Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2013 Article ID 682827 10 pageshttpdxdoiorg1011552013682827

Research ArticleAn Approach for the Visualization of TemperatureDistribution in Tissues According to Changes in UltrasonicBackscattered Energy

Jingjing Xia1 Qiang Li1 Hao-Li Liu2 Wen-Shiang Chen3 and Po-Hsiang Tsui45

1 School of Electronic Information Engineering Tianjin University Tianjin 300072 China2Department of Electrical Engineering Chang-Gung University Taoyuan 33302 Taiwan3Department of Physical Medicine and Rehabilitation National Taiwan University Hospital and College of MedicineTaipei 10002 Taiwan

4Department of Medical Imaging and Radiological Sciences College of Medicine Chang-Gung University Taoyuan 33302 Taiwan5Healthy Aging Research Center Chang-Gung University Taoyuan 33302 Taiwan

Correspondence should be addressed to Po-Hsiang Tsui tsuiphmailcguedutw

Received 15 May 2013 Accepted 10 September 2013

Academic Editor Huafeng Liu

Copyright copy 2013 Jingjing Xia et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Previous studies developed ultrasound temperature-imaging methods based on changes in backscattered energy (CBE) to monitorvariations in temperature during hyperthermia In conventional CBE imaging tracking and compensation of the echo shift due totemperature increase need to be done Moreover the CBE image does not enable visualization of the temperature distribution intissues during nonuniform heating which limits its clinical application in guidance of tissue ablation treatment In this study weinvestigated a CBE imaging method based on the sliding window technique and the polynomial approximation of the integratedCBE (ICBEpa image) to overcome the difficulties of conventional CBE imaging We conducted experiments with tissue samplesof pork tenderloin ablated by microwave irradiation to validate the feasibility of the proposed method During ablation the rawbackscattered signals were acquired using an ultrasound scanner for B-mode and ICBEpa imagingThe experimental results showedthat the proposed ICBEpa image can visualize the temperature distribution in a tissue with a very good contrast Moreover trackingand compensation of the echo shift were not necessary when using the ICBEpa image to visualize the temperature profile Theexperimental findings suggested that the ICBEpa image a new CBE imaging method has a great potential in CBE-based imagingof hyperthermia and other thermal therapies

1 Introduction

Previous studies have shown that hyperthermia complementschemotherapy and radiotherapy increasing the success ofcancer treatment [1ndash3] When using hyperthermia monitor-ing temperature is essential to ensure accurate and appro-priate thermal dosage The development of temperature-imaging techniques to measure the distribution of temper-ature has therefore been a long-term critical research goal

Magnetic resonance imaging (MRI) is currently the stan-dard imaging method used to monitor temperature changesin tissues [4 5] Previous studies have shown that MRI canprovide satisfactory spatial resolution with a temperature

accuracy of 1∘C However imaging temperature variationsin heated regions using MRI might be difficult in practicebecause of the requirements for significant capital investmentand the development of compatible heating therapies [6]Compared toMRI ultrasound imaging provides a convenientand powerful tool because of low cost use of nonionizingradiation simple signal processing and real-time capabil-ity Ultrasound imaging might therefore provide a moreappropriate option for the clinical monitoring of temperaturedistributions

The frequently used acoustic parameters for the monitor-ing of temperature include (1) echo shifts caused by changesin tissue thermal expansion and speed of sound [7 8]

2 Computational and Mathematical Methods in Medicine

(2) variations in acoustic attenuation [9] and (3) changes inthe backscattered energy (CBE) of ultrasound [10 11] Eachmethod has specific temperature sensitivities applicationsand limitations Previous studies identified that the CBEin comparison with echo shifts and attenuation is nearlymonotonic in the clinical hyperthermia temperature range[10ndash12] Considering the clinical value of imaging tools thatvisually display temperature profiles in tissues investigatorsfurther proposed the CBE image based on a parametricmapping of CBEs as an ultrasound temperature-imagingmethod for the monitoring of regions undergoing heating [613 14] The recent literature has confirmed the usefulness oftheCBE image for detecting variations in tissue temperatures

In practice use of the CBE image for temperature esti-mation may have some difficulties First the CBE image isa ratio map obtained from the envelope image divided bythe reference envelope image on a pixel-to-pixel basis [13]Because temperature change induces the displacement ofimage features [13] the tracking of pixels between imagesobtained at adjacent temperatures is necessary to obtain thecorrect CBE at each pixelMotion tracking and compensationare typically the most computationally intensive componentsof temperature imaging and hinder its real-time implementa-tion [7 8 15 16] On the other hand increasing temperaturemight also increase the degree of acoustic nonlinearity [17]In this condition local waveforms of the received radio-frequency (RF) signals can differ resulting in greater errorwhen performing pixel-by-pixel division between two imagesfollowing motion tracking and compensation [18] In addi-tion the CBE image cannot clearly illustrate the contoursof temperature distribution in a tissue during nonuniformheating by high-intensity focused ultrasound (HIFU) ormicrowave ablation This is because the CBE image behavesin the same manner as a speckle image reducing sensitivityand contrast for illustration of the temperature profile

Clinical application of CBE imaging during hyperthermiaand other thermal therapies might therefore require adifferent imaging method for guidance of the tissue ablationprocess based on the CBE concept This study investigateda new CBE imaging method based on the mathematicpolynomial approximation of the integrated CBE (ICBEpa)estimated using the sliding window technique which haveresolved the limitations of the conventional CBE image

In the next section we introduce the theoretical back-ground of the CBE image and present the concept and detailsof the new CBE imaging method Then we describe theexperimental procedures used to validate the feasibility of theproposed method The results are presented for discussionThe impact and contributions of this study are summarizedin conclusion

2 Methods

21 Conventional CBE Imaging Method Previous studieshave extensively investigated the temperature dependence ofthe CBE and the CBE imaging algorithm [6 10ndash14] Accord-ing to the above literatures we briefly review the principle ofthe CBE Changes in backscattered energy with temperature

are primarily caused by thermal effects on the backscattercoefficientThe temperature dependence of the backscatteredenergy can be simplified by normalizing it to the baselinevalue obtained at a reference temperature (typically 37∘C)removing the influence of factors with little or no temperaturedependence The CBE as a function of temperature for asingle scatterer can then be approximated as the ratio of thetemperature-dependent backscatter coefficients (120578 values) attemperature 119879 and reference temperature 119879

119877

120578 (119879)

120578 (119879119877)

= ((120588119898

119888(119879)2

119898

minus 120588119904119888(119879)2

119904

120588119904119888(119879)2

119904

)

2

+1

3(

3120588119904

minus 3120588119898

2120588119904

+ 120588119898

)

2

)

times ((120588119898

119888(119879119877)2

119898

minus 120588119904119888(119879119877)2

119904

120588119904119888(119879119877)2

119904

)

2

+1

3(

3120588119904

minus 3120588119898

2120588119904

+ 120588119898

)

2

)

minus1

(1)

where 120588 is the mass density 119888(119879) is the temperature-dependent sound speed and the 119898 and 119904 subscripts referto the medium and scatterer respectively From the modeldescribed in (1) it can be predicted that the backscatteredenergy contributed by lipid-based scatterers would increasewith increasing temperature whereas that corresponding toaqueous scatterers would decrease [10ndash12]

The algorithmic procedure used to form the CBE tem-perature image has been described previously [13 14] Inbrief the speckle motions (echo shift) caused by changes insound speed and tissue thermal expansion were tracked andcompensated by maximizing the cross-correlation betweenimages obtained at adjacent temperatures Optimization andimage resampling were performed to eliminate the depen-dence of the image on the spatial sampling period Envelopedata of the compensated images at each temperature wereobtained using Hilbert transform Envelope values weresquared to determine the backscattered energy The CBEimage was then obtained by calculating the ratio of thebackscattered energy at each temperature relative to thereference at each pixel

22 Proposed CBE Imaging Method The proposed algorithmfor CBE imaging first used a square window within theenvelope image at temperature 119879 to collect the regionalbackscattered envelopes ℎ(119879) If 119864[sdot] denotes the statisti-cal mean then the regional CBE value (in decibels dB)calculated using the data acquired by the window (CBE

119908)

compared to the reference temperature 119879119877 can be calculated

using

CBE119908

= 10 sdot log10

(119864 [ℎ(119879)

2

]

119864 [ℎ(119879119877)2

]) (2)

The regional CBE119908was assigned as the new pixel located in

the center of the windowThe described process was repeatedwith the window moving throughout the entire envelopeimage in steps of a certain number of pixels determined bythe window overlap ratio (WOR) yielding the CBE

119908image

as the map of regional CBE119908values

Computational and Mathematical Methods in Medicine 3

The absolute value map of the CBE119908image was then

used as the integrated CBE (ICBE) image The ICBE mapneeds further processing for visualization of temperaturedistributions and heat transfer in ablated tissue duringnonuniform heating Previous studies have extensively usedthe mathematic polynomial approximation to fit experi-mental data and predict temperature distribution and heatconduction behavior [19ndash21] This study applied the polyno-mial approximation during ICBE image processing Supposethat the original ICBE image prior to smoothing is 119883

119894119895

where 119894 and 119895 are indices of the image depth and widthrespectively We assumed that the function in each directionwas a polynomial of order 119901 Because 119901 is much smaller thanthe number of pixels in the axial and lateral directions the119883

119894119895

data were used to determine the optimal polynomial usingthe least-squares method 119883

119894119895was replaced with the value

calculated by the optimal polynomial This approximationwas performed along each line in the axial and lateral direc-tion with 119891

119901(sdot 119881) being the optimal polynomial of order 119901

reconstructed from the vector 119881 = (1198811 1198812 119881

119899) located at

indices 1 2 119899 After applying polynomial approximationsin the lateral and axial directions image 119883

119894119895was constructed

using the following two procedures

119883lowast

119894119895

= 119891119901

(119894 1198831119899119889 119895

) for each 119895

119883119894119895

= 119891119901

(119895 119883lowast

1198941119899119908

) for each 119894

(3)

where 119899119889and 119899

119908are the numbers of pixels in the axial

(depth) and lateral (width) directions respectively 1198831119899119889 119895

isthe vector119883

1119895 1198832119895

119883119899119889 119895

119883lowast119894119895

is the intermediate imageand 119883

119894119895is the ICBEpa image

3 Experimental Verification

31 Ablation Experiments The feasibility of the proposedmethod to monitor the distribution of temperature duringnonuniform heating was evaluated by conducting tissueablation experiments on excised tissues The tissue samplewas prepared from pork tenderloin extracted from the psoasmajor muscle along the central spine Tissue ablation wasconducted using a microwave delivery system (UMC-1Chinese PLAGeneralHospital Institute 207 of theAerospaceIndustry Company Beijing China) that operates at a fre-quency of 245GHz andhas electrical power ranging from 1 to99WThe tenderloin sample was preheated by a temperature-regulated water tank to an initial reference temperatureof 37∘C The microwave antenna was then inserted intothe sample for irradiation Ablation treatment performedat 2W for 420 s produced significant and stable increasesin temperature A commercial ultrasound scanner (Model2000 Terason Burlington MA USA) that can output rawRF signals digitized at a sampling rate of 30MHz was usedto image the tissue during heating A wideband linear arrayprobe (Model 10L5 Terason) with a central frequency ofapproximately 7MHzwas used A pulse echo test of the trans-ducer showed that the pulse length was 07mm The imageraw data were acquired every 20 s Each image consisted of

128 scan lines of backscattered signals and Hilbert transformwas applied to each scan line to obtain the correspondingenvelope image The temperature as a function of ablationtimewasmeasured using a thermocouple that was attached tothe microwave antenna Measurements of five tissue sampleswere performedThe experimental setup is shown in Figure 1

32 Data Analysis The envelope signals obtained from tissuesamples were used for B-mode and CBE imaging The B-mode image formation was based on the log-compressedenvelopes with a dynamic range of 60 dB A sliding squarewindow with side lengths corresponding to one pulse length(07mm) was selected to construct the CBE

119908 ICBE and

ICBEpa images To evaluate the performances of the newCBEimage in temperature estimation the image data were used tocalculate the pixel magnitude as a function of heating timeMoreover the contrast-to-noise ratio (CNR) was calculatedas an estimate of the contrast resolution defined as

CNR =

1003816100381610038161003816100381610038161003816100381610038161003816

120583ablation region minus 120583background

120590ablation region + 120590background

1003816100381610038161003816100381610038161003816100381610038161003816

(4)

where 120583 and 120590 are the mean and standard deviation of thepixel values in the images respectivelyThe above quantitativedata analyses were based on data acquired from the regionsof interest (ROI) located in the background and the ablationzone The sizes of the ROI were 5mm times 5mm

4 Results

Figure 2 shows the temperature as a function of ablationtime and the typical image for the cross-section of porktenderloin after microwave ablation The temperature in theablation region surrounding the antenna increased fromapproximately 37∘C to 46∘C during heating In the endof ablation a tissue denaturation region with a roughlycircular shape with a diameter of about 1 cm was formedin the tissue background Figure 3 shows typical B-scans ofpork tenderloin obtained during microwave ablation and thecorresponding CBE

119908images (a WOR of 80 was used) The

brightness of the red-blue interlaced shading in the CBE119908

image gradually increased with increasing temperature Fig-ure 4 shows the results of the ICBE image and the averageICBE as a function of heating time The brightness of theICBE image increased during heating corresponding to theaverage ICBE value increase from 0 dB to 4 dB

Figure 5(a) shows the results of the ICBEpa images (usingorder 7) We observed that the brightness of the ICBEpaimage gradually increased during heating for 420 s with theaverage ICBEpa value increasing from 0 dB to approximately2 dB as shown in Figure 5(b) This demonstrated that theICBEpa image can visualize the temperature distribution inthe tissue To evaluate the enhancement of the contrast afterapplying polynomial approximation the curves of the CNRwere plotted as a function of heating time in Figure 6 Thedynamic range of the CNR during the heating for the ICBEimage was approximately 16 In contrast the dynamic rangeof the CNR for the ICBEpa image was 134The ICBEpa image

4 Computational and Mathematical Methods in Medicine

Microwave system

Pork tenderloin

Transducer

Ablation antenna

Stage

Thermocouple

systemTerason 2000

(a)

Antenna

Thermocouple

Microwave system

Ultrasound system and transducer

(b)

Figure 1 (a) Schematic diagram of the experimental setup (b) A real representation of the experimental setup

Time (s)0 100 200 300 400

34

36

38

40

42

44

46

48

50

Tem

pera

ture

(∘C)

(a) (b)

Figure 2 Temperature measurement during microwave ablation and the typical image of tissue section after ablation

thus allows the temperature profile to be visualized withexcellent image contrast

Figure 7 shows examples of the CBE119908 ICBE and ICBEpa

images postheating for 400 s using WORs of 20 50 and80 respectively We observed that a lower WOR degradedthe resolutions of the CBE

119908and ICBE images because of the

use of fewer pixels to form the image However the featuresand patterns of the ICBEpa image did not exhibit significantchanges with the ICBEpa image still well-describing thecontour of the temperature distribution Figure 8 displays

ICBEpa images of pork tenderloin obtained postheating for400 s using polynomial approximations of different ordersCompared with the cross-sections of pork tenderloin shownin Figure 2 the ICBEpa image might overestimate the tem-perature distribution when using lower order polynomialapproximations The ICBEpa image might reflect the actualtemperature distribution when using polynomial approxi-mations of orders of 6 to 7 whereas using higher orderpolynomial approximations might underestimate the rangeof the temperature distribution

Computational and Mathematical Methods in Medicine 5

5 10 15 20

5

10

15

20

(mm)

(mm

)20 s

(a)

5 10 15 20

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10

15

20

(mm)(m

m)

80 s

(b)

5 10 15 20

5

10

15

20

(mm)

(mm

)

180 s

(c)

5 10 15 20

5

10

15

20

605040302010

(mm)

(mm

)

320 s

(d)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(e)

5 10 15 20

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10

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20

(mm)

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)

(f)

5 10 15 20

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10

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20

(mm)

(mm

)

(g)

5 10 15 20

5

10

15

20

86420minus2minus4minus6minus8

(mm)

(mm

)

(h)

Figure 3 ((a)ndash(d)) Typical B-mode images of pork tenderloin obtained at different heating times and the corresponding ((e)ndash(h)) CBE119908

images

5 10 15 20

5

10

15

20

(mm)

(mm

)

20 s

(a)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

80 s

(b)

5 10 15 20(mm)

5

10

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(mm

)180 s

(c)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

320 s

(d)

Time (s)0 100 200 300 400

ICBE

(dB)

0

1

2

3

4

5

6

n = 5

(e)

Figure 4 ((a)ndash(d)) Typical ICBE images obtained at different heating times (e) ICBE values as a function of heating time

6 Computational and Mathematical Methods in Medicine

2

15

1

05

2

15

1

05

2

15

1

05

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15

1

05

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20

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(mm

)

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20(m

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)

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)

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(mm

)

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)

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5 10 15 20

(mm)

20 s 40 s 60 s 80 s 100 s

120 s 140 s 160 s 180 s 200 s

220 s 240 s 260 s 280 s 300 s

320 s 340 s 360 s 380 s 400 s

(a)

0 100 200 300 400

00

05

10

15

20

25

Time (s)

ICBE

pa(d

B)

n = 5

(b)

Figure 5 (a) Examples of ICBEpa images of pork tenderloin obtained at different heating times (b) ICBEpa values obtained in the tissueablation experiments as a function of heating time

Computational and Mathematical Methods in Medicine 7

Time (s)0 100 200 300 400

CNR

0

510

15

20

ICBE imageICBEpa image

n = 5

Figure 6 Contrast-to-noise ratios as functions of heating times forICBE and ICBEpa images

5 Discussion

51 The Significance of This Study Implementing real-timetemperature imaging based on the CBE concept in dif-ferent clinical applications requires the development of anew CBE imaging method to overcome the limitations ofconventional CBE imaging In our opinion CBE imagingfor clinical purposes should have two essential features (i)reduced dependency of the image performance on echo shifttracking and compensation with no requirement for echoshift compensation being the objective and (ii) the abilityto visualize the contour of temperature distribution duringnonuniform heating enabling its application in guidance oftissue ablation The current results have demonstrated thatthe proposed CBE imaging method fulfills the above tworequirements

52 Window Size for Constructing the Proposed CBE ImagingIn our proposedCBE imagingmethod the algorithm replacesthe pixel-to-pixel calculation with a ldquoregion-to-regionrdquo calcu-lationThe reason is that using datawithin awindowed regionreflected average trend of backscattered energy which mayreduce the influence of echo shifts and waveform distortiondue to heating tissues Under this assumption how to selectan appropriatewindow size for regional CBE computation is akey determination to implement visualization of temperaturedistributions in the absence of echo shift tracking and com-pensation According to the analysis by Seip and Ebbini [22]the movement of a scatterer caused by thermal expansionwhen the temperature increases from 37∘C to 50∘C is typicallyless than 2 120583m Over this temperature range the maximumspeckle motion caused by changes in the sound speed fordifferent types of tissues is approximately 05mm in the axialand lateral directions [13] In this study the side length ofthe square window used for regional CBE computation wasdetermined by the pulse length of the used transducer which

is larger than the maximum echo shift between 37∘C and50∘C revealed in the previous study In this circumstance theresolution of the CBE image constructed using the slidingwindow technique is actually not enough to describe thebehavior of echo shift This may be the reason why our CBEimaging methodology can work without echo shift trackingand compensation

53 Polynomial Approximation of the CBE Image The ideafor the proposed algorithmic procedure is similar to theconcept of ultrasound Doppler imaging We can betterunderstand the spirit of the new CBE imaging method fromthe comparison with Doppler ultrasound The Doppler shiftsignals in color Doppler ultrasound imaging are presented incolor and superimposed on grayscale images to reflect bloodflow information associated with velocity and directionLimitations of the color Doppler ultrasound image includeangle dependence aliasing and insensitivity to slow flows[23] These limitations are less significant in power Dopplerimages that include positive and negative components of theDoppler shift signals [23 24]

As discussed the ultrasound CBE increases with increas-ing temperature for lipid-based scatterers and decreases withincreasing temperature for aqueous scatterers Similar tothe shadings of color Doppler ultrasound correspondingto different flow directions the conventional CBE imagetypically also has two shadings one for lipid-based scatter-ers (increasing CBE) and the other for aqueous scatterers(decreasing CBE) However these two shading types can beambiguous if CBE imaging is performed without echo shifttracking and compensationThis shading ambiguity could betreated as the aliasing effect of theCBE image which is similarto the aliasing effect caused by an insufficient pulse repetitionrate in color Doppler ultrasound Like the concept of powerDoppler ultrasound the ICBE image is formed by integratingthe positive and negative CBE values as the strengths In thiscondition the ICBE image cannot reflect the properties ofscatterers in a tissue (lipid-based or aqueous) Neverthelessit may be treated as an aliasing-independent CBE image toprovide a better sensitivity and contrast for the depiction oftemperature distribution in a nonuniform heating region

However we found that the speckle-like features inthe ICBE image still hinder improving the performance oftemperature profile visualization The ICBE image has theability to describe the temperature distribution in ablatedtissues but it did not have a relatively high CNR In thecontrary the speckle-free ICBEpa image had a larger CNRdemonstrating that the polynomial approximation providesthe ICBE image with the ability to highlight the region andlocation of ablation by reflecting temperature informationwith very good contrast

54 Considerations on Performing Polynomial Approximationof the CBE Image Some aspects of the algorithmic parame-ters for construction of the ICBEpa image require further dis-cussion to point out some considerations in practice At firstour results demonstrated that the WOR did not significantlyaffect the ICBEpa image This suggested that constructing

8 Computational and Mathematical Methods in Medicine

5

10

15

20

5 10 15 20(mm)

(mm

)WOR = 20

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

WOR = 50

(b)

5

10

15

20

5 10 15 20(mm)

(mm

)

86420minus2minus4minus6minus8

WOR = 80

(c)

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10

15

20

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(mm

)

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

(e)

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10

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20

5 10 15 20(mm)

(mm

)

87654321

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)(g)

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10

15

20

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(mm

)

(h)

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(i)

Figure 7 Examples of ((a)ndash(c)) CBE119908

((d)ndash(f)) ICBE and ((g)ndash(i)) ICBEpa images of pork tenderloin postheating for 400 s constructedusing WORs of 20 50 and 80 respectively

the ICBEpa temperature image using a lower WOR is feasibleto reduce the computational load Second the order selectionof conducting polynomial approximation would affect theaccuracy of estimations of the effective range and size of thetemperature profile for the transfer of heat in ablated tissue[25] This difficulty can be confirmed by our experimentalresults indicating that using an inappropriate order for thepolynomial approximation can result in overestimation orunderestimation of the temperature profile Some previousstudies have also shown that using a polynomial might not berobust to outliers which can cause fitting errors in ultrasounddata [26 27] Future studies should aim to explore the optimalpolynomial approximation for producing clinical ICBEpaimages

55 Limitations and Future Work For temperature eleva-tions higher than 45∘C the major limitation of ultrasoundtemperature estimation comes from the irreversible changesin the acoustic properties of tissue caused by necrosis Thismay explain why the image parameter and the temperature

do not have a linear relationship On the other hand theproposed CBE image is dedicated to the visualization of thetemperature distribution in a tissue Absolute temperaturevalues are unavailable from the reading of the proposedCBE image However this limitation may be overcome byestablishing a calibration table for further applications oftemperature measurements

It is worth noting that the construction of the proposedCBE imaging method just needs raw RF signals acquiredfrom a standard pulse-echo ultrasound system and doesnot require echo shift compensation This implies that thealgorithm of the proposed CBE imaging method can becombined with most commercial ultrasound systems mak-ing it possible to implement real-time temperature imagingHowever the frame rate of real-time temperature imaging isdifficult to estimate in the current stage because the com-putational efficiency may depend on system specificationsand programming skills In future developments we wouldsuggest using hardware and parallel processing techniques asthe algorithmic kernel to make the frame rate of temperatureimaging close to that of ultrasound B-scan

Computational and Mathematical Methods in Medicine 9

5

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20

5 10 15 20(mm)

(mm

)Order = 3

(a)

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(mm

)

Order = 4

(b)

Order = 5

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(mm

)

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1

05

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(mm

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(mm

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(e)

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(mm

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15

1

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(f)

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(mm

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(g)

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(mm

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(h)

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(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

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Disease Markers

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PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Research and TreatmentAIDS

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Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

2 Computational and Mathematical Methods in Medicine

(2) variations in acoustic attenuation [9] and (3) changes inthe backscattered energy (CBE) of ultrasound [10 11] Eachmethod has specific temperature sensitivities applicationsand limitations Previous studies identified that the CBEin comparison with echo shifts and attenuation is nearlymonotonic in the clinical hyperthermia temperature range[10ndash12] Considering the clinical value of imaging tools thatvisually display temperature profiles in tissues investigatorsfurther proposed the CBE image based on a parametricmapping of CBEs as an ultrasound temperature-imagingmethod for the monitoring of regions undergoing heating [613 14] The recent literature has confirmed the usefulness oftheCBE image for detecting variations in tissue temperatures

In practice use of the CBE image for temperature esti-mation may have some difficulties First the CBE image isa ratio map obtained from the envelope image divided bythe reference envelope image on a pixel-to-pixel basis [13]Because temperature change induces the displacement ofimage features [13] the tracking of pixels between imagesobtained at adjacent temperatures is necessary to obtain thecorrect CBE at each pixelMotion tracking and compensationare typically the most computationally intensive componentsof temperature imaging and hinder its real-time implementa-tion [7 8 15 16] On the other hand increasing temperaturemight also increase the degree of acoustic nonlinearity [17]In this condition local waveforms of the received radio-frequency (RF) signals can differ resulting in greater errorwhen performing pixel-by-pixel division between two imagesfollowing motion tracking and compensation [18] In addi-tion the CBE image cannot clearly illustrate the contoursof temperature distribution in a tissue during nonuniformheating by high-intensity focused ultrasound (HIFU) ormicrowave ablation This is because the CBE image behavesin the same manner as a speckle image reducing sensitivityand contrast for illustration of the temperature profile

Clinical application of CBE imaging during hyperthermiaand other thermal therapies might therefore require adifferent imaging method for guidance of the tissue ablationprocess based on the CBE concept This study investigateda new CBE imaging method based on the mathematicpolynomial approximation of the integrated CBE (ICBEpa)estimated using the sliding window technique which haveresolved the limitations of the conventional CBE image

In the next section we introduce the theoretical back-ground of the CBE image and present the concept and detailsof the new CBE imaging method Then we describe theexperimental procedures used to validate the feasibility of theproposed method The results are presented for discussionThe impact and contributions of this study are summarizedin conclusion

2 Methods

21 Conventional CBE Imaging Method Previous studieshave extensively investigated the temperature dependence ofthe CBE and the CBE imaging algorithm [6 10ndash14] Accord-ing to the above literatures we briefly review the principle ofthe CBE Changes in backscattered energy with temperature

are primarily caused by thermal effects on the backscattercoefficientThe temperature dependence of the backscatteredenergy can be simplified by normalizing it to the baselinevalue obtained at a reference temperature (typically 37∘C)removing the influence of factors with little or no temperaturedependence The CBE as a function of temperature for asingle scatterer can then be approximated as the ratio of thetemperature-dependent backscatter coefficients (120578 values) attemperature 119879 and reference temperature 119879

119877

120578 (119879)

120578 (119879119877)

= ((120588119898

119888(119879)2

119898

minus 120588119904119888(119879)2

119904

120588119904119888(119879)2

119904

)

2

+1

3(

3120588119904

minus 3120588119898

2120588119904

+ 120588119898

)

2

)

times ((120588119898

119888(119879119877)2

119898

minus 120588119904119888(119879119877)2

119904

120588119904119888(119879119877)2

119904

)

2

+1

3(

3120588119904

minus 3120588119898

2120588119904

+ 120588119898

)

2

)

minus1

(1)

where 120588 is the mass density 119888(119879) is the temperature-dependent sound speed and the 119898 and 119904 subscripts referto the medium and scatterer respectively From the modeldescribed in (1) it can be predicted that the backscatteredenergy contributed by lipid-based scatterers would increasewith increasing temperature whereas that corresponding toaqueous scatterers would decrease [10ndash12]

The algorithmic procedure used to form the CBE tem-perature image has been described previously [13 14] Inbrief the speckle motions (echo shift) caused by changes insound speed and tissue thermal expansion were tracked andcompensated by maximizing the cross-correlation betweenimages obtained at adjacent temperatures Optimization andimage resampling were performed to eliminate the depen-dence of the image on the spatial sampling period Envelopedata of the compensated images at each temperature wereobtained using Hilbert transform Envelope values weresquared to determine the backscattered energy The CBEimage was then obtained by calculating the ratio of thebackscattered energy at each temperature relative to thereference at each pixel

22 Proposed CBE Imaging Method The proposed algorithmfor CBE imaging first used a square window within theenvelope image at temperature 119879 to collect the regionalbackscattered envelopes ℎ(119879) If 119864[sdot] denotes the statisti-cal mean then the regional CBE value (in decibels dB)calculated using the data acquired by the window (CBE

119908)

compared to the reference temperature 119879119877 can be calculated

using

CBE119908

= 10 sdot log10

(119864 [ℎ(119879)

2

]

119864 [ℎ(119879119877)2

]) (2)

The regional CBE119908was assigned as the new pixel located in

the center of the windowThe described process was repeatedwith the window moving throughout the entire envelopeimage in steps of a certain number of pixels determined bythe window overlap ratio (WOR) yielding the CBE

119908image

as the map of regional CBE119908values

Computational and Mathematical Methods in Medicine 3

The absolute value map of the CBE119908image was then

used as the integrated CBE (ICBE) image The ICBE mapneeds further processing for visualization of temperaturedistributions and heat transfer in ablated tissue duringnonuniform heating Previous studies have extensively usedthe mathematic polynomial approximation to fit experi-mental data and predict temperature distribution and heatconduction behavior [19ndash21] This study applied the polyno-mial approximation during ICBE image processing Supposethat the original ICBE image prior to smoothing is 119883

119894119895

where 119894 and 119895 are indices of the image depth and widthrespectively We assumed that the function in each directionwas a polynomial of order 119901 Because 119901 is much smaller thanthe number of pixels in the axial and lateral directions the119883

119894119895

data were used to determine the optimal polynomial usingthe least-squares method 119883

119894119895was replaced with the value

calculated by the optimal polynomial This approximationwas performed along each line in the axial and lateral direc-tion with 119891

119901(sdot 119881) being the optimal polynomial of order 119901

reconstructed from the vector 119881 = (1198811 1198812 119881

119899) located at

indices 1 2 119899 After applying polynomial approximationsin the lateral and axial directions image 119883

119894119895was constructed

using the following two procedures

119883lowast

119894119895

= 119891119901

(119894 1198831119899119889 119895

) for each 119895

119883119894119895

= 119891119901

(119895 119883lowast

1198941119899119908

) for each 119894

(3)

where 119899119889and 119899

119908are the numbers of pixels in the axial

(depth) and lateral (width) directions respectively 1198831119899119889 119895

isthe vector119883

1119895 1198832119895

119883119899119889 119895

119883lowast119894119895

is the intermediate imageand 119883

119894119895is the ICBEpa image

3 Experimental Verification

31 Ablation Experiments The feasibility of the proposedmethod to monitor the distribution of temperature duringnonuniform heating was evaluated by conducting tissueablation experiments on excised tissues The tissue samplewas prepared from pork tenderloin extracted from the psoasmajor muscle along the central spine Tissue ablation wasconducted using a microwave delivery system (UMC-1Chinese PLAGeneralHospital Institute 207 of theAerospaceIndustry Company Beijing China) that operates at a fre-quency of 245GHz andhas electrical power ranging from 1 to99WThe tenderloin sample was preheated by a temperature-regulated water tank to an initial reference temperatureof 37∘C The microwave antenna was then inserted intothe sample for irradiation Ablation treatment performedat 2W for 420 s produced significant and stable increasesin temperature A commercial ultrasound scanner (Model2000 Terason Burlington MA USA) that can output rawRF signals digitized at a sampling rate of 30MHz was usedto image the tissue during heating A wideband linear arrayprobe (Model 10L5 Terason) with a central frequency ofapproximately 7MHzwas used A pulse echo test of the trans-ducer showed that the pulse length was 07mm The imageraw data were acquired every 20 s Each image consisted of

128 scan lines of backscattered signals and Hilbert transformwas applied to each scan line to obtain the correspondingenvelope image The temperature as a function of ablationtimewasmeasured using a thermocouple that was attached tothe microwave antenna Measurements of five tissue sampleswere performedThe experimental setup is shown in Figure 1

32 Data Analysis The envelope signals obtained from tissuesamples were used for B-mode and CBE imaging The B-mode image formation was based on the log-compressedenvelopes with a dynamic range of 60 dB A sliding squarewindow with side lengths corresponding to one pulse length(07mm) was selected to construct the CBE

119908 ICBE and

ICBEpa images To evaluate the performances of the newCBEimage in temperature estimation the image data were used tocalculate the pixel magnitude as a function of heating timeMoreover the contrast-to-noise ratio (CNR) was calculatedas an estimate of the contrast resolution defined as

CNR =

1003816100381610038161003816100381610038161003816100381610038161003816

120583ablation region minus 120583background

120590ablation region + 120590background

1003816100381610038161003816100381610038161003816100381610038161003816

(4)

where 120583 and 120590 are the mean and standard deviation of thepixel values in the images respectivelyThe above quantitativedata analyses were based on data acquired from the regionsof interest (ROI) located in the background and the ablationzone The sizes of the ROI were 5mm times 5mm

4 Results

Figure 2 shows the temperature as a function of ablationtime and the typical image for the cross-section of porktenderloin after microwave ablation The temperature in theablation region surrounding the antenna increased fromapproximately 37∘C to 46∘C during heating In the endof ablation a tissue denaturation region with a roughlycircular shape with a diameter of about 1 cm was formedin the tissue background Figure 3 shows typical B-scans ofpork tenderloin obtained during microwave ablation and thecorresponding CBE

119908images (a WOR of 80 was used) The

brightness of the red-blue interlaced shading in the CBE119908

image gradually increased with increasing temperature Fig-ure 4 shows the results of the ICBE image and the averageICBE as a function of heating time The brightness of theICBE image increased during heating corresponding to theaverage ICBE value increase from 0 dB to 4 dB

Figure 5(a) shows the results of the ICBEpa images (usingorder 7) We observed that the brightness of the ICBEpaimage gradually increased during heating for 420 s with theaverage ICBEpa value increasing from 0 dB to approximately2 dB as shown in Figure 5(b) This demonstrated that theICBEpa image can visualize the temperature distribution inthe tissue To evaluate the enhancement of the contrast afterapplying polynomial approximation the curves of the CNRwere plotted as a function of heating time in Figure 6 Thedynamic range of the CNR during the heating for the ICBEimage was approximately 16 In contrast the dynamic rangeof the CNR for the ICBEpa image was 134The ICBEpa image

4 Computational and Mathematical Methods in Medicine

Microwave system

Pork tenderloin

Transducer

Ablation antenna

Stage

Thermocouple

systemTerason 2000

(a)

Antenna

Thermocouple

Microwave system

Ultrasound system and transducer

(b)

Figure 1 (a) Schematic diagram of the experimental setup (b) A real representation of the experimental setup

Time (s)0 100 200 300 400

34

36

38

40

42

44

46

48

50

Tem

pera

ture

(∘C)

(a) (b)

Figure 2 Temperature measurement during microwave ablation and the typical image of tissue section after ablation

thus allows the temperature profile to be visualized withexcellent image contrast

Figure 7 shows examples of the CBE119908 ICBE and ICBEpa

images postheating for 400 s using WORs of 20 50 and80 respectively We observed that a lower WOR degradedthe resolutions of the CBE

119908and ICBE images because of the

use of fewer pixels to form the image However the featuresand patterns of the ICBEpa image did not exhibit significantchanges with the ICBEpa image still well-describing thecontour of the temperature distribution Figure 8 displays

ICBEpa images of pork tenderloin obtained postheating for400 s using polynomial approximations of different ordersCompared with the cross-sections of pork tenderloin shownin Figure 2 the ICBEpa image might overestimate the tem-perature distribution when using lower order polynomialapproximations The ICBEpa image might reflect the actualtemperature distribution when using polynomial approxi-mations of orders of 6 to 7 whereas using higher orderpolynomial approximations might underestimate the rangeof the temperature distribution

Computational and Mathematical Methods in Medicine 5

5 10 15 20

5

10

15

20

(mm)

(mm

)20 s

(a)

5 10 15 20

5

10

15

20

(mm)(m

m)

80 s

(b)

5 10 15 20

5

10

15

20

(mm)

(mm

)

180 s

(c)

5 10 15 20

5

10

15

20

605040302010

(mm)

(mm

)

320 s

(d)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(e)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(f)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(g)

5 10 15 20

5

10

15

20

86420minus2minus4minus6minus8

(mm)

(mm

)

(h)

Figure 3 ((a)ndash(d)) Typical B-mode images of pork tenderloin obtained at different heating times and the corresponding ((e)ndash(h)) CBE119908

images

5 10 15 20

5

10

15

20

(mm)

(mm

)

20 s

(a)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

80 s

(b)

5 10 15 20(mm)

5

10

15

20

(mm

)180 s

(c)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

320 s

(d)

Time (s)0 100 200 300 400

ICBE

(dB)

0

1

2

3

4

5

6

n = 5

(e)

Figure 4 ((a)ndash(d)) Typical ICBE images obtained at different heating times (e) ICBE values as a function of heating time

6 Computational and Mathematical Methods in Medicine

2

15

1

05

2

15

1

05

2

15

1

05

2

15

1

05

5

10

15

20

5 10 15 20

(mm

)

5

10

15

20(m

m)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

20 s 40 s 60 s 80 s 100 s

120 s 140 s 160 s 180 s 200 s

220 s 240 s 260 s 280 s 300 s

320 s 340 s 360 s 380 s 400 s

(a)

0 100 200 300 400

00

05

10

15

20

25

Time (s)

ICBE

pa(d

B)

n = 5

(b)

Figure 5 (a) Examples of ICBEpa images of pork tenderloin obtained at different heating times (b) ICBEpa values obtained in the tissueablation experiments as a function of heating time

Computational and Mathematical Methods in Medicine 7

Time (s)0 100 200 300 400

CNR

0

510

15

20

ICBE imageICBEpa image

n = 5

Figure 6 Contrast-to-noise ratios as functions of heating times forICBE and ICBEpa images

5 Discussion

51 The Significance of This Study Implementing real-timetemperature imaging based on the CBE concept in dif-ferent clinical applications requires the development of anew CBE imaging method to overcome the limitations ofconventional CBE imaging In our opinion CBE imagingfor clinical purposes should have two essential features (i)reduced dependency of the image performance on echo shifttracking and compensation with no requirement for echoshift compensation being the objective and (ii) the abilityto visualize the contour of temperature distribution duringnonuniform heating enabling its application in guidance oftissue ablation The current results have demonstrated thatthe proposed CBE imaging method fulfills the above tworequirements

52 Window Size for Constructing the Proposed CBE ImagingIn our proposedCBE imagingmethod the algorithm replacesthe pixel-to-pixel calculation with a ldquoregion-to-regionrdquo calcu-lationThe reason is that using datawithin awindowed regionreflected average trend of backscattered energy which mayreduce the influence of echo shifts and waveform distortiondue to heating tissues Under this assumption how to selectan appropriatewindow size for regional CBE computation is akey determination to implement visualization of temperaturedistributions in the absence of echo shift tracking and com-pensation According to the analysis by Seip and Ebbini [22]the movement of a scatterer caused by thermal expansionwhen the temperature increases from 37∘C to 50∘C is typicallyless than 2 120583m Over this temperature range the maximumspeckle motion caused by changes in the sound speed fordifferent types of tissues is approximately 05mm in the axialand lateral directions [13] In this study the side length ofthe square window used for regional CBE computation wasdetermined by the pulse length of the used transducer which

is larger than the maximum echo shift between 37∘C and50∘C revealed in the previous study In this circumstance theresolution of the CBE image constructed using the slidingwindow technique is actually not enough to describe thebehavior of echo shift This may be the reason why our CBEimaging methodology can work without echo shift trackingand compensation

53 Polynomial Approximation of the CBE Image The ideafor the proposed algorithmic procedure is similar to theconcept of ultrasound Doppler imaging We can betterunderstand the spirit of the new CBE imaging method fromthe comparison with Doppler ultrasound The Doppler shiftsignals in color Doppler ultrasound imaging are presented incolor and superimposed on grayscale images to reflect bloodflow information associated with velocity and directionLimitations of the color Doppler ultrasound image includeangle dependence aliasing and insensitivity to slow flows[23] These limitations are less significant in power Dopplerimages that include positive and negative components of theDoppler shift signals [23 24]

As discussed the ultrasound CBE increases with increas-ing temperature for lipid-based scatterers and decreases withincreasing temperature for aqueous scatterers Similar tothe shadings of color Doppler ultrasound correspondingto different flow directions the conventional CBE imagetypically also has two shadings one for lipid-based scatter-ers (increasing CBE) and the other for aqueous scatterers(decreasing CBE) However these two shading types can beambiguous if CBE imaging is performed without echo shifttracking and compensationThis shading ambiguity could betreated as the aliasing effect of theCBE image which is similarto the aliasing effect caused by an insufficient pulse repetitionrate in color Doppler ultrasound Like the concept of powerDoppler ultrasound the ICBE image is formed by integratingthe positive and negative CBE values as the strengths In thiscondition the ICBE image cannot reflect the properties ofscatterers in a tissue (lipid-based or aqueous) Neverthelessit may be treated as an aliasing-independent CBE image toprovide a better sensitivity and contrast for the depiction oftemperature distribution in a nonuniform heating region

However we found that the speckle-like features inthe ICBE image still hinder improving the performance oftemperature profile visualization The ICBE image has theability to describe the temperature distribution in ablatedtissues but it did not have a relatively high CNR In thecontrary the speckle-free ICBEpa image had a larger CNRdemonstrating that the polynomial approximation providesthe ICBE image with the ability to highlight the region andlocation of ablation by reflecting temperature informationwith very good contrast

54 Considerations on Performing Polynomial Approximationof the CBE Image Some aspects of the algorithmic parame-ters for construction of the ICBEpa image require further dis-cussion to point out some considerations in practice At firstour results demonstrated that the WOR did not significantlyaffect the ICBEpa image This suggested that constructing

8 Computational and Mathematical Methods in Medicine

5

10

15

20

5 10 15 20(mm)

(mm

)WOR = 20

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

WOR = 50

(b)

5

10

15

20

5 10 15 20(mm)

(mm

)

86420minus2minus4minus6minus8

WOR = 80

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

87654321

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

(h)

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(i)

Figure 7 Examples of ((a)ndash(c)) CBE119908

((d)ndash(f)) ICBE and ((g)ndash(i)) ICBEpa images of pork tenderloin postheating for 400 s constructedusing WORs of 20 50 and 80 respectively

the ICBEpa temperature image using a lower WOR is feasibleto reduce the computational load Second the order selectionof conducting polynomial approximation would affect theaccuracy of estimations of the effective range and size of thetemperature profile for the transfer of heat in ablated tissue[25] This difficulty can be confirmed by our experimentalresults indicating that using an inappropriate order for thepolynomial approximation can result in overestimation orunderestimation of the temperature profile Some previousstudies have also shown that using a polynomial might not berobust to outliers which can cause fitting errors in ultrasounddata [26 27] Future studies should aim to explore the optimalpolynomial approximation for producing clinical ICBEpaimages

55 Limitations and Future Work For temperature eleva-tions higher than 45∘C the major limitation of ultrasoundtemperature estimation comes from the irreversible changesin the acoustic properties of tissue caused by necrosis Thismay explain why the image parameter and the temperature

do not have a linear relationship On the other hand theproposed CBE image is dedicated to the visualization of thetemperature distribution in a tissue Absolute temperaturevalues are unavailable from the reading of the proposedCBE image However this limitation may be overcome byestablishing a calibration table for further applications oftemperature measurements

It is worth noting that the construction of the proposedCBE imaging method just needs raw RF signals acquiredfrom a standard pulse-echo ultrasound system and doesnot require echo shift compensation This implies that thealgorithm of the proposed CBE imaging method can becombined with most commercial ultrasound systems mak-ing it possible to implement real-time temperature imagingHowever the frame rate of real-time temperature imaging isdifficult to estimate in the current stage because the com-putational efficiency may depend on system specificationsand programming skills In future developments we wouldsuggest using hardware and parallel processing techniques asthe algorithmic kernel to make the frame rate of temperatureimaging close to that of ultrasound B-scan

Computational and Mathematical Methods in Medicine 9

5

10

15

20

5 10 15 20(mm)

(mm

)Order = 3

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 4

(b)

Order = 5

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 6

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 7

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 8 2

15

1

05

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 9

(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 10

(h)

2

15

1

05

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 3

The absolute value map of the CBE119908image was then

used as the integrated CBE (ICBE) image The ICBE mapneeds further processing for visualization of temperaturedistributions and heat transfer in ablated tissue duringnonuniform heating Previous studies have extensively usedthe mathematic polynomial approximation to fit experi-mental data and predict temperature distribution and heatconduction behavior [19ndash21] This study applied the polyno-mial approximation during ICBE image processing Supposethat the original ICBE image prior to smoothing is 119883

119894119895

where 119894 and 119895 are indices of the image depth and widthrespectively We assumed that the function in each directionwas a polynomial of order 119901 Because 119901 is much smaller thanthe number of pixels in the axial and lateral directions the119883

119894119895

data were used to determine the optimal polynomial usingthe least-squares method 119883

119894119895was replaced with the value

calculated by the optimal polynomial This approximationwas performed along each line in the axial and lateral direc-tion with 119891

119901(sdot 119881) being the optimal polynomial of order 119901

reconstructed from the vector 119881 = (1198811 1198812 119881

119899) located at

indices 1 2 119899 After applying polynomial approximationsin the lateral and axial directions image 119883

119894119895was constructed

using the following two procedures

119883lowast

119894119895

= 119891119901

(119894 1198831119899119889 119895

) for each 119895

119883119894119895

= 119891119901

(119895 119883lowast

1198941119899119908

) for each 119894

(3)

where 119899119889and 119899

119908are the numbers of pixels in the axial

(depth) and lateral (width) directions respectively 1198831119899119889 119895

isthe vector119883

1119895 1198832119895

119883119899119889 119895

119883lowast119894119895

is the intermediate imageand 119883

119894119895is the ICBEpa image

3 Experimental Verification

31 Ablation Experiments The feasibility of the proposedmethod to monitor the distribution of temperature duringnonuniform heating was evaluated by conducting tissueablation experiments on excised tissues The tissue samplewas prepared from pork tenderloin extracted from the psoasmajor muscle along the central spine Tissue ablation wasconducted using a microwave delivery system (UMC-1Chinese PLAGeneralHospital Institute 207 of theAerospaceIndustry Company Beijing China) that operates at a fre-quency of 245GHz andhas electrical power ranging from 1 to99WThe tenderloin sample was preheated by a temperature-regulated water tank to an initial reference temperatureof 37∘C The microwave antenna was then inserted intothe sample for irradiation Ablation treatment performedat 2W for 420 s produced significant and stable increasesin temperature A commercial ultrasound scanner (Model2000 Terason Burlington MA USA) that can output rawRF signals digitized at a sampling rate of 30MHz was usedto image the tissue during heating A wideband linear arrayprobe (Model 10L5 Terason) with a central frequency ofapproximately 7MHzwas used A pulse echo test of the trans-ducer showed that the pulse length was 07mm The imageraw data were acquired every 20 s Each image consisted of

128 scan lines of backscattered signals and Hilbert transformwas applied to each scan line to obtain the correspondingenvelope image The temperature as a function of ablationtimewasmeasured using a thermocouple that was attached tothe microwave antenna Measurements of five tissue sampleswere performedThe experimental setup is shown in Figure 1

32 Data Analysis The envelope signals obtained from tissuesamples were used for B-mode and CBE imaging The B-mode image formation was based on the log-compressedenvelopes with a dynamic range of 60 dB A sliding squarewindow with side lengths corresponding to one pulse length(07mm) was selected to construct the CBE

119908 ICBE and

ICBEpa images To evaluate the performances of the newCBEimage in temperature estimation the image data were used tocalculate the pixel magnitude as a function of heating timeMoreover the contrast-to-noise ratio (CNR) was calculatedas an estimate of the contrast resolution defined as

CNR =

1003816100381610038161003816100381610038161003816100381610038161003816

120583ablation region minus 120583background

120590ablation region + 120590background

1003816100381610038161003816100381610038161003816100381610038161003816

(4)

where 120583 and 120590 are the mean and standard deviation of thepixel values in the images respectivelyThe above quantitativedata analyses were based on data acquired from the regionsof interest (ROI) located in the background and the ablationzone The sizes of the ROI were 5mm times 5mm

4 Results

Figure 2 shows the temperature as a function of ablationtime and the typical image for the cross-section of porktenderloin after microwave ablation The temperature in theablation region surrounding the antenna increased fromapproximately 37∘C to 46∘C during heating In the endof ablation a tissue denaturation region with a roughlycircular shape with a diameter of about 1 cm was formedin the tissue background Figure 3 shows typical B-scans ofpork tenderloin obtained during microwave ablation and thecorresponding CBE

119908images (a WOR of 80 was used) The

brightness of the red-blue interlaced shading in the CBE119908

image gradually increased with increasing temperature Fig-ure 4 shows the results of the ICBE image and the averageICBE as a function of heating time The brightness of theICBE image increased during heating corresponding to theaverage ICBE value increase from 0 dB to 4 dB

Figure 5(a) shows the results of the ICBEpa images (usingorder 7) We observed that the brightness of the ICBEpaimage gradually increased during heating for 420 s with theaverage ICBEpa value increasing from 0 dB to approximately2 dB as shown in Figure 5(b) This demonstrated that theICBEpa image can visualize the temperature distribution inthe tissue To evaluate the enhancement of the contrast afterapplying polynomial approximation the curves of the CNRwere plotted as a function of heating time in Figure 6 Thedynamic range of the CNR during the heating for the ICBEimage was approximately 16 In contrast the dynamic rangeof the CNR for the ICBEpa image was 134The ICBEpa image

4 Computational and Mathematical Methods in Medicine

Microwave system

Pork tenderloin

Transducer

Ablation antenna

Stage

Thermocouple

systemTerason 2000

(a)

Antenna

Thermocouple

Microwave system

Ultrasound system and transducer

(b)

Figure 1 (a) Schematic diagram of the experimental setup (b) A real representation of the experimental setup

Time (s)0 100 200 300 400

34

36

38

40

42

44

46

48

50

Tem

pera

ture

(∘C)

(a) (b)

Figure 2 Temperature measurement during microwave ablation and the typical image of tissue section after ablation

thus allows the temperature profile to be visualized withexcellent image contrast

Figure 7 shows examples of the CBE119908 ICBE and ICBEpa

images postheating for 400 s using WORs of 20 50 and80 respectively We observed that a lower WOR degradedthe resolutions of the CBE

119908and ICBE images because of the

use of fewer pixels to form the image However the featuresand patterns of the ICBEpa image did not exhibit significantchanges with the ICBEpa image still well-describing thecontour of the temperature distribution Figure 8 displays

ICBEpa images of pork tenderloin obtained postheating for400 s using polynomial approximations of different ordersCompared with the cross-sections of pork tenderloin shownin Figure 2 the ICBEpa image might overestimate the tem-perature distribution when using lower order polynomialapproximations The ICBEpa image might reflect the actualtemperature distribution when using polynomial approxi-mations of orders of 6 to 7 whereas using higher orderpolynomial approximations might underestimate the rangeof the temperature distribution

Computational and Mathematical Methods in Medicine 5

5 10 15 20

5

10

15

20

(mm)

(mm

)20 s

(a)

5 10 15 20

5

10

15

20

(mm)(m

m)

80 s

(b)

5 10 15 20

5

10

15

20

(mm)

(mm

)

180 s

(c)

5 10 15 20

5

10

15

20

605040302010

(mm)

(mm

)

320 s

(d)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(e)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(f)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(g)

5 10 15 20

5

10

15

20

86420minus2minus4minus6minus8

(mm)

(mm

)

(h)

Figure 3 ((a)ndash(d)) Typical B-mode images of pork tenderloin obtained at different heating times and the corresponding ((e)ndash(h)) CBE119908

images

5 10 15 20

5

10

15

20

(mm)

(mm

)

20 s

(a)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

80 s

(b)

5 10 15 20(mm)

5

10

15

20

(mm

)180 s

(c)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

320 s

(d)

Time (s)0 100 200 300 400

ICBE

(dB)

0

1

2

3

4

5

6

n = 5

(e)

Figure 4 ((a)ndash(d)) Typical ICBE images obtained at different heating times (e) ICBE values as a function of heating time

6 Computational and Mathematical Methods in Medicine

2

15

1

05

2

15

1

05

2

15

1

05

2

15

1

05

5

10

15

20

5 10 15 20

(mm

)

5

10

15

20(m

m)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

20 s 40 s 60 s 80 s 100 s

120 s 140 s 160 s 180 s 200 s

220 s 240 s 260 s 280 s 300 s

320 s 340 s 360 s 380 s 400 s

(a)

0 100 200 300 400

00

05

10

15

20

25

Time (s)

ICBE

pa(d

B)

n = 5

(b)

Figure 5 (a) Examples of ICBEpa images of pork tenderloin obtained at different heating times (b) ICBEpa values obtained in the tissueablation experiments as a function of heating time

Computational and Mathematical Methods in Medicine 7

Time (s)0 100 200 300 400

CNR

0

510

15

20

ICBE imageICBEpa image

n = 5

Figure 6 Contrast-to-noise ratios as functions of heating times forICBE and ICBEpa images

5 Discussion

51 The Significance of This Study Implementing real-timetemperature imaging based on the CBE concept in dif-ferent clinical applications requires the development of anew CBE imaging method to overcome the limitations ofconventional CBE imaging In our opinion CBE imagingfor clinical purposes should have two essential features (i)reduced dependency of the image performance on echo shifttracking and compensation with no requirement for echoshift compensation being the objective and (ii) the abilityto visualize the contour of temperature distribution duringnonuniform heating enabling its application in guidance oftissue ablation The current results have demonstrated thatthe proposed CBE imaging method fulfills the above tworequirements

52 Window Size for Constructing the Proposed CBE ImagingIn our proposedCBE imagingmethod the algorithm replacesthe pixel-to-pixel calculation with a ldquoregion-to-regionrdquo calcu-lationThe reason is that using datawithin awindowed regionreflected average trend of backscattered energy which mayreduce the influence of echo shifts and waveform distortiondue to heating tissues Under this assumption how to selectan appropriatewindow size for regional CBE computation is akey determination to implement visualization of temperaturedistributions in the absence of echo shift tracking and com-pensation According to the analysis by Seip and Ebbini [22]the movement of a scatterer caused by thermal expansionwhen the temperature increases from 37∘C to 50∘C is typicallyless than 2 120583m Over this temperature range the maximumspeckle motion caused by changes in the sound speed fordifferent types of tissues is approximately 05mm in the axialand lateral directions [13] In this study the side length ofthe square window used for regional CBE computation wasdetermined by the pulse length of the used transducer which

is larger than the maximum echo shift between 37∘C and50∘C revealed in the previous study In this circumstance theresolution of the CBE image constructed using the slidingwindow technique is actually not enough to describe thebehavior of echo shift This may be the reason why our CBEimaging methodology can work without echo shift trackingand compensation

53 Polynomial Approximation of the CBE Image The ideafor the proposed algorithmic procedure is similar to theconcept of ultrasound Doppler imaging We can betterunderstand the spirit of the new CBE imaging method fromthe comparison with Doppler ultrasound The Doppler shiftsignals in color Doppler ultrasound imaging are presented incolor and superimposed on grayscale images to reflect bloodflow information associated with velocity and directionLimitations of the color Doppler ultrasound image includeangle dependence aliasing and insensitivity to slow flows[23] These limitations are less significant in power Dopplerimages that include positive and negative components of theDoppler shift signals [23 24]

As discussed the ultrasound CBE increases with increas-ing temperature for lipid-based scatterers and decreases withincreasing temperature for aqueous scatterers Similar tothe shadings of color Doppler ultrasound correspondingto different flow directions the conventional CBE imagetypically also has two shadings one for lipid-based scatter-ers (increasing CBE) and the other for aqueous scatterers(decreasing CBE) However these two shading types can beambiguous if CBE imaging is performed without echo shifttracking and compensationThis shading ambiguity could betreated as the aliasing effect of theCBE image which is similarto the aliasing effect caused by an insufficient pulse repetitionrate in color Doppler ultrasound Like the concept of powerDoppler ultrasound the ICBE image is formed by integratingthe positive and negative CBE values as the strengths In thiscondition the ICBE image cannot reflect the properties ofscatterers in a tissue (lipid-based or aqueous) Neverthelessit may be treated as an aliasing-independent CBE image toprovide a better sensitivity and contrast for the depiction oftemperature distribution in a nonuniform heating region

However we found that the speckle-like features inthe ICBE image still hinder improving the performance oftemperature profile visualization The ICBE image has theability to describe the temperature distribution in ablatedtissues but it did not have a relatively high CNR In thecontrary the speckle-free ICBEpa image had a larger CNRdemonstrating that the polynomial approximation providesthe ICBE image with the ability to highlight the region andlocation of ablation by reflecting temperature informationwith very good contrast

54 Considerations on Performing Polynomial Approximationof the CBE Image Some aspects of the algorithmic parame-ters for construction of the ICBEpa image require further dis-cussion to point out some considerations in practice At firstour results demonstrated that the WOR did not significantlyaffect the ICBEpa image This suggested that constructing

8 Computational and Mathematical Methods in Medicine

5

10

15

20

5 10 15 20(mm)

(mm

)WOR = 20

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

WOR = 50

(b)

5

10

15

20

5 10 15 20(mm)

(mm

)

86420minus2minus4minus6minus8

WOR = 80

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

87654321

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

(h)

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(i)

Figure 7 Examples of ((a)ndash(c)) CBE119908

((d)ndash(f)) ICBE and ((g)ndash(i)) ICBEpa images of pork tenderloin postheating for 400 s constructedusing WORs of 20 50 and 80 respectively

the ICBEpa temperature image using a lower WOR is feasibleto reduce the computational load Second the order selectionof conducting polynomial approximation would affect theaccuracy of estimations of the effective range and size of thetemperature profile for the transfer of heat in ablated tissue[25] This difficulty can be confirmed by our experimentalresults indicating that using an inappropriate order for thepolynomial approximation can result in overestimation orunderestimation of the temperature profile Some previousstudies have also shown that using a polynomial might not berobust to outliers which can cause fitting errors in ultrasounddata [26 27] Future studies should aim to explore the optimalpolynomial approximation for producing clinical ICBEpaimages

55 Limitations and Future Work For temperature eleva-tions higher than 45∘C the major limitation of ultrasoundtemperature estimation comes from the irreversible changesin the acoustic properties of tissue caused by necrosis Thismay explain why the image parameter and the temperature

do not have a linear relationship On the other hand theproposed CBE image is dedicated to the visualization of thetemperature distribution in a tissue Absolute temperaturevalues are unavailable from the reading of the proposedCBE image However this limitation may be overcome byestablishing a calibration table for further applications oftemperature measurements

It is worth noting that the construction of the proposedCBE imaging method just needs raw RF signals acquiredfrom a standard pulse-echo ultrasound system and doesnot require echo shift compensation This implies that thealgorithm of the proposed CBE imaging method can becombined with most commercial ultrasound systems mak-ing it possible to implement real-time temperature imagingHowever the frame rate of real-time temperature imaging isdifficult to estimate in the current stage because the com-putational efficiency may depend on system specificationsand programming skills In future developments we wouldsuggest using hardware and parallel processing techniques asthe algorithmic kernel to make the frame rate of temperatureimaging close to that of ultrasound B-scan

Computational and Mathematical Methods in Medicine 9

5

10

15

20

5 10 15 20(mm)

(mm

)Order = 3

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 4

(b)

Order = 5

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 6

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 7

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 8 2

15

1

05

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 9

(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 10

(h)

2

15

1

05

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

4 Computational and Mathematical Methods in Medicine

Microwave system

Pork tenderloin

Transducer

Ablation antenna

Stage

Thermocouple

systemTerason 2000

(a)

Antenna

Thermocouple

Microwave system

Ultrasound system and transducer

(b)

Figure 1 (a) Schematic diagram of the experimental setup (b) A real representation of the experimental setup

Time (s)0 100 200 300 400

34

36

38

40

42

44

46

48

50

Tem

pera

ture

(∘C)

(a) (b)

Figure 2 Temperature measurement during microwave ablation and the typical image of tissue section after ablation

thus allows the temperature profile to be visualized withexcellent image contrast

Figure 7 shows examples of the CBE119908 ICBE and ICBEpa

images postheating for 400 s using WORs of 20 50 and80 respectively We observed that a lower WOR degradedthe resolutions of the CBE

119908and ICBE images because of the

use of fewer pixels to form the image However the featuresand patterns of the ICBEpa image did not exhibit significantchanges with the ICBEpa image still well-describing thecontour of the temperature distribution Figure 8 displays

ICBEpa images of pork tenderloin obtained postheating for400 s using polynomial approximations of different ordersCompared with the cross-sections of pork tenderloin shownin Figure 2 the ICBEpa image might overestimate the tem-perature distribution when using lower order polynomialapproximations The ICBEpa image might reflect the actualtemperature distribution when using polynomial approxi-mations of orders of 6 to 7 whereas using higher orderpolynomial approximations might underestimate the rangeof the temperature distribution

Computational and Mathematical Methods in Medicine 5

5 10 15 20

5

10

15

20

(mm)

(mm

)20 s

(a)

5 10 15 20

5

10

15

20

(mm)(m

m)

80 s

(b)

5 10 15 20

5

10

15

20

(mm)

(mm

)

180 s

(c)

5 10 15 20

5

10

15

20

605040302010

(mm)

(mm

)

320 s

(d)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(e)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(f)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(g)

5 10 15 20

5

10

15

20

86420minus2minus4minus6minus8

(mm)

(mm

)

(h)

Figure 3 ((a)ndash(d)) Typical B-mode images of pork tenderloin obtained at different heating times and the corresponding ((e)ndash(h)) CBE119908

images

5 10 15 20

5

10

15

20

(mm)

(mm

)

20 s

(a)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

80 s

(b)

5 10 15 20(mm)

5

10

15

20

(mm

)180 s

(c)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

320 s

(d)

Time (s)0 100 200 300 400

ICBE

(dB)

0

1

2

3

4

5

6

n = 5

(e)

Figure 4 ((a)ndash(d)) Typical ICBE images obtained at different heating times (e) ICBE values as a function of heating time

6 Computational and Mathematical Methods in Medicine

2

15

1

05

2

15

1

05

2

15

1

05

2

15

1

05

5

10

15

20

5 10 15 20

(mm

)

5

10

15

20(m

m)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

20 s 40 s 60 s 80 s 100 s

120 s 140 s 160 s 180 s 200 s

220 s 240 s 260 s 280 s 300 s

320 s 340 s 360 s 380 s 400 s

(a)

0 100 200 300 400

00

05

10

15

20

25

Time (s)

ICBE

pa(d

B)

n = 5

(b)

Figure 5 (a) Examples of ICBEpa images of pork tenderloin obtained at different heating times (b) ICBEpa values obtained in the tissueablation experiments as a function of heating time

Computational and Mathematical Methods in Medicine 7

Time (s)0 100 200 300 400

CNR

0

510

15

20

ICBE imageICBEpa image

n = 5

Figure 6 Contrast-to-noise ratios as functions of heating times forICBE and ICBEpa images

5 Discussion

51 The Significance of This Study Implementing real-timetemperature imaging based on the CBE concept in dif-ferent clinical applications requires the development of anew CBE imaging method to overcome the limitations ofconventional CBE imaging In our opinion CBE imagingfor clinical purposes should have two essential features (i)reduced dependency of the image performance on echo shifttracking and compensation with no requirement for echoshift compensation being the objective and (ii) the abilityto visualize the contour of temperature distribution duringnonuniform heating enabling its application in guidance oftissue ablation The current results have demonstrated thatthe proposed CBE imaging method fulfills the above tworequirements

52 Window Size for Constructing the Proposed CBE ImagingIn our proposedCBE imagingmethod the algorithm replacesthe pixel-to-pixel calculation with a ldquoregion-to-regionrdquo calcu-lationThe reason is that using datawithin awindowed regionreflected average trend of backscattered energy which mayreduce the influence of echo shifts and waveform distortiondue to heating tissues Under this assumption how to selectan appropriatewindow size for regional CBE computation is akey determination to implement visualization of temperaturedistributions in the absence of echo shift tracking and com-pensation According to the analysis by Seip and Ebbini [22]the movement of a scatterer caused by thermal expansionwhen the temperature increases from 37∘C to 50∘C is typicallyless than 2 120583m Over this temperature range the maximumspeckle motion caused by changes in the sound speed fordifferent types of tissues is approximately 05mm in the axialand lateral directions [13] In this study the side length ofthe square window used for regional CBE computation wasdetermined by the pulse length of the used transducer which

is larger than the maximum echo shift between 37∘C and50∘C revealed in the previous study In this circumstance theresolution of the CBE image constructed using the slidingwindow technique is actually not enough to describe thebehavior of echo shift This may be the reason why our CBEimaging methodology can work without echo shift trackingand compensation

53 Polynomial Approximation of the CBE Image The ideafor the proposed algorithmic procedure is similar to theconcept of ultrasound Doppler imaging We can betterunderstand the spirit of the new CBE imaging method fromthe comparison with Doppler ultrasound The Doppler shiftsignals in color Doppler ultrasound imaging are presented incolor and superimposed on grayscale images to reflect bloodflow information associated with velocity and directionLimitations of the color Doppler ultrasound image includeangle dependence aliasing and insensitivity to slow flows[23] These limitations are less significant in power Dopplerimages that include positive and negative components of theDoppler shift signals [23 24]

As discussed the ultrasound CBE increases with increas-ing temperature for lipid-based scatterers and decreases withincreasing temperature for aqueous scatterers Similar tothe shadings of color Doppler ultrasound correspondingto different flow directions the conventional CBE imagetypically also has two shadings one for lipid-based scatter-ers (increasing CBE) and the other for aqueous scatterers(decreasing CBE) However these two shading types can beambiguous if CBE imaging is performed without echo shifttracking and compensationThis shading ambiguity could betreated as the aliasing effect of theCBE image which is similarto the aliasing effect caused by an insufficient pulse repetitionrate in color Doppler ultrasound Like the concept of powerDoppler ultrasound the ICBE image is formed by integratingthe positive and negative CBE values as the strengths In thiscondition the ICBE image cannot reflect the properties ofscatterers in a tissue (lipid-based or aqueous) Neverthelessit may be treated as an aliasing-independent CBE image toprovide a better sensitivity and contrast for the depiction oftemperature distribution in a nonuniform heating region

However we found that the speckle-like features inthe ICBE image still hinder improving the performance oftemperature profile visualization The ICBE image has theability to describe the temperature distribution in ablatedtissues but it did not have a relatively high CNR In thecontrary the speckle-free ICBEpa image had a larger CNRdemonstrating that the polynomial approximation providesthe ICBE image with the ability to highlight the region andlocation of ablation by reflecting temperature informationwith very good contrast

54 Considerations on Performing Polynomial Approximationof the CBE Image Some aspects of the algorithmic parame-ters for construction of the ICBEpa image require further dis-cussion to point out some considerations in practice At firstour results demonstrated that the WOR did not significantlyaffect the ICBEpa image This suggested that constructing

8 Computational and Mathematical Methods in Medicine

5

10

15

20

5 10 15 20(mm)

(mm

)WOR = 20

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

WOR = 50

(b)

5

10

15

20

5 10 15 20(mm)

(mm

)

86420minus2minus4minus6minus8

WOR = 80

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

87654321

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

(h)

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(i)

Figure 7 Examples of ((a)ndash(c)) CBE119908

((d)ndash(f)) ICBE and ((g)ndash(i)) ICBEpa images of pork tenderloin postheating for 400 s constructedusing WORs of 20 50 and 80 respectively

the ICBEpa temperature image using a lower WOR is feasibleto reduce the computational load Second the order selectionof conducting polynomial approximation would affect theaccuracy of estimations of the effective range and size of thetemperature profile for the transfer of heat in ablated tissue[25] This difficulty can be confirmed by our experimentalresults indicating that using an inappropriate order for thepolynomial approximation can result in overestimation orunderestimation of the temperature profile Some previousstudies have also shown that using a polynomial might not berobust to outliers which can cause fitting errors in ultrasounddata [26 27] Future studies should aim to explore the optimalpolynomial approximation for producing clinical ICBEpaimages

55 Limitations and Future Work For temperature eleva-tions higher than 45∘C the major limitation of ultrasoundtemperature estimation comes from the irreversible changesin the acoustic properties of tissue caused by necrosis Thismay explain why the image parameter and the temperature

do not have a linear relationship On the other hand theproposed CBE image is dedicated to the visualization of thetemperature distribution in a tissue Absolute temperaturevalues are unavailable from the reading of the proposedCBE image However this limitation may be overcome byestablishing a calibration table for further applications oftemperature measurements

It is worth noting that the construction of the proposedCBE imaging method just needs raw RF signals acquiredfrom a standard pulse-echo ultrasound system and doesnot require echo shift compensation This implies that thealgorithm of the proposed CBE imaging method can becombined with most commercial ultrasound systems mak-ing it possible to implement real-time temperature imagingHowever the frame rate of real-time temperature imaging isdifficult to estimate in the current stage because the com-putational efficiency may depend on system specificationsand programming skills In future developments we wouldsuggest using hardware and parallel processing techniques asthe algorithmic kernel to make the frame rate of temperatureimaging close to that of ultrasound B-scan

Computational and Mathematical Methods in Medicine 9

5

10

15

20

5 10 15 20(mm)

(mm

)Order = 3

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 4

(b)

Order = 5

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 6

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 7

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 8 2

15

1

05

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 9

(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 10

(h)

2

15

1

05

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 5

5 10 15 20

5

10

15

20

(mm)

(mm

)20 s

(a)

5 10 15 20

5

10

15

20

(mm)(m

m)

80 s

(b)

5 10 15 20

5

10

15

20

(mm)

(mm

)

180 s

(c)

5 10 15 20

5

10

15

20

605040302010

(mm)

(mm

)

320 s

(d)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(e)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(f)

5 10 15 20

5

10

15

20

(mm)

(mm

)

(g)

5 10 15 20

5

10

15

20

86420minus2minus4minus6minus8

(mm)

(mm

)

(h)

Figure 3 ((a)ndash(d)) Typical B-mode images of pork tenderloin obtained at different heating times and the corresponding ((e)ndash(h)) CBE119908

images

5 10 15 20

5

10

15

20

(mm)

(mm

)

20 s

(a)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

80 s

(b)

5 10 15 20(mm)

5

10

15

20

(mm

)180 s

(c)

5 10 15 20(mm)

5

10

15

20

(mm

)

87654321

320 s

(d)

Time (s)0 100 200 300 400

ICBE

(dB)

0

1

2

3

4

5

6

n = 5

(e)

Figure 4 ((a)ndash(d)) Typical ICBE images obtained at different heating times (e) ICBE values as a function of heating time

6 Computational and Mathematical Methods in Medicine

2

15

1

05

2

15

1

05

2

15

1

05

2

15

1

05

5

10

15

20

5 10 15 20

(mm

)

5

10

15

20(m

m)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

20 s 40 s 60 s 80 s 100 s

120 s 140 s 160 s 180 s 200 s

220 s 240 s 260 s 280 s 300 s

320 s 340 s 360 s 380 s 400 s

(a)

0 100 200 300 400

00

05

10

15

20

25

Time (s)

ICBE

pa(d

B)

n = 5

(b)

Figure 5 (a) Examples of ICBEpa images of pork tenderloin obtained at different heating times (b) ICBEpa values obtained in the tissueablation experiments as a function of heating time

Computational and Mathematical Methods in Medicine 7

Time (s)0 100 200 300 400

CNR

0

510

15

20

ICBE imageICBEpa image

n = 5

Figure 6 Contrast-to-noise ratios as functions of heating times forICBE and ICBEpa images

5 Discussion

51 The Significance of This Study Implementing real-timetemperature imaging based on the CBE concept in dif-ferent clinical applications requires the development of anew CBE imaging method to overcome the limitations ofconventional CBE imaging In our opinion CBE imagingfor clinical purposes should have two essential features (i)reduced dependency of the image performance on echo shifttracking and compensation with no requirement for echoshift compensation being the objective and (ii) the abilityto visualize the contour of temperature distribution duringnonuniform heating enabling its application in guidance oftissue ablation The current results have demonstrated thatthe proposed CBE imaging method fulfills the above tworequirements

52 Window Size for Constructing the Proposed CBE ImagingIn our proposedCBE imagingmethod the algorithm replacesthe pixel-to-pixel calculation with a ldquoregion-to-regionrdquo calcu-lationThe reason is that using datawithin awindowed regionreflected average trend of backscattered energy which mayreduce the influence of echo shifts and waveform distortiondue to heating tissues Under this assumption how to selectan appropriatewindow size for regional CBE computation is akey determination to implement visualization of temperaturedistributions in the absence of echo shift tracking and com-pensation According to the analysis by Seip and Ebbini [22]the movement of a scatterer caused by thermal expansionwhen the temperature increases from 37∘C to 50∘C is typicallyless than 2 120583m Over this temperature range the maximumspeckle motion caused by changes in the sound speed fordifferent types of tissues is approximately 05mm in the axialand lateral directions [13] In this study the side length ofthe square window used for regional CBE computation wasdetermined by the pulse length of the used transducer which

is larger than the maximum echo shift between 37∘C and50∘C revealed in the previous study In this circumstance theresolution of the CBE image constructed using the slidingwindow technique is actually not enough to describe thebehavior of echo shift This may be the reason why our CBEimaging methodology can work without echo shift trackingand compensation

53 Polynomial Approximation of the CBE Image The ideafor the proposed algorithmic procedure is similar to theconcept of ultrasound Doppler imaging We can betterunderstand the spirit of the new CBE imaging method fromthe comparison with Doppler ultrasound The Doppler shiftsignals in color Doppler ultrasound imaging are presented incolor and superimposed on grayscale images to reflect bloodflow information associated with velocity and directionLimitations of the color Doppler ultrasound image includeangle dependence aliasing and insensitivity to slow flows[23] These limitations are less significant in power Dopplerimages that include positive and negative components of theDoppler shift signals [23 24]

As discussed the ultrasound CBE increases with increas-ing temperature for lipid-based scatterers and decreases withincreasing temperature for aqueous scatterers Similar tothe shadings of color Doppler ultrasound correspondingto different flow directions the conventional CBE imagetypically also has two shadings one for lipid-based scatter-ers (increasing CBE) and the other for aqueous scatterers(decreasing CBE) However these two shading types can beambiguous if CBE imaging is performed without echo shifttracking and compensationThis shading ambiguity could betreated as the aliasing effect of theCBE image which is similarto the aliasing effect caused by an insufficient pulse repetitionrate in color Doppler ultrasound Like the concept of powerDoppler ultrasound the ICBE image is formed by integratingthe positive and negative CBE values as the strengths In thiscondition the ICBE image cannot reflect the properties ofscatterers in a tissue (lipid-based or aqueous) Neverthelessit may be treated as an aliasing-independent CBE image toprovide a better sensitivity and contrast for the depiction oftemperature distribution in a nonuniform heating region

However we found that the speckle-like features inthe ICBE image still hinder improving the performance oftemperature profile visualization The ICBE image has theability to describe the temperature distribution in ablatedtissues but it did not have a relatively high CNR In thecontrary the speckle-free ICBEpa image had a larger CNRdemonstrating that the polynomial approximation providesthe ICBE image with the ability to highlight the region andlocation of ablation by reflecting temperature informationwith very good contrast

54 Considerations on Performing Polynomial Approximationof the CBE Image Some aspects of the algorithmic parame-ters for construction of the ICBEpa image require further dis-cussion to point out some considerations in practice At firstour results demonstrated that the WOR did not significantlyaffect the ICBEpa image This suggested that constructing

8 Computational and Mathematical Methods in Medicine

5

10

15

20

5 10 15 20(mm)

(mm

)WOR = 20

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

WOR = 50

(b)

5

10

15

20

5 10 15 20(mm)

(mm

)

86420minus2minus4minus6minus8

WOR = 80

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

87654321

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

(h)

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(i)

Figure 7 Examples of ((a)ndash(c)) CBE119908

((d)ndash(f)) ICBE and ((g)ndash(i)) ICBEpa images of pork tenderloin postheating for 400 s constructedusing WORs of 20 50 and 80 respectively

the ICBEpa temperature image using a lower WOR is feasibleto reduce the computational load Second the order selectionof conducting polynomial approximation would affect theaccuracy of estimations of the effective range and size of thetemperature profile for the transfer of heat in ablated tissue[25] This difficulty can be confirmed by our experimentalresults indicating that using an inappropriate order for thepolynomial approximation can result in overestimation orunderestimation of the temperature profile Some previousstudies have also shown that using a polynomial might not berobust to outliers which can cause fitting errors in ultrasounddata [26 27] Future studies should aim to explore the optimalpolynomial approximation for producing clinical ICBEpaimages

55 Limitations and Future Work For temperature eleva-tions higher than 45∘C the major limitation of ultrasoundtemperature estimation comes from the irreversible changesin the acoustic properties of tissue caused by necrosis Thismay explain why the image parameter and the temperature

do not have a linear relationship On the other hand theproposed CBE image is dedicated to the visualization of thetemperature distribution in a tissue Absolute temperaturevalues are unavailable from the reading of the proposedCBE image However this limitation may be overcome byestablishing a calibration table for further applications oftemperature measurements

It is worth noting that the construction of the proposedCBE imaging method just needs raw RF signals acquiredfrom a standard pulse-echo ultrasound system and doesnot require echo shift compensation This implies that thealgorithm of the proposed CBE imaging method can becombined with most commercial ultrasound systems mak-ing it possible to implement real-time temperature imagingHowever the frame rate of real-time temperature imaging isdifficult to estimate in the current stage because the com-putational efficiency may depend on system specificationsand programming skills In future developments we wouldsuggest using hardware and parallel processing techniques asthe algorithmic kernel to make the frame rate of temperatureimaging close to that of ultrasound B-scan

Computational and Mathematical Methods in Medicine 9

5

10

15

20

5 10 15 20(mm)

(mm

)Order = 3

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 4

(b)

Order = 5

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 6

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 7

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 8 2

15

1

05

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 9

(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 10

(h)

2

15

1

05

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

6 Computational and Mathematical Methods in Medicine

2

15

1

05

2

15

1

05

2

15

1

05

2

15

1

05

5

10

15

20

5 10 15 20

(mm

)

5

10

15

20(m

m)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

5

10

15

20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5

10

15

20

5 10 15 20

(mm

)

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

5 10 15 20

(mm)

20 s 40 s 60 s 80 s 100 s

120 s 140 s 160 s 180 s 200 s

220 s 240 s 260 s 280 s 300 s

320 s 340 s 360 s 380 s 400 s

(a)

0 100 200 300 400

00

05

10

15

20

25

Time (s)

ICBE

pa(d

B)

n = 5

(b)

Figure 5 (a) Examples of ICBEpa images of pork tenderloin obtained at different heating times (b) ICBEpa values obtained in the tissueablation experiments as a function of heating time

Computational and Mathematical Methods in Medicine 7

Time (s)0 100 200 300 400

CNR

0

510

15

20

ICBE imageICBEpa image

n = 5

Figure 6 Contrast-to-noise ratios as functions of heating times forICBE and ICBEpa images

5 Discussion

51 The Significance of This Study Implementing real-timetemperature imaging based on the CBE concept in dif-ferent clinical applications requires the development of anew CBE imaging method to overcome the limitations ofconventional CBE imaging In our opinion CBE imagingfor clinical purposes should have two essential features (i)reduced dependency of the image performance on echo shifttracking and compensation with no requirement for echoshift compensation being the objective and (ii) the abilityto visualize the contour of temperature distribution duringnonuniform heating enabling its application in guidance oftissue ablation The current results have demonstrated thatthe proposed CBE imaging method fulfills the above tworequirements

52 Window Size for Constructing the Proposed CBE ImagingIn our proposedCBE imagingmethod the algorithm replacesthe pixel-to-pixel calculation with a ldquoregion-to-regionrdquo calcu-lationThe reason is that using datawithin awindowed regionreflected average trend of backscattered energy which mayreduce the influence of echo shifts and waveform distortiondue to heating tissues Under this assumption how to selectan appropriatewindow size for regional CBE computation is akey determination to implement visualization of temperaturedistributions in the absence of echo shift tracking and com-pensation According to the analysis by Seip and Ebbini [22]the movement of a scatterer caused by thermal expansionwhen the temperature increases from 37∘C to 50∘C is typicallyless than 2 120583m Over this temperature range the maximumspeckle motion caused by changes in the sound speed fordifferent types of tissues is approximately 05mm in the axialand lateral directions [13] In this study the side length ofthe square window used for regional CBE computation wasdetermined by the pulse length of the used transducer which

is larger than the maximum echo shift between 37∘C and50∘C revealed in the previous study In this circumstance theresolution of the CBE image constructed using the slidingwindow technique is actually not enough to describe thebehavior of echo shift This may be the reason why our CBEimaging methodology can work without echo shift trackingand compensation

53 Polynomial Approximation of the CBE Image The ideafor the proposed algorithmic procedure is similar to theconcept of ultrasound Doppler imaging We can betterunderstand the spirit of the new CBE imaging method fromthe comparison with Doppler ultrasound The Doppler shiftsignals in color Doppler ultrasound imaging are presented incolor and superimposed on grayscale images to reflect bloodflow information associated with velocity and directionLimitations of the color Doppler ultrasound image includeangle dependence aliasing and insensitivity to slow flows[23] These limitations are less significant in power Dopplerimages that include positive and negative components of theDoppler shift signals [23 24]

As discussed the ultrasound CBE increases with increas-ing temperature for lipid-based scatterers and decreases withincreasing temperature for aqueous scatterers Similar tothe shadings of color Doppler ultrasound correspondingto different flow directions the conventional CBE imagetypically also has two shadings one for lipid-based scatter-ers (increasing CBE) and the other for aqueous scatterers(decreasing CBE) However these two shading types can beambiguous if CBE imaging is performed without echo shifttracking and compensationThis shading ambiguity could betreated as the aliasing effect of theCBE image which is similarto the aliasing effect caused by an insufficient pulse repetitionrate in color Doppler ultrasound Like the concept of powerDoppler ultrasound the ICBE image is formed by integratingthe positive and negative CBE values as the strengths In thiscondition the ICBE image cannot reflect the properties ofscatterers in a tissue (lipid-based or aqueous) Neverthelessit may be treated as an aliasing-independent CBE image toprovide a better sensitivity and contrast for the depiction oftemperature distribution in a nonuniform heating region

However we found that the speckle-like features inthe ICBE image still hinder improving the performance oftemperature profile visualization The ICBE image has theability to describe the temperature distribution in ablatedtissues but it did not have a relatively high CNR In thecontrary the speckle-free ICBEpa image had a larger CNRdemonstrating that the polynomial approximation providesthe ICBE image with the ability to highlight the region andlocation of ablation by reflecting temperature informationwith very good contrast

54 Considerations on Performing Polynomial Approximationof the CBE Image Some aspects of the algorithmic parame-ters for construction of the ICBEpa image require further dis-cussion to point out some considerations in practice At firstour results demonstrated that the WOR did not significantlyaffect the ICBEpa image This suggested that constructing

8 Computational and Mathematical Methods in Medicine

5

10

15

20

5 10 15 20(mm)

(mm

)WOR = 20

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

WOR = 50

(b)

5

10

15

20

5 10 15 20(mm)

(mm

)

86420minus2minus4minus6minus8

WOR = 80

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

87654321

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

(h)

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(i)

Figure 7 Examples of ((a)ndash(c)) CBE119908

((d)ndash(f)) ICBE and ((g)ndash(i)) ICBEpa images of pork tenderloin postheating for 400 s constructedusing WORs of 20 50 and 80 respectively

the ICBEpa temperature image using a lower WOR is feasibleto reduce the computational load Second the order selectionof conducting polynomial approximation would affect theaccuracy of estimations of the effective range and size of thetemperature profile for the transfer of heat in ablated tissue[25] This difficulty can be confirmed by our experimentalresults indicating that using an inappropriate order for thepolynomial approximation can result in overestimation orunderestimation of the temperature profile Some previousstudies have also shown that using a polynomial might not berobust to outliers which can cause fitting errors in ultrasounddata [26 27] Future studies should aim to explore the optimalpolynomial approximation for producing clinical ICBEpaimages

55 Limitations and Future Work For temperature eleva-tions higher than 45∘C the major limitation of ultrasoundtemperature estimation comes from the irreversible changesin the acoustic properties of tissue caused by necrosis Thismay explain why the image parameter and the temperature

do not have a linear relationship On the other hand theproposed CBE image is dedicated to the visualization of thetemperature distribution in a tissue Absolute temperaturevalues are unavailable from the reading of the proposedCBE image However this limitation may be overcome byestablishing a calibration table for further applications oftemperature measurements

It is worth noting that the construction of the proposedCBE imaging method just needs raw RF signals acquiredfrom a standard pulse-echo ultrasound system and doesnot require echo shift compensation This implies that thealgorithm of the proposed CBE imaging method can becombined with most commercial ultrasound systems mak-ing it possible to implement real-time temperature imagingHowever the frame rate of real-time temperature imaging isdifficult to estimate in the current stage because the com-putational efficiency may depend on system specificationsand programming skills In future developments we wouldsuggest using hardware and parallel processing techniques asthe algorithmic kernel to make the frame rate of temperatureimaging close to that of ultrasound B-scan

Computational and Mathematical Methods in Medicine 9

5

10

15

20

5 10 15 20(mm)

(mm

)Order = 3

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 4

(b)

Order = 5

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 6

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 7

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 8 2

15

1

05

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 9

(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 10

(h)

2

15

1

05

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 7

Time (s)0 100 200 300 400

CNR

0

510

15

20

ICBE imageICBEpa image

n = 5

Figure 6 Contrast-to-noise ratios as functions of heating times forICBE and ICBEpa images

5 Discussion

51 The Significance of This Study Implementing real-timetemperature imaging based on the CBE concept in dif-ferent clinical applications requires the development of anew CBE imaging method to overcome the limitations ofconventional CBE imaging In our opinion CBE imagingfor clinical purposes should have two essential features (i)reduced dependency of the image performance on echo shifttracking and compensation with no requirement for echoshift compensation being the objective and (ii) the abilityto visualize the contour of temperature distribution duringnonuniform heating enabling its application in guidance oftissue ablation The current results have demonstrated thatthe proposed CBE imaging method fulfills the above tworequirements

52 Window Size for Constructing the Proposed CBE ImagingIn our proposedCBE imagingmethod the algorithm replacesthe pixel-to-pixel calculation with a ldquoregion-to-regionrdquo calcu-lationThe reason is that using datawithin awindowed regionreflected average trend of backscattered energy which mayreduce the influence of echo shifts and waveform distortiondue to heating tissues Under this assumption how to selectan appropriatewindow size for regional CBE computation is akey determination to implement visualization of temperaturedistributions in the absence of echo shift tracking and com-pensation According to the analysis by Seip and Ebbini [22]the movement of a scatterer caused by thermal expansionwhen the temperature increases from 37∘C to 50∘C is typicallyless than 2 120583m Over this temperature range the maximumspeckle motion caused by changes in the sound speed fordifferent types of tissues is approximately 05mm in the axialand lateral directions [13] In this study the side length ofthe square window used for regional CBE computation wasdetermined by the pulse length of the used transducer which

is larger than the maximum echo shift between 37∘C and50∘C revealed in the previous study In this circumstance theresolution of the CBE image constructed using the slidingwindow technique is actually not enough to describe thebehavior of echo shift This may be the reason why our CBEimaging methodology can work without echo shift trackingand compensation

53 Polynomial Approximation of the CBE Image The ideafor the proposed algorithmic procedure is similar to theconcept of ultrasound Doppler imaging We can betterunderstand the spirit of the new CBE imaging method fromthe comparison with Doppler ultrasound The Doppler shiftsignals in color Doppler ultrasound imaging are presented incolor and superimposed on grayscale images to reflect bloodflow information associated with velocity and directionLimitations of the color Doppler ultrasound image includeangle dependence aliasing and insensitivity to slow flows[23] These limitations are less significant in power Dopplerimages that include positive and negative components of theDoppler shift signals [23 24]

As discussed the ultrasound CBE increases with increas-ing temperature for lipid-based scatterers and decreases withincreasing temperature for aqueous scatterers Similar tothe shadings of color Doppler ultrasound correspondingto different flow directions the conventional CBE imagetypically also has two shadings one for lipid-based scatter-ers (increasing CBE) and the other for aqueous scatterers(decreasing CBE) However these two shading types can beambiguous if CBE imaging is performed without echo shifttracking and compensationThis shading ambiguity could betreated as the aliasing effect of theCBE image which is similarto the aliasing effect caused by an insufficient pulse repetitionrate in color Doppler ultrasound Like the concept of powerDoppler ultrasound the ICBE image is formed by integratingthe positive and negative CBE values as the strengths In thiscondition the ICBE image cannot reflect the properties ofscatterers in a tissue (lipid-based or aqueous) Neverthelessit may be treated as an aliasing-independent CBE image toprovide a better sensitivity and contrast for the depiction oftemperature distribution in a nonuniform heating region

However we found that the speckle-like features inthe ICBE image still hinder improving the performance oftemperature profile visualization The ICBE image has theability to describe the temperature distribution in ablatedtissues but it did not have a relatively high CNR In thecontrary the speckle-free ICBEpa image had a larger CNRdemonstrating that the polynomial approximation providesthe ICBE image with the ability to highlight the region andlocation of ablation by reflecting temperature informationwith very good contrast

54 Considerations on Performing Polynomial Approximationof the CBE Image Some aspects of the algorithmic parame-ters for construction of the ICBEpa image require further dis-cussion to point out some considerations in practice At firstour results demonstrated that the WOR did not significantlyaffect the ICBEpa image This suggested that constructing

8 Computational and Mathematical Methods in Medicine

5

10

15

20

5 10 15 20(mm)

(mm

)WOR = 20

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

WOR = 50

(b)

5

10

15

20

5 10 15 20(mm)

(mm

)

86420minus2minus4minus6minus8

WOR = 80

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

87654321

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

(h)

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(i)

Figure 7 Examples of ((a)ndash(c)) CBE119908

((d)ndash(f)) ICBE and ((g)ndash(i)) ICBEpa images of pork tenderloin postheating for 400 s constructedusing WORs of 20 50 and 80 respectively

the ICBEpa temperature image using a lower WOR is feasibleto reduce the computational load Second the order selectionof conducting polynomial approximation would affect theaccuracy of estimations of the effective range and size of thetemperature profile for the transfer of heat in ablated tissue[25] This difficulty can be confirmed by our experimentalresults indicating that using an inappropriate order for thepolynomial approximation can result in overestimation orunderestimation of the temperature profile Some previousstudies have also shown that using a polynomial might not berobust to outliers which can cause fitting errors in ultrasounddata [26 27] Future studies should aim to explore the optimalpolynomial approximation for producing clinical ICBEpaimages

55 Limitations and Future Work For temperature eleva-tions higher than 45∘C the major limitation of ultrasoundtemperature estimation comes from the irreversible changesin the acoustic properties of tissue caused by necrosis Thismay explain why the image parameter and the temperature

do not have a linear relationship On the other hand theproposed CBE image is dedicated to the visualization of thetemperature distribution in a tissue Absolute temperaturevalues are unavailable from the reading of the proposedCBE image However this limitation may be overcome byestablishing a calibration table for further applications oftemperature measurements

It is worth noting that the construction of the proposedCBE imaging method just needs raw RF signals acquiredfrom a standard pulse-echo ultrasound system and doesnot require echo shift compensation This implies that thealgorithm of the proposed CBE imaging method can becombined with most commercial ultrasound systems mak-ing it possible to implement real-time temperature imagingHowever the frame rate of real-time temperature imaging isdifficult to estimate in the current stage because the com-putational efficiency may depend on system specificationsand programming skills In future developments we wouldsuggest using hardware and parallel processing techniques asthe algorithmic kernel to make the frame rate of temperatureimaging close to that of ultrasound B-scan

Computational and Mathematical Methods in Medicine 9

5

10

15

20

5 10 15 20(mm)

(mm

)Order = 3

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 4

(b)

Order = 5

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 6

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 7

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 8 2

15

1

05

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 9

(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 10

(h)

2

15

1

05

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

8 Computational and Mathematical Methods in Medicine

5

10

15

20

5 10 15 20(mm)

(mm

)WOR = 20

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

WOR = 50

(b)

5

10

15

20

5 10 15 20(mm)

(mm

)

86420minus2minus4minus6minus8

WOR = 80

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

87654321

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

(h)

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(i)

Figure 7 Examples of ((a)ndash(c)) CBE119908

((d)ndash(f)) ICBE and ((g)ndash(i)) ICBEpa images of pork tenderloin postheating for 400 s constructedusing WORs of 20 50 and 80 respectively

the ICBEpa temperature image using a lower WOR is feasibleto reduce the computational load Second the order selectionof conducting polynomial approximation would affect theaccuracy of estimations of the effective range and size of thetemperature profile for the transfer of heat in ablated tissue[25] This difficulty can be confirmed by our experimentalresults indicating that using an inappropriate order for thepolynomial approximation can result in overestimation orunderestimation of the temperature profile Some previousstudies have also shown that using a polynomial might not berobust to outliers which can cause fitting errors in ultrasounddata [26 27] Future studies should aim to explore the optimalpolynomial approximation for producing clinical ICBEpaimages

55 Limitations and Future Work For temperature eleva-tions higher than 45∘C the major limitation of ultrasoundtemperature estimation comes from the irreversible changesin the acoustic properties of tissue caused by necrosis Thismay explain why the image parameter and the temperature

do not have a linear relationship On the other hand theproposed CBE image is dedicated to the visualization of thetemperature distribution in a tissue Absolute temperaturevalues are unavailable from the reading of the proposedCBE image However this limitation may be overcome byestablishing a calibration table for further applications oftemperature measurements

It is worth noting that the construction of the proposedCBE imaging method just needs raw RF signals acquiredfrom a standard pulse-echo ultrasound system and doesnot require echo shift compensation This implies that thealgorithm of the proposed CBE imaging method can becombined with most commercial ultrasound systems mak-ing it possible to implement real-time temperature imagingHowever the frame rate of real-time temperature imaging isdifficult to estimate in the current stage because the com-putational efficiency may depend on system specificationsand programming skills In future developments we wouldsuggest using hardware and parallel processing techniques asthe algorithmic kernel to make the frame rate of temperatureimaging close to that of ultrasound B-scan

Computational and Mathematical Methods in Medicine 9

5

10

15

20

5 10 15 20(mm)

(mm

)Order = 3

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 4

(b)

Order = 5

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 6

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 7

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 8 2

15

1

05

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 9

(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 10

(h)

2

15

1

05

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Computational and Mathematical Methods in Medicine 9

5

10

15

20

5 10 15 20(mm)

(mm

)Order = 3

(a)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 4

(b)

Order = 5

5

10

15

20

5 10 15 20(mm)

(mm

)

2

15

1

05

(c)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 6

(d)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 7

(e)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 8 2

15

1

05

(f)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 9

(g)

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 10

(h)

2

15

1

05

5

10

15

20

5 10 15 20(mm)

(mm

)

Order = 11

(i)

Figure 8 ((a)ndash(i)) Examples of ICBEpa images of pork tenderloin postheating for 400 s constructed using polynomial approximations ofdifferent orders

6 Conclusion

In this study we have proposed a new CBE imaging methodbased on the combination of the sliding window techniqueand the polynomial approximation (ie ICBEpa image)to successfully implement the visualization of temperaturedistribution in the ablated tissue The ICBEpa approach isan aliasing-independent and speckle-free temperature imagethat visualizes temperature profile with no requirement forecho shift tracking and compensation indicating the poten-tial clinical application of CBE imaging in guidance of tissueablation and other thermal therapies

Acknowledgments

This work was supported in part by the National ScienceCouncil (Taiwan) under Grant no NSC100-2628-E-182-003-MY2 and the Chang Gung Memorial Hospital (LinkouTaiwan) under Grant no CMRPD1C0161 This work was alsosupported by the Chang Gung Medical Research Program(CMRP) for Proton Therapy Basic Research (Grant noCMRPD1C0661)

References

[1] S-H Wang C-W Wei S-H Jee and P-C Li ldquoQuantitativethermal imaging for plasmonic photothermal therapyrdquo Journalof Medical and Biological Engineering vol 31 no 6 pp 387ndash3932011

[2] E L Jones J R Oleson L R Prosnitz et al ldquoRandomized trialof hyperthermia and radiation for superficial tumorsrdquo Journalof Clinical Oncology vol 23 no 13 pp 3079ndash3085 2005

[3] E G Moros P M Corry and C G Orton ldquoThermoradio-therapy is underutilized for the treatment of cancerrdquo MedicalPhysics vol 34 no 1 pp 1ndash4 2007

[4] J Gellermann W Wlodarczyk A Feussner et al ldquoMethodsand potentials of magnetic resonance imaging for monitoringradiofrequency hyperthermia in a hybrid systemrdquo InternationalJournal of Hyperthermia vol 21 no 6 pp 497ndash513 2005

[5] B D De Senneville B Quesson and C T W Moonen ldquoMag-netic resonance temperature imagingrdquo International Journal ofHyperthermia vol 21 no 6 pp 515ndash531 2005

[6] R M Arthur D Basu Y Guo J W Trobaugh and E GMoros ldquo3-D in vitro estimation of temperature using thechange in backscattered ultrasonic energyrdquo IEEE Transactions

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

10 Computational and Mathematical Methods in Medicine

on Ultrasonics Ferroelectrics and Frequency Control vol 57 no8 pp 1724ndash1733 2010

[7] R Maass-Moreno and C A Damianou ldquoNoninvasive temper-ature estimation in tissue via ultrasound echo-shifts Part IAnalytical modelrdquo Journal of the Acoustical Society of Americavol 100 no 4 pp 2514ndash2521 1996

[8] R Maass-Moreno C A Damianou and N T Sanghvi ldquoNon-invasive temperature estimation in tissue via ultrasound echo-shifts Part II In vitro studyrdquo Journal of the Acoustical Society ofAmerica vol 100 no 4 pp 2522ndash2523 1996

[9] C A Damianou N T Sanghvi F J Fry and R Maass-MorenoldquoDependence of ultrasonic attenuation and absorption in dogsoft tissues on temperature and thermal doserdquo Journal of theAcoustical Society of America vol 102 no 1 pp 628ndash634 1997

[10] W L Straube and R Martin Arthur ldquoTheoretical estimation ofthe temperature dependence of backscattered ultrasonic powerfor noninvasive thermometryrdquo Ultrasound in Medicine andBiology vol 20 no 9 pp 915ndash922 1994

[11] R M Arthur W L Straube J D Starman and E G MorosldquoNoninvasive temperature estimation based on the energy ofbackscattered ultrasoundrdquo Medical Physics vol 30 no 6 pp1021ndash1029 2003

[12] R M Arthur W L Straube J W Trobaugh and E G MorosldquoNon-invasive estimation of hyperthermia temperatures withultrasoundrdquo International Journal of Hyperthermia vol 21 no6 pp 589ndash600 2005

[13] R M Arthur J W Trobaugh W L Straube and E GMoros ldquoTemperature dependence of ultrasonic backscatteredenergy in motion-compensated imagesrdquo IEEE Transactions onUltrasonics Ferroelectrics and Frequency Control vol 52 no 10pp 1644ndash1652 2005

[14] J W Trobaugh R M Arthur W L Straube and E G MorosldquoA simulation model for ultrasonic temperature imaging usingchange in backscattered energyrdquo Ultrasound in Medicine andBiology vol 34 no 2 pp 289ndash298 2008

[15] C Simon P Vanbaren and E S Ebbini ldquoTwo-dimensionaltemperature estimation using diagnostic ultrasoundrdquo IEEETransactions on Ultrasonics Ferroelectrics and Frequency Con-trol vol 45 no 4 pp 1088ndash1099 1998

[16] H-L Liu M-L Li T-C Shih et al ldquoInstantaneous frequency-based ultrasonic temperature estimation during focused ultra-sound thermal therapyrdquo Ultrasound in Medicine and Biologyvol 35 no 10 pp 1647ndash1661 2009

[17] X Liu X Gong C Yin J Li and D Zhang ldquoNoninva-sive estimation of temperature elevations in biological tissuesusing acoustic nonlinearity parameter imagingrdquo Ultrasound inMedicine and Biology vol 34 no 3 pp 414ndash424 2008

[18] P-H Tsui Y-T Chien H-L Liu Y-C Shu and W-S ChenldquoUsing ultrasound CBE imaging without echo shift compensa-tion for temperature estimationrdquo Ultrasonics vol 52 pp 925ndash935 2012

[19] I C Enoch E Ozil and R C Birkebak ldquoPolynomial approx-imation solution of heat transfer by conduction and radia-tion in a one-dimensional absorbing emitting and scatteringmediumrdquo Numerical Heat Transfer vol 5 no 3 pp 353ndash3581982

[20] P Keshavarz and M Taheri ldquoAn improved lumped analysis fortransient heat conduction by using the polynomial approxima-tion methodrdquo Heat and Mass Transfer vol 43 no 11 pp 1151ndash1156 2007

[21] RKubotaN Suetake EUchinoGHashimoto THiro andMMatsuzaki ldquopolynomial-based boundary extraction of plaque

in intravascular ultrasound image by using its local statisticalinformationrdquo ICIC Express Letters vol 2 pp 387ndash393 2008

[22] R Seip and E S Ebbini ldquoNoninvasive estimation of tissue tem-perature response to heating fields using diagnostic ultrasoundrdquoIEEE Transactions on Biomedical Engineering vol 42 no 8 pp828ndash839 1995

[23] UM Hamper M R DeJong C I Caskey and S Sheth ldquoPowerdoppler imaging clinical experience and correlation with colordoppler US and other imaging modalitiesrdquo Radiographics vol17 no 2 pp 499ndash513 1997

[24] K K Shung ldquoDiagnostic ultrasound past present and futurerdquoJournal of Medical and Biological Engineering vol 31 no 6 pp371ndash374 2011

[25] P H Tsui Y C Shu W S Chen H L Liu I T Hsiaoand Y T Chien ldquoUltrasound temperature estimation based onprobability variation of backscatter datardquo Medical Physics vol39 pp 2369ndash2385 2012

[26] G Ye J A Noble and P P Smith ldquoAmodel-based displacementoutlier removal algorithm for ultrasonic temperature estima-tionrdquo IEEE Ultrasonics Symposium Proceedings pp 2080ndash20832008

[27] G Ye P P Smith and J A Noble ldquoModel-based ultrasoundtemperature visualization during and following hifu exposurerdquoUltrasound in Medicine and Biology vol 36 no 2 pp 234ndash2492010

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MEDIATORSINFLAMMATION

of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Behavioural Neurology

EndocrinologyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Disease Markers

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

OncologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Oxidative Medicine and Cellular Longevity

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational and Mathematical Methods in Medicine

OphthalmologyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Diabetes ResearchJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Research and TreatmentAIDS

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Gastroenterology Research and Practice

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom