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Power Evaluation of High Intensity Focused Ultrasound Transducer Based on Acoustic Filed Measurement in Pre-focal Region
Available online at www.sciencedirect.com
ScienceDirect Physics Procedia 70 (2015) 1144 – 1147
2015 International Congress on Ultrasonics, 2015 ICU Metz
Power Evaluation of High Intensity Focused Ultrasound Transducer Based on Acoustic Filed Measurement in Pre-focal Region Cheng Wanga, Huifeng Zhenga, Yuebing Wanga, Yonggang Caoa a
China Jiliang University, Hangzhou, 310018, China
Abstract A novel technique for measurement of high intensity focused ultrasound output power of a transducer was introduced in this study. A needle point hydrophone, which was fixed in the pre-focal region of the transducer by a scanning system, was used to measure the acoustic pressure in both amplitude and phase. By using sound pressure method, the predicated power at pocus was calculated and compared with the actual measured one. It was found that the uncertainty between the measured and calculated acoustic power was about 10%. The near field measurement method is applicable to the evaluation of the focused transducer, and it can avoid the damage to measuring equipment of direct measurement. Keywords: high intensity focused ultrasound ; focused transducer ; near-field measurement ; acoustic power;
1 Introduction High intensity focused ultrasound (HIFU) has been developed rapidly in recent years, especially in medical field. The ultrasonic wave could been converged to human tissue, and lesions in vivo are took treatment by cavitation, mechanical effects, thermal effects of ultrasonic wave, while other normal tissue does not been damaged. The main parameters to descript focused ultrasound field are acoustic pressure, acoustic power, and acoustic focal region etc. Acoustic field of HIFU has three characteristics: First, the acoustic pressure is very large at focus. It is likely to cause the medium cavitation. And the sensor may be damaged due to the rupture of cavitation bubbles. Second, the energy is concentrated at focus region. It will cause the increase of the temperature of the measurement devices. Last, the focal region is small. Because of the limitation of small size, better measurement systems (such as high precision and high stability) are required. Therefore, it is a challenge to measure the acoustic field of a HIFU transducer precisely without breaking the hydrophone[1]. Near-field measurement[2,3] can solve the problem of HIFU acoustic field measurement as an indirect method. It moves the measurement area to pre-focal region instead of focal region, and get the field distribution of focal region by sound propagation theory. So that, the using hydrophone could be protected. In this study, we conducted research on measurement system and acoustic power evaluation of focused transducer based on near-field measurement. 2 Basic theory of near-field measurements Acoustic propagation is expressed by Helmholtz equation In an ideal fluid medium: 2P k 2P
0
1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of ICU 2015 doi:10.1016/j.phpro.2015.08.245
˄1˅
1145
Cheng Wang et al. / Physics Procedia 70 (2015) 1144 – 1147
where is the Laplace operator, P is the acoustic pressure. The response of point source can been called Green's functions in equation (1) in certain boundary and initial conditions, represented by G (r , r c) : 2 G (r , r c) k 2G ( r , r c) 4SG ( r r c) where G (r r c) is the Dirac pulse function, r and r c are coordinates of spatial points.
˄2˅
The distribution of acoustic field can been obtained with a known point source acoustic field by following equation: P(r )
³³ [G ( r , r c) Sc
wG ( r , r c) wP (r c) P (r c) ]dS c wn wn
˄3˅
where n is the outward normal In the static fluid, without considering reflection and fluid boundary, boundary condition is G (r , r c) 0 , with the derivation of G (r , r c) : wG (r , r c) wn
1 exp( jkr ) ( z z c)(1 jkr ) 2S r3
˄4˅
With those conditions, equation (3) is simplified to: P ( x, y , z )
1 u 2S
³³ P( xc, yc, z c) Sc
1 - jkr ( z z c) jkr e dx cdy c r r2
˄5˅
where r ( x xc) 2 ( y yc) 2 ( z z c) 2 , P( x, y, z ) is acoustic pressure at an arbitrary point in space; P ( xc, y c, z c) is measurement acoustic pressure. Setting h( x, y, z )
1 jkr z jkr e , the equation (5) can been written as convolution: 4Sr 2 r
P ( x, y , z )
³³ P( xc, y c, z c)h( x xc, y y c, z z c)dxcdy c
˄6˅
Sc
The equation (6) can been calculated with fourier transform : P(k x , k y , z )
where H (k x , k y , z z c) e
j k 2 k x2 k y2 ( z zc)
P(k x , k y , z c) H ( k x , k y , z z c)
˄7˅
is the Fourier transform of the spread factor.
It shows that, any wave surface can be decomposed into different directions ( k x , k y , k z ) superposition of plane waves propagation. The wavefront at a time can be calculated by the wavefront at another time, whether it is a question of forward problem (calculate acoustic field by the source) or inverse problem (rebuild source by the acoustic field), which is the principle of the near-field measurement method. Calculation of acoustic power and other parameters are based on the unified standard IEC 62127-1: E
P2 uS Uc
˄8˅
where P the acoustic prediction pressure, U is the density of the liquid medium, c is the speed of sound, S is the calculation area. It can obtain that as following with further derivation: E
³³ S
p 2 ( x, y , z ) dS Uc
˄9˅
Thus, the acoustic power at focus can been predicted. It is emphasized that: HIFU is nonlinear in the process of communication, which will affect the acoustic intensity distribution, but does not change the total acoustic power. Therefore,it can still get the total acoustic power based on near-field measurement.
1146
Cheng Wang et al. / Physics Procedia 70 (2015) 1144 – 1147
3 Measurement System Synchronization Signal Digital Oscilloscope
SignalGenerator
Power Amplifier
Computer
Preamplifier
Three-dimensional Mechanical Mechanism
Focused transducer
Hydrophone cistern
Fig.1. Measurement system diagram
As shown in Fig.1, a signal generated by Signal Generator was amplified, and then excited a focused transducer. A hydrophone is mounted on three-dimensional mechanical mechanism which was controlled by a computer. The ultrasound signals detected by the hydrophone were shown by Digital Oscilloscope and saved by the computer[4]. To avoid the effect of acoustic reflection , input signal was burst pulse signal which had both the pulse nature and a stable state. The valid signal was extracted before the arrival of the echo signal, so that the influence of the reflection signal was ignored[5]. 4 Analysis of the Experimental Data and Results The work frequency of transducer is 750kHz. Firstly, we find the focus through moving Hydrophone.Then A plane was measured 10mm in front of focus. In order to contain most of the acoustic energy, the measurement area in front of focus is 20mm u 20mm ,the measurement interval is 0.5mm; the measurement area at focus is 10mm u 10mm ,the measurement interval is 0.2mm. In this experiment, the acoustic pressure output at the measuring point is close to sinusoidal because of the output of the acoustic power output not big enough. Therefore, the energy of higher harmonics can be ignored. In order to verify the calculation theory of near field acoustic holography in computing sound field distribution in focus , the measurement pressure 10mm in front of focus were used to compute the measurement pressure at focus through equation (1), predicted distribution of acoustic pressure and measured distribution of acoustic pressure at focus are as shown in Fig.2., and the focal diameter is 2.4mm when the pressure dropping 0.5 times was seemed as boundary value: a
1147
Cheng Wang et al. / Physics Procedia 70 (2015) 1144 – 1147 4 c
b
Fig.2. (a): measured distribution of acoustic pressure 10mm in front of focus;(b) measured distribution of acoustic pressure at focus; (c) prediction distribution of acoustic pressure at focus
The prediction error of acoustic pressure and acoustic power are as shown in Table1˖ Table 1. prediction error of acoustic pressure and acoustic power Distance of measurement plane to focus(mm) Acoustic pressure error˄%˅ Acoustic power error˄%˅
10 6.98 5.87
As shown in Fig.2. and Table1., the prediction acoustic pressure distribution is seem as the measurement pressure distribution , and the calculation error is within 10%. At the time of the experiment, we need to pay attention to the following: First, The distance of measurement plane should not be far from the focus; Second, the distance should not be close to the transducer surface, what will affect the acceptance of the hydrophone. 5 Conclusion It is a novel technique that acoustic power measurement and evaluation of HIFU based on acoustic filed measurement in pre-focal region. Since acoustic intensities in the pre-focal region are much lower than on the focus for a high power transducer, the damage to measurement devices, especially hydrophones, can be reduced, and results will become more reliable. The current measurement results have a certain limitation because of ignoring the non-linear impact, and we will further carry out the nonlinear measurement under high intensity. 6 Acknowledgements This work was finally the National Natural Science Foundation of China(11474259), National Defense Basic Research Program of China(JSJC2013604C012) and Zhejiang Province Welfare Technology Research (2014C31109). References [1] Zhou Y. 2015. Acoustic power measurement of high-intensity focused ultrasound transducer using a pressure sensor. Medical engineering & physics, 37(3), 335-340. [2] Greussing D, Cavallari M, Bonhoff H A, et al. 2012. The conception of structure-borne-sound-based near-field holography. Journal of Sound and Vibration, 331(18), 4132-4144. [3] Barnard A R, Hambric S A, Maynard J D. 2012. Underwater measurement of narrowband sound power and directivity using Supersonic Intensity in Reverberant Environments. Journal of Sound and Vibration, 331(17), 3931-3944. [4] Williams E G. 2001. Regularization methods for near-field acoustical holography. The Journal of the Acoustical Society of America, 110(4), 1976-1988. [5] He Yuanan, Jiang Junqi. 2003. Space field transformation based on the plane acoustic holography: Large underwater acoustic emission plane arrays of nah experiment, 28(1), 45-51.
ScienceDirect Physics Procedia 70 (2015) 1144 – 1147
2015 International Congress on Ultrasonics, 2015 ICU Metz
Power Evaluation of High Intensity Focused Ultrasound Transducer Based on Acoustic Filed Measurement in Pre-focal Region Cheng Wanga, Huifeng Zhenga, Yuebing Wanga, Yonggang Caoa a
China Jiliang University, Hangzhou, 310018, China
Abstract A novel technique for measurement of high intensity focused ultrasound output power of a transducer was introduced in this study. A needle point hydrophone, which was fixed in the pre-focal region of the transducer by a scanning system, was used to measure the acoustic pressure in both amplitude and phase. By using sound pressure method, the predicated power at pocus was calculated and compared with the actual measured one. It was found that the uncertainty between the measured and calculated acoustic power was about 10%. The near field measurement method is applicable to the evaluation of the focused transducer, and it can avoid the damage to measuring equipment of direct measurement. Keywords: high intensity focused ultrasound ; focused transducer ; near-field measurement ; acoustic power;
1 Introduction High intensity focused ultrasound (HIFU) has been developed rapidly in recent years, especially in medical field. The ultrasonic wave could been converged to human tissue, and lesions in vivo are took treatment by cavitation, mechanical effects, thermal effects of ultrasonic wave, while other normal tissue does not been damaged. The main parameters to descript focused ultrasound field are acoustic pressure, acoustic power, and acoustic focal region etc. Acoustic field of HIFU has three characteristics: First, the acoustic pressure is very large at focus. It is likely to cause the medium cavitation. And the sensor may be damaged due to the rupture of cavitation bubbles. Second, the energy is concentrated at focus region. It will cause the increase of the temperature of the measurement devices. Last, the focal region is small. Because of the limitation of small size, better measurement systems (such as high precision and high stability) are required. Therefore, it is a challenge to measure the acoustic field of a HIFU transducer precisely without breaking the hydrophone[1]. Near-field measurement[2,3] can solve the problem of HIFU acoustic field measurement as an indirect method. It moves the measurement area to pre-focal region instead of focal region, and get the field distribution of focal region by sound propagation theory. So that, the using hydrophone could be protected. In this study, we conducted research on measurement system and acoustic power evaluation of focused transducer based on near-field measurement. 2 Basic theory of near-field measurements Acoustic propagation is expressed by Helmholtz equation In an ideal fluid medium: 2P k 2P
0
1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of ICU 2015 doi:10.1016/j.phpro.2015.08.245
˄1˅
1145
Cheng Wang et al. / Physics Procedia 70 (2015) 1144 – 1147
where is the Laplace operator, P is the acoustic pressure. The response of point source can been called Green's functions in equation (1) in certain boundary and initial conditions, represented by G (r , r c) : 2 G (r , r c) k 2G ( r , r c) 4SG ( r r c) where G (r r c) is the Dirac pulse function, r and r c are coordinates of spatial points.
˄2˅
The distribution of acoustic field can been obtained with a known point source acoustic field by following equation: P(r )
³³ [G ( r , r c) Sc
wG ( r , r c) wP (r c) P (r c) ]dS c wn wn
˄3˅
where n is the outward normal In the static fluid, without considering reflection and fluid boundary, boundary condition is G (r , r c) 0 , with the derivation of G (r , r c) : wG (r , r c) wn
1 exp( jkr ) ( z z c)(1 jkr ) 2S r3
˄4˅
With those conditions, equation (3) is simplified to: P ( x, y , z )
1 u 2S
³³ P( xc, yc, z c) Sc
1 - jkr ( z z c) jkr e dx cdy c r r2
˄5˅
where r ( x xc) 2 ( y yc) 2 ( z z c) 2 , P( x, y, z ) is acoustic pressure at an arbitrary point in space; P ( xc, y c, z c) is measurement acoustic pressure. Setting h( x, y, z )
1 jkr z jkr e , the equation (5) can been written as convolution: 4Sr 2 r
P ( x, y , z )
³³ P( xc, y c, z c)h( x xc, y y c, z z c)dxcdy c
˄6˅
Sc
The equation (6) can been calculated with fourier transform : P(k x , k y , z )
where H (k x , k y , z z c) e
j k 2 k x2 k y2 ( z zc)
P(k x , k y , z c) H ( k x , k y , z z c)
˄7˅
is the Fourier transform of the spread factor.
It shows that, any wave surface can be decomposed into different directions ( k x , k y , k z ) superposition of plane waves propagation. The wavefront at a time can be calculated by the wavefront at another time, whether it is a question of forward problem (calculate acoustic field by the source) or inverse problem (rebuild source by the acoustic field), which is the principle of the near-field measurement method. Calculation of acoustic power and other parameters are based on the unified standard IEC 62127-1: E
P2 uS Uc
˄8˅
where P the acoustic prediction pressure, U is the density of the liquid medium, c is the speed of sound, S is the calculation area. It can obtain that as following with further derivation: E
³³ S
p 2 ( x, y , z ) dS Uc
˄9˅
Thus, the acoustic power at focus can been predicted. It is emphasized that: HIFU is nonlinear in the process of communication, which will affect the acoustic intensity distribution, but does not change the total acoustic power. Therefore,it can still get the total acoustic power based on near-field measurement.
1146
Cheng Wang et al. / Physics Procedia 70 (2015) 1144 – 1147
3 Measurement System Synchronization Signal Digital Oscilloscope
SignalGenerator
Power Amplifier
Computer
Preamplifier
Three-dimensional Mechanical Mechanism
Focused transducer
Hydrophone cistern
Fig.1. Measurement system diagram
As shown in Fig.1, a signal generated by Signal Generator was amplified, and then excited a focused transducer. A hydrophone is mounted on three-dimensional mechanical mechanism which was controlled by a computer. The ultrasound signals detected by the hydrophone were shown by Digital Oscilloscope and saved by the computer[4]. To avoid the effect of acoustic reflection , input signal was burst pulse signal which had both the pulse nature and a stable state. The valid signal was extracted before the arrival of the echo signal, so that the influence of the reflection signal was ignored[5]. 4 Analysis of the Experimental Data and Results The work frequency of transducer is 750kHz. Firstly, we find the focus through moving Hydrophone.Then A plane was measured 10mm in front of focus. In order to contain most of the acoustic energy, the measurement area in front of focus is 20mm u 20mm ,the measurement interval is 0.5mm; the measurement area at focus is 10mm u 10mm ,the measurement interval is 0.2mm. In this experiment, the acoustic pressure output at the measuring point is close to sinusoidal because of the output of the acoustic power output not big enough. Therefore, the energy of higher harmonics can be ignored. In order to verify the calculation theory of near field acoustic holography in computing sound field distribution in focus , the measurement pressure 10mm in front of focus were used to compute the measurement pressure at focus through equation (1), predicted distribution of acoustic pressure and measured distribution of acoustic pressure at focus are as shown in Fig.2., and the focal diameter is 2.4mm when the pressure dropping 0.5 times was seemed as boundary value: a
1147
Cheng Wang et al. / Physics Procedia 70 (2015) 1144 – 1147 4 c
b
Fig.2. (a): measured distribution of acoustic pressure 10mm in front of focus;(b) measured distribution of acoustic pressure at focus; (c) prediction distribution of acoustic pressure at focus
The prediction error of acoustic pressure and acoustic power are as shown in Table1˖ Table 1. prediction error of acoustic pressure and acoustic power Distance of measurement plane to focus(mm) Acoustic pressure error˄%˅ Acoustic power error˄%˅
10 6.98 5.87
As shown in Fig.2. and Table1., the prediction acoustic pressure distribution is seem as the measurement pressure distribution , and the calculation error is within 10%. At the time of the experiment, we need to pay attention to the following: First, The distance of measurement plane should not be far from the focus; Second, the distance should not be close to the transducer surface, what will affect the acceptance of the hydrophone. 5 Conclusion It is a novel technique that acoustic power measurement and evaluation of HIFU based on acoustic filed measurement in pre-focal region. Since acoustic intensities in the pre-focal region are much lower than on the focus for a high power transducer, the damage to measurement devices, especially hydrophones, can be reduced, and results will become more reliable. The current measurement results have a certain limitation because of ignoring the non-linear impact, and we will further carry out the nonlinear measurement under high intensity. 6 Acknowledgements This work was finally the National Natural Science Foundation of China(11474259), National Defense Basic Research Program of China(JSJC2013604C012) and Zhejiang Province Welfare Technology Research (2014C31109). References [1] Zhou Y. 2015. Acoustic power measurement of high-intensity focused ultrasound transducer using a pressure sensor. Medical engineering & physics, 37(3), 335-340. [2] Greussing D, Cavallari M, Bonhoff H A, et al. 2012. The conception of structure-borne-sound-based near-field holography. Journal of Sound and Vibration, 331(18), 4132-4144. [3] Barnard A R, Hambric S A, Maynard J D. 2012. Underwater measurement of narrowband sound power and directivity using Supersonic Intensity in Reverberant Environments. Journal of Sound and Vibration, 331(17), 3931-3944. [4] Williams E G. 2001. Regularization methods for near-field acoustical holography. The Journal of the Acoustical Society of America, 110(4), 1976-1988. [5] He Yuanan, Jiang Junqi. 2003. Space field transformation based on the plane acoustic holography: Large underwater acoustic emission plane arrays of nah experiment, 28(1), 45-51.