An MRI Calorimetry Technique to MeasureTissue Ultrasound Absorption

Yao Wang† and Donald B. Plewes*

High-intensity focused ultrasound (US) surgery guided by mag-netic resonance imaging (MRI) is a very promising form ofminimally invasive thermal therapy. To apply this techniqueoptimally, the interaction mechanisms of high-intensity US withtissue need to be better understood, in particular, the variationof ultrasound absorption with frequency and temperature. How-ever, agreement on the value of measured tissue US absorptionis poor, largely because of intrinsic experimental complicationsof prior investigations. A new approach toward measuringtissue US absorption, based on a form of MRI calorimetry, isproposed here, which allows non-invasive energy measurementthrough spatial temperature mapping with MRI. A modifiedtwo-dimensional spoiled gradient-echo sequence has beenimplemented to map temperature based on proton resonancefrequency (PRF) shift. Validation experiments show excellentagreement of MRI measured energy with that delivered by acalibrated source. MRI calorimetry of US heating of tissue-mimicking polyethylene glycerol material has been performed.Using a hydrophone measurement of the incident US field, itsUS absorption coefficient was measured as 0.032 cm 21. As thisapproach can be applied over a range of frequencies, tissues,and temperatures, it should provide a much improved means ofmeasuring absolute tissue US absorption coefficients to im-prove US therapy planning, future transducer design, and USdosimetry models. Magn Reson Med 42:158–166, 1999. r 1999Wiley-Liss, Inc.

Key words: US absorption, US thermal therapy, MRI thermom-etry, proton resonance frequency shift

Recently, there has been renewed interest in the use ofhigh-intensity focused ultrasound (US) for minimally inva-sive MRI-guided thermal therapy (1,2). The tissue damageinduced by high-intensity US depends on the interactionmechanisms of high-intensity US with tissue and the USintensity in situ. Both the US absorption and scatteringproperties of tissue need to be carefully investigated (3–6)in order to control lesion size, shape, and location prop-erly. In particular, a sound knowledge of the US absorptionin tissue is critical as this dictates the conversion of USenergy to heat. While the study of US properties of tissueshas been conducted extensively over the past severaldecades (7–11), agreement on the value of measured tissueabsorption is poor. For example, available measurementsof liver tissue ex vivo at 1 MHz and room temperature from

various studies show as much as a fourfold variation for theUS absorption coefficient (12). This is largely a result ofexperimental assumptions and the use of invasive thermo-couples to measure tissue temperature elevation, whichthemselves alter the heating and absorption properties ofthe tissue. This has motivated us to consider a newapproach to measure tissue US absorption based on a formof MRI calorimetry that allows non-invasive energy mea-surement through accurate spatial mapping of temperatureelevation with MRI. This concept, introduced elsewhere(13), detailed the US aspects of the problem and theirapplication to measurements with liver tissue. In thispaper, optimization of the MRI aspects of this concept isfully explained, validating the accuracy of MRI to measuresmall amounts of thermal energy and demonstrating its usein measuring the absorption coefficient of an US tissuemimicking material.

MRI CALORIMETRY OF US ABSORPTION

Concept

As shown in Fig. 1, a 1 MHz US transducer of 17 mmdiameter mounted at one end of an MR-compatible cham-ber is used to insonate a 1 ml sample of tissue embedded atthe center of a cylindrical agarose gel block (102 mm indiameter and 200 mm in length). As a result of tissue USabsorption, the tissue sample will experience a smalltemperature elevation on the order of 17C. After insonation,the energy absorbed by the tissue sample slowly diffusesinto the surrounding gel. Using phase-difference MRI, onecould monitor temperature-induced proton resonant fre-quency (PRF) shifts. Consequently, mapping the gel andtissue temperature elevation inside a region surroundingthe tissue sample, referred to as the ‘‘integration volume,’’will allow measurement of the total absorbed energythrough a knowledge of the thermal capacity of the gel.Accordingly, the surrounding gel serves as an energy bufferto trap and temporarily store the energy absorbed by thetissue sample. In this way, we have avoided the use ofconventional invasive devices that alter the US field andcompound the accurate measurement of tissue US absorp-tion.

We have shown elsewhere (13) that the US pressureabsorption coefficient a can be calculated as:

a 5rC e DT(V)dV

2 e I0(s)ds ? DxDt[1]

where DT(V) is the temperature elevation distribution inthe calorimeter apparatus, rC is the thermal capacity of geland tissue over a volume V, Dt is the duration of in-sonation, and Dx is the thickness of the tissue sample in theUS propagating direction.

Department of Medical Biophysics, University of Toronto, and Imaging Re-search, Sunnybrook & Women’s College Health Sciences Centre, Toronto,Ontario, Canada.†Yao Wang is now in the Department of Biomedical Engineering at theUniversity of Michigan, Ann Arbor, Michigan.Grant sponsor: Terry Fox Programme Project Grant of the National CancerInstitute of Canada.*Correspondence to: Donald B. Plewes, Sunnybrook & Women’s CollegeHealth Sciences Centre, University of Toronto, S669-2075 Bayview Avenue,Toronto, ON, Canada M4N 3M5. E-mail: dbp@srcl.sunnybrook.utoronto.caReceived 27 August 1998; revised 22 February 1999; accepted 5 April 1999.

Magnetic Resonance in Medicine 42:158–166 (1999)

158r 1999 Wiley-Liss, Inc.

If the spatial temperature distribution changes slowlyrelative to the imaging time, it can be resolved by MRI.Thus this information, together with a measurement of USintensity distribution incident on the tissue sample I0(s),will allow a calculation of the US pressure absorptioncoefficient through Eq. [1]. This method relies on a quanti-tative understanding of the PRF shifts as a function of geltemperature. Previous studies have shown that the PRFshift for gel is linear in a temperature range of 207C to 907C(14).

To investigate the duration of energy storage and theamplitude of temperature elevation in this apparatus, anumerical study was conducted for US insonation of a 1cm3 cube of tissue with an US pressure absorption coeffi-cient of 0.05 cm21 and no US absorption in the gel. The gelblock was modeled as a 10 3 10 3 10 cm region withthermally free conducting boundaries. The insonationduration was 100 sec, with a uniform incident intensity of1.4 W/cm2 corresponding to 14 J of absorbed energy intissue. This was followed by a period of 500 sec of thermaldiffusion. The temperature field in the calorimeter wasmodeled as (15):

rCdT

dt5 k=2T 1 q [2]

where T is the distribution of temperature elevation, t istime, k is the thermal diffusion coefficient of gel and tissue,both assumed to equal that of water (12), and q is thethermal source due to the absorbing tissue sample.

This calculation (13) showed less than 1% loss ofthermal energy outside a 4.5 cm spherical integrationvolume for a period up to 500 sec after insonation. Assum-ing that an MR image can be taken on the order of 10 sec,many measurements of the temperature field can be madebefore thermal energy dissipates significantly from theagarose phantom. The peak temperature was less than 17C.

Currently, phase-difference gradient-recalled echo (GRE)sequences based on PRF chemical shift remains the most

sensitive method to measure temperature compared withother MRI thermometry techniques such as apparent diffu-sion coefficient (ADC) measurement and T1 mapping(16,17). With the phase-difference method, detection oftemperature changes of approximately 17C has beenachieved by several groups (14,18–21) with optimizedimaging parameters. However, this sensitivity will notpermit adequate accuracy to detect the minute amount ofenergy absorbed in the tissue sample. While inducing largetemperature elevations in the tissue sample could over-come this limitation, this could potentially alter tissue USabsorption due to thermal denaturation (7,22). Alterna-tively, one can significantly improve MR thermometrysensitivity by a judicious choice of imaging parameters, inparticular, spatial sampling requirements.

Parameter Optimization

The temperature sensitivity for the MRI phase image isproportional to 1/signal-to-noise ratio (SNR) (23,24), whichin turn is related to TE, TR, flip angle u, and spatialresolution (field of view (FOV) and sampling matrix).Since the SNR in the phase difference images is propor-tional to TE · e2TE/T*2, the choice of TE should be TE 5 T*2 tomaximize SNR. The steady-state saturation-recovery MRsignal at the Ernest angle can be shown (25) to be propor-

tional to Î(1 2 e2TR/T1)/(1 1 eTR/T1). Assuming a fixed imag-ing time, the SNR of GRE phase images can be expressed as:

SNR ~1

ÎTR?Î1 2 e2TR/T1

1 1 e2TR/T1

. [3]

Analysis of this expression shows that the choice of TR isnot critical in terms of SNR improvement (12). For ex-ample, assuming a T1 of 500 msec, reducing TR from 500 to10 msec improves SNR by only 4%. So, 0.1 mM MnCl2-doped 0.8% agarose gel was used with a T1 of 500 msec anda T2 of 60 msec, similar to those of tissue and an intermedi-ate values of TR 5 250 msec, u 5 607, and TE 60 msec werechosen.

The SNR can be significantly increased through a reduc-tion in spatial resolution. However, a number of factors canmitigate against such a strategy. In particular, reducingresolution sacrifices the accuracy of temperature mappingdue to inadequate spatial sampling. Furthermore, thephase angle in a large voxel reflects the angle of theintegrated magnetization vector, but not necessarily theaverage phase angle. Therefore, reduced resolution canlead to significant phase and temperature errors.

To study the effect of these factors, another simulationwas conducted whereby the three-dimensional (3D) tem-perature distributions, as calculated in the Concept sectionabove, were sampled in a 2D plane through the center ofthe simulated tissue cube with truncations in k-space tosimulate the effect of decreased resolution. These 2Dsampled temperature maps, modeled as phase angle distri-butions, were fitted to 2D Gaussian profiles Ae2(r/B)2toextract the fitted peak temperature A and the width B byminimizing o(T(r) 2 Ae2(r/B)2)2 where r is the radial dis-tance. The Gaussian profiles were then integrated over a 3D

FIG. 1. Schematic of MRI calorimetry technique. Degassed waterwas pumped through the coupling water chamber to remove heatgenerated by the transducer during insonation. Calculated US fieldpattern was superimposed on the tissue containing gel. Castor oilwas used to attenuate the transmitted US beam. A 15 cm diameterlinear transmit and receive birdcage coil was used for MRI.

MRI Calorimetry Technique 159

spherical volume (4.5 cm radius) to calculate total thermalenergy by rC o Ae2(r/B)2 · 2pr2Dr.

This calculation was repeated for different MR resolu-tions and slice thicknesses. To quantify the discrepancybetween the true energy derived from a 3D temperaturedistribution and that from a Gaussian approximation, wecalculated a relative error given by:

0Etruth 2 EGaussian0

Etruth[4]

Figure 2 shows the relative errors from these simulationsfor several sampling matrices with slice thicknesses of 10,5, and 1 mm. As can be seen, decreasing the samplingmatrix from 64 3 64 to 32 3 32 results in small accuracyloss while leading to a fourfold increase in temperaturesensitivity. However using a sampling matrix of 16 3 16,the error in calculated energy is substantially increased.Considering the balance of energy calculation accuracy

and the temperature sensitivity, a sampling matrix of 32 3

32 with FOV of 12 cm and slice thickness of 10 mm waschosen as optimal in this application. These simulationsshow that the largest error in calculated energy occursimmediately following the insonation period, when thetemperature profile is neither Gaussian in shape, norsymmetric. Later on, the distribution approaches a symmet-ric Gaussian profile resulting in improved accuracy incalculated energy. At the end of the energy storage period,the errors in calculated energy increase as thermal energystarts escaping from the integration volume. In light ofthese findings, the optimal period of data sampling shouldbe during the period of minimum error. Accordingly, theenergy measurement period started at 90 sec after thetermination of insonation, which corresponds to a ballradius of 10 mm. The data sampling was then continued foran additional 310 sec. By doing so, errors in calculatedenergy were less than 3%. Thus, reducing the samplingmatrix from 256 3 128 with a slice thickness of 1 mm for

FIG. 2. Comparison of percent error in energycalculated with different sampling strategies. a:Slice thickness 10 mm. b: Slice thickness 5 mm.c: Slice thickness 1 mm.

FIG. 3. Simulation results show error due tothermal diffusion during MRI (32 3 32 samplingmatrix with an FOV of 12 cm and a slice thick-ness of 1 cm).

160 Wang and Plewes

conventional MR imaging to 32 3 32 with 10 mm slicethickness results in a 320-fold increase in MR SNR withoutdegrading the accuracy of the energy measurement.

A third simulation, conducted to investigate the effect ofthermal diffusion during MR imaging, could potentiallyintroduce ghosting artifacts. To quantify the blurring er-rors, a figure of merit (FOM) was calculated by:

FOM5Îoi

oj

[img(i,j) 2 img0(i,j)]2/oio

j[img0(i,j)2] [5]

where img(i,j) is the reconstructed phase image from datasampled at different stages of thermal diffusion and img0(i,j)is that obtained if k-space data were collected instantlywhen the k-space center of img(i,j) occurred. The result of a10 sec imaging sequence for a 32 3 32 image with the first 1sec devoted to steady-state equilibrium and the last 1 sec asan interval between serial images is shown in Fig. 3. Thiseffect is negligible, indicating the slow progress of thermal

diffusion relative to the MR imaging time. At the end of theinsonation period, a sudden change in the thermal conduc-tion equation alters the thermal diffusion rate. Thus, adiscontinuity occurs at 100 sec.

Calorimetry Experiment

Background Phase Drift

Phase-difference MR thermometry is prone to artifactsfrom system instability, as reported by other groups (14,21).Although a correction scheme using a reference phantomcan be applied, small deviations in the phase values due tosystem instability remain. Harth et al. reported a maximumerror of 61.57C with this scheme (21). Peters et al reporteda strong correlation between temperature fluctuations inthe electronics room that was thought to influence thereference clock frequency and the corresponding phase(14). As our goal was to detect small temperature changes,system stability was a concern. This is shown in the left

FIG. 4. MRI phase drift correction. Before planar correction, the background phase drift was linear across the field of view with no preferablespatial orientation (phase-encoding or frequency-encoding). Imaging sequence parameters used: TR 250 msec, TE 30 msec, flip angle 30°,FOV 12 cm with 64 3 32 sampling matrix. After phase correction, these errors were substantially reduced.

MRI Calorimetry Technique 161

column of Fig. 4, which plots three phase-differenceimages of the phantom gel, with no US insonation, at threearbitrary times during an imaging experiment using a 1.5 Timager (Signa, GE Medical Systems, Milwaukee, WI). Thesequence parameters are TR 250 msec, TE 30 msec, u 307,and a sampling matrix of 64 3 32. Four reference images ofthe phantom gel were acquired and averaged as a baseline

image. By subtracting subsequent images from this base-line, phase difference and temperature maps were pro-duced (19). This was calculated by:

DT 5

atan 1 I2Q1 2 I1Q2

I2I1 1 Q2Q12

bgB0 ? TE ?2p[6]

FIG. 5. Schematic of experimental validation ofMRI calorimetry. A tiny, hand-made copper resis-tor with known resistance was embedded in ablock of gel. Known amounts of thermal energywere deposited in the phantom. MR estimates ofthe thermal energy were gathered and com-pared to the known thermal deposition.

FIG. 6. Temperature maps during validation experiment. When the resistor current was on, local B0 was disturbed, and the phase-differencemap was distorted as shown in a. After heating, the measured 2D temperature maps clearly showed the thermal diffusion process. b: 15 secafter heating. c: 95 sec after heating. d: 195 sec after heating.

162 Wang and Plewes

where I1, Q1, I2, and Q2 are the real and imaginary channeldata of the averaged baseline and the subsequent images,respectively, B0 is the main magnetic field, g is the gyromag-netic ratio, and b is the thermal frequency shift constanttaken to be 0.01 ppm/7C (14). The phase drift patternappears linear over the image with no preferable orienta-tion. This can be corrected by subtracting a fitted planeobtained by setting three reference regions at the periph-eral of the phantom gel to ax 1 by 1 c where x and y arespatial indices and a, b, and c are fitting parameters. Thecorrection results, shown in the right column of Fig. 4,indicate much reduced phase variation across the FOV.

Validation Experiments

To demonstrate the accuracy of MRI calorimetry, a valida-tion experiment was conducted whereby a known amountof energy with a similar distribution was delivered into thecalorimeter through a resistive heating source (Fig. 5). Acopper resistor with a diameter of 1.5 mm and a resistanceof 1.8 V was soldered to 24 gauge copper wires with a muchsmaller resistance (0.02 V). It was embedded in the same

cylindrical gel phantom block. Copper was chosen toachieve minimal susceptibility difference with agarose gelto avoid B0 inhomogeneities near the resistor. The size ofthe resistor was small to avoid signal void in MR images(26,27). A calibrated power supply was used to delivervarying amounts of energy through the known resistancefor varying amounts of time as calculated by I2 · R Z Dtwhere I is the measured current, R is the resistance, and Dtis the duration. MRI images were taken both during andafter applying the current. They were converted to tempera-ture maps by Eq. [5].

Figure 6 shows the resulting MRI images during onesuch validation experiment when local B0 was disturbeddue to current through the connecting wires and the phasedifference map was distorted during heating (Fig. 6a). Themeasured 2D temperature maps in Figs. 6b–d (correspond-ing to 15, 95, and 195 sec after insonation) clearly show thethermal diffusion process after heating.

Applying the energy calculation procedures outlined theParameter Optimization section above, in the fitted peaktemperature and radius were calculated. An example isshown in Fig. 7a and 7b for a resistor energy deposition of

FIG. 7. Energy calculation process for one vali-dation experiment. a: Fitted peak temperature.b: Fitted width of Gaussian distribution. c: Calcu-lated energy.

MRI Calorimetry Technique 163

13.68 J with calculated thermal energy plotted in Fig. 7c.The energy measurement started when the fitted radiusreached 10 mm and lasted for 310 secs. The fluctuations incalculated energy increased at later thermal diffusionstages as thermal energy dissipating from the imaging slice.The mean measured energy was 13.74 J with a standarderror of 0.17 J. Additional validation experiments wererepeated over an energy range of 7–28 J, as shown in Fig. 8.This shows that MR measured energy is in excellentagreement with the delivered energy with an uncertainty of0.5 J, which reflects the sensitivity of this method.

Absorption Measurement of PolyethyleneGlytherol Material

Figure 9 shows the experimental 2D temperature mapsduring and after US insonation of a 1 ml cube of atissue-mimicking ultrasound material composed of polyeth-ylene glytherol (PEG). This illustrates that the temperatureprofile builds up during insonation (Fig. 9a,b) and slowlydiffuses outward after insonation (Fig. 9c,d). The USenergy was delivered by a 1 MHz piston US transducerwith an input electrical power of 25 W and a duration of100 sec.

FIG. 8. MRI measured deposited energy plotted against energydelivered with a calibrated resistor. Line of identity was plotted assolid line. The uncertainty of each measurement was within 0.5 J.

FIG. 9. Experimental temperature maps during US insonation of a cube of polyethylene glytherol (PEG) material located at the center of FOV.a: 5 sec of insonation. b: 95 sec of insonation. c: 95 sec after insonation. d: 145 sec after insonation.

164 Wang and Plewes

Applying the same energy calculation procedures asoutlined before, the fitted peak temperature and radius areshown in Fig. 10a and b, with the calculated thermalenergy plotted in Fig. 10c. The mean energy obtainedduring the measurement window, as discussed earlier, was14.55 J, with a standard error of 0.18 J.

To calculate the US absorption coefficient, the incidentUS intensity distribution on the PEG material in the MRIimaging plane was measured with a calibrated needlehydrophone (NTR Systems, Seattle, WA). The measuredUS field was superimposed on a high-resolution MRIimage of the PEG-containing gel at the same plane. The USintensity incident on the PEG material was integrated pixelby pixel to obtain a measurement of the US input power.From these measurements (thermal energy absorbed andinput US power), the US pressure absorption coefficient ofthe tissue-mimicking PEG ultrasound material was calcu-lated to be 0.032 cm21 at 1 MHz and room temperature,which is similar to the absorption coefficient of liver tissue.US absorption coefficient of freshly excised bovine livertissue sample has also been measured by this method andfound to be 0.058/cm, which is within the measured valuesof previous investigators (13).

DISCUSSION

In this paper, a new approach for the measurement of theUS absorption coefficient in tissue samples has been

proposed and implemented based on high-sensitivity phase-difference MR thermometry.

The phase noise in experimental images with high SNRcan be expressed as s/S where s is the standard deviationof Gaussian noise in the real or imaginary data and S is thesignal intensity in the magnitude images (23,24). As thephase difference data used an average of four images as thebaseline, the equivalent phase noise is given by:Î(s/S)2 1 (s/2S)2. In these calorimetry experiments, calcu-lation of s/S resulted in a phase noise of 0.0015 rad. UsingEq. [6] led to an equivalent temperature noise of 6.3 m7C. Inprinciple, this number can still be improved by replacingthe linear birdcage cage transmit/receive coil used in thisexperiment with a quadrature coil. However, this is onlythe theoretical prediction, which reflects the lowest phasenoise in the absence of phase drift errors due to systeminstability. Actual measurement of phase noise in theperiphery of the phantom gel shows a maximal phase noise5 times as great as that calculated from the SNR in themagnitude images (12). Nevertheless, this temperatureprecision is still substantially better than both the commer-cial optical thermoprobes with a temperature precision of0.37C (LUXTRON, Santa Clara, CA) and other currentlyreported MRI thermometry sensitivities (14,19,21). Achiev-ing high temperature sensitivity through reduction inspatial resolution is noteworthy to clinical MR thermom-etry where high sensitivity, but coarse spatial resolution

FIG. 10. Thermal energy calculation for tem-perature maps in Fig. 9. a: Fitted peak tempera-ture. b: Fitted width of Gaussian distribution. c:Calculated energy.

MRI Calorimetry Technique 165

temperature map, can be superimposed on high-resolutionMR images to improve temperature sensitivity and tempo-ral resolution for therapy guidance and monitoring.

In principle, 3D sampling of the temperature distributionwould be preferable to avoid any assumption of 3D symme-try. However, a volume acquisition would take more time,so that changing thermal pattern due to thermal diffusionduring imaging could introduce errors. In view of thisdisadvantage and the excellent results with 2D implemen-tation, 3D calorimetry was not implemented; however, itwarrants further investigation.

As discussed elsewhere (12), the thermal elevation dueto US absorption in the gel has been found to be less than0.8% of that in tissue and therefore this did not interferewith calorimetry experiments.

In principle, this technique can be extended to study theUS absorption property of biological tissue ex vivo as afunction of temperature or thermal dose. These measure-ments should be of interest to US thermal therapy in termsof predicting lesion size and shape. This approach can beapplied over a range of frequencies, tissues, and tempera-tures, which should provide a new and non-invasivemeans of measuring absolute tissue US absorption coeffi-cients to improve US therapy planning, US dosimetrymodels, and future therapeutic transducer design (22).

ACKNOWLEDGMENTS

The authors acknowledge C.T. Chin, D. Hope-Simpson,R.D. Peters, and C. Macgowan for their helpful discussions;Douglas Henderson for his craftsmanship in the construc-tion of the calorimetry apparatus; and Christine Sudeykofor her proofreading.

REFERENCES1. Hynynen K, Darkazanli A, Unger E, Schenck J. MRI-guided noninvasive

ultrasound therapy. Med Phys 1993;20:107–115.2. Cline HE, Hynynen K, Watkins R, Adams W, Schenck JF, Ettinger RH,

Freud W, Vetro JP, Jolesz FA. Focused ultrasound system for MRimaging-guided tumor ablation. Radiology 1995;194:731–737.

3. Lele PP. Production of deep focal lesions by focused ultrasound—current status. Ultrasonics 1967;5:105–122.

4. Damianou C, Hynynen K. The various physical parameters on the sizeand shape of necrosed tissue volume during ultrasound surgery. JAcoust Soc Am 1994;95:1641–1649.

5. Damianou C, Hynynen K. Focal spacing and near-field heating duringpulsed high temperature ultrasound therapy. Ultrasound Med Biol1993;19:777–787.

6. Hynynen K, Chung A, Colucci V, Jolesz F. Potential adverse effects ofhigh-intensity focused ultrasound exposure on blood vessels in vivo.Ultrasound Med Biol 1996;22:193–201.

7. Damianou C, Sanghvi N, Fry F, Maass-Moreno R. Dependence ofultrasound attenuation and absorption in dog soft tissues on tempera-ture and thermal dose. J Acoust Soc Am 1997;102:628–634.

8. Parker K. Ultrasound absorption and attenuation in liver tissue. Ultra-sound Med Biol 1983;9:363–369.

9. Carstensen E. Absorption of sound in tissue. Natl Bureau StandardsSpecial Publications 1979;525:29–35.

10. Wells PNT. Review of absorption and dispersion of ultrasound in tissue.Ultrasound Med Biol 1974;1:369–376.

11. Goss SA, Cobb J, Frizzell L. Effect of beam width and thermocouple sizeon the measurement of ultrasonic absorption using the thermoelectrictechnique. IEEE Ultrasound Sympo Proc, 1977. p 206–211.

12. Wang Y. MRI calorimetry for the measurement of tissue ultrasoundabsorption, Master’s thesis, University of Toronto, 1998.

13. Wang Y, Hunt JW, Foster FS, Plewes DB. Tissue ultrasound absorptionmeasurement with MRI calorimetry. IEEE Trans UFFC, In press.

14. Peters RD, Hinks RS, Henkelman RM. Ex-vivo tissue-type indepen-dence in proton-resonance frequency shift MR thermometry. MagnReson Med 1998;40:454–459.

15. Ozisik MN. Heat conduction. New York: John Wiley & Sons; 1993. p436–501.

16. Poorter JD, Wagter CD, Deene YD, Thomsen C, Stahlberg F, Achten E.The proton-resonance-frequency-shift method compared with molecu-lar diffusion for quantitative measurement of two-dimensional time-dependent temperature distribution in a phantom. J Magn Reson B1994;103:234–241.

17. Stepanow B, Brix G, Lorentz W. A novel method for fast temperaturemapping. In: Proceedings of the ISMRM, 1993. p 737.

18. Ishihara Y, Kuroda K. A precise and fast temperature mapping usingwater proton chemical shift. Magn Reson Med 1995;34:814–823.

19. Poorter JD, Wagter CD, Deene YD, Thomsen C, Stahlberg F. Non-invasive MRI thermometry with the proton resonance frequency (PRF)method: in vivo results in human muscle. Magn Reson Med 1995;33:77–81.

20. Chung AH, Hynynen K, Colucci V, Oshio K, Cline HE, Jolesz FA.Optimization of spoiled gradient-echo phase imaging for in vivolocalization of a focused ultrasound beam. Magn Reson Med 1996;36:745–752.

21. Harth T, Kahn T, Rassek M, Schwabe B, Schwarzmaier H, Lewin J,Modder U. Determination of laser-induced temperature distributionsusing echo-shifted turbo-FLASH. Magn Reson Med 1997;38:238–245.

22. Johnston RL, Dunn F. Ultrasonic absorbed dose, dose rate and producedlesion volume. Ultrasonics 1976;July:153–155.

23. Pelc NJ, Berstein MA, Shimakawa A, Glover GH. Encoding strategies forthree-direction phase-contrast MR imaging of flow. J Magn ResonImaging 1991;1:405–413.

24. Gubdjartsson H, Patz S. The Rician distribution of noisy MR data. MagnReson Med 1995;34:910–914.

25. Nishimura D. Principles of magnetic resonance imaging. Stanford:Stanford University; 1996.

26. Schenck JF. The role of magnetic susceptibility in magnetic resonanceimaging: MRI compatibility of the first and second kinds. Med Phys1996;23:815–850.

27. Camacho CR, Plewes DB, Henkelman RM. Nonsusceptibility artifactsdue to metallic objects in MR imaging. J Magn Reson Imaging 1995;5:75–88.

166 Wang and Plewes