate system is adjusted to the geometry of the load-bearing area. The coordinates of a selected point (T) are (Fig.2A)

$$\mathfrak{x} = r \cos \varphi \sin \theta \,\tag{7}$$

$$y = r \sin \varphi\_{\prime} \tag{8}$$

$$z = r \cos \varphi \cos \theta. \tag{9}$$

The infinitesimal element of the surface area is given by

$$\mathbf{d} \mathbf{S} = r^2 \cos \varphi (\cos \varphi \sin \theta, \sin \varphi, \cos \varphi \cos \theta) \mathbf{d} \varphi \mathbf{d} \theta. \tag{10}$$

The space angle *γ* is the angle between the radius vector to the stress pole and the radius vector to the selected point on the articular surface, hence we can use the dot product to define the angle,

$$\cos \gamma = \frac{\mathbf{r} \cdot \mathbf{r}\_{\text{pole}}}{r^2} \,, \tag{11}$$

where

$$\mathbf{r} = r(\sin\theta\cos\varphi, \sin\varphi, \cos\theta\cos\varphi),\tag{12}$$

and

$$\mathbf{r}\_{\text{pole}} = r(\sin\Theta\cos\Phi, \sin\Phi, \cos\Theta\cos\Phi). \tag{13}$$

The dot product yields

$$\mathbf{r} \cdot \mathbf{r}\_{\text{pole}} = r^2 (\sin \theta \cos \varphi \sin \Theta \cos \Phi + \sin \varphi \sin \Phi + \cos \theta \cos \varphi \cos \Theta \cos \Phi) \tag{14}$$

so that

$$
\cos\gamma = \sin\theta\cos\varphi\sin\Theta\cos\Phi + \sin\varphi\sin\Phi + \cos\theta\cos\varphi\cos\Theta\cos\Phi. \tag{15}
$$

In the chosen coordinate system, the position of the pole is given by two angles (Φ and Θ). However, for clarity and simplicity we rotate the hip in the coordinate system so that the pole is at the top of the articular sphere (Fig.2B),

$$\cos \vec{\Theta} = 1,\tag{16}$$

and

4 Will-be-set-by-IN-TECH

<sup>z</sup> A B

pole pole

y

The coordinate system is adjusted to the geometry of the load-bearing area. The coordinates

The space angle *γ* is the angle between the radius vector to the stress pole and the radius vector to the selected point on the articular surface, hence we can use the dot product to define the

cos *<sup>γ</sup>* <sup>=</sup> **<sup>r</sup>** · **<sup>r</sup>**pole

Fig. 2. Schematic presentation of the articular sphere and the coordinate system.

x

CE-

*x* = *r* cos *ϕ* sin *ϑ*, (7)

<sup>2</sup> cos *ϕ*(cos *ϕ* sin *ϑ*, sin *ϕ*, cos *ϕ* cos *ϑ*)d*ϕ*d*ϑ*. (10)

**r** = *r*(sin *ϑ* cos *ϕ*, sin *ϕ*, cos *ϑ* cos *ϕ*), (12)

**r**pole = *r*(sin Θ cos Φ, sin Φ, cos Θ cos Φ). (13)

**<sup>r</sup>** · **<sup>r</sup>**pole <sup>=</sup> *<sup>r</sup>*2(sin *<sup>ϑ</sup>* cos *<sup>ϕ</sup>* sin <sup>Θ</sup> cos <sup>Φ</sup> <sup>+</sup> sin *<sup>ϕ</sup>* sin <sup>Φ</sup> <sup>+</sup> cos *<sup>ϑ</sup>* cos *<sup>ϕ</sup>* cos <sup>Θ</sup> cos <sup>Φ</sup>) (14)

cos *γ* = sin *ϑ* cos *ϕ* sin Θ cos Φ + sin *ϕ* sin Φ + cos *ϑ* cos *ϕ* cos Θ cos Φ. (15)

In the chosen coordinate system, the position of the pole is given by two angles (Φ and Θ). However, for clarity and simplicity we rotate the hip in the coordinate system so that the pole

*y* = *r* sin *ϕ*, (8) *z* = *r* cos *ϕ* cos *ϑ*. (9)

*<sup>r</sup>*<sup>2</sup> , (11)

cos Θ˜ = 1, (16)

y

 z 

T

The infinitesimal element of the surface area is given by

**dS** = *r*

x

angle,

where

and

so that

The dot product yields

is at the top of the articular sphere (Fig.2B),

of a selected point (T) are (Fig.2A)

$$
\sin \bar{\Theta} = 0,\tag{17}
$$

while Φ˜ = 0 so that

$$\cos \vec{\Phi} = 1,\tag{18}$$

and

$$
\sin \tilde{\Phi} = 0.\tag{19}
$$

It follows from Eqs.(15) and (16)– (19) that in the rotated system

$$
\cos \gamma = \cos \varphi \cos \theta. \tag{20}
$$

#### **2.1 Contact hip stress in relation to resultant hip force**

Using expressions (5), (6), (10) and (20), the components of the vector equation for the resultant hip force in the rotated system are expressed as

$$R\_X = p\_0 r^2 \int \cos^3 \varphi \mathrm{d}\varphi \int \cos \theta \sin \theta \mathrm{d}\theta \,\tag{21}$$

*Ry* = *p*0*r*<sup>2</sup> cos<sup>2</sup> *ϕ* sin *ϕ*d*ϕ* cos *ϑ*d*ϑ*, (22)

$$R\_z = p\_0 r^2 \int \cos^3 \varphi \mathbf{d} \,\varphi \int \cos^2 \theta \mathbf{d} \theta. \tag{23}$$

In order to calculate the coordinates of the pole Θ and Φ and the value of stress at the pole *p*<sup>0</sup> we must solve the above system of equations. For this we must define the boundaries of the load - bearing area within the articular surface.

We take for simplicity that the lateral border of the load - bearing area is defined by the lateral rim of the acetabulum. Neglecting the detailed anatomy of the border and taking that the rim presents a part of a circle on the sphere with the centre at the centre of the sphere, the rim is described by an intersection of the articular sphere and a plane passing through the center of the sphere. The plane is inclined by an angle *ϑ*<sup>L</sup> with respect to the vertical axis. The coordinate system is then rotated for an angle −Φ so that the lateral border is symmetric with respect to the frontal plane through the centre of the articular sphere. Stress represents loading only if it is positive. Therefore the medial border of the load - bearing area is defined at points on the articular sphere where stress vanishes,

$$
\cos \gamma = 0.\tag{24}
$$

This condition includes points which are for *π*/2 away from the stress pole.

Consider a hip with the lateral coverage *ϑ*<sup>L</sup> and the pole of stress (given by angles Θ and Φ) located laterally with respect to the sagittal plane through the centre of the femoral head. The coordinate system is rotated for angles −Θ and −Φ, so in the rotated system, the lateral border is at *ϑ* = *ϑ*<sup>L</sup> − Θ. As the pole is at the top of the rotated system, the medial border in the rotated system is at *ϑ* = −*π*/2. Parameter *ϕ* is bounded within the interval [−*π*/2,*π*/2].

increased. The derivation of the result was practically inaccessible by simply following the instructions given in (Ipavec (1999)). Probably this added to the fact that a typing mistake in the equations in (Ipavec (1999)) was deleterious for potential users of the model. The authors are indebted to W. Wilson and B.V. Rietbergen from Eindhoven University of Technology, who found the mistake while they were trying to repeat the derivation. An erratum was published in J. Biomech. (Ipavec (2002)), however, a thorough description of the model is still required

Role of Biomechanical Parameters in Hip Osteoarthritis and Avascular Necrosis of Femoral Head 353

In attempting to develop models with slightly more sophisticated load - bearing areas (such as after the Chiari osteotomy in which additional load - bearing area is created by a roof created by the cut iliac bone) the spherical coordinates used in (Ipavec (1999)) were found of practically no use and finding a more convenient coordinate system was prerequisite for description of the system. The coordinates presented above yielded considerably simpler

It can be seen that the simple, transparent and almost analytical form of the system of equations (35) - (37) does not mean that the model and the derivation of equations are simple. The simplicity and elegance of the result is primarily a consequence of the symmetry of the

It can also be mentioned that another choice of configuration preceded the above models. Inspired by Brinckmann et al., (Brinckmann (1981)), we chose the configuration in which the system was rotated so that the resultant hip force would point in the vertical direction (Igliˇc (1993b)). This model was however restricted to resultant hip force lying in the frontal plane of the body. It was a major achievement of the improved model described in (Ipavec (1999)) that regardless of the direction of the resultant hip force, within the described model, a coordinate system can always be found in which the above defined load-bearing area is symmetric.

To assess contact hip stress by a single numerical value, peak stress on the load - bearing area *p*max is given. If the stress pole is located inside the load - bearing area, *p*max is equal to the value of stress at the pole *p*0. If the stress pole lies outside the load - bearing area, contact stress is the highest at the point of the load - bearing area which is closest to the stress pole

Not only stress, but also stress differences between adjacent cell layers can be important in development of tissues (Daniel (2003)). These differences are expressed by the stress gradient,

where *r* is the magnitude of the radius vector while *θ* and *φ* are the polar and the azimuthal

**2.2 Index of the hip stress gradient and functional angle of load-bearing area**

<sup>∇</sup>*<sup>p</sup>* = ( *<sup>∂</sup><sup>p</sup> ∂r* , 1 *r ∂p ∂θ* , <sup>1</sup> *r* sin *θ*

*p*max = *p*<sup>0</sup> cos(*ϑ*<sup>L</sup> − Θ). (38)

*x* = *r* cos *φ* sin *θ*, (40)

*∂φ* ) (39)

*∂p*

as to help the potential users of the model to verify all steps.

derivation which was then first published in (Herman (2002)).

load - bearing area and of the stress distribution function.

and can be determined by using Eq.(5).

coordinates of the spherical system (Fig.3).

In this system

Taking into account that

$$\int \cos^3 \varphi \,\mathrm{d}\varphi = \sin \varphi - \frac{1}{3} \sin^3 \varphi,\tag{25}$$

$$
\int \cos \theta \sin \theta \mathrm{d}\theta = \frac{1}{2} \sin^2 \theta,\tag{26}
$$

$$\int \cos^2 \varphi \sin \varphi \mathrm{d}\varphi = -\frac{1}{3} \cos^3 \varphi,\tag{27}$$

$$
\int \cos \theta \,\mathrm{d}\theta = \sin \theta \,\tag{28}
$$

$$\int \cos^2 \theta \,\mathrm{d}\theta = \frac{1}{2} (\theta + \frac{1}{2} \sin 2\theta) \,\mathrm{}\,\tag{29}$$

and considering the boundaries, the components of the force are

$$R\_{\rm x} = -p\_0 r^2 \frac{2}{3} \cos^2(\theta\_{\rm L} - \Theta) \tag{30}$$

$$R\_{\mathcal{Y}} = 0 \tag{31}$$

and

$$R\_z = p\_0 r^2 \frac{2}{3} (\theta\_\mathcal{L} - \Theta + \frac{\pi}{2} + \frac{1}{2} \sin 2(\theta\_\mathcal{L} - \Theta)). \tag{32}$$

The resultant hip force is given by the vector

$$\mathbf{R} = R(-\sin\theta\_R\cos\varphi\_R, \sin\varphi\_{R'}\cos\theta\_R\cos\varphi\_R) \tag{33}$$

which is in the rotated system expressed as

$$\mathbf{R} = R(-\sin(\theta\_R + \Theta), 0, \cos(\theta\_R + \Theta))\tag{34}$$

since

$$
\Phi = -\varphi\_R.\tag{35}
$$

The ratio *Rx*/*Rz* yields

$$\tan(\theta\_{\rm R} + \Theta) = \frac{\cos^2(\theta\_{\rm L} - \Theta)}{(\theta\_{\rm L} - \Theta + \frac{\pi}{2} + \frac{1}{2}\sin 2(\theta\_{\rm L} - \Theta))}.\tag{36}$$

Eq.(36) is a nonlinear equation for Θ which can be solved numerically, for example by using the Newton method. The value of stress at the pole is then expressed from Eqs.(30) and (34),

$$p\_0 = \frac{3R}{2r^2} \frac{\sin(\theta\_R + \Theta)}{\cos^2(\theta\_L - \Theta)}.\tag{37}$$

The solution (Eqs.(36) and (37)) first appeared in (Ipavec (1999)). Due to the geometry of the articular sphere, the first choice of coordinates were spherical coordinates. In such coordinate system, the load - bearing area was subject to boundaries in which the two angles were related, so the load - bearing area had to be divided into 6 segments with different types of boundary shapes. Although yielding the same relatively simple result (Eq.(36)), the calculation was tedious and due to many terms in the integrals the probability of making the mistake was increased. The derivation of the result was practically inaccessible by simply following the instructions given in (Ipavec (1999)). Probably this added to the fact that a typing mistake in the equations in (Ipavec (1999)) was deleterious for potential users of the model. The authors are indebted to W. Wilson and B.V. Rietbergen from Eindhoven University of Technology, who found the mistake while they were trying to repeat the derivation. An erratum was published in J. Biomech. (Ipavec (2002)), however, a thorough description of the model is still required as to help the potential users of the model to verify all steps.

In attempting to develop models with slightly more sophisticated load - bearing areas (such as after the Chiari osteotomy in which additional load - bearing area is created by a roof created by the cut iliac bone) the spherical coordinates used in (Ipavec (1999)) were found of practically no use and finding a more convenient coordinate system was prerequisite for description of the system. The coordinates presented above yielded considerably simpler derivation which was then first published in (Herman (2002)).

It can be seen that the simple, transparent and almost analytical form of the system of equations (35) - (37) does not mean that the model and the derivation of equations are simple. The simplicity and elegance of the result is primarily a consequence of the symmetry of the load - bearing area and of the stress distribution function.

It can also be mentioned that another choice of configuration preceded the above models. Inspired by Brinckmann et al., (Brinckmann (1981)), we chose the configuration in which the system was rotated so that the resultant hip force would point in the vertical direction (Igliˇc (1993b)). This model was however restricted to resultant hip force lying in the frontal plane of the body. It was a major achievement of the improved model described in (Ipavec (1999)) that regardless of the direction of the resultant hip force, within the described model, a coordinate system can always be found in which the above defined load-bearing area is symmetric.

To assess contact hip stress by a single numerical value, peak stress on the load - bearing area *p*max is given. If the stress pole is located inside the load - bearing area, *p*max is equal to the value of stress at the pole *p*0. If the stress pole lies outside the load - bearing area, contact stress is the highest at the point of the load - bearing area which is closest to the stress pole and can be determined by using Eq.(5).

$$p\_{\text{max}} = p\_0 \cos(\vartheta\_{\text{L}} - \Theta). \tag{38}$$

#### **2.2 Index of the hip stress gradient and functional angle of load-bearing area**

Not only stress, but also stress differences between adjacent cell layers can be important in development of tissues (Daniel (2003)). These differences are expressed by the stress gradient,

$$\nabla p = (\frac{\partial p}{\partial r}, \frac{1}{r} \frac{\partial p}{\partial \theta}, \frac{1}{r \sin \theta} \frac{\partial p}{\partial \phi}) \tag{39}$$

where *r* is the magnitude of the radius vector while *θ* and *φ* are the polar and the azimuthal coordinates of the spherical system (Fig.3).

In this system

6 Will-be-set-by-IN-TECH

<sup>3</sup> sin3 *<sup>ϕ</sup>*, (25)

<sup>2</sup> sin2 *<sup>ϑ</sup>*, (26)

<sup>3</sup> cos<sup>3</sup> *<sup>ϕ</sup>*, (27)

<sup>2</sup> sin 2*ϑ*), (29)

<sup>2</sup> sin 2(*ϑ*<sup>L</sup> <sup>−</sup> <sup>Θ</sup>)). (32)

<sup>3</sup> cos2(*ϑ*<sup>L</sup> <sup>−</sup> <sup>Θ</sup>) (30)

*Ry* = 0 (31)

Φ = −*ϕR*. (35)

<sup>2</sup> sin 2(*ϑ*<sup>L</sup> <sup>−</sup> <sup>Θ</sup>)). (36)

. (37)

**R** = *R*(− sin *ϑ<sup>R</sup>* cos *ϕR*, sin *ϕR*, cos *ϑ<sup>R</sup>* cos *ϕR*) (33)

**R** = *R*(− sin(*ϑ<sup>R</sup>* + Θ), 0, cos(*ϑ<sup>R</sup>* + Θ)) (34)

cos *ϑ*d*ϑ* = sin *ϑ*, (28)

cos<sup>3</sup> *<sup>ϕ</sup>*d*<sup>ϕ</sup>* <sup>=</sup> sin *<sup>ϕ</sup>* <sup>−</sup> <sup>1</sup>

cos *<sup>ϑ</sup>* sin *<sup>ϑ</sup>*d*<sup>ϑ</sup>* <sup>=</sup> <sup>1</sup>

cos<sup>2</sup> *<sup>ϕ</sup>* sin *<sup>ϕ</sup>*d*<sup>ϕ</sup>* <sup>=</sup> <sup>−</sup><sup>1</sup>

2 (*ϑ* + 1

> *π* <sup>2</sup> <sup>+</sup> 1

and considering the boundaries, the components of the force are

*Rz* <sup>=</sup> *<sup>p</sup>*0*r*<sup>2</sup> <sup>2</sup>

The resultant hip force is given by the vector

which is in the rotated system expressed as

3

cos<sup>2</sup> *<sup>ϑ</sup>*d*<sup>ϑ</sup>* <sup>=</sup> <sup>1</sup>

*Rx* <sup>=</sup> <sup>−</sup>*p*0*r*<sup>2</sup> <sup>2</sup>

(*ϑ*<sup>L</sup> − Θ +

tan(*ϑ<sup>R</sup>* <sup>+</sup> <sup>Θ</sup>) = cos2(*ϑ*<sup>L</sup> <sup>−</sup> <sup>Θ</sup>) (*ϑ*<sup>L</sup> <sup>−</sup> <sup>Θ</sup> <sup>+</sup> *<sup>π</sup>*

> *<sup>p</sup>*<sup>0</sup> <sup>=</sup> <sup>3</sup>*<sup>R</sup>* 2*r*<sup>2</sup>

Eq.(36) is a nonlinear equation for Θ which can be solved numerically, for example by using the Newton method. The value of stress at the pole is then expressed from Eqs.(30) and (34),

The solution (Eqs.(36) and (37)) first appeared in (Ipavec (1999)). Due to the geometry of the articular sphere, the first choice of coordinates were spherical coordinates. In such coordinate system, the load - bearing area was subject to boundaries in which the two angles were related, so the load - bearing area had to be divided into 6 segments with different types of boundary shapes. Although yielding the same relatively simple result (Eq.(36)), the calculation was tedious and due to many terms in the integrals the probability of making the mistake was

<sup>2</sup> <sup>+</sup> <sup>1</sup>

sin(*ϑ<sup>R</sup>* + Θ) cos2(*ϑ*<sup>L</sup> − <sup>Θ</sup>)

Taking into account that

and

since

The ratio *Rx*/*Rz* yields

$$\mathbf{x} = r \cos \phi \sin \theta \,\tag{40}$$

Θ *> ϑ*L) then *Gp >* 0. If the pole of stress distribution lies inside the load - bearing area (i.e.,

Role of Biomechanical Parameters in Hip Osteoarthritis and Avascular Necrosis of Femoral Head 355

We defined another biomechanical parameter which describes the size of the load - bearing area: the functional angle *ϑ*F. The functional angle is equal to the load - bearing area divided

The index of the hip stress gradient at the lateral acetabular rim *Gp* is in a simple way connected to the size of the load-bearing area which is proportional to the functional angle

Population studies have shown that long lasting high peak stress is unfavorable and leads to osteoarthritis of the hip, however, even if the peak stress is not very high, large positive index of the hip stress gradient at the lateral acetabular rim and small functional angle of the load -

Index of the hip stress gradient at the lateral acetabular rim *G*p characterizes the slope of the contact stress distribution at the lateral border of the load - bearing area while the functional angle of the load-bearing area *ϑ*<sup>F</sup> describes the amount of the articular sphere occupied by the load - bearing area. To illustrate these parameters Fig.4 presents stress distribution and parameter *ϑ*<sup>F</sup> in two hips with different pelvic geometry: normal hip (A) and dysplastic hip (B). In hip A the pole of stress distribution lies within the load - bearing area and contact stress increases from the lateral edge in the medial direction, reaches its maximum and then decreases towards the medial border of the load - bearing area. The corresponding value of *Gp* is negative and the functional angle of the load - bearing area *ϑ*<sup>F</sup> is large. In hip B the pole lies outside the load - bearing area so that at the lateral edge of the load - bearing area stress steeply decreases in the medial direction. The corresponding value of *Gp* is positive and the functional angle of the load - bearing area *ϑ*<sup>F</sup> is small. The lower (more negative) the index of gradient and the larger the functional angle of the load - bearing area, the more favorable is stress distribution. In a population study it was shown (Pompe (2003)) that the change of sign of *Gp* correlates well with clinical evaluation of hip dysplasia, i.e. positive values of *Gp* correspond to dysplastic hips. The functional angle of the load-bearing area *ϑ*<sup>F</sup> which does not critically depend on the size of the pelvis and femur was proved the most relevant in samples with large scattering in the size of the geometrical parameters, as for example in a group of children (Vengust (2001)) or if there is a possibility that the magnification of radiographs varies considerably. In these cases the effect of the parameters *R*, *p*max and *Gp* (strongly dependent on the magnification of radiographs) can not be envisaged due to large

Population studies have shown that in dysplastic hips, the peak stress is on the average for a factor 2 higher than in healthy hips (Mavˇciˇc (2002)) while the index of stress gradient at the lateral acetabular rim is negative in normal hips and positive in dysplastic hips (Pompe (2003)). The differences were statistically significant (*p <* 0.001). In a study including 65 hips

<sup>2</sup> <sup>+</sup> *<sup>ϑ</sup>*CE <sup>−</sup> <sup>Θ</sup>. (50)

cos *ϑ*F. (51)

*<sup>ϑ</sup>*<sup>F</sup> <sup>=</sup> *<sup>π</sup>*

*Gp* <sup>=</sup> *<sup>p</sup>*<sup>0</sup> *r*

**2.3 Clinical relevance of hip stress with respect to osteoarthritis development**

bearing area express unfavorable stress distribution.

scattering and concomitant poor statistical significance.

if Θ *< ϑ*L) then *Gp <* 0.

of the load-bearing area,

by 2*r*2,

$$y = r \sin \phi \sin \theta \tag{41}$$

and

$$z = r \cos \theta,\tag{42}$$

while the coordinates of the pole are

$$\mathbf{x}\_{\rm P} = r \cos \phi\_{\rm P} \sin \theta\_{\rm P'} \tag{43}$$

$$y\_{\rm P} = r \sin \phi\_{\rm P} \sin \theta\_{\rm P} \tag{44}$$

and

$$z\_{\mathbf{P}} = r \cos \theta\_{\mathbf{P}}.\tag{45}$$

The space angle derived from the dot product is

$$
\cos\gamma = \cos\theta\sin\phi\cos\phi\_\mathsf{P}\sin\theta\_\mathsf{P} + \sin\phi\sin\theta\sin\phi\_\mathsf{P}\sin\theta\_\mathsf{P} + \cos\theta\cos\theta\_\mathsf{P}.\tag{46}
$$

As in the rotated system the stress pole is at the top of the sphere, ˜ *θ*<sup>p</sup> = *φ*˜p = 0, the above expression simplifies into

$$
\cos \gamma = \cos \theta.\tag{47}
$$

It follows from Eqs.(39) and (47) that the gradient is

$$
\nabla p = (0, -\frac{p\_0}{r}\sin\theta, 0). \tag{48}
$$

Here, *r* is the radius of the articular sphere. The stress gradient is a vector pointing in the direction of strongest change of stress. It would however be convenient to assess the gradient by a single numerical value. By mapping the three dimensional problem onto two dimensions we introduced the index of the hip stress gradient at the lateral acetabular rim *Gp* (Daniel (2002); Pompe (2003)),

$$G\_p = -\frac{p\_0}{r}\sin(\theta\_\mathcal{L} - \Theta). \tag{49}$$

The absolute value of *Gp* is equal to the magnitude of stress gradient ∇*p* at the lateral acetabular rim. If the pole of stress distribution lies outside the load - bearing area (i.e., if 8 Will-be-set-by-IN-TECH

z

Fig. 3. Schematic presentation of the articular sphere in the spherical coordinate system.

T

cos *γ* = cos *θ* sin *φ* cos *φ*<sup>p</sup> sin *θ*<sup>p</sup> + sin *φ* sin *θ* sin *φ*<sup>p</sup> sin *θ*<sup>p</sup> + cos *θ* cos *θ*p. (46)

pole

y

*y* = *r* sin *φ* sin *θ* (41)

*z* = *r* cos *θ*, (42)

*x*<sup>p</sup> = *r* cos *φ*<sup>p</sup> sin *θ*p, (43)

*y*<sup>p</sup> = *r* sin *φ*<sup>p</sup> sin *θ*<sup>p</sup> (44)

*z*<sup>p</sup> = *r* cos *θ*p. (45)

cos *γ* = cos *θ*. (47)

sin *θ*, 0). (48)

sin(*ϑ*<sup>L</sup> − Θ). (49)

*θ*<sup>p</sup> = *φ*˜p = 0, the above

x

and

and

while the coordinates of the pole are

expression simplifies into

(2002); Pompe (2003)),

The space angle derived from the dot product is

It follows from Eqs.(39) and (47) that the gradient is

As in the rotated system the stress pole is at the top of the sphere, ˜

<sup>∇</sup>*<sup>p</sup>* = (0, <sup>−</sup> *<sup>p</sup>*<sup>0</sup>

*Gp* <sup>=</sup> <sup>−</sup> *<sup>p</sup>*<sup>0</sup> *r*

*r*

Here, *r* is the radius of the articular sphere. The stress gradient is a vector pointing in the direction of strongest change of stress. It would however be convenient to assess the gradient by a single numerical value. By mapping the three dimensional problem onto two dimensions we introduced the index of the hip stress gradient at the lateral acetabular rim *Gp* (Daniel

The absolute value of *Gp* is equal to the magnitude of stress gradient ∇*p* at the lateral acetabular rim. If the pole of stress distribution lies outside the load - bearing area (i.e., if

A

Θ *> ϑ*L) then *Gp >* 0. If the pole of stress distribution lies inside the load - bearing area (i.e., if Θ *< ϑ*L) then *Gp <* 0.

We defined another biomechanical parameter which describes the size of the load - bearing area: the functional angle *ϑ*F. The functional angle is equal to the load - bearing area divided by 2*r*2,

$$
\theta\_{\rm F} = \frac{\pi}{2} + \theta\_{\rm CE} - \Theta. \tag{50}
$$

The index of the hip stress gradient at the lateral acetabular rim *Gp* is in a simple way connected to the size of the load-bearing area which is proportional to the functional angle of the load-bearing area,

$$G\_p = \frac{p\_0}{r} \cos \theta\_\text{F.}\tag{51}$$

#### **2.3 Clinical relevance of hip stress with respect to osteoarthritis development**

Population studies have shown that long lasting high peak stress is unfavorable and leads to osteoarthritis of the hip, however, even if the peak stress is not very high, large positive index of the hip stress gradient at the lateral acetabular rim and small functional angle of the load bearing area express unfavorable stress distribution.

Index of the hip stress gradient at the lateral acetabular rim *G*p characterizes the slope of the contact stress distribution at the lateral border of the load - bearing area while the functional angle of the load-bearing area *ϑ*<sup>F</sup> describes the amount of the articular sphere occupied by the load - bearing area. To illustrate these parameters Fig.4 presents stress distribution and parameter *ϑ*<sup>F</sup> in two hips with different pelvic geometry: normal hip (A) and dysplastic hip (B). In hip A the pole of stress distribution lies within the load - bearing area and contact stress increases from the lateral edge in the medial direction, reaches its maximum and then decreases towards the medial border of the load - bearing area. The corresponding value of *Gp* is negative and the functional angle of the load - bearing area *ϑ*<sup>F</sup> is large. In hip B the pole lies outside the load - bearing area so that at the lateral edge of the load - bearing area stress steeply decreases in the medial direction. The corresponding value of *Gp* is positive and the functional angle of the load - bearing area *ϑ*<sup>F</sup> is small. The lower (more negative) the index of gradient and the larger the functional angle of the load - bearing area, the more favorable is stress distribution. In a population study it was shown (Pompe (2003)) that the change of sign of *Gp* correlates well with clinical evaluation of hip dysplasia, i.e. positive values of *Gp* correspond to dysplastic hips. The functional angle of the load-bearing area *ϑ*<sup>F</sup> which does not critically depend on the size of the pelvis and femur was proved the most relevant in samples with large scattering in the size of the geometrical parameters, as for example in a group of children (Vengust (2001)) or if there is a possibility that the magnification of radiographs varies considerably. In these cases the effect of the parameters *R*, *p*max and *Gp* (strongly dependent on the magnification of radiographs) can not be envisaged due to large scattering and concomitant poor statistical significance.

Population studies have shown that in dysplastic hips, the peak stress is on the average for a factor 2 higher than in healthy hips (Mavˇciˇc (2002)) while the index of stress gradient at the lateral acetabular rim is negative in normal hips and positive in dysplastic hips (Pompe (2003)). The differences were statistically significant (*p <* 0.001). In a study including 65 hips

A B C

Fig. 5. A: healthy hip, B: initial phase of avascular necrosis of the femoral head when the femoral head is still spherical, C: advanced phase of avascular necrosis of the femoral head in

Role of Biomechanical Parameters in Hip Osteoarthritis and Avascular Necrosis of Femoral Head 357

which the femoral head is deformed while the femoral head is unable to bear load.

Fig. 6. Bilateral necrosis of the femoral head in an advanced stage.

From the archive of the Department of Orthopaedic Surgery, Ljubljana University Medical Centre we selected standard anterior - posterior radiograms of pelvis and proximal femora of 32 adult male persons (32 hips) who were treated due to AN between 1972 and 1991. It was assumed that prior to necrosis both hips had had the same geometry. As the necrotic process had already caused changes in the geometry of some hips, the hips contralateral to the necrotic ones were considered in the study. For comparison, we selected radiograms of 23 male persons (46 normal hips) pertaining to patients who had had a radiogram of the pelvic region taken at the same institution for reasons other than hip joint disease (e.g. lumbalgia). In our study we have considered only male hips. As the values of peak hip stress importantly depend on the gender (Kersniˇc (1997)) it is important to have gender-matched groups in

**3.2 Methods**

statistical analysis.

Fig. 4. Stress distribution in a frontal plane through the centre of the femoral head. The length of the line indicates the value of stress. The functional angle of the load - bearing area is shown. A: normal hip, B: dysplastic hip.

that underwent total hip replacement due to idiopathic osteoarthritis of the hip, the age at the replacement negatively correlated with peak stress (*p <* 0.001) (Reˇcnik (2009a)). These results indicate that contact hip stress plays an important role in progression of osteoarthritis.

## **3. Hip stress as etiological factor for avascular necrosis of femoral head**

## **3.1 Introduction**

Avascular necrosis of the femoral head (AN) is characterized by deterioration of the bone tissue (Figs.5,6). It represents together with secondary osteoarthritis a serious orthopaedic problem affecting mostly young and middle - aged populations (Mont (1995)). In spite of numerous studies, mechanisms leading to ischemic and necrotic processes are not yet understood. In about one third of patients the risk factors cannot be determined (Mahoney (2005)) while disorders and risk factors connected to the onset of AN include alcoholism (Mont (1995)), corticosteroid therapy in patients with connective tissue diseases and transplants (Mont (1995)), sickle cell anemia (Herndon (1972)), HIV (Miller (2002); Mahoney (2005)), antiphospholipid syndrome (Tektonidou (2003)) pregnancy (Cheng (1982); Mahoney (2005)) and some others (Bolland (2004); Macdonald (2001); Rollot (2005)). It was suggested that recidivant microfractures in the region of highly loaded femoral head may lead to microvascular trauma and thereby induce development of AN (Kim (2000)). A question can therefore be posed whether biomechanical parameters such as stresses in the hip are important in the onset of AN. It is the aim of this work to investigate the role of the above biomechanical parameters in the onset of AN.

Fig. 5. A: healthy hip, B: initial phase of avascular necrosis of the femoral head when the femoral head is still spherical, C: advanced phase of avascular necrosis of the femoral head in which the femoral head is deformed while the femoral head is unable to bear load.

Fig. 6. Bilateral necrosis of the femoral head in an advanced stage.

#### **3.2 Methods**

10 Will-be-set-by-IN-TECH

A B

<sup>F</sup> <sup>F</sup>

Fig. 4. Stress distribution in a frontal plane through the centre of the femoral head. The length of the line indicates the value of stress. The functional angle of the load - bearing area

**3. Hip stress as etiological factor for avascular necrosis of femoral head**

that underwent total hip replacement due to idiopathic osteoarthritis of the hip, the age at the replacement negatively correlated with peak stress (*p <* 0.001) (Reˇcnik (2009a)). These results indicate that contact hip stress plays an important role in progression of osteoarthritis.

Avascular necrosis of the femoral head (AN) is characterized by deterioration of the bone tissue (Figs.5,6). It represents together with secondary osteoarthritis a serious orthopaedic problem affecting mostly young and middle - aged populations (Mont (1995)). In spite of numerous studies, mechanisms leading to ischemic and necrotic processes are not yet understood. In about one third of patients the risk factors cannot be determined (Mahoney (2005)) while disorders and risk factors connected to the onset of AN include alcoholism (Mont (1995)), corticosteroid therapy in patients with connective tissue diseases and transplants (Mont (1995)), sickle cell anemia (Herndon (1972)), HIV (Miller (2002); Mahoney (2005)), antiphospholipid syndrome (Tektonidou (2003)) pregnancy (Cheng (1982); Mahoney (2005)) and some others (Bolland (2004); Macdonald (2001); Rollot (2005)). It was suggested that recidivant microfractures in the region of highly loaded femoral head may lead to microvascular trauma and thereby induce development of AN (Kim (2000)). A question can therefore be posed whether biomechanical parameters such as stresses in the hip are important in the onset of AN. It is the aim of this work to investigate the role of the above biomechanical

is shown. A: normal hip, B: dysplastic hip.

**3.1 Introduction**

parameters in the onset of AN.

From the archive of the Department of Orthopaedic Surgery, Ljubljana University Medical Centre we selected standard anterior - posterior radiograms of pelvis and proximal femora of 32 adult male persons (32 hips) who were treated due to AN between 1972 and 1991. It was assumed that prior to necrosis both hips had had the same geometry. As the necrotic process had already caused changes in the geometry of some hips, the hips contralateral to the necrotic ones were considered in the study. For comparison, we selected radiograms of 23 male persons (46 normal hips) pertaining to patients who had had a radiogram of the pelvic region taken at the same institution for reasons other than hip joint disease (e.g. lumbalgia). In our study we have considered only male hips. As the values of peak hip stress importantly depend on the gender (Kersniˇc (1997)) it is important to have gender-matched groups in statistical analysis.

to outline the influence of hip geometry on stress. The respective average values in the test group and the control group were compared by the pooled two - sided Student t - test.

Role of Biomechanical Parameters in Hip Osteoarthritis and Avascular Necrosis of Femoral Head 359

Parameter (SD) Test group Control group Δ (%) p *ϑ*<sup>F</sup> [degrees] 105 (13) 113 (13) 7 0.008 Θ [degrees] 15.4 (7.2) 11.8 (7.6) 27 0.037 *Gp*/*W*<sup>B</sup> [103 m−3] -17.32 (17.16) -26.05 (16.85) 40 0.028 *p*max/*W*<sup>B</sup> [m−2] 2172 (785) 2090 (502) 4 0.604 *R*/*W*<sup>B</sup> 2.49 (0.21) 2.53 (0.18) 2 0.382

Table 1. Mean biomechanical parameters with standard deviation in brackets in the test group (32 hips contralateral to the necrotic hips) and in the control group (46 normal hips). Table 1 shows the biomechanical parameters: functional angle of the load bearing area *ϑ*F, position of the stress pole, normalized index of the contact stress gradient (*Gp*/*W*B), normalized peak stress (*p*max/*W*B) and normalized resultant hip force (*R*/*W*B) in the test group and in the control group. Hips in the test group are on average less favorable with respect to *ϑ*F, *Gp*/*W*<sup>B</sup> and *p*max/*W*B. The differences in *ϑ*<sup>F</sup> (7%), Θ (27%) and *Gp*/*W*<sup>B</sup> (40%) are statistically significant (p = 0.008, p = 0.037 and p = 0.028, respectively) while the difference in *p*max/*W*<sup>B</sup> (4%) is not statistically significant (p = 0.604). The magnitude of the resultant hip force *R* is smaller (more favorable) in the test group, however the difference is very small (2%)

Parameter (SD) Test group Control group Δ (%) p C [mm] 60.0 (10.0) 58.5 (8.6) 3 0.463 H [mm] 163.0 (19.6) 162.4 (9.8) 0.4 0.867 l [mm] 203.1 (17.5) 199.6 (8.9) 2 0.305 *Tx* [mm] 12.5 (7.6) 7.6 (6.4) 49 0.002 *Tz* [mm] 74.7 (11.3) 69.7 (7.7) 7 0.033 r [mm] 28.5 (3.1) 27.7 (1.7) 3 0.187 *ϑ*CE[degrees] 30.4 (5.6) 34.7 (6.1) 13 0.002 Table 2. Mean geometrical parameters with standard deviation in brackets in the test group (32 hips contralateral to the necrotic hips) and in the control group (46 normal hips).

In order to better understand the differences in biomechanical parameters, the differences in geometrical parameters used in the models for the above biomechanical parameters were studied (Table 2). The center-edge angle *ϑ*CE is smaller (less favorable) in the test group than in the control group, the difference (13%) is statistically significant (p = 0.002). The lateral position of the insertion point of the effective muscle on the greater trochanter (*Tz*) is statistically significantly more favorable in the test group than in the control group (p = 0.033), while its inferior position (*Tx*) is considerably (49%) and statistically significantly more favorable in the control group (p = 0.002). The differences in other geometrical parameters are

**3.3 Results**

and statistically insignificant (p = 0.382).

small and statistically insignificant.

Fig. 7. Geometrical parameters of hip and pelvis which are needed to determine the resultant hip force within the HIPSTRESS method.

The three-dimensional biomechanical model for resultant hip force (Igliˇc (1993a)) and the above described model for hip stress were used to estimate the magnitude of the resultant hip force in the representative body position (one - legged stance) (Debevec (2010)). The contact stress distribution was given by its peak value *p*max, location of its pole Θ, index of the contact stress gradient at the lateral acetabular rim *G*p and functional angle of the load - bearing area *ϑ*F. The input parameters of the model for the resultant hip force are geometrical parameters of the hip and pelvis: interhip distance *l*, pelvic height *H*, pelvic width laterally from the femoral head center *C* and coordinates of the effective insertion point of abductors on the greater trochanter (point coordinates *Tx*, *Tz*) in the frontal plane (Fig.7).

The model of the resultant hip force is based on the equilibria of forces and torques acting between the body segments. To calculate the resultant hip force the three-dimensional reference coordinates of the muscle attachment points were taken from the work of Dostal and Andrews (Dostal (1981)) and scaled with regard to the pelvic parameters (*l*,*C*, *H*, *Tx*, *Tz*). To calculate stress, additionally, the radius of the articular surface (taken as the radius of the femoral head) and the angle of the lateral coverage of the femoral head (taken as the centre edge angle of Wiberg *ϑ*<sup>L</sup> ≡ *ϑ*CE) were assessed from anterior - posterior radiograms for each individual subject. In some radiograms of the patients with AN the upper part of the pelvis was not visible. In these patients the contour was extrapolated on the basis of the visible parts. As in some hips with AN the femoral head was considerably flattened superiorly, centers of rotation on both sides corresponding to the pre - necrotic situation were determined by circles fitting the outlines of the acetabular shells.

To describe stress distribution, we determined biomechanical parameters *R*, *p*max, *Gp* and *ϑ*<sup>F</sup> for each hip. The parameters *R*, *p*max and *Gp* were normalized to the body weight (*W*B) to outline the influence of hip geometry on stress. The respective average values in the test group and the control group were compared by the pooled two - sided Student t - test.

#### **3.3 Results**

12 Will-be-set-by-IN-TECH

*l*

Fig. 7. Geometrical parameters of hip and pelvis which are needed to determine the resultant

The three-dimensional biomechanical model for resultant hip force (Igliˇc (1993a)) and the above described model for hip stress were used to estimate the magnitude of the resultant hip force in the representative body position (one - legged stance) (Debevec (2010)). The contact stress distribution was given by its peak value *p*max, location of its pole Θ, index of the contact stress gradient at the lateral acetabular rim *G*p and functional angle of the load - bearing area *ϑ*F. The input parameters of the model for the resultant hip force are geometrical parameters of the hip and pelvis: interhip distance *l*, pelvic height *H*, pelvic width laterally from the femoral head center *C* and coordinates of the effective insertion point of abductors on the

The model of the resultant hip force is based on the equilibria of forces and torques acting between the body segments. To calculate the resultant hip force the three-dimensional reference coordinates of the muscle attachment points were taken from the work of Dostal and Andrews (Dostal (1981)) and scaled with regard to the pelvic parameters (*l*,*C*, *H*, *Tx*, *Tz*). To calculate stress, additionally, the radius of the articular surface (taken as the radius of the femoral head) and the angle of the lateral coverage of the femoral head (taken as the centre edge angle of Wiberg *ϑ*<sup>L</sup> ≡ *ϑ*CE) were assessed from anterior - posterior radiograms for each individual subject. In some radiograms of the patients with AN the upper part of the pelvis was not visible. In these patients the contour was extrapolated on the basis of the visible parts. As in some hips with AN the femoral head was considerably flattened superiorly, centers of rotation on both sides corresponding to the pre - necrotic situation were determined by circles

To describe stress distribution, we determined biomechanical parameters *R*, *p*max, *Gp* and *ϑ*<sup>F</sup> for each hip. The parameters *R*, *p*max and *Gp* were normalized to the body weight (*W*B)

greater trochanter (point coordinates *Tx*, *Tz*) in the frontal plane (Fig.7).

CE

z

*H*

*C*

*x*

hip force within the HIPSTRESS method.

fitting the outlines of the acetabular shells.

T


Table 1. Mean biomechanical parameters with standard deviation in brackets in the test group (32 hips contralateral to the necrotic hips) and in the control group (46 normal hips).

Table 1 shows the biomechanical parameters: functional angle of the load bearing area *ϑ*F, position of the stress pole, normalized index of the contact stress gradient (*Gp*/*W*B), normalized peak stress (*p*max/*W*B) and normalized resultant hip force (*R*/*W*B) in the test group and in the control group. Hips in the test group are on average less favorable with respect to *ϑ*F, *Gp*/*W*<sup>B</sup> and *p*max/*W*B. The differences in *ϑ*<sup>F</sup> (7%), Θ (27%) and *Gp*/*W*<sup>B</sup> (40%) are statistically significant (p = 0.008, p = 0.037 and p = 0.028, respectively) while the difference in *p*max/*W*<sup>B</sup> (4%) is not statistically significant (p = 0.604). The magnitude of the resultant hip force *R* is smaller (more favorable) in the test group, however the difference is very small (2%) and statistically insignificant (p = 0.382).


Table 2. Mean geometrical parameters with standard deviation in brackets in the test group (32 hips contralateral to the necrotic hips) and in the control group (46 normal hips).

In order to better understand the differences in biomechanical parameters, the differences in geometrical parameters used in the models for the above biomechanical parameters were studied (Table 2). The center-edge angle *ϑ*CE is smaller (less favorable) in the test group than in the control group, the difference (13%) is statistically significant (p = 0.002). The lateral position of the insertion point of the effective muscle on the greater trochanter (*Tz*) is statistically significantly more favorable in the test group than in the control group (p = 0.033), while its inferior position (*Tx*) is considerably (49%) and statistically significantly more favorable in the control group (p = 0.002). The differences in other geometrical parameters are small and statistically insignificant.

patients with osteoarthritis (Gangji (2003)). Thereby, stresses in the hip including the contact

Role of Biomechanical Parameters in Hip Osteoarthritis and Avascular Necrosis of Femoral Head 361

Unfavorable stress distribution importantly influences development of the hip and may present a risk factor for osteoarthritis progression as well as for progression of the avascular

Authors are indebted to A. Igliˇc for discussions and to R. Štukelj and L. Drobne for technical

Bolland, M.J., Hood, G., Bastin, S.T., King, A.R., Grey, A., (2004). Bilateral femoral head

Brand, R.A., Igliˇc, A., Kralj-Igliˇc, V., (2001). Contact stresses in human hip: implications for

Brinckmann, P., Frobin, W., Hierholzer, E.,(1981). Stress on the articular surface of the hip

Cheng, N., Burssens, A., Mulier, J.C., (1982). Pregnancy and post-pregnancy avascular necrosis of the femoral head. *Arch Orthop Trauma Surg*, 100, (199-210), ISSN 0936-8051 Daniel, M., Antoliˇc, V., Igliˇc, A., Kralj Igliˇc., V., (2001). Determination of contact hip stress

Daniel, M., Sochor, M., Igliˇc, A., Herman, S., Kralj-Igliˇc, V., (2002). Gradient of contact stress

Daniel, M., Sochor, M., Igliˇc, A., Kralj-Igliˇc, V., (2003). Hypothesis of regulation of hip joint

Daniel, M., Dolinar, D., Herman, S., Sochor, M., Igliˇc, A., Kralj-Igliˇc, V., (2006). Contact stress

Daniel, M., Igliˇc A., Kralj - Igliˇc, V., (2011). Human hip joint loading - mathematical

Debevec, H., Pedersen, D. R., Igliˇc, A., Daniel, M. (2010). One-legged stance as a representative

disease and treatment. *Hip Int*, 11, (117-126), ISSN 1120-7000

*Biomech*, 14, (149-156), ISSN 0044-3220

osteonecrosis after septic shock and multiorgan failure. *J Bone Min Res*, 19, (517-520),

joint in healthy adults and persons with idiopathic osteoarthrosis of the hip joint. *J*

from nomograms based on mathematical model. *Med Eng Phys*, 23, (347-357), ISSN

in normal and dyplastic human hips. *Acta Bioeng Biomech, Suppl.* 1, (280-281), ISSN

cartilage activity by mechanical loading. *Medical Hypotheses*, 60, (936-937), ISSN

in hips with osteonecrosis of the femoral head. *Clin Orhop Rel Res*, 447, (92-99), ISSN

modeling.Reaction forces and contact pressures. *VDM Verlag Dr. Müller e.K.*, ISBN

static body position for calculation of hip contact stress distribution in clinical studies

hip stress could contribute to the acceleration of the processes leading to AN.

**4. Conclusion**

assistance.

**6. References**

necrosis of the femoral head.

ISSN 0884-0431

1350-4533

1509409X

0306-9877

0009-921X

978-3-639-26120-2

*J Appl Biomech* , ISSN 1065-8483

**5. Acknowledgement**

#### **3.4 Discussion**

Our results show that the peak contact hip stress *p*max/*W*<sup>B</sup> in the group of hips contralateral to necrotic ones and in the group of normal hips are not statistically significantly different, however, the shape of the stress distribution (given by parameters *ϑ*<sup>F</sup> and *Gp*/*W*B) is statistically significantly less favorable in the group of hips contralateral to necrotic ones.

The differences in the biomechanical parameters can be explained by the differences in the geometrical parameters. The difference in pelvic height *H* and width *C* and in the interhip distance *l* were very small (below 3%) and statistically insignificant while the difference in the vertical coordinate of the insertion of the effective muscle on the greater trochanter (*Tx*) was statistically significant, but this parameter does not influence much the biomechanical parameters (Daniel (2001)). The differences in the remaining three parameters (lateral coordinate of the insertion of the effective muscle on the greater trochanter, radius of the femoral head and center-edge angle) can however contribute to the explanation of the differences in biomechanical parameters. The centre - edge angle CE is the most important parameter in determination of contact stress distribution. Larger CE corresponds to lower *p*max/*W*<sup>B</sup> and smaller *Gp*/*W*B. Table 2 shows that *ϑ*CE is statistically significantly lower in the test group (p = 0.002) indicating that *p*max/*W*<sup>B</sup> and *Gp*/*W*<sup>B</sup> would be higher in hips contralateral to the necrotic ones. However, *p*max/*W*<sup>B</sup> and *Gp*/*W*<sup>B</sup> strongly depend also on the radius of the femoral head (*p*max/*W*<sup>B</sup> is inversely proportional to the square of *r* and *Gp*/*W*<sup>B</sup> is inversely proportional to the third power of *r*). Although the difference in the radii of the two groups is not statistically significant (p = 0.187), the difference (3%) is in favor of hips in the test group. Further, the lateral position of the insertion of the effective muscle is for 7% statistically significantly larger (more favorable) in the test group than in the control group (p = 0.002). The effect of the smaller center-edge angle is therefore counterbalanced by the effect of larger femoral head and more laterally extended greater trochanter. The shape of the stress distribution (described by *ϑ*<sup>F</sup> and *Gp*/*W*B) is on average considerably and statistically significantly different in both groups. In the test group the distribution is steeper, the pole lies more laterally, the gradient index is larger (less negative) and the functional angle of the load-bearing area is smaller than in the control group. This renders hips with increased risk for AN less favorable regarding the stress distribution. However, we did not find a statistically significant difference in *p*max/*W*B.

The magnification of the radiograph was not known, as no unit with known length was visible in the picture. As the magnification may vary considerably contributing to the scattering in the measured distances, poor statistical significance in parameters *p*max/*W*<sup>B</sup> and *R*/*W*<sup>B</sup> can be the consequence of the lack of knowledge of magnification of the radiograms.

It has been hypothesized that transient osteoporosis of the bone marrow oedema syndrome may be the initial phase of osteonecrosis of the femoral head (Hofmann (1994)) and that there may be a common patophysiology. Transient osteoporosis is connected to recidivant microfractures and microvascular trauma at highly loaded regions of the bone leading to the ishemia of the affected part of the bone (Ficat (1981)). Higher contact hip stress may increase the probability and extent of microfractures of the affected bone thereby making the repair more difficult. Furthermore, the replicative capacity of osteoblast cells of the intertrochanteric area of the femur in osteonecrosis patients was found to be significantly reduced compared to patients with osteoarthritis (Gangji (2003)). Thereby, stresses in the hip including the contact hip stress could contribute to the acceleration of the processes leading to AN.

#### **4. Conclusion**

14 Will-be-set-by-IN-TECH

Our results show that the peak contact hip stress *p*max/*W*<sup>B</sup> in the group of hips contralateral to necrotic ones and in the group of normal hips are not statistically significantly different, however, the shape of the stress distribution (given by parameters *ϑ*<sup>F</sup> and *Gp*/*W*B) is statistically significantly less favorable in the group of hips contralateral to necrotic ones.

The differences in the biomechanical parameters can be explained by the differences in the geometrical parameters. The difference in pelvic height *H* and width *C* and in the interhip distance *l* were very small (below 3%) and statistically insignificant while the difference in the vertical coordinate of the insertion of the effective muscle on the greater trochanter (*Tx*) was statistically significant, but this parameter does not influence much the biomechanical parameters (Daniel (2001)). The differences in the remaining three parameters (lateral coordinate of the insertion of the effective muscle on the greater trochanter, radius of the femoral head and center-edge angle) can however contribute to the explanation of the differences in biomechanical parameters. The centre - edge angle CE is the most important parameter in determination of contact stress distribution. Larger CE corresponds to lower *p*max/*W*<sup>B</sup> and smaller *Gp*/*W*B. Table 2 shows that *ϑ*CE is statistically significantly lower in the test group (p = 0.002) indicating that *p*max/*W*<sup>B</sup> and *Gp*/*W*<sup>B</sup> would be higher in hips contralateral to the necrotic ones. However, *p*max/*W*<sup>B</sup> and *Gp*/*W*<sup>B</sup> strongly depend also on the radius of the femoral head (*p*max/*W*<sup>B</sup> is inversely proportional to the square of *r* and *Gp*/*W*<sup>B</sup> is inversely proportional to the third power of *r*). Although the difference in the radii of the two groups is not statistically significant (p = 0.187), the difference (3%) is in favor of hips in the test group. Further, the lateral position of the insertion of the effective muscle is for 7% statistically significantly larger (more favorable) in the test group than in the control group (p = 0.002). The effect of the smaller center-edge angle is therefore counterbalanced by the effect of larger femoral head and more laterally extended greater trochanter. The shape of the stress distribution (described by *ϑ*<sup>F</sup> and *Gp*/*W*B) is on average considerably and statistically significantly different in both groups. In the test group the distribution is steeper, the pole lies more laterally, the gradient index is larger (less negative) and the functional angle of the load-bearing area is smaller than in the control group. This renders hips with increased risk for AN less favorable regarding the stress distribution. However, we did not find a statistically

The magnification of the radiograph was not known, as no unit with known length was visible in the picture. As the magnification may vary considerably contributing to the scattering in the measured distances, poor statistical significance in parameters *p*max/*W*<sup>B</sup> and *R*/*W*<sup>B</sup> can

It has been hypothesized that transient osteoporosis of the bone marrow oedema syndrome may be the initial phase of osteonecrosis of the femoral head (Hofmann (1994)) and that there may be a common patophysiology. Transient osteoporosis is connected to recidivant microfractures and microvascular trauma at highly loaded regions of the bone leading to the ishemia of the affected part of the bone (Ficat (1981)). Higher contact hip stress may increase the probability and extent of microfractures of the affected bone thereby making the repair more difficult. Furthermore, the replicative capacity of osteoblast cells of the intertrochanteric area of the femur in osteonecrosis patients was found to be significantly reduced compared to

be the consequence of the lack of knowledge of magnification of the radiograms.

**3.4 Discussion**

significant difference in *p*max/*W*B.

Unfavorable stress distribution importantly influences development of the hip and may present a risk factor for osteoarthritis progression as well as for progression of the avascular necrosis of the femoral head.

#### **5. Acknowledgement**

Authors are indebted to A. Igliˇc for discussions and to R. Štukelj and L. Drobne for technical assistance.

#### **6. References**


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**16** 

*Brazil* 

Amanda Freitas Valentim,

*Universidade Federal de Minas Gerais* 

**Development and Clinical Application of** 

Andréa Rodrigues Motta, Monalise Costa Batista Berbert, Márcio Falcão Santos Barroso, Cláudio Gomes da Costa,

Iracema Maria Utsch Braga and Estevam Barbosa de Las Casas

**Instruments to Measure Orofacial Structures** 

Renata Maria Moreira Moraes Furlan, Tatiana Vargas de Castro Perilo,

The human body consists of a series of systems, which work in an integrated way for perfect functioning. One of these systems, the muscular system, consists of a set of muscles that are able to contract and relax, resulting in the generation of diverse and varied movements that

The muscle groups that integrate the human body have different characteristics. There are long muscles, which are powerful but not so precise in their movements, while another set of muscles is described by their small size and high accuracy in generated movements.

The muscles which compose the orofacial system are characterized by their small sizes and the ability to generate highly precise and differentiated movements that includes a series of rapid shape changes. This is made possible due to the large amount of innervations and the complex organization of the muscle fibers. These muscles play an essential role in mastication, swallowing, speech, breathing and suction, functions that require fast and complex movements. They also contribute to the orientation of facial bone growth and

Like all systems that constitute the body, many diseases can cause changes in the structures that compose the muscular system. Changes, such as muscle weakening, that interfere in tongue and lips movements can hamper activities related to various physiological processes. When any disorder or other conditions causes an improper functioning of orofacial muscles, it is necessary to rehabilitate the impaired muscle group. This muscular rehabilitation work, named myotherapy, includes orientations and rehabilitative exercises and it shall be carefully planned in order to achieve fast and effective results. However, to organize a work

Currently, the evaluation by speech-language pathologists of these muscles is routinely made in a qualitative way. One of the current evaluation techniques consists of asking the patient to perform a contraction against an imposed obstacle, such as a gloved finger. Based

plan it is essential to perform a well-structured assessment of muscular condition.

on experience, the speech-language pathologist classifies the force as normal or not.

allow the person to walk, eat and talk, and perform many other actions.

**1. Introduction** 

maintenance of teeth position.


## **Development and Clinical Application of Instruments to Measure Orofacial Structures**

Amanda Freitas Valentim, Renata Maria Moreira Moraes Furlan, Tatiana Vargas de Castro Perilo, Andréa Rodrigues Motta, Monalise Costa Batista Berbert, Márcio Falcão Santos Barroso, Cláudio Gomes da Costa, Iracema Maria Utsch Braga and Estevam Barbosa de Las Casas *Universidade Federal de Minas Gerais Brazil* 

## **1. Introduction**

18 Will-be-set-by-IN-TECH

364 Applied Biological Engineering – Principles and Practice

Vengust, R., Daniel, M., Antoliˇc, V., Zupanc, O., Igliˇc, A., Kralj-Igliˇc, V., (2001). Biomechanical

Zupanc, O., Križanˇciˇc, M., Daniel, M., Mavˇciˇc, B., Antoliˇc, V., Igliˇc, A., Kralj-Igliˇc, V., (2008).

study. *Arch Orthop Trauma Surg*, 121, (511-516), ISSN 0936-8051

epiphysis. *J Pediatr Orthoped*, 28, (444-451), ISSN 0271-6798

evaluation of hip joint after Salter innominate osteotomy: a long-term follow-up

shear stress in epiphyseal growth plate is a risk factor for slipped capital femoral

The human body consists of a series of systems, which work in an integrated way for perfect functioning. One of these systems, the muscular system, consists of a set of muscles that are able to contract and relax, resulting in the generation of diverse and varied movements that allow the person to walk, eat and talk, and perform many other actions.

The muscle groups that integrate the human body have different characteristics. There are long muscles, which are powerful but not so precise in their movements, while another set of muscles is described by their small size and high accuracy in generated movements.

The muscles which compose the orofacial system are characterized by their small sizes and the ability to generate highly precise and differentiated movements that includes a series of rapid shape changes. This is made possible due to the large amount of innervations and the complex organization of the muscle fibers. These muscles play an essential role in mastication, swallowing, speech, breathing and suction, functions that require fast and complex movements. They also contribute to the orientation of facial bone growth and maintenance of teeth position.

Like all systems that constitute the body, many diseases can cause changes in the structures that compose the muscular system. Changes, such as muscle weakening, that interfere in tongue and lips movements can hamper activities related to various physiological processes. When any disorder or other conditions causes an improper functioning of orofacial muscles, it is necessary to rehabilitate the impaired muscle group. This muscular rehabilitation work, named myotherapy, includes orientations and rehabilitative exercises and it shall be carefully planned in order to achieve fast and effective results. However, to organize a work plan it is essential to perform a well-structured assessment of muscular condition.

Currently, the evaluation by speech-language pathologists of these muscles is routinely made in a qualitative way. One of the current evaluation techniques consists of asking the patient to perform a contraction against an imposed obstacle, such as a gloved finger. Based on experience, the speech-language pathologist classifies the force as normal or not.

Development and Clinical Application of Instruments to Measure Orofacial Structures 367

The dorsum of the tongue is divided by the longitudinal sulcus, which is continuous from the back to an orifice called the foramen cecum. From the foramen cecum, a shallow Vshaped sulcus, called terminal sulcus, has its anterior and laterally path toward the edges of the tongue. This is the anatomical reference point that separates two anatomically and functionally distinct regions, the anterior two thirds and the posterior third of the tongue. In the anterior two thirds, the dorsum has a rough surface and contains the taste papillae, while the posterior third of the tongue looks smoother and contains numerous mucous

The lingual septum divides the tongue into halves and its muscles are considered in pairs. The muscles of the tongue are classified as extrinsic and intrinsic. The extrinsic muscles (Figure 1) originate in adjacent structures and are inserted into the tongue, being responsible for movement in different directions. They are: genioglossus, styloglossus, palatoglossus and hyoglossus. The genioglossus is the largest of the extrinsic muscles and is fan-shaped. The contraction of the posterior fibers moves the tongue forward, protruding the apex, while the contraction of the anterior fibers causes tongue retraction and the contraction of the whole muscle moves the tongue down. The styloglossus, during its contraction, moves the tongue upward and backward, and along with the superior longitudinal muscle, directs the sides of the tongue upward to make the dorsum concave. The function of the muscle palatoglossus is to lower the soft palate or to raise the back of the tongue grooving the

glands and lymph vessels that form the lingual tonsil (Zemlin 1997).

dorsum. The hyoglossus retracts and depresses the tongue (Zemlin 1997).

Fig. 1. Extrinsic tongue muscles and the inferior longitudinal

muscle narrows and lengthens the body (Zemlin 1997).

The intrinsic muscles (Figure 2) are contained in the tongue itself and are responsible for changing the shape of the organ. They are: superior longitudinal, inferior longitudinal, transverse and vertical. The superior longitudinal muscle shortens the tongue and turns its apex upward. The oblique fibers help turn the side margins up, leaving the back concave. The inferior longitudinal shortens the tongue, pushes the apex downward and leaves the dorsum convex. The vertical muscle flattens and extends the tongue, while the transverse

For several years, an effective method has been sought to quantify the force or pressure that orofacial structures are able to exert. This method would allow comparing the values with the parameters obtained in the qualitative evaluation and to measure performance during the main functions and exercises. A quantitative evaluation can improve diagnosis, especially in cases of slight changes in force and is more sensitive in detecting the small differences in strength observed with the progression of the disease or therapy.

The field of Biomechanical Engineering combines engineering with biology and physiology, using principles of mechanics to design, model, develop and analyze equipment and systems. In Brazil there are Biomechanics research groups in different regions of the country, although mostly concentrated in Southeast of the country. In this region is the Biomechanics Engineering Group from the Universidade Federal de Minas Gerais, an interdisciplinary group, was created in 1998, and includes researchers from the fields of engineering and health care. The purpose of the group is to study the mechanical behavior of tissues, organs and biomaterials under the action of external loads and other types of actions using computational and experimental techniques. In 2002, a professor and a few Speech Language Pathology undergraduate students joined the group with a project that aimed to develop instruments for quantifying the forces of orofacial structures in order to help in orofacial myology assessment. The first instrument created was FORLING, to measure tongue force. After that, the group started to grow, with more undergraduate and graduate students, and started a new project: the development of an instrument to measure lips force, FORLAB. Both of them were intended to be used in the stages of diagnosis, prognosis and therapeutic follow-up.

This chapter focuses on describing the development of devices and quantitative techniques created by the Group, to quantify forces and improve the assessment of orofacial muscles. It also includes an analysis of the obtained values of tongue and lip forces and a discussion on the consequences of the obtained data on clinical practice.

## **2. Tongue**

## **2.1 Anatomy and physiology of the tongue**

The tongue is a highly specialized organ of the body and a focal point for many professionals from several fields of knowledge. It actively participates in functions such as sucking, mastication, swallowing and speech, which are fundamental in maintaining the quality of life. It is a mobile structure that can take many shapes and positions, in extremely fast sequences, due to its high innervations and complex organization of muscle fibers (Zemlin 1997).

It is characterized as being essentially a muscular organ, which occupies the functional space of the oral cavity. It is formed by striated muscle tissue and covered by a flat mucosa in the lower part and is irregular on the top due to the large number of papillae (Aprile et al. 1975).

The tongue can be divided into body and root, or, based on its relationship with the palate, into apex and body. The body can be subdivided into the front and back part. The apex of the tongue is the part closest to the anterior teeth; the region just below the hard palate is the front and the region located below the soft palate is the posterior (Zemlin 1997).

For several years, an effective method has been sought to quantify the force or pressure that orofacial structures are able to exert. This method would allow comparing the values with the parameters obtained in the qualitative evaluation and to measure performance during the main functions and exercises. A quantitative evaluation can improve diagnosis, especially in cases of slight changes in force and is more sensitive in detecting the small

The field of Biomechanical Engineering combines engineering with biology and physiology, using principles of mechanics to design, model, develop and analyze equipment and systems. In Brazil there are Biomechanics research groups in different regions of the country, although mostly concentrated in Southeast of the country. In this region is the Biomechanics Engineering Group from the Universidade Federal de Minas Gerais, an interdisciplinary group, was created in 1998, and includes researchers from the fields of engineering and health care. The purpose of the group is to study the mechanical behavior of tissues, organs and biomaterials under the action of external loads and other types of actions using computational and experimental techniques. In 2002, a professor and a few Speech Language Pathology undergraduate students joined the group with a project that aimed to develop instruments for quantifying the forces of orofacial structures in order to help in orofacial myology assessment. The first instrument created was FORLING, to measure tongue force. After that, the group started to grow, with more undergraduate and graduate students, and started a new project: the development of an instrument to measure lips force, FORLAB. Both of them were intended to be used in the stages of diagnosis,

This chapter focuses on describing the development of devices and quantitative techniques created by the Group, to quantify forces and improve the assessment of orofacial muscles. It also includes an analysis of the obtained values of tongue and lip forces and a discussion on

The tongue is a highly specialized organ of the body and a focal point for many professionals from several fields of knowledge. It actively participates in functions such as sucking, mastication, swallowing and speech, which are fundamental in maintaining the quality of life. It is a mobile structure that can take many shapes and positions, in extremely fast sequences, due to its high innervations and complex organization of muscle fibers

It is characterized as being essentially a muscular organ, which occupies the functional space of the oral cavity. It is formed by striated muscle tissue and covered by a flat mucosa in the lower part and is irregular on the top due to the large number of papillae (Aprile et al.

The tongue can be divided into body and root, or, based on its relationship with the palate, into apex and body. The body can be subdivided into the front and back part. The apex of the tongue is the part closest to the anterior teeth; the region just below the hard palate is the

front and the region located below the soft palate is the posterior (Zemlin 1997).

differences in strength observed with the progression of the disease or therapy.

prognosis and therapeutic follow-up.

**2. Tongue** 

(Zemlin 1997).

1975).

the consequences of the obtained data on clinical practice.

**2.1 Anatomy and physiology of the tongue** 

The dorsum of the tongue is divided by the longitudinal sulcus, which is continuous from the back to an orifice called the foramen cecum. From the foramen cecum, a shallow Vshaped sulcus, called terminal sulcus, has its anterior and laterally path toward the edges of the tongue. This is the anatomical reference point that separates two anatomically and functionally distinct regions, the anterior two thirds and the posterior third of the tongue. In the anterior two thirds, the dorsum has a rough surface and contains the taste papillae, while the posterior third of the tongue looks smoother and contains numerous mucous glands and lymph vessels that form the lingual tonsil (Zemlin 1997).

The lingual septum divides the tongue into halves and its muscles are considered in pairs. The muscles of the tongue are classified as extrinsic and intrinsic. The extrinsic muscles (Figure 1) originate in adjacent structures and are inserted into the tongue, being responsible for movement in different directions. They are: genioglossus, styloglossus, palatoglossus and hyoglossus. The genioglossus is the largest of the extrinsic muscles and is fan-shaped. The contraction of the posterior fibers moves the tongue forward, protruding the apex, while the contraction of the anterior fibers causes tongue retraction and the contraction of the whole muscle moves the tongue down. The styloglossus, during its contraction, moves the tongue upward and backward, and along with the superior longitudinal muscle, directs the sides of the tongue upward to make the dorsum concave. The function of the muscle palatoglossus is to lower the soft palate or to raise the back of the tongue grooving the dorsum. The hyoglossus retracts and depresses the tongue (Zemlin 1997).

Fig. 1. Extrinsic tongue muscles and the inferior longitudinal

The intrinsic muscles (Figure 2) are contained in the tongue itself and are responsible for changing the shape of the organ. They are: superior longitudinal, inferior longitudinal, transverse and vertical. The superior longitudinal muscle shortens the tongue and turns its apex upward. The oblique fibers help turn the side margins up, leaving the back concave. The inferior longitudinal shortens the tongue, pushes the apex downward and leaves the dorsum convex. The vertical muscle flattens and extends the tongue, while the transverse muscle narrows and lengthens the body (Zemlin 1997).

Development and Clinical Application of Instruments to Measure Orofacial Structures 369

Posen (1972) measured maximum tongue force in subjects with and without problems in occlusion. The instrument was made of a gauge to give a reading of up to 50 N when pushing a spring that was attached to the gauge. At the other end of the spring, there was a concave piece where the tongue exerted force. Subjects with normal occlusion exerted forces

Dworkin (1980) measured tongue strength using one semiconductor strain gauge welded to a tubular stem for easy insertion into the mouth and a single channel pen-writing portable recording system. The force transducer could be positioned anteriorly between the upper and lower incisor teeth, or laterally, between the canine and first bicuspid teeth, and the subject was requested to bite down on the stem and apply tongue pressure against the transducer with the tongue tip. The maximum force exerted by normal subjects was 20 N

Scardella et al. (1993) measured tongue force using a force transducer that translated direct compression forces generated by the tongue into an active arm outside the mouth connected to a strain gauge with a linear response for forces between 50 gf and 100 gf, which was incorporated into a two-arm active bridge circuit. Five normal male subjects (ages 21 to 36) were evaluated. The maximum force ranged between 9.50 N and 16.33 N, with an average

Mortimore et al. (1999) used a transducer consisting of a machined nylon hand grip and a mouthpiece. The mouthpiece consisted of a 1-cm diameter nylon plate behind which was positioned a 6 kgf button load cell, which responded to tension and compression. Behind the plate, the mouthpiece consisted of a groove approximately 2-mm deep and 2-mm wide. Subjects were asked to rest their upper and lower incisor teeth against the groove in order for the transducer to reach steady state. The force was then exerted on the plate by the subject's tongue. The transducer was connected to a linear visual scale displaying the force in Newton (N) or as a percentage of the subject's maximum force (measured during a previous trial). Eighty-six females and eighty-one males aged between 42 and 62 years were evaluated. An

Bu Sha et al. (2000) measured tongue force using a custom-designed lingual force transducer housed in a piece of polyvinyl chloride tube. The tube was bisected lengthwise and a latex balloon catheter was mounted between the two halves of the tube and secured in place with dental impression material. The balloon was positioned so that when it was inflated with 4 mL of saline, it protruded 1.0 cm beyond the end of the tube. A 2-mm thick rubber sheath covered the end of the tube, providing the subject a soft, stable surface to bite when producing protrusion efforts. The sheath was marked at 0.5 cm intervals from the balloon end of the tube over a length of 4.0 cm. The balloon catheter was connected to a pressure transducer and the output was amplified, recorded and reconverted into force. The subject held the transducer in the mouth and bit down on the tube. With the tip of the tongue on the balloon, increasing or decreasing the depth of the transducer in the oral cavity increased or decreased the length of the tongue muscle fibers. The maximum measured force was 28.0 ±

A study was conducted with a device developed by the Biomechanical Engineering Group of UFMG named FORLING. It was composed of a piston-cylinder assembly attached to a double silicon protector and to a head that connected it to the cylinder. The oral protector was inserted

average maximum force of 26 ± 8 N for men and 20 ± 7 N for women was recorded.

2.0 N. Most subjects had a maximum force at a transducer position of 2.5 cm.

between 6 N and 25 N.

anteriorly and 16 N laterally.

maximum force of 12.67 ± 1.25 N.

Fig. 2. Intrinsic tongue muscles and genioglossus

Although the genioglossus muscle is considered the most powerful extrinsic lingual muscle (Zemlin 1997), in cases of a protruding tongue against a resistance, genioglossus activation plays an important role, but not a primary one. It actually provides a stable platform against which the intrinsic muscles of the tongue in the anterior part can develop strength (Pittman and Bailey 2009).

Both intrinsic and extrinsic tongue muscles are innervated by the hypoglossal nerve (cranial nerve XII) (Zemlin 1997); Douglas 2002), except the palatoglossus muscle, which is innervated by the glossopharyngeal (the ninth pair of cranial nerves) (Douglas 2002). As for sensitivity, the tongue presents refined taste activity, which results from the action of some nerves, such as the trigeminal nerve, which provides the overall sensitivity of the anterior two-thirds, the glossopharyngeal nerve, responsible for the overall sensitivity of the posterior third and the facial nerve, which is responsible for taste in the anterior two-thirds (Dangelo and Fattini 1998).

### **2.2 Instruments described in the literature to measure tongue force/pressure**

Kydd (1956) quantified tongue force of an edentulous 30-year-old man using a device composed of a denture base made of methyl methacrylate, whose vertical dimensions were maintained between the bases by four vertical rods embedded in the lower denture base. There were three blocks of methyl methacrylate between the rods, positioned to replace the lingual surface of the lower incisor area and second premolar-first molar areas. Electric resistance strain gauges were attached to these blocks. The pressure exerted by the tongue on the block produced a deformation on the gauge, modifying its resistance. An alternating current amplifier and a multichannel pen recorder were used to provide dynamic as well as static recordings. It was found that 23.13 N was the maximum force exerted anteriorly, and 11.56 N and 10.23 N laterally in the right and left lower first molar-second premolar areas, respectively.

Although the genioglossus muscle is considered the most powerful extrinsic lingual muscle (Zemlin 1997), in cases of a protruding tongue against a resistance, genioglossus activation plays an important role, but not a primary one. It actually provides a stable platform against which the intrinsic muscles of the tongue in the anterior part can develop strength (Pittman

Both intrinsic and extrinsic tongue muscles are innervated by the hypoglossal nerve (cranial nerve XII) (Zemlin 1997); Douglas 2002), except the palatoglossus muscle, which is innervated by the glossopharyngeal (the ninth pair of cranial nerves) (Douglas 2002). As for sensitivity, the tongue presents refined taste activity, which results from the action of some nerves, such as the trigeminal nerve, which provides the overall sensitivity of the anterior two-thirds, the glossopharyngeal nerve, responsible for the overall sensitivity of the posterior third and the facial nerve, which is responsible for taste in the anterior two-thirds

**2.2 Instruments described in the literature to measure tongue force/pressure** 

Kydd (1956) quantified tongue force of an edentulous 30-year-old man using a device composed of a denture base made of methyl methacrylate, whose vertical dimensions were maintained between the bases by four vertical rods embedded in the lower denture base. There were three blocks of methyl methacrylate between the rods, positioned to replace the lingual surface of the lower incisor area and second premolar-first molar areas. Electric resistance strain gauges were attached to these blocks. The pressure exerted by the tongue on the block produced a deformation on the gauge, modifying its resistance. An alternating current amplifier and a multichannel pen recorder were used to provide dynamic as well as static recordings. It was found that 23.13 N was the maximum force exerted anteriorly, and 11.56 N and 10.23 N laterally in the right and left lower first molar-second premolar areas,

Fig. 2. Intrinsic tongue muscles and genioglossus

and Bailey 2009).

respectively.

(Dangelo and Fattini 1998).

Posen (1972) measured maximum tongue force in subjects with and without problems in occlusion. The instrument was made of a gauge to give a reading of up to 50 N when pushing a spring that was attached to the gauge. At the other end of the spring, there was a concave piece where the tongue exerted force. Subjects with normal occlusion exerted forces between 6 N and 25 N.

Dworkin (1980) measured tongue strength using one semiconductor strain gauge welded to a tubular stem for easy insertion into the mouth and a single channel pen-writing portable recording system. The force transducer could be positioned anteriorly between the upper and lower incisor teeth, or laterally, between the canine and first bicuspid teeth, and the subject was requested to bite down on the stem and apply tongue pressure against the transducer with the tongue tip. The maximum force exerted by normal subjects was 20 N anteriorly and 16 N laterally.

Scardella et al. (1993) measured tongue force using a force transducer that translated direct compression forces generated by the tongue into an active arm outside the mouth connected to a strain gauge with a linear response for forces between 50 gf and 100 gf, which was incorporated into a two-arm active bridge circuit. Five normal male subjects (ages 21 to 36) were evaluated. The maximum force ranged between 9.50 N and 16.33 N, with an average maximum force of 12.67 ± 1.25 N.

Mortimore et al. (1999) used a transducer consisting of a machined nylon hand grip and a mouthpiece. The mouthpiece consisted of a 1-cm diameter nylon plate behind which was positioned a 6 kgf button load cell, which responded to tension and compression. Behind the plate, the mouthpiece consisted of a groove approximately 2-mm deep and 2-mm wide. Subjects were asked to rest their upper and lower incisor teeth against the groove in order for the transducer to reach steady state. The force was then exerted on the plate by the subject's tongue. The transducer was connected to a linear visual scale displaying the force in Newton (N) or as a percentage of the subject's maximum force (measured during a previous trial). Eighty-six females and eighty-one males aged between 42 and 62 years were evaluated. An average maximum force of 26 ± 8 N for men and 20 ± 7 N for women was recorded.

Bu Sha et al. (2000) measured tongue force using a custom-designed lingual force transducer housed in a piece of polyvinyl chloride tube. The tube was bisected lengthwise and a latex balloon catheter was mounted between the two halves of the tube and secured in place with dental impression material. The balloon was positioned so that when it was inflated with 4 mL of saline, it protruded 1.0 cm beyond the end of the tube. A 2-mm thick rubber sheath covered the end of the tube, providing the subject a soft, stable surface to bite when producing protrusion efforts. The sheath was marked at 0.5 cm intervals from the balloon end of the tube over a length of 4.0 cm. The balloon catheter was connected to a pressure transducer and the output was amplified, recorded and reconverted into force. The subject held the transducer in the mouth and bit down on the tube. With the tip of the tongue on the balloon, increasing or decreasing the depth of the transducer in the oral cavity increased or decreased the length of the tongue muscle fibers. The maximum measured force was 28.0 ± 2.0 N. Most subjects had a maximum force at a transducer position of 2.5 cm.

A study was conducted with a device developed by the Biomechanical Engineering Group of UFMG named FORLING. It was composed of a piston-cylinder assembly attached to a double silicon protector and to a head that connected it to the cylinder. The oral protector was inserted

Development and Clinical Application of Instruments to Measure Orofacial Structures 371

A study used the Iowa Oral Performance Instrument (IOPI) to measure tongue pressure of 39 young adults (17 men and 22 women). IOPI is a commercially available tongue pressure measurement system composed of an air-filled bulb connected to a pressure transducer. The bulb was placed in three different positions in the oral cavity, so that they could measure tongue protrusion, lateralization and elevation. In the last two positions, a blade was used to hold the bulb. Three measurements were made for each subject and the higher value was considered the maximum pressure. The average maximum tongue pressures found for all subjects were around 55 kPa for lateralization, 62 kPa for elevation and 65 kPa for

The Myometer 160 used by Lambrechts et al. (2010) contained a probe consisting of two plates that were screwed together on one side. On the other side (probe tip), the two plates could be pushed towards each other. The applied force was measured by an electronic device installed between the plates and shown on a bar graph. To measure tongue force, the patient placed the lips around the opening of the plate and protruded the tongue as hard as possible against the probe tip. Tongue pressure of 107 subjects (63 females and 44 males) between 7 and 45 years old were measured. The average tongue pressure was 1.66 N.

The prototype of the device developed by the Group of Biomechanics of UFMG for measuring the force of the tongue, Portable FORLING, has the following characteristics: good fixation and stability in the patient's mouth; portability; lightweight; low cost; simple operation; reliable indication of tongue force protrusion; a wide range of force; good repeatability; small size; immune to external influences (temperature or voltage fluctuation); comfortable for the

Portable FORLING is shown in Figure 3. It consists of two parts, one that goes in the mouth of the patient (where the sensor is located) and another for the data acquisition system.

patient; made of biocompatible material; resistant to crashes and easy to sanitize.

Fig. 3. Portable device for measuring the force of the tongue: Portable FORLING.

protrusion (Clark et al. 2009).

**2.3 Instrument proposed to measure tongue force** 

and fitted in the mouth of the patient, who was required to push the cylinder head with the tongue with the maximum force he could exert for 10 seconds. This procedure was repeated three times, with 1-minute intervals between them. The cylinder head hydraulically transmitted the produced force to a pressure sensor. The pressure sensor measurements were transmitted through a data acquisition device to a personal computer. The method was tested with four healthy subjects, two women and two men aged from 23 to 32 years. The obtained results for the maximum force were 25.7 N, 21.7 N, 21.6 N and 21.1 N, while those for the average force were 20.6 N, 18.2 N, 17.4 N and 18.6 N (Motta et al. 2004).

Another group measured tongue protrusion force using a force transducer (Grass FT10 Force Displacement Transducer) trapped in a vertical surface. The instrument had a piece that was to be placed in the oral cavity. This piece had a cushion for teeth positioning, which the subjects had to bite and press the tongue against a round 20-mm diameter button connected to the force transducer by a cylindrical steel beam of 5 mm diameter and 50 mm length. The button protruded 25 mm from the cushion inside the oral cavity. The maximum protrusion force in voluntary contraction was measured for 5 seconds and the percentage of the force related to maximum force was shown in an oscilloscope to provide visual feedback. The measurements were performed in 12 male subjects with an average age of 23 years, and the maximum obtained force was 24.3 ± 6.7 N (O'Connor et al. 2007).

The palatal plate developed by Kieser et al. (2008) was designed to simultaneously measure pressure at diverse locations in the mouth and was constructed from a chrome-cobalt alloy. To measure pressure during swallowing, an anterior pair of gauges measured lingual and labial contact against the left central incisor tooth, while two pairs of gauges measured pressure contributions of the lateral tongue margin and cheeks on the canine and first molar teeth. Finally, lingual pressure on the midline of the palate was measured by two gauges, one at the position of the premolars and one on the posterior boundary of the hard palate. The 8-channel output was gathered simultaneously and then recorded and displayed on a computer. They recorded intraoral pressures in five adult volunteers during swallowing of 10 mL of water. The pressure ranged from 13.05 kPa to 289.75 kPa.

Utanohara et al. (2008) used a tongue pressure measurement device consisting of a disposable oral probe, an infusion tube as a connector and a recording device. The probe was assembled with a small, partially inflated bulb made from medical grade latex, a plastic pipe as a connector and a syringe cylinder for the patient to hold on. A recording device with a manual autopressurization system was used. By pushing the pressurization button, the probe was inflated with air at an initial pressure of 19.6 kPa. This pressure was taken as the standard and measurements were performed after zero calibration. The subjects were asked to place the bulb in their mouth, holding the plastic pipe at the midpoint of their central incisors with closed lips, to raise the tongue and compress the bulb onto the palate with maximum voluntary effort, and the maximum value was recorded. Tongue pressure was measured in 843 subjects between 20 and 79 years old. The average maximum tongue pressure was 41.7 ± 9.7 kPa in subjects between 20 and 29; 41.9 ± 9.9 kPa (30 to 39 years old); 40.4 ± 9.8 kPa (40 to 49 years old); 40.7 ± 9.8 kPa (50 to 59 years old); 37.6 ± 8.8 kPa (60 to 69 years old) and 31.9 ± 8.9 kPa (70 to 79 years old).

Another study made with FORLING (Barroso et al. 2009) quantified tongue force of 10 subject aged between 14 and 80 years whose tongues were classified as normal or as having a small deficit in force and found average force values between 3.55 N and 13.24 N and maximum force values between 4.97 N and 19.96 N.

and fitted in the mouth of the patient, who was required to push the cylinder head with the tongue with the maximum force he could exert for 10 seconds. This procedure was repeated three times, with 1-minute intervals between them. The cylinder head hydraulically transmitted the produced force to a pressure sensor. The pressure sensor measurements were transmitted through a data acquisition device to a personal computer. The method was tested with four healthy subjects, two women and two men aged from 23 to 32 years. The obtained results for the maximum force were 25.7 N, 21.7 N, 21.6 N and 21.1 N, while those for the

Another group measured tongue protrusion force using a force transducer (Grass FT10 Force Displacement Transducer) trapped in a vertical surface. The instrument had a piece that was to be placed in the oral cavity. This piece had a cushion for teeth positioning, which the subjects had to bite and press the tongue against a round 20-mm diameter button connected to the force transducer by a cylindrical steel beam of 5 mm diameter and 50 mm length. The button protruded 25 mm from the cushion inside the oral cavity. The maximum protrusion force in voluntary contraction was measured for 5 seconds and the percentage of the force related to maximum force was shown in an oscilloscope to provide visual feedback. The measurements were performed in 12 male subjects with an average age of 23

The palatal plate developed by Kieser et al. (2008) was designed to simultaneously measure pressure at diverse locations in the mouth and was constructed from a chrome-cobalt alloy. To measure pressure during swallowing, an anterior pair of gauges measured lingual and labial contact against the left central incisor tooth, while two pairs of gauges measured pressure contributions of the lateral tongue margin and cheeks on the canine and first molar teeth. Finally, lingual pressure on the midline of the palate was measured by two gauges, one at the position of the premolars and one on the posterior boundary of the hard palate. The 8-channel output was gathered simultaneously and then recorded and displayed on a computer. They recorded intraoral pressures in five adult volunteers during swallowing of

Utanohara et al. (2008) used a tongue pressure measurement device consisting of a disposable oral probe, an infusion tube as a connector and a recording device. The probe was assembled with a small, partially inflated bulb made from medical grade latex, a plastic pipe as a connector and a syringe cylinder for the patient to hold on. A recording device with a manual autopressurization system was used. By pushing the pressurization button, the probe was inflated with air at an initial pressure of 19.6 kPa. This pressure was taken as the standard and measurements were performed after zero calibration. The subjects were asked to place the bulb in their mouth, holding the plastic pipe at the midpoint of their central incisors with closed lips, to raise the tongue and compress the bulb onto the palate with maximum voluntary effort, and the maximum value was recorded. Tongue pressure was measured in 843 subjects between 20 and 79 years old. The average maximum tongue pressure was 41.7 ± 9.7 kPa in subjects between 20 and 29; 41.9 ± 9.9 kPa (30 to 39 years old); 40.4 ± 9.8 kPa (40 to 49 years old); 40.7 ± 9.8 kPa (50 to 59 years old); 37.6 ± 8.8 kPa (60 to 69

Another study made with FORLING (Barroso et al. 2009) quantified tongue force of 10 subject aged between 14 and 80 years whose tongues were classified as normal or as having a small deficit in force and found average force values between 3.55 N and 13.24 N and

average force were 20.6 N, 18.2 N, 17.4 N and 18.6 N (Motta et al. 2004).

years, and the maximum obtained force was 24.3 ± 6.7 N (O'Connor et al. 2007).

10 mL of water. The pressure ranged from 13.05 kPa to 289.75 kPa.

years old) and 31.9 ± 8.9 kPa (70 to 79 years old).

maximum force values between 4.97 N and 19.96 N.

A study used the Iowa Oral Performance Instrument (IOPI) to measure tongue pressure of 39 young adults (17 men and 22 women). IOPI is a commercially available tongue pressure measurement system composed of an air-filled bulb connected to a pressure transducer. The bulb was placed in three different positions in the oral cavity, so that they could measure tongue protrusion, lateralization and elevation. In the last two positions, a blade was used to hold the bulb. Three measurements were made for each subject and the higher value was considered the maximum pressure. The average maximum tongue pressures found for all subjects were around 55 kPa for lateralization, 62 kPa for elevation and 65 kPa for protrusion (Clark et al. 2009).

The Myometer 160 used by Lambrechts et al. (2010) contained a probe consisting of two plates that were screwed together on one side. On the other side (probe tip), the two plates could be pushed towards each other. The applied force was measured by an electronic device installed between the plates and shown on a bar graph. To measure tongue force, the patient placed the lips around the opening of the plate and protruded the tongue as hard as possible against the probe tip. Tongue pressure of 107 subjects (63 females and 44 males) between 7 and 45 years old were measured. The average tongue pressure was 1.66 N.

## **2.3 Instrument proposed to measure tongue force**

The prototype of the device developed by the Group of Biomechanics of UFMG for measuring the force of the tongue, Portable FORLING, has the following characteristics: good fixation and stability in the patient's mouth; portability; lightweight; low cost; simple operation; reliable indication of tongue force protrusion; a wide range of force; good repeatability; small size; immune to external influences (temperature or voltage fluctuation); comfortable for the patient; made of biocompatible material; resistant to crashes and easy to sanitize.

Portable FORLING is shown in Figure 3. It consists of two parts, one that goes in the mouth of the patient (where the sensor is located) and another for the data acquisition system.

Fig. 3. Portable device for measuring the force of the tongue: Portable FORLING.

Development and Clinical Application of Instruments to Measure Orofacial Structures 373

FlexiForce sensors use technology based on resistivity. The application of a force in a sensitive area elicits a change in resistance of a sensing element inversely proportional to the

The sensors are encapsulated and their movements are restricted to prevent errors in the

To ensure accurate and repeatable readings of force, care has to be taken to assure that the applied load is evenly distributed in the sensitive area of the sensor and is not supported by

The signal conditioning is made using operational amplifiers for signal linearization and conversion of electrical resistance into electrical voltage. The signal goes through an amplification system to ensure the adequate quality of the result, since the data acquisition

The sampling rate is 10 Hz, ensuring compatibility with the characteristics of USB communication and is sufficient to obtain the desired information about tongue force.

Communication with the personal computer is controlled by software as well as the timing between the data and the computer, which is used as a monitoring system, storage system

The software was developed by one of the researchers at the Universidade Federal São João Del Rei, using a Matlab platform that allows the evaluator to conduct the evaluation process

At the end of three measurements, a report is generated that presents the force profile of the patient. This report records the graphics of force over time (profile) of the three

generated force signal. In addition, there is an adequate guide to the force applicator.

Fig. 5. FlexiForce Sensor (Tekscan) Model A201.

system is at a considerable distance from the measuring point. The data acquisition system is composed of three main modules:

applied force.

the external area.



control and data acquisition.

and store all relevant information.

The mouthguard consists of a commercially available double mouth protector used by boxers, with an anatomical shape composed of a biocompatible, nontoxic, lightweight and flexible material so as not to cause discomfort, and allows reuse. It is made of moldable material, acquiring the shape of dental arches, which makes it adaptable to patients with malocclusion.

The function of the mouthguard is to keep the device stable in the patient's mouth, so that the position of the force applicator plate is always the same for a given patient. It is also important to guarantee that the relative motion of the patient's body does not interfere with the force measurement. The dimensions of the mouthguard coincide with the teeth, length of dental arches and relationships between the positions of the tooth centers, as described in the literature (Wheeler and Major 1987; Silva and Pecora 1998; Proffit et al. 2007). The mouthguard has a cutout to accommodate the upper and lower lip frenulum and an opening in its front to accommodate the base piece.

There is a set of small pieces at the inner surface of the mouthguard, which consists of a base, a force sensor, an applicator pin, a holder and a force applicator. This set is positioned this way to absorb the force of protrusion of the tongue. All components of the prototype are biocompatible. The mouthguard and its internal parts are shown in Figure 4. The sensor is positioned between the base and pin applicator.

Fig. 4. Illustration of the mouthguard and its internal parts.

The inner parts of the mouthguard were made by stereolithography in epoxy, providing the required mechanical characteristics of stiffness and strength.

The prototype was designed to use small size, thinness, lightness, flexibility and low-cost force sensors, the FlexiForce type A201. A picture of the sensor used is shown in Figure 5.

Fig. 5. FlexiForce Sensor (Tekscan) Model A201.

FlexiForce sensors use technology based on resistivity. The application of a force in a sensitive area elicits a change in resistance of a sensing element inversely proportional to the applied force.

The sensors are encapsulated and their movements are restricted to prevent errors in the generated force signal. In addition, there is an adequate guide to the force applicator.

To ensure accurate and repeatable readings of force, care has to be taken to assure that the applied load is evenly distributed in the sensitive area of the sensor and is not supported by the external area.

The signal conditioning is made using operational amplifiers for signal linearization and conversion of electrical resistance into electrical voltage. The signal goes through an amplification system to ensure the adequate quality of the result, since the data acquisition system is at a considerable distance from the measuring point.

The data acquisition system is composed of three main modules:


372 Applied Biological Engineering – Principles and Practice

The mouthguard consists of a commercially available double mouth protector used by boxers, with an anatomical shape composed of a biocompatible, nontoxic, lightweight and flexible material so as not to cause discomfort, and allows reuse. It is made of moldable material, acquiring the shape of dental arches, which makes it adaptable to patients with

The function of the mouthguard is to keep the device stable in the patient's mouth, so that the position of the force applicator plate is always the same for a given patient. It is also important to guarantee that the relative motion of the patient's body does not interfere with the force measurement. The dimensions of the mouthguard coincide with the teeth, length of dental arches and relationships between the positions of the tooth centers, as described in the literature (Wheeler and Major 1987; Silva and Pecora 1998; Proffit et al. 2007). The mouthguard has a cutout to accommodate the upper and lower lip frenulum and an

There is a set of small pieces at the inner surface of the mouthguard, which consists of a base, a force sensor, an applicator pin, a holder and a force applicator. This set is positioned this way to absorb the force of protrusion of the tongue. All components of the prototype are biocompatible. The mouthguard and its internal parts are shown in Figure 4. The sensor is

The inner parts of the mouthguard were made by stereolithography in epoxy, providing the

The prototype was designed to use small size, thinness, lightness, flexibility and low-cost force sensors, the FlexiForce type A201. A picture of the sensor used is shown in Figure 5.

malocclusion.

opening in its front to accommodate the base piece.

positioned between the base and pin applicator.

Fig. 4. Illustration of the mouthguard and its internal parts.

required mechanical characteristics of stiffness and strength.


The sampling rate is 10 Hz, ensuring compatibility with the characteristics of USB communication and is sufficient to obtain the desired information about tongue force.

Communication with the personal computer is controlled by software as well as the timing between the data and the computer, which is used as a monitoring system, storage system control and data acquisition.

The software was developed by one of the researchers at the Universidade Federal São João Del Rei, using a Matlab platform that allows the evaluator to conduct the evaluation process and store all relevant information.

At the end of three measurements, a report is generated that presents the force profile of the patient. This report records the graphics of force over time (profile) of the three

Development and Clinical Application of Instruments to Measure Orofacial Structures 375

Since the inferior lip position depends on mandibular movements, this is the more mobile of the two and also the faster. Most of the facial expression muscles are inserted into the lips,

Another important function of the lips is to exert pressure on the teeth in the superior and inferior dental arch. The lips balance the force made by the tongue on teeth. Tongue muscles push the teeth outwards while the lips, when closed, provide resistance to that force, as their contraction presses teeth intraorally. This force balance allows dental elements to erupt and remain in the correct position in the oral cavity (Proffit and Fields 2002). The orbicularis oris together with other muscles act like a muscle strip, orienting growth of the jaws. When the lips are not sealed, there is no action of this muscle strip, possibly leading to some dysfunctions in jaw growth and teeth eruption (Gonzalez and

Dysfunctions in lip muscles can initiate important functional problems, one of which is speech distortion characterized chiefly by imprecision of the sounds that require orbicularis oris contraction (Farias et al. 1996). Another one is a dysfunction in feeding functions, like mastication and swallowing, in which the non-closure of the lips leads to difficulties in maintaining food in the oral cavity and generating negative intraoral pressure, which is

The first studies on lips force measurement are from the 1970s. Although the efforts to obtain a numerical value are valid, it is important to observe the agreement with clinical practice diagnosis. Garliner (1971) described the use of a dynamometer, which was adapted into a shirt button attached to a wire. An important question about that study, although it measured values of force, is that traction of the wire was made by the patient, which introduced a subjective element, since the applied force varied from patient to patient and did not allow the establishment of appropriate relationships between

Posen (1976) reported the development of a device to measure the force of the perioral muscles using a rigid rod and a small circular shaped insert. In this case, the patient was asked to position the lips surrounding this insert and impose traction with the head against the rod as hard as possible. The author evaluated 170 women and 166 men aged between 8 and 18 years with normal occlusion, and categorized the measurements carried out as follows: 160 g to 175 g for individuals with weak lips; 180 g to 195 g for individuals with slightly weak lips; 200 g to 215 g for those with moderate lips force; 220 g to 235 g for those with slightly increased lips force and 240 g to 260 g for individuals classified as having increased lips force. The subjective component was still considerable because head

A study aimed to determine whether advancing age could significantly interfere with the generation of oral forces. Forty women aged between 20 and 100 years were evaluated. For that, leverage force sensors coupled to the incisor teeth were used in both the upper and lower dental arches. The contraction time required for each examination was 5 seconds. Measurements were made during oral functions and maximum voluntary

which contribute to the great variability of labial movements (Zemlin 1997).

indispensable for correct food propulsion (Biazevic et al. 2010).

**3.2 Instruments described in the literature to measure lips force** 

Lopes 2000).

individuals.

movement was used in addition to the lips.

measurements taken, as well as the values of maximum and average forces of each measurement, the overall mean and standard deviation of these parameters.

## **3. Lips**

## **3.1 Anatomy and physiology of the lips**

The orbicularis oris muscle (Figure 6) is the facial muscle responsible for the lips shape and function. Its motor innervation is provided by the facial nerve and its sensitivity by the trigeminal nerve (Cosenza 2005). The orbicularis oris is elliptical, and consists of upper and lower fibers, which form the upper and lower lips that interact in the region of the labial commissure (Figun and Garino 2003). Each of those parts consists of pars peripheralis and pars marginalis segments. The pars marginalis fibers have narrow diameters and are localized in the vermilion area of the lip. When this pars contracts, it presses the lip to the maxillary teeth or inverts it, making the lip cover the incisal and occlusal borders of the teeth. The pars peripheralis consists of horizontal, oblique and longitudinal fibers and surrounds the pars previously described. Contraction of this pars results in labial elevation, an action involved in both facial expression and speech (Rogers et al. 2009).

Fig. 6. Orbucularis oris muscle and vermilion area

Lips contraction is essential for many oral functions as it produces closure of the mouth and is necessary in speech, food prehension and swallowing. Lips also participate in the actions of blowing, sucking, kissing and whistling (Figun and Garino 2003). In suction and swallowing, the sealing of the lips is necessary to promote intraoral pressure; in speech, lips work by interrupting the air flow, favoring the pronunciation of different phonemes such as /f/, /v/, /b/, /p/ and /m/ (Douglas 2002), or modifying the shape of the oral cavity, changing voice resonance and helping to produce the vowels.

measurements taken, as well as the values of maximum and average forces of each

The orbicularis oris muscle (Figure 6) is the facial muscle responsible for the lips shape and function. Its motor innervation is provided by the facial nerve and its sensitivity by the trigeminal nerve (Cosenza 2005). The orbicularis oris is elliptical, and consists of upper and lower fibers, which form the upper and lower lips that interact in the region of the labial commissure (Figun and Garino 2003). Each of those parts consists of pars peripheralis and pars marginalis segments. The pars marginalis fibers have narrow diameters and are localized in the vermilion area of the lip. When this pars contracts, it presses the lip to the maxillary teeth or inverts it, making the lip cover the incisal and occlusal borders of the teeth. The pars peripheralis consists of horizontal, oblique and longitudinal fibers and surrounds the pars previously described. Contraction of this pars results in labial elevation, an action involved in both facial expression and speech (Rogers

Lips contraction is essential for many oral functions as it produces closure of the mouth and is necessary in speech, food prehension and swallowing. Lips also participate in the actions of blowing, sucking, kissing and whistling (Figun and Garino 2003). In suction and swallowing, the sealing of the lips is necessary to promote intraoral pressure; in speech, lips work by interrupting the air flow, favoring the pronunciation of different phonemes such as /f/, /v/, /b/, /p/ and /m/ (Douglas 2002), or modifying the shape of the oral cavity,

measurement, the overall mean and standard deviation of these parameters.

**3. Lips** 

et al. 2009).

**3.1 Anatomy and physiology of the lips** 

Fig. 6. Orbucularis oris muscle and vermilion area

changing voice resonance and helping to produce the vowels.

Since the inferior lip position depends on mandibular movements, this is the more mobile of the two and also the faster. Most of the facial expression muscles are inserted into the lips, which contribute to the great variability of labial movements (Zemlin 1997).

Another important function of the lips is to exert pressure on the teeth in the superior and inferior dental arch. The lips balance the force made by the tongue on teeth. Tongue muscles push the teeth outwards while the lips, when closed, provide resistance to that force, as their contraction presses teeth intraorally. This force balance allows dental elements to erupt and remain in the correct position in the oral cavity (Proffit and Fields 2002). The orbicularis oris together with other muscles act like a muscle strip, orienting growth of the jaws. When the lips are not sealed, there is no action of this muscle strip, possibly leading to some dysfunctions in jaw growth and teeth eruption (Gonzalez and Lopes 2000).

Dysfunctions in lip muscles can initiate important functional problems, one of which is speech distortion characterized chiefly by imprecision of the sounds that require orbicularis oris contraction (Farias et al. 1996). Another one is a dysfunction in feeding functions, like mastication and swallowing, in which the non-closure of the lips leads to difficulties in maintaining food in the oral cavity and generating negative intraoral pressure, which is indispensable for correct food propulsion (Biazevic et al. 2010).

## **3.2 Instruments described in the literature to measure lips force**

The first studies on lips force measurement are from the 1970s. Although the efforts to obtain a numerical value are valid, it is important to observe the agreement with clinical practice diagnosis. Garliner (1971) described the use of a dynamometer, which was adapted into a shirt button attached to a wire. An important question about that study, although it measured values of force, is that traction of the wire was made by the patient, which introduced a subjective element, since the applied force varied from patient to patient and did not allow the establishment of appropriate relationships between individuals.

Posen (1976) reported the development of a device to measure the force of the perioral muscles using a rigid rod and a small circular shaped insert. In this case, the patient was asked to position the lips surrounding this insert and impose traction with the head against the rod as hard as possible. The author evaluated 170 women and 166 men aged between 8 and 18 years with normal occlusion, and categorized the measurements carried out as follows: 160 g to 175 g for individuals with weak lips; 180 g to 195 g for individuals with slightly weak lips; 200 g to 215 g for those with moderate lips force; 220 g to 235 g for those with slightly increased lips force and 240 g to 260 g for individuals classified as having increased lips force. The subjective component was still considerable because head movement was used in addition to the lips.

A study aimed to determine whether advancing age could significantly interfere with the generation of oral forces. Forty women aged between 20 and 100 years were evaluated. For that, leverage force sensors coupled to the incisor teeth were used in both the upper and lower dental arches. The contraction time required for each examination was 5 seconds. Measurements were made during oral functions and maximum voluntary

Development and Clinical Application of Instruments to Measure Orofacial Structures 377

The insert (Figure 8) has an elliptical shape with parabolic curvature and a lateral dimension of 60 mm. The manufacturing process was rapid prototyping using nontoxic polymers,

The insert is positioned as in the qualitative evaluation, leaving a gap between the lips and the dental arch, so that the patient can pull it with the lips (Figure 9), thereby generating a resistance force. This force is transmitted to the load cell by mechanical coupling, in this case, provided by a steel wire. The load cell has a capacity of 50 N, is electronically connected in bridge and generates an analog signal when pulled in traction. A head support is used to prevent the person from generating the force with the head instead of the lips.

Fig. 7. Portable device for measuring the force of the lips: FORLAB.

which follows the biosafety recommendations for use in human beings.

Fig. 8. Frontal (A) and lateral (B) view of the insert.

contraction of the lip muscles. The subjects were separated into subgroups according to their age. The mean values of maximal contraction of the upper lip were about 5.8 N for women aged 20 to 60 years, and 4.0 N for women between 80 to 100 years old. For the lower lip, these values ranged from 11.0 N for the first group and 10.0 N for the second. There were significantly higher strength values for the lower lip compared with the upper lip. However, little differences were observed between the subgroups (McHenry et al. 1999).

In the same way, two groups of researchers (Cantero et al. 2003 and Gonzalez et al. 2004) described a method of assessing lips force based on an instrument constructed using a dynamometer. A stainless steel plate was adapted into the dynamometer and the subjects could bite the plate, having a mouthguard as support that was sterilized after use. No further details were given about the methodology. The authors described three measurements for each subject and the analyzed parameter was the highest value of the three trials. In one of these studies, Cantero et al. (2003) evaluated lips force of 90 children before and after speech-language therapy. The measured force values significantly increased after orofacial myofunctional therapy, ranging from 1.68 N to 1.82 N before treatment and from 2.05 N to 2.34 N after treatment. Using the same methodology, another group (Gonzalez et al. 2004) evaluated 180 children between 5 and 12 years old, 90 with lip seal and another 90 with incompetent lip seal. Two measurements were made in children who had incompetent lip seal, one before and one after treatment. The results indicated force values ranging from 1.57 N to 2.15 N before treatment and 2.03 N to 2.72 N after treatment. Moreover, boys presented higher lips forces.

Another usual goal is the verification of malocclusion. Jung et al. (2003) evaluated 32 male students, who had Angle Class I and obtained an average force varying from 3.3 N to 13.1 N, while the maximum force ranged from 4.3 to 20.3 N. Earlier, Unemori and colleagues (1996) examined two individuals before and after orthognathic surgery and obtained force values ranging from 1.0 to 2.2 gf/mm2.

Hägg and Anniko (2008) recently conducted a retrospective study involving 30 subjects aged between 49 and 88 years who had suffered a stroke. They measured lips force using the Lip Force Meter (LF100). This instrument consists of a transducer that is placed between the lips and teeth and is attached to a steel wire, which is connected to a load cell. After acclimatization, the examiner held the instrument and asked the subjects to contract their lips in order to pull the wire. Lips strength evaluation and swallowing performance analyses were done. The evaluations were conducted pre and post myotheraphic intervention. The average lips force was 7 N before starting treatment and 18.5 N after the intervention and this correlation was statistically significant. An improvement in the ability of swallowing after therapeutic intervention was also observed.

#### **3.3 Instrument proposed to measure lips force**

The FORLAB lips measurement system (Figure 7) is composed of an intralips insert, against which the patient presses the lips to generate a counter-resistance force. This force is transmitted to the load cell, by mechanical coupling. The load cell generates an analog signal in tension that is treated, transmitted, processed and saved.

contraction of the lip muscles. The subjects were separated into subgroups according to their age. The mean values of maximal contraction of the upper lip were about 5.8 N for women aged 20 to 60 years, and 4.0 N for women between 80 to 100 years old. For the lower lip, these values ranged from 11.0 N for the first group and 10.0 N for the second. There were significantly higher strength values for the lower lip compared with the upper lip. However, little differences were observed between the subgroups (McHenry et al.

In the same way, two groups of researchers (Cantero et al. 2003 and Gonzalez et al. 2004) described a method of assessing lips force based on an instrument constructed using a dynamometer. A stainless steel plate was adapted into the dynamometer and the subjects could bite the plate, having a mouthguard as support that was sterilized after use. No further details were given about the methodology. The authors described three measurements for each subject and the analyzed parameter was the highest value of the three trials. In one of these studies, Cantero et al. (2003) evaluated lips force of 90 children before and after speech-language therapy. The measured force values significantly increased after orofacial myofunctional therapy, ranging from 1.68 N to 1.82 N before treatment and from 2.05 N to 2.34 N after treatment. Using the same methodology, another group (Gonzalez et al. 2004) evaluated 180 children between 5 and 12 years old, 90 with lip seal and another 90 with incompetent lip seal. Two measurements were made in children who had incompetent lip seal, one before and one after treatment. The results indicated force values ranging from 1.57 N to 2.15 N before treatment and 2.03 N to 2.72 N after treatment.

Another usual goal is the verification of malocclusion. Jung et al. (2003) evaluated 32 male students, who had Angle Class I and obtained an average force varying from 3.3 N to 13.1 N, while the maximum force ranged from 4.3 to 20.3 N. Earlier, Unemori and colleagues (1996) examined two individuals before and after orthognathic surgery and obtained force

Hägg and Anniko (2008) recently conducted a retrospective study involving 30 subjects aged between 49 and 88 years who had suffered a stroke. They measured lips force using the Lip Force Meter (LF100). This instrument consists of a transducer that is placed between the lips and teeth and is attached to a steel wire, which is connected to a load cell. After acclimatization, the examiner held the instrument and asked the subjects to contract their lips in order to pull the wire. Lips strength evaluation and swallowing performance analyses were done. The evaluations were conducted pre and post myotheraphic intervention. The average lips force was 7 N before starting treatment and 18.5 N after the intervention and this correlation was statistically significant. An improvement in the ability

The FORLAB lips measurement system (Figure 7) is composed of an intralips insert, against which the patient presses the lips to generate a counter-resistance force. This force is transmitted to the load cell, by mechanical coupling. The load cell generates an analog signal

1999).

Moreover, boys presented higher lips forces.

values ranging from 1.0 to 2.2 gf/mm2.

of swallowing after therapeutic intervention was also observed.

in tension that is treated, transmitted, processed and saved.

**3.3 Instrument proposed to measure lips force** 

Fig. 7. Portable device for measuring the force of the lips: FORLAB.

The insert (Figure 8) has an elliptical shape with parabolic curvature and a lateral dimension of 60 mm. The manufacturing process was rapid prototyping using nontoxic polymers, which follows the biosafety recommendations for use in human beings.

Fig. 8. Frontal (A) and lateral (B) view of the insert.

The insert is positioned as in the qualitative evaluation, leaving a gap between the lips and the dental arch, so that the patient can pull it with the lips (Figure 9), thereby generating a resistance force. This force is transmitted to the load cell by mechanical coupling, in this case, provided by a steel wire. The load cell has a capacity of 50 N, is electronically connected in bridge and generates an analog signal when pulled in traction. A head support is used to prevent the person from generating the force with the head instead of the lips.

Development and Clinical Application of Instruments to Measure Orofacial Structures 379

After qualitative analysis, the women classified as having normal force according to the judgment of two speech language pathologists were directed to a quantitative assessment of tongue or lips force. These structures were classified as having normal force when they were able to perform protrusion movements against strong resistance exerted by the blade

Ten women were randomly selected to participate in the tongue research using Portable FORLING, and ten women were selected to participate in the lips research using FORLAB. Measurements were made in a clinical room at the Speech-Language Pathology Ambulatory of the University. Participants were seated comfortably in an upright position and instructed to fit the device into the oral cavity with the help of the examiner. The patients had one minute for acclimatization before undergoing three consecutive trials, in which they performed isometric muscle contractions sustained for 10 seconds, the same period of time for the qualitative assessment. It is important to consider that a very long time of sustained maximal contraction can cause muscle fatigue and thereby compromise the results. One-minute time

The interval time for rest and the time for sustained force were controlled by software specially developed for each of the instruments and a beep indicated each of these steps. The

The results obtained by the clinical application of FORLING and FORLAB are presented below. The parameters analyzed were average force and maximum force obtained in the determined period of sustained muscle contraction. Information about data dispersion as standard deviation and coefficient of variation were also recorded. The strength profile of

There were notable differences in the curves of the force over the period of sustained contraction. The tongue's profile can be described as presenting an initial peak of force that gradually decreases. On the other hand, the analysis of data concerning lips force showed a profile characterized by little amount of variability over time and without any noticeable peaks. The decay in the lips' profile curve was slower than that of the tongue. The decay in the tongue/lips strength curve can be explained by physical causes such as muscle fatigue or

both structures was compared, as well as the stability characteristics.

Fig. 10. Qualitative evaluation of tongue (A) and lips (B) force.

intervals were given between trials to avoid fatigue.

sampling rate was 10 Hz.

**4.2 Results and discussion** 

and/or the finger and maintain the force without shaking and deformation.

Fig. 9. FORLAB in detail.

The transmission, processing and storage system was especially developed for this study. It is composed of a data acquisition board (Ontrak), an electronic coupling system and an IBM-PC personal computer. The measurement system interacts with the evaluator by a human-machine interface that uses high level programming language and is distributable in a Windows® platform. The stored signals are used to characterize the force profile of the subject. Besides the force x time curve (profile), it is possible to evaluate relevant typical points like maximum force, average force and variations that characterize the lips force of the subject.

## **4. Studies made with the proposed devices**

The initial studies accomplished using FORLING and FORLAB devices aimed to describe the characteristics of the tongue and lips in healthy subjects without any disturbance to the structures or functions of the oral sensorimotor system.

## **4.1 Methodology**

The studies were conducted with approval of the Human Ethics Committee from the Universidade Federal de Minas Gerais. The sample was composed of 20 young women aged between 21 and 33 years with no history of swallowing, respiratory or speech impairments. Moreover, they had no existing medical condition or medication use that could potentially influence orofacial performance or sensation, and no cognitive or intellectual dysfunction.

After providing their informed consent, the subjects first underwent a qualitative evaluation of tongue and lips force. In the qualitative evaluation of tongue force, the subjects had to press the tip of their tongue against the finger of the examiner and against a tongue blade for 10 seconds, with resistance provided by the examiner (Figure 10A). The qualitative evaluation of lips force was done by palpating the musculature at the resting position and in centric isometric contraction, as well as evaluating the strength of resistance against the finger of the examiner placed in the oral vestibule, also for 10 seconds (Figure 10B).

Fig. 10. Qualitative evaluation of tongue (A) and lips (B) force.

After qualitative analysis, the women classified as having normal force according to the judgment of two speech language pathologists were directed to a quantitative assessment of tongue or lips force. These structures were classified as having normal force when they were able to perform protrusion movements against strong resistance exerted by the blade and/or the finger and maintain the force without shaking and deformation.

Ten women were randomly selected to participate in the tongue research using Portable FORLING, and ten women were selected to participate in the lips research using FORLAB.

Measurements were made in a clinical room at the Speech-Language Pathology Ambulatory of the University. Participants were seated comfortably in an upright position and instructed to fit the device into the oral cavity with the help of the examiner. The patients had one minute for acclimatization before undergoing three consecutive trials, in which they performed isometric muscle contractions sustained for 10 seconds, the same period of time for the qualitative assessment. It is important to consider that a very long time of sustained maximal contraction can cause muscle fatigue and thereby compromise the results. One-minute time intervals were given between trials to avoid fatigue.

The interval time for rest and the time for sustained force were controlled by software specially developed for each of the instruments and a beep indicated each of these steps. The sampling rate was 10 Hz.

### **4.2 Results and discussion**

378 Applied Biological Engineering – Principles and Practice

The transmission, processing and storage system was especially developed for this study. It is composed of a data acquisition board (Ontrak), an electronic coupling system and an IBM-PC personal computer. The measurement system interacts with the evaluator by a human-machine interface that uses high level programming language and is distributable in a Windows® platform. The stored signals are used to characterize the force profile of the subject. Besides the force x time curve (profile), it is possible to evaluate relevant typical points like maximum force, average force and variations that characterize the lips force of

The initial studies accomplished using FORLING and FORLAB devices aimed to describe the characteristics of the tongue and lips in healthy subjects without any disturbance to the

The studies were conducted with approval of the Human Ethics Committee from the Universidade Federal de Minas Gerais. The sample was composed of 20 young women aged between 21 and 33 years with no history of swallowing, respiratory or speech impairments. Moreover, they had no existing medical condition or medication use that could potentially influence orofacial performance or sensation, and no cognitive or

After providing their informed consent, the subjects first underwent a qualitative evaluation of tongue and lips force. In the qualitative evaluation of tongue force, the subjects had to press the tip of their tongue against the finger of the examiner and against a tongue blade for 10 seconds, with resistance provided by the examiner (Figure 10A). The qualitative evaluation of lips force was done by palpating the musculature at the resting position and in centric isometric contraction, as well as evaluating the strength of resistance against the finger of the examiner placed in the oral vestibule, also for 10

Fig. 9. FORLAB in detail.

**4. Studies made with the proposed devices** 

structures or functions of the oral sensorimotor system.

the subject.

**4.1 Methodology** 

intellectual dysfunction.

seconds (Figure 10B).

The results obtained by the clinical application of FORLING and FORLAB are presented below. The parameters analyzed were average force and maximum force obtained in the determined period of sustained muscle contraction. Information about data dispersion as standard deviation and coefficient of variation were also recorded. The strength profile of both structures was compared, as well as the stability characteristics.

There were notable differences in the curves of the force over the period of sustained contraction. The tongue's profile can be described as presenting an initial peak of force that gradually decreases. On the other hand, the analysis of data concerning lips force showed a profile characterized by little amount of variability over time and without any noticeable peaks. The decay in the lips' profile curve was slower than that of the tongue. The decay in the tongue/lips strength curve can be explained by physical causes such as muscle fatigue or

Development and Clinical Application of Instruments to Measure Orofacial Structures 381

Average force (N)

 Tongue 12.3 2.2 17.84 Tongue 7.8 1.9 24.27 Tongue 18.0 1.6 9.00 Tongue 11.6 2.3 19.88 Tongue 10.6 1.5 14.27 Tongue 5.8 1.8 30.24 Tongue 11.0 1.8 16.47 Tongue 20.5 3.0 14.74 Tongue 18.7 1.4 7.26 Tongue 13.6 2.6 18.97 Lips 13.2 1.0 7.68 Lips 7.5 0.4 4.85 Lips 7.0 0.4 5.45 Lips 12.5 0.9 6.95 Lips 5.8 1.0 17.65 Lips 10.2 0.6 5.67 Lips 9.1 0.5 5.99 Lips 8.3 0.8 9.91 Lips 7.5 0.6 7.80 Lips 12.2 0.3 2.47

Table 2. Measurements of central tendency and dispersion of force values obtained in Trial 1.

Average force (N)

 Tongue 16.4 2.0 12.18 Tongue 11.8 2.0 16.79 Tongue 19.8 2.6 13.06 Tongue 12.6 2.8 22.46 Tongue 11.2 1.5 13.58 Tongue 7.7 2.6 33.16 Tongue 9.9 1.0 9.86 Tongue 16.4 4.2 25.32 Tongue 18.5 1.7 9.10 Tongue 14.9 2.4 16.39 Lips 14.4 1.5 10.67 Lips 7.2 0.7 9.75 Lips 7.7 0.5 6.47 Lips 10.6 1.1 10.09 Lips 8.7 0.9 10.55 Lips 10.9 0.7 6.36 Lips 8.2 0.8 9.38 Lips 10.2 1.4 13.53 Lips 8.2 0.5 5.76 Lips 11.0 0.4 4.16

Table 3. Measurements of central tendency and dispersion of force values obtained in Trial 2.

Standard deviation

Standard deviation Coefficient of variation (%)

Coefficient of variation (%)

Participant Structure

Participant Structure

evaluated

N = Newton.

N = Newton.

evaluated

motivational causes such as mental fatigue and lack of interest. Figure 11 shows typical curves obtained from the quantitative evaluations of the tongue and lips.

Fig. 11. Profile of the tongue and lips force over time.

The tongue force was higher than that of the lips, in the analysis of both average force and maximum force. Table 1 presents the results of the trials. It was verified that both parameters increased over successive trials, indicating that there is a learning effect.


N = Newton; SD= Standard Deviation.

Table 1. Maximum force and average force of tongue and lips.

For the analysis of stability, the coefficient of variation (CV) was used, which is a dimensionless value that provides information about the homogeneity of the results. CV is the result of the division of the standard deviation by the average value, involving data from the same series. The lower the magnitude of CV, the greater is the uniformity of results. A CV lower than 10% was considered low, between 10 and 20 % was considered medium, between 20 and 30% was high and above 30% was thought of as very high.

Tables 2, 3 and 4 present the average force values and the analysis of dispersion of these values for each participant in trials 1, 2 and 3, respectively.

The average tongue force had a high CV compared to lips force, which were classified as low or medium. This can be explained by the characteristics of each of these structures, since the tongue is composed of a set of muscles that contract in a coordinated way, while the lips comprise only one muscle. In an attempt to keep the contraction over ten seconds, the participants exerted peaks of force interspersed with regions of decay in the force measured by Portable FORLING, while FORLAB showed a more stable signal.


N = Newton.

380 Applied Biological Engineering – Principles and Practice

motivational causes such as mental fatigue and lack of interest. Figure 11 shows typical curves

The tongue force was higher than that of the lips, in the analysis of both average force and maximum force. Table 1 presents the results of the trials. It was verified that both

TONGUE LIPS

Maximum Force (N) 19.9 21.9 22.5 10.6 11.1 11.1 Maximum force SD 5.5 6.7 5.6 2.5 2.4 2.7 Average Force (N) 15.8 16.9 17.0 9.3 9.0 9.3 Average Force SD 4.9 6.1 4.6 2.6 2.5 2.4

For the analysis of stability, the coefficient of variation (CV) was used, which is a dimensionless value that provides information about the homogeneity of the results. CV is the result of the division of the standard deviation by the average value, involving data from the same series. The lower the magnitude of CV, the greater is the uniformity of results. A CV lower than 10% was considered low, between 10 and 20 % was considered medium,

Tables 2, 3 and 4 present the average force values and the analysis of dispersion of these

The average tongue force had a high CV compared to lips force, which were classified as low or medium. This can be explained by the characteristics of each of these structures, since the tongue is composed of a set of muscles that contract in a coordinated way, while the lips comprise only one muscle. In an attempt to keep the contraction over ten seconds, the participants exerted peaks of force interspersed with regions of decay in the force measured

Trial 1 Trial 2 Trial 3 Trial 1 Trial 2 Trial 3

parameters increased over successive trials, indicating that there is a learning effect.

obtained from the quantitative evaluations of the tongue and lips.

Fig. 11. Profile of the tongue and lips force over time.

Table 1. Maximum force and average force of tongue and lips.

values for each participant in trials 1, 2 and 3, respectively.

by Portable FORLING, while FORLAB showed a more stable signal.

between 20 and 30% was high and above 30% was thought of as very high.

N = Newton; SD= Standard Deviation.

Table 2. Measurements of central tendency and dispersion of force values obtained in Trial 1.


N = Newton.

Table 3. Measurements of central tendency and dispersion of force values obtained in Trial 2.

Development and Clinical Application of Instruments to Measure Orofacial Structures 383

protrusion force can indicate the ability to exert forces in other directions, as shown by some authors (Dworkin and Aronson 1986). In their study about tongue force in the anterior and lateral directions, the results indicated that subjects presenting higher force values in one direction also did so in the other directions, and the same happened to those who showed lower forces. However, the main reason for choosing protrusion force was that it is the force direction usually evaluated by speech pathologists in clinical assessment. Thus, it is possible to establish comparisons between the qualitative and quantitative evaluations. Similarly, the quantitative evaluation of lips has the same principle as that of the qualitative assessment.

> F max T1 (N)

 Tongue 16.1 19.8 19.7 Tongue 11.4 15.0 18.1 Tongue 20.7 23.8 21.9 Tongue 15.0 17.5 18.8 Tongue 13.7 15.0 14.2 Tongue 11.1 12.3 13.2 Tongue 14.2 12.3 16.0 Tongue 26.1 23.3 25.6 Tongue 22.4 23.1 23.6 Tongue 17.2 19.3 19.1 Lips 14.5 16.1 16.0 Lips 8.1 8.7 9.7 Lips 8.1 9.1 8.4 Lips 14.0 13.0 14.2 Lips 8.0 10.2 7.9 Lips 11.6 12.2 11.3 Lips 9.9 10.1 12.1 Lips 9.9 13.2 9.4 Lips 8.7 9.2 9.0 Lips 12.8 12.3 12.3

Data obtained in this research was compared to other studies that used the same assessment direction in maximum voluntary contraction (Kydd 1956; Posen 1972; Dworkin et al. 1980, Mortimore et al. 1999; Motta et al. 2004; Barroso et al. 2009; Lambrechts et al. 2010). The values obtained in this research were similar to the ones achieved by Kydd (1956) (maximum force: 23.13 N), Posen (1972) (maximum force between 6 N and 25 N), Dworkin et al. (1980) (maximum force was 32.9 N for men and 27.5 N for women), Mortimore et al. (1999) (maximum force: 26± 8N for males and 20± 7N for females), and Motta et al. (2004) (maximum force between 21.1 N and 25.7 N and average force between 17.4 N and 20.6 N), and higher than those obtained by Barroso et al. (2009) (average force between 3.55 N and 13.24 N) and by Lambrechts et al. (2010) (average force 1.66± 0.06 N). However, in the study by Barroso et al. (2009), the sample was composed of subjects with tongue strength classified as normal or slightly reduced in the qualitative assessment, which probably resulted in lower tongue force values, combined with the fact that the age range of the sample included

F max T2 (N)

F max T3 (N)

Participant Structure

evaluated

F max= Maximum force; N= Newton ; T1= Trial 1; T2= Trial 2; T3= Trial 3.

Table 5. Maximum force in each trial.


N = Newton.

Table 4. Measurements of central tendency and dispersion of force values obtained in Trial 3.

The variability of the signals is due to the complexity of the biological systems. According to Gill (1987) as cited in Judice et al. (1999), a lot of biological characteristics have a CV between 5 and 50%. The wide variation in the amplitude of lingual force values has also been reported by others (Frohlich et al. 1990; Robinovitch et al. 1991). Robinovitch et al. (1991) also attributed tongue slippage and neural-based fluctuations in causing this variation.

By analyzing the values of maximum force (Table 5), it is noteworthy that 90% of the participants showed higher values in Tests 2 and 3. Therefore, the learning factor can be a reasonable explanation for these results.

Many instruments have been developed to quantify tongue force using different technologies, such as dynamometers (Posen 1972; Trawitzki et al. 2010), bulbs (Bu Sha et al. 2000; Hayashi et al. 2002; Clark et al. 2003; Ball et al. 2006; Utanohara et al. 2008), palatal plates (Hori et al. 2006; Hewitt et al. 2008; Kieser et al. 2008), strain gauges (Kydd 1956; Sanders 1968; Dworkin 1980; Robinovitch et al. 1991; Scardella et al. 1993) and others. Each one has its advantages and disadvantages and can measure maximum tongue force in a different direction and sometimes force during function.

Portable FORLING measures tongue protrusion force. It is believed that from the measurement of the ability of the individual to exert a horizontal force towards the outside of the oral cavity (protrusion force), it is eventually possible to infer about the capacity of the tongue to perform other tasks (Motta et al. 2004). This is because the muscles involved in tongue protrusion, the genioglossus and intrinsic tongue muscles, also act during functions of mastication, swallowing and speech among others. Furthermore, the ability to exert

Average force (N)

1 Tongue 14.8 2.6 17.68 2 Tongue 14.2 2.5 17.49 3 Tongue 18.5 1.6 8.58 4 Tongue 12.8 3.5 27.00 5 Tongue 11 1.7 15.06 6 Tongue 9.6 2.4 24.90 7 Tongue 12.6 1.7 13.42 8 Tongue 18.4 3.7 19.91 9 Tongue 18.1 2.3 12.49 10 Tongue 13.4 3.1 22.95 11 Lips 14.7 1.3 9.24 12 Lips 9.0 0.4 4.74 13 Lips 7.3 0.5 6.30 14 Lips 11.7 2.2 18.51 15 Lips 7.1 0.4 5.17 16 Lips 9.8 1.8 17.99 17 Lips 9.5 1.4 14.45 18 Lips 7.4 1.0 13.56 19 Lips 7.5 0.6 8.17 20 Lips 8.8 0.5 5.57

Table 4. Measurements of central tendency and dispersion of force values obtained in Trial 3.

The variability of the signals is due to the complexity of the biological systems. According to Gill (1987) as cited in Judice et al. (1999), a lot of biological characteristics have a CV between 5 and 50%. The wide variation in the amplitude of lingual force values has also been reported by others (Frohlich et al. 1990; Robinovitch et al. 1991). Robinovitch et al. (1991) also attributed tongue slippage and neural-based fluctuations in causing this variation.

By analyzing the values of maximum force (Table 5), it is noteworthy that 90% of the participants showed higher values in Tests 2 and 3. Therefore, the learning factor can be a

Many instruments have been developed to quantify tongue force using different technologies, such as dynamometers (Posen 1972; Trawitzki et al. 2010), bulbs (Bu Sha et al. 2000; Hayashi et al. 2002; Clark et al. 2003; Ball et al. 2006; Utanohara et al. 2008), palatal plates (Hori et al. 2006; Hewitt et al. 2008; Kieser et al. 2008), strain gauges (Kydd 1956; Sanders 1968; Dworkin 1980; Robinovitch et al. 1991; Scardella et al. 1993) and others. Each one has its advantages and disadvantages and can measure maximum tongue force in a

Portable FORLING measures tongue protrusion force. It is believed that from the measurement of the ability of the individual to exert a horizontal force towards the outside of the oral cavity (protrusion force), it is eventually possible to infer about the capacity of the tongue to perform other tasks (Motta et al. 2004). This is because the muscles involved in tongue protrusion, the genioglossus and intrinsic tongue muscles, also act during functions of mastication, swallowing and speech among others. Furthermore, the ability to exert

Standard deviation Coefficient of variation (%)

Participant Structure

N = Newton.

reasonable explanation for these results.

different direction and sometimes force during function.

evaluated

protrusion force can indicate the ability to exert forces in other directions, as shown by some authors (Dworkin and Aronson 1986). In their study about tongue force in the anterior and lateral directions, the results indicated that subjects presenting higher force values in one direction also did so in the other directions, and the same happened to those who showed lower forces. However, the main reason for choosing protrusion force was that it is the force direction usually evaluated by speech pathologists in clinical assessment. Thus, it is possible to establish comparisons between the qualitative and quantitative evaluations. Similarly, the quantitative evaluation of lips has the same principle as that of the qualitative assessment.


F max= Maximum force; N= Newton ; T1= Trial 1; T2= Trial 2; T3= Trial 3.

Table 5. Maximum force in each trial.

Data obtained in this research was compared to other studies that used the same assessment direction in maximum voluntary contraction (Kydd 1956; Posen 1972; Dworkin et al. 1980, Mortimore et al. 1999; Motta et al. 2004; Barroso et al. 2009; Lambrechts et al. 2010). The values obtained in this research were similar to the ones achieved by Kydd (1956) (maximum force: 23.13 N), Posen (1972) (maximum force between 6 N and 25 N), Dworkin et al. (1980) (maximum force was 32.9 N for men and 27.5 N for women), Mortimore et al. (1999) (maximum force: 26± 8N for males and 20± 7N for females), and Motta et al. (2004) (maximum force between 21.1 N and 25.7 N and average force between 17.4 N and 20.6 N), and higher than those obtained by Barroso et al. (2009) (average force between 3.55 N and 13.24 N) and by Lambrechts et al. (2010) (average force 1.66± 0.06 N). However, in the study by Barroso et al. (2009), the sample was composed of subjects with tongue strength classified as normal or slightly reduced in the qualitative assessment, which probably resulted in lower tongue force values, combined with the fact that the age range of the sample included

Development and Clinical Application of Instruments to Measure Orofacial Structures 385

resistance). This makes comparisons between the two assessments (qualitative and quantitative) possible and consistent. All the subjects analyzed in this study presented normal tongue strength. Future studies are being planned to compare alterations in clinical

Considering the clinical application of FORLAB, some difficulties were found, such as the standardization of the distance between the insert and the frontal teeth, and the correct positioning of the steel wire (mechanic coupling). The distance to the position of the insert was measured subjectively from the region the insert touched the teeth. The traction made by the evaluator caused a displacement of 10 mm, generating a slight projection of the lips. To allow correct mechanical coupling, the wire positioning was also made subjectively. The evaluator adjusted the system parts so that the wire would be as strained as possible. These problems can be solved by substituting the steel wire for a rigid mechanical coupling, like a metal rod, and the marking of a point that allows the visualization of the distance between the teeth and the insert. A new version of this instrument is in development to resolve these

In both instruments, intra-subject analysis presented more significant results, since evaluating biological systems involves the consideration of many particularities and peculiarities. Thus, the quantitative analysis of tongue and lips force can be an efficient

More research is needed in the Biomechanics area, especially related to orofacial structures. The Biomechanics Engineering Group is already developing a new version of FORLAB, which will be portable like Portable FORLING, and will eliminate most of the restrictions associated to the first version. The portable FORLAB will also be able to detect differences in force generated by each side of the orbicular oris muscle which is especially important in the

Next studies in tongue and lips force will explore other parameters beyond maximum and average force: the average force application rate, which is the speed that the force reaches the higher peak, and the area under the graphic, which is related to the energy dissipated during the task. These parameters are also important to characterize tongue and lips force profile and they need to be investigated in a high number of individuals with different

Cheeks form the lateral boundary of the buccal cavity, and display continuity with the lips. They participate, together with the tongue, in the acts of suction, swallowing and mastication. A device to measure cheeks force is also being developed in collaboration with UFRGS (Universidade Federal do Rio Grande do Sul), a university in the Brazilian city of Porto Alegre. It is being based in the same principles of trying to represent the current evaluation technique, proving reliable results and a safe and portable basis. Other devices under development involve gadgets to train and rehabilitate tongue, cheek and lip forces. These developments show an important potential, as they intend to allow pathologists to be sure of how much load the patient is training with, and to make possible to alter the clinical procedure when required, fixing the ideal force value to be used in training as well as the

classifications of force, in order to create standard values for each of these groups.

assessment (diminished or enhanced force) with numerical values.

instrument in comparing the changes in a patient during therapy.

problems.

**5. Future direction** 

evaluation of patients with facial palsy.

individuals older than 60 years. According to Crow and Ship (1996), a reduction in muscle mass happens after 60 years of age due to atrophy and loss of motor neurons. Lambrechts et al. (2010) included children, who had lower tongue strength than adults due to their stage of developmental maturation in muscle morphology and the central nervous system (Potter et al. 2009; Potter and Short 2009). Moreover, the authors did not provide information about the qualitative evaluation of their participants.

It can be argued that several problems are encountered in the process of measuring the strength of the oral structures, such as lips and tongue. This is because they are structures within the complex biological orafacial system, susceptible to environmental, behavioral and anatomical changes. Therefore, as stressed by Ingervall and Janson (1981), assessing the strength of the lips in a quantitative way is not an easy task. There are different methodological approaches for assessing labial force as presented in the literature. Most of these studies have generated a solution by adapting dynamometers (Garliner 1971; Posen 1976; Ingervall and Janson 1981; Thuer and Ingerval 1990; Cantero et al. 2003; Gonzalez et al. 2004). The disadvantage of this line of instrumentation is the need for a person to conduct stabilization or move the traction device pulling the lips, in order to measure the strength of this structure. This introduces subjective components into the process, since each professional will act slightly differently when supporting the instrument. Moreover, the possibility of evaluating different directions of lip contractions makes comparison between the findings of different studies unreliable. Some researchers have sought to evaluate the lip closing force from the closing of a plate positioned horizontally between the upper and lower lips (Jung et al. 2010). When using this instrument, great attention should be given to controlling the action of compensatory muscles, such as the mentalis. Other assessing instruments reported in the literature use force or pressure lip sensors attached to the teeth (Gentil and Tournier 1998; McHenry et al. 1999; Ruan et al. 2007). These electrodes are fixed by special glues or dental adhesive. The disadvantage of these instruments is the difficulty in accommodating the idealized electrodes at points and in the positioning of the electrodes for comparative reassessments. The ultimate goal of researchers using sensors supported on the teeth is to assess the action of these muscles on the correct teeth positioning as well as studying the balance of power between the lips and tongue. A study in the literature (Hägg and Anniko 2008) evaluated the lip force of contraction in the same way as that proposed by the FORLAB report, but with a population of patients who had suffered a stroke. Considering the results obtained by the authors after the process of force lip rehabilitation, higher average values (18.5 N) were observed when compared to those obtained in the measurements performed with FORLAB. It is important to consider that a muscle group exposed to specific training will gain strength in a manner that can also generate greater force against resistance. It is believed that even subjects without functional complaints and with adequate lip strength during qualitative assessment, like the subjects evaluated with FORLAB, can increase their capacity of generating force after being submitted to muscular training.

It is known that clinical evaluation, which is considered subjective as it does not quantify the force values and depends on the clinical experience of the evaluator, is the reference assessment for professionals in this area. The proposal is to develop instruments that can help this assessment by offering quantitative data. The presented systems follow the same principles as those of clinical evaluation, analyzing the same type of force (counterresistance). This makes comparisons between the two assessments (qualitative and quantitative) possible and consistent. All the subjects analyzed in this study presented normal tongue strength. Future studies are being planned to compare alterations in clinical assessment (diminished or enhanced force) with numerical values.

Considering the clinical application of FORLAB, some difficulties were found, such as the standardization of the distance between the insert and the frontal teeth, and the correct positioning of the steel wire (mechanic coupling). The distance to the position of the insert was measured subjectively from the region the insert touched the teeth. The traction made by the evaluator caused a displacement of 10 mm, generating a slight projection of the lips. To allow correct mechanical coupling, the wire positioning was also made subjectively. The evaluator adjusted the system parts so that the wire would be as strained as possible. These problems can be solved by substituting the steel wire for a rigid mechanical coupling, like a metal rod, and the marking of a point that allows the visualization of the distance between the teeth and the insert. A new version of this instrument is in development to resolve these problems.

In both instruments, intra-subject analysis presented more significant results, since evaluating biological systems involves the consideration of many particularities and peculiarities. Thus, the quantitative analysis of tongue and lips force can be an efficient instrument in comparing the changes in a patient during therapy.

## **5. Future direction**

384 Applied Biological Engineering – Principles and Practice

individuals older than 60 years. According to Crow and Ship (1996), a reduction in muscle mass happens after 60 years of age due to atrophy and loss of motor neurons. Lambrechts et al. (2010) included children, who had lower tongue strength than adults due to their stage of developmental maturation in muscle morphology and the central nervous system (Potter et al. 2009; Potter and Short 2009). Moreover, the authors did not provide information about

It can be argued that several problems are encountered in the process of measuring the strength of the oral structures, such as lips and tongue. This is because they are structures within the complex biological orafacial system, susceptible to environmental, behavioral and anatomical changes. Therefore, as stressed by Ingervall and Janson (1981), assessing the strength of the lips in a quantitative way is not an easy task. There are different methodological approaches for assessing labial force as presented in the literature. Most of these studies have generated a solution by adapting dynamometers (Garliner 1971; Posen 1976; Ingervall and Janson 1981; Thuer and Ingerval 1990; Cantero et al. 2003; Gonzalez et al. 2004). The disadvantage of this line of instrumentation is the need for a person to conduct stabilization or move the traction device pulling the lips, in order to measure the strength of this structure. This introduces subjective components into the process, since each professional will act slightly differently when supporting the instrument. Moreover, the possibility of evaluating different directions of lip contractions makes comparison between the findings of different studies unreliable. Some researchers have sought to evaluate the lip closing force from the closing of a plate positioned horizontally between the upper and lower lips (Jung et al. 2010). When using this instrument, great attention should be given to controlling the action of compensatory muscles, such as the mentalis. Other assessing instruments reported in the literature use force or pressure lip sensors attached to the teeth (Gentil and Tournier 1998; McHenry et al. 1999; Ruan et al. 2007). These electrodes are fixed by special glues or dental adhesive. The disadvantage of these instruments is the difficulty in accommodating the idealized electrodes at points and in the positioning of the electrodes for comparative reassessments. The ultimate goal of researchers using sensors supported on the teeth is to assess the action of these muscles on the correct teeth positioning as well as studying the balance of power between the lips and tongue. A study in the literature (Hägg and Anniko 2008) evaluated the lip force of contraction in the same way as that proposed by the FORLAB report, but with a population of patients who had suffered a stroke. Considering the results obtained by the authors after the process of force lip rehabilitation, higher average values (18.5 N) were observed when compared to those obtained in the measurements performed with FORLAB. It is important to consider that a muscle group exposed to specific training will gain strength in a manner that can also generate greater force against resistance. It is believed that even subjects without functional complaints and with adequate lip strength during qualitative assessment, like the subjects evaluated with FORLAB, can increase their capacity of generating force after being submitted to muscular

It is known that clinical evaluation, which is considered subjective as it does not quantify the force values and depends on the clinical experience of the evaluator, is the reference assessment for professionals in this area. The proposal is to develop instruments that can help this assessment by offering quantitative data. The presented systems follow the same principles as those of clinical evaluation, analyzing the same type of force (counter-

the qualitative evaluation of their participants.

training.

More research is needed in the Biomechanics area, especially related to orofacial structures. The Biomechanics Engineering Group is already developing a new version of FORLAB, which will be portable like Portable FORLING, and will eliminate most of the restrictions associated to the first version. The portable FORLAB will also be able to detect differences in force generated by each side of the orbicular oris muscle which is especially important in the evaluation of patients with facial palsy.

Next studies in tongue and lips force will explore other parameters beyond maximum and average force: the average force application rate, which is the speed that the force reaches the higher peak, and the area under the graphic, which is related to the energy dissipated during the task. These parameters are also important to characterize tongue and lips force profile and they need to be investigated in a high number of individuals with different classifications of force, in order to create standard values for each of these groups.

Cheeks form the lateral boundary of the buccal cavity, and display continuity with the lips. They participate, together with the tongue, in the acts of suction, swallowing and mastication. A device to measure cheeks force is also being developed in collaboration with UFRGS (Universidade Federal do Rio Grande do Sul), a university in the Brazilian city of Porto Alegre. It is being based in the same principles of trying to represent the current evaluation technique, proving reliable results and a safe and portable basis. Other devices under development involve gadgets to train and rehabilitate tongue, cheek and lip forces.

These developments show an important potential, as they intend to allow pathologists to be sure of how much load the patient is training with, and to make possible to alter the clinical procedure when required, fixing the ideal force value to be used in training as well as the

Development and Clinical Application of Instruments to Measure Orofacial Structures 387

Biazevic, Maria, José Antunes, Janina Togni, Fabiana Andrade, Marcos Carvalho, and Victor

Bu Sha, Brett, Sandra England, Richard Parisi, and Richard Strobel. 2000. "Force Production

Cantero, Luis, Brismayda Gonzalez, and Mariela Fernandez. 2003. "La Fuerza Labial

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duration and the number of exercise series. It will also be possible to make biofeedback therapy.

## **6. Conclusion**

To effectively rehabilitate orofacial muscles it is important to consider their characteristics. They have precise and complex movements that are specific to function they are responsible for. The tongue for example is constituted not only of one muscle, but of a set of small muscles which are organized in different directions and work in synchrony promoting a wide range of refined movements. The amount of movements can be justified by the complexity of the functions directly related to the tongue, like speech, mastication and swallowing. On the other hand, the lips muscle has quite different characteristics. It has reduced caliber and its movements are not as elaborated as the ones of the tongue. Knowing these features will enable the rehabilitation process to be directed to each muscle group affected.

Tongue and lips are very important in orofacial functions. To be able to perform the functions properly, they need to be able to generate appropriate force. Thus, it is very important to measure tongue and lips force, especially in patients that have orofacial dysfunctions. This chapter presented the development and application of two instruments developed by the Biomechanics Engineering Group that measure forces of orofacial structures. The Portable FORLING measures tongue force and is composed of a mouthpiece, a base, a resistive sensor, pin and force applicator and a holder, all connected to a data acquisition and processing system. FORLAB measures lips force and is composed of an intralips insert, a stainless steel wire, a load cell and data acquisition and processing system. They were used in studies with normal subjects and proved to be effective and helpful for speech pathologists to improve their assessment. In subjects with normal tongue and lips strength in clinical evaluation, average tongue force was 16.6 N, with average CV of 17.3% and average lips force was 9.2 N with average CV of 7.4%. The tongue presents a force profile over time that is characterized by a force peak followed by the decay of force values, while lips demonstrate stability while maintaining maximum contraction over time. Those results indicate that forces of the lips are lower, but more stable than the ones of the tongue. The described developments were possible due to the multidisciplinary character of the group, including an active exchange between professionals of different background and institutions with the common goal of providing useful and reliable solutions for relevant problems in orofacial myology.

## **7. References**


duration and the number of exercise series. It will also be possible to make biofeedback

To effectively rehabilitate orofacial muscles it is important to consider their characteristics. They have precise and complex movements that are specific to function they are responsible for. The tongue for example is constituted not only of one muscle, but of a set of small muscles which are organized in different directions and work in synchrony promoting a wide range of refined movements. The amount of movements can be justified by the complexity of the functions directly related to the tongue, like speech, mastication and swallowing. On the other hand, the lips muscle has quite different characteristics. It has reduced caliber and its movements are not as elaborated as the ones of the tongue. Knowing these features will enable

Tongue and lips are very important in orofacial functions. To be able to perform the functions properly, they need to be able to generate appropriate force. Thus, it is very important to measure tongue and lips force, especially in patients that have orofacial dysfunctions. This chapter presented the development and application of two instruments developed by the Biomechanics Engineering Group that measure forces of orofacial structures. The Portable FORLING measures tongue force and is composed of a mouthpiece, a base, a resistive sensor, pin and force applicator and a holder, all connected to a data acquisition and processing system. FORLAB measures lips force and is composed of an intralips insert, a stainless steel wire, a load cell and data acquisition and processing system. They were used in studies with normal subjects and proved to be effective and helpful for speech pathologists to improve their assessment. In subjects with normal tongue and lips strength in clinical evaluation, average tongue force was 16.6 N, with average CV of 17.3% and average lips force was 9.2 N with average CV of 7.4%. The tongue presents a force profile over time that is characterized by a force peak followed by the decay of force values, while lips demonstrate stability while maintaining maximum contraction over time. Those results indicate that forces of the lips are lower, but more stable than the ones of the tongue. The described developments were possible due to the multidisciplinary character of the group, including an active exchange between professionals of different background and institutions with the common goal of providing useful and reliable solutions for relevant

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Perilo, Monalise Batista, and, Vivian Brito. 2009. "Desenvolvimento de um Sistema Protótipo para Medição Objetiva das Forças Linguais em Humanos." *Sba Controle &* 

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therapy.

**6. Conclusion** 

problems in orofacial myology.

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*Automação* 20(2):156-63.

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