research article ultrasound shear wave simulation of...

Research ArticleUltrasound Shear Wave Simulation of Breast TumorUsing Nonlinear Tissue Elasticity

Dae Woo Park12

1Department of Biomedical Engineering University of Michigan Ann Arbor MI 48105 USA2Department of Mechanical Engineering University of Michigan Ann Arbor MI 48105 USA

Correspondence should be addressed to Dae Woo Park bigrainumichedu

Received 5 March 2016 Revised 18 April 2016 Accepted 3 May 2016

Academic Editor Po-Hsiang Tsui

Copyright copy 2016 Dae Woo ParkThis is an open access article distributed under theCreativeCommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Shear wave elasticity imaging (SWEI) can assess the elasticity of tissues but the shear modulus estimated in SWEI is often lesssensitive to a subtle change of the stiffness that produces only small mechanical contrast to the background tissues Because mostsoft tissues exhibit mechanical nonlinearity that differs in tissue types mechanical contrast can be enhanced if the tissues arecompressed In this study a finite element- (FE-) based simulation was performed for a breast tissue model which consists of acircular (119863 10mm hard) tumor and surrounding tissue (soft)The SWEI was performed with 0 to 30 compression of the breasttissue model The shear modulus of the tumor exhibited noticeably high nonlinearity compared to soft background tissue above10 overall applied compression As a result the elastic modulus contrast of the tumor to the surrounding tissue was increasedfrom 046 at 0 compression to 145 at 30 compression

1 Introduction

Pathological changes such as growth of malignant tumors insoft tissues result in increasing tissue stiffness and this pro-duces elasticity contrast of tumors to the surrounding healthytissues [1ndash3] Sarvazyan et al [4] introduced shear wave elas-ticity imaging (SWEI) for noninvasive diagnosis of changesin tissuemechanical propertiesThe propagation speed of theshear wave is directly related to the underlying tissue shearmodulus Shear waves in soft tissues can be generated byeither direct mechanical vibration [5] or transient ultrasound(US) radiation force excitation [4 6 7]The local tissue shearmodulus can be reconstructed from the displacement fieldof shear waves using an inversion of the Helmholtz equation[6 7] or time-of-flight (TOF) including random sampleconsensus [8] and the radon sum [9] With the continuedprogress of technology and system development SWEI hasbeen investigated for diagnosing some diseases mainly fordetecting breast cancer [10] and liver cirrhosis [11 12] Insome cases pathologic characteristic changes of progressedmalignant lesions have been successfully differentiated bySWEI from the normal surrounding soft tissues However

SWEI may not be sensitive enough to detect small stiffnesschanges especially in early stages of pathological changes[13]

It is known that most soft tissues exhibit significant strainhardening and elastic modulus of tissue can no longer beconsidered constant at large deformation [14] In additionthe strain hardening varies for different tissue types sinceeach tissue type has specific nonlinear elastic parameters [15]The nonlinear characteristics of breast fibrosis and prostatecancer tissues have been demonstrated in their ex vivomechanical measurements [3 16] and these lesions could bedifferentiated better from surrounding normal tissues whenbeing compressed The tissue nonlinearity has been appliedto compressional US elasticity imaging and an inclusion wasdetected with improved contrast and contrast-to-noise ratioin vitro and in vivo animal study [17] The SWEI combinedwith an external compression was proposed and nonlinearshear modulus parameters have been investigated using invitro phantom and ex vivo liver samples [18] This nonlinearSWEI approach has been applied to ex vivo canine liversmeasurements and the increase of shear wave speed waspresented with an increase of hepatic pressure [19] In our

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2016 Article ID 2541325 6 pageshttpdxdoiorg10115520162541325

2 Computational and Mathematical Methods in Medicine

Transducer

TumorSurrounding tissue

Body force

Rib cage

20mm

38mm

Y

X

Figure 1 Schematic diagram of the breast tissue model withdimensions and boundary conditions for finite element simulations

previous study [20] the nonlinear characterization of tissuestiffness changes was demonstrated through in vitro phantommeasurements using SWEI in combination with externallyapplied force We found that the elastic modulus contrastof the inclusion to the surrounding phantom block wasincreased with an increase of the applied force

In this study the feasibility of SWEI combinedwith exter-nal compression for breast tumor detection was investigatedusing in silico finite element (FE) simulation A FE hyperelas-tic breast tissue with a tumor model was designed The shearmodulus of the model was estimated at each compressionlevel from 0 to 30 using TOF-based algorithms [9] Theelastic modulus contrast of the target tumor compared tosurrounding tissue was calculated and analyzed over thecompression levels

2 Materials and Methods

21 Finite Element Modeling A 2D FE breast tissue modelwas developed using a commercially available software pack-age (ABAQUS V613 Simulia Dassault Sytemes RI USA)Figure 1 shows the schematic diagram of the breast tissuemodel with dimensions and boundary conditions for FEsimulations A semiellipse shape of the breast model whichwas 100mm in diameter and 40mm in height was designedThe shape of the tumor field was assumed to be a circle with10mm diameter The tumor was located 20mm from thebottom surface and 38mm from the right side of the modelas shown in Figure 1 The breast model was meshed using2D triangular plane strain elements The bottom boundariesof the breast tissue were fixed in all directions by a sternum(rib cage) to prevent any bulk motion from the local bodyforce excitation for shear wave generation A displacementboundary condition was applied on the top surface of thebreast tissue by a rigid transducer of 45 times 14mmThe contactbetween the surface of the transducer and top surface ofthe breast tissue was modeled as frictionless based on anassumption that ultrasound gel exerts no friction To simulatethe acoustic radiation force excitation body forces wereapplied downward over an area of 3mmwidth through entiredepth of the FE model for 180 120583s to create planar shearwaves at each compression level from 0 to 30 which wascalculated in the middle of the breast model No shear wave

Table 1 Hyperelastic parameters of malignant tumor and benignbreast tissue

Variable Malignant tumor Benign breast tissue11986210

141 times 10minus3

0375 times 10minus3

11986201

141 times 10minus3

0375 times 10minus3

11986211

171 times 10minus2

00256 times 10minus1

11986220

166 times 10minus2


11986202

166 times 10minus2


attenuation was considered within the scope of the studyThe119884 displacements of shear waves over time were extracted overthe entire 119883 (across the body force direction) extent of themesh The temporal and spatial resolution of FE simulationwas 125 120583sec and 02 times 02mm respectively

22 Nonlinear Material Parameters The hyperelastic mate-rial model (polynomial strain-energy function) wasemployed for the tumor and surrounding tissue Thepolynomial strain-energy function [21] which is widely usedin modeling soft tissues such as breast is defined as

119880 =

119873

sum

119894+119895=1

119862119894119895(1198681minus 3)119894

(1198682minus 3)119895

+

119873

sum

119894=1

1

119863119894

(119869el minus 1)2119894

(1)

where119880 is a selected strain energy function and 1198681and 1198682are

the first and second strain invariants respectively 119869el is theelastic volume strain and 119863

119894is a compressibility coefficient

119873 refers to the order of themodel and119873 = 2 in this study119862119894119895

represents the hyperelastic material parameters which deter-mine the intrinsic nonlinear elastic properties of the tissuesThe hyperelastic material parameters 119862

119894119895 were chosen from

previous ex vivo breast tissue measurements [22] Poissonrsquosratio was selected as 0495 based on incompressible tissueassumptions Table 1 presents the dimensionless nonlinearparameters of the normal breast tissue and the malignanttumor

23 SWEI-Modulus Reconstruction To remove wave reflec-tions near the tumor area a 1D directional filter [23]which identifies the backward-moving shear waves in 119883direction and eliminates the waves in the frequency domainwas applied to the 119884 displacements versus time data TOFmethods were used to determine the shear wave speed from119884 displacements field by estimating shear wave arrival timeat each 119883 position and calculating the slope of the positionversus time data [9] The slope was calculated using datafrom the positions within a 3mm kernel in 119883 direction thatwas stepped across the 119883 range Shear wave speeds werereconstructed using a 3mm kernel in 119884 direction and thensmoothed using a 2mm times 2mmmedian filter

The shear modulus was determined from the estimatedshear wave speeds as

119866 = 1205881198882 (2)

where 120588 is density ofmedium and 119888 is speed of the shear waveEach shearmodulus for the tumor and the surrounding tissue

Computational and Mathematical Methods in Medicine 3

Insideinclusion

Outsideinclusion

Time (ms)

05

03

01

1 2 3minus03

minus01

Ydi

spla

cem

ent (120583

m)

233mm202mm

133mm102mm

(a)

Insideinclusion

Outsideinclusion

Time (ms)1 2 3

05

03

01

minus03

minus01

Ydi

spla

cem

ent (120583

m)

233mm202mm

133mm102mm

(b)

Figure 2 119884 displacements versus time profiles of a finite element tissue model at (a) 0 and (b) 30 compression at four119883 positions

was spatially averaged within the area of the tumor size Theaverage shear moduli in the tumor and surrounding tissuewere compared at each compression level up to 30

3 Results

Figure 2 shows 119884 displacements versus time profiles of a FEtissue model at (a) 0 and (b) 30 compression at four 119883positions Two 119883 positions (102mm and 133mm from themiddle of breast) marked with red dashed line and red solidline were selected from inside of the tumorThe other two119883positions (202mm and 233mm from the middle of breast)markedwith blue dashed line and blue solid line were chosenfrom outside of the tumor For both inside and outside of thetumor distance between two 119883 positions was kept the samefor 31mm Higher shear wave speed was estimated insidethe tumor at 0 compression The rate of shear wave speedincrease was distinctively higher by factor of 13 inside theinclusion from 0 to 30 compression

Figure 3(a) presents reconstructed shear modulus mapsnear a tumor region in a FE breast tissue model with 010 20 and 30 compression The black dashed circlerepresents the boundary of a tumor and surrounding tissueThe increase of shear modulus for both tumor and sur-rounding tissue was observed with increase of compressionlevel from 0 to 30 The shear modulus calculated byTOF was spatially averaged in the tumor and surroundingtissue depicted in Figure 3(a) In Figures 3(b) and 3(c) theaverage shear moduli and developed strains for the tumor(diagonal stripe pattern bar) and surrounding tissue (solid

bar) versus compression levels up to 30 are comparedThe error bar represents the standard deviation of spatiallyaveraged shear modulus for the tumor and surroundingtissue At 0 compression the average shear modulus of thetumor was 6 kPa and it sharply increased up to 41 kPa at 30compression The average strain of the tumor was 9 at 10compression and it increased up to 21 at 30 compressionOn the other hand the average shearmodulus of surroundingtissue was 4 kPa at 0 compression and it almost linearlyincreased up to 17 kPa at 30 compressionThe average strainof the surrounding tissue was 10 at 10 compression and itincreased up to 28 at 30 compression

Shear modulus contrast 119862 was calculated for differentcompression levels of 0 10 20 and 30 which isdefined as

119862 =

10038161003816100381610038161003816100381610038161003816

119866tumor minus 119866surr119866surr

10038161003816100381610038161003816100381610038161003816

(3)

where 119866tumor and 119866surr are the corresponding average shearmodulus in the tumor and surrounding tissue respectivelyThe shear modulus contrasts were 046 071 133 and 145at 0 10 20 and 30 compressions respectively Thusthe elastic modulus contrast of the tumor to the surroundingtissue was enhanced by the compression and this allowsmuch better identification of the tumor

4 Discussion

The enhancement of the elastic modulus contrast for SWEIwas demonstrated through a FE simulation using a new


Appl

ied

strai

n (

)

10

0

20

30

Shear modulus (kPa)40

0(a)

50

40

30

20

10

0

Shea

r mod

ulus

(kPa

)

0 10 20 30

Compression ()

Surrounding tissueTumor

(b)

30

20

0

10

Dev

elope

d str

ain

()

0 10 20 30

Compression ()


(c)

Figure 3 Shear wave elasticity imaging on a finite element breast tissue model (a) Reconstructed shear modulus map near a tumor regionwith 0 10 20 and 30 compression (applied strains) Black dashed circle represents the boundary of a tumor and surrounding tissue(b) Average shear modulus versus compression plot for the tumor and surrounding tissue (c) Average developed strain versus compressionplot for the tumor and surrounding tissue

approach of nonlinear SWEI in combination with applyingexternal compression The shear modulus of a breast tumorexhibited noticeably high nonlinearity compared to softbackground tissue above 10 overall applied compressionAs a result the tumor became more visible with increasedcontrast as shown in the reconstructed shear modulus mapin Figure 3(a)

The rate of shear modulus increase was small similarbetween the tumor and surrounding tissue for the appliedcompression level below 10 as shown in Figure 3(b) Thesurrounding tissue plays a significant role in balancing theforce under relatively small applied compression A largeportion of the applied force must have been absorbed bythe large soft surrounding tissue relieving exerting stresson the small tumor The rate of shear modulus increase in

the tumor became higher than the surrounding tissue as theoverall applied compression increased from 10 to 30Thisis because the stress inside the target tumor increased moreonce the surrounding background tissue became stiff over the10 compression

There are two reasons we limited the compression levelto the maximum of 30 in this study Firstly the developedstrains inside the tumor and surrounding tissue that werecalculated from 119884 displacements were 21 and 28 respec-tively with 30 overall applied compression as shown inFigure 3(c) Such levels of developed strainswere high enoughfor breast tissues to exhibit strong nonlinearity Secondlythe 30 applied compression remains within the practicalrange for the clinical application since most soft tissues startexhibiting nonlinearity over 5ndash10 strain [14] and the elastic


modulus contrast enhancement can be achieved withoutcausing any pain by applying excessive deformation on theskin

In this study the acoustic radiation force excitation wassimulated using body forces applied through entire depth ofthe FE model In actual SWEI two quasi-planar shear waveswhich are not parallel to each other are normally generatedusing successive focusing ultrasonic beam at different depths[7] To compute the elastic modulus contrast of the tumorto surrounding tissues under idealistic conditions parallelplanar shear waves were generated using the body forces inthe FE simulation The shear modulus computation dependson the shape of shear wave front [7] and the elastic moduluscontrast of tissues may change if it is computed using thequasi-planar shear waves Thus the effect of quasi-planarshear waves on the elastic modulus contrast needs to befurther investigated by the FEmodel using the actual acousticradiation force excitation

The practical application of the nonlinear SWEI approachwould be identifying lesions by using different nonlinearitycharacteristics for different tissue types In breast fattytissues exhibit almost linear stress-strain relationship whiledisease tissues such as fibrous ductal and intraductal tumorshave their specific tissue nonlinearity characteristics [16]The prostate tumor also has its specific tissue nonlinearitythat is differentiated from surrounding normal tissues [3]The shear modulus contrast of lesions would vary due todifferent nonlinearity characteristics for different tissue typesInvestigating relations between the shear modulus contrastand tissue nonlinear parameters in different tissues wouldhelp for nonlinear SWEI application to potentially classifydisease tissues The nonlinear SWEI approach may be ableto differentiate lesions by applying enough compressionthat can create a large shear modulus contrast betweendifferent disease tissue types and this can be applied tobreast mammography to improve accuracy of diagnosis[24]

There are several limitations of our FE simulationapproach Firstly the elasticmodulus contrast to surroundingtissue computed from the 2D FE model may not representthe elastic modulus contrast of the 3D tissue The tissueelasticity usually varies in the out-of-plane direction as wellas in a 2D plane The elastic modulus contrast may alsochange according to locations of compression in out of planedirection Secondly the shear wave attenuation commonlyoccurs in human tissues due to viscosity [25] and this was notconsidered The amplitude of the shear wave decreases withthe propagation due to shear wave attenuation [25] Thusthe signal-to-noise ratio also decreases with respect to thelateral distance from the location of acoustic force excitation[25] This may affect the shear modulus computation andthe elastic modulus contrast of the tumor to surroundingtissues Thirdly the shear modulus was computed fromthe displacement fields of shear waves without includingultrasonic noise such as jitter The jitter commonly existsin ultrasonically tracked displacement data and substantialfiltering is necessary before processing the data [26] Thefiltering may affect shear modulus reconstruction especiallyat the boundary of a tumor in the tissue model Therefore

these limitations should be considered in a future version ofthe FE model for nonlinear SWEI simulation

The nonlinear SWEI approach has several limitations tobe considered for practical use of this technology Firstlymechanical compression of tissue is necessary for the nonlin-ear SWEI and this limits its applications to areas where clearphysical access can be achieved [27] Secondly consistentforces are necessary to maintain the mechanical compressionof tissue A target inclusion can be out of scanning plane withexcessive compressions and this may change the mechanicalcontrast to background tissues Thirdly the strain generationinside the target inclusion is related to the stress distributionthat depends on the applied force and surrounding anatomy[27] Thus the internal strains in the inclusion may notdevelop high enough to exhibit nonlinearity if the targetinclusion is located too deep from the skin Due to theselimitations the application of nonlinear SWEI approachwould be restricted to skin or organs close to skin surface

In future studies we will perform the nonlinear FEsimulation by changing the boundary conditions of tissuemodel such as tumor size and tumor location The elasticmodulus contrast to surrounding tissuewould vary accordingto the change of stress and strain distributions in tissues Thestress and strain distributions in tissues during compressionare closely related to the boundary conditions In this studythe average stresses of tumor and surrounding tissues were26 kPa and 14 kPa at 30 compression respectivelyThe idealshear modulus contrast computed using the stresses andstrains of the tumor and surrounding tissues was 145 at30 compression Therefore conducting the FE simulationby varying the boundary conditions would be necessary toestablish the nonlinear SWEI application for various tumortypes

5 Conclusion

The in silico FE simulation of nonlinear SWEI combined withexternal deformation demonstrated remarkable enhance-ment of the elastic modulus contrast of breast tumor tosurrounding tissue The encouraging results from in silicoFE simulation warrant further investigation of this techniqueusing disease relevant tissues ex vivo and eventually in vivoWith further development and evaluation the nonlinearSWEI may allow noninvasively assessing and monitoringsubtle stiffness changes in breast tissues due to the growth ofmalignant tumors at early disease stage

Competing Interests

The author declares that they have no competing interests

References

[1] L H Jansen ldquoThe structure of the connective tissue anexplanation of the symptoms of the Ehlers-Danlos syndromerdquoDermatologica vol 110 no 2 pp 108ndash120 1955

[2] M L Palmeri and K R Nightingale ldquoAcoustic radiation force-based elasticity imaging methodsrdquo Interface Focus vol 1 no 4pp 553ndash564 2011


[3] A R Skovoroda A N Klishko D A Gusakyan et alldquoQuantitative analysis of the mechanical characteristics ofpathologically changed soft biological tissuesrdquo Biophysics vol40 no 6 pp 1359ndash1364 1995

[4] A P SarvazyanOV Rudenko S D Swanson J B Fowlkes andS Y Emelianov ldquoShearwave elasticity imaging a newultrasonictechnology of medical diagnosticsrdquoUltrasound inMedicine andBiology vol 24 no 9 pp 1419ndash1435 1998

[5] L Sandrin B Fourquet J-M Hasquenoph et al ldquoTransientelastography a new noninvasive method for assessment ofhepatic fibrosisrdquo Ultrasound in Medicine and Biology vol 29no 12 pp 1705ndash1713 2003

[6] K Nightingale S McAleavey and G Trahey ldquoShear-wavegeneration using acoustic radiation force in vivo and ex vivoresultsrdquo Ultrasound in Medicine and Biology vol 29 no 12 pp1715ndash1723 2003

[7] J Bercoff M Tanter andM Fink ldquoSupersonic shear imaging anew technique for soft tissue elasticity mappingrdquo IEEE Transac-tions on Ultrasonics Ferroelectrics and Frequency Control vol51 no 4 pp 396ndash409 2004

[8] M H Wang M L Palmeri V M Rotemberg N C Rouzeand K R Nightingale ldquoImproving the robustness of time-of-flight based shear wave speed reconstruction methods usingRANSAC in human liver in vivordquo Ultrasound in Medicine andBiology vol 36 no 5 pp 802ndash813 2010

[9] N C Rouze M HWang M L Palmeri and K R NightingaleldquoRobust estimation of time-of-flight shear wave speed using aradon sum transformationrdquo IEEE Transactions on UltrasonicsFerroelectrics and Frequency Control vol 57 no 12 pp 2662ndash2670 2010

[10] M Tanter J Bercoff A Athanasiou et al ldquoQuantitative assess-ment of breast lesion viscoelasticity initial clinical results usingsupersonic shear imagingrdquoUltrasound inMedicine and Biologyvol 34 no 9 pp 1373ndash1386 2008

[11] S Chen W Sanchez M R Callstrom et al ldquoAssessment ofliver viscoelasticity by using shear waves induced by ultrasoundradiation forcerdquo Radiology vol 266 no 3 pp 964ndash970 2013

[12] M L Palmeri M H Wang J J Dahl K D Frinkley and K RNightingale ldquoQuantifying hepatic shear modulus in vivo usingacoustic radiation forcerdquo Ultrasound in Medicine and Biologyvol 34 no 4 pp 546ndash558 2008

[13] T Poynard M Munteanu E Luckina et al ldquoLiver fibrosisevaluation using real-time shear wave elastography applicabil-ity and diagnostic performance using methods without a goldstandardrdquo Journal of Hepatology vol 58 no 5 pp 928ndash9352013

[14] S Y Emelianov R Q ErkampM A Lubinski A R Skovorodaand M OrsquoDonnell ldquoNon-linear tissue elasticity adaptive elas-ticity imaging for large deformationsrdquo in Proceedings of the IEEEUltrasonics Symposium vol 2 pp 1753ndash1756 October 1998

[15] R Q Erkamp A R Skovoroda S Y Emelianov and MOrsquoDonnell ldquoMeasuring the nonlinear elastic properties oftissue-like phantomsrdquo IEEE Transactions on Ultrasonics Ferro-electrics and Frequency Control vol 51 no 4 pp 410ndash419 2004

[16] T A Krouskop T M Wheeler F Kallel B S Garra andT Hall ldquoElastic moduli of breast and prostate tissues undercompressionrdquo Ultrasonic Imaging vol 20 no 4 pp 260ndash2741998

[17] R Q Erkamp S Y Emelianov A R Skovoroda and MOrsquoDonnell ldquoNonlinear elasticity imaging theory and phantomstudyrdquo IEEE Transactions on Ultrasonics Ferroelectrics andFrequency Control vol 51 no 5 pp 532ndash539 2004

[18] H Latorre-Ossa J-L Gennisson E De Brosses and MTanter ldquoQuantitative imaging of nonlinear shear modulus bycombining static elastography and shear wave elastographyrdquoIEEE Transactions on Ultrasonics Ferroelectrics and FrequencyControl vol 59 no 4 pp 833ndash839 2012

[19] V Rotemberg B ByramM Palmeri MWang and K Nightin-gale ldquoUltrasonic characterization of the nonlinear properties ofcanine livers by measuring shear wave speed and axial strainwith increasing portal venous pressurerdquo Journal of Biomechan-ics vol 46 no 11 pp 1875ndash1881 2013

[20] DW Park and K Kim ldquoElastic modulus contrast enhancementin shear wave imaging using mechanical nonlinearity in vitrotissue mimicking phantom studyrdquo in Proceedings of the IEEEInternational Ultrasonics Symposium (ULTSYM rsquo14) pp 2335ndash2338 Chicago Ill USA September 2014

[21] R S Rivlin and D W Saunders ldquoLarge elastic deformationsof isotropic materials VII Experiments on the deformationof rubberrdquo Philosophical Transactions of the Royal Society AMathematical Physical and Engineering Sciences vol 243 no865 pp 251ndash288 1951

[22] J J OrsquoHagan and A Samani ldquoMeasurement of the hyperelasticproperties of 44 pathological ex vivo breast tissue samplesrdquoPhysics in Medicine and Biology vol 54 no 8 pp 2557ndash25692009

[23] A Manduca D S Lake S A Kruse and R L Ehman ldquoSpatio-temporal directional filtering for improved inversion of MRelastography imagesrdquo Medical Image Analysis vol 7 no 4 pp465ndash473 2003

[24] W A Berg L Gutierrez M S NessAiver et al ldquoDiagnosticaccuracy of mammography clinical examination US and MRimaging in preoperative assessment of breast cancerrdquoRadiologyvol 233 no 3 pp 830ndash849 2004

[25] T Deffieux G Montaldo M Tanter and M Fink ldquoShear wavespectroscopy for in vivo quantification of human soft tissuesvisco-elasticityrdquo IEEE Transactions on Medical Imaging vol 28no 3 pp 313ndash322 2009

[26] N C Rouze M HWang M L Palmeri and K R NightingaleldquoParameters affecting the resolution and accuracy of 2D quan-titative shear wave imagesrdquo IEEE Transactions on UltrasonicsFerroelectrics and Frequency Control vol 59 no 8 pp 1729ndash1740 2012

[27] P N T Wells and H-D Liang ldquoMedical ultrasound imagingof soft tissue strain and elasticityrdquo Journal of the Royal SocietyInterface vol 8 no 64 pp 1521ndash1549 2011

Submit your manuscripts athttpwwwhindawicom

Stem CellsInternational

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


MEDIATORSINFLAMMATION

of


Behavioural Neurology

EndocrinologyInternational Journal of



Disease Markers


BioMed Research International

OncologyJournal of



Oxidative Medicine and Cellular Longevity


PPAR Research

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Immunology ResearchHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

ObesityJournal of



Computational and Mathematical Methods in Medicine

OphthalmologyJournal of


Diabetes ResearchJournal of



Research and TreatmentAIDS


Gastroenterology Research and Practice


Parkinsonrsquos Disease

Evidence-Based Complementary and Alternative Medicine

Volume 2014Hindawi Publishing Corporationhttpwwwhindawicom


Transducer

TumorSurrounding tissue

Body force

Rib cage

20mm

38mm

Y

X

Figure 1 Schematic diagram of the breast tissue model withdimensions and boundary conditions for finite element simulations

previous study [20] the nonlinear characterization of tissuestiffness changes was demonstrated through in vitro phantommeasurements using SWEI in combination with externallyapplied force We found that the elastic modulus contrastof the inclusion to the surrounding phantom block wasincreased with an increase of the applied force

In this study the feasibility of SWEI combinedwith exter-nal compression for breast tumor detection was investigatedusing in silico finite element (FE) simulation A FE hyperelas-tic breast tissue with a tumor model was designed The shearmodulus of the model was estimated at each compressionlevel from 0 to 30 using TOF-based algorithms [9] Theelastic modulus contrast of the target tumor compared tosurrounding tissue was calculated and analyzed over thecompression levels

2 Materials and Methods

21 Finite Element Modeling A 2D FE breast tissue modelwas developed using a commercially available software pack-age (ABAQUS V613 Simulia Dassault Sytemes RI USA)Figure 1 shows the schematic diagram of the breast tissuemodel with dimensions and boundary conditions for FEsimulations A semiellipse shape of the breast model whichwas 100mm in diameter and 40mm in height was designedThe shape of the tumor field was assumed to be a circle with10mm diameter The tumor was located 20mm from thebottom surface and 38mm from the right side of the modelas shown in Figure 1 The breast model was meshed using2D triangular plane strain elements The bottom boundariesof the breast tissue were fixed in all directions by a sternum(rib cage) to prevent any bulk motion from the local bodyforce excitation for shear wave generation A displacementboundary condition was applied on the top surface of thebreast tissue by a rigid transducer of 45 times 14mmThe contactbetween the surface of the transducer and top surface ofthe breast tissue was modeled as frictionless based on anassumption that ultrasound gel exerts no friction To simulatethe acoustic radiation force excitation body forces wereapplied downward over an area of 3mmwidth through entiredepth of the FE model for 180 120583s to create planar shearwaves at each compression level from 0 to 30 which wascalculated in the middle of the breast model No shear wave

Table 1 Hyperelastic parameters of malignant tumor and benignbreast tissue

Variable Malignant tumor Benign breast tissue11986210

141 times 10minus3

0375 times 10minus3

11986201

141 times 10minus3

0375 times 10minus3

11986211

171 times 10minus2


11986220

166 times 10minus2


11986202

166 times 10minus2


attenuation was considered within the scope of the studyThe119884 displacements of shear waves over time were extracted overthe entire 119883 (across the body force direction) extent of themesh The temporal and spatial resolution of FE simulationwas 125 120583sec and 02 times 02mm respectively

22 Nonlinear Material Parameters The hyperelastic mate-rial model (polynomial strain-energy function) wasemployed for the tumor and surrounding tissue Thepolynomial strain-energy function [21] which is widely usedin modeling soft tissues such as breast is defined as

119880 =

119873

sum

119894+119895=1

119862119894119895(1198681minus 3)119894

(1198682minus 3)119895

+

119873

sum

119894=1

1

119863119894

(119869el minus 1)2119894

(1)

where119880 is a selected strain energy function and 1198681and 1198682are

the first and second strain invariants respectively 119869el is theelastic volume strain and 119863

119894is a compressibility coefficient

119873 refers to the order of themodel and119873 = 2 in this study119862119894119895

represents the hyperelastic material parameters which deter-mine the intrinsic nonlinear elastic properties of the tissuesThe hyperelastic material parameters 119862

119894119895 were chosen from

previous ex vivo breast tissue measurements [22] Poissonrsquosratio was selected as 0495 based on incompressible tissueassumptions Table 1 presents the dimensionless nonlinearparameters of the normal breast tissue and the malignanttumor

23 SWEI-Modulus Reconstruction To remove wave reflec-tions near the tumor area a 1D directional filter [23]which identifies the backward-moving shear waves in 119883direction and eliminates the waves in the frequency domainwas applied to the 119884 displacements versus time data TOFmethods were used to determine the shear wave speed from119884 displacements field by estimating shear wave arrival timeat each 119883 position and calculating the slope of the positionversus time data [9] The slope was calculated using datafrom the positions within a 3mm kernel in 119883 direction thatwas stepped across the 119883 range Shear wave speeds werereconstructed using a 3mm kernel in 119884 direction and thensmoothed using a 2mm times 2mmmedian filter

The shear modulus was determined from the estimatedshear wave speeds as

119866 = 1205881198882 (2)

where 120588 is density ofmedium and 119888 is speed of the shear waveEach shearmodulus for the tumor and the surrounding tissue


Insideinclusion

Outsideinclusion

Time (ms)

05

03

01

1 2 3minus03

minus01

Ydi

spla

cem

ent (120583

m)

233mm202mm

133mm102mm

(a)

Insideinclusion

Outsideinclusion

Time (ms)1 2 3

05

03

01

minus03

minus01

Ydi

spla

cem

ent (120583

m)

233mm202mm

133mm102mm

(b)



3 Results





119862 =

10038161003816100381610038161003816100381610038161003816


10038161003816100381610038161003816100381610038161003816

(3)


4 Discussion



Appl

ied

strai

n (

)

10

0

20

30


0(a)

50

40

30

20

10

0

Shea

r mod

ulus

(kPa

)

0 10 20 30

Compression ()


(b)

30

20

0

10

Dev

elope

d str

ain

()

0 10 20 30

Compression ()


(c)














5 Conclusion


Competing Interests


References


































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Insideinclusion

Outsideinclusion

Time (ms)

05

03

01

1 2 3minus03

minus01

Ydi

spla

cem

ent (120583

m)

233mm202mm

133mm102mm

(a)

Insideinclusion

Outsideinclusion

Time (ms)1 2 3

05

03

01

minus03

minus01

Ydi

spla

cem

ent (120583

m)

233mm202mm

133mm102mm

(b)



3 Results





119862 =

10038161003816100381610038161003816100381610038161003816


10038161003816100381610038161003816100381610038161003816

(3)


4 Discussion



Appl

ied

strai

n (

)

10

0

20

30


0(a)

50

40

30

20

10

0

Shea

r mod

ulus

(kPa

)

0 10 20 30

Compression ()


(b)

30

20

0

10

Dev

elope

d str

ain

()

0 10 20 30

Compression ()


(c)














5 Conclusion


Competing Interests


References


































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of

















Appl

ied

strai

n (

)

10

0

20

30


0(a)

50

40

30

20

10

0

Shea

r mod

ulus

(kPa

)

0 10 20 30

Compression ()


(b)

30

20

0

10

Dev

elope

d str

ain

()

0 10 20 30

Compression ()


(c)














5 Conclusion


Competing Interests


References


































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
























5 Conclusion


Competing Interests


References


































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of















































of






Disease Markers



OncologyJournal of





PPAR Research



Journal of

ObesityJournal of
















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