acoustic power calibration of high-intensity focused ultrasound transducers using a radiation force...

Acoustic power calibration of high-intensity focused ultrasoundtransducers using a radiation force technique

Subha Maruvada, Gerald R. Harris, and Bruce A. HermanCenter for Devices and Radiological Health, Food and Drug Administration Rockville, Maryland 20850

Randy L. KingKing Acoustic Technologies, LLC, Washington, DC 20007

�Received 19 July 2006; revised 5 December 2006; accepted 6 December 2006�

To address the challenges associated with measuring the ultrasonic power from high-intensityfocused ultrasound transducers via radiation force, a technique based on pulsed measurements wasdeveloped and analyzed. Two focused ultrasound transducers were characterized in terms of aneffective duty factor, which was then used to calculate the power during the pulse at high appliedpower levels. Two absorbing target designs were used, and both gave comparable results anddisplayed no damage and minimal temperature rise if placed near the transducer and away from thefocus. The method yielded reproducible results up to the maximum pulse power generated ofapproximately 230 W, thus allowing the radiated power to be calibrated in terms of thepeak-to-peak voltage applied to the transducer. © 2007 Acoustical Society of America.�DOI: 10.1121/1.2431332�

PACS number�s�: 43.35.Yb �TDM� Pages: 1434–1439

I. INTRODUCTION

Knowledge of the ultrasonic power radiated by thera-peutic ultrasound transducers such as used in high-intensityfocused ultrasound �HIFU� surgery is important from both aneffectiveness and safety standpoint.1–3 The power producedby transducers used in biomedical ultrasound applicationstypically is found by radiation force means, in which theaxial force �i.e., the force in the direction of propagation� ona target attached to a balance is measured.2–18 Two types oftargets are used in a radiation force balance system: reflect-ing and absorbing7 �see Sec. II B�. The relationship betweenthe measured force �F� and the temporal-average acousticpower �PTA� for the case of plane waves and a perfectlyabsorbing target is

PTA = cF , �1�

where c is the speed of sound in the propagation medium,usually water.7,19 For focused fields with beam convergenceangle �=sin−1�dS /2L�,

PTA = 2cF/�1 + cos �� , �2�

where dS and L are the diameter and geometricalfocal length �radius of curvature� of the source transducer,respectively.7,19

Equations �1� and �2� have been used successfully inmany measurement situations, but for high-power focusedbeams these measurements can be challenging.2 For ex-ample, transducer damage can occur if the measurement timeis longer than would be encountered in clinical use. Also, forabsorbing targets, excessive heating can result in measure-ment error or target damage. Furthermore, bubble formationbetween the transducer and target at high powers can intro-duce measurement errors. Acoustic streaming is another po-tential source of measurement error that increases as both
PTA and ultrasonic frequency increase. To overcome these
1434 J. Acoust. Soc. Am. 121 �3�, March 2007 0001-4966/2007/1

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problems, pulsed-mode instead of continuous-wave �cw�measurements can be made to lower the PTA, from which thepower during the pulse can be computed. The objective ofthis work was to analyze this approach for calibrating thetransducer output power in terms of the applied peak-to-peakvoltage.

II. MATERIALS AND METHODS

A. Transducers

Ultrasonic frequencies between 1 and 2 MHz commonlyare employed in HIFU.20 In this study two focused transduc-ers operating in this range were used �1.50 MHz, 10-cm di-ameter, 15-cm focal length, ONDA Corp, Sunnyvale, CA;1.11 MHz, 8-cm diameter, 10-cm focal length, King Acous-tic Technologies, LLC, Washington, DC�. The values ofcos � in Eq. �2� for these two transducers were 0.866 and0.917, respectively. A third transducer �3.33 MHz, 6-cm di-ameter, 5-cm focal length, cos �=0.800� was used to assessthe effect of acoustic streaming at a higher frequency. Alltransducers were matched to an electrical impedance of 50ohms.

B. Targets

For all reflecting targets, plane and conical, the forcevaries with the angle between the beam axis and the normalto the reflecting surface. Most reflecting targets are convexcones, for which precise positioning is necessary to achieveaccurate measurements. Also, a disadvantage of conical re-flectors in focused fields is that the radiation force is verysensitive to the beam convergence angle.18 Furthermore, withthese targets more care is needed in tank design to avoidreflections. For absorbing targets these factors are much lesscritical. However, for high-power transducers, target heating
can cause measurement instability, and for highly focused
© 2007 Acoustical Society of America21�3�/1434/6/$23.00

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beams, target damage can occur. In this work, three absorb-ing targets were employed and efforts were made to over-come the disadvantages.

Two “brush” targets8 were constructed having 10-cm�made in-house� and 12-cm �King Acoustic Technologies,LLC, Washington, DC� diameters with bristles of 4 and6.5 cm length, respectively. Figure 1 shows a picture of the12-cm brush target. Nylon bristles from common cleaningbrushes were pulled and packed densely together and thenpotted in a base of rubber. The approximate diameters of thenylon brush bristles were 0.17 and 0.25 mm, respectively, forthe 10- and 12-cm brush targets. The 10-cm brush was pottedin a silicone elastomer �Sylgard 170, Dow Corning, Midland,MI� and the 12-cm brush was potted in a proprietary two-part rubber material designed to absorb ultrasound �KingAcoustic Technologies, Washington, DC�.

The third target, a commercially available absorbingdesign14,21 �model Ham A, Precision Acoustics Ltd.,Dorchester, UK�, is based on polyurethane rubber material. Itis composed of two layers: a top layer whose acoustic im-pedance is matched to that of water and a backing layer thatis partially air-loaded to increase transmission loss. The tar-get has flat front and back faces and a thickness of 14 mm.The material was cut into a disk of 12 cm diameter.

According to Ref. 7, for unfocused transducers the targetdiameter should be at least 1.5 times the transducer diameterto intercept all significant parts of the field. For focusedtransducers, an equivalent specification based on simple rayacoustics can be expressed as

dT � 1.5dS�L − z�/L , �3�

where dT is the target diameter and z is the transducer-to-target distance.

The transducer-to-target distances stated herein refer tothe distance between the plane defined by the transducer rimand either the tips of the brush bristles or the front face of theflat target. For the 1.11- and 1.50-MHz transducers, mostmeasurements were made at a transducer-to-target distanceof 5 cm to satisfy Eq. �3�, but positions closer to the focuswere used for comparison.

C. Radiation force balance system

The setup of the experiment is shown in Fig. 2. Theabsorbing target was suspended from the bottom of an elec-

FIG. 1. Twelve-cm brush target.

tronic balance �AND HM-202, Bradford, MA�, and the trans-

J. Acoust. Soc. Am., Vol. 121, No. 3, March 2007


ducer was positioned so that it radiated downward onto thetarget. The driving electronics consisted of a function gen-erator �Wavetek 81, Fluke Corp., Everett, WA� and poweramplifier �ENI 2100L or ENI A-300, Rochester, NY�. A50-dB dual-directional coupler �Amplifier Research, modelDC2000, Souderton, PA�, two power sensors �model 8482A,Agilent Tech., Palo Alto, CA�, and a power meter �modelE4419B, Agilent Tech., Palo Alto, CA� were placed betweenthe amplifier and transducer to monitor the forward and re-versed electrical power to the transducer. Operation of theradiation force balance system was accomplished throughMATLAB �The Mathworks Inc., Natick, MA�. MATLAB wasused to control the hardware �function generator, balance,and power meter� as well as to acquire and analyze the data.

The peak-to-peak transducer voltage was measured dur-ing the steady-state portion of the pulse with a digital oscil-loscope �model 54622A, Agilent Tech., Palo Alto, CA�. Thepeak-to-peak rather than rms pulse voltage was measured forconvenience, although either would provide a robust calibra-tion of the transducer and drive electronics combination untilamplifier saturation at high drive levels becomes significant.

D. Effective duty factor „EDF…

Two pulse repetition frequencies, 500 and 1000 Hz,were used in this approach for circumventing the problemsassociated with measuring high temporal-average powers.For both, the pulse duration was chosen to give a duty factor�DF� equal to the product of the pulse repetition frequencyand the pulse duration, of approximately 10%. The powerduring the pulse �PPA� can be calculated from the measuredtemporal-average power as in Eq. �4�,

PPA = PTA/DF. �4�

Equation �4� is exact for a power pulse waveform having atrue rectangular modulating envelope. However, turn-on andturn-off transients can lead to inaccuracies in Eq. �4� that willincrease as the pulses duration decreases. Therefore, first an“effective duty factor” �EDF�, defined as the ratio of pulsed

FIG. 2. Experimental setup of radiation force balance.

to cw power, PPUL/ PCW, was established by measuring

Maruvada et al.: High-power calibration 1435


both PPUL and PCW with the transducer driven at the samepeak-to-peak transducer voltage for five cw PTA’s ap-proximately evenly spaced over the range from 10 to30 W. The EDF was the average valued obtained over thisrange. Then, in pulsed mode the transducer drive levelwas increased and the power during the pulse was calcu-lated from

PPA = PTA/EDF. �5�

E. Other measurement considerations

Each measurement comprised five on-off cycles undercomputer control per the procedure in Ref. 16. The on timewas 9 s, a time sufficient to attain and process a stable bal-ance reading, while the off time was 20 s to allow the targettemperature to return to near baseline �see Sec. III E�. Fourindependent measurements were made at each drive level toassess the type A �random� uncertainty.22

The water was degassed to �2 ppm and measurementswere made at room temperature �22 °C–25 °C�. The speedof sound c in Eq. �2� was adjusted for its variation withtemperature.23

To determine where in the brush targets heating due toultrasound absorption might arise, 250-�m-diameter wire,copper-constantan thermocouples were placed centrally atthree locations within the 10- and 12-cm brush targets: nearthe base of the bristles, in the center of the bristles, and1 mm below the top of the bristles. Temperature measure-ments also were made in the flat target using the same typeof thermocouple placed in the center and approximately1 mm below the front surface.

To assess the effect of acoustic streaming, a6.4-�m-thick low-density polyethylene membrane 12.5 cmin diameter was inserted between the transducer and target inone set of measurements.7 For transducers with planar radi-ating surfaces, it is recommended that the antistreamingmembrane be tilted with respect to the beam axis to elimi-nate the possibility of standing waves. To see if such angu-lation is critical for focused beams, the membrane angle wasvaried from approximately 0° to 5°, 0° corresponding to theplane normal to the beam axis. For the 3.3-MHz transducerused in the acoustic streaming measurements, the target wasplaced 2.5 cm from the transducer and also at an 8-cm dis-

TABLE I. cw and pulsed-mode power values to estransducer.

Upp�V� Pcw�W� PPUL�500��W�

72 9.94 0.8888 15.11 1.34102 20.23 1.79112 24.56 2.17123 29.65 2.62

tance to exacerbate the effects of streaming.

1436 J. Acoust. Soc. Am., Vol. 121, No. 3, March 2007


III. RESULTS AND DISCUSSION

A. Effective duty factor

Continuous wave and pulsed measurements to establishan EDF were performed on the 1.50- and 1.11-MHz trans-ducers. The results for the 1.11-MHz transducer are given inTable I. PPUL�500� and PPUL�1000� are the pulsed modePTA’s at pulse repetition frequencies of 500 and 1000 Hz,respectively. The means and coefficients of variation for thefive EDF values were 0.088 and 0.15% at 500 Hz and 0.085and 0.47% at 1000 Hz. For the 1.50-MHz transducer, themeans and coefficients of variation for the five EDF valueswere 0.094 and 0.7% at 500 Hz and 0.091 and 1.9% at1000 Hz. The corresponding DFs �Eq. �4�� were 0.090 and0.093 for the 1.11- and 1.50-MHz transducers, respectively,indicating a small but measurable effect of the turn-on andturn-off transients. �See also Sec. III G, below.�

B. High-output pulsed mode powers

Figure 3�a� shows the pulsed-mode power �PPA from Eq.�5�� for the 1.11-MHz transducer using the 10-cm brush tar-get vs transducer voltage for the two pulse repetition fre-quencies. The corresponding temporal-average powersranged from 4 to 22 W. Peak acoustic powers during thepulse were calculated from Eq. �4� to be approximately 40 to230 W, the upper value being the highest possible with theavailable amplifiers before noticeable distortion of the sinu-soidal drive voltage was observed. Power-law fits to thesedata lead to calibration equations for the acoustic power ofPTA=0.001 66 UPP

2.037 �coefficient of determination R2

=0.999� and PTA=0.001 68 UPP2.038 �R2=0.999� from the 500-

and 1000-Hz repetition rate results, respectively, where thepower, PTA, has units of watts and the peak-to-peak voltage,UPP, has units of volts.

h an effective duty factor �EDF� for the 1.11-MHz

L�1000��W� EDF �500� EDF �1000�

0.84 0.089 0.0851.29 0.089 0.0851.73 0.088 0.0862.09 0.088 0.0852.53 0.088 0.085

FIG. 3. Comparison of measured pulsed-mode power using the two differ-ent pulse repetition frequencies for the �a� 1.11-MHz transducer and �b�

tablis

PPU

1.50-MHz transducer.

Maruvada et al.: High-power calibration


Similar results were obtained with the 1.50-MHz trans-ducer, for which pulsed-mode temporal-average acousticpowers from 4 to 16 W were measured using the 10-cmbrush target �Fig. 3�b��. Peak acoustic powers during thepulse were calculated to be approximately 40 to 180 W. Thepower law fits were PTA=0.001 09 UPP

2.092 �500 Hz, R2

=0.999� and PTA=0.001 32 UPP2.058 �1000 Hz, R2=0.999�. Al-

though the power-law fits appear to be different, the coeffi-cients and exponents are such that the difference in PTA val-ues calculated for the two repetition rates are small andwithin the experimental error seen in Fig. 3�b�.

C. Comparison of three targets

Pulsed-mode measurements for the 1.50-MHz trans-ducer with all three targets are shown in Fig. 4. The distancebetween transducer and each target was 5 cm. Little varia-tion �less than 2%� was found among the targets, the slightdifference at the highest power being due to difficulty inrecording the peak-to-peak voltage because of instability inthe power amplifier at its maximum output. Similar resultswere seen with the 1.11-MHz transducer.

D. Effect of transducer-to-target distance

The distance between the transducer and target was var-ied using the 1.50-MHz transducer and the two brush targets.The distance was increased from 5 to 11 cm while the trans-ducer was driven in cw mode to provide approximately 10-and 30-W temporal-average acoustic powers. As shown inFig. 5, the measured acoustic power stayed nearly constantvs distance. In only one case, at 30 W with the 12-cm brush,was there a small but statistically significant drop in acousticpower of 2% at 11 cm versus 5 cm. The small attenuation in

FIG. 4. Comparison of three absorbing targets.

FIG. 5. Measured temporal-average power vs distance between transducerand 10- and 12-cm brush target using the 1.50-MHz transducer at 10 and
30 W.


water over this range had no effect on these results. It shouldbe noted, however, that the variation with distance may begreater at higher powers or frequencies where there will bemore nonlinearity in the water and increased absorption andshock loss.

The same experiment was attempted with the 1.11-MHztransducer and 12-cm flat target while the transducer wasdriven at approximately 10-W temporal-average acousticpower. However, visible damage to the target occurred at adistance of 9 cm and the experiment was aborted.

E. Target temperature measurements

Using the 1.50-MHz transducer and 12-cm brush target,the temperature rise measured by the three thermocouplesduring each of the five on-off cycles was recorded and theresults were averaged. The cycle off time did not allow thetemperature to return to baseline, so the final temperature atthe end of each cycle on time was greater than that of theprevious cycle. However, the five temperature rises were ap-proximately the same. The average temperature rise over thefive on cycles was found for PTA from 10 to 30 W for cwexcitation. The temperature rise was recorded at twotransducer-to-target distances of 5 and 10 cm. The results areplotted in Fig. 6. The temperature rise was much larger forthe 10-cm distance as the target was closer to the transducerfocus. The temperature rise was greatest near the top of thebrush and decreased towards the base of the brush. Themaximum temperatures at the end of the fifth cycle on timeof the 30-W sonications were 30 °C, 27 °C, and 24 °C forthe three thermocouple positions when the target was 5 cmfrom the transducer, and 43 °C, 28 °C, and 23 °C when thetarget was 10 cm from the transducer. At this maximum cwpower, the maximum temperature rises were about 4 °C and18 °C for transducer-to-target distances of 5 and 10 cm, re-spectively �see Fig. 6�. Similar results were obtained with the10-cm brush target.

Regarding the flat target, as mentioned above, thermaldamage occurred at a distance of 9 cm. At 5 and 7 cm thepower measured was 10.5 and 10.7 W while the averagetemperature rise was 6 °C and 13 °C, respectively. Themaximum temperatures were 36 °C at 5 cm and 45 °C at

FIG. 6. Average temperature rise vs measured temporal-average acousticpower at three locations in 12-cm brush target at transducer-target distancesof �a� 5 cm and �b� 10 cm using the 1.50-MHz transducer.

7 cm.



F. Acoustic streaming

The attenuation through the antistreaming membrane,determined via hydrophone measurements, was found to beless than 0.15% ��0.01 dB� at 3.3 MHz. For the 3.3-MHztransducer, measurements were made with and without themembrane using cw excitation from 10 to 30 W at distancesof 2.5 and 8 cm between the transducer and 10-cm brushtarget. Figure 7 shows the results for the 2.5-cm target dis-tance both without the membrane and with the membraneplaced 1 cm from the target. At 30 W the membrane causeda reduction in the measured power of 1.1%. �This same mea-surement for the 1.5-MHz transducer and a target distance of5 cm resulted in a decrease of 0.2% at 30 W.�

Figure 8 shows the streaming effects on the measure-ments for the 3.33-MHz transducer when the brush targetwas placed 8 cm from the transducer. Two membrane dis-tances were used: 1 cm from the transducer face and 1 cmfrom the target. The reduction in the measured power was0.6% for the membrane near the transducer and 18% for themembrane near the target at 30 W. This latter result demon-strates that the power lost due to attenuation in the water isrecaptured via streaming. In this regard, it is noted that anantistreaming membrane should be used only if the power atthe target location is desired. To achieve a more accuratemeasurement of the total power radiated by the transducer,no membrane should be used. Also, because streaming isenhanced by nonlinear propagation, its effects will be re-duced by making measurements at reduced temporal-averagepowers as in the present pulsed technique.

FIG. 7. Streaming measurements for 3.33-MHz transducer and 10-cm brushtarget. The transducer-to-target distance was 2.5 cm and the antistreamingmembrane was placed 1 cm from the target.

FIG. 8. Streaming measurements for 3.33-MHz transducer and 10-cm brush
target. The transducer-to-target distance was 8 cm.
1438 J. Acoust. Soc. Am., Vol. 121, No. 3, March 2007


Finally, with the target 8 cm from the 3.3-MHz trans-ducer, tilting the membrane from 0° –5° had no discernibleeffect on the measurements at membrane positions both nearthe transducer and near the target.

G. Application of calibration method

Successful application of the strategy expressed in Eq.�5� relies on the constancy of the EDF as drive level is in-creased. That is, the shape of the pulsed transducer voltagewaveform must remain unchanged with drive level. To vali-date this premise, the rms transducer voltage, normalized bythe peak-to-peak voltage, was measured over the full rangeof drive levels used for the 1.11- and 1.50-MHz transducers.For both transducers, the coefficient of variation was foundto be �1% for 13 measurements between 10 and 180 W. Forthe 1.11-MHz transducer, which was capable of higher out-put, the coefficient of variation was �2% for 16 measure-ments between 10 and 230 W.

Further, in using calibration data obtained under pulsedconditions, it should be recognized that when a HIFU trans-ducer is driven at full �i.e., cw� output, self-heating due to�100% efficiency of operation can affect the acoustic out-put. However, other means can be used to evaluate possibletransducer instability during continuous operation, such asmonitoring the forward and reverse electrical power, achange in which would be indicative of a change in trans-ducer impedance and output due to, for example, thermaldrift in the matching network components. Also, one couldobserve the output over time of a hydrophone placed in alow-intensity region of the field where neither hydrophonedamage nor saturation effects due to nonlinear propagationare expected.

IV. CONCLUSION

Temporal-average acoustic powers of approximately 4to 22 W were measured from focused ultrasound therapytransducers in a pulsed mode. By determining the effectiveduty factor of the pulses at relatively low temporal-averagepower, it was possible to relate peak-to-peak transducer volt-ages to acoustic powers up to 230 W. Three absorbing tar-gets of two designs were used, and powers agreed for alltargets to within the Type A �random� measurement uncer-tainty at all drive levels �maximum coefficient of variation:�2% at 95% confidence level�, indicating that all three aresuitable as absorbing targets. No evidence of cavitation �e.g.,balance instability� was observed at the 500- and 1000-Hzpulse repetition frequencies used and a duty factor of about10%. Brush target temperature rises were less than about4 °C at a target distance of 5 cm. The temperature rises inthe flat target were greater, with thermal damage occurring ifit was placed near the focus. For the brush targets, no sig-nificant variation in measured power was seen for thetransducer-to-target distances used. For these measurementsa distance of 5 cm was found to be a reasonable compromisein that it was small enough to avoid significant focal heating,yet large enough to permit a practical target size according to
Eq. �3�.
Maruvada et al.: High-power calibration


Streaming effects were not observed at 1.50 MHz butwere seen with the 3.33-MHz transducer. A membrane maybe needed to eliminate streaming effects on power measure-ments if the power at the plane of the target is desired. How-ever, at higher frequencies the membrane can introducegreater variation in the measured acoustic power, most likelydue to reflection from the membrane. A membrane may becounterproductive, however, if the total power output is thequantity of interest, since unobstructed streaming allowssome recapture, by the target, of the momentum in the ultra-sound field lost to absorption in the transmitting medium.

These results suggest that a pulsed-mode approach using500–1000-Hz pulse repetition frequencies, approximately10% duty factor, absorbing target not near focus, and well-degassed water should be a suitable method for accuratevoltage-power characterization that avoids transducer or tar-get damage and bubble- or thermal-related measurementanomalies. This technique is appropriate for preclinical re-search, development, and testing of HIFU transducers andsystems where monitoring and control of the transducerdrive electronics is available. For further assessment of trans-ducer performance under cw drive conditions, the forwardand reverse electrical power can be measured, or the outputvs time of a hydrophone placed in a low-intensity region ofthe field can be observed.

Note: The mention of commercial products, theirsources, or their use in connection with material reportedherein is not to be construed as either an actual or impliedendorsement of such products by the U.S. Department ofHealth and Human Services.

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acoustic power calibration of high-intensity focused ultrasound transducers using a radiation force...

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