**6. Measurement of the complex permittivity of the biological tissue as the possible imaging method**

#### **6.1 Introduction**

This sub-chapter describes and evaluates a method for determining complex permittivity, and presents results of permittivity measurement of inhomogeneous agar phantom and living tissue. There are described different approaches for measurement of complex permittivity, in particular the non-invasive method of measuring complex permittivity at the end of the coaxial cable. Vector measurement of the reflection coefficient on the interface between probes and measured samples is performed with the aid of network analyzer in the frequency range from 300 kHz to 2 GHz. The results indicate that using the coaxial probe with dimensions of SMA (subminiature version A) connector is suitable in the frequency range approximately from 300 MHz to 10 GHz. In order to demonstrate the diagnostic potential of this method, measurements were first conducted on artificially created inhomogeneous agar phantom with added mixture of various dielectrics, followed by measurement of living biological tissue.

#### **6.2 Complex permittivity**

Relative permittivity, loss factor and conductivity are basic parameters for electromagnetic field modeling and simulations. Although these parameters could be found in the tables for many materials, their experimental determination is very often necessary (Hippel, 1954). Dielectric properties of biological tissues are determining factors for the dissipation of electromagnetic energy in the human body and therefore they are useful in hyperthermia cancer treatment. Measurement of the dielectric parameters of biological tissues is also a promising method in the medical diagnostics and imaging. Knowledge of the complex permittivity in an treated area, i.e. knowledge of the complex permittivity of healthy and tumor tissue, is very important for example in the diagnosing of tumor regions in the human body (Choi et al., 2004) or in the design of thermo-therapeutic applicators which transform electromagnetic energy into thermal energy in the tissue (Williams et al., 2008). Permittivity is known as

$$
\mathfrak{e} = \mathfrak{e}\_0 \mathfrak{e}\_c \tag{2}
$$

where *ε<sup>0</sup>* is free space permittivity and *ε<sup>c</sup>* is complex relative permittivity. Complex relative permittivity can be written as

$$
\varepsilon\_c = \varepsilon\_r - j\varepsilon\_r \tan \delta \tag{3}
$$

where *ε<sup>r</sup>* is real part of complex relative permittivity and tan *δ* is loss factor.

#### **6.3 Methods of complex permittivity measurement**

The most commonly used method for measuring the complex permittivity is a method of measuring dielectric inserted into a dielectric waveguide. This method is very accurate, but unfortunately requires irreversible changes in the measured material. Another method used for measurement of complex permittivity is RLC measuring bridge. This method is very accurate but there are a few requirements on the quality of the interfaces of the measured material and the capacitor plates (Thompson, 1956). In most cases, this

This sub-chapter describes and evaluates a method for determining complex permittivity, and presents results of permittivity measurement of inhomogeneous agar phantom and living tissue. There are described different approaches for measurement of complex permittivity, in particular the non-invasive method of measuring complex permittivity at the end of the coaxial cable. Vector measurement of the reflection coefficient on the interface between probes and measured samples is performed with the aid of network analyzer in the frequency range from 300 kHz to 2 GHz. The results indicate that using the coaxial probe with dimensions of SMA (subminiature version A) connector is suitable in the frequency range approximately from 300 MHz to 10 GHz. In order to demonstrate the diagnostic potential of this method, measurements were first conducted on artificially created inhomogeneous agar phantom with added mixture of various dielectrics, followed by

Relative permittivity, loss factor and conductivity are basic parameters for electromagnetic field modeling and simulations. Although these parameters could be found in the tables for many materials, their experimental determination is very often necessary (Hippel, 1954). Dielectric properties of biological tissues are determining factors for the dissipation of electromagnetic energy in the human body and therefore they are useful in hyperthermia cancer treatment. Measurement of the dielectric parameters of biological tissues is also a promising method in the medical diagnostics and imaging. Knowledge of the complex permittivity in an treated area, i.e. knowledge of the complex permittivity of healthy and tumor tissue, is very important for example in the diagnosing of tumor regions in the human body (Choi et al., 2004) or in the design of thermo-therapeutic applicators which transform electromagnetic energy into thermal energy in the tissue (Williams et al., 2008).

0 *c*

 

where *ε<sup>0</sup>* is free space permittivity and *ε<sup>c</sup>* is complex relative permittivity. Complex relative

The most commonly used method for measuring the complex permittivity is a method of measuring dielectric inserted into a dielectric waveguide. This method is very accurate, but unfortunately requires irreversible changes in the measured material. Another method used for measurement of complex permittivity is RLC measuring bridge. This method is very accurate but there are a few requirements on the quality of the interfaces of the measured material and the capacitor plates (Thompson, 1956). In most cases, this

(2)

*j* tan (3)

 

 *cr r* 

where *ε<sup>r</sup>* is real part of complex relative permittivity and tan *δ* is loss factor.

**6.3 Methods of complex permittivity measurement** 

**6. Measurement of the complex permittivity of the biological tissue as the** 

**possible imaging method** 

measurement of living biological tissue.

**6.2 Complex permittivity** 

Permittivity is known as

permittivity can be written as

**6.1 Introduction** 

method is used as narrowband. The method of measurement in free space has its limitations in the demand for high-loss dielectrics measured. Electromagnetic wave through the material must be attenuated by at least 10 dB. Otherwise, standing waves will be created, which contribute significantly to the inaccuracy of this method. The method of measurement in cavity resonators gives us results with good accuracy. On the other hand, it is difficult to produce precise machining of the resonator and the measured material inserted inside (Ramachandraiah et al., 1975). Latest often used method for measuring complex permittivity measurement method is the open end of the waveguide, in our case, the coaxial cable. This method can be considered as very accurate. Moreover, we can achieve a good repetition of the results when we maintain the phase stability of the measuring coaxial cable (Tanaba & Joines, 1976). In this work, this application was selected for the main method for measuring complex permittivity of biological tissues because of its non-invasive nature.

#### **6.3.1 Principle of reflection method**

The reflection method represents measurement of reflection coefficient on the interface between two materials, on the open end of the coaxial line and the material under test. It is a well-known method for determining the dielectric parameters (Tanaba & Joines, 1976). This method is based on the fact that the reflection coefficient of an open-ended coaxial line depends on the dielectric parameters of material under test which is attached to it. For calculating the complex permittivity from the measured reflection coefficient, it is useful to use an equivalent circuit of an open-ended coaxial line. The probe translates changes in the permittivity of a material under test into changes of the input reflection coefficient of the probe. The surface of the sample of material under test must be in perfect contact with the probe. The thickness of a measured sample must be at least twice of equivalent penetration depth of the electromagnetic wave. This assures that the waves reflected from the material under test interface are attenuated (Stuchly et al., 1994).

#### **6.4 Measurement probes**

For measurement probes, we have adapted the standard N and SMA RF connectors from which the parts for connecting to a panel were removed. The measurement probes can be described by the equivalent circuit consisting of the coupling capacitance between the inner and outer conductor out of the coaxial structure and radiating conductance which represents propagation losses (Popovic el al., 2005). These capacitance and conductance are frequency and permittivity dependent.

#### **6.4.1 N probe**

Probe for measuring the complex permittivity of biological tissues has been adapted from a standard RF connector for coaxial cable N-type connector, see Fig. 27. The original proposed range of application was fBW = 1 GHz, which together with the development of microwave technology is extended until today's fBW = 12 GHz. N connector used in the construction of the probe is standard N 50Ω connector that can be used up to frequency f = 5 GHz. The measurements were kept with a high degree of the accuracy and repeatability. The measurement probe based on N connectors had significantly less bandwidth, and f1 = 100 MHz and f2 = 1 GHz.

Prospective Applications of Microwaves in Medicine 529

The initial measurements on the inhomogeneous agar phantom were performed (Fig. 29.). As the simulations shows that the effective penetration depth in both cases, for N probe and SMA probe, is an interval of 4 mm to 2 mm depending on the frequency of measurement. Therefore, in this model of inhomogeneous agar phantom, strange dielectric immersion depths lies in the range from 4 mm to 1 mm. Thus, the purpose of this measurement was to detect strange dielectrics that are covered with an agar layer in terms of simulating the electrical parameters of human skin and soft tissue. Inhomogeneous agar phantom was covered with a regular square grid (30 points x 30 points), with the 900 points of measurement. Subsequently, measurements were taken at these points by the N probe and

Fig. 29. Inhomogeneous agar phantom setup, the number shows the depth of strange

The final verification of each experiment is necessary for practical usage. In our case, the experiment consisted of measuring the real biological tissue - the left upper limb of the first author (Fig. 30.). For this measurement, the SMA probe was used due to its ability to operate in higher bandwidth, and also because of its smaller size, and therefore a higher lateral resolution. The author's arm was marked with equidistant grid of measuring points, which then for-SMA probe measurements were carried out over a bandwidth of fMIN = 300 MHz to fMAX = 2 GHz. Measurements were carried out very quickly with a delay of 1s and 2s at each measuring point. The data was saved (with the help of an assistant) in CSV data format in the flash drive connected to the vector analyzer. Frequency sweep was set at 1600 points at a bandwidth of fMIN = 300 MHz to fMAX = 2 GHz and averaging was set to 16 in order to

The data presented here, obtained from measurements of the inhomogeneous phantom agar, are interpreted as a contour graph. Then there is the measurement on the left upper extremity of the author, which is displayed as contour graphs. All measurements were made in the band fMIN = 300 MHz to fMAX = 2 GHz, from whom were selected three representative

**6.5.1 Measurement on inhomogeneous agar phantom** 

SMA-probe.

dielectrics submersion

eliminate unwanted noise.

**6.6 Results** 

**6.5.2 Measurement on biological tissue** 

frequencies f1 = 500 MHz, f2 = 1 GHz and f3 = 2 GHz.

Fig. 27. Basic scheme of the N probe's dimensions

### **6.4.2 SMA probe**

Probe for measuring the complex permittivity based on the SMA-connector was adapted from a standard 50 Ω SMA connector which was developed around 1960 when it was required to create a miniaturized version of the N connector with a higher frequency range of application. Today SMA connectors operate in the band up to f = 18 GHz. SMA connector used for the production of SMA probes, Fig. 28. shows low-cost, standard RF connectors with a usable bandwidth up to f = 12 GHz. This solution is appropriate for the purposes of our measurements because the highest frequency measured is equal to f = 2 GHz.

Fig. 28. Basic scheme of the SMA probe's dimensions

#### **6.5 Measurement setup**

A typical measurement setup using the reflection method on an open-ended coaxial line consists of the network analyzer, the coaxial probe and software. Our measurements were done with the aid of Agilent 6052 network analyzer in the frequency range from 300 MHz to 3 GHz. First the calibration of the vector network analyzer is performed. Then the calibration using a reference material is done. Finally, the reflection coefficient of material under test is measured. The complex permittivity of material under test is evaluated by the MATLAB.

Probe for measuring the complex permittivity based on the SMA-connector was adapted from a standard 50 Ω SMA connector which was developed around 1960 when it was required to create a miniaturized version of the N connector with a higher frequency range of application. Today SMA connectors operate in the band up to f = 18 GHz. SMA connector used for the production of SMA probes, Fig. 28. shows low-cost, standard RF connectors with a usable bandwidth up to f = 12 GHz. This solution is appropriate for the purposes of

A typical measurement setup using the reflection method on an open-ended coaxial line consists of the network analyzer, the coaxial probe and software. Our measurements were done with the aid of Agilent 6052 network analyzer in the frequency range from 300 MHz to 3 GHz. First the calibration of the vector network analyzer is performed. Then the calibration using a reference material is done. Finally, the reflection coefficient of material under test is measured. The complex permittivity of material under test is evaluated by the

our measurements because the highest frequency measured is equal to f = 2 GHz.

Fig. 27. Basic scheme of the N probe's dimensions

Fig. 28. Basic scheme of the SMA probe's dimensions

**6.5 Measurement setup** 

MATLAB.

**6.4.2 SMA probe** 

#### **6.5.1 Measurement on inhomogeneous agar phantom**

The initial measurements on the inhomogeneous agar phantom were performed (Fig. 29.). As the simulations shows that the effective penetration depth in both cases, for N probe and SMA probe, is an interval of 4 mm to 2 mm depending on the frequency of measurement. Therefore, in this model of inhomogeneous agar phantom, strange dielectric immersion depths lies in the range from 4 mm to 1 mm. Thus, the purpose of this measurement was to detect strange dielectrics that are covered with an agar layer in terms of simulating the electrical parameters of human skin and soft tissue. Inhomogeneous agar phantom was covered with a regular square grid (30 points x 30 points), with the 900 points of measurement. Subsequently, measurements were taken at these points by the N probe and SMA-probe.

Fig. 29. Inhomogeneous agar phantom setup, the number shows the depth of strange dielectrics submersion

#### **6.5.2 Measurement on biological tissue**

The final verification of each experiment is necessary for practical usage. In our case, the experiment consisted of measuring the real biological tissue - the left upper limb of the first author (Fig. 30.). For this measurement, the SMA probe was used due to its ability to operate in higher bandwidth, and also because of its smaller size, and therefore a higher lateral resolution. The author's arm was marked with equidistant grid of measuring points, which then for-SMA probe measurements were carried out over a bandwidth of fMIN = 300 MHz to fMAX = 2 GHz. Measurements were carried out very quickly with a delay of 1s and 2s at each measuring point. The data was saved (with the help of an assistant) in CSV data format in the flash drive connected to the vector analyzer. Frequency sweep was set at 1600 points at a bandwidth of fMIN = 300 MHz to fMAX = 2 GHz and averaging was set to 16 in order to eliminate unwanted noise.

#### **6.6 Results**

The data presented here, obtained from measurements of the inhomogeneous phantom agar, are interpreted as a contour graph. Then there is the measurement on the left upper extremity of the author, which is displayed as contour graphs. All measurements were made in the band fMIN = 300 MHz to fMAX = 2 GHz, from whom were selected three representative frequencies f1 = 500 MHz, f2 = 1 GHz and f3 = 2 GHz.

Prospective Applications of Microwaves in Medicine 531

the various measurements still occur in the same places. Among the limitations of the method, we can mention a small depth of penetration shown in Fig. 32c) at frequency f = 2000 MHz; as a result, we can register only the layer of skin. The actual depth of penetration can be improved by using of probes based on the waveguide thus having a greater radiating aperture that would better achieve the quasi-plane waves, but the loss of lateral resolution of the probe. Overcoming this eternal compromise can be achieved through a combination of two probes for a single measurement, one with an emphasis on greater penetration depth and the second for acceptable lateral resolution. When comparing the results of this measurement shown in Fig. 32., we can find among them a high degree of correlation pointing out that in real biological tissue this measuring method will able to detect coherent tissue structure having the same

 a) b) c) Fig. 32. Results of the measurement on real biological tissue (contour graph of real part of

Measurements on inhomogeneous agar phantom showed the potential of this imaging method, because the strange dielectrical materials were detectable beneath the surface of agar. Based on this result, the measurement of the left upper extremity of the author was performed, and the contour map of the real part of complex permittivity shown the detectable difference between the tissues. The contour graphs of the real part of complex permittivity of biological tissue give us the hope for the future development that this method may be used as a imaging method. After proving more interaction on the pathological changes in tissues, such as growth

Research described in this chapter was supported by Grant Agency of the Czech Republic, projects: 102/08/H081:,,Non-standard application of physical fields - analogy, modelling, verification and simulation" and P102/11/0649: "Research and measurements of signals

complex permittivity on frequency a) f1 = 500 MHz, b) f2 = 1 GHz, c) f3 = 2 GHz

of tumor tissue, we can consider this method for diagnostic purposes.

value of the real part of complex permittivity.

**6.7 Evaluation** 

**7. Conclusions**  Research described

**8. Acknowledgment** 

Fig. 30. Measurement on real biological tissue

#### **6.6.1 Results of measurement on inhomogeneous agar phantom**

For the measurement on inhomogeneous agar phantom was designed with a submerged object of Teflon εr = 2.1 and Bakelite εr = 4.1, immersed in a variable depth of 4 mm to 1 mm into the agar phantom. After solidify of the agar surface was applied spatially equidistant grid (30 x 30) with 900 data points.

Fig. 31. Results of the measurement on inhomogeneous agar phantom (contour graph of real part of complex permittivity on frequency f = 500 MHz)

Measurements were performed by the SMA probe. Obtained values of the real part of complex permittivity have been rewritten into MATLAB and displayed as a contour graph image, see Fig. 31. The results of the measurement on the inhomogeneous agar phantom have shown the potential of imaging usability of this method for further investigations on real living tissue.

#### **6.6.2 Results of measurement on biological tissue**

Testing the imaging potential for complex permittivity measurement of biological tissue was finally performed on the left upper extremity of the author, see Fig. 30. SMA probe was used for this measurement. For a small separation of complex permittivity of biological tissue, these data are displayed only in the contour graph. It is very difficult to assess tissue formations without further visual assessment, using MRI and subsequent processing of data segmentation algorithms, but the Fig. 32a,b. shows that contours of real part of complex permittivity during

For the measurement on inhomogeneous agar phantom was designed with a submerged object of Teflon εr = 2.1 and Bakelite εr = 4.1, immersed in a variable depth of 4 mm to 1 mm into the agar phantom. After solidify of the agar surface was applied spatially equidistant

Fig. 31. Results of the measurement on inhomogeneous agar phantom (contour graph of real

Measurements were performed by the SMA probe. Obtained values of the real part of complex permittivity have been rewritten into MATLAB and displayed as a contour graph image, see Fig. 31. The results of the measurement on the inhomogeneous agar phantom have shown the potential of imaging usability of this method for further investigations on real living tissue.

Testing the imaging potential for complex permittivity measurement of biological tissue was finally performed on the left upper extremity of the author, see Fig. 30. SMA probe was used for this measurement. For a small separation of complex permittivity of biological tissue, these data are displayed only in the contour graph. It is very difficult to assess tissue formations without further visual assessment, using MRI and subsequent processing of data segmentation algorithms, but the Fig. 32a,b. shows that contours of real part of complex permittivity during

Fig. 30. Measurement on real biological tissue

part of complex permittivity on frequency f = 500 MHz)

**6.6.2 Results of measurement on biological tissue** 

grid (30 x 30) with 900 data points.

**6.6.1 Results of measurement on inhomogeneous agar phantom** 

the various measurements still occur in the same places. Among the limitations of the method, we can mention a small depth of penetration shown in Fig. 32c) at frequency f = 2000 MHz; as a result, we can register only the layer of skin. The actual depth of penetration can be improved by using of probes based on the waveguide thus having a greater radiating aperture that would better achieve the quasi-plane waves, but the loss of lateral resolution of the probe. Overcoming this eternal compromise can be achieved through a combination of two probes for a single measurement, one with an emphasis on greater penetration depth and the second for acceptable lateral resolution. When comparing the results of this measurement shown in Fig. 32., we can find among them a high degree of correlation pointing out that in real biological tissue this measuring method will able to detect coherent tissue structure having the same value of the real part of complex permittivity.

Fig. 32. Results of the measurement on real biological tissue (contour graph of real part of complex permittivity on frequency a) f1 = 500 MHz, b) f2 = 1 GHz, c) f3 = 2 GHz

#### **6.7 Evaluation**

Measurements on inhomogeneous agar phantom showed the potential of this imaging method, because the strange dielectrical materials were detectable beneath the surface of agar. Based on this result, the measurement of the left upper extremity of the author was performed, and the contour map of the real part of complex permittivity shown the detectable difference between the tissues. The contour graphs of the real part of complex permittivity of biological tissue give us the hope for the future development that this method may be used as a imaging method. After proving more interaction on the pathological changes in tissues, such as growth of tumor tissue, we can consider this method for diagnostic purposes.
