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Quantitative Assessment of Acoustic Intensity in the Focused Ultrasound Field Using Hydrophone and Infrared Imaging
Ultrasound in Med. & Biol., Vol. 39, No. 11, pp. 2021–2033, 2013 Copyright Ó 2013 World Federation for Ultrasound in Medicine & Biology Printed in the USA. All rights reserved 0301-5629/$ - see front matter
http://dx.doi.org/10.1016/j.ultrasmedbio.2013.05.004
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Original Contribution QUANTITATIVE ASSESSMENT OF ACOUSTIC INTENSITY IN THE FOCUSED ULTRASOUND FIELD USING HYDROPHONE AND INFRARED IMAGING YING YU,*y GUOFENG SHEN,* YUFENG ZHOU,z JINGFENG BAI,* and YAZHU CHEN* * Biomedical Instrument Institute, School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China; y School of Computer, Jiangxi University of Traditional Chinese Medicine, Nanchang, China; and z School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore (Received 28 August 2012; revised 8 May 2013; in final form 10 May 2013)
Abstract—With the popularity of ultrasound therapy in clinics, characterization of the acoustic field is important not only to the tolerability and efficiency of ablation, but also for treatment planning. A quantitative method was introduced to assess the intensity distribution of a focused ultrasound beam using a hydrophone and an infrared camera with no prior knowledge of the acoustic and thermal parameters of the absorber or the configuration of the array elements. This method was evaluated in both theoretical simulations and experimental measurements. A three-layer model was developed to calculate the acoustic field in the absorber, the absorbed acoustic energy during the sonication and the consequent temperature elevation. Experiments were carried out to measure the acoustic pressure with the hydrophone and the temperature elevation with the infrared camera. The percentage differences between the derived results and the simulation are ,4.1% for on-axis intensity and ,21.1% for 26-dB beam width at heating times up to 360 ms in the focal region of three phased-array ultrasound transducers using two different absorbers. The proposed method is an easy, quick and reliable approach to calibrating focused ultrasound transducers with satisfactory accuracy. (E-mail: [email protected]) Ó 2013 World Federation for Ultrasound in Medicine & Biology. Key Words: Acoustic intensity, Focused ultrasound, Infrared imaging, Temperature elevation, Hydrophone, Beam width.
with good sensitivity, broad bandwidth and a small active element are used to measure the acoustic pressure waveform, from which acoustic intensity is derived. The acoustic power from the ultrasound transducer can be measured with the radiation force balance. However, it is hard to obtain the value and distribution of the acoustic intensity. Schlieren imaging could characterize the ultrasound beam within minutes by Raman-Nath diffraction of light in water non-invasively without disturbing the acoustic field (Neumann and Ermert 2006). Quantitative acoustic pressure or intensity can be derived after calibration with a hydrophone in the linear acoustic range (Charlebois and Pelton 1995; Schneider and Shung 1996). In recent years, an infrared (IR) camera has been used to measure the temperature elevation at the surface of an absorber, from which the relative distribution as well as the absolute intensity value of the HIFU transducer can be determined (Bobkova et al. 2010; Giridhar et al. 2012; Hand et al. 2009; Myers and Giridhar 2011; Shaw and Hodnett 2008; Shaw and Nunn 2010; Shaw et al. 2011). One of the attractive features of this method is the rapid assessment of 2-D and 3-D ultrasound beams.
INTRODUCTION An emerging medical treatment that uses high-intensity focused ultrasound (HIFU) has been recognized as a potential non-invasive technique for cancer therapy. HIFU has been successfully used to ablate solid tumors within the breast, prostate, pancreas, liver, bone, brain and uterine fibroids in clinical trials (Al-Bataineh et al. 2012; Hynynen 2011; Kennedy et al. 2003; Mason 2011; Ter Haar and Coussios 2007). Quantitative characterization of the acoustic field is important for the development and pre-clinical validation of HIFU devices, as well as in the planning of clinical procedures. Several techniques have been applied and accepted by national and international standards (GB/T 19890-2005; IEC 62555 Ed. 1.0; IEC 62556 Ed. 1.0). Poly(vinyl difluoride) membrane and needle (Lewin et al. 2005) or fiber-optic (Zhou et al. 2006) membranes
Address correspondence to: Guofeng Shen, School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200030, China. E-mail: [email protected] 2021
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Quantitative assessment is challenging, however, because of the complicated physical phenomena involved in sonication. There are three media in the acoustic wave propagation path (water, absorber, air). Because of the limited transmission of infrared energy through liquid, an air layer should be located between the IR camera and the acoustic absorber. The ultrasound beam will be reflected from the absorber/air interface with nearly equal amplitude but opposite phase with respect to the incident beam. Thus, the net intensity at the interface, but not inside the absorber, is approximately zero. Although the absorber used for IR measurements is thin (usually 2 mm thick), the thermal diffusion of absorbed acoustic energy toward the top should be considered and compensated for (Bobkova et al. 2010; Shaw et al. 2011). The intensity profiles of ultrasound beams under the assumption of a Gaussian shape were derived to further compensate the axial and radial diffusion of heat (Myers and Giridhar 2011). However, there is 10% error between focal intensities and beam widths determined via the IR approach and those determined with hydrophone measurements (Giridhar et al. 2012), which are likewise dependent on the duration of sonication duration. In addition, in the quantitative assessment of acoustic intensities, the acoustic and thermal parameters of the absorbers must be known. In this study, the distribution of acoustic intensities was determined using a hydrophone and an IR camera, with no prior knowledge of the acoustic and thermal parameters of the absorber or the configuration of the phased-array elements. A three-layer model was developed to calculate the acoustic field in the absorber, the absorbed acoustic energy during the ultrasound exposure and the consequent temperature elevation. An experiment was performed to measure acoustic pressure with a hydrophone and temperature elevation with an IR camera. Then the distribution of acoustic intensities derived with our proposed method was compared with theoretical simulations using three phased-array transducers and two different absorbers at heating times up to 360 ms. The differences between derived and simulated results are ,4.1% for axial intensity and ,21.1% for 26-dB beam width in the focal region of the ultrasound transducer. The proposed method provides an easy, quick and reliable approach to calibration of focused ultrasound transducers.
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path, as shown in Figure 1. The temperature at the absorber/air interface is dependent on the acoustic field in the absorber, which is the sum of the waves emitted from interfaces I and II and the properties of the absorber (i.e., dffusivity, conductivity and attenuation) (Fan and Hynynen 1992, 1994; Li et al. 2011). For a phased-array transducer, each circular piston was divided into finite elements that are typically smaller than one-sixth of the wavelength and can be regarded as point sources. The complex acoustic velocity potential in a homogenous medium is calculated using the Rayleigh-Sommerfeld diffraction integral (Fan and Hynynen 1994; O’Neil 1949) j5
M X m51
um
N 1 X e2jkrmn Smn 2p n 5 1 rmn
(1)
where Smn is the area of finite element, N is the number of elements of the mth piston, M is the number of pistons, um 5 u0 ejut is the complex particle velocity normal to the surface of the mth piston, k 5 2 pf/c – jm is the complex wavenumber, f is the frequency, c is the speed of sound in the medium, m is the attenuation coefficient and rmn is the distance between the point of interest and the source. The particle velocity, u, in the propagation direction is given by the derivative of the velocity potential (Fan and Hynynen 1994)
METHODS Acoustic and thermal field in the absorber When an acoustic absorber is positioned normal to the transducer axis with its anterior and posterior surfacea immersed in de-gassed water and air, respectively, there are three layers of media in the acoustic propagation
Fig. 1. Schematic drawing of acoustic wave propagation and focusing in a three-layer model (water, absorber, air). HIFU 5 high-intensity focused ultrasound.
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u52
M N vj X jk X e2jkrmn j 12 Smn 5 um vr m 5 1 2p n 5 1 rmn krmn
(2)
The planar acoustic wave reflects and refracts at interfaces I and II between the two layers, as illustrated in Figure 1. Under continuous boundary conditions at these two interfaces, the transmission and reflection coefficients of the normal particle velocity at interface II in a three-layer model can be expressed as (Du et al. 2001) 2Z1 ðZ2 1Z3 Þ 8 t 5u2t 5 < 2u ui ðZ1 1Z2 ÞðZ2 1Z3 Þ1ðZ2 2Z1 ÞðZ3 2Z2 Þe22jk2 D : u2r 2Z1 ðZ2 2Z3 Þe22jk2 D r2u 5 5 22jk D 2 ui ðZ11Z2 ÞðZ2 1Z3 Þ1ðZ2 2Z1 ÞðZ3 2Z2 Þe (3) where Z1 5 r1 c1 =cosqi ; Z2 5 r2 c2 =cosq2t ; Z1 5 r3 c3 =cosq3t q2t 5 sin21 ðc2 sinqi =c1 Þ; q3t 5 sin21 ðc3 sinqi =c1 Þ (4) D is the thickness of the absorber; Z is the acoustic impedance of medium; subscripts 1, 2 and 3 denote the water, acoustic absorber and air, respectively; subscripts i, r and t represent the incident, reflected and transmitted waves, respectively. Therefore, the normal particle velocity inside the absorber can be calculated as u2 5 u2t 1u2r 5 ui ,t2u 1ui ,r2u
(5)
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rC
vT 5 V,ðKVTÞ1Q vt
where C is specific heat capacity, T is temperature, t is time and K is thermal conductivity. Continuity of the temperature and heat flux is required across the interface at equilibrium: vT2 vT3 T2 jz 5 0 5 T3 jz 5 0 ; K2 5 K3 (10) vz z 5 0 vz z 5 0
Estimating the intensity distribution Under the assumption of planar acoustic wave propagation at the focal plane and ignorance of reflections from the water/absorber interface, the acoustic field in the absorber consists of the incident wave and the reflected wave from the absorber/air interface (Bobkova et al. 2010; Giridhar et al. 2012; Myers and Giridhar 2011; Shaw et al. 2011). The heat deposition in the absorber is Q 5 4aIðx; y; zÞjz 5 0 expð22aDÞ½12cosð2kzÞ
(12)
p2 ðx; y; zÞ 5 p2t ðx; y; zÞ1p2r ðx; y; zÞ 5 ðu2t 1u2r ÞZ2 5 ðui ,t2u 1ui ,r2u ÞZ2 ) X M N mn
mn
mn
mn jk1 X e2jk1 rmn j 12 Smn t2u qi ,cos qi 1r2u qi ,cos qi 5 um Z2 2p n 5 1 rmn k1 rmn m51
I2 5 p2 u2 5 jp2 j =2r2 c2 2
(7)
The heat deposition is (Cobbold 2006) Q2 5 2
vI2 vz
(8)
The thermal field in the medium is given by the heat equation
(11)
where I(x,y,z)jz 5 0 is acoustic intensity in water, a is the absorption coefficient of the absorber, and k 5 2 pf/c is the wavenumber. Therefore, the energy deposition and temperature elevation at the interface are related as vT2 ðx; y; z; tÞ r2 C 2 5 4aIðx; y; zÞjz50 $expð22aDÞ$Hðr; tÞ vt z50
The acoustic pressure in the absorber is given by
The corresponding acoustic intensity is calculated from the pressure amplitude in the quasi-plane wave approximation as
(9)
(6)
where H(r,t) is a function of position and time, r2 5 x2 1 y2. If the pressure distribution is assumed to be in a Gaussian function, it can be expressed as (Myers and Giridhar 2011) 2 12expð24k2 k2 tÞ 4k2 t=rb2 r Hðr; tÞ 5 ,exp 114k2 t=rb2 rb2 114k2 t=rb2 (13) where k2 is thermal diffusivity, and rb is beam width at the focal plane. H(r,t) describes the effect of the acoustic field in the absorber and thermal diffusion on the temperature
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Fig. 2. Top views of (a) transducer 1 (b) transducer 2 and (c) transducer 3 used in the study.
at the interface, and has a maximum value during heating, depending on the thermal properties of the absorber and the beam width of the ultrasound wave. Then G is defined as max½Iðx; y; zÞjz 5 0 r2 C2 G5 z 4aexpð22aDÞmax½Hðr; tÞ max vT2 ðx; y; zÞjz 5 0 =vt (14) where vT2jz 5 0/vt is the temperature change rate (TCR) at the focal plane. vT2 ðx; y; z; tÞjz 5 0 T2 ðx; y; z; t1DtÞjz 5 0 2T2 ðx; y; z; tÞjz 5 0 5 vt Dt (15) where T2(x,y,z,t)jz 5 0 is the temperature measured at the interface at time t, and Dt is the interval time. The derivative was obtained after de-noising (i.e., by discrete wavelet transform) and linear interpolation of the data, from which the maximum TCR is determined. The location of the maximum TCR corresponds to the highest intensity I(x,y,z)jz 5 0 at the measurement plane. Substituting eqn (14) into eqn (12) gives the assessment of the free-field distribution of acoustic intensity: vT2 ðx; y; z; tÞjz 5 0 Iðx; y; zÞjz 5 0 5 G,max (16) vt
Theoretical simulations Circular pistons made of PZT-8 material (Shanghai Institute of Ceramic Chinese Academy of Science, Shanghai, China) with a working frequency of 1.36 MHz were attached to a concave surface to build the phased-array ultrasound transducers (Ji et al. 2009, 2012; Li et al. 2011). The configurations and geometries of the transducers used in this study are illustrated in
Figure 2 and summarized in Table 1. Absorbers 1 and 2, both with similar thermal and acoustic parameters similar to those of soft tissue but with different attenuation coefficients (Table 2), were used in the theoretical simulation. Absorber 2 can be used repeatedly above 65 C without significant changes in its physical properties (Chen et al. 2009). Uniform mesh size was set as 1/10th and 1/40th of the acoustic wavelength for the xy-plane and z-axis of the absorber, respectively, which is a trade-off between simulation accuracy and computation burden. The acoustic intensity at the focus was set at 100 W/cm2 in the simulations, which is within the linear acoustic range (Bobkova et al. 2010; Myers and Giridhar 2011). Furthermore, three planes in the acoustic field were considered in the simulation: focal plane, pre-focal plane (z 5 5.1, 5.2 and 6.6 mm), and post-focal plane (z 5 25.0, 25.1 and 26.4 mm for transducers 1, 2 and 3, respectively), where the intensities are half that at the focus. All numerical calculations were performed in MATLAB (The MathWorks, Natick, MA, USA). Experimental measurement A hydrophone and an infrared camera were employed to assess the acoustic intensity values and distribution of the phased-array focused transducer. Figure 3 is a schematic diagram of the experimental setup. Absorbers 3 (black rubber) and 4 (milky white silicon rubber) used in the measurement were purchased on the Table 1. The configuration and geometries of phasedarray transducer Transducer
Number of pistons
Focal length (mm)
Diameter (mm)
Diameter of piston (mm)
1 2 3
144 90 65
180 180 130
180 170 100
10 14 10
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Table 2. The acoustic and thermal parameters of media Material
Speed of sound (m/s)
Density (kg/m3)
Attenuation (Np/m$MHz)
Thermal conductivity (W/ m∙ C)
Specific heat (J/kg∙ C)
Water Air Absorber 1 Absorber 2*
1500 334 1569 1550
1060 1.21 1138 1020
0 9 5
0.52 0.6
3770 2941.18
* Value was selected from Chen et al. 2009; others from Li et al. 2011.
Internet; they were both 2 mm thick, but their acoustic and thermal propertie were unknown. A Lucite water tank (L 3 W 3 H 5 400 3 400 3 300 mm), whose inner wall was lined with absorbent rubber to reduce reflection and scattering, was filled with de-gassed water (O2 , 4 mg/L, T z 25 C). The phased-array transducer was operated in the single-focus mode by a lab-developed 65-channel ultrasound driving system. A calibrated needle hydrophone (NCS-1, Institute of Acoustics, Chinese Academy of Sciences, Beijing, China) composed of PbTiO3 with an active diameter of 0.8 mm and a sensitivity of 0.11 mV/Pa at 1.36 MHz was attached to a three-axis computer-controlled translational stage with a step size of 0.1 mm (Zolix Instruments, Beijing, China) to scan the acoustic field. Absorbent rubber (UA-1, Institute of Acoustics, Chinese Academy of Sciences) was attached to the hydrophone holder to minimize acoustic reflection, especially that from the top of the water. Pressure waveforms picked up by the hydrophone were registered on a digital oscilloscope (54622-D, Agilent, Santa Clara, CA, USA) at a sampling rate of 200 MS/s, and then the digitized waveforms were transferred to a PC for further data processing. A
Y X Step Motor Controller
Oscilloscope
Z
program in LabVIEW (National Instruments, Austin, TX, USA) controlled the work flow. An uncooled IR camera (IR108 A, Guide, Wuhan, China) with a lens of 75 mm/F1.0 and real-time video output of 384 3 288 pixels was vertically positioned to measure the temperature at the absorber/air interface. The spatial and thermal resolutions are 0.59 mm and 0.08 C, respectively. Images were transferred to the PC at 25 fps via an IEEE 1394 adapter. The trigger of the IR camera and HIFU transducer was synchronized with a delay time fixed at 200 ms. Before each experimental measurement, the IR camera was warmed up for at least half an hour and self-calibrated using an established protocol (Yang and Chen 2011). Briefly, IR images of water captured at approximately each 5 C increase from a mixture of ice and water (0 C) to boiling (100 C) were compared with measurements on a mercury thermometer. The acoustic absorber was placed at the bottom of a custom-built water-proof holder (L 3 W 3 H 5 200 3 200 3 50 mm), which was attached to the 3-D translational stage. Our measurement consists of three steps. First, the acoustic intensity at the focal point of the phased-array
IR Camera Water Tank with filtered, degassed water
Z
IEEE 1394 Y X
Absorbent Rubber Holder 1
Holder 2
Step Motor Controller
Needle Hydrophone Computer
Computer Acoustic Absorber
Membrane
Acoustic Absorber
Membrane Signal Generator
Signal Generator
RF Amplifier
RF Amplifier HIFU Array
Fig. 3. Schematic diagram of infrared and hydrophone systems used to measure acoustic intensity. Components are not drawn to scale. IR 5 infrared, RF 5 radiofrequency.
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transducer was measured using the calibrated hydrophone by finding the maximum pressure in the focal region. The speed of sound in water was calculated at ambient temperature and pressure (Marczak 1997). The density of water over the temperature range 0 C to 30.9 C was obtained from an established table (Walker 2010). Second, the hydrophone was removed; a custom-built holder with only air inside and an acoustic absorber attached at the bottom was connected to the translational stage, with the top of absorber positioned coarsely to the focal plane, which was marked by a laser pointer to the tip of the hydrophone after searching the focal point. Any visible bubbles attached to the absorber and holder wall were carefully removed. The ultrasound transducer was turned on continuously for 200 ms. The thermal field of the absorber was measured with the IR camera at the same heating time used when moving the holder vertically. The focal plane is determined as the location with the maximum temperature rise, and the positional uncertainty was estimated to be 0.1–0.2 mm. G in eqn (14) was obtained from the temperature elevation data, and then the free-field acoustic intensity and its distribution at the focal plane were assessed using eqn (16). Finally, the absorber was moved along the axis to the pre- and post-focal planes, and the IR measurements were repeated. The water level should not exceed the top of the absorber holder in motion, and no change in the shape of the absorber was observed at all locations. At each location, at least three measurements were carried out, from which the mean and standard deviation were calculated. There was an interval of at least 2 min between sonications, allowing the complete thermal diffusion from the absorber to water and convection from the absorber to air.
RESULTS Temperature elevation The temperature elevation and corresponding TCR at the absorber/air interface obtained with the IR camera were compared with the simulation results obtained using transducer 3 and absorber 2 at a heating time of 200 ms (Fig. 4). There was good agreement between these results, notably during the period of sonication. After the ultrasound exposure, the temperature continued to increase for about 100 ms, because the thermal flux flows to the top surface of the absorber, similar to the temperature lag phenomenon. The maximum acoustic intensity and consequent maximum temperature elevation is located about 0.3 mm below the surface in our simulation (Fig. 5). Afterward, the temperature decays exponentially. Fluctuations in measurements were caused by the noise of the IR camera as well as motion of the absorber in response to the acoustic radiation force.
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Fig. 4. Comparison of the infrared measurement (solid line) and theoretical simulation (dashed line) of the (a) temperature elevation and (b) temperature change rate at the surface of absorber 2 aligned at the focal plane of transducer 3 for a heating time of 200 ms.
Effect of heating time To choose an appropriate operation parameter in the measurement, the heating time was varied from 40 to 360 ms in the simulation. Figure 5 is the profile of axial
Fig. 5. Comparison of the simulated temperature distributions on the axis of absorber 2 using the transducer 3 at the end of heating from 40 to 360 ms using the three-layer medium model (solid line) and Meyer’s model (dashed line). The absorber/air interface is aligned at the focal plane of the transducer.
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temperature elevation in the absorber at the end of sonication. In comparison to the simulation results assuming planar wave incidence (Myers and Giridhar 2011), similarities are found within z 5 0–0.6 mm (half wavelength in absorber 2). However, differences become pronounced at deep locations, especially at z 5 1.8–2.0 mm, which is close to the absorber/water interface. Discrepancies are due to ultrasound incident convergence and reflective divergence at the posterior interface (absorber/air) and the presence of the anterior interface (water/absorber) in our three-layer media model. To evaluate the accuracy of estimation, the acoustic intensities derived from the simulated acoustic field and from the temperature elevations using the proposed method were compared. Figure 6 illustrates the radial distribution of acoustic intensity at the focal, pre-focal and post-focal planes using transducer 3 and absorber 2 at heating times (continuous exposure to ultrasound wave) of 40, 120, 200, 280 and 360 ms. Both assessed main and side lobes fit the theoretical simulation fairly well. The percentage differences in maximum acoustic intensity and 26-dB beam width are summarized in Tables 3 and 4, respectively. The maximum acoustic intensity derived in the pre-focal plane is higher than that in the theoretical simulation (,5%), but lower than that in the post-focal plane. The exception occurs when the heating time is longer than 280 ms using absorber 2. There are more percentage differences in 26-dB beam width with increases inheating time and distance from the focal plane. The significant thermal diffusion effect and invalidation of the planar wave assumption may lead to a broad distribution of thermal energy at the surface of the absorber. The percentage differences for transducer 3, which has a larger F-number of 1.3, are lower than the others because of the larger beam width. Overall, the proposed method can quantitatively assess the value and distribution of the focused ultrasound field with satisfactory accuracy.
Experimental measurement Figure 7 illustrates the distribution of acoustic intensities in the focal region obtained with the theoretical simulation, hydrophone measurement and the proposed method using transducer 3 at a heating time of 200 ms. The acoustic intensity at the focus was measured as 33.9 W/cm2 and used in the theoretical simulation and proposed estimation method. Maximum acoustic intensity and 26-dB beam width are compared in Table 5. Hydrophone measurements were found to fit the theoretical simulation fairly well, especially for the shape and beam width of the main lobe, despite the higher acoustic
Fig. 6. Comparison of the distribution of acoustic intensity derived from the simulation and by the proposed method from the simulated thermal field using transducer 3 and absorber 2 for heating times ranging from 40 to 360 ms at (a) z 5 0 mm (the focal plane), (b) z 5 7 mm and (c) z 5 26 mm, where the acoustic intensity on axis is half of that at the focus of the phased-array transducer.
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Table 3. Percentage difference between the maximum intensity on-axis using the proposed method in the simulated thermal field and that in the theoretical prediction for different transducers, heating time, absorbers, and locations Absorber 1
Absorber 2
Heating Pre-focal Post-focal Pre-focal Post-focal Transducer time (ms) (%) (%) (%) (%) 1
2
3
40 120 200 280 360 40 120 200 280 360 40 120 200 280 360
3.53 3.40 3.49 3.51 3.62 4.08 3.44 3.44 3.51 3.55 1.72 1.73 1.77 1.75 1.69
21.56 21.59 21.40 21.25 20.99 21.40 21.81 21.67 21.44 21.20 21.18 21.11 20.99 20.84 20.68
2.31 2.42 2.59 2.79 3.02 2.50 2.38 2.48 2.60 2.75 1.11 0.91 0.86 0.85 0.85
20.99 20.78 20.36 0.09 0.56 20.95 20.91 20.55 20.17 0.24 20.40 20.47 20.23 0.07 0.37
intensities measured at the off-focal plane. The discrepancy may be due to the mis-alignment of pistons during installation, non-uniform pressure distribution on the piston surface and position error of the hydrophone. Although the maximum acoustic intensities estimated by the proposed method using these two absorbers are quite similar, the beam widths derived using absorber 3 are much larger than those obtained using absorber 4, which may be due to more absorbed energy and significant diffusion (G 5 4.4 and 3.5 for absorbes 3 and 4, respectively). In Figure 8, the 2-D (xz and yz) distribution of acoustic intensity determined with the proposed method using transducer 3 and absorber 3 at a heating time of
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200 ms was compared with the theoretical simulation. Comparison of the intensity distributions obtined by theoretical simulation, hydrophone measurement and the proposed method exhibit fair agreement on the axis of the phased-array transducer, with the difference between the hydrophone measurement and derived value varying from 30.81% to 19.47% (see Fig. 9). In most of the focal region, there was no statistical difference between hydrophone and IR measurements (p . 0.05). However, the assessed intensity was found to be non-symmetric, which may be due to the non-uniformity of the absorber, misalignment of pistons and small titling angle of the absorber with respect to the axis. In addition, the background noise of the IR camera may deteriorate the intensity assessment beyond the main lobe at such a short heating time. DISCUSSION In this study, a method of measuring the distribution of acoustic intensity using a hydrophone and an IR camera was introduced. One of the advantages of this approach is that prior knowledge of the acoustic and thermal properties of the absorber is not required, in contrast to existing IR-based methods (Bobkova et al. 2010; Giridhar et al. 2012; Hand et al. 2009; Myers and Giridhar 2011; Shaw and Nunn 2010). G defined in eqn (14) has already accounted for the thermal conduction and diffusion in the absorber which should be considered in the IR measurement (Bobkova et al. 2010; Myers and Giridhar 2011). Without knowledge of the intensity distribution (i.e., beam width) and diffusivity of the absorber, it is hard to determine explicitly the function H(r,t). Here the maximum value of H(r,t) (at the location of the maximum TCR where it
Table 4. Percentage difference between the -6 dB beam width using the proposed method in the simulated thermal field and that in the theoretical prediction for different transducers, heating time, absorbers, and locations Absorber 1
Absorber 2
Transducer
Heating time (ms)
Pre-focal (%)
Focal (%)
Post-focal (%)
Pre-focal (%)
Focal (%)
Post-focal (%)
1
40 120 200 280 360 40 120 200 280 360 40 120 200 280 360
3.80 5.53 7.53 9.50 11.38 3.40 5.44 7.77 10.01 12.16 3.54 5.07 6.95 9.31 11.65
2.97 4.36 5.94 7.49 8.99 2.64 3.86 5.66 7.40 9.07 1.95 2.77 3.74 4.70 5.63
3.64 5.07 6.75 8.82 10.86 4.07 5.69 7.55 9.37 11.14 3.62 4.87 6.30 7.72 9.12
5.99 8.80 12.54 16.35 19.84 6.22 9.56 13.10 16.93 21.09 5.32 8.83 12.57 16.02 20.27
4.83 7.05 9.53 11.89 14.14 4.57 7.03 9.76 12.36 14.83 3.14 4.49 6.01 7.49 8.92
5.29 8.23 11.54 14.63 17.51 5.78 8.52 11.83 15.42 18.74 4.93 7.15 9.40 11.94 14.52
2
3
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Fig. 7. Comparison of the acoustic intensity distribution from theoretical simulation, hydrophone measurement and results derived from the proposed method on the x-axis (left column) and y-axis (right column) using transducer 3 and absorbers 3 and 4 at a heating time of 200 ms at (a) z 5 0 mm, (b) z 5 7.5 mm, and (c) z 5 26 mm. x- and y-axes are the left-right and front-back directions of the transducer, respectively.
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Table 5. Comparison of the maximum acoustic intensity and -6 dB beam width calculated using different methods in the focal region at the heating time of 200 ms Theoretical simulation
Absorber 3
Absorber 4
16.2 6 0.9 21.9 6 0.7
13.6 18.2
16.5 6 4.2 21 6 1.1
13.9 6 2.0 20.8 6 3.1
2.04 6 0.07 3 2.27 6 0.11 2.27 6 0.47 3 3.37 6 0.79 2.04 6 0.47 3 2.23 6 0.66
2.06 2.33 2.26
3.04 6 0.41 3 3.09 6 0.81 6.05 6 1.26 3 7.12 6 1.66 5.40 6 1.60 3 4.10 6 1.55
2.62 6 0.06 3 2.70 6 0.52 3.89 6 0.55 3 6.56 6 0.88 2.88 6 2.35 3 2.83 6 0.63
Maximum acoustic intensity (W/cm2)
Hydrophone measurement
z 5 7.5 mm z 5 -6 mm -6 dB beam width (mm) z 5 0 mm z 5 7.5 mm z 5 -6 mm
coincides with the focal point) was used to calculate G in an experimentally simple way, and the constant G was used for the entire focal region. Although errors exist between this value and that of an off-axis point, the relative difference was found acceptable in our measurements (the error is estimated up to about 8.5% within the 26-dB focal region in the simulation using our HIFU transducer in Fig. 6). In future studies, the spatial function of G(x,y,z) will be developed to derive the acoustic intensity. At variations in frequency, beam width and the absorber’s thermal diffusivity by [0.5, 3], [0.5, 2] and [0.75, 1.25] folders, respectively, the error within the 26-dB focal region at heating times of 100–400 ms is estimated to be as high as17% in our simulation. The acoustic intensity at the focus was measured directly, and then the distribution of acoustic intensities in the entire focal region was derived using the thermal image. Even though acoustic field mapping is time consuming because of the alignment of the hydrophone parallel with the transducer axis (alignment error within 0.1 wavelength [GB/T 16846-2008], searching for the focal point is fairly straightforward. Therefore, hydrophone measurement of acoustic intensity at the focus will not increase the complexity, time and cost of measurement significantly. Appropriate choice of the heating time is critical in the quantitative assessment of acoustic intensities. Low temperature elevation after a short sonication, which is below the thermal resolution of the IR camera, would result in a low signal-to-noise ratio. For example, if the heating time is 40 ms, the corresponding temperature elevations at the focus of transducer 3 in absorbers 3 and 4 are 0.17 C and 20.11 C (the negative value is due to the uncertainty of the IR camera for small temperature elevations), respectively, which is similar to the measurement variation at the interface, about 0.12 C, and the resolution of the IR camera, 0.08 C (Fig. 10). The minimum exposure time is usually a few tenths of seconds for a desired temperature rise of about 1 C. At a heating time of 200 ms, a significant temperature elevation and sharp profile were found in both absorbers. So this value was used for our studies. In contrast, a long heating time may cause irreversible changes in the
acoustic and thermal properties of the absorber although below its melting point. Non-uniformity and inhomogeneity in the absorber would further increase the systemic error in the subsequent measurements. A significant thermal diffusion effect would invalidate our use of the constant G value in the entire focal region. Thus, the heating time in our study is much lower than that used in other studies (Giridhar et al. 2012; Myers and Giridhar 2011). In addition, the influence of convective heat transfer becomes significant at high temperature elevations, although the upper limit is estimated to be 15 s for a 1MHz beam and a tissue diffusivity of 0.15 mm2/s (Giridhar et al. 2012). With an increase in frequency, the highest temperature inside the absorber is considerably closer to the surface temperature. As a result, the upper limit of sonication duration may decrease dramatically. Determination of the onset of sonication is another critical issue in the existing IR measurement. Although IR recording should be synchronized with the power output to the ultrasound transducer, the IR camera is usually turned on before the sonication because of the slow response and low frame rate (25–30 fps). The ‘‘inflection-point’’ method was used to determine the starting time from the IR temperature trace (Giridhar et al. 2012). However, its error (i.e., on the order of 100 ms) is comparable to the total sonication duration in our experiments. The maximum temperature change rate, instead of the starting time of sonication, was calculated from the IR images obtained in this study, which proved to be easy, sensitive and reliable in the IR measurement without compromising the derivation accuracy of the acoustic intensities. Both theoretical and experimental results indicate that appropriate choice of the absorber would increase the accuracy of assessment of acoustic intensities (Tables 3–5, Figs. 6 and 7). The ideal absorber may have high attenuation, low thermal conductivity, high stability and small thickness. As expected, higher temperature elevations in short sonications and less thermal diffusion may be able to increase the signal-to-noise ratio and minimize systemic errors. The attenuation length of infrared electromagnetic energy of silicon rubber is about
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Fig. 9. Comparison of the acoustic intensity distribution from theoretical simulation, hydrophone measurement and results derived using the proposed method on the z-axis using transducer 3 and absorber 3 at a heating time of 200 ms in the infrared measurement.
Fig. 8. Comparison of acoustic intensity distribution derived with the proposed method at the (a) xz and (b) yz planes in the infrared measurement using transducer 3 and absorber 3 at a heating time of 200 ms with the (c) the theoretical simulation in the free field.
0.06 mm (Pline 1989; Wang et al. 2008), less than the acoustic wavelength of the absorber. Therefore, the elevated temperature inside the silicone absorber will not be picked up by the IR camera (Giridhar et al. 2012; Myers and Giridhar 2011). A thin water-based
coating (on the order of 1 mm) for the necessary IR attenuation, although transparent to acoustic propagation, could also limit IR penetration (Giridhar et al. 2012). Further research into the impact of thermal and acoustic parameters will be carried out. Improvements in the IR-based assessment of acoustic intensity are greatly needed. When the absorber moved away from the focal plane, the difference between the derived and measured acoustic intensities did increase. The reason may be the invalidation of the planar wave assumptions in the absorber in deriving eqn (16). Transducers with larger F-numbers (i.e., transducer 3 in this study) have a smaller gain and, consequently, a smaller error of acoustic intensity quantization in the IR measurement, which was also confirmed in another study (Giridhar et al. 2012). There are errors around 40% at the pre- and post-focal planes for higher-gain transducers, which may be unacceptable in acoustic field calibration. Efforts should be made to overcome these defects to establish IR-based measurement as a standard calibration method. Furthermore, it was found that the measured temperatures at the side foci of a 2-D phased array are only about half those predicted by a simple model (Bobkova et al. 2010). Although the reason is not well understood and no pressure mapping was carried out to confirm such a low side lobe, correct assessment of the side foci is important to the safety profile of HIFU ablation to avoid unintended damage to vital tissue (i.e., artery and nerve). Efforts should be made to establish IR-based measurement as a standard calibration method.
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REFERENCES
Fig. 10. Comparison of the temperature elevations measured at the top surface of absorber 3 (a) and absorber 4 (b) by the infrared camera using transducer 3 at heating times from 40 to 360 ms.
CONCLUSIONS The method proposed for quantitative assessment of acoustic intensities using a hydrophone and an IR camera with no prior knowledge of the properties of the absorber and configuration of the phased array has a satisfactory percentage difference, in both maximum intensity (,3.5%) and 26-dB beam width (,13.1%) in the focal region, in comparison to the theoretical simulation using a three-layer medium model and hydrophone measurement at a heating time of 200 ms from an ultrasound transducer with F-numbers of 1.25–2. The percentage difference increases with distance from the focal plane, heating time, and thermal conductivity of the absorber, but decreases with the F-number of the transducer. Acknowledgments—We thank Vera Khokhlova, Matthew R. Myers and Junru Wu for guidance in calculation of the acoustic field and for providing the physical parameters of the absorber. This study was supported by the National Natural Science Foundation of China (No. 30800246) and the Key Technologies R&D Program of Shanghai, China (No. 09441900500).
Al-Bataineh O, Jenne J, Huber P. Clinical and future applications of high intensity focused ultrasound in cancer. Cancer Treat Rev 2012;38: 346–353. Bobkova S, Gavrilov L, Khokhlova V, Shaw A, Hand J. Focusing of high-intensity ultrasound through the rib cage using a therapeutic random phased array. Ultrasound Med Biol 2010;36:888–906. Charlebois T, Pelton R. Quantitative 2 D and 3 D Schlieren imaging for acoustic power and intensity measurements. Med Electronics 1995;789–792. Chen D, Fan T, Zhang D, Wu J. A feasibility study of temperature rise measurement in a tissue phantom as an alternative way for characterization of the therapeutic high intensity focused ultrasonic field. Ultrasonics 2009;49:733–742. Cobbold RSC. Foundations of biomedical ultrasound. New York: Oxford University Press; 2006. Du G, Zhu Z, Gong X. Fundamentals of acoustics, Nanjing. Nanjin University Press; 2001. Fan X, Hynynen K. The effect of wave reflection and refraction at soft tissue interfaces during ultrasound hyperthermia treatments. J Acoust Soc Am 1992;91:1727–1736. Fan X, Hynynen K. The effects of curved tissue layers on the power deposition patterns of therapeutic ultrasound beams. Med Phys 1994;21:25–34. GB/T 16846-2008. Requirement for the declaration of the acoustic output of medical diagnostic ultrasonic equipment. 24 March 2008 GB/T 19890–2005. Acoustics—Measurement and characterisation of ultrasonic fields in the frequency range 0.5 MHz to 15 MHz— Hydrophone method. 9 September 2005. ISBN: 155066.1–26918. Giridhar D, Robinson RA, Liu Y, Sliwa J, Zderic V, Myers MR. Quantitative estimation of ultrasound beam intensities using infrared thermography—Experimental validation. JAcoust Soc Am 2012; 131:4283. Hand JW, Shaw A, Sadhoo N, Rajagopal S, Dickinson RJ, Gavrilov LR. A random phased array device for delivery of high intensity focused ultrasound. Phys Med Biol 2009;54:5675–5693. Hynynen K. MRIgHIFU: A tool for image-guided therapeutics. J Magn Reson Imaging 2011;34:482–493. International Electrochemical Commission (IEC) 62555 Ed. 1.0. Ultrasonics—Power measurement—Output power measurement for high intensity therapeutic ultrasound (HITU) transducers and systems. September 2009. International Electrochemical Commission (IEC) 87/489/CD. Ultrasonics—Surgical systems—Specification and measurement of field parameters for high intensity therapeutic ultrasound (HITU) transducers and systems. 4 November 2011. Ji X, Bai JF, Shen GF, Chen YZ. High-intensity focused ultrasound with large scale spherical phased array for the ablation of deep tumors. J Zhejiang Univ Sci B 2009;10:639–647. Ji X, Shen G, Bai J, Chen Y. The characterization of an ultrasound spherical phased array for the ablation of deep-seated tissue. Applied Acoustics 2012;73:529–534. Kennedy JE, Ter Haar GR, Cranston D. High intensity focused ultrasound: Surgery of the future? Br J Radiol 2003;76:590–599. Lewin PA, Mu C, Umchid S, Daryoush A, El-Sherif M. Acousto-optic, point receiver hydrophone probe for operation up to 100 MHz. Ultrasonics 2005;43:815–821. Li D, Shen G, Bai J, Chen Y. Focus shift and phase correction in soft tissues during focused ultrasound surgery. IEEE Trans Biomed Eng 2011;58:1621–1628. Marczak W. Water as a standard in the measurements of speed of sound in liquids. J Acoust Soc Am 1997;102:2776–2779. Mason TJ. Therapeutic ultrasound an overview. Ultrason Sonochem 2011;18:847–852. Myers MR, Giridhar D. Theoretical framework for quantitatively estimating ultrasound beam intensities using infrared thermography. J Acoust Soc Am 2011;129:4073–4083. Neumann T, Ermert H. Schlieren visualization of ultrasonic wave fields with high spatial resolution. Ultrasonics 2006;44:e1561–e1566. O’Neil H. Theory of focusing radiators. J Acoust Soc Am 1949;21: 516.
Acoustic intensity assessment d Y. YU et al. Pline AD. Infrared surface temperature measurements for the surface tension driven convection experiment, MS Thesis. Cleveland, OH: Case Western Reserve University; 1989:1. Schneider B, Shung KK. Quantitative analysis of pulsed ultrasonic beam patterns using a Schlieren system. IEEE TransUltrason Ferroelectr Freq Control 1996;43:1181–1186. Shaw A, Hodnett M. Calibration and measurement issues for therapeutic ultrasound. Ultrasonics 2008;48:234–252. Shaw A, Khokhlova V, Bobkova S, Gavrilov L, Hand J. Calibration of HIFU intensity fields measured using an infra-red camera. Journal of Physics: Conference Series 2011;279. Shaw A, Nunn J. The feasibility of an infrared system for real-time visualization and mapping of ultrasound fields. Physics in Medicine and Biology 2010;55.
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Ter Haar G, Coussios C. High intensity focused ultrasound: Physical principles and devices. International Journal of Hyperthermia 2007;23:89–104. Walker R. Density of water (g/cm3) at temperatures from 0 C (liquid state) to 30.9 C by 0.1 C inc. 2010. http://www.simetric.co.uk/ si_water.htm#expansion. Wang Q, Li X, Yang S, Meng X, Zhang H. Studies on the relationship between sound absorption and molecular structure of polymers. Acta Polym Sin 2008;517–521. Yang R, Chen Y. Design of a 3-D infrared imaging system using structured light. IEEE Trans Instrum Meas 2011;60:608–617. Zhou Y, Zhai L, Simmons R, Zhong P. Measurement of high intensity focused ultrasound fields by a fiber optic probe hydrophone. J Acoust Soc Am 2006;120:676–685.
http://dx.doi.org/10.1016/j.ultrasmedbio.2013.05.004
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Original Contribution QUANTITATIVE ASSESSMENT OF ACOUSTIC INTENSITY IN THE FOCUSED ULTRASOUND FIELD USING HYDROPHONE AND INFRARED IMAGING YING YU,*y GUOFENG SHEN,* YUFENG ZHOU,z JINGFENG BAI,* and YAZHU CHEN* * Biomedical Instrument Institute, School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai, China; y School of Computer, Jiangxi University of Traditional Chinese Medicine, Nanchang, China; and z School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore (Received 28 August 2012; revised 8 May 2013; in final form 10 May 2013)
Abstract—With the popularity of ultrasound therapy in clinics, characterization of the acoustic field is important not only to the tolerability and efficiency of ablation, but also for treatment planning. A quantitative method was introduced to assess the intensity distribution of a focused ultrasound beam using a hydrophone and an infrared camera with no prior knowledge of the acoustic and thermal parameters of the absorber or the configuration of the array elements. This method was evaluated in both theoretical simulations and experimental measurements. A three-layer model was developed to calculate the acoustic field in the absorber, the absorbed acoustic energy during the sonication and the consequent temperature elevation. Experiments were carried out to measure the acoustic pressure with the hydrophone and the temperature elevation with the infrared camera. The percentage differences between the derived results and the simulation are ,4.1% for on-axis intensity and ,21.1% for 26-dB beam width at heating times up to 360 ms in the focal region of three phased-array ultrasound transducers using two different absorbers. The proposed method is an easy, quick and reliable approach to calibrating focused ultrasound transducers with satisfactory accuracy. (E-mail: [email protected]) Ó 2013 World Federation for Ultrasound in Medicine & Biology. Key Words: Acoustic intensity, Focused ultrasound, Infrared imaging, Temperature elevation, Hydrophone, Beam width.
with good sensitivity, broad bandwidth and a small active element are used to measure the acoustic pressure waveform, from which acoustic intensity is derived. The acoustic power from the ultrasound transducer can be measured with the radiation force balance. However, it is hard to obtain the value and distribution of the acoustic intensity. Schlieren imaging could characterize the ultrasound beam within minutes by Raman-Nath diffraction of light in water non-invasively without disturbing the acoustic field (Neumann and Ermert 2006). Quantitative acoustic pressure or intensity can be derived after calibration with a hydrophone in the linear acoustic range (Charlebois and Pelton 1995; Schneider and Shung 1996). In recent years, an infrared (IR) camera has been used to measure the temperature elevation at the surface of an absorber, from which the relative distribution as well as the absolute intensity value of the HIFU transducer can be determined (Bobkova et al. 2010; Giridhar et al. 2012; Hand et al. 2009; Myers and Giridhar 2011; Shaw and Hodnett 2008; Shaw and Nunn 2010; Shaw et al. 2011). One of the attractive features of this method is the rapid assessment of 2-D and 3-D ultrasound beams.
INTRODUCTION An emerging medical treatment that uses high-intensity focused ultrasound (HIFU) has been recognized as a potential non-invasive technique for cancer therapy. HIFU has been successfully used to ablate solid tumors within the breast, prostate, pancreas, liver, bone, brain and uterine fibroids in clinical trials (Al-Bataineh et al. 2012; Hynynen 2011; Kennedy et al. 2003; Mason 2011; Ter Haar and Coussios 2007). Quantitative characterization of the acoustic field is important for the development and pre-clinical validation of HIFU devices, as well as in the planning of clinical procedures. Several techniques have been applied and accepted by national and international standards (GB/T 19890-2005; IEC 62555 Ed. 1.0; IEC 62556 Ed. 1.0). Poly(vinyl difluoride) membrane and needle (Lewin et al. 2005) or fiber-optic (Zhou et al. 2006) membranes
Address correspondence to: Guofeng Shen, School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200030, China. E-mail: [email protected] 2021
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Quantitative assessment is challenging, however, because of the complicated physical phenomena involved in sonication. There are three media in the acoustic wave propagation path (water, absorber, air). Because of the limited transmission of infrared energy through liquid, an air layer should be located between the IR camera and the acoustic absorber. The ultrasound beam will be reflected from the absorber/air interface with nearly equal amplitude but opposite phase with respect to the incident beam. Thus, the net intensity at the interface, but not inside the absorber, is approximately zero. Although the absorber used for IR measurements is thin (usually 2 mm thick), the thermal diffusion of absorbed acoustic energy toward the top should be considered and compensated for (Bobkova et al. 2010; Shaw et al. 2011). The intensity profiles of ultrasound beams under the assumption of a Gaussian shape were derived to further compensate the axial and radial diffusion of heat (Myers and Giridhar 2011). However, there is 10% error between focal intensities and beam widths determined via the IR approach and those determined with hydrophone measurements (Giridhar et al. 2012), which are likewise dependent on the duration of sonication duration. In addition, in the quantitative assessment of acoustic intensities, the acoustic and thermal parameters of the absorbers must be known. In this study, the distribution of acoustic intensities was determined using a hydrophone and an IR camera, with no prior knowledge of the acoustic and thermal parameters of the absorber or the configuration of the phased-array elements. A three-layer model was developed to calculate the acoustic field in the absorber, the absorbed acoustic energy during the ultrasound exposure and the consequent temperature elevation. An experiment was performed to measure acoustic pressure with a hydrophone and temperature elevation with an IR camera. Then the distribution of acoustic intensities derived with our proposed method was compared with theoretical simulations using three phased-array transducers and two different absorbers at heating times up to 360 ms. The differences between derived and simulated results are ,4.1% for axial intensity and ,21.1% for 26-dB beam width in the focal region of the ultrasound transducer. The proposed method provides an easy, quick and reliable approach to calibration of focused ultrasound transducers.
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path, as shown in Figure 1. The temperature at the absorber/air interface is dependent on the acoustic field in the absorber, which is the sum of the waves emitted from interfaces I and II and the properties of the absorber (i.e., dffusivity, conductivity and attenuation) (Fan and Hynynen 1992, 1994; Li et al. 2011). For a phased-array transducer, each circular piston was divided into finite elements that are typically smaller than one-sixth of the wavelength and can be regarded as point sources. The complex acoustic velocity potential in a homogenous medium is calculated using the Rayleigh-Sommerfeld diffraction integral (Fan and Hynynen 1994; O’Neil 1949) j5
M X m51
um
N 1 X e2jkrmn Smn 2p n 5 1 rmn
(1)
where Smn is the area of finite element, N is the number of elements of the mth piston, M is the number of pistons, um 5 u0 ejut is the complex particle velocity normal to the surface of the mth piston, k 5 2 pf/c – jm is the complex wavenumber, f is the frequency, c is the speed of sound in the medium, m is the attenuation coefficient and rmn is the distance between the point of interest and the source. The particle velocity, u, in the propagation direction is given by the derivative of the velocity potential (Fan and Hynynen 1994)
METHODS Acoustic and thermal field in the absorber When an acoustic absorber is positioned normal to the transducer axis with its anterior and posterior surfacea immersed in de-gassed water and air, respectively, there are three layers of media in the acoustic propagation
Fig. 1. Schematic drawing of acoustic wave propagation and focusing in a three-layer model (water, absorber, air). HIFU 5 high-intensity focused ultrasound.
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u52
M N vj X jk X e2jkrmn j 12 Smn 5 um vr m 5 1 2p n 5 1 rmn krmn
(2)
The planar acoustic wave reflects and refracts at interfaces I and II between the two layers, as illustrated in Figure 1. Under continuous boundary conditions at these two interfaces, the transmission and reflection coefficients of the normal particle velocity at interface II in a three-layer model can be expressed as (Du et al. 2001) 2Z1 ðZ2 1Z3 Þ 8 t 5u2t 5 < 2u ui ðZ1 1Z2 ÞðZ2 1Z3 Þ1ðZ2 2Z1 ÞðZ3 2Z2 Þe22jk2 D : u2r 2Z1 ðZ2 2Z3 Þe22jk2 D r2u 5 5 22jk D 2 ui ðZ11Z2 ÞðZ2 1Z3 Þ1ðZ2 2Z1 ÞðZ3 2Z2 Þe (3) where Z1 5 r1 c1 =cosqi ; Z2 5 r2 c2 =cosq2t ; Z1 5 r3 c3 =cosq3t q2t 5 sin21 ðc2 sinqi =c1 Þ; q3t 5 sin21 ðc3 sinqi =c1 Þ (4) D is the thickness of the absorber; Z is the acoustic impedance of medium; subscripts 1, 2 and 3 denote the water, acoustic absorber and air, respectively; subscripts i, r and t represent the incident, reflected and transmitted waves, respectively. Therefore, the normal particle velocity inside the absorber can be calculated as u2 5 u2t 1u2r 5 ui ,t2u 1ui ,r2u
(5)
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rC
vT 5 V,ðKVTÞ1Q vt
where C is specific heat capacity, T is temperature, t is time and K is thermal conductivity. Continuity of the temperature and heat flux is required across the interface at equilibrium: vT2 vT3 T2 jz 5 0 5 T3 jz 5 0 ; K2 5 K3 (10) vz z 5 0 vz z 5 0
Estimating the intensity distribution Under the assumption of planar acoustic wave propagation at the focal plane and ignorance of reflections from the water/absorber interface, the acoustic field in the absorber consists of the incident wave and the reflected wave from the absorber/air interface (Bobkova et al. 2010; Giridhar et al. 2012; Myers and Giridhar 2011; Shaw et al. 2011). The heat deposition in the absorber is Q 5 4aIðx; y; zÞjz 5 0 expð22aDÞ½12cosð2kzÞ
(12)
p2 ðx; y; zÞ 5 p2t ðx; y; zÞ1p2r ðx; y; zÞ 5 ðu2t 1u2r ÞZ2 5 ðui ,t2u 1ui ,r2u ÞZ2 ) X M N mn
mn
mn
mn jk1 X e2jk1 rmn j 12 Smn t2u qi ,cos qi 1r2u qi ,cos qi 5 um Z2 2p n 5 1 rmn k1 rmn m51
I2 5 p2 u2 5 jp2 j =2r2 c2 2
(7)
The heat deposition is (Cobbold 2006) Q2 5 2
vI2 vz
(8)
The thermal field in the medium is given by the heat equation
(11)
where I(x,y,z)jz 5 0 is acoustic intensity in water, a is the absorption coefficient of the absorber, and k 5 2 pf/c is the wavenumber. Therefore, the energy deposition and temperature elevation at the interface are related as vT2 ðx; y; z; tÞ r2 C 2 5 4aIðx; y; zÞjz50 $expð22aDÞ$Hðr; tÞ vt z50
The acoustic pressure in the absorber is given by
The corresponding acoustic intensity is calculated from the pressure amplitude in the quasi-plane wave approximation as
(9)
(6)
where H(r,t) is a function of position and time, r2 5 x2 1 y2. If the pressure distribution is assumed to be in a Gaussian function, it can be expressed as (Myers and Giridhar 2011) 2 12expð24k2 k2 tÞ 4k2 t=rb2 r Hðr; tÞ 5 ,exp 114k2 t=rb2 rb2 114k2 t=rb2 (13) where k2 is thermal diffusivity, and rb is beam width at the focal plane. H(r,t) describes the effect of the acoustic field in the absorber and thermal diffusion on the temperature
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Fig. 2. Top views of (a) transducer 1 (b) transducer 2 and (c) transducer 3 used in the study.
at the interface, and has a maximum value during heating, depending on the thermal properties of the absorber and the beam width of the ultrasound wave. Then G is defined as max½Iðx; y; zÞjz 5 0 r2 C2 G5 z 4aexpð22aDÞmax½Hðr; tÞ max vT2 ðx; y; zÞjz 5 0 =vt (14) where vT2jz 5 0/vt is the temperature change rate (TCR) at the focal plane. vT2 ðx; y; z; tÞjz 5 0 T2 ðx; y; z; t1DtÞjz 5 0 2T2 ðx; y; z; tÞjz 5 0 5 vt Dt (15) where T2(x,y,z,t)jz 5 0 is the temperature measured at the interface at time t, and Dt is the interval time. The derivative was obtained after de-noising (i.e., by discrete wavelet transform) and linear interpolation of the data, from which the maximum TCR is determined. The location of the maximum TCR corresponds to the highest intensity I(x,y,z)jz 5 0 at the measurement plane. Substituting eqn (14) into eqn (12) gives the assessment of the free-field distribution of acoustic intensity: vT2 ðx; y; z; tÞjz 5 0 Iðx; y; zÞjz 5 0 5 G,max (16) vt
Theoretical simulations Circular pistons made of PZT-8 material (Shanghai Institute of Ceramic Chinese Academy of Science, Shanghai, China) with a working frequency of 1.36 MHz were attached to a concave surface to build the phased-array ultrasound transducers (Ji et al. 2009, 2012; Li et al. 2011). The configurations and geometries of the transducers used in this study are illustrated in
Figure 2 and summarized in Table 1. Absorbers 1 and 2, both with similar thermal and acoustic parameters similar to those of soft tissue but with different attenuation coefficients (Table 2), were used in the theoretical simulation. Absorber 2 can be used repeatedly above 65 C without significant changes in its physical properties (Chen et al. 2009). Uniform mesh size was set as 1/10th and 1/40th of the acoustic wavelength for the xy-plane and z-axis of the absorber, respectively, which is a trade-off between simulation accuracy and computation burden. The acoustic intensity at the focus was set at 100 W/cm2 in the simulations, which is within the linear acoustic range (Bobkova et al. 2010; Myers and Giridhar 2011). Furthermore, three planes in the acoustic field were considered in the simulation: focal plane, pre-focal plane (z 5 5.1, 5.2 and 6.6 mm), and post-focal plane (z 5 25.0, 25.1 and 26.4 mm for transducers 1, 2 and 3, respectively), where the intensities are half that at the focus. All numerical calculations were performed in MATLAB (The MathWorks, Natick, MA, USA). Experimental measurement A hydrophone and an infrared camera were employed to assess the acoustic intensity values and distribution of the phased-array focused transducer. Figure 3 is a schematic diagram of the experimental setup. Absorbers 3 (black rubber) and 4 (milky white silicon rubber) used in the measurement were purchased on the Table 1. The configuration and geometries of phasedarray transducer Transducer
Number of pistons
Focal length (mm)
Diameter (mm)
Diameter of piston (mm)
1 2 3
144 90 65
180 180 130
180 170 100
10 14 10
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Table 2. The acoustic and thermal parameters of media Material
Speed of sound (m/s)
Density (kg/m3)
Attenuation (Np/m$MHz)
Thermal conductivity (W/ m∙ C)
Specific heat (J/kg∙ C)
Water Air Absorber 1 Absorber 2*
1500 334 1569 1550
1060 1.21 1138 1020
0 9 5
0.52 0.6
3770 2941.18
* Value was selected from Chen et al. 2009; others from Li et al. 2011.
Internet; they were both 2 mm thick, but their acoustic and thermal propertie were unknown. A Lucite water tank (L 3 W 3 H 5 400 3 400 3 300 mm), whose inner wall was lined with absorbent rubber to reduce reflection and scattering, was filled with de-gassed water (O2 , 4 mg/L, T z 25 C). The phased-array transducer was operated in the single-focus mode by a lab-developed 65-channel ultrasound driving system. A calibrated needle hydrophone (NCS-1, Institute of Acoustics, Chinese Academy of Sciences, Beijing, China) composed of PbTiO3 with an active diameter of 0.8 mm and a sensitivity of 0.11 mV/Pa at 1.36 MHz was attached to a three-axis computer-controlled translational stage with a step size of 0.1 mm (Zolix Instruments, Beijing, China) to scan the acoustic field. Absorbent rubber (UA-1, Institute of Acoustics, Chinese Academy of Sciences) was attached to the hydrophone holder to minimize acoustic reflection, especially that from the top of the water. Pressure waveforms picked up by the hydrophone were registered on a digital oscilloscope (54622-D, Agilent, Santa Clara, CA, USA) at a sampling rate of 200 MS/s, and then the digitized waveforms were transferred to a PC for further data processing. A
Y X Step Motor Controller
Oscilloscope
Z
program in LabVIEW (National Instruments, Austin, TX, USA) controlled the work flow. An uncooled IR camera (IR108 A, Guide, Wuhan, China) with a lens of 75 mm/F1.0 and real-time video output of 384 3 288 pixels was vertically positioned to measure the temperature at the absorber/air interface. The spatial and thermal resolutions are 0.59 mm and 0.08 C, respectively. Images were transferred to the PC at 25 fps via an IEEE 1394 adapter. The trigger of the IR camera and HIFU transducer was synchronized with a delay time fixed at 200 ms. Before each experimental measurement, the IR camera was warmed up for at least half an hour and self-calibrated using an established protocol (Yang and Chen 2011). Briefly, IR images of water captured at approximately each 5 C increase from a mixture of ice and water (0 C) to boiling (100 C) were compared with measurements on a mercury thermometer. The acoustic absorber was placed at the bottom of a custom-built water-proof holder (L 3 W 3 H 5 200 3 200 3 50 mm), which was attached to the 3-D translational stage. Our measurement consists of three steps. First, the acoustic intensity at the focal point of the phased-array
IR Camera Water Tank with filtered, degassed water
Z
IEEE 1394 Y X
Absorbent Rubber Holder 1
Holder 2
Step Motor Controller
Needle Hydrophone Computer
Computer Acoustic Absorber
Membrane
Acoustic Absorber
Membrane Signal Generator
Signal Generator
RF Amplifier
RF Amplifier HIFU Array
Fig. 3. Schematic diagram of infrared and hydrophone systems used to measure acoustic intensity. Components are not drawn to scale. IR 5 infrared, RF 5 radiofrequency.
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transducer was measured using the calibrated hydrophone by finding the maximum pressure in the focal region. The speed of sound in water was calculated at ambient temperature and pressure (Marczak 1997). The density of water over the temperature range 0 C to 30.9 C was obtained from an established table (Walker 2010). Second, the hydrophone was removed; a custom-built holder with only air inside and an acoustic absorber attached at the bottom was connected to the translational stage, with the top of absorber positioned coarsely to the focal plane, which was marked by a laser pointer to the tip of the hydrophone after searching the focal point. Any visible bubbles attached to the absorber and holder wall were carefully removed. The ultrasound transducer was turned on continuously for 200 ms. The thermal field of the absorber was measured with the IR camera at the same heating time used when moving the holder vertically. The focal plane is determined as the location with the maximum temperature rise, and the positional uncertainty was estimated to be 0.1–0.2 mm. G in eqn (14) was obtained from the temperature elevation data, and then the free-field acoustic intensity and its distribution at the focal plane were assessed using eqn (16). Finally, the absorber was moved along the axis to the pre- and post-focal planes, and the IR measurements were repeated. The water level should not exceed the top of the absorber holder in motion, and no change in the shape of the absorber was observed at all locations. At each location, at least three measurements were carried out, from which the mean and standard deviation were calculated. There was an interval of at least 2 min between sonications, allowing the complete thermal diffusion from the absorber to water and convection from the absorber to air.
RESULTS Temperature elevation The temperature elevation and corresponding TCR at the absorber/air interface obtained with the IR camera were compared with the simulation results obtained using transducer 3 and absorber 2 at a heating time of 200 ms (Fig. 4). There was good agreement between these results, notably during the period of sonication. After the ultrasound exposure, the temperature continued to increase for about 100 ms, because the thermal flux flows to the top surface of the absorber, similar to the temperature lag phenomenon. The maximum acoustic intensity and consequent maximum temperature elevation is located about 0.3 mm below the surface in our simulation (Fig. 5). Afterward, the temperature decays exponentially. Fluctuations in measurements were caused by the noise of the IR camera as well as motion of the absorber in response to the acoustic radiation force.
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Fig. 4. Comparison of the infrared measurement (solid line) and theoretical simulation (dashed line) of the (a) temperature elevation and (b) temperature change rate at the surface of absorber 2 aligned at the focal plane of transducer 3 for a heating time of 200 ms.
Effect of heating time To choose an appropriate operation parameter in the measurement, the heating time was varied from 40 to 360 ms in the simulation. Figure 5 is the profile of axial
Fig. 5. Comparison of the simulated temperature distributions on the axis of absorber 2 using the transducer 3 at the end of heating from 40 to 360 ms using the three-layer medium model (solid line) and Meyer’s model (dashed line). The absorber/air interface is aligned at the focal plane of the transducer.
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temperature elevation in the absorber at the end of sonication. In comparison to the simulation results assuming planar wave incidence (Myers and Giridhar 2011), similarities are found within z 5 0–0.6 mm (half wavelength in absorber 2). However, differences become pronounced at deep locations, especially at z 5 1.8–2.0 mm, which is close to the absorber/water interface. Discrepancies are due to ultrasound incident convergence and reflective divergence at the posterior interface (absorber/air) and the presence of the anterior interface (water/absorber) in our three-layer media model. To evaluate the accuracy of estimation, the acoustic intensities derived from the simulated acoustic field and from the temperature elevations using the proposed method were compared. Figure 6 illustrates the radial distribution of acoustic intensity at the focal, pre-focal and post-focal planes using transducer 3 and absorber 2 at heating times (continuous exposure to ultrasound wave) of 40, 120, 200, 280 and 360 ms. Both assessed main and side lobes fit the theoretical simulation fairly well. The percentage differences in maximum acoustic intensity and 26-dB beam width are summarized in Tables 3 and 4, respectively. The maximum acoustic intensity derived in the pre-focal plane is higher than that in the theoretical simulation (,5%), but lower than that in the post-focal plane. The exception occurs when the heating time is longer than 280 ms using absorber 2. There are more percentage differences in 26-dB beam width with increases inheating time and distance from the focal plane. The significant thermal diffusion effect and invalidation of the planar wave assumption may lead to a broad distribution of thermal energy at the surface of the absorber. The percentage differences for transducer 3, which has a larger F-number of 1.3, are lower than the others because of the larger beam width. Overall, the proposed method can quantitatively assess the value and distribution of the focused ultrasound field with satisfactory accuracy.
Experimental measurement Figure 7 illustrates the distribution of acoustic intensities in the focal region obtained with the theoretical simulation, hydrophone measurement and the proposed method using transducer 3 at a heating time of 200 ms. The acoustic intensity at the focus was measured as 33.9 W/cm2 and used in the theoretical simulation and proposed estimation method. Maximum acoustic intensity and 26-dB beam width are compared in Table 5. Hydrophone measurements were found to fit the theoretical simulation fairly well, especially for the shape and beam width of the main lobe, despite the higher acoustic
Fig. 6. Comparison of the distribution of acoustic intensity derived from the simulation and by the proposed method from the simulated thermal field using transducer 3 and absorber 2 for heating times ranging from 40 to 360 ms at (a) z 5 0 mm (the focal plane), (b) z 5 7 mm and (c) z 5 26 mm, where the acoustic intensity on axis is half of that at the focus of the phased-array transducer.
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Table 3. Percentage difference between the maximum intensity on-axis using the proposed method in the simulated thermal field and that in the theoretical prediction for different transducers, heating time, absorbers, and locations Absorber 1
Absorber 2
Heating Pre-focal Post-focal Pre-focal Post-focal Transducer time (ms) (%) (%) (%) (%) 1
2
3
40 120 200 280 360 40 120 200 280 360 40 120 200 280 360
3.53 3.40 3.49 3.51 3.62 4.08 3.44 3.44 3.51 3.55 1.72 1.73 1.77 1.75 1.69
21.56 21.59 21.40 21.25 20.99 21.40 21.81 21.67 21.44 21.20 21.18 21.11 20.99 20.84 20.68
2.31 2.42 2.59 2.79 3.02 2.50 2.38 2.48 2.60 2.75 1.11 0.91 0.86 0.85 0.85
20.99 20.78 20.36 0.09 0.56 20.95 20.91 20.55 20.17 0.24 20.40 20.47 20.23 0.07 0.37
intensities measured at the off-focal plane. The discrepancy may be due to the mis-alignment of pistons during installation, non-uniform pressure distribution on the piston surface and position error of the hydrophone. Although the maximum acoustic intensities estimated by the proposed method using these two absorbers are quite similar, the beam widths derived using absorber 3 are much larger than those obtained using absorber 4, which may be due to more absorbed energy and significant diffusion (G 5 4.4 and 3.5 for absorbes 3 and 4, respectively). In Figure 8, the 2-D (xz and yz) distribution of acoustic intensity determined with the proposed method using transducer 3 and absorber 3 at a heating time of
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200 ms was compared with the theoretical simulation. Comparison of the intensity distributions obtined by theoretical simulation, hydrophone measurement and the proposed method exhibit fair agreement on the axis of the phased-array transducer, with the difference between the hydrophone measurement and derived value varying from 30.81% to 19.47% (see Fig. 9). In most of the focal region, there was no statistical difference between hydrophone and IR measurements (p . 0.05). However, the assessed intensity was found to be non-symmetric, which may be due to the non-uniformity of the absorber, misalignment of pistons and small titling angle of the absorber with respect to the axis. In addition, the background noise of the IR camera may deteriorate the intensity assessment beyond the main lobe at such a short heating time. DISCUSSION In this study, a method of measuring the distribution of acoustic intensity using a hydrophone and an IR camera was introduced. One of the advantages of this approach is that prior knowledge of the acoustic and thermal properties of the absorber is not required, in contrast to existing IR-based methods (Bobkova et al. 2010; Giridhar et al. 2012; Hand et al. 2009; Myers and Giridhar 2011; Shaw and Nunn 2010). G defined in eqn (14) has already accounted for the thermal conduction and diffusion in the absorber which should be considered in the IR measurement (Bobkova et al. 2010; Myers and Giridhar 2011). Without knowledge of the intensity distribution (i.e., beam width) and diffusivity of the absorber, it is hard to determine explicitly the function H(r,t). Here the maximum value of H(r,t) (at the location of the maximum TCR where it
Table 4. Percentage difference between the -6 dB beam width using the proposed method in the simulated thermal field and that in the theoretical prediction for different transducers, heating time, absorbers, and locations Absorber 1
Absorber 2
Transducer
Heating time (ms)
Pre-focal (%)
Focal (%)
Post-focal (%)
Pre-focal (%)
Focal (%)
Post-focal (%)
1
40 120 200 280 360 40 120 200 280 360 40 120 200 280 360
3.80 5.53 7.53 9.50 11.38 3.40 5.44 7.77 10.01 12.16 3.54 5.07 6.95 9.31 11.65
2.97 4.36 5.94 7.49 8.99 2.64 3.86 5.66 7.40 9.07 1.95 2.77 3.74 4.70 5.63
3.64 5.07 6.75 8.82 10.86 4.07 5.69 7.55 9.37 11.14 3.62 4.87 6.30 7.72 9.12
5.99 8.80 12.54 16.35 19.84 6.22 9.56 13.10 16.93 21.09 5.32 8.83 12.57 16.02 20.27
4.83 7.05 9.53 11.89 14.14 4.57 7.03 9.76 12.36 14.83 3.14 4.49 6.01 7.49 8.92
5.29 8.23 11.54 14.63 17.51 5.78 8.52 11.83 15.42 18.74 4.93 7.15 9.40 11.94 14.52
2
3
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Fig. 7. Comparison of the acoustic intensity distribution from theoretical simulation, hydrophone measurement and results derived from the proposed method on the x-axis (left column) and y-axis (right column) using transducer 3 and absorbers 3 and 4 at a heating time of 200 ms at (a) z 5 0 mm, (b) z 5 7.5 mm, and (c) z 5 26 mm. x- and y-axes are the left-right and front-back directions of the transducer, respectively.
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Table 5. Comparison of the maximum acoustic intensity and -6 dB beam width calculated using different methods in the focal region at the heating time of 200 ms Theoretical simulation
Absorber 3
Absorber 4
16.2 6 0.9 21.9 6 0.7
13.6 18.2
16.5 6 4.2 21 6 1.1
13.9 6 2.0 20.8 6 3.1
2.04 6 0.07 3 2.27 6 0.11 2.27 6 0.47 3 3.37 6 0.79 2.04 6 0.47 3 2.23 6 0.66
2.06 2.33 2.26
3.04 6 0.41 3 3.09 6 0.81 6.05 6 1.26 3 7.12 6 1.66 5.40 6 1.60 3 4.10 6 1.55
2.62 6 0.06 3 2.70 6 0.52 3.89 6 0.55 3 6.56 6 0.88 2.88 6 2.35 3 2.83 6 0.63
Maximum acoustic intensity (W/cm2)
Hydrophone measurement
z 5 7.5 mm z 5 -6 mm -6 dB beam width (mm) z 5 0 mm z 5 7.5 mm z 5 -6 mm
coincides with the focal point) was used to calculate G in an experimentally simple way, and the constant G was used for the entire focal region. Although errors exist between this value and that of an off-axis point, the relative difference was found acceptable in our measurements (the error is estimated up to about 8.5% within the 26-dB focal region in the simulation using our HIFU transducer in Fig. 6). In future studies, the spatial function of G(x,y,z) will be developed to derive the acoustic intensity. At variations in frequency, beam width and the absorber’s thermal diffusivity by [0.5, 3], [0.5, 2] and [0.75, 1.25] folders, respectively, the error within the 26-dB focal region at heating times of 100–400 ms is estimated to be as high as17% in our simulation. The acoustic intensity at the focus was measured directly, and then the distribution of acoustic intensities in the entire focal region was derived using the thermal image. Even though acoustic field mapping is time consuming because of the alignment of the hydrophone parallel with the transducer axis (alignment error within 0.1 wavelength [GB/T 16846-2008], searching for the focal point is fairly straightforward. Therefore, hydrophone measurement of acoustic intensity at the focus will not increase the complexity, time and cost of measurement significantly. Appropriate choice of the heating time is critical in the quantitative assessment of acoustic intensities. Low temperature elevation after a short sonication, which is below the thermal resolution of the IR camera, would result in a low signal-to-noise ratio. For example, if the heating time is 40 ms, the corresponding temperature elevations at the focus of transducer 3 in absorbers 3 and 4 are 0.17 C and 20.11 C (the negative value is due to the uncertainty of the IR camera for small temperature elevations), respectively, which is similar to the measurement variation at the interface, about 0.12 C, and the resolution of the IR camera, 0.08 C (Fig. 10). The minimum exposure time is usually a few tenths of seconds for a desired temperature rise of about 1 C. At a heating time of 200 ms, a significant temperature elevation and sharp profile were found in both absorbers. So this value was used for our studies. In contrast, a long heating time may cause irreversible changes in the
acoustic and thermal properties of the absorber although below its melting point. Non-uniformity and inhomogeneity in the absorber would further increase the systemic error in the subsequent measurements. A significant thermal diffusion effect would invalidate our use of the constant G value in the entire focal region. Thus, the heating time in our study is much lower than that used in other studies (Giridhar et al. 2012; Myers and Giridhar 2011). In addition, the influence of convective heat transfer becomes significant at high temperature elevations, although the upper limit is estimated to be 15 s for a 1MHz beam and a tissue diffusivity of 0.15 mm2/s (Giridhar et al. 2012). With an increase in frequency, the highest temperature inside the absorber is considerably closer to the surface temperature. As a result, the upper limit of sonication duration may decrease dramatically. Determination of the onset of sonication is another critical issue in the existing IR measurement. Although IR recording should be synchronized with the power output to the ultrasound transducer, the IR camera is usually turned on before the sonication because of the slow response and low frame rate (25–30 fps). The ‘‘inflection-point’’ method was used to determine the starting time from the IR temperature trace (Giridhar et al. 2012). However, its error (i.e., on the order of 100 ms) is comparable to the total sonication duration in our experiments. The maximum temperature change rate, instead of the starting time of sonication, was calculated from the IR images obtained in this study, which proved to be easy, sensitive and reliable in the IR measurement without compromising the derivation accuracy of the acoustic intensities. Both theoretical and experimental results indicate that appropriate choice of the absorber would increase the accuracy of assessment of acoustic intensities (Tables 3–5, Figs. 6 and 7). The ideal absorber may have high attenuation, low thermal conductivity, high stability and small thickness. As expected, higher temperature elevations in short sonications and less thermal diffusion may be able to increase the signal-to-noise ratio and minimize systemic errors. The attenuation length of infrared electromagnetic energy of silicon rubber is about
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Fig. 9. Comparison of the acoustic intensity distribution from theoretical simulation, hydrophone measurement and results derived using the proposed method on the z-axis using transducer 3 and absorber 3 at a heating time of 200 ms in the infrared measurement.
Fig. 8. Comparison of acoustic intensity distribution derived with the proposed method at the (a) xz and (b) yz planes in the infrared measurement using transducer 3 and absorber 3 at a heating time of 200 ms with the (c) the theoretical simulation in the free field.
0.06 mm (Pline 1989; Wang et al. 2008), less than the acoustic wavelength of the absorber. Therefore, the elevated temperature inside the silicone absorber will not be picked up by the IR camera (Giridhar et al. 2012; Myers and Giridhar 2011). A thin water-based
coating (on the order of 1 mm) for the necessary IR attenuation, although transparent to acoustic propagation, could also limit IR penetration (Giridhar et al. 2012). Further research into the impact of thermal and acoustic parameters will be carried out. Improvements in the IR-based assessment of acoustic intensity are greatly needed. When the absorber moved away from the focal plane, the difference between the derived and measured acoustic intensities did increase. The reason may be the invalidation of the planar wave assumptions in the absorber in deriving eqn (16). Transducers with larger F-numbers (i.e., transducer 3 in this study) have a smaller gain and, consequently, a smaller error of acoustic intensity quantization in the IR measurement, which was also confirmed in another study (Giridhar et al. 2012). There are errors around 40% at the pre- and post-focal planes for higher-gain transducers, which may be unacceptable in acoustic field calibration. Efforts should be made to overcome these defects to establish IR-based measurement as a standard calibration method. Furthermore, it was found that the measured temperatures at the side foci of a 2-D phased array are only about half those predicted by a simple model (Bobkova et al. 2010). Although the reason is not well understood and no pressure mapping was carried out to confirm such a low side lobe, correct assessment of the side foci is important to the safety profile of HIFU ablation to avoid unintended damage to vital tissue (i.e., artery and nerve). Efforts should be made to establish IR-based measurement as a standard calibration method.
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REFERENCES
Fig. 10. Comparison of the temperature elevations measured at the top surface of absorber 3 (a) and absorber 4 (b) by the infrared camera using transducer 3 at heating times from 40 to 360 ms.
CONCLUSIONS The method proposed for quantitative assessment of acoustic intensities using a hydrophone and an IR camera with no prior knowledge of the properties of the absorber and configuration of the phased array has a satisfactory percentage difference, in both maximum intensity (,3.5%) and 26-dB beam width (,13.1%) in the focal region, in comparison to the theoretical simulation using a three-layer medium model and hydrophone measurement at a heating time of 200 ms from an ultrasound transducer with F-numbers of 1.25–2. The percentage difference increases with distance from the focal plane, heating time, and thermal conductivity of the absorber, but decreases with the F-number of the transducer. Acknowledgments—We thank Vera Khokhlova, Matthew R. Myers and Junru Wu for guidance in calculation of the acoustic field and for providing the physical parameters of the absorber. This study was supported by the National Natural Science Foundation of China (No. 30800246) and the Key Technologies R&D Program of Shanghai, China (No. 09441900500).
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