2. Subject and methods

As mentioned above, the open-air MRI device is primarily used in medical diagnostics, so designation of three planes formed by x, y, and z axes follows medical terminology used for human body planes [7]. The plane dividing the body vertically into ventral (anterior) and dorsal (posterior) parts is called a coronal (frontal) plane. The second vertical plane dividing the body to left and right sides is a sagittal plane. The horizontal plane that divides the human body into superior (upper) and inferior (lower) parts is called a transverse (cross-sectional) plane. During sequence execution, the gradient coil pair corresponding to the chosen scan orientation is activated, it consequently vibrates, and acoustic noise is radiated in the surrounding air. Two basic types of sequences called spin echo (SE) and gradient echo (GE) arising from MRI physical principles [8] are preferred in this type of MRI device. The volume size of the tested object/subject is another important factor having an influence on the intensity of the produced vibration and noise in the scanning area of the MRI device. A tested person/sample/phantom as a part of the whole vibrating mechanical system changes the overall mass, stiffness, and damping by loading the lower gradient coil structure in the patient's bed.

#### 2.1 Sensors for measurement in a weak magnetic field environment

If the vibration and noise signals are recorded during MR scanning, interaction with the stationary magnetic field B<sup>0</sup> in the scanning area must be eliminated; otherwise, the quality of the acquired images would not be preserved. It means that the vibration sensors placed in the MRI scanning area with the static magnetic field cannot contain any part made from a ferromagnetic material. In MRI equipment, working with a weak magnetic field the interaction problem can be solved by a proper choice of the measuring device and its arrangement. Usually, it is sufficient to locate it in an adequate distance from the noise signal source outside the magnetic field area. Since the noise intensity as well as its spectral properties depends on the position of the measuring instrument, the recording/measuring microphone must have high sensitivity, an appropriate pickup pattern, type of the microphone, and a position in regard to the central point of the MRI scanning area (distance, direction angle, working height). The best solution is to use a microphone with a variable pattern having two diaphragms that share a common back plate. Such a microphone behaves as two back-to-back cardioid microphones. If one membrane is connected to a constant polarization voltage and the second one is polarized by a variable voltage, principally any directional pattern can be created. Basic omnidirectional, figure-of-eight, and cardioid patterns corresponding to both same voltages of the same polarity, the opposite polarity, and one zero voltage are represented in an ideal form by a polar equation:

Analysis of Energy Relations between Noise and Vibration Produced by a Low-Field MRI Device DOI: http://dx.doi.org/10.5772/intechopen.85275

$$\rho(\theta) = A + B \cdot \cos \theta, \qquad \qquad A + B = \mathbf{1}, \tag{1}$$

where A = 1, B = 0 for omnidirectional, A = 0, B = 1 for figure-of-eight, and A = 0.5, B = 0.5 for cardioid directional patterns.

The noise distribution in the scanning area of the MRI equipment and its neighborhood has to be mapped prior to the selection of the proper recording microphone location. C-weighting was used for SPL measurement to accommodate the objective noise intensity to the subjective loudness at high sound levels. The Cweighting filter frequency response in s-domain is given by the equation

$$H(s) = G \cdot \frac{\left(2\pi f\_2\right)^2 \cdot s^4}{\left(s + 2\pi f\_1\right)^2 \cdot \left(s + 2\pi f\_2\right)^2},\tag{2}$$

where f<sup>1</sup> = 20.6 Hz, f<sup>2</sup> = 12,194 Hz, and 20 log G = 0.062 dB [9]. To get the transfer function of the digital IIR filter, the frequency scale is warped by the bilinear transform from s-plane to z-plane

$$s \to 2 \cdot \frac{\mathbf{1} - \mathbf{z}^{-1}}{\mathbf{1} + \mathbf{z}^{-1}}. \tag{3}$$

The sensors measuring vibration signals are placed inside the MRI scanning area where the basic stationary magnetic field of the MRI device is present together with the superimposed pulse magnetic field generated by the gradient system as well as the high voltage field originated during activation of the excitation RF coil. These fields would disturb a signal picked up by the sensor from ferromagnetic material or damage electronics integrated with the sensor [10, 11], which can be avoided using the vibration sensor with a piezoelectric transducer. The sensor must have good sensitivity and maximally flat frequency response with the frequency range covering the vibration and noise harmonic frequencies that fall into the low band due to frequency-limited gradient pulses. As a similar frequency range can be found in basic processing of speech signals, it is very important in the case of 3D scanning of the human vocal tract by MRI with parallel recording of a speech signal [5].

The mentioned requirements imposed on the vibration sensor can be met by the sensor for acoustic musical instruments [12]. Its first usage in the magnetic field environment must be preceded by a calibration procedure and a measurement of its sensitivity and frequency response. The measured frequency response is used to determine a correction curve for filtering of the picked-up vibration signal and consecutive linearization operation that has effect on correctness of all analyzed spectral properties determined from the vibration signals—see the block diagram in Figure 1. The correction filter is proposed by a standard procedure of second-order shelving filter design [13]:

$$H(z) = \frac{b\_0 + b\_1 z^{-1} + b\_2 z^{-2}}{a\_0 + a\_1 z^{-1} + a\_2 z^{-2}}.\tag{4}$$

For the sampling frequency fs, the polynomial filter coefficients a0,1,2 and b0,1,2 are derived from three input parameters—gain G, mid-point frequency fc, and quality factor Q—in the following manner:

$$A = 10^{\frac{\mathcal{G}}{\mathcal{G}}}, o\_{\mathcal{c}} = 2\pi \cdot \frac{f\_{\mathcal{c}}}{f\_{\mathcal{s}}},\tag{5}$$

exposure [6]. In order to minimize these negative factors, this work is focused on mapping of energy relationship between vibration and noise signals measured in the MRI scanning area and its vicinity with the final aim to choose the proper scan sequence and its parameters—repetition time (TR), echo time (TE), orientation of scan slices, etc. Apart from real-time recording of the vibration and noise signals, the sound pressure level (SPL) was measured by a sound level meter using frequency weighting to match human perception of noise. The measured data and recorded signals were further processed off-line—the determined energetic features were statistically analyzed and the results were compared visually and numerically.

As mentioned above, the open-air MRI device is primarily used in medical diagnostics, so designation of three planes formed by x, y, and z axes follows medical terminology used for human body planes [7]. The plane dividing the body vertically into ventral (anterior) and dorsal (posterior) parts is called a coronal (frontal) plane. The second vertical plane dividing the body to left and right sides is a sagittal plane. The horizontal plane that divides the human body into superior (upper) and inferior (lower) parts is called a transverse (cross-sectional) plane. During sequence execution, the gradient coil pair corresponding to the chosen scan orientation is activated, it consequently vibrates, and acoustic noise is radiated in the surrounding air. Two basic types of sequences called spin echo (SE) and gradient echo (GE) arising from MRI physical principles [8] are preferred in this type of MRI device. The volume size of the tested object/subject is another important factor having an influence on the intensity of the produced vibration and noise in the scanning area of the MRI device. A tested person/sample/phantom as a part of the whole vibrating mechanical system changes the overall mass, stiffness, and damping by loading the lower gradient coil structure in the patient's bed.

2.1 Sensors for measurement in a weak magnetic field environment

If the vibration and noise signals are recorded during MR scanning, interaction

with the stationary magnetic field B<sup>0</sup> in the scanning area must be eliminated; otherwise, the quality of the acquired images would not be preserved. It means that the vibration sensors placed in the MRI scanning area with the static magnetic field cannot contain any part made from a ferromagnetic material. In MRI equipment, working with a weak magnetic field the interaction problem can be solved by a proper choice of the measuring device and its arrangement. Usually, it is sufficient to locate it in an adequate distance from the noise signal source outside the magnetic field area. Since the noise intensity as well as its spectral properties depends on the position of the measuring instrument, the recording/measuring microphone must have high sensitivity, an appropriate pickup pattern, type of the microphone, and a position in regard to the central point of the MRI scanning area (distance, direction angle, working height). The best solution is to use a microphone with a variable pattern having two diaphragms that share a common back plate. Such a microphone behaves as two back-to-back cardioid microphones. If one membrane is connected to a constant polarization voltage and the second one is polarized by a variable voltage, principally any directional pattern can be created. Basic omnidirectional, figure-of-eight, and cardioid patterns corresponding to both same voltages of the same polarity, the opposite polarity, and one zero voltage are represented in an ideal

2. Subject and methods

Noise and Vibration Control - From Theory to Practice

form by a polar equation:

98

For basic visual comparison of spectral properties of the recorded vibration and noise signals, the periodogram representing an estimate of the power spectral density (PSD) can be successfully used. The basic spectral properties can be determined from the spectral envelope, and subsequently, the histograms of spectral values can be calculated and compared. They also include the basic resonance frequencies FV1 and FV2 and their ratios, and the spectral decrease (tilt-Stilt) as the degree of fall of the power spectrum calculated by a linear regression using the mean square

Analysis of Energy Relations between Noise and Vibration Produced by a Low-Field MRI Device

The supplementary spectral features describe the shape of the power spectrum of the noise signal. The spectral centroid (Scentr) determines a center of gravity of the spectrum—the average frequency weighted by the values of the normalized

<sup>k</sup>¼<sup>1</sup> kS k j j ð Þ <sup>2</sup>

<sup>k</sup>¼<sup>1</sup> j j S kð Þ <sup>2</sup> : (12)

<sup>k</sup>¼<sup>1</sup> j j S kð Þ <sup>2</sup> : (13)

: (14)

∑NFFT

The spectral flatness (Sflat) is useful to determine the degree of periodicity in the signal, and it can be calculated as a ratio of the geometric and the arithmetic mean

<sup>k</sup>¼<sup>1</sup> j j S kð Þ <sup>2</sup> h i <sup>2</sup> NFFT

The spectral entropy is a measure of spectral distribution. It quantifies a degree of randomness of spectral probability density represented by normalized frequency components of the spectrum. The Shannon spectral entropy (SHE) can be calcu-

The performed measurements were focused on analysis of vibration and noise

conditions in the scanning area and in the neighborhood of the open-air MRI equipment E-scan Opera by Esaote S.p.A., Genoa [15] located at the Institute of Measurement Science, SAS, Bratislava. The experiments were realized in four steps: in the preliminary phase, the calibration was carried out, and the sensitivity and the frequency response of the used vibration sensor were determined. Next, the noise was measured using different directional patterns of the pickup microphone and the influence of the pickup pattern on the spectral properties of the recorded noise signal was analyzed. Then, the main vibration and noise measurement and recording experiment were realized. The recorded signals were subsequently processed and statistically analyzed. Finally, a detailed analysis of the influence of chosen scan parameters on the time duration of the used MR sequences and on the quality factor of the MR images was performed with the aim to find a suitable setting to minimize

j j S kð Þ <sup>2</sup> log <sup>2</sup>j j S kð Þ <sup>2</sup>

energy of each frequency component in the spectrum

DOI: http://dx.doi.org/10.5772/intechopen.85275

values of the power spectrum

lated using the following formulas:

Scentr <sup>¼</sup> fs

Sflat ¼

SHE ¼ � ∑

exposition of the examined persons to noise and vibration.

NFFT � ∑NFFT

QNFFT

2 NFFT <sup>∑</sup>NFFT

NFFT k¼1

3. Description of performed measurements and experiments

method.

101

Figure 1.

Block diagram of processing of the picked-up vibration signal.

$$q\_{\varepsilon} = \frac{\sqrt{A}}{Q} \cdot \sin \alpha\_{\varepsilon} \cdot q\_{\varepsilon 1} = (A + 1) \cdot \cos \alpha\_{\varepsilon} \cdot q\_{\varepsilon 2} = (A - 1) \cdot \cos \alpha\_{\varepsilon} \tag{6}$$

$$\mathfrak{a}\_0 = \mathbf{A} + \mathbf{1} - q\_{c2} + q\_s, \ \mathfrak{a}\_1 = \mathbf{2} \cdot \begin{bmatrix} \mathbf{A} - \mathbf{1} - q\_{c1} \end{bmatrix}, \ \mathfrak{a}\_2 = \mathfrak{a}\_0 - \mathfrak{Q}\_s,\tag{7}$$

$$b\_0 = \mathbf{A} \cdot \left[\mathbf{A} + \mathbf{1} + q\_{c2} + q\_s\right], \ b\_1 = -\mathbf{2A} \cdot \left[\mathbf{A} - \mathbf{1} + q\_{c1}\right], \ b\_2 = b\_0 - \mathbf{2q}\_s. \tag{8}$$

#### 2.2 Features for description of vibration and noise signals

Several methods can be used to determine the energy of a periodical signal:

• The standard root mean square (RMS) is calculated from a signal x(n) in a defined region of interest (ROI) with the length of M samples

$$\text{Signal}\_{\text{RMS}} = \sqrt{\frac{1}{M} \sum\_{n=1}^{M} \left| \varkappa(n) \right|^2}. \tag{9}$$

• The absolute value of the mean of the Teager-Kaiser energy operator OTK [14] is used to calculate the energy EnTK

$$\mathbf{U}\_{\rm TK} = \mathbf{x}(n)^2 - \mathbf{x}(n-1) \cdot \mathbf{x}(n+1), \qquad \mathbf{E}n\_{\rm TK} = abs \left( \frac{\mathbf{1}}{M-2} \sum\_{n=1}^{M-2} \mathbf{O}\_{\rm TK}(n) \right). \tag{10}$$

• The frame energy is estimated by the first cepstral coefficient c<sup>0</sup> or the autocorrelation coefficient r<sup>0</sup> after processing the signal x(n) in frames using NFFT-point FFT to compute magnitude spectrum and power spectrum |S(k)|<sup>2</sup> ,

$$En\_{c0} = \sqrt{\left[\prod\_{k=1}^{N\_{FFT}/2} \left|\mathbf{S}(k)\right|^2\right]^{\frac{2}{N\_{FFT}}}}, \qquad En\_{r0} = \frac{2}{N\_{FFT}} \sum\_{k=1}^{N\_{FFT}/2} \left|\mathbf{S}(k)\right|^2. \tag{11}$$

Analysis of Energy Relations between Noise and Vibration Produced by a Low-Field MRI Device DOI: http://dx.doi.org/10.5772/intechopen.85275

For basic visual comparison of spectral properties of the recorded vibration and noise signals, the periodogram representing an estimate of the power spectral density (PSD) can be successfully used. The basic spectral properties can be determined from the spectral envelope, and subsequently, the histograms of spectral values can be calculated and compared. They also include the basic resonance frequencies FV1 and FV2 and their ratios, and the spectral decrease (tilt-Stilt) as the degree of fall of the power spectrum calculated by a linear regression using the mean square method.

The supplementary spectral features describe the shape of the power spectrum of the noise signal. The spectral centroid (Scentr) determines a center of gravity of the spectrum—the average frequency weighted by the values of the normalized energy of each frequency component in the spectrum

$$S\_{centr} = \frac{f\_s}{N\_{FFT}} \cdot \frac{\sum\_{k=1}^{N\_{FFT}} k \left| S(k) \right|^2}{\sum\_{k=1}^{N\_{FFT}} \left| S(k) \right|^2}. \tag{12}$$

The spectral flatness (Sflat) is useful to determine the degree of periodicity in the signal, and it can be calculated as a ratio of the geometric and the arithmetic mean values of the power spectrum

$$\mathbf{S}\_{flat} = \frac{\left[\prod\_{k=1}^{N\_{FFT}} \left|\mathbf{S}(k)\right|^2\right]^{\frac{2}{N\_{FFT}}}}{\frac{2}{N\_{FFT}} \sum\_{k=1}^{N\_{FFT}} \left|\mathbf{S}(k)\right|^2}. \tag{13}$$

The spectral entropy is a measure of spectral distribution. It quantifies a degree of randomness of spectral probability density represented by normalized frequency components of the spectrum. The Shannon spectral entropy (SHE) can be calculated using the following formulas:

$$\text{SSE} = -\sum\_{k=1}^{N\_{\text{FFT}}} |\mathbf{S}(k)|^2 \log\_2 |\mathbf{S}(k)|^2. \tag{14}$$

#### 3. Description of performed measurements and experiments

The performed measurements were focused on analysis of vibration and noise conditions in the scanning area and in the neighborhood of the open-air MRI equipment E-scan Opera by Esaote S.p.A., Genoa [15] located at the Institute of Measurement Science, SAS, Bratislava. The experiments were realized in four steps: in the preliminary phase, the calibration was carried out, and the sensitivity and the frequency response of the used vibration sensor were determined. Next, the noise was measured using different directional patterns of the pickup microphone and the influence of the pickup pattern on the spectral properties of the recorded noise signal was analyzed. Then, the main vibration and noise measurement and recording experiment were realized. The recorded signals were subsequently processed and statistically analyzed. Finally, a detailed analysis of the influence of chosen scan parameters on the time duration of the used MR sequences and on the quality factor of the MR images was performed with the aim to find a suitable setting to minimize exposition of the examined persons to noise and vibration.

qs ¼

Figure 1.

ffiffiffiffi A p

b<sup>0</sup> ¼ A � A þ 1 þ qc<sup>2</sup> þ qs

a<sup>0</sup> ¼ A þ 1 � qc<sup>2</sup> þ qs

Block diagram of processing of the picked-up vibration signal.

Noise and Vibration Control - From Theory to Practice

is used to calculate the energy EnTK

Enc<sup>0</sup> ¼

100

<sup>Q</sup> � sinωc, qc<sup>1</sup> <sup>¼</sup> ð Þ� <sup>A</sup> <sup>þ</sup> <sup>1</sup> cosωc, qc<sup>2</sup> <sup>¼</sup> ð Þ� <sup>A</sup> � <sup>1</sup> cosωc, (6)

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

j j x nð Þ <sup>2</sup>

� �, a<sup>2</sup> <sup>¼</sup> <sup>a</sup><sup>0</sup> � <sup>2</sup>qs

� �, b<sup>2</sup> <sup>¼</sup> <sup>b</sup><sup>0</sup> � <sup>2</sup>qs

<sup>M</sup> � <sup>2</sup> <sup>∑</sup> M�2 n¼1

NFFT

∑ NFFT=2

k¼1

� �

, (7)

: (9)

OTKð Þ n

j j S kð Þ <sup>2</sup>

: (8)

: (10)

: (11)

,

, a<sup>1</sup> ¼ 2 � A � 1 � qc<sup>1</sup>

Several methods can be used to determine the energy of a periodical signal:

• The standard root mean square (RMS) is calculated from a signal x(n) in a

s

1 <sup>M</sup> <sup>∑</sup> M n¼1

• The absolute value of the mean of the Teager-Kaiser energy operator OTK [14]

autocorrelation coefficient r<sup>0</sup> after processing the signal x(n) in frames using NFFT-point FFT to compute magnitude spectrum and power spectrum |S(k)|<sup>2</sup>

• The frame energy is estimated by the first cepstral coefficient c<sup>0</sup> or the

vuuut , Enr<sup>0</sup> <sup>¼</sup> <sup>2</sup>

� �, b<sup>1</sup> ¼ �2<sup>A</sup> � <sup>A</sup> � <sup>1</sup> <sup>þ</sup> qc<sup>1</sup>

defined region of interest (ROI) with the length of M samples

SignalRMS ¼

OTK <sup>¼</sup> x nð Þ<sup>2</sup> � x nð Þ� � <sup>1</sup> x nð Þ <sup>þ</sup> <sup>1</sup> , EnTK <sup>¼</sup> abs <sup>1</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

j j S kð Þ <sup>2</sup> " # <sup>2</sup> NFFT

N YFFT=<sup>2</sup>

k¼1

2.2 Features for description of vibration and noise signals
