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Measurement of high intensity focused ultrasound fieldsby a fiber optic probe hydrophone

Yufeng Zhou, Liang Zhai, Rebecca Simmons, and Pei Zhonga�

Department of Mechanical Engineering and Materials Science, Duke University,Durham, North Carolina 27708

�Received 31 January 2006; revised 16 May 2006; accepted 19 May 2006�

The acoustic fields of a high intensity focused ultrasound �HIFU� transducer operating either at itsfundamental �1.1 MHz� or third harmonic �3.3 MHz� frequency were measured by a fiber opticprobe hydrophone �FOPH�. At 1.1 MHz when the electric power applied to the transducer wasincreased from 1.6 to 125 W, the peak positive/negative pressures at the focus were measured to bep+=1.7–23.3 MPa and p−=−1.2–−10.0 MPa. The corresponding spatial-peak pulse-average �ISPPA�and spatial-average pulse-average �ISAPA� intensities were ISPPA=77–6000 W/cm2 and ISAPA

=35–4365 W/cm2. Nonlinear propagation with harmonics generation was dominant at highintensities, leading to a reduced −6 dB beam size �L�W� of the compressional wave �11.5�1.8–8.8�1.04 mm� but an increased beam size of the rarefactional wave �12.5�1.6–13.2�2.0 mm�. Enhancement ratio of absorbed power density in water increased from 1.0 to 3.0. Incomparison, the HIFU transducer working at 3.3 MHz produced higher peak pressures �p+

=3.0–35.1 MPa and p−=−2.5–−13.8 MPa� with smaller beam size �0.5�4 mm�. Overall, FOPHwas found to be a convenient and reliable tool for HIFU exposimetry measurement. © 2006Acoustical Society of America. �DOI: 10.1121/1.2214131�

PACS number�s�: 43.25.Zx, 43.80.Ev, 43.25.Cb �CCC� Pages: 676–685

I. INTRODUCTION

In recent years, high intensity focused ultrasound�HIFU� has been used increasingly as a new and effectivetreatment modality for cancer therapy.1–4 By focusing acous-tic energy into a small cigar-shaped volume, HIFU �ISPTA

�1000 W/cm2� can produce thermal ablation �temperature�65 °C� and tissue necrosis �i.e., a lesion� in a well-definedvolume in the target tumor.5 Treatment of the whole tumor isaccomplished by scanning the HIFU beam line-by-line andlayer-by-layer under the guidance of B-mode ultrasound orMRI imaging. For safe and effective HIFU treatment in theclinic, it is critical to predict and control the lesion sizeproduced.6 Towards this goal, a fundamental knowledge ofthe acoustic field and acoustic energy output of the HIFUsystem is essential and needs to be accurately determined.

Several techniques have been developed to measure theacoustic output of HIFU transducers. For example,calorimetry7 and radiation force measurements8 have beenused to determine the total acoustic power produced by aHIFU transducer, from which the total energy flux throughthe beam cross-sectional area �or intensity� can be estimated.Although convenient to use, these techniques cannot resolvethe pressure variation and distribution within the focal vol-ume. Currently, polyvinylidene fluoride �PVDF� membraneor needle hydrophones �with a sensing element of0.5–1.0 mm� are often used for mapping the acoustic field ofa HIFU transducer. However, to avoid cavitation damage tothe hydrophone, measurements were typically carried outfirst at a low output level, and then the pressure amplitudes

a�
Electronic mail: [email protected]
676 J. Acoust. Soc. Am. 120 �2�, August 2006 0001-4966/2006/1

and distribution at high output levels were extrapolatedbased on linear propagation model.9,10 Since wave form dis-tortion due to nonlinear propagation and cavitation producedat high output levels will significantly alter the size andshape of the lesion formed,6,11–14 the extrapolation methodmay not provide accurate and satisfactory results. Moreover,once cavitation damage is produced on the surface of thesensing element of the hydrophone, the probe must be re-paired and recalibrated before further use. Alternatively, op-tical methods based on Schlieren imaging15 and optical dif-fraction tomography16 have been used to quantify thepressure field of ultrasound transducers. Yet, the applicabilityof these optical methods is also limited to conditions underlow-pressure amplitudes associated with linear wave propa-gation. Altogether, current methods used for HIFU exposim-etry measurement are either limited by their spatial or tem-poral resolutions or unreliability in determining the HIFUfield at clinically relevant high intensity output levels.

In this work, a self-calibrated fiber optic probe hydro-phone �FOPH�17 was used for HIFU exposimetry measure-ment. FOPH was originally developed for measurement ofshock waves of high pressure amplitude with short risetimein a lithotripter field.17 Because of its small probe size�0.1 mm sensing element�, broad bandwidth �50 MHz�, im-proved robustness in high tensile pressure field, and longev-ity �a probe tip can be easily prepared after cavitation dam-age�, it may provide a reliable and accurate means for HIFUexposimetry measurement. Using a FOPH, we have mea-sured the pressure wave forms produced in the focal volumeof a focused HIFU transducer operating at either its funda-mental �1.1 MHz� or third harmonic �3.3 MHz� frequency. Itwas found that pressure wave form distortion appeared at
moderate output levels and grew significantly at high output
© 2006 Acoustical Society of America20�2�/676/10/$22.50

levels of the HIFU transducer. Based on the pressure waveforms measured, the beam size, intensity, and acoustic powerof the HIFU transducer were calculated and the primary fea-tures of nonlinear propagation and associated energy absorp-tion enhancement were quantified.

II. MATERIALS AND METHODS

A. Fiber optic probe hydrophone „FOPH… and PVDFmembrane hydrophone

In this study, a fiber optic probe hydrophone �FOPH-500, RP Acoustics, Leutenbach, Germany� was used forHIFU field measurement. The working principle of FOPHhas been described previously.17 Briefly, the FOPH-500 em-ploys a pigtailed laser diode ��=810 nm� that is connectedto one leg of a 1�2 fiber coupler. The light reflection at a100 �m fiber/water interface is measured by a fast photode-tector with an integrated amplifier of 30 MHz bandwidth,connected to the other leg of the coupler. Conversion of thereflected light intensity to pressure can be carried out off-lineusing a calibration program based on the Fresnel formula forthe pressure-dependent refractive index at the fiber tip/waterinterface. With deconvolution process, the bandwidth of theFOPH can be enhanced to 50 MHz without loss in thesignal-to-noise ratio �SNR� and the sensitivity of hydrophoneis about 2 mV/MPa based on the specification of the manu-facturer. The measurements of the FOPH was first comparedwith a recently calibrated PVDF membrane hydrophone�GEC-Marconi Research Center, Essex, UK� with an activeelement of 0.5 mm diameter, operated in combination with amatched amplifier, yielding a sensitivity of 41 mV/MPa at1 MHz.

B. HIFU transducer and pressure measurementprotocol

An annular focused HIFU transducer �H-102, OuterDiameter=69.94 mm, Inner Diameter=22.0 mm, F=62.64 mm, Sonic Concepts, Woodinville, WA� was used inthis study �Fig. 1�. The HIFU transducer, mounted at thebottom of a Lucite tank �L�W�H=40.5�30.5�15 cm�filled with degassed and deinoized water �O2�4 mg/L, T�25 °C�, was driven by sinusoidal bursts produced by afunction generator �33120A, Agilent, Palo Alto, CA� to-gether with a 55 dB power amplifier �A150, ENI, Rochester,NY�. A 50 � attenuator �up to 22.1 dB attenuation, Kay El-emetrics Corp., Lincoln Park, NJ� could be inserted betweenthe function generator and the power amplifier to further re-duce the electric power input to the HIFU transducer. TheHIFU transducer was running either at its fundamental�1.1 MHz� or third harmonic �3.3 MHz� frequency. To mapthe acoustic field of the HIFU transducer, the FOPH probewas connected to a three-dimensional positioning system�step motors: VXM-2, lead screws: BiSlide-M02, Velmex,Bloomfield, NY�, which has a minimum step size of 5 �mand a maximum scan range of 250 mm. The output of theFOPH was first recorded by a digital oscilloscope �LeCroy9310A, Chestnut Ridge, NY� operated at 100 MHz samplingrate, and then transferred to a PC for off-line pressure con-
version and analysis. To streamline the experiment, a Visual
J. Acoust. Soc. Am., Vol. 120, No. 2, August 2006 Zho

Basic program was written and used to control automaticallythe output of the function generator, data acquisition andtransfer, and scanning of the FOPH probe via GPIB bus andRS-232 port, respectively.

To minimize temperature increase and cavitation activitynear the probe tip, the HIFU transducer was operated in burstmode with a duty cycle of 0.1 %–0.2 % �i.e.,10–20 cycles/burst�, and the peak-to-peak output voltagefrom the function generator, Vpp, was set to be less than0.5 V. Above this output level, cavitation was frequently in-duced at the probe tip, leading to wave form contaminationand probe damage. Averaging over 300 bursts was used toimprove the SNR of the measured pressure wave forms. Thegeometric focus of the HIFU transducer was determined bysearching for the location of maximum signal strength at alow output level with a burst delay time of �41.76 �s,which is the time needed for a linear acoustic wave to propa-gate from the surface to the focus of the HIFU transducer. Atthe low output level the geometric focus was assumed tocoincide with the acoustical focus of the HIFU transducer.An x-y-z coordinate system was then established with itsorigin coinciding with the geometric focus of the transducerand the z axis along the transducer axis �Fig. 1�. Acousticfield characterization of the HIFU transducer was carried outby line or area scan. For line scan, the pressure distributionstransverse to and along the transducer axis within the rangeof x=−3–3 mm and z=−50–50 mm were measured at a stepsize of �x=0.12 mm and �z=0.5 mm, respectively. For areascan, the pressure distributions in the x-y or x-z plane�x=−2–2 mm, y=−2–2 mm, z=−10–10 mm, �x=�y

FIG. 1. �Color online� A schematic diagram of the experimental setup forHIFU exposimetry measurement using a computer controlled three-dimensional pressure mapping system.

=0.1 mm, �z=1 mm� were recorded.

u et al.: High-intensity focused ultrasound field measurement 677

C. Data analysis

Following the measurements, the peak positive/negative�compressional/rarefactional� pressure distributions wereplotted, respectively, from which the −6 dB beam size andmain lobe size were calculated. Spectrum analysis was per-formed by using fast Fourier transform �FFT� with minimalspectrum leakage techniques. First, the recorded full ampli-tude wave form was truncated to an integer number of cycleswith zero-crossing points on both ends. Second, the trun-cated wave form was replicated to about 4000 samplingpoints. Third, Fourier transformation was performed on thestretched wave form to determine its fundamental frequencyand harmonics. The spectrum could be further normalized bythe total energy of the wave form. In addition, the spectra ofthe compressional and rarefactional components of the waveform were analyzed individually to evaluate their differentnonlinear propagation characteristics.18

Based on the pressure wave-form data, the spatial-peakpulse-average intensity �ISPPA�, typically at the focus of theHIFU transducer, can be calculated by

ISPPA =1

nT�

t0

t0+nT p2�t��0c0

dt , �1�

where �0 is the ambient density of water, c0 is the small-signal sound speed in water, p�t� is the time varying pressurewave form, T is the period of the wave form, n is the integernumber of cycles in the selected pressure wave form, t0 is theretarded time for the first full amplitude period, and t istime.19 In addition, the spatial-average pulse-average inten-sity �ISAPA� can be calculated as

ISAPA = �S

ISPPAdS��S

dS , �2�

where S is the integration area, which is usually the −6 dBbeam area in the focal plane. Here the ISPPA as defined inEq. �1� is used in a broad sense to indicate pulse-averageintensity at the measurement point.

The electrical input power to the HIFU transducer �Pin�was determined by Pin=Vrms

2 cos / Z, where Vrms is the rmsvoltage applied to the HIFU transducer, Z is the magnitudeand is the phase angle of the impedance Z. According tothe specifications from the manufacturer, the impedance pa-rameters of the HIFU transducer at 1.1 and 3.3 MHz with the50 � matching unit are Z=62.5 �, 43.9 �, and =0.334°,0.925°, respectively. The acoustic power of the HIFU trans-ducer �P� was estimated by integrating ISPPA through a largearea including the main and side lobes of the HIFU trans-ducer. Subsequently the energy conversion efficiency of theHIFU transducer was determined by P / Pin.

D. Power absorption

In the focal region of a HIFU transducer, significantnonlinear propagation will cause the acoustic energy to shiftfrom the fundamental frequency to higher harmonics, each of
which has a different focal geometry and absorption prop-
678 J. Acoust. Soc. Am., Vol. 120, No. 2, August 2006

erty. As shown previously by Clarke and ter Haar12 the ab-sorbed acoustic power density A�P� can be calculated fromspectra data by

A�P� = n=1

6

In�P��fn� , �3�

where In�P� is the acoustic intensity of nth harmonic atacoustic power P, �fn�=2.5�10−4fn

2Np / cm/MHz is theabsorption coefficient at the harmonic frequency fn in wa-ter. Here only six harmonics are included because of theirsatisfactory SNRs. The initial lesion formation in a HIFUfield is believed to occur at the point where the absorbedpower density reaches a maximum.9

When the output of the HIFU transducer increases, therate of harmonics generation and acoustic to thermal energyconversion will also change nonlinearly. The enhancementratio for the absorbed acoustic power per unit volume,EA�P�, can be determined using the following equation:

EA�P� =A�P�

P � A�Pref�Pref

, �4�

where Pref is the lowest power of the HIFU transducer�i.e., in this study the output voltage of the function gen-erator was 0.05 V with additional 22.1 dB attenuation at1.1 MHz� in the range of linear acoustics.5

III. RESULTS

A. Comparison of FOPH and PVDF membranehydrophone

The acoustic pressures produced by the 1.1 MHz HIFUtransducer in the linear range measured by the FOPH and thePVDF membrane hydrophone, respectively, were comparedin Fig. 2. At low output level the noise in the FOPH mea-sured wave form was significant even after signal averaging,especially at the wave crest and trough. Overall, however,the wave-form profiles measured by these two different hy-

FIG. 2. �Color online� Comparison of the measured pressure wave forms bythe FOPH and the PVDF membrane hydrophone in the 1.1 MHz HIFU fieldproduced at a peak-to-peak output voltage of 50 mV with 15 dB insert at-tenuation.

drophones were symmetric and similar to each other. It was

Zhou et al.: High-intensity focused ultrasound field measurement

noticed that in the linear range the measured peak-to-peakpressure by the FOPH was usually higher than that of thePVDF membrane hydrophone and this difference was pro-portional to the output voltage of the HIFU transducer.

When converting the electric signal to the correspondingacoustic pressure measured by a PVDF membrane hydro-phone, the sensitivity at the fundamental frequency of themeasured pulse is often used. At high output levels shift ofthe acoustic energy from the fundamental frequency to itsharmonics due to nonlinear propagation is significant. Thesensitivity of the PVDF membrane hydrophone used in thisstudy decreases by about 20% from 1 MHz to 20 MHz.Hence, the use of the full calibration chart in the frequencyrange �deconvolution of the frequency response of the hydro-phone� may lead to more accurate conversion of the pressurewave form. For example, at Vpp=0.5 V the deconvolutedwave form produced by the 3.3 MHz HIFU transducer had a5% higher peak positive pressure than the correspondingvalue calculated using only the sensitivity at the fundamentalfrequency �Fig. 3�a��.

Figure 3�b� compares the lateral pressure distributions ofthe 3.3 MHz HIFU transducer at Vpp=0.2 V, measured byusing the FOPH �solid line� and the PVDF membrane �longdashed line� hydrophone, respectively. The FOPH measure-ments revealed much higher peak pressure at the focus�17.9 MPa� and smaller −6 dB beam width �0.37 mm�, com-pared to the corresponding values measured by the PVDFmembrane hydrophone �8.9 MPa and 0.48 mm�. It is inter-esting to note that if the FOPH measured pressure distribu-tion was averaged through an area of 0.5 mm in diameter�representing the sensor size of the PVDF membrane hydro-phone�, the final results would change significantly �shortdashed line in Fig. 3�b��. The pressure distribution lookssimilar to that of the PVDF membrane hydrophone with thepeak pressure decreasing to 12 MPa and the −6 dB beamwidth increasing to 0.63 mm. According to the InternationalElectrotechnical Commission standards �IEC 61102�, themaximum hydrophone size for measuring this 3.3 MHzHIFU field should be less than 0.27 mm in order to avoid thespatial averaging effect imposed by the size of the sensor.20

B. Nonlinear effects in HIFU field

The pressure wave forms produced by the 1.1 MHzHIFU transducer were measured in the range of Vpp

=0.05–0.5 V �Fig. 4�. Combined with the 55 dB power am-plifier, the corresponding electrical input power into thetransducer was calculated to be 1.6–125 W �Table I�. Thepressure wave forms measured by the FOPH are consistentand reproducible. Over a 2-month period, the variations inpeak positive �p+� and negative �p−� pressures from six ex-periments were found to be within 5% except at the lowestoutput level ��10% � that may be caused partially by a pos-sible longtime baseline variation of the oscilloscope or thelaser intensity of the FOPH ��0.1 MPa at Vpp=50 mV�, asystem error that cannot be reduced by signal averaging. Theacoustic intensities and acoustic powers were calculatedbased on the measured pressure wave forms �Table I�. Within
this output range ISPPA and ISAPA were found to increase

from 77 to 6000 W/cm2 and from 37 to 4365 W/cm2, re-spectively. When the acoustic power was increased from1.1 to 81.6 W, the corresponding power conversion effi-ciency was found to vary in the range of 62%–73%, which isclose to the value specified by the manufacturer based onradiation force measurements.

At the geometric focus, wave-form distortion from sinu-soidal to “sawtooth” shape due to nonlinear propagation21

was observed as the output of the transducer was increased�Fig. 5�a��. The nonlinear effects in the HIFU field led tosignificantly different electric input-dependent relationshipof p+ and p−. Within the range of Vpp=0.05–0.5 V, p− in-creased almost linearly from −1.2 to −10.0 MPa while p+

rose much more rapidly from 1.7 to 23.3 MPa �Fig. 4�. Thenonlinear propagation was also manifested by harmonicsgeneration in the wave forms �Fig. 5�b��. At low output level�Vpp=0.05 V�, the fundamental frequency was found to ac-

FIG. 3. �Color online� �a� The effect of deconvolution on the conversion ofelectric signal to pressure wave form measured by the PVDF membranehydrophone at the focus of a 3.3 MHz HIFU transducer with Vpp=0.5 V. �b�Comparison of the pressure distribution measured by the FOPH �solid line�and the PVDF membrane hydrophone �long dashed line� in the focal planeof the 3.3 MHz HIFU transducer with Vpp=0.2 V. Furthermore, the pressuredistribution measured by the FOPH was averaged through an area of0.5 mm in diameter �short dashed line�. Vpp: peak-to-peak output voltage ofthe function generator.

count for about 85% in the normalized spectrum while the


second harmonic was less than 5% �solid line in Fig. 5�b��.Hence, most acoustic energy was stored in the fundamentalfrequency. In contrast, at high output level �0.5 V�, the fun-damental frequency decreased to 46% while the second har-monic increased to 19%, and higher �third and fourth� har-monics became significant �dashed line in Fig. 5�b��.Therefore, substantial portion of the wave form energy wasshifted from the fundamental frequency into higher harmon-ics. Furthermore, the intensities of all harmonics were foundto increase linearly with the acoustic intensity, ISPPA, �inset inFig. 5�b�� and the calculated slopes �Table II� were found tobe similar to the results of previous studies.12,18 Furthermore,the nonlinearity has different influence on compressional andrarefactional waves. The fundamental frequency of the com-pressional wave was found to shift upwards from 1.1 MHzwhile that of the rarefactional wave shifted downwards. Athigher output the rate of harmonics generation for the com-pressional components increased much faster than that of therarefactional components �Table II�. As a result, thesechanges lead to the asymmetric distortion of the wave form�Fig. 5�a��.

The pressure distributions along the transverse �x� andaxial �z� direction of the 1.1 MHz HIFU transducer areshown in Fig. 6, which were found to be fairly symmetric inthe focal plane. Although the peak pressures increased with

FIG. 4. �Color online� The electric input dependency of peak positive �p+�and negative �p−� pressure at the focus of the HIFU transducer working ateither 1.1 or 3.3 MHz. Vpp is the peak-to-peak output voltage of the functiongenerator. The percentage of standard deviation over mean value is listed inthe plot for the 1.1 MHz HIFU transducer. Results were calculated from sixexperiments performed in a 2-month period.

TABLE I. Acoustic intensity, power output, and1.1 MHz HIFU transducer.

Output Vpp �V� ISPPA �W/cm2� ISAPA �W/c

0.05 77.4 36.50.1 281 1460.2 1082 6050.3 2458 14260.4 4433 26570.5 5996 4365


the output power, the size of the main lobe remained almostunchanged, i.e., L�W=20.5�2.7 mm. At the highest outputlevel �Vpp=0.5 V�, the maximum p+ was measured at a po-sition slightly ��0.5 mm� beyond the geometric focus of thetransducer, while the maximum p− was found to shift�2.5 mm proximal to the transducer. Similar phenomenonhas been observed in a lithotripter field, which is attributed tononlinear propagation of the shock wave.22 The correspond-

ic-to-acoustic energy conversion efficiency of the

ISAPA/ ISPPA Pin �W� P �W� P / Pin

0.47 1.56 1.14 72.7%0.52 6.36 3.95 62.1%0.56 23.5 15.0 63.0%0.58 51.5 33.1 64.3%0.60 86.2 59.6 69.2%0.73 125 81.6 65.6%

FIG. 5. �Color online� �a� Normalized pressure wave forms measured by theFOPH at the focus of the 1.1 MHz HIFU transducer when the peak-to-peakoutput voltage �Vpp� of the function generator was set at 0.05 and 0.5 V,respectively, and �b� the corresponding normalized spectra and harmonicintensities of the pressure wave forms and the electric input dependency ofharmonic generation �inset� with respect to the referenced pressure of1 MPa.

electr

m2�


ing −6 dB beam sizes both in the focal plane and along thecentral axis of the 1.1 MHz HIFU transducer were calculated�Fig. 7�. Because of the strong nonlinear propagation and theassociated harmonics generation, the −6 dB beam size of p+

was found to decrease significantly with output power. Incontrast, the −6 dB beam size of p− was found to increaseslightly, presumably because of the downwards shift of thefundamental frequency of the rarefactional wave at higheroutput levels.

The distribution of normalized harmonic spectra and ab-solute harmonic intensities along the x and z axis at Vpp

TABLE II. Slopes of harmonic intensity vs axial int

n

1.1 MHz

Whole Compressional Rarefactio

1 0.96 1.16 0.812 1.93 2.41 1.563 2.94 N/A 1.634 3.81 3.44 1.855 4.71 4.11 2.08

FIG. 6. �Color online� Pressure distribution �a� transverse to and �b� alongthe 1.1 MHz HIFU transducer axis at the peak-to-peak output voltage of the
function generator Vpp=0.1, 0.2, and 0.3 V.

=0.1 V and 0.3 V are shown in Fig. 8. At the focus of theHIFU transducer, a significant portion of the wave energyshifted from the fundamental frequency to higher order har-monics. Therefore, the focal point becomes a local minimumfor the normalized fundamental component but a maximumfor harmonic components at Vpp=0.1 V. In particular, theharmonic generation is more apparent at high output level�0.3 V�. In addition, along the x and z axis, the maxima andminima of the fundamental component correspond to theminima and maxima of the second harmonic. It was foundthat the −6 dB beam size along both the transverse and cen-tral axis of the transducer decreases with the harmonic num-ber by n−1/2, which is consistent with results from previousstudies.12

C. Comparison of HIFU fields at 1.1 and 3.3 MHz

At the same output voltage, Vpp, the peak pressures pro-duced by the HIFU transducer at 3.3 MHz were much higherthan the corresponding values at 1.1 MHz �Fig. 4�. For ex-ample, at Vpp=0.5 V the peak positive and negative pres-sures at 3.3 MHz were 35.1±0.1 MPa and −13.8±0.6 MPa;while the corresponding values at 1.1 MHz were23.3±0.6 MPa and −10±0.4 MPa, respectively. In conse-quence, the calculated ISPPA at 3.3 MHz was much higher�Table III�. When Vpp�0.3 V, the rate of increase for p+

began to saturate, presumably because of the significantlyincreased attenuation of higher order harmonics during non-

for different harmonic components.

3.3 MHz

Whole Compressional Rarefactional

0.95 1.07 0.881.91 2.20 1.422.69 N/A 1.553.58 2.70 1.834.47 4.10 2.14

FIG. 7. �Color online� The −6 dB beam size of the peak positive �p+� andnegative �p−� pressure distribution around the focus of the 1.1 MHz HIFUtransducer at different peak-to-peak output voltage of the function generator

ensity

nal

Vpp.


linear wave propagation. It was found that the electric inputpower and electric-to-acoustic energy conversion ratio of theHIFU transducer at 3.3 MHz were similar to those at1.1 MHz �Tables I and III�. In addition, the nonlinear effectson wave-form distortion and the beam size change at3.3 MHz were found to be similar to those at 1.1 MHz. Forexample, there is no significant difference in the calculated
slopes of the acoustic intensities from all harmonics pro-

duced at either 3.3 MHz or 1.1 MHz �Table II�, which sug-gests that harmonics generation is independent to the centralfrequency of the burst.

The pressure distributions of the 3.3 MHz HIFU trans-ducer both transverse to and along the central axis of theHIFU transducer are shown in Fig. 9. In comparison to thoseproduced at 1.1 MHz, the beam size became much smaller

FIG. 8. �Color online� Harmonics dis-tribution of the 1.1 MHz HIFU trans-ducer at different peak-to-peak outputvoltage of the function generator Vpp

�0.1 V and 0.3 V�. Left column is nor-malized spectrum and right column isharmonic intensity with respect to thereference pressure of 1 MPa. Plots in�a� and �b� are transverse �x� whileplots in �c� and �d� are along �z� thetransducer axis.

��0.5�4 mm� and the side lobe was less significant, sug-


gesting that the acoustic energy is concentrated more towardsthe focus. As a result, the peak pressure and acoustic inten-sity become much larger at the similar electric input power.At higher output voltage, the nodes in the pressure distribu-tion of the compressional wave at 3.3 MHz, both transverseto and along the central axis of the HIFU transducer, gradu-ally disappeared and began to merge with the main lobe. Incontrast, the node in the rarefactional pressure distributionalways existed. In addition, when Vpp�0.2 V, two pressurepeaks, both compressional wave and rarefactional wave, ap-

TABLE III. Acoustic intensity, power output, and3.3 MHz HIFU transducer.

Output Vpp �V� ISPPA �W/cm2� ISAPA �W/c

0.05 240 1270.1 981 5510.2 3728 23380.3 7088 48010.4 9730 68490.5 10 967 8144

FIG. 9. �Color online� Pressure distribution �a� transverse to and �b� alongthe 3.3 MHz HIFU transducer axis with the output voltage in the range of
0.1–0.5 V.

peared along the central axis of the HIFU transducer at aboutz=2 mm. The reason for this unique feature is not com-pletely known.

As a result of nonlinear propagation in water, the en-hancement ratio of absorbed acoustic power density of theHIFU transducer at the beam focus was found to increasefrom 1.0 to 3.0 at 1.1 MHz �Fig. 10�. In comparison, thecorresponding enhancement ratio at 3.3 MHz was lower at agiven intensity and the theoretically predicted reduction inenhancement factor at higher power �ISPPA

�10 000 W/cm2� was also observed.12,18 The initial in-crease of the enhancement ratio at 1.1 MHz was very slowup to 100 W/cm2, which was similar to the nonlinear propa-gation threshold for 1.7 MHz focused ultrasound in waterbased on the measurements by a PVDF membranehydrophone.12 Above 100 W/cm2, the enhancement ratiogrew much more quickly. It should be noted that becauseultrasound absorption coefficients in water and biological tis-sues are frequency dependent, the total acoustic power ab-sorbed at 3.3 MHz is significantly higher than that at1.1 MHz, which has been confirmed by thermocouple mea-surement �data not shown�.

IV. DISCUSSION

Accurate exposimetry measurement of HIFU systems isessential for determining the causal relationship between ul-

ric-to-acoustic energy conversion efficiency of the

ISAPA/ ISPPA Pin �W� P �W� P / Pin

0.53 1.10 0.72 65.4%0.56 4.38 2.92 66.8%0.63 17.52 12.71 72.5%0.68 40.75 28.05 68.8%0.70 73.36 50.54 68.9%0.74 109.56 62.90 57.4%

FIG. 10. �Color online� The enhancement ratio for absorbed acoustic powerper unit volume at the focus of the HIFU transducer operating at either 1.1

elect

m2�

or 3.3 MHz.


trasound exposure and resultant bioeffects, and for ensuringthe effectiveness and safety of clinical HIFU treatment. Fromthe regulatory point of view, exposimetry information is alsoimportant for quality control and comparison between differ-ent HIFU systems. Currently available methods are eitherlimited by their temporal and spatial resolution �calorimetryand radiation force measurement� or their accuracy and reli-ability under clinically relevant HIFU intensities �opticaltechniques, PVDF membrane and needle hydrophones�. Inthis study, we evaluated the feasibility of using a self-calibrated FOPH17 for HIFU exposimetry measurement,which offers the unique advantages of small probe size�0.1 mm�, broad bandwidth �50 MHz�, robustness underhigh-pressure amplitude, and longevity. The calibration ofthe FOPH is done strictly based on the relation between pres-sure and reflection coefficient at the fiber tip �measured bythe photodetector� that is defined exclusively by the materialproperties of the fiber and surround medium �i.e., water�.17

For calibration of the FOPH only a dc-photodiode voltageneeds to be determined before the measurement without anyreference standards. Therefore, FOPH is especially conve-nient for harmonics measurement in a HIFU field comparedto PVDF membrane and needle hydrophones, which, in ad-dition to their susceptibility to cavitation damage, must becalibrated at different discrete frequencies.

The small sensor size of the FOPH is also advantageousfor resolving high frequency components in HIFU fields. Ac-cording to the IEC 61102 guideline, in order to reduce theinfluence of spatial averaging the effective diameter �dh� ofthe hydrophone active element must satisfy the followingcriterion:

dh � �0.5�z/ds, z/ds � 1,

0.5� , z/ds � 1,� �5�

where � is the acoustic wavelength at the center frequency, zis the source-to-hydrophone distance, and ds is the relevantsource dimension.20 Based on this criterion, both the FOPHand PVDF hydrophone can resolve well the 1.1 MHz HIFUfield �see Fig. 2�. However, the PVDF membrane hydro-phone will suffer significantly from signal averaging ef-fect when measuring the 3.3 MHz HIFU field �see Fig. 3�.Furthermore, low frequency response of a hydrophone isalso important for reliable measurement of lithotripsy anddiagnostic pulses.23 With deconvolution, the bandwidth ofFOPH can be extended towards both low and high fre-quencies. In contrast, the low frequency response ofPVDF membrane hydrophone is limited �i.e., its sensitiv-ity at frequency lower than 100 kHz is usually veryweak�.24 It should be noted, however, that when the crite-rion is satisfied and for weak pressure signals within lin-ear propagation range, the PVDF membrane hydrophonecan resolve the pressure signals much better because of itssignificantly higher sensitivity than the FOPH �see Fig. 2�.

Using the FOPH we have measured the pressure waveforms produced by a focused HIFU transducer working ateither 1.1 or 3.3 MHz in a wide range of output intensities�ISPPA=1–11 000 W/cm2�. Significant wave-form distortion,which is characteristic of nonlinear propagation,21 was pro-
duced at mediate and high output levels �Fig. 5�. The char-

acteristics of harmonics generation �see Fig. 5�b� and TableII� and harmonics beam size variation �Fig. 8� at both 1.1 and3.3 MHz are similar to the results of 1.7 MHz HIFU fieldreported previously using a PVDF membrane hydrophone.12

The most immediate consequence of nonlinear propagationis the narrowing of beam size due to harmonics generationwith the associated increase of energy concentration towardthe focus. This can be seen from the increased ratio ofISAPA/ ISPPA within the output range investigated in this work�Tables I and III�. Moreover, harmonics generation can leadto significant enhancements in energy absorption due tohigher attenuation coefficients at harmonic frequencies.12,21

Previous studies have suggested that the enhancements maycontribute primarily to the initiation of lesion or cavitationon the transducer axis.6,12

Theoretical modeling of acoustic and thermal field pro-duced by a HIFU transducer is important for better predict-ing and controlling lesion formation in clinical therapy. Sev-eral numerical simulations have been carried out, using theKhokhlov-Zabolotskaya-Kuznetsov �KZK� equation formodeling nonlinear propagation of high intensity acousticbeams25,26 and the BioHeat transfer equation �BHTE�27 tomodel the temperature elevation in tissue. A reliable charac-terization of the HIFU field �pressure wave form, pressureand thermal distribution� will be important for validatingthese numerical simulations.

In summary, FOPH has been shown to be an appropriateand reliable tool for HIFU exposimetry measurement, espe-cially at high output intensity levels. It can be used to mea-sure the pressure wave forms, distribution, and characterizethe nonlinear propagation features in a HIFU field. Further-more, the measurement data can be used to calculate theacoustical power and intensity output of the HIFU trans-ducer, and to provide essential and critical information fordevice characterization and comparison, as well as for mod-eling nonlinear wave propagation and cavitation effect in aHIFU field.

ACKNOWLEDGMENTS

This work was supported in part by NIH through GrantsNos. RO1-DK52958, RO1-EB02682, and R21-EB03299.The authors also wish to thank George Keilman of SonicConcepts for helpful discussion on determination of the elec-trical input power to the HIFU transducer and ProfessorWolfgang Eisenmenger and Dr. Rainer Pecha for their help-ful comments on the paper.

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