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EVALUATIONOFTHEIMPACTOFSTRAIN-CORRECTIONONTHEORIENTATIONOFCARDIACDIFFUSIONTENSORSWITHIN-VIVOANDEX-VIVOPORCINEHEARTSPedroFFerreira1*,SoniaNielles-Vallespin2,AndrewDScott1,RanildeSilva1,PhilipJKilner1,DanielBEnnis3,

DanielAAuger4,JonathanDSuever5,XiaodongZhong6,BruceSSpottiswoode7,DudleyJPennell1,Andrew

EArai2,DavidNFirmin1

1-CardiovascularBRU,RoyalBromptonHospital,London,UnitedKingdom

2-NHLBI,NationalInstitutesofHealth,MD,UnitedStates

3-DepartmentofRadiologicalSciences,UniversityofCalifornia,LosAngeles,CA,UnitedStates

4-BiomedicalEngineering,UniversityofVirginia,VA,UnitedStates

5-GeisingerMedicalCenter,PA,UnitedStates

6-SiemensHealthcare,GA,UnitedStates

7-SiemensHealthcare,TN,UnitedStates

WordCount:5157

*Addressforcorrespondence:

Dr.PedroFerreira

CardiovascularBRU,RoyalBromptonHospital,

London,SW36NP,UK

Email:p.ferreira@rbht.nhs.uk

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ABSTRACTPurpose: To evaluate the importance of strain-correcting STEAM-EPI cardiac diffusion tensor imaging

(cDTI).

Methods:Healthypigs(N=11)weresuccessfullyscannedwitha3DcineDENSEandaSTEAM-EPIDTIse-

quenceat3Tduringdiastasis,peaksystole,andstrainsweet-spotsinamid-ventricularshort-axisslice.The

sameDTIsequencewasrepeatedex-vivoafterarrestingthehearts ineithera relaxed (KCl-induced)or

contracted(BaCl2-induced)state.

TheDENSEdatawereusedtostrain-correctthein-vivocDTIindiastoleandsystole.Theorientationofthe

primary(HA)andsecondary(E2A)diffusioneigenvectorswascomparedwithandwithoutstrain-correction

andtothestrain-freeex-vivodata.

Results:Strain-correctionreducessystolicE2Asignificantlywhencomparedtowithoutstrain-correction

andex-vivo[medianabsoluteE2A=34.3ovsE2A=57.1o(P=0.01),E2A=60.5o(P=0.006)respectively].

ThesystolicdistributionofE2Awithoutstrain-correction isclosertothecontractedex-vivodistribution

thanwithstrain-correction,rootmeansquaredeviationof0.027vs0.038.

Conclusion:Thecurrentstrain-correctionmodelamplifiesthecontributionofmicroscopicstraintodiffu-

sionresulting inanover-correctionofE2A.Resultsshowthatanewmodelthatconsiderscellularrear-

rangementisrequired.

Keywords:cardiac;diffusiontensorimaging;strain;microstructure;cardiomyocyte;sheetlets.

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INTRODUCTIONMyocardialmicro-architectureisremarkablycomplex.Cardiomyocytesexhibitatransmuralhelicalorgan-

izationwithhelixangles(HA)rotatingsmoothlyfrompositiveintheendocardiumtonegativeintheepi-

cardium[1–3].Additionally,cardiomyocyteshavealaminarorganization,wheresheetsofcardiomyocytes

are surrounded by collagen-lined shear layers, as found histologically in many explanted mammalian

hearts[4–7].Thesemyolaminaeplayamajorroleintheradialthickeningandlongitudinalshorteningduring

theheartcycle[8–12].Thecollectiverotationofsheetletsaccommodatedbyshearlayerslippage,driven

bycardiomyocytecontraction,isthedominantcontributortotheradialthickeningandlongitudinalshort-

eningobservedin-vivo.Muchsmallercontributionsarisefromsarcomeredrivenchangesincardiomyocyte

shape[13].Becausemyolaminaearediscreteandexistonlyverylocally,Halesetal.referredtothemas

sheetlets[14].

CardiacDiffusionTensorImaging(cDTI)isanMRimagingtechniquethatencodestheself-diffusionofwater

moleculesinthreedimensions.Adiffusiontensoriscalculatedforeachvoxelandseveraldiffusionrelated

parameterscanbeextracted.Theorientationofthetensoriscloselylinkedtothevoxels’microstructure.

Ithasbeenshownthattheprincipaldirectionofdiffusionalignswiththecardiomyocytelong-axis,while

thesecondaryandtertiarydirectionsofdiffusionprovidecross-cardiomyocytesheetlet-planeandsheetlet-

normaldirectionsrespectively[15–20].Morerecentex-vivocDTIstudieshavebeenperformedwithhearts

inrelaxedandcontractedstates,thusprobingmicrostructuralreorganizationduringcontraction[14,21].

NosubstantialchangesofHAweremeasured,butthesheetletplaneswerefoundtorotatefromalmost

perpendiculartothelocalmyocardialwallinsystoletomorewallparallelindiastole,inagreementwith

currentmodelsofsheetletrotationduringcardiaccontraction.

In-vivocDTIhasattractedrenewedinterestaidedbynewtechnicaladvancementsinbothhardwareand

pulsesequencedesign[22–26].Douetal. in2002reportedin-vivorotationofsheetletstowardsamore

radialconformationduringsystoliccontractioninonehealthyvolunteer[27].Morerecentstudiesconfirm

asimilarpatternofsheetletrotationinacohortofhealthyvolunteersandabnormalsheetletdynamicsin

cardiomyopathypatients[28–30].

Twocommonapproachesexistforencodingdiffusionin-vivo:amotioncompensatedspin-echowiththe

encodinglastingforonlyafewtensofmilliseconds[24,26];andamonopolarstimulated(STEAM)approach

wherediffusionisencodedoveranentirecardiaccycle[31].Thespin-echoapproachencodesdiffusionin

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asingleheartbeat,althoughthediffusionencodingtimeisaroundtwoordersofmagnitudeshorterwhen

comparedwiththeSTEAMapproach,whichresultsinprobingsmallermicrostructural lengthscalesand

concomitantlyhighermeasureddiffusivities[32–34].

ASTEAMapproachtakesfulladvantageofcardiacmotionbeingperiodic,withthediffusionencoding/de-

codinggradientsappliedwhentheheartisatthesamepositioninsuccessivecardiaccycles.Thistechnique

requiresbreath-holdingordedicatedrespiratorytriggering.However,awell-knowndisadvantageofthe

STEAMapproachisregularlydebated:cardiacstrainsensitivity.Eventhoughtheheartreturnstoitsorigi-

nal position,measuring diffusionwith a STEAM sequence requires consideration of themyocardium’s

strainhistoryduringthediffusionencodingperiod[35–37].Recentlywehavesuccessfullyacquiredin-vivo

cDTIdataonbothhealthyandcardiomyopathypatientswithamonopolarSTEAMecho-planar imaging

(EPI)sequencewithboth intraand inter-centerreproducibility[28,30,38,39],butquestionsaboutstrain

effectsremainedunanswered,inparticulartheeffectsonthemeasurementofsheetletrotationbetween

systoleanddiastole.

Myocardialstrainthroughoutthecardiaccyclecanbemeasuredandsubsequentlyapplyacorrectionto

thediffusion tensordata acquired in systoleordiastole[29,36].However, the current strain-correction

modelignoressheetletrotationasamajorcontributortowallthickening,andthereforelikelyto“correct”

thediffusiondataforanexaggeratedstraineffect.

Theobjectiveofthisstudywastoevaluatetheeffectofstrain-correctingcDTIdatabydirectlycomparing

in-vivocDTIdatawithandwithoutstrain-correctionaccordingtotheestablishedmodelproposedbyReese

etal.[36],withstrain-freeex-vivoDTIdataofthesameporcineheartsarrestedinadiastolic-likeorsystolic-

likeconformations.

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METHODSTheporcinecDTIdataanalyzedherearepartofalargerdatasetpreviouslyusedtocomparedin-vivo,in-

situ,andex-vivoDTIscanswithhistologywhereinnostrainanalysisorcorrectionwasapplied[30].Here,

wereportdatafromasubsetinwhich3Dstrainwasacquiredsuccessfully.Ashortenedversionofthiswork

hasbeenpresentedatSCMR2017[40].

EXPERIMENTALDESIGNAnimalprocedureswereapprovedbytheNationalHeart,Lung,andBloodInstituteAnimalCareandUse

Committee.SixteenYorkshirepigs(weight30to35kg)werestudied.Anesthesiawasinducedwiththeuse

ofatropine,butorphanol,ketamine,andxylazineandmaintainedwiththeuseofinhaledsevofluraneand

supplementalIVpropofol,togetherwithmechanicalventilation.

Allimagingwasperformedat3T(MAGNETOMSkyra,Siemens,Germany)usinginvestigationalprototype

sequences,aphasedarraySiemenstorsocoilandspinearraycombination.Themeancardiaccyclelength

was737±82ms.

Followinginitialscans,whichincludedbreath-holdretro-gatedcines,thepigswerescannedwithamulti-

slice cine-DENSE sequencewith3Ddisplacementencoding[41] covering theentire left-ventricle (LV) in

ordertoobtain3Dstraintensorsthroughouttheentirecardiaccycle.ThiswasfollowedbycDTIacquisitions

inonemid-ventricularsliceatmultipletimepointsthroughoutthecardiaccycle includingdiastasisand

peaksystoleasdeterminedfromashort-axiscineinthesameplane.

Alltheanimalsweresubsequentlyeuthanizedunderanesthesiaineithera“diastoliclike”statewithan

intravenousadministrationofKCl(4meq/Kg)(N=8),ora“systoliclike”statebyintravenousadministration

ofBaCl2(40meq/Kg)(N=8).Theheartswereexcisedandrinsedinnormalsaline.Preparationfollowed

theprotocolsdescribedbyKungetal.[18].Thecoronaryarterieswereflushed,andthecardiacchambers

filledwithvinylpolysiloxane(MicrosonicInc.USA).Theheartswereplacedinacylindricalcontainerfilled

withasusceptibilitymatchingfluid(FomblinY-LVAC6-06,SolvaySolexis,USA)andweresupportedusing

open-cellfoam.cDTIwasthenrepeatedinthestaticexcisedheartsforamid-ventricularsliceusingthe

samesequenceasused in-vivo.This slicewasvisuallypositionedtomatch the in-vivosliceasmuchas

possible.

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STRAINIMAGINGAfreebreathingnavigator-gated2Dmulti-slicespiralcineDENSEimagingwith3Ddisplacementencoding

wasperformedwithcontiguousslicescoveringtheentireLV.Sequenceparametersincluded:inplaneFOV

320mmx320mmwithavoxelsizeof2.5x2.5mm2,slice-thickness8mm,flip-angle10degrees,timeof

repetition14ms,echotime1.16ms,temporalresolution32ms,displacementencodingfrequencyat0.10

cycles/mm,6spiralinterleaves.

WhileDENSEdatawasacquiredtocovertheentireLVonly5sliceswereusedfor3Dstraincalculation:two

slicesbothaboveandbelowthechosenmid-ventricularsliceof interest, theremainingslicesweredis-

carded.TheDENSEdatapost-processingmatrixwastherefore128x128x5pixels.

3D strain and right stretch tensorswere calculated from the DENSE data for themid-ventricular slice

throughoutthecardiaccyclewithMATLAB(Mathworks,Massachusetts,USA)basedsoftwaredeveloped

attheUniversityofVirginia[41,42].Theinitialmyocardialsegmentationwasperformedsemi-automati-

callyusingtheopen-sourcesoftwareDENSEanalysis[43,44].

Thestraindatawereusedfortwopurposes: firstly, to identifythetwosweet-spottimes inthecardiac

cycle(Figure1A);andsecondly,toderiveandregisterstretchtensorstothediffusiondatatobecorrected

(Figure1B)(seeSupportingInformation).

Thecomponentsofstrainalongthelocalcoordinatesofthediffusioneigensystemwascalculatedatpeak

systole.Torsionwasalsocalculatedbetweenthemostbasalandthemostapicalsliceaccordingtoequation

2fromRüsseletal.[45].

DIFFUSIONTENSORIMAGINGBreath-holdin-vivoDTIdatawasacquiredinonemid-ventricularsliceat6to9timepointsinthecardiac

cycle.ASTEAM-EPIsequencewithamonopolardiffusionencodingschemewasusedwiththefollowingb-

values:bref=50s/mm2(20averages)inasingledirection;b=500s/mm2(20averages)in6diffusionen-

codingdirections;b=150 s/mm2andb=350 s/mm2 in6directions (2averages). Zonalexcitation; fat

saturation;diffusionweightingtime1RRinterval;echotimeTE=30ms;BW=1838Hz/pixel;SENSEparallel

imagingaccelerationfactorof2;FOV=320mmx120mm;matrix=160x60pixels;EPIechotrainlength

=30readouts;echospacing=0.65ms;EPIreadoutduration=19.5ms;spatialresolution=2x2x8mm3

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interpolatedto1x1x8mm3byzerofillingk-space.Ex-vivoDTIscanswereperformedwithanidenticalpro-

tocol,witharepetitiontimesetto1400ms(diffusiontime700ms).

DTIdatawereanalyzedfromonlyfourcardiacphases:diastasis,peaksystole,andthetwoacquisitions

closesttothesweet-spottimesgivenbythecircumferentialstraincurve.

TheDTI datawere post-processedwith software developed in-house (MATLAB). Themyocardiumwas

manuallysegmentedexcludingtherightventricle,bloodpoolandpapillarymuscle.Threeparametersre-

latedtothediffusiontensororientationwereextracted:twoanglesconcerningtheprimaryeigenvector:

helix-angle(HA),andtransverseangle(TA);andananglerelatedtothesecondaryeigenvectorE2A[18,28]

(Figure2).IncontrasttoHA,TAandE2Ademonstratenoobvioustransmuralorganization,thereforefor

simplicity,themedianabsoluteangleisrepresentedwithoutthepolarityoftheangle.However,forcom-

pletenesstheanglepolarityisincludedintheDTIparametermapsandhistograms.Themeandiffusivity

(MD)ofthediffusiontensorwasalsocalculated.

Thediastolicandsystolicdiffusion tensordatawerecalculatedwithandwithoutstrain-correction,and

comparedtothesweet-spotsandtotheex-vivodiffusiondataofthesamemid-ventricularslice.

WilcoxonranksumandKruskal-Wallis (with follow-onpairwisecomparisons) testswereusedtoassess

differences.AP-valueequalorlowerthan0.01wasusedforthefollow-onpairwisecomparisonstoreduce

theprobabilityoftypeIerrorswhenperformingmultiplecomparisons.Inaninitialanalysis,wefailedto

findanyconsistentsignificantdifferencesbetweendifferentsectorsofthewallforDTImeasuresandhave

thereforekeptouranalysisglobaltoreducemeasurementnoise.

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RESULTSDiffusiontensordataweresuccessfullyacquiredforallpigsand3Dstraindataweresuccessfullyextracted

fromtheDENSEdatafor11oftheoriginal16pigs.TheremainingfivepigshadpoorqualityDENSEimage

dataand/orphase-unwrappingissues.Allsubsequentanalysisisthereforeshownfor11pigsonly(6with

adiastolicarrest,5withasystolicarrest).TheDTIacquisitiontriggertimeclosesttothecalculatedsweet-

spottimeswasdifferentby24±12ms.TwoDTIsweet-spotdatasets(of22)wereexcludedastheclosest

DTItriggertimedifferedbymorethan40ms.Themeanheart-ratewas83(10)bpm,andtheLVejection

fractionwas0.49(0.06)%.

STRAINMEASUREMENTSThemid-ventricularmeanradial,circumferential,andlongitudinalstrain-timecurvesareshowninfigure

3A.Themeasuredmean(standarddeviation)peakradial,circumferentialandlongitudinalstrainswere:

Err=0.21(0.06),Ecc=-0.14(0.02),Ell=-0.11(0.01).Thesweet-spotsgivenbytheEcccurvesarelocatedat

24%(7%)and74%(12%)oftheRRintervaltime.Globaltorsionwas5.3(1.5)degrees(figure3B).Thelargest

componentsofstrainarealignedwiththesheetlets(Esspositivestrain)andwiththemyocytes(Emmneg-

ativestrain).Theshearcomponents(Ems,Emn,andEsn)aresmalleratpeaksystole(figure3C).

DIFFUSIONTENSORDATAThemeasuredDTIparametersareshownintable1.Therearesignificantdifferencesbetweendiastolicand

systolicE2Avaluesforin-vivowithoutandwithstrain-correction(P<0.001andP=0.005respectively)and

forex-vivo(P=0.004).Additionallytherearesignificantdifferencesforthein-vivotransverseanglewithout

strain-correction(P=0.015),andfortheex-vivoHArange(P=0.004:P=0.03).Nosignificantdifferenceswere

foundforanymeasurebetweensweet-spot1andsweet-spot2.Meandiffusivitywasfoundstatistically

differentbetweendiastoleandsystoleforbothwithandwithoutstrain-correction(P<0.01andP=0.001

respectively)butnotforex-vivo(P=0.66).MDisapproximately40%lowerfortheex-vivoheartscompared

tothein-vivo.

Inadditiontomeasuringchangesfromdiastoletosystole,wealsocomparedthein-vivoresultswithand

withoutstrain-correctionwiththeex-vivoarrestedheartsinthesamecorrespondingstate(bottomoftable

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1).ExamplemapsshowingthethreeDTIorientationmeasuresin-vivo(bothwithandwithoutstrain-cor-

rection)andex-vivoareshowninFigure4fortwohearts,onearrestedinarelaxeddiastolic-likeandone

inacontractedsystolic-likeconformation.VisuallyHAandTAmapsshowasimilarconfigurationbetween

diastoleandsystole,andbetweenwithout/withstrain-correctionandex-vivo.E2Amapsshowpronounced

differencesbetweendiastoleandsystoleforthedatawithoutstrain-correction,withstrain-correction,and

ex-vivo.E2Amapsindiastoleshowlowpositiveandnegativeangleswhileinsystoletheyhavehighpositive

andnegativeangles.InbothdiastoleandsystolethereisasignificantdifferenceinE2Abetweenwithand

withoutstrain-correction(P=0.003andP=0.01respectively).Ex-vivoE2Asdiffersignificantlyfromthere-

spective systolic strain-correctedE2A (P=0.006)but less so from thediastolicnon-strain-correctedE2A

(P=0.037).Additionalangulardifferenceswerefoundbetweenthestrain-correcteddataandtheex-vivo

dataforthesystolicendocardialHAmeanvalues(P<0.001)andbetweenthediastolicTAwithandwithout

strain-correction(P=0.007).

TheabsolutemedianE2AvaluesfromTable1arealsodisplayedinascatterplot(Figure5).Themobilityof

the individual myocardial median E2A values between diastole and systole for the in-vivo data with-

out/withstrain-correction,betweenthetwosweet-spottimes,andtherespectivearrestedex-vivovalues

areshown.AlargerotationofE2isseeninthenon-strain-correcteddatafromamorewallparallelconfor-

mationindiastole(lowangles),toamorewall-perpendicularconformationinsystole(highangles).Asim-

ilareffectisseeninthestrain-correcteddata,althoughtherotationissmaller.Thebiggestdifferencebe-

tweenin-vivodatawithandwithoutstrain-correctionisinthesystolicphasewherethestrain-corrected

E2Aissignificantlylowerthanthenon-strain-correctedandtheex-vivocontractedsystolic-likearrests[me-

dianabsoluteE2A=34.3ovsE2A=57.1o(P=0.01),E2A=60.5o(P=0.006)respectively].AsinTable1,E2Ais

similarbetweenthetwosweet-spots.

Figure6andFigure7provideadditionalanalysisofHA,TAandE2A.Figure6plotsthemeantransmuralHA

lineprofiles,andhistogramsofthemyocardialdistributionofHAvalues.Thereisalineartransmuralpro-

gressionofHAvaluesinallcases,andaslightlywiderdistributionofHAvaluesintheex-vivodata.Noclear

transmuralorganizationwasfoundforTAandE2A.Figure7showsthedistributionofTAandE2Avalues.

ThereisnoapparentdifferencebetweentheTAwithandwithoutstrain-correctioninanyoftheplots,in

contrasttothelargedifferencesinE2A.AsobservedinFigure5,thesystolicdistributionsofE2Aangles

withoutstrain-correctionappearmoresimilartotheex-vivorelaxedandcontracteddistributionsthanaf-

terstrain-correction.Thein-vivosystolicdistributionappearstobethemostdifferentbetweenwithand

10

withoutstrain-correction;whilethedistributionpeaksat±90degreeswithoutstrain-correction,thepeak

occursatamuch lowerabsoluteangleof25degreeswithstrain-correction.Thecombinedsystolicand

diastolicrootmeansquaredeviationofthein-vivohistogramswithoutandwithstrain-correctiontothe

ex-vivohistogramsis0.027and0.038respectively.Thein-vivohistogramswithoutstrain-correctionare

thereforeclosertotheex-vivo.

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DISCUSSIONInpreviousworkweshowedthatinhealthyhumanheartsthereisasignificantrotationofE2Aastheheart

contractsfromdiastoletosystole,whileHAremainsrelativelyunchanged;however,theconfoundingcon-

tributionofstraintotheseresultswasunclear[28].Subsequentpre-clinicalstudieshavedemonstrateda

similarpatternofE2Arotationinaporcinemodelimagedin-vivo,andin-situandex-vivointheabsenceof

straineffects.Thesimilarityofthein-vivo,in-situandex-vivoresultsenabledustoinferthatthatpotential

straineffectsmustbesmall,althoughnostrain-correctionwasperformedinourpreviousreports.Inthis

work,weassessedtheperformanceofthestandardstrain-correctionmodel[35]bydirectlycomparingin-

vivoDTIdatabeforeandafterstrain-correctionwithex-vivostrain-freedata.Webelievethistobethefirst

studycomparingin-vivodiffusiondatawithandwithoutstrain-correctionwiththesameheartsafterarrest.

Apreviousstudypresentedstrain-correctedSTEAM-EPIdataacquiredinpeak-systoleanddiastole,demon-

stratingtheeffectsofstrain-correction[29].However,thesestudieslackedaground-truthwhichwehave

includedintheformofex-vivoDTIinthesamehearts.Wewerethereforeabletoquantifytheeffectof

strainonin-vivocDTIandassesstheperformanceofconventionalstrain-correction.

Severalimportantresultswerefoundregardingtensororientation.ChangesinHAandTAthroughoutthe

cardiaccycleweresmallandtheseparameterswere largelyunaffectedbystrain-correction.Ex-vivoHA

andTAvaluesanddistributionweresimilartoin-vivo,althoughtheex-vivoHAdistributionwasflatterthan

thein-vivocounterparts.Itisnoteworthythatourdatashowedverylowtransverseanglesatallcardiac

phasesinterrogated,indicatingahighlycoherentmyocyteorientation.IncontrastE2Avariesastheheart

contracts.Figure5andFigure7(lowerpanel)showthatin-vivoE2Achangedfrompredominantlylowab-

soluteanglesindiastoletopredominantlyhighabsoluteanglesinsystolewithoutstrain-correction.The

samedatawithstrain-correctionshowedamuchsmallershiftbetweensystoleanddiastole,withthelarg-

estdifferencesobservedinsystolewhenpre-andpost-strain-correctiondatawerecompared.Asexpected,

thedistributionofE2Avaluesatthetwosweet-spotswassimilar,becausetheheartwasinasimilarcon-

figuration.Whencomparingwithoutandwithstrain-correctiondatawiththecorrespondingex-vivore-

sults,wherenotissuestrainhistoryispresent,thewithoutstrain-correctiondatamorecloselyresembles

theex-vivodistributionsofE2A.Theseresultsareconsistentwithasubstantial rotationofE2between

diastoleandsystole, inkeepingwithcurrentmodelsofcardiaccontractionduetorotationofsheetlets

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withshearlayerslippage.Thecurrentstrain-correctionmodelartefactuallyreducesmeasuredE2Amobil-

ity.Astheheartspendsalongerproportionofthecardiaccycleinarelaxedratherthancontractedstate,

theeffectofstrain-correctionismostmarkedondataacquiredatpeaksystole.

ThechangeindistributionofE2Aanglesfromdiastoletosystolewasmuchmorepronouncedthanthat

measuredinaLangendorffperfusedratheartmodelfromHalesetal.[14].Moreworkisneededtoascer-

tain ifthisdisparity isduetoprotocoldifferences, inparticulartheshorterdiffusionmixingtimeofthe

spin-echo sequenceusedbyHalesetal.,oranatomicalandphysiologicaldifferencesbetween the two

species.

Thein-vivoresultspresentedhereareconsistentwiththoseofStoecketal.inhumanhearts[29]andalso

withnumericalsimulations(seesupportingfigureS1andsupportingtableS1).Strain-correctingthediffu-

siondatasignificantlyreducedE2Amobility,andbroughtsystolicE2Avaluesclosetothesweet-spotvalues

wherestraineffectsareminimal.TheobservationthatE2Amobilityisreducedbystrain-correctionisnot

unexpected.MacroscopictissuestrainmeasuredwithMRIisintimatelyconnectedtocellularrearrange-

mentandsheetletshear,andthereforedirectlycorrelatedwithE2AmobilityasmeasuredbycDTI.Asthese

measuresareinextricablyinterconnected,correctingformacroscopicstraininevitablyleadstoalteredE2A

mobility.

Theeffectsofstrain-correctioncanbecategorizedaccordingtothreecardiacorthogonalcoordinates.The

diffusion tensororientationmeasuresareonlyaffectedby strain thathascomponentsalong thesame

directionsastherespectiveeigenvectors.Forexample,theprimaryeigenvectorofdiffusion,whichdefines

HA,iscommonlyalignedclosetothelongitudinal-circumferentialplane,withonlysmallcomponentsinthe

radialdirection.HAisthereforeminimallyaffectedbyradialstrain,commonlythedirectionwiththegreat-

estmeasuredstrain.Additionally,itwasfoundthattheeffectsoflongitudinalandcircumferentialstrain,

whicharetypicallyofsimilaramplitude,haveopposingeffectsonHA(seesupportingtableS2).Thiswork

thereforesuggeststhattheglobaleffectofstrainandstrain-correctiononHAissmall.Bycontrast,E2is

mainlyaffectedbythecumulativeeffectofradialandlongitudinalstrains,resultinginE2beingaffected

morebystrain-correction.

Thestrain-correctionmodelestablishedbyReeseetal.[35]assumesthehearttobeformedofagelatin

likematerialwhichisstretchedandcompressedatdifferentstagesofthecardiaccycle.Ifwearemeasuring

13

diffusionatpeaksystole,thenwhilethediffusionisbeingencodedmyocardialtissueinitiallyshortensra-

diallybeforecontractingtoitsoriginalposition.Thediffusionencodingintheradialdirectionistherefore

enhancedbythehistoryofmaterialstrain(Figure8).Converselyifmeasuringdiffusioninadiastolicstate,

thenthematerialwillbestretchedintheradialdirectionbeforecomingbacktoitsoriginalposition,re-

sultinginareductionofthemeasureddiffusionintheradialdirection.Analogousstraineffectswillhappen

inthelongitudinalandcircumferentialdirection.Thisisthebasisofthepreviouslyproposedstrain-correc-

tionmodel:fromthe3Dstretchtensorhistorythroughoutthecardiaccycle,onecancorrectthemeasured

3D diffusion tensor to cancel these strain effects. However, this model assumes a uniform diffusivity

throughoutthecardiaccycle,withnobarriersonthescaleswemeasurediffusionon;additionally,itas-

sumesthatmacroscopiccardiacdeformationisaresultofelasticmaterialstretchonly.Itisnowgenerally

recognizedthatthemajorityofwallthickening,andlongitudinalshortening,isnotduetocardiomyocyte

stretchbutduetocellularreorganizationandtransmuralshearmoderatedbyitslaminarorganization.For

thisreason,itisthoughtthatthepreviouslyproposedmodelmaysignificantlyoverestimatetheeffectsof

microscopiccardiomyocytestrainbasedonthemeasuredmacroscopictissuedeformation.

TheworkbySonnenblicketal.measuredareductionof15%inthelengthofthecardiomyocytesarcomere

inthecanineheart[13],whichresultsinapproximately8%increaseinradiusforincompressiblecardiomy-

ocytes.Thein-vivomedianwallthickeninginthisstudywasapproximately28%.Assumingwehavesimilar

cardiomyocytesarcomerelengthandradiuschangesintheporcineheart,thenapproximately30%ofthe

macroscopicwallthickeningcouldbeduetomicroscopiccardiomyocytestrain.Microstructuralstrainand

reorganizationofthetissuewillthereforeimpactonthemeasuredtensor,butthemodelrequiredtode-

scribethisishighlycomplexandyettobeelucidated.Inthispaper,wemainlyanalyzetensororientation,

butthereisanimportantrotationalinvariantmeasurethatweshoulddiscuss:meandiffusivity.MDpro-

videsameasureofthemeansquaredistancediffusedbywatermoleculesinagiventime.WiththeSTEAM

sequence,diffusionisencodedoveranentireheartcycle.Diffusivitymeasurementswilldependonmyo-

cyteshape,strainandperfusioneffects;allthreevarythroughoutthecardiaccycle.Withoutstrain-correc-

tion,MDdecreasesbetweendiastoleandsystole(1.11to0.99x10-3mm2s-1,p=0.01),andtheopposite

happenswithstrain-correction(1.00to1.14x10-3mm2s-1,p=0.001).AsimilarresultwasfoundbyStoeck

etal. inthehumanheart[29].Themeasuredex-vivodiffusivitiesareapproximately40%lower,whichis

expected when diffusion measurements change from body temperature to room temperature. Im-

portantly,thereisnosignificantchangeinMDex-vivofromdiastoletosystole(P=0.66),wherenostrainor

perfusioneffectsarepresent.

14

WehavesimplifiedtheTAandE2Aanalysisbycalculatingthemedianvaluefromtheabsolutedistribution,

ignoringanglepolarity.WebelievethistobeavalidsimplificationbecausethesignedTAandE2Adistribu-

tionsfromFigure7appearsymmetric.ThemedianvalueofabsoluteE2Aisthereforeameasureofsheetlet

tiltrelativetothelocalheartwall.

Inthiswork,weassumethattheex-vivoarrestedrelaxedandcontractedconformationsapproximateto

diastoleandsystolein-vivo.Duetothelackofbloodpressureloading,thearrestedcontractedheartwall

thicknesswasfoundtobe140%ofthein-vivosystolicwallthickness.Histologyoftheseex-vivopighearts

afterfixationwasperformedforanotherstudyandsheetletandshearlayerorientationswerefoundto

correlatetodiffusionE2orientationmeasuredwithDTIinbothex-vivoandin-vivodata[30].Wetherefore

believethattheex-vivocontractedsystolic-likestateapproximatesthein-vivoconformationofthemicro-

structure.

Therearetwoimportantlimitationstothiswork:thelownumberofanimalsstudied,andtheavailable

spatial-resolutionofcurrentin-vivoMRmeasurementsofstrainanddiffusion.Diffusiontensorestimation

fromavoxelcontainingalargenumberofcardiomyocytesandmyolaminaecanonlybemeaningfulifthere

iscoherenceofthemicrostructure.Histologystudieshaveobservedtwopopulationsofcountersloping

sheetletsandshearlayers[18];moreadvanceddiffusiontechniqueswillberequiredtointerrogatethese

multiplepopulations[46].Theaccuracyofradialandlongitudinalstrainisalsoaffectedbythelowspatial

resolutionused inDENSE imaging.Porcinestrainvaluesmeasured inthisworkwerefoundtobe lower

than typical valuesmeasured in humans, therefore the effects of strain-correction are expected to be

greaterinhumans.DENSEcineimagingusesprospectiveECGgating,andthereforethelateststagesofthe

cardiaccyclemaynotbeimaged.Someoftheindividualstraincurvesexhibitalatesystolicpeak(more

than60%oftheRR-interval)whichisnotphysiologicalandlikelyduetounderestimationoftheR-Rinterval

anderrorsintheDENSEanalysis.Microvascularperfusionwill influenceourdiffusionmeasurementsin-

vivo,inparticularmeandiffusivity[47],althoughitdoesnotseemtosubstantiallyimpactprincipaleigen-

vectororientationsignificantly[48].

15

CONCLUSIONSThecurrentlyacceptedmodelofstrain-correctionfordiffusiondataobtainedwithaSTEAM-EPIsequence

doesnotsignificantlyaltermeasuresrelatingtotheprimaryeigenvector(HAandTA).However,ithasa

considerable impacton theorientationof thesecondaryeigenvector (E2A). In-vivoE2Avalueswithout

strain-correctionapproximatemorecloselytothestrain-freeex-vivovaluesinarelaxeddiastolic-likeand

contractedsystolic-likestates,thanafterstrain-correction.Amorecompletemodelofdynamicmyocardial

microstructureisneededtoenableaccuratestrain-correctiontakingintoaccountcellularrearrangement

andsheetletshear.

16

FIGURECAPTIONS

Figure1–A:diagramshowinghowthesweet-spottimesarecalculated.Thesweet-spottimesaredefinedwhenthemeasuredstrainequalsitsmeanvalue.ThemeanLVcircumferentialstrain-timecurvewasused,asthehighernumberofpixelsalongthecircumferentialdirectionarelikelytomakeitmorerobustthanthe radialor longitudinal strain curves.B: flowchart showinghow thestrain-correction isapplied to thediffusiontensors.Dobsisthediffusiontensorbeforestrain-correction;U(t)isthestretchtensorthroughoutanentirecardiaccycleD;Disthediffusiontensorafterstrain-correction.

Figure2–DiagramshowingthedefinitionsofHA,TAandE2A.TocalculateHA,E1isprojectedinthelocallongitudinal-circumferential plane shown in blue (E1proj). The anglebetweenE1 and E1proj defines TA.The angleof E1proj to the circumferential axis definesHA.HA is positive for a right-handedhelixwhenviewedfromtheapex.TAispositiveifitrotatesclockwisefromthelongitudinal-circumferentialplaneandnegativeifitrotatescounterclockwise,whenlookingalongthecircumferentialaxisdirection.Theprojec-tionof E1 is thenused todefine theplaneperpendicular to it, knownas the cross-cardiomyocyteplaneshowninred.Thisplanecontainstwoorthogonaldirections:theradialdirectionandthewalltangentdi-rection.ThesecondaryeigenvectorE2 isprojected intothisplaneandtheanglebetweenE2projandthewall-tangentdirectiondefinesE2A.E2A ispositive ifpointing towards theapexandnegative ifpointingtowardsthebase.

Figure3– (A)Radial (Err),circumferential (Ecc),and longitudinal (Ell) straincurvesnormalizedtotheRRintervalfortheanterior,lateral,inferiorandseptumsectors.Thethinlinesrepresentthesubjects’meanstrain curves averagedover the LV sliceof interest, and the thick lines represent the intersubjectmeanstraincurve.(B)globaltorsioncurves.(C)Straintensorcomponentsalongthediffusiontensorcoordinatesystematpeaksystole(mm–alongmyocytes,ss–alongsheetlets,nn–alongsheetlet-normal;shearcom-ponents:ms–myocytesheetlet,mn–myocytesheetlet-normal,sn–sheetletsheetlet-normal).

Figure 4 – ExampleDTImapsof tensororientationmeasurements:HA, E2A, and TA for twohearts, onearrestedindiastole(left)andonearrestedinsystole(right).

Figure5–MedianabsoluteE2Avalues.Thein-vivovaluesshowthemobilityofE2Afromadiastolictoasystolic phasewith andwithout strain-correction and at the two-time points closest to the sweet-spottimes.Therespectivecolor-codedex-vivoheartsarealsoshownforeitheradiastolicorsystolicarrest.

Figure6–Top:meantransmuralHAlineprofileswithintersubjectinterquartilerangeattheendocardium;mesocardium; epicardium. Line profiles are shown for diastole and systole with and without strain-correction,atthetwosweet-spottimes,andforthearrestedex-vivohearts.TheR2valuesaretheadjusted

17

R2 for a linear fit. Bottom:HA histograms of allmyocardial voxels at diastole (with andwithout strain-correction),systole(withandwithoutstrain-correction),thetwosweet-spots,andfortheexplantedheartsarrested in a diastolic/systolic like state. Thehistogram curves show the intersubjectmedian and inter-quartilerange;binsizeis10degrees.

Figure 7 – TA (Top) and E2A (Bottom)histogramsof allmyocardial voxels at diastole (with andwithoutstrain-correction),systole(withandwithoutstrain-correction),thetwosweet-spots,andfortheexplantedheartsarrested inadiastolic/systolic likestate.Thehistogramcurvesshowthe intersubjectmedianandinterquartilerange;binsizeis10degrees.

Figure8–Simulationoftheeffectsofanelasticstretchonafreediffusioncloudofparticles.Astretch>1loop of the material during diffusion encoding will result in a reduction of the diffusivity along thatdirection.Astretch<1loopwillhavetheoppositeeffect.

SupportingFigureS1–Simulateddiffusiontensors,andtherespectiveHA,E2AandTAmapsandhistogramswithandwithoutstrain-correctionforadiastolicandsystolictensorconformation.

18

TABLETITLESANDCAPTIONS

Table1–Diffusionparameters

Top:Diffusionparametersin-vivowithandwithoutstrain-correction,atthein-vivosweet-spotsandattheex-vivoarrestedhearts.HArange isthemeananglerangefromendocardiumtoepicardium.TAandE2AarethemedianoftheabsolutevaluesofallLVmyocardialvoxels.MDisthemeanoverallLVmyocardialvoxels.Allvaluesareshownas intersubjectmedian[interquartilerange].* (red)-denotesastatisticallysignificantdifferencewhencomparedtothecorrespondingsystolicorsweet-spot2value(P<0.05).

Bottom:Pvalueswhencomparingbetweenin-vivowithoutandwithstrain-correction(sc)andex-vivoar-rested. HA range is themean angle range from endocardium to epicardium. *(red) - denotes statisticaldifference (P<=0.01; P-value threshold with a Bonferroni correction for 3multiple tests, conservativelyroundeddownto0.01).

Supporting tableS1–Numerical simulations:effectsof strain-correctiononDTIparameters.HArange isthemeananglerangefromendocardiumtoepicardium.TAandE2Aarethemedianoftheabsolutevaluesofallmyocardialvoxels.

SupportingtableS2–SummaryoftheeffectsofeachstraindirectiontoHArangeandE2A.TAisnotcon-siderablyaffectedbyanystraindirection.↗=increase;↘=decrease;−=noconsiderableeffect.

19

ACKNOWLEDGMENTSThisworkwassupportedbytheBritishHeartFoundation;theNationalInstituteofHealthResearchCardi-

ovascularBiomedicalResearchUnitattheRoyalBromptonHospitalandImperialCollege,London;andthe

NationalHeart,Lung,andBloodInstitute,NationalInstitutesofHealth,DivisionofIntramuralResearch,

DepartmentofHealthandHumanServices(HL004607-14CPB).

DISCLOSURESProfessorDudleyPennell receives researchsupport fromSiemens,and isastockholderanddirectorof

CardiovascularImagingSolutions.ProfessorDavidFirminreceivesresearchsupportfromSiemens.

20

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2015;74(2).DOI:10.1002/mrm.25418

withoutstrain-correction withstrain-correction sweet-spots exvivoarrests

diastole systole diastole systole sweet-spot1 sweet-spot2 diastole systole

HArange

(deg)

[36.9[6.9]:-

52.4[9.3]]

(P=0.14:P=0.58)

[40.3[4.7]:-

53.3[11.8]]

-

[35.7[6.7]:-

55.7[16.0]]

(P=0.79:P=0.39)

[37.2[3.9]:-

47.5[15.1]]

-

[37.8[4.0]:-

60.6[9.0]]

(P=0.34:P=0.92)

[31.4[10.9]:-

53.7[13.3]]

-

[35.0*[5.0]:-

51.8*[2.1]]

(P=0.004:P=0.03)

[46.5[3.7]:-

60.1[5.2]]

-

absolute

E2A(deg)

12.2*[2.6]

(P<0.001)

57.1[14.2]

-

19.3*[8.64]

(P=0.005)

34.3[11.4]

-

22.9[19.2]

(P=0.91)

24.7[10.0]

-

18.2*[5.42]

(P=0.004)

60.5[5.05]

-

absolute

TA(deg)

6.08*[1.46]

(P=0.015)

7.45[2.94]

-

8.3[2.38]

(P=0.89)

8.67[1.85]

-

6.42[2.17]

(P=0.18)

7.25[1.29]

-

5.92[0.56]

(P=0.13)

7.62[2.34]

-

MD(10-3

mm2s-1)

1.11*[0.07]

(P=0.010)

0.99[0.12]

-

1.00*[0.08]

(P=0.001)

1.14[0.07]

-

1.05[0.12]

(P=0.31)

1.10[0.19]

-

0.61[0.09]

(P=0.66)

0.66[0.11]

-

Betweengroupscomparison(Kruskal-Walliswithfollow-onpairwisecomparisons)

withoutscvswithsc withoutscvsex-vivo withscvsex-vivo

diastole

HArange(deg) P=0.98:P=0.72 P=0.59:P=0.99 P=0.48:P=0.77

absoluteE2A(deg) P=0.003 P=0.037 P=0.94

absoluteTA(deg) P=0.007 P=0.99 P=0.044

systole

HArange(deg) P=0.26:P=0.72 P=0.047:P=0.57 P<0.001:P=0.23

absoluteE2A(deg) P=0.01 P=0.74 P=0.006

absoluteTA(deg) P=0.91 P=0.76 P=0.56

Table1–Diffusionparameters

Top:Diffusionparametersin-vivowithandwithoutstrain-correction,atthein-vivosweet-spotsandattheexvivoarrestedhearts.HArange is themeananglerangefromendocardiumtoepicardium.TAandE2Aarethemedianoftheabsolutevalues of all LVmyocardial voxels.MD is themeanover all LVmyocardial voxels. All values are shownas intersubjectmedian[interquartilerange].*(red)-denotesastatisticallysignificantdifferencewhencomparedtothecorrespondingsystolicorsweet-spot2value(P<0.05).

Bottom:Pvalueswhencomparingbetweenin-vivowithoutandwithstrain-correction(sc)andex-vivoarrested.HArangeis the mean angle range from endocardium to epicardium. *(red) - denotes statistical difference (P<=0.01; P-valuethresholdwithaBonferronicorrectionfor3multipletests,conservativelyroundeddownto0.01).

SUPPORTINGINFORMATION

STRAINCORRECTIONTherightstretchtensorU(t)throughoutthecardiaccyclewascalculatedfromthestraintensordata

E(t):

! " = 2& " + ((1)

whereIistheidentitymatrix.

Justlikethediffusiontensors,thestretchtensorsarepositive-definite.Inordertoregisterthestretch

tensorstothediffusiontensorsandmaintainthepositive-definitenessalog-Euclideanmetric[1]was

usedwithanon-rigiddemonregistration[2].Thisregistrationstepwasperformedforthediffusion

datameasured(Dobs)atdiastasisandpeaksystole.

Toperformstrain-correction,thestretchtensorsareintegratedoveranentirecardiaccycleDwith

theinitialintegrationtimet=0atthesamecardiacphaseasthediffusiondatatobecorrected:

,obs =1Δ !(")12,!(")12d"

∆

5(2)

Dobs is the diffusion tensor without strain-correction and D is the diffusion tensor with strain-

correction.TheequationaboveneedstobesolvedforDasdescribedbyReeseetal.[3].

NUMERICALSIMULATIONSStretchtensorsanddiffusiontensorsweresimulatedbyusingthemedianeigenvaluesandthemedian

HAandE2Afromallthemeasuredin-vivodata.Ahollowdiscwasusedtosimulatethemyocardium

oftheLVinamid-slice.Thetensorshapeisgivenbytheeigenvalues,andthetensororientationby

thetransmuralHAdistributionwithahomogenousE2A.Tensordirectionalnoisewasintroducedby

3D rotating the diffusion tensors with a distribution of pseudorandom angles between [-10, 10]

degrees.Thisintroducedsometensororientationuncertaintywithoutchangingthetensorshape.

Theaveragestraincurvesfromfigure3wereusedtosimulatestretchtensorsthroughoutthecardiac

cycle with eigenvectors aligned with the local cardiac coordinates (radial, circumferential,

longitudinal).Theeffectsofstrain-correctingthediffusiontensorswerethenanalyzedforanaverage

diastolicandsystolicconformation.

Thenumericallysimulateddiffusiontensorsareshown insupportingfigureS1.Thevaluesandthe

effects of strain-correction agreewell with the animal data. E2A is themost affected parameter,

especiallyinsystole.ThiseffectcanbeseenasarotationofthediffusiontensorsaroundE1,withE2

towardsamorewallparallelorientationwithstrain-correction(frompanelCtopanelD).HAandTA

remain very similar throughout. The effects of the simulated strain-correction are summarized in

supportingtableS1.

SupportingtableS2showstheeffectsofeachstraindirectionindividuallytoHAandE2A.TAisnot

considerablyaffectedbyanystraindirection.

Supporting Figure S1 - Simulated diffusion tensors, and the respective HA, E2A and TA maps and

histogramswithandwithoutstrain-correctionforadiastolicandsystolictensorconformation.

diastole systole

input output input output

HArange(deg) [-48.631.9] ~ [-49.732.8] [-4934.2] ~ [-48.533.4]

absoluteE2A(deg) 12.2 ↗ 20.0 56.6 ↘ 40.7

absoluteTA(deg) 5.4 ↗ 7.3 5.6 ↘ 4.2

SupportingtableS1-Numericalsimulations:effectsofstrain-correctiononDTIparameters.HArange

isthemeananglerangefromendocardiumtoepicardium.TAandE2Aarethemedianoftheabsolute

valuesofallmyocardialvoxels.

diastole systole

Err Ecc Ell Err Ecc Ell

HArange(deg) − ↗ ↘ − ↘ ↗

absoluteE2A(deg) ↗ − ↗ ↘ − ↘

SupportingtableS2–SummaryoftheeffectsofeachstraindirectiontoHArangeandE2A.TAisnot

considerablyaffectedbyanystraindirection.↗=increase;↘=decrease;−=noconsiderableeffect.

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