ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012 1

Temperature Imaging Using UltrasoundR. Martin Arthur, Ph.D.

I. INTRODUCTION

Thermal therapies for the treatment of pathological tissuesrange from freezing with cryosurgery to high-temperatureablation1–11. The application and impact of these methodseither alone as an alternative or adjuvant to radiotherapy orchemotherapy is the subject of ongoing investigation12–19. Inparticular the significance and impact of high temperatureablation therapies is growing rapidly4,6–9,20–24.

A major limitation of thermal therapies, however, is the lackof detailed thermal information available to monitor and guidethe therapy13,14,16,25–29. Temperatures are routinely measuredwith sparse invasive measurements. The limited number ofmeasurements may produce temperature distributions with lessdetail than is necessary to assess thermal dosimetry prop-erly16,26. With the advent of multi-element heating devices,there is increased need for temperature measurements thatcould provide detailed feedback about temperature distribu-tions. This information in near real time would considerablyimprove the ability to deliver consistently effective temperaturedistributions30–34.

To meet the capability of present and forthcoming heatingtechnologies for hyperthermia, a clinically useful method isneeded to measure 3D temperature distributions to within1oC with spatial resolution within 1 cm3 or better. A non-invasive method for volumetrically determining temperaturedistribution during treatment would greatly enhance the abilityto uniformly heat tumors at therapeutic levels in patientsreceiving thermal therapy35.

Many investigators have looked at ways of measuring tem-perature non-invasively. Possible methods include impedancetomography36, microwave radiometry37, and magnetic reso-nance imaging (MRI)4,38. MRI temperature imaging appearsto have the required accuracy and spatial resolution for manythermal therapy scenarios, but it is expensive, requires a fixedinstallation and may be difficult to use along with some heatingtherapies38. Nevertheless, at present MRI is the most advancedclinical technology for non-invasive monitoring of thermaltherapies39,40.

On the other hand, ultrasound is a non-ionizing, convenient,and inexpensive modality with relatively simple signal pro-cessing requirements. These attributes make it an attractivemethod to use for temperature estimation if a temperature-dependent ultrasonic parameter can be identified, measured,and calibrated. Methods for using ultrasound as a non-invasivethermometer fall into three categories: 1) Those exploitingthermal strain, which are based on echo-shifts due to changesin tissue thermal expansion and speed of sound (SOS), 2)Those that use the measurement of acoustic attenuation coef-

R. M. Arthur is with the Department of Electrical and Systems Engineering,Washington University School of Engineering. e-mail: rma@ese.wustl.edu

ficient, and 3) Those that exploit the change in backscatteredenergy (CBE) from tissue inhomogeneities.

In this work, we explore ongoing efforts in temperatureestimation with ultrasound using shifts in echo position, ther-mal strain, variations in ultrasonic attenuation, and changesin backscattered ultrasonic energy that occur due to thermaleffects. This chapter is an extension of a review articlepublished in 200541. That article focused on the hyperthermiatemperature range. We examine approaches that appear to havethe greatest potential for monitoring temperatures in both thehyperthermia (41-45oC) range and in ablation border zones (>60oC).

II. THERMAL EFFECTS ON BACKSCATTEREDULTRASOUND

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Fig. 1. Changes in backscattered ultrasound with temperature. Left) Echoesmeasured from a single site in a 1 cm thick sample of fresh bovine liver attemperatures from 37 to 50oC. The two delineated echoes (indicated by bandsmarked #1 and #2) shift with temperature and have energies that appear tochange with temperature (Similar to Figure 4 in Arthur et al. 42). Right) RFimages of a fixed region in bovine liver showing apparent motion from 37 to50oC. The right panel shows the image at 50oC after motion compensation(Similar to Figure 3 in Arthur et al. 43).

As tissue is insonified during heating, at least two effectsare easily seen in ultrasonic backscattered signals and images.They are a shift in apparent position of scattering regions andchanges in signal strength from those regions. These changesare associated with thermal effects on SOS in tissue and ontissue attenuation and backscatter-coefficient properties.

A. Echo Shifts and Changes in Signal Strength

Amplitude-mode backscattered signals and radio-frequency(RF) images from samples of bovine liver during uniformheating in a water bath are shown in Fig. 1. With temperatureincrease, the time it took for echoes from the liver specimeninterfaces and scattering regions to reach the insonifying trans-ducer changed in the A-mode echo signals. Apparent motionin the RF images occurred in part because SOS changes withtemperature. SOS, however, was assumed fixed at 1540 m/sby the imaging system.

The rectangular region in the RF images of Fig. 1 highlightsan image feature that appears to move as the specimen was

2 ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012

heated. Movement in the axial direction in images is similarto the shifts in the A-mode echo signals. Apparent motiontowards the transducer is consistent with the change in SOSin the water bath. The images show, however, that there is alsoan apparent lateral movement, presumably due to changes inthe tissue alone.

There are also clear changes in backscattered signal strengthwith temperature. This effect is seen in the delineated bands ofthe A-mode signals in Fig. 1, which isolate scattering regionswhose energy increased (band #1) or decreased (band #2) withtemperature.

B. Non-thermal and Unwanted Thermal Effects

To rule out non-thermal sources in backscattered signalsand images, changes in ultrasonic signals and images mustbe determined over the duration of a measurement paradigmwhen no heating occurs. Unwanted thermal effects includethose on the measurement system itself. Spurious thermaleffects may be seen in tissue as well. For example, in echoshift measurements, the heated region has a tendency to causea ’thermal lens’ effect that distorts the image of the tissuebeyond the heated region, where this effect can cause artifactsin temperature estimation44.

Thermal effects on a typical phased array transducer in awater bath have been seen in B-mode images of the stainlesssteel wires in the AIUM 100 mm test object45. Apparentmotion towards the transducer occurred with an increase intemperature during heating from 37 to 50oC43. That motion,however, can be accounted for by the change in SOS in thewater bath. The changes in backscattered signal level due tothermal effects on the AIUM wires and transducer, however,were small. The change in signal level from a wire in theAIUM test object over one hour was < ± 0.1 dB at a constanttemperature. Images at 37 and 50oC showed a change in signallevel of about 0.3 dB. The small changes over time and withtemperature due to effects on the test object and transducerare usually negligible compared to thermal effects in tissue.

We also tested our system under conditions for which we ex-pected to see no change in backscattered energy. We measuredthe energy in backscattered signal levels in bovine liver overthe time required for an experiment, but without heating, todetermine the magnitude of non-thermal effects. Signal-levelchanges of < ± 0.2 dB were typically seen over 80 minutes,twice the approximate duration of an experiment42.

III. IMAGE MOTION

Tracking the echoes from tissue interfaces and scatteringregions is important for any temperature estimation methodbecause a key challenge for in vivo studies is measurement ofthermal effects in the presence of real motion in a perfusedliving system, in addition to apparent motion from thermaleffects. Quantifying the time dependence of echo positionsis important because echo shift is the basis for much of therecent work on temperature estimation. In addition, in order tocompare signal strengths under consistent conditions, motionof scattering regions must be tracked so that compensation forthat motion can be applied as shown in Fig. 2.

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Fig. 2. Left) Conventional B-mode images at various temperatures froma specimen of turkey breast muscle before motion compensation. Apparentmotion can be seen clearly in the boxes. Right) Conventional B-mode imagesat the same temperatures after motion compensation. The patterns isolated inthe boxes show both motion compensation and a change in the signal strengthwith temperature. Figure from Guo 46 with permission.

Techniques for motion estimation in ultrasonic images, thatis, for estimation of the displacement between two imageregions, comprise an active field of research47–51 and havebeen used successfully for elasticity imaging, phase aberrationcorrection, blood velocity estimation, and other applications.In these areas, motion estimation is typically called speckletracking or time-delay estimation. Work based on exploitingthermal effects that induce tissue strain has been aimed atguiding focused ultrasound therapies, as well as estimation oftemperature52–55.

Measurement of echo shifts and the tracking of real andapparent motion has been based on correlation techniques.Employing RF signals permits the use of cross-correlation asa similarity measure for automatic tracking of regions as afunction of temperature. The result of maximizing 2D cross-correlation to estimate displacement and then shifting andresampling images to apply that displacement is shown inthe RF images of Fig. 1. Motion-compensated RF images canthen be envelope detected to yield the motion-compensatedconventional B-mode images of Fig. 2.

Potential pitfalls with motion tracking and compensationtechniques involve 1) propagation of errors in displacementestimation over the temperature range and 2) non-rigid imagemotion, i.e., apparent motion over temperatures that cannotbe compensated by a simple shift of the images. Errors indisplacement estimation depend on multiple factors, including:quantization errors that depend on the image sampling rate(or pixel size); decorrelation of the RF signals due to smallchanges in the underlying scattering structure56; signal-to-noise ratio and size of the region46,57; and artifacts or featuresthat appear in only one of the images.

There are two primary objectives for motion tracking inultrasonic temperature imaging. For methods based on echoshifts, tracking is local and most effective in 1D. For methodsthat use signal strength changes, tracking is global, that is overa tissue volume and in 2D or 3D, where motion is likely tobe non-rigid.

ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012 3

A. Tracking Echo Shifts

Of the ultrasonic thermometry methods explored to date,the use of echo shifts has received the most attention in thelast decade. Most of these efforts have been geared towards RFablation and high intensity focused ultrasound (HIFU) therapy,which typically heats small volumes of tissue to above 60oC.

Apparent and actual displacements of scattering regions areproduced by changes in SOS and thermal expansion, respec-tively. Temperature estimation using these effects is basedon measuring displacements in the direction of propagationz, which can be related to changes in SOS and to thermalexpansion44,58–61. The echo shift tδ(z)

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(1)where t(z) is the propagation and return time for an echo fromdepth z after heating, t0(z) is the time before heating, c is theSOS, which is a function of depth ζ and the temperature θ(ζ)at that depth. The linear coefficient of thermal expansion, α,depends on the medium and is also a function of depth52. Inthis approach, variation in SOS with temperature is assumed tobe linear up to about 45oC, but the method has proved usefulin assessing high-temperature ablation62.

The echo shift occurring between two successive RF imagesis estimated using the speckle tracking technique describedabove has been most successful in the axial dimension, thatis, along the propagation axis. Repeating this process alongadjacent beams can generate 2D or 3D map of the shiftsin a region of interest60. Shifts in the lateral and elevationare usually smaller than those in the axial direction and theirassessment tends to more subject to noise. Temperature mapsare typically generated in 1D, based on differentiation of shiftsalong the propagation direction, because shifts in this directionare less influenced by noise, using the time-shift relation,tδ(z), in Eq. 1 given above. Its application is illustrated inthe section on thermal strain imaging below.

B. Tracking and Compensating for Real and Apparent Motion

Estimation of tissue motion is a key step in manyapplications associated with ultrasonic imaging, such aselasticity imaging49,63–65, estimation of the velocity of bloodflow66–68, and non-invasive temperature estimation, includingour work43,69–71. These approaches have focused on 2Dmotion in ultrasound images.

1) Rigid Motion: Apparent tissue motion from rigid-motion, cross-correlation algorithms in both axial and lateraldirections from eight overlapping regions in 10 by 40 mmimages of four specimens of bovine liver, two of turkey breast,and one of pork-rib muscle had mean values within ± 0.5mm over the 37 to 50oC temperature range43. Tissue featuresappeared to move closer to the transducer in the turkey, pork,and two of the liver specimens, which is consistent with theincrease in the SOS in the water path between the tissue andtransducer. In the other two liver specimens presumably non-uniform thermal effects in tissue were larger than the changesdue to SOS changes in the water bath.

A non-uniform component of tissue motion in the 7 spec-imens cited above was indicated by the lateral motion. Thistissue-dependent component also contributed to the axial mo-tion, particularly at temperatures above 47oC. There werealso differences in the apparent lateral motion in the twospecimens of turkey breast. One exhibited nearly constantlateral motion. Its tissue fibers were parallel to the arrayof transducer elements. The other one showed a change ofseveral tenths of a millimeter near 47oC. Its striations wereperpendicular to the array.

Fig. 3. Non-rigid Motion in 2D in a live nude mouse from 37.5 to 38.0, 39.5to 40.0, and 42.5 to 43.0oC. Motion is clearly non-rigid in all three frames.Arrow lengths are 50 times the actual motion field. (Similar to Figure 5 inArthur et al. 72.)

2) Non-Rigid Motion: Differences in apparent motion fromvarying fixed regions suggest that apparent motion duringheating may not be rigid. If a rigid-motion assumption doesnot hold, the size of the tissue region over which rigid motion-compensation will be successful is limited. To overcome thislimitation and to compensate for motion over the whole tissueregion of interest in a single operation, we developed non-rigidmotion-compensation algorithms that can operate in 1D, 2D,or 3D. They are based on optimization of a function of thecross-correlation of an image at a particular temperature witha reference image46,73.

The cost function for our motion-compensation algorithmsis the normalized cross-correlation function of two RFdatasets. Let Ir(x) and It(x) be the image at the referencetemperature r and a shifted image at temperature t, respec-tively, where

Ir(x) = It(x + ∆x) , (2)

where x,∆x ∈ R2 or R3 are the spatial coordinates and themotion in those coordinates. Our goal was to find an estimateof the motion, ∆̂x, such that It(x+∆̂x) is as close to Ir(x) aspossible. The similarity between the two images was measuredby their correlation:

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For motion compensation prior to CBE computation, ∆̂xwas modeled to vary linearly over the image region. Specifi-cally, it was a linear function of the motion at control points,chosen as the corners of the 2D image or 3D image volume

∆̂x = g(∆x1, . . . ,∆xn) , (4)

where n is the number of control points. Our goal offinding ∆̂x is equivalent to searching for the estimate of∆x1, ...,∆xn that maximizes the correlation function. This

4 ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012

procedure is a multi-variable optimization problem with thecorrelation as the cost function

(∆̂x1, . . . , ∆̂xn) = argmax(∆x1,...,∆xn)C[Ir(x), It(x+∆̂x)] .(5)

We used the build-in functions in Matlab R© to solve thisoptimization problem. The motion field over a tissue volumewas represented as a linear function of 3D motion vectorsat eight reference points, the corners of the data volume.Examples of motion fields in 2D are shown in Fig. 3 fromimages a live nude mouse72. The direction of the arrowsrepresents the direction of motion, the length of the arrowsrepresents the magnitude of the motion. It is clear that themotion was non-rigid.

Our 3D motion-compensation algorithm has been used tocorrect for the motion in the images during 3D heating ex-periments73. In each experiment, a sequence of ultrasound RFimages in 3D was obtained at increasing temperature. Motionbetween adjacent pairs of 3D image sets was estimated andaccumulated relative to the reference image set. Fig. 4 showsthe 3D frame for one specimen of turkey breast muscle, alongwith the motion in the axial, lateral, and elevation directionswith temperature at the center slice of the 3D volume.

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volume. Left) Typical 3D motion field with 5x magnification at the cornersof the tissue volume. Center Left, Center Right, and Right) Axial, lateral,and elevation displacements for one specimen of turkey breast muscle at thecenter image (#15) of the 3D image set. Displacement values were foundvia trilinear interpolation of the estimated non-rigid 3D motion field over theimage volume. The magnitude of the motion in a 0.5oC step was < 20µm.(Similar to Figure 3 in Arthur et al. 73.)

Accumulated motion in all directions shown in Fig. 4was < 340µm. On average, tissue movement was < 20µmper 0.5oC step. This small change is consistent with visualobservation of echo shift and apparent motion in images. Thatdisplacement is nearly an order of magnitude less than mo-tion tracking and compensation methods based on correlationcan handle in this application. Displacements for which wecompensated took place over several minutes. Frame intervalsfor conventional ultrasound imaging systems can be orders ofmagnitude smaller. A typical frame interval is 30 msec. Thusmotion between frames encountered during clinical applica-tions of ultrasonic thermometry can be much smaller than we

encountered in our in vitro studies. Thus frames intervals forthermometry can be tailored to optimize the effectiveness andspeed of motion-compensation algorithms.

IV. ULTRASONIC MEASUREMENT OFTEMPERATURE

Temperature dependence of ultrasonic tissue parameters hasbeen reported extensively from in vitro analyses of propertiesthat characterize tissue response to insonification74–84. Theseearly investigations reported changes in tissue characteristicswith temperature in order to evaluate thermal errors in tissuecharacterization. Some investigators did consider, however,the possibility of using temperature dependence of tissueproperties as a means to track temperature changes76,77,85.

The primary ultrasonic parameter examined for its depen-dence on temperature in early work on measurement of tem-perature was SOS77,80,85. In these initial studies investigatorstried to obtain SOS maps of the medium from which to infertemperature distributions. This approach, however, has neverbeen instituted clinically86. Perhaps this approach has not beenimplemented because in order to measure SOS, it is necessaryto measure both distance and time, to image an identifiabletarget from two directions, or to use a crossed-beam (multiplebeams) method87. Such measurement is further complicatedby the fact that ultrasonic windows do not always exist invivo to allow insonification of a region of interest from twoviews. Another problem is that the temperature dependence ofSOS differs depending on the tissue type, e.g. whether tissuehas high water or fat content.

More recently the use of ultrasonic parameters as a guidefor thermal therapy has been revisited with several differ-ent parameters being considered. In particular, papers bySun and Ying35, Seip, Simon, Ebbini and coworkers59,60,88,Maass-Moreno, Damianou, and coworkers58,89,90, and ourgroup42,70,91 have reported the changes in received ultrasonicsignals due to changes in ultrasonic tissue characteristicswith temperature. These changes have been investigated boththeoretically and in vitro with an eye towards using thesesignals for non-invasive monitoring of thermal therapy. Mostof these investigators have looked at the consequences ofchanges in SOS and thermal expansion with temperature thatcause echo shifts or changes in the amplitudes of backscatteredultrasonic signals.

A. Experimental Concerns

Among the inherent advantages of using ultrasound fortemperature imaging is that it is non-ionizing, convenient,and relatively inexpensive. A-mode signals and phased-arrayimages are routinely produced in real time. To take advantageof these attributes, effective temperature imaging should beexpected to operate in real time with relatively simple ad-ditional signal processing requirements that employ existingultrasonic equipment using ultrasonic properties extracted, ifpossible, from a single backscatter view.

To obtain sufficiently accurate measures of ultrasonicproperties for temperature imaging, it may be necessaryto compensate for known limitations of image generation

ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012 5

in conventional imaging systems. These include effects ofthe measurement system itself, insertion loss, reflection andtransmission losses, attenuation in tissue, and effects of beamdiffraction92–98,98,99.

1) Temperature standards: The conventional standard fortemperature measurements in tissue is a reading from a ther-mocouple, which can fit into a hypodermic needle. Because oftheir invasive nature, however, thermocouple grids can only beused sparsely in tissue. For in vivo temperature imaging MRIis the standard modality during thermal therapy38–40,100,101.Nevertheless, MRI volumetric measurements themselves arecorroborated with thermocouple readings.

Thermocouples are calibrated with a National Institute ofStandards and Technology traceable thermometer. Typicallyindividual thermocouples are accurate to within ± 0.1oC.To calibrate the thermocouples and the system that monitorsthem, they may be placed in a water bath with a heater. Atequilibrium for a temperature of interest in the water bath,the NIST traceable standard reading and the thermocouplevalue are taken simultaneously. This process is repeatedover the temperature range of interest. Typically multiplecalibration experiments must be conducted to assess themean thermocouple errors and their standard deviations. Thethermocouple monitoring system may employ an internalreference that varies each time the unit is used. This offsetmust be measured and used to correct the thermocouplereading during each experiment to calibrate thermocoupletemperatures to within 0.2oC.

2) Calibration of Tissue Properties during Uniform Heat-ing: Measurements of temperature-dependent ultrasonic prop-erties can be made by heating specimens in an insulatedtank filled with deionized water, which had been degassed byvacuum pumping in an appropriate vessel. Degassing is nec-essary to prevent the formation of bubbles during heating. Gasbubbles scatter ultrasound and corrupt quantitative assessmentof ultrasonic parameters.

Most ultrasonic imaging systems are based on notebookcomputers or other forms of computer-based systems. Thecomputer in these imaging systems can be used to controltissue heating by setting the temperature a circulating heater.The temperature in the tissue, monitored by a thermocouple,can be reported to a routine in the computer of the imagingsystem. When the desired temperature is reached the heatercan be turned off and an image frame or image loop acquiredand saved. The computer can also be used to automaticallycontrol the position of the transducer array position in theelevation direction via stepper motor to acquire 3D imagesets. This process can be fully automated. For example, allkeystrokes needed to switch between peripheral control andimaging can be administered, for example, using keystroke-emulation software, such as AutoIT (hiddensoft.com). Analternate for some imaging system is control all of theoperations via a proprietary software developers kit.

3) Temperature Imaging during Non-Uniform Heating:Heat sources in thermal therapies produce non-uniform tem-

Fig. 5. Configuration for non-uniform heating experiments. Tissue wasimaged in a 37oC water bath with a 7.5 MHz linear array in the plane of thetissue. Heating was provided by 65oC water pumped through a 1 cm diametersilicon tube in the center of the tissue specimen. Thermocouple holders withfitted slots for the thermocouple shafts provided support to reduce movementof the thermocouple tips in the tissue.

perature distributions because of the nature of the sourceitself or because of inhomogeneity in the tissue being heated.Hyperthermia heating is more nearly uniform than ablationtherapy, which is concentrated to destroy a tumor or aberrantpathway in the heart, for example. The computer of theimaging system can be used to automate heating and imageacquisition, as noted above.

A non-uniform heat source may have many forms dependingon the therapy. Heat sources include microwave antennas andlow-frequency ultrasonic arrays for hyperthermia, and high-intensity ultrasound and RF electrodes for high-temperatureablation. These sources may be used in experiments to testultrasonic thermometry for clinical settings, but other sourcesmay be used to develop ultrasonic temperature imaging in thelaboratory.

We created the fixture shown in Figure 5 to heat gelationphantoms and tissue specimens102 from a central hot-watersource, while the phantom or tissue is surrounded by water atfixed reference temperature, usually 37oC. This fixture usesa thermocouple grid to corroborate ultrasonic temperatureimages estimates. A 3D image set can be taken in which thetips of the thermocouples on each side of the specimen canbe seen in the first and last images of the set, which are notused in generating temperature images, but can be used toplace the thermocouple reading in the temperature imagesto assess their accuracy. Furthermore, with the metal of thethermocouples and their holders removed, the fixture can beused to perform MRI temperature imaging with the samehot-water heating source.

B. Attenuation

The accepted method for measuring the attenuation coef-ficient is by use of a shadowed-reflector ”substitution” tech-nique. A reference RF trace (corresponding to the specularecho from a stainless-steel reflector through water only) andan RF trace corresponding to the reflected signal after it haspassed through the tissue specimen are required. If the powerspectra of the reference trace and the through-sample trace arefound, then attenuation can be computed by subtracting the

6 ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012

power spectrum through the sample from the spectrum of thereference in the logarithmic domain, correcting for interfaceinsertion losses, then normalizing the resulting spectrum bythe sample thickness103. The frequency dependence of theattenuation coefficient is usually determined by a linear fitto the data over the useful bandwidth of the measurementsystem103–105.

Attenuation is more difficult to measure from singlebackscattered signals in tissue, that is, without a referencesignal. Methods for setting bounds on the estimates of theattenuation of small tissue regions, particularly at temperaturesbelow 50oC, may be useful in determining limits on accuracyand spatial resolution of attenuation-based temperatures106.The slope of attenuation found for a linear fit of attenuationshown in Fig. 6 for four temperatures in dog myocardium islinear with temperature75. The attenuation curves at 2 MHzare not fit well, however, by a straight line, but are by a single-pole model107 curves superimposed on the measurements inthis figure. The pole locations shown in Fig. 6 as a functionof temperature may be a better choice for characterizingthe temperature dependence of attenuation for temperatureimaging, particularly at temperatures below 50oC.

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Fig. 6. Left) Attenuation of dog myocardium at four temperatures predictedby a single-pole tissue model. Data points were taken from the work ofO’Donnell et al. 75. Temperatures indicated with each part are in degreesCelsius. Height of the vertical bar at each measurement is the standard error.Right) Dependence of relaxation frequency of the single-pole model on thetemperature of dog myocardium 107. Transfer functions of the single-polemodel were calculated from data shown in the left panel above.

Attenuation changes with temperature appears to be morepronounced at temperatures above 50oC than in the hyper-thermia range. Several groups have investigated the temper-ature dependence above 50oC in tissue90,108,109. Damianouand coworkers investigated the temperature and the frequencydependence of ultrasonic attenuation and absorption in softtissues90. They found that attenuation was highly dependenton temperature, but only at temperatures > 50oC. Techavipooand coworkers measured attenuation of canine tissue from25 to 95oC with different tissue samples heated to differenttarget temperatures to reduce cumulative tissue degradation.They found that attenuation at 3, 4, and 5 MHz was rel-atively unchanged from 40 to 60oC, but increased sharplyabove 60oC110. In measurements of insertion loss at roomtemperature before and after heating, increases in attenuationof up to 2.4 dB/cm at 3.5 MHz were found in porcine liverafter heating to 80oC in 300 sec.109.

Ribault and coworkers also looked at the effect of tem-perature rise on frequency-dependent attenuation and found

that tissue damage (lesion formation) caused a change inattenuation in porcine liver in vitro5. This effect was foundby looking at the backscattered signal over the volume of thelesion, and comparing the power received before and afterhigh intensity focused ultrasound (HIFU). Other investigatorshave observed similar effects in the past111. Thus attenuationis of interest for thermometry, and may have applicationwith appropriate processing at temperatures below 50oC, butappears to a parameter of interest at temperatures above 50oC,which may make it an attractive parameter for assessing high-temperature ablation.

C. Thermal Strain using Echo Shift

Temperature maps based on thermal strain to find the changein temperature ∆T (z) along the propagation direction can beestimated by differentiating Eq. 1, the expression for echo shifttδ(z)

58.

∆T (z) = k∂

∂ztδ(z) , (6)

where k is based on the change in SOS with temperature andthe thermal expansion coefficient α of the medium of interest.For example, Maass-Moreno and coworkers investigated theability to predict temperature in HIFU therapy from echo shiftsin turkey breast muscle58,89. They found that results wereconsistent with their theoretical predictions. In investigationsby Ebbini and coworkers, tracking echo shifts from scatter-ing volumes was shown to be promising, as was the workof other investigators looking at echo shift for temperatureestimation44,60,88.

Combining echo shift temperature estimation with elas-tography can improve the quality of monitoring of thermallesions induced by focused-ultrasound112. Furthermore, echo-shift estimation has been implemented with a zero-crossingmethod for tracking temporal positions of echo to determinethe difference between A-mode signals gelatin phantoms be-fore and after heating113. This technique yielded as much as a7-fold improvement in computational efficiency compared toconventional cross-correlation methods with similar tempera-ture estimation results.

Sun and Ying have also found some success in beingable to predict temperatures using time-gated echo shifts,but they acknowledge the difficulty of using this method forgeneral temperature monitoring because prior knowledge ofboth SOS and thermal expansion coefficients is necessary35.Obtaining a priori knowledge of both SOS and thermalexpansion coefficients is a formidable problem for the in vivocase, as demonstrated by a quick look at the early tissue-characterization literature, which shows that SOS can varygreatly in different types of tissues. In fact the speed changedue to temperature in lipid tissue is opposite in directionto the SOS change in aqueous tissue. These complicationscould cause difficulties in determining temperature in thecomplicated inhomogeneous tissues, likely to be found in anin vivo situation.

Varghese, Zagzebski, and coworkers investigated the spatialdistribution of heating using echo shifts in studies that included

ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012 7

Fig. 7. 1D thermal strain temperature image from axial echo shifts in turkeybreast muscle during non-uniform heating using the fixture in Fig. 5. Tissuewas surrounded by water at 37oC. At time = 0 seconds 65oC water waspumped through the tissue center (black disk). Compare to the 3D CBE imagein Fig. 14 from a different specimen of turkey. Thermocouple readings inplanes adjacent to the image were used to scale the strain image to givetemperature estimates.

in vivo measurements61 and more recently in vivo tempera-ture estimates during high-temperature ablation62. Tempera-ture estimates were obtained using cross-correlation methodsdescribed previously and Eqn. 1. Resulting temperature mapswere used to display the initial temperature rise and to con-tinuously update a thermal map of the treated region that wassimultaneously monitored using thermosensors. Fig. 7 showsa thermal strain image in a specimen of turkey breast musclewe generated from measurements taken with the fixture in Fig.5. The constant k in Eq. 6 was estimated by comparison ofthe thermal strain image to thermocouple readings.

D. Change in Backscattered Energy

In a search for an ultrasonic parameter that changed mono-tonically with temperature, we modeled the backscatteredenergy from individual scatterers to an interrogating ultrasonicwave91. According to that model, the change in backscatteredenergy due to temperature was primarily dependent on thechanges in SOS and density of the medium compared to theirvalues in sub-wavelength inhomogeneities (scatterers) withinthe medium. Our predicted change in backscattered energy(CBE) at any temperature T with respect to its value at somereference temperature TR is

CBE(T ) =α(TR)

α(T )

η(T )

η(TR)

[1− e−2α(T )x]

[1− e−2α(TR)x], (7)

where, as functions of temperature, α(T) is the attenuationwithin the tissue volume and η(T) is the backscatter coefficientof the tissue volume. Distance x is the path length in thetissue volume. We inferred the temperature dependence of thebackscatter coefficient from the scattering cross section of asub-wavelength scatterer114,115. Neglecting the effect of the

small change in the wavenumber (< 1.5%) with temperature,we assumed91

η(T )

η(TR)=

(ρmc(T )2m−ρsc(T )2s

ρsc(T )2s

)2+ 1

3

(3ρs−3ρm2ρs+ρm

)2(ρmc(TR)2m−ρsc(TR)2s

ρsc(TR)2s

)2+ 1

3

(3ρs−3ρm2ρs+ρm

)2 , (8)

where ρ and c are the density and speed of sound of the scat-terer s and medium m. This expression applies to conditionswhere the wavelength λ is larger than 2πa, where a is theradius of the scatterer. Assuming a speed of sound of 1.5mm/µs and a frequency of 7.5 MHz, λ is 0.2 mm, whichmeans that Eq. 7 using Eq. 8 applies to scatterers smaller than30 µm.

dB

mm

CBE Reference (37oC)

5 10 15 20

2

4

6 −10

0

10

CBE @ 41oC

5 10 15 20

2

4

6 −10

0

10

mm

mm

CBE @ 45oC

5 10 15 20

2

4

6 −10

0

10

mm

CBE @ 50oC

5 10 15 20

2

4

6 −10

0

10

Fig. 8. Change in backscattered energy in ultrasound images of bovine liverfrom 37 to 50oC after compensation for apparent motion. All images werereferred, pixel-by-pixel, to the energy in the reference image at 37oC. Eachcolorbar is in dB. (Similar to Figure 6, but from a different specimen andover a larger region of interest, in Arthur et al. 43.)

Changes in backscattered energy were modeled assumingthat the scattering potential of the volume was proportionalto the scattering cross-section of sub-wavelength scatterers.We predicted with this model that the change in backscatteredenergy could increase or decrease depending on what typeof inhomogeneity caused the scattering. These calculationssuggested that the change in backscattered energy could varydepending on the type of scatterers in a given tissue region.

In 1D studies, we showed that it is possible to isolateand measure backscattered energy from individual scatteringregions, and that measured CBE was nearly monotonicallydependent on temperature42. In our studies of CBE in images,apparent motion of image features has been tracked and com-pensated for automatically as described above, so that CBE canbe measured at each pixel in motion-compensated images70.Fig. 8 shows CBE images, that is, the energy changes relativeto the reference image at 37oC. As predicted the energychange is both positive (increasing) or negative (decreasing)with temperature. This approach allows use of the wholeultrasonic image rather than just the signals from selectedscattering regions, but at the price of possibly increasing noisein estimates of CBE.

8 ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012

36 38 40 42 44 46 48 50

−4

−2

0

2

4

6

Lipid Scatterer

Aqueous Scatterer

Temperature (oC)

Ch

ang

e in

Bac

ksca

tter

ed E

ner

gy,

dB

Predicted Effect of Backscatter Coefficient

Positive CBENegative CBE

36 38 40 42 44 46 48 50−3

−2

−1

0

1

2

3

4CBE from Simulated Images with Additive Noise

Temperature (oC)

dB

Mean of Positive CBEMean of Negative CBE

36 38 40 42 44 46 48 50

−4

−2

0

2

4

6

Temperature (oC)

dB

Positive & Negative CBE in Tissue

Bovine LiverTurkey BreastPork Muscle

Fig. 9. Left) Predicted CBE for single, sub-wavelength lipid and aqueousscatterers in an aqueous medium with thermal properties given by our initialtheoretical study (Similar to Figure 5 in Arthur et al. 91). Center) CBE fromsimulated 1 x 1 cm B-mode images with collections of scatterers (2000aqueous and lipid scatterers in a 2:1 ratio) in the presence of noise (Similarto Figure 8 in Trobaugh et al. 57). Right) Means of measured CBE in positiveand negative regions of backscattered-energy images in four specimens ofbovine liver, two of turkey breast, and one of pork muscle. The error bar isthe standard error of the mean estimated from eight regions of interest in eachof the tissue specimens (Similar to Figure 8 in Arthur et al. 43).

After compensating for apparent motion in images ofbovine liver, turkey breast, and pork muscle, the mean changein backscattered energy at each pixel over 8 image regionsin all tissue specimens was calculated with respect to areference temperature (37oC). As temperature increased, forsome scattering regions the CBE was positive, for others itwas negative as seen in Fig. 9 for our initial predictions,from simulations of images of scatterer populations, and fromin vitro measurements in different types of tissue. Becausethe means of CBE from pixels with positive and negativerelative backscattered energy changed nearly monotonicallyCBE is a suitable parameter for temperature estimation. Fromuniform-heating studies its accuracy and spatial resolutionappear to be suitable for temperature imaging73.

1) Stochastic-Signal Framework: In our initial work, CBEfrom backscattered signals was computed as a ratio at eachpixel in the envelope detected images of energies at temper-ature T and TR

43. It was characterized by averaging ratioslarger than and less than 1, denoted as positive CBE (PCBE)and negative CBE (NCBE), which describe the increase anddecrease in the backscattered energy, respectively.

When ien is represented by a random process, computationof the signal ratio can be modeled as a ratio between tworandom variables, yT and yR 46

z =yTyR

(9)

where yR and yT are the random variables representingthe B-scans at the reference and current temperatures. Theratio, z, is also a random variable whose probability densityfunction (PDF), fZ(z), is determined by the joint distributionof (yR, yT )116

fZ(z) =

∫ ∞−∞|yR|fYRYT

(yR, yRz)dyR , (10)

where yR, yT and z > 0.The computation of PCBE in our initial work can be written

as

PCBE =1

N+

∑k∈{k|zk>1}

zk =

1N

∑k∈{k|zk>1}

zk

N+

N

,

36 38 40 42 44 46−3

−2

−1

0

1

2

3

4

Temperature (oC)

CB

E (

dB

)

CBE with Various SNR. μ ± σ of 25 Trials.

SNR:17dBSNR:23dBSNR:29dB

36 38 40 42 44 46−3

−2

−1

0

1

2

3

4

Temperature (oC)

CB

E (

dB

)

CBE at SNR = 17dB. μ ± σ of 25 Trials.

CBE without noiseCBE with noiseCBE from pdf

Fig. 10. Left) Mean ± standard deviation of positive (PCBE) and negative(NCBE) CBE from simulated images over the range of signal-to-noise ratios(SNRs) seen in our experiments. CBE was calculated from the means ofthe image ratios. Both the initial value of CBE (at 37 +o C) and the slopewith temperature are affected by SNR 57. Right) Mean ± standard deviationof positive (PCBE) and negative (NCBE) CBE from simulated images withSNRs of 17dB computed from the means of the image ratios. These curvesare compared to CBE from images with infinite SNR and CBE computedusing pdfs from the 17dB SNR images. CBE from the pdfs in each case isclose to CBE found without noise (infinite SNR). Figures from Guo 46 withpermission.

where N is the number of pixels in image and N+ is thenumber of ratio pixels with value larger than 1. Assumingzk’s are independent, identically distributed random variables,the nominator approximates the integral

∫∞1zfZ(z)dz. The

denominator approximates the probability of z being largerthan 1. Thus, PCBE is defined as the normalized mean of zover z ∈ [1,∞). Similarly, NCBE is defined as normalizedmean of z over z ∈ (0, 1). Thus

PCBE =

∫∞1zfZ(z)dz∫∞

1fZ(z)dz

; NCBE =

∫ 1

0zfZ(z)dz∫ 1

0fZ(z)dz

.

(11)From these definitions, PCBE and NCBE are in fact statisticsof the signal ratio and are determined by the ratio distributionfZ(z)46.

Fig. 11. Top) Simulated temperatures based on a finite-element simulationof heating from a 65oC source in the center and a fixed 37oC surroundingtemperature. Bottom) Temperature images estimated with CBE from simulatedimages for a homogeneous scatterer distribution over the heated region withan SNR of 24dB. The mean estimation error for was 0.4 ± 0.2oC. Figurefrom Basu 102 with permission.

2) Effect of Signal-to-Noise Ratio, Temperature Range, andInsonification Frequency: In order to investigate CBE forpopulations of scatterers, we developed an ultrasonic imagesimulation model, including temperature dependence for in-

ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012 9

dividual scatterers based on predictions from our theoreticalmodel57. CBE computed from images simulated for popula-tions of randomly distributed scatterers behaves similarly toexperimental results, with monotonic variation of CBE forboth individual pixel measurements and over image regions.Effects on CBE of scatterer type and distribution, size ofthe image region and signal-to-noise ratio affect temperatureaccuracy and spatial resolution. This simulation model alsoprovides the basis for gaining a better understanding of theeffects of motion on CBE, limitations of motion-compensationtechniques and accuracy of temperature estimation, includingtradeoffs between temperature accuracy and available spatialresolution.

Signal-to-noise ratio (SNR) in images from a given regionsize, with a particular scatterer type and population, affectsthe accuracy of the CBE temperature image from that tissueregion. Fig. 10 shows CBE from simulated images withvarious SNRs, typical of those seen in experiments. The initial(37oC) value of CBE and the slope with temperature are afunction of SNR. Fig. 10 also shows the effect of CBE of usingthe framework described in the previous section that allows forreduction of the noise effect by using the probability densityfunction (pdf) from the low (17dB) SNR images. Reduction ofthe noise effects on CBE improves temperature accuracy fora given spatial resolution. Noise effects can also be reducedby image averaging. Averaging 20 images results in about thesame improvement in CBE shown in Fig. 10 by using the pdfsfrom the images.

We studied effects of noise level on temperature imagingusing Pennes’ bioheat equation, which has had widespreadapplication in the reconstruction of temperature fields inbiological tissue117. For the in vitro case, in which perfusionand metabolism can be neglected, the heat flow equation attemperature T becomes

ρCp∂T

∂t= ∇(k∇T ) +Q , (12)

where where ρ is density, Cp is specific heat, k is heatconductivity, and Q is the heat delivered to the specimen.

The bioheat equation (Eq. 12) was implemented usingfinite-element software to simulate temperature distributionsexpected in the experimental fixture shown in Fig. 5102,118.Thermal parameters were taken from values for muscle givenin the literature119. Temperature images with time are shownin the upper panel of Fig. 11 for an initial temperaturesurrounding the medium of 37oC. At time zero, temperatureon the inner surface (location of a heating tube in experiments)was raised to 65oC to match subsequent experiments102.

CBE with non-uniform heating was computed from sim-ulated B-mode images with additive Gaussian random noiseusing the FEM temperature images. Fig. 11 also shows tem-perature maps based on the computed CBE for an SNR of24 dB, typical of that seen in an experiment. For noiseless B-mode images, the CBE temperature images followed the FEMsimulated temperature maps closely. The error in estimationfor the noise-less condition was 0.01 ± 0.2oC. The meanestimation error for 24dB SNR was 0.4±0.2oC. Note that theCBE temperature image was less affected by noise where the

change in temperature was largest, that is, where CBE valuewas larger than the noise.

35 40 45 50 55 600

1

2

3

4

5

6

Temperature (oC)

dB

CBE to 60oC from a 7.5 MHz Phased Array

Positive CBE

40 45 500

1

2

3

4

5

6

Temperature (oC)

dB

CBE from a 2.25 MHz Synthetic−Aperture

STD of CBE

Fig. 12. CBE Thermal Sensitivity from 37 to 60oC at 7.5 MHz and from37 to 50oC at 2.25 MHz. Left) Positive change in backscattered energy at7.5 MHz from an ex vivo specimen of porcine muscle. Right) CBE fromsynthetic-focus images at 2.25 MHz in a 10x30 mm region of bovine liver.

Another aspect of noise effects is seen in Fig. 12, whichshows CBE increasing to 60oC. This behavior may makeCBE temperature imaging useful in high-temperature ablationborder zones. The initial jump in CBE near 37oC indicatesB-mode images that were more noisy than usual for ourimaging system. On the right in Fig. 12, however, thejump at 37oC is small. The noise levels were reduced bysynthetic-aperture imaging. In this case the completed dataset(642 signals) from a 64-element array was used to generatedeach pixel in the each B-mode image, resulting in noisereduction due to spatial averaging compared to conventionalphased-array imaging. Note too that the array operated at 2.25Mhz, which shows that CBE can be effective for temperatureimaging at both 2.25 and 7.5 MHz.

3) 3D Calibration and Temperature Estimation during Uni-form Heating: To investigate the effect of temperature onbackscattered energy in 3D using backscattered energy, wecalibrated CBE in 1 cm3 volumes of turkey breast muscleduring uniform heating. This volume size was selected tomatch our long-term goal is to measure 3D temperaturedistributions to within 0.5oC in 1 cm3 volumes for monitoringhyperthermia treatments35,120.

Temperature was estimated in separate 1 cm3 volumes ofturkey73. Both calibration and estimation were done after com-pensation for motion in 3D. CBE as a function of temperaturewas measured in 20 1 cm3 volumes from eight specimens ofturkey breast muscle using the standard deviation of the energyratio in a given tissue volume43. The slope of each CBE curvewas well matched with a linear regression line (see Fig. 13.Correlation coefficients ranged from 0.991 to 0.999. The errorof the regression-line fit over all volumes and temperatures was0± 0.07 dB. By definition, CBE at the reference temperature(37oC) is zero. The slope for the 20 cubic centimeter volumeswas 0.300± 0.016 dB/oC.

Temperature estimation in 1 cm3 volumes of turkey breastmuscle was based on calibration from a linear regressionfor measured CBE in a separate 1 cm3 volume of turkeybreast muscle. Figure 13 shows an example of estimation oftemperature based on calibration using a fixed CBE thermalsensitivity (0.3 dB/oC). Maximum positive and minimum

10 ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012

36 38 40 42 44 46−0.5

0

0.5

1

1.5

2

2.5

3

Temperature (oC)

dB

CBE Calibration in Turkey Breast Muscle

Slope = 0.3 dB/oC

36 38 40 42 44 46−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

Temperature (oC)

Err

or

(oC

)

Temperature Estimation: CBE Sensitivity = 0.3 dB/oC

Fig. 13. Calibration of CBE thermal sensitivity and temperature estimationin turkey breast muscle 73. Left) Mean ± standard deviation of the change inbackscattered energy (CBE) in 20 volumes (1 cm3 each) from eight 4x6x2 cmspecimens of turkey breast muscle. Right) Mean estimation error ± standarddeviation of error values for temperature estimation using CBE over all 20tissue volumes with a fixed CBE sensitivity of 0.3 dB/oC.

negative errors were 0.53 and -0.39oC.

The mean of the maxima of the absolute value of theerrors encountered in this in vitro study of CBE temperatureestimation over all 1 cm3 volumes was < 0.5oC fortemperatures from 38 to 42oC over all possible estimationtests using a single, separate cubic centimeter region forcalibration and < 1oC for all temperatures. These resultsshow that CBE, whose thermal behavior is monotonic, canserve as the basis for accurate volumetric temperature imaging.

Fig. 14. Upper panels) CBE temperature images during non-uniform heatingof turkey breast muscle at 90, 180, and 300 seconds using the fixture inFig. 5. Tissue was surrounded by water at 37oC. At time = 0 seconds 65oCwater was pumped through the tissue center (double ring). Lower sequence)Thermocouple readings in planes adjacent to the 3D image set were used toverify CBE temperature estimates. CBE values were within about 1oC of thethermocouple readings. Figure from Basu 102 with permission.

4) Temperature Imaging during Non-Uniform Heating: Togenerate and validate CBE temperature images during non-uniform heating, the fixture shown in Fig. 5 was used tohold and heat abattoir specimens of turkey breast muscle102.The specimen was allowed to come to equilibrium at 37oC,then 65oC water was pumped through a silicone tube in thecenter of the specimen, using ultrasonic gel as a coupling agentbetween the tissue and the tube.

3D ultrasonic volumes were obtained at 7.5MHz by movinga transducer array in the elevation direction under steppermotor control. The first and last images of the 3 mm thick 3Dset captured the position of thermocouple tips for validatingthe CBE temperature images, as shown in Fig. 14. The CBEtemperature images were found after motion compensationusing the sensitivity of CBE to temperature determined in thecalibration studies, namely 0.3 dB/oC.

Figures 14 also shows the CBE-estimated and measuredtemperatures at the location of four thermocouples at threetimes after the start of heating. For this specimen CBEtemperatures errors within about 1oC over the 900s periodof heating. Similar results were found over multiple spec-imens102. As expected, the estimated temperature patternsshowed temperature increasing outwards from the heat sourcewith consistent patterns over time, although not in a radialpattern as seen in homogeneous gelatin phantoms, perhaps dueto inhomogeneous tissue structures.

V. DISCUSSION

Ultrasonic thermometry is based on thermal effects in softtissue that are manifest as changes in the speed of sound, at-tenuation, and backscatter of ultrasound. The use of echo shiftsand changes in backscattered energy are the most promisingtechniques for estimating temperatures in the hyperthermia(41-45oC) range. Both methods are useful to temperaturesabove 60oC, which make them attractive for temperatureimaging in the border zones of high-temperature ablations.Although attenuation is more difficult to measure than eitherecho shift or change in energy, its increased sensitivity totemperatures above 50oC also makes it of interest for assessinghigh-temperature ablation.

A key processing step common to all the methods justmentioned is the tracking of apparent motion of scatteringregions in vitro. Motion detection takes on even more impor-tance during in vivo studies because of the likely additionalmotion of the subject. Time shift as a function of depth isthe basis for temperature estimation using echo shifts. Motionmust be tracked and correction applied before temperature canbe estimated using changes in backscattered energy. Giventhe importance of determining tissue motion for estimatingtemperature with ultrasound and that its determination is themost computationally intensive part of ultrasonic temperatureimaging, it is likely that more efficient and sophisticatedmethods for motion tracking are likely to be applied tothis problem. If temperature estimation based on both echo-shift and CBE continue to show promise, the accuracy andreliability of temperature estimation with ultrasound may beenhanced by a technique that combines both approaches.

ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012 11

Echo-shift, attenuation and CBE methods depend on beingable to accurately calibrate, that is, find the thermal sensitivityto those parameters. The echo-shift method, in addition toprecise knowledge of the echo shift with tissue depth, requiresa knowledge of α, the linear coefficient of thermal expansionand β, a descriptor of the change in SOS with temperature.Similarly, calibration of the CBE method requires a knowledgeof how backscattered energy changes for a given type of tissue.The sensitivity to noise for these calibration data has yet tobe fully determined for either method. That sensitivity willdetermine the temperature accuracy that is possible for a givenspatial resolution for either method. A crucial step in identi-fying a viable ultrasonic approach to temperature estimationremains careful evaluation of its performance during in vivoapplication.

Volumetric temperature imaging is an important tool forguiding and assessing the effects of thermal therapy. AlthoughMRI provides volumetric temperature information, it is expen-sive, adds increased complexity and duration to treatments, andmay not be available in many hospitals. If ultrasound methods,which have been successful at imaging complex temperaturepatterns in vitro, can be shown to provide adequate thermaland spatial accuracy in vivo, they would provide importantadvantages over MRI temperature imaging. The significanceof such systems would be high and could be an importantelement in increasing the utilization of thermal therapies.

VI. SUMMARY AND CONCLUSIONS

Ultrasound is an attractive modality for volumetric tem-perature imaging to monitor thermal therapies because it isnon-ionizing, portable, convenient, inexpensive, and has rel-atively simple signal-processing requirements. This modalityhas proven useful for estimation of temperatures from thehyperthermia range (41-45oC) to border zones of regions ofhigh-temperature ablation (> 60oC).

The most prominent methods for exploiting ultrasound asa non-invasive thermometer rely on either 1) echo shifts dueto changes in tissue thermal expansion and speed of sound(SOS), 2) variation in the attenuation coefficient, or 3) changein backscattered energy from tissue inhomogeneities. Eachmethod has its strengths in terms of temperature range forwhich it yields a useful thermal signal and how well it canhandle tradeoffs between temperature accuracy and spatialresolution.

The use of echo shifts has received the most attention inthe last decade. By tracking scattering volumes and measuringthe time shift of received echoes, investigators have been ableto estimate temperature with encouraging preliminary in vivostudies. Acoustic attenuation is dependent on temperature, butwith significant changes occurring only at temperatures above50oC. This property may lead to further development of its usein high-temperature thermal ablation therapy. Minimal changein attenuation, however, below this temperature range reducesits attractiveness for use in clinical hyperthermia.

The change in backscattered energy is scatterer dependent.Taking advantage of scatterer-dependent behavior enhancesthe thermal signal. This behavior has been matched with

novel simulation methods for diverse scatterer populations andcan be enhanced with stochastic signal processing methods.Monotonic thermal dependence of the change in backscatteredenergy has been measured to 60oC. Temperature maps with 1-2oC accuracy and 0.5 cm2 spatial resolution can be producedroutinely during non-uniform heating in vitro.

All of the ultrasonic thermometry methods, just like temper-ature imaging from MRI, must be able to cope with motion ofthe image features on which temperature estimates are based.Echo shift methods track and exploit that motion. Motion mustbe compensated in attenuation and CBE thermometry. Motiontracking and compensation are usually the most computation-ally intensive components of ultrasonic temperature imagingand limit frame rates for temperature imaging.

Thermal therapies are poised for rapid development andadvancement due in part to a shift to volumetric temperatureimaging from sparse invasive thermometry, offering improvedmonitoring as well as feedback for improved therapy control.Noninvasive temperature imaging with ultrasound could better1) monitor and guide both hyperthermia treatment and high-temperature ablation and 2) deepen our understanding of tissuechanges during hyperthermia and in ablation border zonesnow performed blindly, with limited invasive thermometry, ormore expensive fixed-installation MRI thermometry that maylimit options for heating sources. A crucial step in identifyinga viable ultrasonic approach to temperature estimation is itsperformance during in vivo tests. The potential for significantclinical impact of ultrasonic thermometry is imminent withminimal addition if any to the existing hardware of ultrasonicimaging systems.

12 ARTHUR: TEMPERATURE IMAGING USING ULTRASOUND, AUGUST 8, 2012

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CONTENTS

I INTRODUCTION 1

II THERMAL EFFECTS ON BACKSCATTERED UL-TRASOUND 1

II-A Echo Shifts and Changes in Signal Strength . 1II-B Non-thermal and Unwanted Thermal Effects . 2

III IMAGE MOTION 2III-A Tracking Echo Shifts . . . . . . . . . . . . . . 3III-B Tracking and Compensating for Real and Ap-

parent Motion . . . . . . . . . . . . . . . . . 3III-B1 Rigid Motion . . . . . . . . . . . . 3III-B2 Non-Rigid Motion . . . . . . . . . 3

IV ULTRASONIC MEASUREMENT OF TEMPERA-TURE 4

IV-A Experimental Concerns . . . . . . . . . . . . . 4IV-A1 Temperature standards . . . . . . . 5IV-A2 Calibration of Tissue Properties

during Uniform Heating . . . . . . 5IV-A3 Temperature Imaging during Non-

Uniform Heating . . . . . . . . . . 5IV-B Attenuation . . . . . . . . . . . . . . . . . . . 5IV-C Thermal Strain using Echo Shift . . . . . . . . 6IV-D Change in Backscattered Energy . . . . . . . 7

IV-D1 Stochastic-Signal Framework . . . 8IV-D2 Effect of Signal-to-Noise Ratio,

Temperature Range, and Insonifica-tion Frequency . . . . . . . . . . . 8

IV-D3 3D Calibration and TemperatureEstimation during Uniform Heating 9

IV-D4 Temperature Imaging during Non-Uniform Heating . . . . . . . . . . 10

V DISCUSSION 10

VI SUMMARY AND CONCLUSIONS 11