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McGrath, Deirdre, Ravikumar, Nishant, Beltrachini, Leandro, Wilkinson, Iain, Frangi, Alejandro

and Taylor, Zeike 2016. Evaluation of wave delivery methodology for brain MRE: Insights from

computational simulations. Magnetic Resonance in Medicine 78 (1) , pp. 341-356.

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1

EvaluationofWaveDeliveryMethodologyforBrainMRE:Insightsfrom

ComputationalSimulations

DeirdreM.McGrath1,2*

NishantRavikumar1

LeandroBeltrachini1

IainD.Wilkinson2

AlejandroF.Frangi1

ZeikeA.Taylor1

1CISTIBCentreforComputationalImaging&SimulationTechnologiesinBiomedicine,

INSIGNEOInstituteforinsilicoMedicine,

TheUniversityofSheffield,

Sheffield,

UK

2AcademicUnitofRadiology,

FacultyofMedicine,Dentistry&Health,


Sheffield,

UK

*Addressofauthorforcorrespondence:

DeirdreMcGrath,

CentreforComputationalImaging&SimulationTechnologiesinBiomedicine(CISTIB),

DepartmentofElectronicandElectricalEngineering,


2

C14,PamLiversidgeBuilding,

MappinStreet,

Sheffield,

S13JD

Tel:0114-2225398

[email protected]

Note:A.F.FrangiandZ.A.Taylorarejointseniorauthors

Wordcount:

Running head: Simulation of cranial vibration during brain MRE to evaluate wave delivery

methodologies

3

ABSTRACT

Purpose:Magneticresonanceelastography(MRE)of thebrain isbeingexploredasabiomarkerof

neurodegenerativediseasesuchasdementia.However,MREmeasuresforhealthybrainhavevaried

widely.Differingwavedeliverymethodologiesmayhaveinfluencedthis,hencefiniteelement-based

simulationswerecarriedouttoexplorethispossibility.

Methods:Thenaturalfrequenciesofaseriesofcranialmodelswerecalculated,andMRE-associated

vibration was simulated for different wave delivery methods at varying frequency. Displacement

fields and the corresponding brain constitutive properties estimated by standard inversion

techniqueswerecomparedacrossdeliverymethodsandfrequencies.

Results: The deliverymethods producedwidely differentMREdisplacement fields and inversions.

Furthermore, resonancesatnatural frequencies influenced thedisplacementpatterns. Twoof the

wavedeliverymethods(head-cradleandacousticpillow)gaverisetolowerinversionerrors,e.g.,at

90Hztheerrorinthestoragemoduluswas11%lessthanforthebite-barmethod.

Conclusion: Wave delivery has an important impact on brain MRE reliability. Assuming small

variations in brain biomechanics, as recently reported to accompany neurodegenerative disease

(e.g., 7% for Alzheimer's disease), the effect of wave delivery is important. Hence, a consensus

should be established on the optimum methodology, to ensure diagnostic and prognostic

consistency.

KEYWORDS:Magnetic resonance elastography; brain; skull; finite element modeling simulation;

naturalfrequencies;dementia

4

INTRODUCTION

Magnetic resonance elastography (MRE) (1) is a non-invasive method for measuring the

biomechanicalpropertiesofbiologicaltissue.Thisisachievedbydeliveryofmechanicalwavestothe

site of interest, and measurement of the resulting displacement field using MRI. Biomechanical

properties, such as stiffness and viscosity, are reconstructed from the displacement field using

inversionalgorithms.MREofthebrainiscurrentlybeingexploredforthediagnosisofneurological

andneurodegenerativediseasesuchasdementia(2-11).Thisevaluation iscomplicatedbythefact

thattheMREmeasuresobtainedsofarforhealthybrainhavevariedwidely(12-15).Inareviewof

healthybrainMREdata(12)theshearmodulusvaluesreportedforwhitemattervariedbetween2.5

and15.2kPa,andforgreymatterbetween2.8and12.9kPa.Additionally,someMREstudieshave

reportedadependencyofbrainelasticity andviscosityonageandgender (16,17).Moreover, the

expectedinfluenceofneurodegenerativediseaseonbrainbiomechanicsislow,e.g.,in(2)onlya7%

decreaseinshearstiffnesswasreportedforAlzheimer'sdiseasecomparedwithhealthycontrols.

WhilethevariationinhealthybrainMREdatamayreflecttrueheterogeneityacrosspopulations,itis

also possible that thesemeasureswere influencedbymethodological variations between studies,

suchasdifferentinversionalgorithmsorotherpost-processingstepssuchasfilters,orthesignalto

noise(SNR)oftheacquisitions.Forinstance,in(18)itwasfoundthatMREmeasuresforbrainwere

strongly dependent on SNR and on the region of interest selected. Another possibility is that

differencesinwavedeliverymethodmethodologyandexcitationfrequencyhadaninfluence..MRE

wavesaretransmittedtothebrainviavibrationoftheskull.However,asyet little isknownabout

themotionofthecraniumduringthisprocess,whichislikelytodependonthemechanismofwave

delivery, the wave frequency, and the specific characteristics and inter-subject variability of the

anatomyoftheskull.Themodeofwavedeliveryhasvariedgreatlybetweenstudies,e.g.,bitebar

(19)mechanicalheadactuator (16),andacousticpillow(2).Thewave frequencyhasalsodiffered;

however, as brain tissue exhibits viscoelastic properties, different viscoelastic moduli values are

expected for different frequencies, and some studies have sought to characterize frequency-

dependenteffects(16,20,21).

Much previous work has been carried out using finite element model (FEM) based analysis to

simulatemotionof thehumanheadduring injury (22). Somestudieshavesimulatedormeasured

the natural frequencies (NFs) of the human skull, to predict the response of the skull to collision

impact (23,24), tomodel the conduction of sound through the skull to aid hearing (25,26), or to

understand skull vibrationduring surgical intervention (27).Recently,ourgroupused steady state

harmonicanalysistomodelMRE-associatedwavepropagationinthehumanbraintoinvestigatethe

5

influence of reflections and heterogeneity across boundaries of anatomical structures, i.e., the

processesoftheduramaterandtheventricles(28). Itwasfoundthatthisanatomyinfluencedthe

displacementfieldsandledtoerrorartifactsintheinversioncalculationofthebrainbiomechanical

properties.Inthisearlierwork,tosimplifythemodelingofwavedeliverytothebrain,theskullwas

notincludedinthemodel,andvibrationdeliverywasmodeledfromthepiamaterofthebrainusing

displacement loading with a uniform direction and magnitude. However, this simplification also

excludesthepossibilityofmodelingtheeffectsofdifferentskullexcitationapproaches.

InthecurrentstudyitwassoughttoextendourFEMsimulationframeworktomodelthevibration

dynamicsoftheskullduringMRE,andtherebytodeterminetheirdependencyonthewavedelivery

approachandfrequency.Moreover,itwassoughttodeterminetheimpactofvaryingwavedelivery

attheskullontheMREdisplacementfieldinthebrain,andonthederivedbiomechanicalproperties.

Thehypothesiswasthatthemethodofwavedeliveryandwavefrequencywould leadtodifferent

vibrationfieldsintheskullandthereforeinthebrain,whichwouldinturninfluencetheestimation

ofthebiomechanicalpropertiesofthebrain.Asapreliminarystep,modalanalysiswascarriedoutto

understand the influenceof the skull’s various anatomical featureson its natural frequencies and

associatedmodesofvibration.Tothebestofourknowledge,this isthefirstreportaddressingthe

modelingofvibrationdynamicsofthewholehumanheadduringMRE.

METHODS

OverviewofFEMsimulations

AllsimulationswerecarriedoutusingAbaqusv6.12(DassaultSystèmesSimuliaCorp,Johnston,RI,

USA),anddetailsarelistedinTable1.

Modalanalysistodeterminenaturalfrequencies

FEM-basednaturalfrequency(modal)analysiswascarriedoutonskull-onlymodelsandafullhead

modelderivedfromtheXCATphantom(adatasetbasedonimaging,defininganatomicalstructures

of the human body at high resolution) (29). The purpose of this investigation was to gain

understanding of the influence of different anatomical components on cranial vibration. Varying

materialpropertiesanddifferentboundaryconditionswerealsocompared.Furthermore,forinter-

subjectcomparison,modalanalysiswascarriedoutonaskull-onlymodelderivedfromCTdata.

HarmonicanalysistopredictMREwavepropagationpatterns

6

MREwavepropagationwassimulatedusingharmonicanalysiswiththeXCATandCTderivedmodels

toinvestigatehowskullvibrationchangeswithwavedeliverymethodandfrequency.Comparisonof

theskull-onlyandfullheadXCATmodelsgivesinsightintotheinfluenceofthesofttissuesoncranial

vibration. Moreover, the full head model allows simulation of the complete propagation of

vibrationsfromtheskulltothebrain,asdesired,andexplorationoftheinfluenceofwavedelivery

modesandfrequencyonbraindisplacementfieldsand,thereby,recoveredtissueproperties.

ModelsderivedfromtheXCATphantom(XM)

AsetofskullmodelsandafullheadmodelwerederivedfromtheXCATphantom(29)(XM1-XM6,

Fig. 1). Surface meshes from the phantom were first interpolated onto a regular grid to create

individual segmentations for the included anatomical structures. For the full head model, the

segmentations were assigned different labels and merged to create a single multi-label

segmentation. Next, a volumetric (tetrahedral) finite element mesh was generated in Matlab

(R2012a,Mathworks Inc.,Natick,MA)using the ISO2MESHsoftwarepackage (30). Thevolumetric

mesh generation algorithm used within ISO2MESH is based on the CGAL library (CGAL,

Computational Geometry Algorithms Library, cgal.org). The primary advantage of generating a

volumetric mesh from a multi-label segmentation in this manner is the automatic generation of

shared nodes between adjacent structures. Additionally, the ISO2MESH package provides user

control over the tetrahedral element size to be applied to each region in the mesh, for

computationalefficiency.

The XM models included various combinations of anatomical components, to evaluate their

respectiveinfluences(Fig.1).XM1:upperskull,excludingjawandneck;XM2:upperskull including

jaw, but excluding neck; XM3: upper skull, plus jaw and neck. The upper skull contained a cavity

correspondingtothesinuses.FormodelsXM1-XM3allbonewasassignedpropertiesasforcortical

bone(seesection:"Tissuematerialproperties").XM4:afurtherrefinedmodelwasgeneratedfrom

XM3,inwhichextrastructuresweredefinedattheconnectionpointsofthejawwiththeskull,and

assignedmaterialpropertiesasforcartilage(twoversions:Cartilage#1andCartilage#2inTable2).

XM5:thismodelwasarefinementofXM4inwhichtheupperskullandjawincludedinnerregionsof

cancellousbone.ThecancellousbonewasaddedusingISO2MESHbyerodingtheskullvolume,while

avoidingintersectionswiththesinuses.Theerosionwasperformeduntilarealisticgeometryforthe

cancellous bone was obtained, as assessed by visual comparison with the Colin 27 atlas

segmentation(31).

XM6wasa refinementofXM5 inwhichadditional regionswereadded:1)brain in the inner skull

cavity;2)alayerofcerebrospinalfluid(CSF)surroundingthebraintoapproximatethemeninges;3)

7

avolumetodefinetheventriclesinsidethebrain,filledwithCSF;4)theprocessesoftheduramater,

thefalxcerebriandthetentoriumandfalxcerebellimembranes(denoted"FTM"),whichliebetween

the hemispheres of the cortex, between the cortex and the cerebellum, and between the

hemispheres of the cerebellum, respectively; 5) a single volume for the tissues (skin,muscle, fat,

etc.)surroundingtheskullandneck;and6)thesectionofspinalcordontheinsideoftheneck.The

meningesandFTMwerenotincludedintheoriginalXCATphantomdatabutwereaddedbasedon

estimations informed by manual segmentations of other anatomical MRI data. The approximate

volume of the finite elements of the brain, CSF and FTMmeshesmatched that of the equivalent

meshesemployed in (28) (i.e.,£ 2mm3),while, for computational efficiency, theother structures

weremodeledwitha lowerelementdensity(i.e.,elementvolume£4mm3).AsthebrainandCSF

regions were modeled as near incompressible material, they were meshed with hybrid (linear-

pressure) elements, which discretize and solve for the pressure field independently of the

displacements,toavoidvolumetriclocking.

SkullmodelderivedfromCTdata(CTM)

ToexplorethegeneralityofthefindingsfortheXCATskull,asecondskullmodelwasprepared.This

model (CTM, Fig 2a) was generated from a probabilistic atlas derived from the computed

tomography(CT)imagesofpatients(n=33),providedinapublicdomaindatabaseforcomputational

anatomy (imagenglab.com/pddca_18.html). The probabilistic atlas was used as it represents the

averageskullshapeforapopulation,andhencedescribesamoregeneralanatomy.Additionally,in

comparison to the rawpatientCT images, theatlas is lessnoisyandhenceeasier toprocess. The

skull was segmented semi-automatically from the atlas using ITK-SNAP (32). The segmentation

processinvolvedacombinationofintensitythresholdingandgeodesicactivecontourpropagationto

segment the skull (including the jaw) and the first three vertebrae. A volumetric mesh was

subsequentlygeneratedfromtheskullsegmentation,similarlytothepreparationoftheXMmodels.

Themodelincludedtheskull,jawandneckandagapforthesinuses,andthematerialpropertiesof

elastic cortical bone were employed for the whole skull (i.e., no cartilage or cancellous bone

included).

Tissuematerialproperties

AlltissueconstitutivepropertiesaresummarizedinTable2.Corticalboneandcancellousbonewere

modeledinitiallyaslinearelasticsolidswithpropertiesasdefinedin(33).Viscousdampingwaslater

addedtoboth, inaccordancewith(34).Brainwasmodeledasasofthomogeneousisotropiclinear

viscoelasticnear-incompressiblematerial,withstorage(G')and loss(G'')modulivaluestakenfrom

MREmeasurementsinhealthybrainat25-90Hz(16,19)andthedensitywasapproximatedtothat

8

of water (1,000 kg/m3) (16). The Poisson's ratio was set to 0.499999; estimated using the

approximatespeedofsoundinthebrain(1,550ms-1).Cerebrospinalfluid(CSF)inthemeningesand

ventricles wasmodeled as a soft viscoelastic solid (33). All other tissues weremodeled as linear

elastic solids, with parameters taken from the following sources: cartilage Young's modulus and

density were estimated from (35), and two different Poisson's ratio values (0.5 and 0.1) were

assumedtoexploretheeffectofvaryingthecartilageproperties,andtherebyinfluencingtherange

of relative movement between the jaw and skull; tissues surrounding the skull and neck (skin,

muscle,fat,etc.)weremodeledasauniformvolumewithpropertiesofthescalpusedin(33);spinal

cord was modeled as a linear elastic solid, with the elastic modulus taken from (36), with an

approximatedPoisson's ratioanddensity;and theprocessesof theFTMwereassignedproperties

from(24).

Boundaryconditions

Differentboundary conditions (BC)wereapplied for thevarious simulations (Table1, Fig.1).BC1:

free boundaries; BC2: formodels XM1 and XM2, inwhich the neckwas excluded, nodes near to

wheretheneckwouldattachtotheskullweretethered(x,yandzdisplacementssettozero);BC3:

formodelsincludingtheneck(XM3-XM6),asetofnodesatthebaseoftheneckweretethered;BC4:

forXM6thenodesattheendoftheoutertissueoftheneckwerealsotetheredtoapproximatethe

connectionof theneck to the restof thebody,and to reduce the reflectionofwaveenergyback

fromtheendsurfaceofthenecktissue.

Modalanalysis

Thenaturalfrequencies(oreigenfrequencies)ofvibrationwerecalculatedinAbaqusbyeigenvalue

extraction using the Lanczos eigensolver. This analysis was carried out for each XM model and

materialcombinationwithvaryingBCs(seeTable1),andforCTMwithcorticalboneonlyandBC3.

ThefirstsixNFswerecomparedforthemodelsXM1-XM6andCTM.

MREwavepropagationsimulation

MRE-associated mechanical vibration at specific frequencies was simulated in Abaqus using the

direct-solutionsteady-statedynamicanalysis (hereafter referredtoasharmonicanalysis).This isa

perturbation procedure in which the response of a model to an applied harmonic vibration is

calculatedaboutabasestate,toproducefrequency-spacesteady-statenodaldisplacementsu:

u(x, �) = u(x)exp(��) (1)

9

wherewistheangularfrequency,andxand�arespatialandtemporalcoordinates,respectively.

UsingmodelsXM5,XM6andCTM,MREsimulationwascarriedoutforfrequenciesat5Hzintervals

in the range 5-150 Hz, and additionally at 37.5 and 62.5 Hz, to correspond with the frequencies

includedinthebrainmaterialspecification(Table2).HumanbrainMREisusuallycarriedoutat<100

Hz, as brain exhibits viscoelastic behavior and strongly attenuates the MRE waves at higher

frequencies,resultinginlowdisplacementamplitudesandpoordataquality.Theupperlimitof150

Hzwaschosenheretoinvestigateeffectsinthevicinityof100Hz.

Displacement loading with an amplitude of 10 μm (chosen to approximate wave amplitudes

observed in brainMRE)was delivered to sets of nodes at different positions on the skull surface

correspondingtothedifferentbrainMREwavedeliverymethods(Fig.2):L1:"head-cradle",temples

vibratedinthehead-footdirection;L2:templesvibratedleft-rightinoppositedirections;L3:temples

vibrated left-right in the same direction; L4: "acoustic pillow" (2), nodes at the back of the skull

vibratedinanterior-posteriordirection;L5:"bitebar"(19),nodesonupperandlowerjawvibratedin

left-right direction. For consistency of wave delivery between XM5 and XM6, the loading was

delivered to the skull surface inXM6 rather than theouter skin surface. In the first instance, 100

nodes were selected on the skull for each loading location. To determine the sensitivity to the

numberofloadingnodes,for50and90Hzthenumberofloadingnodeswasvariedto50and200

foreachloadingoption.

The vibration fields in the skull and brain were compared for the different loading options. The

viscoelasticmoduli (G' andG'')were reconstructedusingdirect inversion (28). This algorithmwas

implementedinMatlabthroughderivativecalculationusingafinitedifferencemethodona"virtual

imagingvoxel"grid,whichwasinterpolatedat3mmintervalsfromtheFEnodaldisplacements.To

evaluate the inversion accuracy, themean absolutepercentagedifference (MAPD)was calculated

forthetotalbrainvolume:

�� =011

2

3456378

345

29 (2)

whereNisthetotalnumberofvoxels,nisthevoxelnumber,�;<thegroundtruthvalue(ofG'orG'')

and�=9theinversionvalue.Forselectionofthevolumecorrespondingtothefullbrain,a3Dmask

wascreated.Thevoxelsattheedgeofthebrainareaffectedbyvarioussourcesoferror,including

averagingwiththesurroundingtissues frominterpolation,derivativecalculation,smoothingofthe

curlvector fieldduring inversion,errors inthedirect inversioncausedbytissueheterogeneityand

interference patterns resulting fromwave reflections at tissue boundaries (28). Hence theMAPD

10

was also calculated using a mask eroded by a margin of 3 voxels. By excluding this margin,

understanding can be gained of the specific influence of the errors at the brain tissue edges. To

explorethepossiblebenefitofcombiningtheresultsofdifferentactuationmethods,theG'andG''

voxeldatawasaveragedfor the fivedifferent loadingmethods,andtheMAPDscalculatedfor the

fullanderodedbrainvolumes.

RESULTS

NaturalfrequenciesoftheXCATskullmodels

Thefirstsix(non-zero)NFsoftheXCATskullmodelsare listedinTable3.(ForallmodelswithBC1

thefirstsixvibrationmodeswillalways,trivially,berigidbodymodes,withtheoreticalfrequencies

of0Hz;onlyfrequenciesfornon-rigidmodes,i.e.,non-zerofrequencies,wereincludedinTable3).

For simulations #1-#6 (models XM1-XM3with varying BCs) all of the first six non-zero NFs differ

widelybetweensimulations,indicatingtheinfluenceofthevariousanatomicalcomponentsandthe

boundary conditions. For simulation#6 (XM3,BC3) the first fourNFs are54, 82, 124and281Hz.

Visualizationof theassociateddisplacement fields revealed that the first threeNFsareassociated

withthedirectionsofrotationoftheheadabouttheneck,whilethefourthNFwasassociatedwith

motionofthejaw(Fig.2g-j).Forsimulation#7(XM4withCartilage#1,BC3)thefirstthreeNFsare

unchanged,whileNF#4andsubsequentNFswerealtered.Forsimulation#8(XM4,Cartilage#2,BC3)

thefirstthreeNFswereagainunchanged,whileNF#4andsubsequentNFswereagainaltered.For

XM5,withtheadditionofcancellousbone(simulation#9,BC3),alltheNFsareslightlyaltered,while

the first fourarestillassociatedwiththesamemodesofvibration (Fig.2g-j).Withtheadditionof

viscositytothecorticalandcancellousbone(simulation#10)thefirstsixNFsareunaltered.Hence

the inclusion or exclusion of the jaw and neck had amajor impact on skull vibration, as did the

boundaryconditionoftetheringatthebaseoftheneck.Basedontheresultsofthisanalysis,forthe

MREsimulationintheskullandwholeheadmodelsitwasdeemednecessarytoincludethejawand

neckandtetheringatthebaseoftheneck.

FortheXM6fullheadmodel(simulation#11,BC3+BC4),theNFcalculationwasstronglyinfluenced

bythesoftbraintissue,andthiswasconfirmedbyvisualizationof theassociatedeigenmodes, for

whichvariousresonancepatternsoccurredinthesoftbraintissue.Resonancesoccurredatintervals

ofapproximately1Hz,fromtheminimumNF15.4Hz.IntheMREsimulationswithXM6itwasnoted

that resonantpeaksoccurredatparticular frequenciesassociatedwith rotationof theheadabout

theneck (Fig.2g-i) (see later section:Effectofwavedeliveryand frequencyonMREdisplacement

fieldsandinversions inXM6). ItwasalsoobservedthatforNFsofXM6closetoorattheresonant

11

frequencies for theMRE simulations of XM6, the associated eigenmodes demonstrated a strong

influenceofaparticulardirectionofwholeheadmotionabouttheneck,andhencetheoverallskull

andbraindisplacementswerelargerattheseNFs.

Effectofwavedeliveryandfrequencyondisplacementfieldsinskull-onlymodels

InFigure3themeandisplacementcomponents inthex,yandzdirections(seeFig.1fortheaxes

orientations) and the displacement vector magnitude are compared for the different MRE wave

delivery methods (loading, L) and frequencies for XM5 and CTM. The plots demonstrate that

resonances occur at the NFs of the models. However, for the various loading options, different

resonancepeaksarepresentorabsent,dependingonthedirectionofmotionoftheskullprescribed

and controlled by the loading. For example, for XM5 with L1 (Fig. 3(a)), a peak occurs for the

displacementsinthexandydirectionsaround125Hz,whichcorrespondstoNF#3at127Hz,while

peaks forNF#1andNF#2are absent. ForCTMwith L1 (Fig. 3(b)), no resonancepeaks are visible;

however,thereappearstobeagradual increasetowardsapeak,whichwouldoccuratthehigher

frequencyof230Hz forNF#3.ForXM5withL2 (Fig.3(c)),a resonancepeakoccurs for theyandz

components at 55 Hz, corresponding to NF#1 of 55 Hz, while for CTM (Fig. 3(d)), resonance is

apparentaround115Hz,correspondingtotheNF#1ofCTM.Therearesimilarpatternsofparticular

resonances occurring for the other wave delivery options (L3-L5). Furthermore (far from the

resonance peaks) for each wave delivery method, displacement is predominantly in a single

direction(x,yorz)correspondingtothedirectionofloadingtotheskull.Itisalsoofimportanceto

notethatthedifferentloadingmethodsachievedifferentdisplacementamplitudes(x,yandz)and

magnitudes. For example at 37.5 Hz (far from resonance) themean displacementmagnitudes of

XM5forL1-L5are:20μm;7μm;9μm;9μm;7μm.ForCTMat37.5Hzsimilarmeandisplacements

magnitudeswereobservedforL1-L5:17μm;5μm;8μm;10μm;7μm.

Figure4presentsthedisplacementmagnitudesplottedontheskullsurfaceforXM5forthevarious

loadingmethods. Ineachcase,vibration is shownat resonance,and foranexamplenon-resonant

frequency.Thedisplacementfieldsdifferbetweenloadingmethods.Additionally,foreachmethod,

the displacement field alters greatly at resonance, when it resembles that of the corresponding

eigenmode(Fig.2g-i).Owingtothe largedisparity inthedisplacementsatresonanceandfar from

resonance,differentcolorscalesareemployedinFig.4forthefrequenciesfarfromresonance,and

theresonantfrequencies.Thisallowscomparisonbetweentheloadingmethodsforresonantandfar

from resonance frequencies withclear depiction of the displacement patterns, and allows ready

comparisonwiththeeigenmodes(Fig.2g-i).

12

EffectofwavedeliveryandfrequencyonMREdisplacementfieldsandinversionsinXM6

Figure5presentsplotsofthemeandisplacements(x,y,zandmagnitude)intheskullandbrainof

theXM6model forthedifferent loadingmethodsandfrequencies.Fortheskull, thedisplacement

componentsagaindifferinmagnitude,andthepredominantdirectionvarieswiththewavedelivery

direction.Furthermore,resonancepeakswhosefrequenciesliewithinabout10Hzofresonancesfor

theXM5(skull-only)model(Fig.3)arevisible.NotalltheNFsofXM6haveanapparentinfluenceon

theseplots,butonlytheNFswitheigenmodesassociatedwithheadrotationabouttheneck(Fig.2g-

i). These have a stronger influence on the displacement plots in Fig. 5 as the overall head

displacements are higher at these frequencies. The relative proportions of the displacement

componentsintheskullaremirroredinthedisplacementcomponentsofthebrain,andlikewisethe

brain resonancepeaksoccur in the vicinityof the resonances in the skull. Figure5f compares the

displacement magnitudes between the loading methods, revealing that for the same (10 μm)

displacement loadingontheskullsurface,L1achievedthehighestdisplacementamplitudes inthe

skullandbrain,whileL2achievedthe lowest (e.g.,at50Hz, themeandisplacementmagnitude in

thebrainwas26μmforL1and5μmforL2).

Figure6displaystherealcomponentsofthecomplexdisplacementfields,themagnitudeofthecurl

andinversionresultsforacentralaxialbrainsliceofXM6at50and90Hz.Thewavepatternsforthe

different displacement components differ widely between loadingmethods and frequencies. The

frequenciesof50and90Hzwerechosenasmoregenerallyrepresentativeoftheloadingmethods,

as they lie far fromtheresonancepeaks forallmethods.Theyalsoaretwoof the frequencies for

whichG'andG''arespecifiedforthebrainmaterial(Table2).LoadingmethodsL1andL4gaverise

tosimilarpatternsinthex,yandzdisplacementfieldsandintheinversionresults,whichisperhaps

to be expected, as bothmethods result in a similar noddingmotion of the head. Also, there are

somesimilaritiesinthepatternsobservedinthez-componentimagesliceofL1andL4andthe50Hz

real displacement component image in (16), where a device is employed which would result in

noddingmotionoftheheadsimilartoL1andL4.Correspondingly,methodsL3andL5,whichboth

prescribe a left-rightmotion of the head, also resulted in similar displacement field patterns and

inversionresults.ForL5at90Hzsimilarx-,y-andz-displacementpatternswereobservedtothose

presented in (19), where 90 Hz actuation is achieved via a bite-bar similar to L5. Conversely, L2

resultedinverydifferentdisplacementpatternsfromalltheothermethods,thoughthepatternsof

errors in the inversion results are similar to thoseof L3 and L5. Themagnitudeof the curl of the

displacement fieldalsodiffersbetween loadingoptionsand frequencies,withgenerally largercurl

magnitudesatthehigherfrequencyof90Hz,asexpectedforamorerapidlyvaryingwaveform,i.e.,

13

ashorterwavelength.Inthedisplayedslices,L2andL4hadloweroverallcurlmagnitudescompared

to theothermethods forboth frequencies.Certain locationson theslicearea tendtohave larger

curlmagnitudes,suchaseithersideofthefalxcerebri(seelastpanelinFigure1forlocationofthe

falxcerebriinanaxialslicethroughthebrain),especiallyforL3andL5.Thismaybeassociatedwith

wavereflectionoffthefalx,butalsopossiblewavetransmissionfromthefalx.

Figure 7 presents plots ofmeanG' andG'' over the brain volume for the differentwave delivery

methods and frequencies, with separate error bar plots (standard deviation error bars) for the

differentloadingmethodstocomparetheerrorsbetweenmethods,andcombinedplotscomparing

the mean values for all loading methods. TheMAPD of G' and G'' for the full and eroded brain

volumes,forthefivefrequenciesofthegroundtruthdata(Table2)arealsopresentedinseparate

error bar plots and combined plots for the five loadingmethods. At higher frequencies, G' varies

betweenthemethodsby~500Pa(Fig.7a),andG''by~300Pa(Fig.7b).Tointerprettheshapeofthe

plotsinFigs.7aand7bitisnecessarytoknowthegroundtruthmodulithatAbaqusemployedinthe

simulations: for frequency-dependent viscoelastic materials, Abaqus interpolates parameters

linearlywithin the rangeof specified frequencies (Table 2), and caps parameters at the bounding

valuesoutsideofthisrange(i.e.atfrequencies<25Hz,the25Hzmoduliareused,andat>90Hz,the

90Hzmoduli are used). Figure 7a-b demonstrate how the variations inG' andG'' over the brain

volumevarywithactuationmethod,andthestandarddeviationinG'andG''overthebrainvolume

tendstobelowerforL1andL4thanfortheothermethods.ThevariationinG'andG''overthebrain

volumealsoincreaseswithfrequency.

TheMAPDsalsovarybetweenactuationmethods,andoverallL1andL4resultinlowererrorsthan

theothermethods(Fig.7c-d)e.g.,at90Hz,MAPDofG'forL1andL4wasapproximately11%less

thanforL3andL5,whileforG''at37.5Hz,itwasapproximately17%lowerforL1andL4compared

with L3.. For the eroded volume, the MAPDs are vastly reduced, though L1 and L4 still have

predominantlythelowererrorvalues,exceptatthehigherfrequencies(62.5and90Hz).However,

the differences between deliverymethods for the erodedmask are only on the order of 1%.The

MAPDsalsovarywithfrequency.ForthefullbrainvolumetheerrorsonG'tendtobehigherforthe

twoextremesof25and90Hz(andthestandarddeviationoftheerror isalsolarger)comparedto

the other frequencies,while forG'' theopposite holds, i.e., 25 and 90Hz have lower errors (and

standarddeviationsoftheerror).Fortheerodedbrainvolume(Fig.7e-f)alltheerrorsarereduced

substantially comparedwith the full volume,and theerrorsand standarddeviationsof theerrors

arehigherfor25and90HzforbothG'andG''.

14

Figure 7g presents error bar plots for the MAPD of the voxel-wise average G' and G'' for all

five loading methods, for the full and eroded brain volumes. Averaging was found to lead to

marginal reductions of 1-2 % in the lowest MAPD values for G' for the full brain volumes for

frequencies 25, 37.5, 50 and 62.5 Hz, while it did not achieve lower errors for 90 Hz, i.e., a

29% error compared to the lowest error at 90 Hz of 25% for L4 (Fig.7c). For the eroded brain

volume for each frequency the differences between the lowest MAPDs of G' and the MAPD

of the average G' were generally <1%. However for G'' averaging increased the errors

substantially for the full and eroded brain volumes for all five frequencies, e.g., for the full

brain volume, while the maximum error for the non-averaged G'' was 76% at 37.5 Hz for L3

(Fig.7d) the error at 37.5 Hz for the averaged G'' was 85%. The average error (over the

frequencies) of the eroded volume for the averaged G'' was 52% (the minimum error of 22%

was at 90 Hz, Fig. 7g), while the errors for the non-averaged G'' for the eroded volume were

all < 7 % (Fig.7f). Furthermore, averaging of the G' and G'' voxel values tended to reduce the

standard deviation of the MAPD over the brain volume for the full and eroded masks. With

regardtotestingthesensitivitytothenumberof loadingnodes, itwasfoundthat formostofthe

wave delivery methods that changing the number of nodes only led to minor variations in the

displacementfieldsandtheinversionmapsofG'andG'',withtheexceptionofL2.TheMAPDofG'

andG''generallyvariedbylessthan1%between50,100and200nodesforloadingforL1,L3,L4and

L5. However for L2 theMAPDs variedmore substantially. For L2 at 50 Hzwith 50, 100, and 200

nodes, theMAPDofG'was18±23%,17±21%and16±19%respectively,while for theMAPDofG''

thevalueswere74±110%,70±101%,and66±90%.Hence,theMAPDandthestandarddeviationof

theMAPD decreased with increasing loading nodes, however the reductions in error weremore

pronouncedforG''.For90Hzasimilareffectwasobserved:with50,100,and200nodes,theMAPD

of G'was 35±37%, 30±30% and 28±26% respectively,while for theMAPD of G'' the valueswere

63±67%,62±64%,and62±62%.Howeverfor90HzthereductionsinG'weremorepronouncedthan

thoseofG''.ThevariationsininversionerrorsforL2appearstobemainlyassociatedwithvariations

in thedirections and amplitudesof thedisplacement field, anddifferentwave interactions at the

borders of the brain tissue, leading to different reflection and interference effects.While for the

otherloadingmethodsthedirectionofthewaveswasrelativelyunalteredbythechangingnumber

ofloadingnodes. Thatthevariationsaremainlyatthebraintissuebordersissupportedbythefact

thatfortheerodedbrainvolumetheMAPDsandstandarddeviationoftheMAPDvariedbylessthan

1%forL2.

DISCUSSION

15

NaturalfrequenciesofXCATandCTMskullmodels

TheNFanalysisof the skullmodelsXM1-XM5 revealed important informationon the influenceof

thevariousanatomicalcomponentsonskullvibration.AsthedeliveryofMREwavestothebrainis

mainlyachievedviatransmissionthroughtheskull,itisimportanttodeterminetherelevantNFsof

the skull (i.e., those that lie in the typical frequency range for brain MRE: 20-100 Hz), and to

understand the factors that influence the eigenmodes. The inclusion of the jaw and neck, and

tetheringatthebaseoftheneckstronglyinfluencedthevibrationoftheskullandtheNFs.

TheNFsdifferedbetweenCTMandthematchingXM3model(simulations#6and#12,Table3).The

material specifications were identical for these simulations, however the volume (and therefore

mass)ofCTMwaslowerthanthatofXM3.NFstypicallyscaleinverselywiththesquarerootofthe

mass, and hence the NFs for CTM are higher than those for XM3. However, structural variation

betweenthemodelswillalso influencemodaldynamics.While theNFsvarybetweenmodels, the

modesofvibrationforthefirstfourNFsarethesameforbothmodels(Fig.2g-j).

PreviousinvestigatorshavesoughttomeasureorsimulatethevibrationandNFsofthehumanskull.

Howeverthemethodologyhasvariedwidelybetweenstudies:somesimulationsormeasurements

excludedthejaw(24)ortheneck(27),orboth(23),andwhilesomemeasurementswerecarriedout

in dry skull models (27), others were made in live human subjects (25), or both (37,38), and

therefore the reportedNFs have also variedwidely between studies. In (24) two FE skullmodels

werecompared:oneexcludingthejawandneck,andtheotherexcludingthejawbutincludingthe

neck.Tetheringwasalsoincludedatthebaseoftheskullorneck.In(24)therangeofthefirstfour

NFsforthemodelwithouttheneckwas149.1-860.2Hz,whiletherangeofthefirstfourNFsofthe

nearestcorrespondingmodelinthisstudy(XM1withBC2)was321-1488Hz.Asinthepresentstudy,

in (24) itwasfoundthatwhentheneckwas includedtheNFswerereduced(first four:88.9-399.4

Hz),andfurthermoretherotationalmotionoftheskullforthefirstthreemodeswassimilartothose

observedinthisstudy(Fig.2g-j),whilethefourthwasassociatedwithhead-footmotionoftheskull.

However,in(24)theydidnotincludethejawbone,whereasinthepresentstudyitwasfoundthat

thefourthNFwasassociatedwithjawmotion.Moreover,inthisstudyforBC3,NF#4was>200Hz

forXM3and>400HzforCTM;asbrainMREistypicallycarriedoutat<100Hz,thissuggeststhat

jawmotionmayhaveasmallerinfluenceonthemotionoftheskullduringMRE.

In this study theNFs of the full headmodel (XM6)were very different to those of the skull-only

model (XM5). The XM6modal analysis was strongly influenced by the soft brain tissue, and the

differentanatomicalstructureswithinthecranium,andNFsoccurredatintervalsofapproximately1

16

Hz, from theminimumNF of 15.4 Hz. This differed greatly from reported NFs for in vivo human

head:Hakanssonetal. (25)measuredNFs in the range500-7,500Hz for invivohumanskullsand

found14-19 resonances,with theaverageof the two lowest frequenciesat972Hz.Caietal. (37)

alsomadeinvivomeasurementsintherange2-52kHzandmadeacomparisonwithdryskulls.They

found complex resonances and antiresonances in both the dry skulls and live head, which were

stronglydependentonthetransducerposition,andfoundthatdampingintheliveheadreducedthe

resonancepeaks.

TheeffectofdampingfromsofttissuescouldbeobservedintheMREsimulationwithXM6,asthe

resonancepeakswereshiftedwithrespecttotheXM5skull-onlymodel(Figs.3and5).Furthermore,

theMREsimulationcouldexploretheeffectofdeliveringwaveenergyatdifferentpositions,andthe

associatedvibrationeffectsofeachdeliverymode.Hence,forXM6theMREsimulationsweremore

informativethanthemodalanalysis.

Inter-subjectdifferencesinskullNFsandpossibleimplicationsforMRE

ThedifferentNFsoftheXM3andCTMmodelsindicatethattheNFswillchangebetweenindividuals

dependingonthesizeandshapeoftheskull.ThedifferentresonanceeffectsintheMREsimulations

ofXM5andXM6also indicatehowNFswill shiftdue to thedampingeffectsof the tissues in the

head, and this is likely to vary between individuals. According to the in vivo measurements of

(25,37),theNFsoftheinvivohumanheadarelikelytooccurat>500Hz,whichiswelloutsidethe

typicalfrequenciesemployedforbrainMRE,i.e.,20-100Hz.However,thesimulationsinthisstudy

have demonstrated that when resonances do occur at or in the vicinity of the MRE excitation

frequency they can have a major impact on the wave fields in the brain. Hence, it is the

recommendation of this study that further exploration should be carried out with volunteers to

determinetheresonancesofthehumanheadandtheimpactoftheseontheMREmeasurements.If

actuation is carried out at a resonance frequency, there is the possibility of persistent nodes and

anti-nodes occurring in the brain tissue, whichmay lead to errors in the inversions. As theMRE

simulationsofthisstudycalculatedtheharmonicsteadystatedisplacements,itwasnotpossibleto

observetheoccurrenceofpersistentnodes,and,moreover,theerrorsintheinversionsofthisstudy

appeared mainly related to the effects at the boundaries of brain tissue with other anatomy.

However in the natural frequency simulations with the full head model XM6, symmetric

displacement patterns were observed in the brain tissue that would suggest the likelihood of

persistent nodes occurring in real acquisitions. This is therefore an important avenue for future

investigationviaMREacquisition.

17

ImplicationsofthechoiceofwavedeliverymethodandfrequencyinbrainMRE

Theresultsof this studyhaveproventhehypothesis that, in thecontextof simulation,MREwave

deliverymethodologyandfrequencyaffect thedisplacement fields intheskullandbrain,andalso

the inversion accuracy. Different displacement components were dominant for the different

methods,whilesomemethodshadsimilarpatternsofdisplacementandinversionerror,i.e.,L1was

similar to L4, and L3 was similar to L5. Furthermore, if the NFs lie at or close to theMRE wave

frequency, a resonance peak can occur in the MRE displacement fields. Also, only particular NF

resonancesoccur for thedifferent loadingmethods,andthepeakscanaccentuatethedifferences

betweendisplacementcomponents.Foraccurateinversionitisimportanttohavebalancebetween

thedisplacementcomponentsinordertoachievefullrankinthesystemofequationssolvedinthe

direct inversion (39). Hence, large disparities between displacement components caused by a

particular wave delivery or resonancesmay lead to inaccurate inversion. However, as brainMRE

studieshavenotreportedsucha largedisparitybetweendisplacementcomponents, thispotential

effectofresonance,orindeedtheparticulardirectionofwavedelivery,appearsunlikelytooccurin

reality,andthemanyapproximations involved in thesesimulationsmayaccount for theseeffects.

However it is a recommendation of this study that future MRE studies should investigate the

possibleinfluencesofresonancesorthepreferentialdirectionofwavesduetothedeliverymethod,

andverifythebalanceofdisplacementcomponents.

OverallL1(head-cradle)andL4(acousticpillow)producedthelowesterrorsintheinversions.InFig.

6,theinversionerrorsappeartobemainlyassociatedwithinteractionofthewavefieldwiththefalx

cerebrimembrane, as large inversionerrorsoccur at either sideof this structure. Formethods L1

andL4thedisplacementfieldismovingpredominantlyinadirectionparalleltothefalx(y-direction),

whilefortheothermethodsthedominantmotionisleft-right(x-direction),andlesserartifactsoccur

for L1 and L4 (especially at 50Hz, Fig. 6). In our previous brainMRE simulationwork (28) itwas

found that inversion artifacts occurred close to interfaces between brain tissue and the FTM and

ventricles.Theconclusionofthatearlierstudywasthaterrorsattheboundarieswerecausedbya

combinationoffactors:1)reflection,refractionandscatteringattissueboundariesleadingtowave

interference, which results in inversion artifacts at larger sampling steps (3 mm); 2) material

heterogeneity bringing about errors in the direct inversion algorithm (which assumes local

homogeneity (39)); 3) averaging across the tissue boundaries due to interpolation, derivative

calculationsandsmoothingofthecurlvectorfieldduringtheinversion(28).However,thefindingsof

this present study emphasize the importance of wave reflection and the resulting interference

patterns, as the different wave delivery methods produce different predominant directions of

18

motionaccompaniedbydifferentmagnitudesofinversionerror.Somesensitivitytothenumberof

loadingnodeswasalsoobserved,andparticularlyforL2.Basedontheseobservations,inrealMRE

acquisitionsitwouldbeimportanttodeterminethesensitivitytotheareaofcontactandpositioning

oftheactuator,andperhapscarryoutoptimizationofthesefactors.

AveragingoftheG'andG''dataoverthefiveactuationmethodsdemonstratedonlyaminorbenefit

totheaccuracyofG',andwasdetrimentaltotheaccuracyofG''.Howeverasthesimulationsofthis

studyweresimplifiedinmanyaspects,averagingovermultipleactuationmethodsmayprovemore

beneficial in real MRE acquisitions, and comparison of different actuation methods will inform

assessmentofthestabilityandreliabilityofmeasurements.Infactrecentworkhasaddressedthisin

the comparison of themethod of (16)with a new remote actuationmethod for brainMRE (40).

Acquisition via multiple actuation methods may be facilitated by newer faster MRE sequences

(41,42).

Limitationsofthecurrentstudyandfuturework

Themajor limitationofthisstudywasthesimplicityofthemodelsemployed, intermsofanatomy

andmaterial specifications.Theapproximations involved in theFEmodelingandsimulationswere

furtherlimitations.Forinstance,theanatomicalmodelsemployedwerebasedontheanatomyofa

single individual (XM) and on the average model of a small cohort (CTM), and therefore do not

captureallthevariabilityofanatomyacrossthepopulation.Skullshapeislikelytovarywithfactors

suchgender,ageandrace.Futureworkwillinvestigatethevariabilityofresonantfrequenciesacross

thepopulationbymeansofstatisticalshapemodelingof theskullbasedonawiderpopulationof

data.Themodelswerealsosimplified intermsofthestructures includedandthematerialmodels

used,suchasasoftviscoelasticsolidforCSFasopposedtoafluid.Furthermore,themeningeshave

inrealityacomplexstructure:theduramater(attachedtotheskull)isconnectedtothepiamater

(attached to the brain) via filaments called trabeculae running through the subarachnoid space,

whichispermeatedwithCSF.Thebrainisalsotetheredtotheskullatthebrainstemandviaother

vascularandneuralconnections.Furthermore,inrealityslippageoccursbetweentheskullandbrain,

andthemeningesarelikelytohavenon-linearmaterialproperties,andthesefactorshavenotbeen

accounted for in themodels. Given the findings ofMRI spin taggingmotion tracking of the brain

duringimpact(43),themotionofthebrainwithintheskullduringMREislikelytobeverycomplex,

with displacement, deformation and rotational motion occurring to varying degrees at different

locationsat thebrain-skull boundary. Another studymeasuringMREwave transmission from the

skulltobrain(44)concludedthatthemeningesstronglyattenuateMREwaves.Furthermore,other

anatomicalfeaturesintheheadthatwerenotincludedarelikelytocausewaveattenuationthrough

19

viscosityandscatteringattissueinterfaces,andindeedbraintissueitselfisinrealityheterogeneous

(20),meaningwavesarelikelytobescatteredattheinterfacesofdifferentbrainregions(45).Based

on the degree of wave and motion damping measured in (43,44) the degree of damping of the

resonancepeaksfortheXM6model(Fig.5)islikelytobeunderestimated.Furthermore,braintissue

isanisotropic,asthewhitematterisfibrous(46),andthiswouldinfluenceMREdisplacementfields.

Brain tissue is likely to be under anisotropic pre-stress, which will affect estimates of material

parametersobtainedusingthedifferentwavedeliverylocationsanddirections.Indeedrecentwork

has found that theMREmeasures for brain whitematter differed depending on whether waves

were delivered in the anterior-posterior direction or the left-right direction (47). Therefore the

interactionofwaveswith theanisotropicstructuresof thebrainmayaccount for thevariability in

measures obtained from different brain MRE studies employing varying actuation methods, as

opposed to differences in the overall displacement fields and wave interactions at the brain

boundaries, or differences in inversionmethods employed or other post-processing steps. Future

studieswillexplorethesensitivityofthefindingsofthisworktovariationsinmaterialpropertiesof

thedifferentanatomicalstructures.

However,thevariabilitythatmightoccurbetweenindividualsandtheapproximationsemployedin

thematerialmodelingdonotnegatetheoverallfindingsofthiswork, i.e.,thatthechoiceofwave

delivery methodology can influence brain MRE data. Rather, studies with wider populations and

varied properties would provide a better estimate of the actual impact of using different wave

deliverymethods.

Althoughfurthersimulationsarewarrantedtoexplorethe limitationsof thefindingsof thisstudy,

ultimatelyinvivoMREstudiesarerequiredtodeterminetheactualimpactonvaryingwavedelivery.

Hence, the main recommendation from this work is that volunteer studies comparing MRE

acquisitions with different wave deliverymethods be undertaken. In fact, in the recent study by

Fehlner at al. (40) athe actuation method of (16) wascompared with a newer remote excitation

method,anditwasfoundthatthemagnitudeandphaseofthecomplexshearmoduluscoulddiffer

byasmuchas6and13%respectivelyinthebrainregionsexamined.Furthersimilarstudiesshould

becarriedouttodetermineaconsensusmethodologyforoptimumaccuracyandstability,although

patientcomfortandthepracticalityofthemethodareotherprimaryconsiderations.

CONCLUSIONS

Throughsimulation,thisstudyhasdemonstratedthatinbrainMREthemethodofwavedeliveryand

wavefrequencystrongly influencethedisplacementfields intheskullandbrain,andconsequently

20

theaccuracyoftheinversionreconstructionsofthebrainbiomechanicalproperties(e.g.,at90Hzan

11%lowerinversionerrorforthehead-cradle(L1)andacoustic-pillow(L4)comparedwiththebite

bar (L5)). However, most of these differences are associated with brain tissue located at the

boundaries with other anatomy, and it is uncertain how much of the inversion error in these

locationsisassociatedwiththeinversionmethodorothersourcesoferrorfromthesimulation,and

futurework should employ other inversionmethods for comparison. But given that the inversion

errorsatthebrainboundariesdifferedstronglybetweentheloadingmethods,itislikelythatthese

errors areassociatedwithdifferent reflection, scatteringand interferenceeffects, anddestructive

interference and standing waves from interference pose very difficult challenges for inversion.

Furthermore,thenaturalfrequenciesofvibrationoftheheadcouldinfluencetheMREdisplacement

fields inthebrainandthereforethe inversionaccuracy,throughtheoccurrenceofstandingwaves

withpersistentnodesandanti-nodes,oranimbalanceindisplacementcomponentsatresonance.

Asthemodelsemployedinthisstudyweregeneratedfromalimitedrepresentationofhumanhead

anatomyandwere simplified in variousaspects, future simulation studies are required toexplore

thelimitationsofthesefindings.Furthermore,itisrecommendedthatinvivoMREstudiesaremade

onvolunteersusing thevariouswavedeliverymethodsandvarying frequencies, todetermine the

stability of the measures of brain tissue biomechanics, and the possible influence of resonant

frequencies.

ACKNOWLEDGEMENTS

ThisstudywasfundedbytheEuropeanUnion’sSeventhFrameworkProgramme(FP7/2007–2013)

aspartoftheprojectVPH-DARE@IT(grantagreementno.601055).Therearenoconflictsofinterest

associatedwiththiswork.

21

REFERENCES

1. MuthupuillaiR,LomasDJ,RossmanPJ,GreenleafJF,ManducaA,EhmanRL.Magnetic

resonanceelastographybydirectvisualizationofpropagatingacousticstrainwaves.Science

1995;269(5232):1854-1857.

2. MurphyMC,HustonJI,JackCRJ,GlaserKJ,ManducaA,FelmleeJP,EhmanRL.Decreased

brainstiffnessinAlzheimer'sdiseasedeterminedbymagneticresonanceelastography.J

MagnResonIm2011;34:494-498.

3. WuerfelJ,PaulF,BeierbachB,HamhaberU,KlattD,PapazoglouS,ZippF,MartusP,BraunJ,

SackI.MR-elastographyrevealsdegradationoftissueintegrityinmultiplesclerosis.

Neuroimage2010;49:2520-2525.

4. SchregelK,WuerfelE,GarteiserP,GemeinhardtI,ProzorovskiT,AktasO,MerzH,Petersen

D,WuerfelJ,SinkusR.Demyelinationreducesbrainparenchymalstiffnessquantifiedinvivo

bymagneticresonanceelastography.PNATLACADSCIUSA2012;109(17):6650-6655.

5. MurphyMC,CurranGL,GlaserKJ,RossmanPJ,HustonJI,PodusloJF,JackCRJ,FelmleeJP,

EhmanRL.MagneticresonanceelastographyofthebraininamousemodelofAlzheimer's

disease:initialresults.MagnResonImaging2012;30:535-539.

6. StreitbergerKJ,SackI,KreftingD,PfullerC,BraunJ,PaulF,WuerfelJ.Brainviscoelasticity

alterationinchronic-progressivemultiplesclerosis.PLoSOne2012;7(1):e29888.

7. FreimannFB,StreitbergerKJ,KlattD,LinK,McLaughlinJ,BraunJ,SprungC,SackI.Alteration

ofbrainviscoelasticityaftershunttreatmentinnormalpressurehydrocephalus.

Neuroradiology2012;54(3):189-196.

8. StreitbergerKJ,WienerE,HoffmannJ,FreimannFB,KlattD,BraunJ,LinK,McLaughlinJ,

SprungC,KlingebielR,SackI.Invivoviscoelasticpropertiesofthebraininnormalpressure

hydrocephalus.NMRBiomed2011;24(4):385-392.

9. LippA,TrbojevicR,PaulF,FehlnerA,HirschS,ScheelM,NoackC,BraunJ,SackI.Cerebral

magneticresonanceelastographyinsupranuclearpalsyandidiopathicParkinson'sdisease.

NeuroimageClin2013;3:381-387.

10. RiekK,MillwardJM,HamannI,MuellerS,PfuellerCF,PaulF,BraunJ,Infante-DuarteC,Sack

I.Magneticresonanceelastographyrevealsalteredbrainviscoelasticityinexperimental

autoimmuneencephalomyelitis.NeuroimageClin2012;1(1):81-90.

11. HustonJ,3rd,MurphyMC,BoeveBF,FattahiN,AraniA,GlaserKJ,ManducaA,JonesDT,

EhmanRL.Magneticresonanceelastographyoffrontotemporaldementia.JMagnReson

Imaging2015.

12. DiIevaA,GrizziF,RognoneE,TseZT,ParittotokkapornT,RodriguezYBF,TschabitscherM,

MatulaC,TrattnigS,RodriguezYBR.Magneticresonanceelastography:ageneraloverview

ofitscurrentandfutureapplicationsinbrainimaging.NeurosurgRev2010;33(2):137-145;.

13. GlaserKJ,ManducaA,EhmanRL.ReviewofMRelastographyapplicationsandrecent

developments.JMagnResonIm2012;36(4):757-774.

14. KruseSA,RoseGH,GlaserKJ,ManducaA,FelmleeJP,JackCR,Jr.,EhmanRL.Magnetic

resonanceelastographyofthebrain.Neuroimage2008;39(1):231-237.

15. ChatelinS,ConstantinescoA,WillingerR.Fiftyyearsofbraintissuemechanicaltesting:from

invitrotoinvivoinvestigations.Biorheology2010;47(5-6):255-276.

16. SackI,BeierbachB,WuerfelJ,KlattD,HamhaberU,PapazoglouS,MartusP,BraunJ.The

impactofagingandgenderonbrainviscoelasticity.Neuroimage2009;46(3):652-657.

17. AraniA,MurphyMC,GlaserKJ,ManducaA,LakeDS,KruseSA,JackCRJ,EhmanRL,Huston

JI.MeasuringtheeffectsofagingandsexonregionalbrainstiffnesswithMRelastographyin

healthyolderadults.Neuroimage2015;111:59-64.

18. MurphyMC,HustonJ,3rd,JackCR,Jr.,GlaserKJ,SenjemML,ChenJ,ManducaA,Felmlee

JP,EhmanRL.Measuringthecharacteristictopographyofbrainstiffnesswithmagnetic

resonanceelastography.PLoSOne2013;8(12):e81668.

22

19. GreenMA,BilstonLE,SinkusR.Invivobrainviscoelasticpropertiesmeasuredbymagnetic

resonanceelastography.NMRBiomed2008;21(7):755-764.

20. GuoJ,HirschS,FehlnerA,PapazoglouS,ScheelM,BraunJ,SackI.Towardsanelastographic

atlasofbrainanatomy.PLoSOne2013;8(8):e71807.

21. DittmannF,HirschS,TzschätzschH,GuoJ,BraunJ,SackI.Invivowidebandmultifrequency

MRelastographyofthehumanbrainandliver.MagnResonMed2015:Epub

10.1002/mrm.26006.

22. TseKM,LimSP,TanVBC,LeeHP.Areviewofheadinjuryandfiniteelementheadmodels.

AmericanJournalofEngineering,TechnologyandSociety2014;1(5):28-52.

23. NickellRE,MarcalPV.In-vacuomodaldynamicresponseofthehumanhead.JEngInd-T

ASME1974;96(2):490-494

24. HuangBW,OuY-W,ChangCH,ChenGS,YenKY,TsengJ-G.Dynamiccharacteristicsofthe

skullwiththeneckeffect.LifeSciJ2013;10(2):265-270.

25. HakanssonB,BrandtA,CarlssonP,TjellstromA.Resonancefrequenciesofthehumanskull

invivo.JAcoustSocAm1994;95(3):1474-1481.

26. KimN,ChangY,StenfeltS.Athree-dimensionalfinite-elementmodelofahumandryskull

forbone-conductionhearing.BiomedResInt2014;2014:519429.

27. HuangBW,KungHK,ChangK-Y,HsuPK,TsengJ-G.HumanCraniumDynamicAnalysis.Life

SciJ2009;6(4):15-22.

28. McGrathDM,RavikumarN,WilkinsonID,FrangiAF,TaylorZ.Magneticresonance

elastographyofthebrain:Aninsilicostudytodeterminetheinfluenceofcranialanatomy.

MagnResonMed2015;doi:10.1002/mrm.25881.

29. SegarsWP,SturgeonG,MendoncaS,GrimesJ,TsuiBM.4DXCATphantomformultimodality

imagingresearch.MedPhys2010;37(9):4902-4915.

30. FangQ,BoasD.Tetrahedralmeshgenerationfromvolumetricbinaryandgray-scaleimages.

ProcIEEEIntSympBiomedImaging2009:1142-1145.

31. Aubert-BrocheB,EvansAC,CollinsL.Anewimprovedversionoftherealisticdigitalbrain

phantom.Neuroimage2006;32(1):138-145.

32. YushkevichPA,PivenJ,HazlettHC,SmithRG,HoS,GeeJC,GerigG.User-guided3Dactive

contoursegmentationofanatomicalstructures:significantlyimprovedefficiencyand

reliability.Neuroimage2006;31(3):1116-1128.

33. YangJ.Investigationofbraintraumabiomechanicsinvehicletrafficaccidentsusinghuman

bodycomputationalmodels.AWitteketal(eds),Computationalbiomechanicsformedicine:

Softtissuesandthemusculoskeletalsystem,Springer2011:5-14.

34. Ed.JMiddletonGP,MLJones.Computermethodsinbiomechanicsandbiomedical

engineering-2:CRCPress;1999.126p.

35. PalS.Designofartificalhumanjointsandorgans:Springer;2014.

36. BilstonLE,ThibaultLE.Themechanicalpropertiesofthehumancervicalspinalcordinvitro.

AnnBiomedEng1996;24:67-74.

37. CaiZ,RichardsDG,LenhardtML,MadsenAG.Responseofhumanskulltobone-conducted

soundintheaudiometric-ultrasonicrange.IntTinnitusJ2002;8(1):3-8.

38. FrankeEK.Theresponseofthehumanskulltomechanicalvibrations.Ohio,USA:Wright-

PattersonAirForceBase1954.

39. HonarvarM,SahebjavaherR,SinkusR,RohlingR,SalcudeanS.Curl-basedFiniteElement

ReconstructionoftheShearModulusWithoutAssumingLocalHomogeneity:TimeHarmonic

Case.IEEETransMedImaging2013.

40. FehlnerA,PapazoglouS,McGarryMD,PaulsenKD,GuoJ,StreitbergerKJ,HirschS,BraunJ,

SackI.CerebralmultifrequencyMRelastographybyremoteexcitationofintracranialshear

waves.NMRBiomed2015;28:1426-1432.

23

41. JohnsonCL,HoltropJL,McGarryMD,WeaverJB,PaulsenKD,GeorgiadisJG,SuttonBP.3D

multislab,multishotacquisitionforfast,whole-brainMRelastographywithhighsignal-to-

noiseefficiency.MagnResonMed2014;71(2):477-485.

42. SahebjavaherRS,FrewS,BylinskiiA,terBeekL,GarteiserP,HonarvarM,SinkusR,

SalcudeanS.ProstateMRelastographywithtransperinealelectromagneticactuationanda

fastfractionallyencodedsteady-stategradientechosequence.NMRBiomed

2014;27(7):784-794.

43. FengY,AbneyTM,OkamotoRJ,PlessRB,GeninGM,BaylyPV.Relativebraindisplacement

anddeformationduringconstrainedmildfrontalheadimpact.JRSocInterface

2010;7(53):1677-1688.

44. ClaytonEH,GeninGM,BaylyPV.Transmission,attenuationandreflectionofshearwavesin

thehumanbrain.JRSocInterface2012;9(76):2899-2910.

45. PapazoglouS,XuC,HamhaberU,SiebertE,BohnerG,KlingebielR,BraunJ,SackI.Scatter-

basedmagneticresonanceelastography.PhysMedBiol2009;54(7):2229-2241.

46. RomanoA,ScheelM,HirschS,BraunJ,SackI.Invivowaveguideelastographyofwhite

mattertractsinthehumanbrain.MagnResonMed2012;68(5):1410-1422.

47. AndersonAT,JohnsonCL,HoltropJL,VanHoutenEE,McGarryMD,PaulsenKD,SuttonBP,

GeorgiadisJG.Propertydifferencesinwhitematterstructuresduetodistinctwave

propagationdirectionsinMRelastography.ProcIntSocMagnResonMed2015;23:1058.

24

Table1Simulationdetails

Simulation

No.

NF/MRE Model No.of

Elements

Element

volume

Boundary

conditions

andloading

Materials

1 NF XM1 823001 £2mm3 BC1 Corticalbone






7 NF XM4 838627 £2mm3 BC3 Corticalbone+cartilage#1

8 NF XM4 838627 £2mm3 BC3 Corticalbone+cartilage#2

9 NF XM5 838627 £2mm3 BC3 Cortical+cancellousbone+

cartilage#2

10 NF XM5 838627 £2mm3 BC3 Viscoelasticcorticalviscoelastic

cancellousbone+cartilage#2

11 NF XM6 1420763 £4mm3

(brain,CSF

andFTM£

2mm3)

BC3+BC4 Viscoelasticcorticalandcancellous

bone,cartilage#2,outerhead,

brain,spinalcord,FTM,CSF

12 NF CTM 712434 £2mm3 BC3 Corticalbone

13 MRE(5-

150Hz)

XM5 838627 £2mm3 BC3+L1 Viscoelasticcorticalbone+

viscoelasticcancellousbone+

cartilage#2

14 MRE(5-

150Hz)



cartilage#2

15 MRE(5-

150Hz)



cartilage#2

16 MRE(5-

150Hz)



cartilage#2

25

17 MRE(5-

150Hz)



cartilage#2

18 MRE(5-

150Hz)

CTM 712434 £2mm3 BC3+L1 Corticalbone

19 MRE(5-

150Hz)


20 MRE(5-

150Hz)


21 MRE(5-

150Hz)


22 MRE(5-

150Hz)


23 MRE(5-

150Hz)

XM6 1420763 £4mm3

(brain,CSF

andFTM£

2mm3)

BC3+BC4+L1 Viscoelasticcorticalandcancellous



24 MRE(5-

150Hz)

XM6 1420763 £4mm3

(brain,CSF

andFTM£

2mm3)




25 MRE(5-

150Hz)

XM6 1420763 £4mm3

(brain,CSF

andFTM£

2mm3)




26 MRE(5-

150Hz)

XM6 1420763 £4mm3

(brain,CSF

andFTM£

2mm3)




27 MRE(5-

150Hz)

XM6 1420763 £4mm3

(brain,CSF

andFTM£

2mm3)




26

Table2:Constitutiveparametervaluesemployedinsimulations

Tissuetype Parametervalues

Young'smodulus

(MPa)

Poisson'sratio Density(kg/m3)

Corticalbone 15,000 0.21 1,900

Cancellous

bone

4,600 0.05 1,500

Cartilage#1 1 0.5 1,100

Cartilage#2 1 0.1 1,100

Outerhead

tissues

16.7 0.42 1,000

Spinalcord 1.02 0.5 1,000

FTM 31.5 0.45 1,130

Brain Frequency(Hz) G'(Pa) G''(Pa) 1,000

25 1110 480

37.5 1310 570

50 1520 600

62.5 2010 800

90 3100 2500

CSF G0(Pa) G¥(Pa) b(s-1) K(MPa) 1,000

1,000 900 80 1,050

Viscous

damping

corticalbone

t(s) 10 102 10

3 10

4 10

5

G(t)/G0 0.973 0.95 0.915 0.853 0.773

Viscous

damping

cancellousbone

t(s) 1 2 3 4 5 6 7 8 9 10

G(t)/G0 0.93 0.9 0.888 0.873 0.865 0.875 0.852 0.834 0.74 0.7

27

Table3:Firstsixnon-zeronaturalfrequenciesforsimulations

Simulationdetails NaturalFrequencies(Hz)

No. Model BC MaterialTypes #1 #2 #3 #4 #5 #6

1 XM1 BC1 Corticalbone 2747 3223 3733 3833 3998 4507






7 XM4 BC3 Corticalbone

+cartilage#1

54 82 124 275 402 598

8 XM4 BC3 Corticalbone

+cartilage#2

54 82 124 233 384 586

9 XM5 BC3 Cortical+

cancellousbone+

cartilage#2

55 84 127 233 387 578

10 XM5 BC3 Viscoelasticcorticaland

cancellousbone+cartilage

#2

55 84 127 233 387 578

11 XM6 BC3+BC4 Viscoelasticcorticaland

cancellousbone,cartilage#2,

outerhead,brain,spinal

cord,FTM,CSF

15.4 16.0 16.1 16.4 17.1 17.8

12 CTM BC3 Corticalbone 115 127 230 406 974 1087

28

FIGURELEGENDS

Figure1:ModelsfromXCATphantom(ananatomicaldatasetderivedfromimaging).Themodels

aredenotedXM, and contain varying anatomical components andmaterial properties. XM1:

upperskull,excludingjawandneck;XM2:upperskullincludingjaw,butexcludingneck;XM3:

upper skull, plus jaw and neck. (XM1-XM3 were ascribed uniform material properties of

corticalbone).XM4:a refinementofXM3,withextra structuresat the connectionpointsof

thejawwiththeskull,whichweremodeledascartilage.XM5:arefinementofXM4inwhich

theupperskullandjawincludedinnerregionsofcancellousbone.XM6:arefinementofXM5

adding: 1) brain; 2) cerebrospinal fluid (CSF) surrounding the brain to approximate the

meninges;3)ventricles,filledwithCSF;4)theprocessesoftheduramater,thefalxcerebriand

thetentoriumandfalxcerebellimembranes(denoted"FTM");5)asinglevolumefortheouter

headtissues(skin,muscle,fat,etc.);6)thesectionofspinalcordontheinsideoftheneck.The

nodes selected for the prescribed boundary conditions (BC) are also displayed (BC1: free

vibrationofallnodes).BC2:tetheringofnodesatthebaseoftheskullclosetowheretheneck

wouldconnect;BC3:tetheringofnodesatthebaseoftheneck;BC4:tetheringofnodesatthe

basesurfaceoftheouterheadtissues.

Figure2:a)ThemodelderivedfromthepopulationaverageofCTdatafrompatients(CTM).b)-f)

Loading(L)positionsanddirectionsdisplayedwithXM3model(derivedfromXCATphantomand

consistingofskull, jawandneck,anduniformmaterialpropertiessettocorticalbone)..b)L1or

"headcradle",with templesvibrating inhead-footdirection. c) L2 templesvibrating left-right in

oppositedirections.d)L3templesvibratingleft-rightinsamedirection.e)L4or"acousticpillow",

posteriorofskullvibratinginanterior-posteriordirection.f)L5or"bite-bar",upperandlowerjaw

vibrating in left-right direction. g)-j) Motion of skull associated with the first four natural

frequencies(NF)ofXM4(refinementofXM3withconnectpointsbetweenskullandjawmodeled

ascartilage)withboundaryconditionBC3:g)NF#1;h)NF#2;i)NF#3;j)NF#4.

Figure 3: Comparison of mean x, y and z displacement components and overall displacement

magnitudesagainstfrequencyforskull-onlymodelsfordifferentwavedeliverymethods(loading,

L).XM5isthemodelderivedfromXCATphantomandconsistsofskull, jawandneck,regionsof

cartilageandcancellousbone,whiletheCTMmodelisderivedfromthepopulationaverageofCT

datafrompatientsandincludesonlycorticalbone.a)XM5L1;b)CTML1;c)XM5L2;d)CTML2;e)

XM5L3;f)CTML3;g)XM5L4;h)CTML4;i)XM5L5;j)CTML5.

29

Figure4:MRE simulationnodaldisplacementmagnitudes in theXM5model (derived fromXCAT

phantomand consistsof skull, jawandneck, regionsof cartilageand cancellousbone) far from

resonanceandattheresonancepeaksfordifferentwavedeliverymethods(loading,L,seeFig.2)

foraloadingamplitudeof10μm:a)examplefrequenciesfarfromresonance:L1at50Hz,L2at90

Hz,L3at90Hz,L4,at50Hz,L5,at30Hz;b)exampleresonantfrequencies:L1at125Hz,L2at55

Hz,L3at55Hz,L4at85Hz,andL5at55Hzand115Hz.

Figure5:ForXM6model(fullheadmodelderivedfromXCATphantom),comparisonofskulland

brain mean x, y and z displacement components and overall displacement magnitudes against

frequency for different wave delivery methods (loading, L): a) L1; b) L2; c) L3; d) L4; e) L5; f)

Comparisonofmeandisplacementmagnitudesforwavedeliverymethodsforskullandbrain.

Figure 6: Comparison of the real component of the displacement fields in x, y and z, and the

magnitudeofthecurl,andinversionreconstructionsofG'andG''at50Hzand90Hzfordifferent

wavedeliveryoptions (loading,L).Thedisplacementcomponentsareplottedon thesamecolor

scale of -0.03 to 0.03mm for ready comparison between directions,methods and frequencies.

However for Re(uy) of L1 at 90Hz the displacements are also plotted on themore appropriate

scaleof0to0.07mm.

Figure 7: ComparisonofmeanG' andG'' from inversions ofMRE simulations in XM6 (full head

modelderivedfromXCATphantom),andMeanabsolutepercentagedifferencewithgroundtruth

(MAPD)ofG'andG''forfullanderodedbrainmasksfordifferentwavedeliverymethods(loading,

L),andMAPDsofvoxel-wiseaverageofallfiveloadingmethodsforG'andG''.a)MeanG'forfull

brainmask against frequency, separate error bar plots for each loadingmethodwith standard

deviationerrorbars,andplotcomparingmeanvaluesforloadingmethodswithouterrorbars;b)

MeanG'' forfullbrainmaskagainstfrequency,separateerrorbarplots,andcomparisonplot;c)

MAPDofG'forfullbrainmaskforfivegroundtruthfrequenciesusedinmaterialspecificationfor

brain tissue, error bar plots and comparison plot; d)MAPDofG'' for full brainmask, error bar

plots and comparison plot; e) G'MAPD for eroded brainmask, error bar plots and comparison

plot;f)G''MAPDforerodedbrainmask,errorbarplotsandcomparisonplot;g)Errorbarplotsfor

voxel-wiseaverageoverloadingmethodsofG'andG'',forfullanderodedbrainvolumes.

this is an open access document downloaded from orca ...orca.cf.ac.uk/101022/1/modelling skull...

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