Estimating cardiac contraction through high resolution data assimilation of a personalized mechanical model

ContentslistsavailableatScienceDirect

Journal of Computational Science

j o u r n al ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / j o c s

Impact of patient-specific LVOT inflow profiles on aortic valve prosthesis and ascending aorta hemodynamics

Jan Bruening

, Florian Hellmeier

, Pavlo Yevtushenko

, Marcus Kelm

,

Sarah Nordmeyer

, Simon H. Sündermann

, Titus Kuehne

, Leonid Goubergrits

aDepartmentofCongenitalHeartDiseaseandPaediatricCardiology,DeutschesHerzzentrumBerlin,AugustenburgerPlatz1,13353Berlin,Germany

bDepartmentofPaediatricCardiology,Charité–UniversitätsmedizinBerlin,AugustenburgerPlatz1,13353Berlin,Germany

cDepartmentofCardiothoracicandVascularSurgery,DeutschesHerzzentrumBerlin,AugustenburgerPlatz1,13353Berlin,Germany

dInstituteforComputationalandImagingScienceinCardiovascularMedicine,Charité–UniversitätsmedizinBerlin,AugustenburgerPlatz1,13353Berlin, Germany

a r t i c l e i n f o

Articlehistory:

Received29December2016 Receivedinrevisedform 13September2017 Accepted7November2017 Availableonline8November2017

Keywords:

Virtualtreatmentplanning Patient-specifichaemodynamics Image-basedcomputationalfluiddynamics Aortichaemodynamics

Cardiovascularmodelling Heartvalveprosthesis

a b s t r a c t

Patient-specificmodelsbecomeincreasinglyimportantincardiovascularresearchastheyallowpredic- tionofsurgicalprocedures.Whiletheleftventricularoutflowprofileisanessentialboundarycondition,it remainsunknownbeforetreatmenttakesplace.Toovercomethisproblem,hemodynamicsaftervirtual valvereplacementwerecalculatedbasedondifferentinletprofilesattheleftventricularoutflowtract:

agenericplugprofileandaprofilederivedfrom4D-flow-MRI.Spatiallyaveragedparameterswithinthe aortawerenotsignificantlyalteredusingeitherprofile.Agenericprofilemightbesufficientforthepre- dictionofhemodynamics,circumventingtheproblemofpredictingchangeinpatient-specificboundary conditions.

©2017ElsevierB.V.Allrightsreserved.

1. Introduction

Theassessmentofhemodynamicsusingcontinuouslydevelop- ingcomputationalfluiddynamics(CFD)isplaying anincreasing roleintheunderstandingofcardiovascularprocessesanddiseases [36].Thepossibilityofspatiallyandtemporallywellresolvedanal- ysisofhemodynamicswithoutanyneedforinvasivenessisone ofthereasonsthatCFDprovidesidealassistanceincardiovascular research.Furthermore,patient-specificplanningofdifferenttreat- mentmodalitiesmightbefeasibleinclinicswithinthenearfuture.

Thus,differenttreatmentstrategiesforaspecificpatientanddis- easemightbeinvestigatedandtestedin-silicobeforetheactual treatmentprocedure.

A requirement for using CFD in patient-specific analysis or treatmentplanningisthatthereconstructionofthecardiovascu- larsystem’sanatomyisfeasiblewithimagingtechniquessuchas

∗ Corresponding author at: Biofluid Mechanics Laboratory, Institute for ComputationalandImagingScienceinCardiovascularMedicine,Charité–Univer- sitätsmedizinBerlin,AugustenburgerPlatz1,13354Berlin,Germany.

E-mailaddress:[email protected](J.Bruening).

magneticresonanceimaging(MRI)andx-raycomputedtomogra- phy(CT).However,specificationofpatient-specificinletboundary conditionsisoftendifficultduetolackofinformationabouthemo- dynamics within the patient. Therefore, generalized boundary conditions,suchasparabolicorconstantinletvelocity(plug)pro- filesandliterature-basedflowrates,werecommonlyusedinthe past[15,25].

Duetoanincreasedavailabilityofmodernimagingtechniques inaclinicalworkflow,asforexamplefour-dimensionalvelocity encoded MRI (4D-VEC-MRI),acquisition of patient-specificflow conditionsandvelocityprofilesbecamepossible[1,11,30].Recent studiessuggestthatincorporationofpatient-specificvelocitypro- filesasinflowboundaryconditionimprovesaccuracyofCFD-based analysisofcardiovascularhemodynamics[6,17,28].Forexample, usageofpatient-specificinflowprofilesresultedinanoverallmore helicalflow,increasedwallshearstressandasignificantreduction ofpredictedpressurelossesinsimulationsofaorticcoarctations, comparedtosimulationsusinggenericinflowprofiles[17].Con- sequently,morerecentstudiesincorporatepatient-specificinlet boundaryconditionsintoimage-basedCFD-workflows[38].

Thus, usage of patient-specific inflow profiles should be favoured for numerical investigation of cardiovascular dis-

https://doi.org/10.1016/j.jocs.2017.11.005 1877-7503/©2017ElsevierB.V.Allrightsreserved.

eases.However,whenperformingpredictivetreatmentplanning, patient-specificinflowprofilesmightnotalwaysbeavailable.In general,useofclinicallyacquiredflowdataischallengingdueto alowerresolutionof4D-flow-MRIdatacomparedtoanatomical MRIorCTdata[17].SincedataofdifferentMRIsequencesforflow andanatomyhavetobeused,additionalstepsfordataregistration arerequired.Thesestepsmightbeasourceofadditionalerrors.

MisalignmentbetweentheMRIdatasetsfor anatomyand flow mightresultin misalignedinflowprofiles.Duetothemeasured noisewithinthe4D-flow-MRIsequence,velocitiesoutsideofthe vessellumenmightbeincorporatedintotheinletvelocityprofile andthusresultinadditionalerrorsduringthesimulation.

Recent studies indicate that flow patterns and parameters describingorientationandposition,ofthemainflowwithinthe ascending aortacorrelatewith diseasesand remodellingof the aortasuchasaneurysmgrowthandatherosclerosis[8,16,27].Usu- ally those patterns are divided into main and secondary flow patterns. While the main flow patterns characterize (through- plane)flowparalleltothevesselorientation,asforexamplethejet eccentricity,secondaryflowpatterns,asforexampleswirl,recir- culationandhelicitycharacterizeflowperpendiculartothevessel orientation(in-plane).However,noclinicallyrelevantthresholdsof theseparametersweredefinedasofyet.Nonetheless,itmightbe beneficialtoconsidertheseparametersuponjudgingthesuccess ofaspecifictreatmentinthefuture.Whilethoseparameterscanbe measuredin-vivousing4D-flow-MRI,predictingtheirchangeafter treatmentisnotyetpossible.

Ageneralaimisthedevelopmentamethodology forvirtual aorticvalvetreatment,whichallowspredictionofhemodynamic changesduetotreatmentofdiseasedaorticvalves.Thismethodol- ogyrequiresmodellingoftheleftventricularoutflowtract(LVOT), theaorticvalve prosthesisandthe aorta.As mentionedbefore, patient-specificvelocityinletprofileswithintheLVOTcouldaffect accuracyandoutcomeofpredictedpost-treatmenthemodynam- ics.However,anaorticvalvereplacementproceduremightalter theventricularfunctionaswellastheLVOT’sgeometryandthus thehemodynamicswithintheLVOTseverely.Thesechanges,and therefore patient-specific boundary conditions as well,are not knownaprioriandthereisnowaytopredictthemasofyet.

Thepresentedstudyfocussesontheimpactofchosenveloc- ityinflowprofilesattheLVOTonestimatedhemodynamicsafter apatient-specificaorticvalvereplacementprocedure.Desirably, thechoiceofvelocityinflowprofileshasnooronlyminorimpact onthesepredictedhemodynamics.Thisstudy’shypothesisisthat position,sizeandtypeoftheaorticvalvearethemaincontributors indefiningaortichemodynamics.Itishypothesizedthattheimpact ofthechosenvelocityinletprofileonthesehemodynamicsisonlyof minorimportance,sincethevalveprosthesisitselfstronglyaffects

andsculptsthehemodynamics.Thetransitionfromthevascular tissuetowardtheartificialvalveprosthesisisusuallynotsmooth.

Disturbancescausedatthejunctionsbetweentissueandprosthesis aswellasthenon-physiologicshapeoftheprosthesesmighthave ahigherimpactontheaorticflowthanthevariabilityofflowpro- fileswithintheLVOT,upstreamoftheprosthesis.Ifthisassumption isvalid,usageofgenericnon-patient-specificvelocityinletpro- filesmightbeusedforpredictionofhemodynamicoutcomeafter replacementofadiseasedaorticvalve.

InordertounderstandtheimpactofLVOTinflowconditionson theaorticvalveandtheascendingaortahemodynamics,anMRI- basedCFDstudyofanaorticvalvereplacementprocedurewith mechanicalorbiologicalvalveprosthesesintenpatientswasper- formed.Agenericpluginletvelocityprofilewascomparedagainst patient-specificLVOTvelocityinletprofiles.Hemodynamicparam- eterscharacterizingvalveprosthesisfunctionandaorticflowwere compared.

2. Materialsandmethods 2.1. Studypopulation

Tenpatients,whounderwentaorticvalvereplacement,were included within this retrospective study. Treatment of these patientswasperformedattheDepartmentofCongenitalHeartDis- easeandPediatricCardiologyoftheGermanHeartInstituteBerlin.

Allbutonepatientweremaleandthemeanageofthissample was41years.Sixpatientsreceivedamechanicalandthreepatients a biological valve prosthesis.In theremaining patient,thedis- easedaorticvalvewasreplacedusinghisautologouspulmonary valve(Rossprocedure).DetailedinformationisprovidedinTable1.

Informedconsentwassignedbyallpatientsandusageofretrospec- tiveimaging datawasapprovedbytheresponsibleinstitutional reviewboard.

2.2. Imagingdata

Conventionalaswellasvelocityencoded(4D-flow)MRIimages wereacquiredwithinonescanningsessionusinga1.5TeslaAchieva MRI scanner (Philips Medical Systems, Best, The Netherlands).

Reconstructedvoxelsizeswereequaltoorbelow1.8×1.8×2.0 mm³ for conventional MRI images (see Table 1 for exact val- ues), while the spatial resolution of 4D-flow-MRI images was 2.3×2.3×2.8mm³.ConventionalMRIsequencesforreconstruc- tionoftheanatomywereonlyacquiredfortheend-diastolicstate, whilethe4D-flow-MRIsequenceformeasuringthepatient-specific hemodynamicshadatemporalresolutionof1/25thofthecardiac cycle.

Table1

Overviewofpatientsincludedwithinthisstudy.Thepatients’ageandsexarespecifiedaswellasthetypeofvascularandvalveprosthesisusedduringsurgicalvalve replacement.Thediameterspecifiedequalsthenominalsizeofthevalveprosthesisaccordingtothemanufacturer’sinformation.Incaseofpatient02thediameterequals theinnerdiameterofthevalveprosthesis.Ifavasculargraftwasusedtoreplacetheascendingaorta,thegrafttypeanddiameterusedarespecified.Sincespatialresolutions forconventionalMRIdatavariedbetweenpatients,theresolutionisspecifiedaswell.

Patient AorticValveProsthesis VasclularGraft MRIinformation

ID Sex Age Type Manufacturer Model Diameter Type,Diameter Voxelresolution

01 M 18 mech. St.JudeMedical Regent 25mm none 1.42×1.42×2mm³

02 M 15 biol. autologouspulmonaryvalve – 25mm none 1.42×1.42×2mm³

03 M 32 mech. St.JudeMedical Regent 25mm Hemashield,32mm 1.42×1.42×2mm³

04 M 67 biol. CarpentierEdwards MagnaEase 21mm none 1.83×1.83×2mm³

05 M 20 mech. St.JudeMedical Regent 25mm Hemashield,30mm 1.42×1.42×2mm³

06 M 50 biol. CarpentierEdwards MagnaEase 25mm none 1.42×1.42×2mm³

07 F 61 biol. Medtronic HancockII 21mm none 1.42×1.42×2mm³

08 M 13 mech. Medtronic OpenPivot 21mm Hemashield,24mm 1.39×1.39×2mm³

09 M 71 mech. St.JudeMedical Regent 23mm none 0.91×0.91×2mm³

10 M 60 mech. Medtronic OpenPivot 25mm none 0.61×0.61×2mm³

2.3. Segmentation

Pre-interventional,patient-specificgeometriesoftheleftven- tricularoutflowtract,aswellastheaorta,includingtheascending aorta,theaorticarchandthedescendingaorta,weresegmented fromconventionalMRIimages.Duetotheresolutionofthecon- ventionalMRIimages,thethinleafletsoftheaorticvalve could notbesegmented.Therefore,thepre-interventionalstateofthe aorticvalve couldnot be reconstructed. Thesegmentation was performedmostlymanuallyusingZIBAmira(v.2015.28,ZuseInsti- tuteBerlin,Germany).Roughsurfacegeometrieswerethencreated fromsegmentationsandsubsequently smoothedusingReMESH (v.2.0,IMATI,Genoa,Italy).Thissegmentationprocesshasbeen describedindetailearlier[17].

2.4. Virtualintervention

Virtual interventions were performed by altering pre- interventional patient-specific geometries obtained after segmentation and subsequent smoothing. Those geometries werealtered accordingto surgery reports of realinterventions performedonpatients.In alltencasesa geometryof theaortic valve prosthesis used during surgery was virtually implanted withintheaorticgeometry.Tofacilitatethis,theregionsurround- ingtheoriginalaorticvalveannuluswasremovedfromthevessel geometrybycutsperpendiculartothevesselorientationandthe correspondingvalveprosthesisgeometrywastheninsertedand alignedwithinthiscutoffregionusingZIBAmira.Thesizeofthe removedregionwaschoseninrespecttothechosen prosthesis typetoensure,thatthegapcreatedwasbigenoughfortheartificial valve.Afterwards,thevalveprosthesisgeometrieswerestitched totheaorticbulbusaswellastheleftventricularoutflowtract (LVOT)usingGAMBIT(v.2.4.6,ANSYS,Inc.,Canonsburg,USA).

Bothmechanicalvalveprosthesismodelsusedwithinthisstudy werereverse-engineeredusingSolidWorks(v.2011,DassaultSys- tèmes, Vélizy-Villacoublay, France). The prostheses’ geometries werereconstructedfromtheadvertisingbrochuresandmanuals

both manufacturers provideontheirrespective websites. Mea- sures,suchastheinner and outerdiameters oftheprostheses, werederivedfromthesesourcesaswell.Theopeninganglesof bothprostheses werenotspecifiedbythemanufacturer.There- fore,measurementsbyDumontetal.wereusedtocorrectlymodel theopeninganglesofbothbi-leafletprostheses[9].Allvalveswere modelled in a fullyopened positionand details of theleaflets’

hingeswerenotconsidered.Mechanicalvalveswererotatedwithin thevalveregion,sothatleafletswereparalleltothecardiacseptum.

Thisistheusualorientationofmechanicalaorticvalveprostheses duringsurgery[31].

Biologicalvalveprosthesesusedfortreatmentofthreepatients were modelled using an optically scanned Fisics-Incor valve (INCOR,HospitaldasClínicas,UniversityofSãoPaulo,SãoPaulo, Brazil)[35].Thisvalvewasscannedinacompletelyopenedposition aswell.Biologicalvalveprostheseswererotatedtoalignthevalve leafletswiththethreeaorticsinuses.Thisprocedureisexemplarily showninFig.1Aforabiologicalvalveprosthesis.

Foronepatient,noartificialvalveprosthesis,buttheautologous pulmonaryvalveofthatpatientwasusedtoreplacetheaorticvalve.

ThisvalvewasmodelledinSolidWorksusingageometricdefinition oftri-leafletaorticvalvesproposedby[24].

Ifavasculargraftwasimplantedduringsurgery,abenttube withmatchingconstantdiameterandpositionwascreatedusing ZIBAmira.Theaorticsectionreplacedduringsurgerywascutoffthe virtualaorticgeometryaswell.Theartificialtubewasthenstitched toremainingpartsofthevesselusingGAMBIT(v.2.4.6,ANSYS,Inc., Canonsburg,USA).Thisprocedurewasperformedforthepatients 03,05and08.

2.5. Meshgeneration

Generation of computational meshes was performed using GAMBIT.Anodedistanceofapproximately0.6mmwasspecified forthecompletevolumedownstreamoftheaorticvalve.Here,a boundarylayerconsistingofthreeprismcelllayerswasspecified.

Thefirstlayer’sheightwassetto20percentofthenodedistance,

Fig.1.Visualizationofthegeometryofavirtualvalveprosthesisequaltothemodelusedwithintherealsurgicalinterventionalignedandstitchedtotheaorticroot(A).

Thenumericaldomainisshowntogetherwithchosenboundaryconditions(B).Attheleftventricularoutflowtract(LVOT)eitheranidealizedplugvelocityprofilewitha constantvelocityorapatient-specificvelocityprofilesextractedfrom4D-flow-MRIwasspecified(C).

Fig.2. Visualizationofinletboundaryshapesandvelocitymagnitudesofpatient-specificinletprofilesderivedfrom4D-flow-MRI.Thescaleforalltengeometriesisidentical.

Allgeometrieswererotatedinawaythattheobserverlooksfromtheventricleintotheaorta.Themitralvalvewouldbepositionedrightoftheprofiles.

whilethesubsequentlayer’sheightincreasedbyafactorof1.2.A nodedistanceofapproximately0.2mmwasspecifiedwithinthe aorticroottocompensateforthelackofaboundarylayer,which couldnotbeappliedduetothecomplexgeometriesoftheaor- ticvalveprosthesesused.Theresolutionusedwasshown tobe sufficientformeshindependentresultswithintheascendingaorta [17].Ameshindependencystudyforthepresentednumericalsetup indicated,thattheresolutionwassufficientformeshindependent resultsofthetransvalvularpressuredrop,whichvariedlessthan onepercentusinghigherresolutions,aswellasderivativesofthe flowfieldasforexamplethewallshearstresses.Detailsonthe meshesweredepictedinearlierwork[20].

2.6. Assessmentofpatient-specificvelocityinletprofiles

UsingGTFlow(gyroToolsLLC,Zurich,Switzerland),peakflow ratesattheascendinganddescendingaortawereacquiredfrom 4D-flow-MRIimages.Extractionofpatient-specificvelocityinlet profilesattheLVOTwasperformedusingMEVISFlow(v.9.0,Fraun- hoferMEVIS,Bremen,Germany).Segmentationoftheaortausing 4D-flow-MRIdata is difficult. However, a segmented geometry isnecessary tocorrectlydefinethepositionof theLVOTplane.

Therefore,abinaryDICOMimagestackwascreatedusingthevirtu- allytreatedgeometry.TheseimageswereloadedintoMEVISFlow togetherwiththe4D-flow-MRIimages.Firstly,thealignmentof 4D-flowandconventionalMRIimageswascheckedandaninter- activeregistrationwasperformedifnecessary.Thus,thecorrect positionoftheplaneforextractionofthevelocityinletprofiles couldeasilybedetermined.Afterthisregistrationstep,theveloc- ityinletprofilewasexportedasasetof3Dvelocityvectorswithin theplanechoseninMEVISflow.Thosevelocityvectorcomponents weretheninterpolatedontotheverticesoftheLVOTinletbound- aryusingZIBAmira.TheshapeoftheLVOTinletboundaryaswell asthevelocityinletprofileforeachpatientareshowninFig.2.

2.7. Computationalfluiddynamics

Steady-statesimulationsofthepeak-systolicaorticflowwere performedusingANSYSFluent(v.16.1,ANSYS,Inc.,Canonsburg, USA).Vesselwallsaswellasthevalveprosthesiswereassumed toberigid,andano-slip boundaryconditionwasappliedatall walls.Anoutflowboundaryconditionwasspecifiedforeachtrun- catingbranchingvesseloftheaorticarch,aswellasthedescending aorta.While theflow rateswithin theascending and descend-

Table2

Overviewofparameterscalculatedforeachpatient.Reynold’snumberswerecalculatedusingtheaverageflowvelocity,kinematicviscosityof3.33·10⁻⁶m²/sandthe nominalprosthesisdiameter(seeTable1).CoefficientsofdeterminationwerecalculatedforWSSaswellasvelocitymagnitudes.Pressuredropsacrosstheaorticvalve(p), thenormalizedflowdisplacement(NFD)aswellasthesecondaryflowdegree(SFD)withintheascendinganddescendingaortawerecalculated.Surface-averagedWSS withintheascendingaortaandaveragedturbulentkineticenergy(TKE)wereevaluatedforbothconditions.

ID Re R²[1] p[mmHg] NFD[1] SFDAoAsc[1] SFDAoDecs[1] WSSAvg,Asc[Pa] TKE[cm²/s²]

vel. WSS MRI plug MRI plug MRI plug MRI plug MRI plug MRI plug

01 11,800 0.776 0.819 6.3 7.8 0.095 0.091 0.70 0.74 0.11 0.17 20.7 19.3 250 210

02 6300 0.779 0.835 3.1 3.2 0.112 0.105 0.37 0.37 0.33 0.28 13.9 13.2 148 79

03 3850 0.675 0.627 8.6 12.1 0.029 0.025 0.85 0.89 0.16 0.15 15.5 18.4 350 20

04 4800 0.572 0.694 0.9 2.8 0.016 0.030 0.33 0.33 0.18 0.15 5.9 6.6 53 60

05 4250 0.339 0.458 1.4 3.9 0.092 0.048 0.57 0.59 0.15 0.29 5.6 4.3 350 20

06 3200 0.385 0.486 5.0 8.4 0.016 0.070 1.21 1.06 0.26 0.32 6.2 8.5 115 84

07 5400 0.723 0.658 6.2 7.8 0.021 0.030 1.54 1.53 0.53 0.54 4.5 4.9 117 146

08 3300 0.729 0.759 34.6 40.5 0.098 0.126 0.96 0.98 0.12 0.29 50.2 47.6 712 653

09 4650 0.388 0.535 4.5 13.7 0.066 0.137 0.81 1.00 0.62 0.64 15.1 12.0 245 112

10 2300 0.494 0.503 9.9 12.5 0.074 0.099 1.12 1.12 0.10 0.10 5.6 8.6 185 185

mean 5000 0.586 0.637 8.0 11.3 0.062 0.0760 0.84 0.86 0.26 0.29 14.3 14.3 232 167

SD 2650 0.173 0.139 9.7 11.0 0.038 0.0416 0.38 0.36 0.16 0.17 13.8 12.8 189 180

p-value 0.002(STT) .203(STT) .235(WSR) .577(STT) 0.978(WSR) 0.021(WSR)

Forallparametersfeaturingsignificantdifferences,p-valueswerehighlightedusingboldtext.

ingaortawasmeasuredusing4D-flow-MRI,flowratesflowingoff throughthebranchingvesselsoftheaorticarchweremodelled usingMurray’s Law [29]. Thissetupis visualizedin Fig.1B. To modelturbulenceobservedwithinsystolicaortichemodynamics [21],astandardk-omegaSSTturbulencemodelwithaturbulence intensityof5percentatthevelocityinletwasapplied.Theuseof aturbulencemodelisindicated,sincemeanReynoldsnumbersfor the10casessimulatedwas5000(seeTable2).Whiletheturbu- lencemodelusedisnotideallysuitedforcalculationofturbulence parameters,itissufficientforcalculationofhemodynamicparam- etersinvestigatedinthisstudy,asforexamplethepressuredrop [22]andthewallshearstresses[34].Bloodwasmodelledasanon- Newtonianfluidwithaconstantdensityof1050kg/m³andashear ratedependentviscosity[37].Forhighshearratesabove1000s⁻¹, thedynamicviscositywas3.5mPas. Eventhoughtherheology modelusedhasonlyaminorimpactonflowsimulationsduring peaksystole[23],modellingthenon-Newtonianbehaviourofblood reproducesin-vivoconditions,reducingadditionaluncertaintyin theresults[26].

AttheLVOT,a velocityinletboundaryconditionwasapplied usingeitheraplugvelocityprofileorthepatient-specificvelocity profileextractedfrom4D-flow-MRIusingMEVISFlow(seeFig.1C).

2.8. Qualitativeandquantitativeanalysisofhemodynamics

The flow withinthe valve prostheses and aorta wasvisual- izedusingZIBAmira.StreamlinesseededfromtheLVOTwereused aswellasvelocitymagnitudeprofilesimmediatelydownstream

theaorticvalveprosthesis.Besidesthisqualitativecomparisonof hemodynamicscalculatedusingbothvelocityinletprofiles,quan- titativecomparison ofrelevant flowparameters wasperformed aswell.Thepressuredropacrossthevalveprosthesiswascalcu- latedusingZIBAmira.Acenterlinewithevenlydistributednodes of0.1mmdistancewasgenerated.Thestaticpressurefieldcalcu- latedusingCFDwasaveraged,sothateachnodeofthecenterline representedtherespectiveaveragecross-sectionpressurewithin theaorta.Thesurfaceaveragedwallshearstresswithintheascend- ingaortawascalculatedforallcasesaswellasthesecondaryflow degreewithin onecross sectionof theascending anddescend- ingaorta.Thesecondaryflowdegreeisanindexdescribing the

“straightness”of tubularflow andis definedastheratioof the averageinplanevelocityandtheaveragethroughplanevelocity inonechosenplane.Furthermore,thenormalizedflowdisplace- ment(NFD)wasevaluated.Thisparameter,whichisdefinedasthe differencebetweenthecenterofthevesselandthecenterofthe flow,normalizedbythevesseldiameter[32],wasevaluatedinan aorticcrosssection,whichwasorientedatthecranialborderofthe rightpulmonaryartery.

Since numericalmeshes used for simulationswithplug and patient-specific velocity inlet profiles were identical, cell-wise comparisonofflowparametersbetweenbothvelocityinletprofile conditions wasfeasible.Correlation coefficients betweenveloc- ity,magnitudesaswellasthewallshearstressescalculatedusing bothinletprofiles,wereevaluatedasmeanstodescribespatially resolvedsimilaritywithintheflowfields.

Fig.3. Visualizationofhemodynamicscalculatedusingeitherthepatient-specific(left)ortheplug(middle)velocityinletprofileusingstreamlineswhicharecolored accordingtothevelocitymagnitudes.Additionally,thevirtuallytreatedgeometryisshownforeachpatient(right).

2.9. Statisticalanalysis

StatisticalanalysiswasperformedusingSPSSversion23(IBM, Armonk,USA).Differencesinallparameterscalculatedusingboth inletprofilesweretestedfornormaldistributionusingtheShapiro- Wilktest.Student’st-test(STT)wasthenusedtotestforsignificant differences within normally distributed parameter differences, whiletheWilcoxonsignedranktest(WSR)wasusedfortesting non-normallydistributed parameterdifferences.Alltestsuseda standardsignificancelevelof0.05andwereperformedtwo-sided.

3. Results

3.1. Qualitativecomparisonofhemodynamics

Hemodynamicoutcomescalculatedusingeithertheconstant plugorthepatient-specificvelocityinletprofileareshowninFig.3 visualizedbyusingstreamlines,whicharecolourcodedusingthe velocitymagnitude.Thevirtuallytreatedaorticgeometryisshown aswelltoindicateorientationandrotationofthevalveprosthe- sesusedinrelationtothevesselgeometry.Eventhoughthis is onlyaqualitativecomparison,notabledifferencesbetweenhemo- dynamicscalculatedusingbothconditionscouldbefoundinsome patients,whiletherewerehardlyanydifferencesinotherpatients.

Inpatient04,differencesinflowpatternsandvelocitymagni- tudescouldbeobservedwithintheLVOTaswellasthevicinity ofthevalveprosthesis.Thepluginletconditionresultedinhigher velocitiesnearthewalloftheLVOT.However,nodistincthemo- dynamicdifferenceswithintheascendingaortaortheaorticarch wereobservedbetweenbothconditions.Anoverallmoreequally distributedblood flowacrossthevalveprosthesisofpatient 05 couldbeobservedusingthepluginletcondition.UsingtheMRIinlet condition,ajetwaspassingbetweenoneleafletofthemechanical prosthesisandtheaorticwall,resultingintheflowbeingattached tooppositesitesinbothconditions.Bloodflowintheascending aortaofthepluginletconditionfeaturedmoreswirlsandwasover- alllessstraight.Inpatient06adistinctjetcouldbeseenintheMRI inletcondition.Thisjet,whichisformedbythebiologicalvalve prosthesis,wasorientedalongthecenteroftheascendingaorta.

Eventhough,usingapluginletprofileresultedinajetaswell,that jetwasorienteddirectlyattheaorticwall,resultinginhighveloc- itymagnitudesnearthewallaswellasarecirculationfeaturing velocitymagnitudesnearzero. Althoughorientationof stream- linesnearthewallwasthesameforboth conditionsinpatient 09,theascendingaortahemodynamicsfeatureddistinctivediffer- ences.Usingapluginletprofileresultedinabiggerrecirculation zone.Inpatient10ajetwaspredictedusingapluginletprofile.

Whileajetcouldalsobeobservedusingthepatient-specificpro- file,thisjetwasshorterandfannedoutquickly.Therefore,thelarge recirculationregionintheascendingaorta,observedusingtheplug inletcondition,wasnotpresentusingthepatient-specificvelocity inlet.Qualitativecomparisonofflowfieldsinthedescendingaorta revealednocleardifferencesinanypatient.

3.2. Quantitativecomparisonofhemodynamics

These findings agreedwith quantitativecomparison of flow field. Cell-wise correlations and corresponding coefficients of determination(R²)werecalculated forWSS aswellas velocity magnitudes(seeTable2).Theaveragecoefficientofdetermina- tionforWSScalculatedusingbothmethodswasR²_WSS=0.59,while theaveragecoefficientforvelocitymagnitudeswasR²_velocity=0.64.

However,coefficientscalculatedforindividualpatientsvariedindi- viduallyandrangedfrom0.34<R²_WSS<0.78and0.46<R²_velocity<

0.84respectively.Therefore,differencesbetweenhemodynamics

Fig.4. Bland-Altman-diagramforvisualizationofthedifferencesinthepressure dropcalculatedbothinletprofiles.

calculatedusingbothinletconditionswerebiggerinsomepatients thaninothers.Inpatientswereaqualitativecomparisonalready revealedhemodynamicdifferences,relativelylowcoefficientsof determinationwereobserved:patients04,05, 09and10.How- ever,coefficientsofdeterminationcalculatedforpatient06were below0.5aswell,indicatinglowagreementbetweenhemodynam- icscalculatedusingbothinletprofiles.

AccordingtotheShapiro-Wilktest,thefollowingparameterdif- ferencesbetweenbothconditionswerenotnormallydistributed (p<0.05): secondary flow degree within the ascending aorta (SFD_AoAsc),averagedturbulentkineticenergy(TKE).Consequently, differencesinthepressuredropacrossthevalveprosthesis(p), thesurface-averagedwallshearstress(WSSAvg,Asc),thenormalized flowdisplacement(NFD),aswellasthesecondaryflowdegreein thedescendingaorta(SFD_AoDesc)andthenormalizedflowdisplace- mentwerenormallydistributed.

Using a plug velocity inlet profile resulted in a significant increase in the pressure drop across the valve of 3.3mmHg, comparedtotheMRIinletprofilecondition(STT,p=0.002).Fur- thermore,pressuredropscalculatedusingbothmethodscorrelated significantly(R²=0.96,p<0.001)(Fig.4).

Volume-averagedTKE wassignificantlyincreased in simula- tionsusingaMRIinletprofilecomparedtothepluginletprofile condition(WSR,p=0.021).Inallotherparameters,nosignificant differencebetweenbothconditionswasobserved.

3.3. Changeinhemodynamicsdistallytothevalveprostheses

Toallowcomparisonofbloodflowintheimmediatevicinity ofthevalve,velocitymagnitudeprofilesimmediatelydownstream oftheaorticvalveprostheseswereextractedandvisualized(see Fig.5).Whilequalitativecomparisonofhemodynamicswithinthe wholeaorticdomainrevealedgoodagreementsinatleastsixout oftenpatients, goodagreementsin velocitymagnitudeprofiles downstreamoftheaorticvalveprosthesiswereonlyobservedin patient01, 03 and 07.In allother patients,notable differences betweenprofilescalculatedwitheitherinletprofilewasobserved.

Thesedifferencescomprisedshiftofthevelocitymaximum,differ- encesinvelocitymagnitudesandtheshapeofhighvelocityflow patterns.Norelationshipbetweentheagreementofflowprofiles downstreamofthevalveprosthesisandoftheinletprofile(see Fig.1)couldbeidentified. Whilethe inletprofileof patient07 featurednoclearcenter,profilesofpatients01and03featureda distinctcenteredmaximum.Inallothercases,wheretheflowpro-

Fig.5.Comparisonofvelocitymagnitudeprofilescalculatedusingbothvelocityprofileconditions.Theprofileswereevaluatedatacrosssectionimmediatelyafterthevalve.

Thedistancebetweentheleaflets’tipsandthedisplayedcrosssectionwasapproximately5mm.Theorientationandtypeofthevalveprosthesisusedineachpatientis indicatedusingagenericstencil.

filesdownstreamoftheprosthesescalculatedusingbothmethods differed,nocommonfeatureoftheinletprofilescouldbeidentified either.

4. Discussion

While insomepatientsstrongqualitativeas wellasquanti- tativesimilarityofhemodynamicscalculatedusingbothvelocity inletprofileswasobserved,thesehemodynamicsdifferedclearly inotherpatients.Infourpatients,correlationcoefficientsofwall shearstressesorvelocitymagnitudesbelow0.5wereobserved, revealinggrossdifferencesincalculatedflowfieldsandthusindi- catinganon-neglectableeffectofthevelocityinletprofilechoice towardsspatiallyresolvednumericalresults.

Eventhoughtherewasnoidealagreementinspatiallyresolved values in any patient, several spatially averaged parameters featurednosignificantdifferencebetweenbothvelocityinletcon- ditions.ThisincludestheSFD_AoAscandSFD_AoDesc,aswellastheNFD, whichareaveragedmeasuresoforientationandpositionofthe mainflow.Thisindicates,thatthesefeaturesaremainlyaffectedby thegeometryoftheaorticvalveprosthesesaswellasthegeome- tryoftheaortaitself.Assessmentofthoseparametersseemsrobust againstchangesinthevelocityinletprofileused.However,whether theorientationanddisplacementoftheflowismainlydefinedby theaorticvalveprosthesisortheaorticgeometrycannotbedeter- minedusingthisapproach.

While the interaction between hemodynamics and vascu- lar remodelling is not fully understood as of yet, correlations betweenabnormalhemodynamicsandaorticaneurysms,dilation

andatherosclerosisweresuggested[7,8,16,27].Therefore,notonly immediate measuresas thetransvalvularpressure drop should betakenintoaccountwhendeterminingthesuccessofanaortic valvereplacementprocedure.However,assessmentofparameters describingtheorientationanddisplacementofaorticbloodflow becamepossibleonlyrecently.Clinicallyrelevantthresholdsand marginsmust yet bedetermined.Especially becausesecondary flowpatternswereobservedinhealthysubjectsaswell[14,30].

First resultssuggest, forexample, that theNFD correlateswith futureascendingaorticgrowthinpatientssufferingfrombicuspid valvedisease[5].Whileassessmentoftheseparametersispossible beforeandaftertheinterventionusingEchocardiographyand4D- flow-MRI,theirpredictioncanonlybefacilitatedusingnumerical methods.Asthisstudysuggests,usingagenericpluginletprofile hasnomajorimpactontheseparameters.

No significant differences within the surface-averaged WSS werefoundeither.WSSareameasurefortheinteractionbetween bloodandthevesselwallandcorrelatewithexchangeprocesses aswellastheoverallloadactingontheendothelialcells.Thisfind- ing,however,wastobeexpected,becausevolumeflowratesin bothvelocityinletprofileconditionswereidenticandnosignifi- cantdifferencesinSFDwerefound.Nonetheless,lowcoefficients ofdeterminationforcell-wisecomparisonofWSSindicates,that therearelargedifferencesinspatiallyresolvedWSS,eventhough the surface-averaged WSS aresimilar in both groups. WSS are associatedwithvasculardiseasesaswellasremodelling[7,27].A spatiallyresolvedevaluationisnotfeasibleusingthemethodpro- posedinthisstudy,sincethechoiceofthevelocityinletprofilehas

anon-negligibleimpactonspatiallyresolvedparameterssuchas theWSS.

Therearetwoexemptionsfromtheobservationthatspatially- averagedparameterscalculatedusingeitherinletprofilecondition agreedwell:thetransvalvularpressuredropandtheaveragedtur- bulentkineticenergy.

Usingpatient-specificvelocityinletprofilesasboundarycon- ditionsresultedin significantlylowerpressuredropsacrossthe aorticvalvecomparedtothosecalculatedusingaplugprofile.This peaksystolicpressuredropisoneessentialparameterinevalu- ationof treatmentsuccess. Commonly,pressuredropsequal or lowerthan20mmHgareconsiderednormal.Higherpressuredrops might indicatea possiblestenosis of the prosthesis[39]. Thus, theobserved average differencein pressure dropof 3.3mmHg accountsfor16.5percentofthisclinicalthreshold.However,the transvalvularpressuredropiscommonlyestimatedbymeasuring thevelocitymaximumdownstream thevalveusingechocardio- graphy. From these velocity measurements, a pressure drop is thencalculatedfromthevelocitymagnitudedistaltotheprosthe- sisusingasimplifiedBernoulliequation:p=v²_proximal·^mmHg_m2^s2, or more accurately using the proximal velocity as well p=

v²_distal−v²_proximal

·^mmHg_m2^s2 [2,39].

Thus,thepressuredropisonlymeasuredindirectlywithinclin- icalroutineandisusuallyoverpredictingtherealpressuredrop, becausethepressuregainduetodecelerationoftheflowdown- streamthevalveisnottakenintoaccount[3,39].It istherefore necessarytovalidatetransvalvularpressuredropscalculatedin- silicoagainstthose measuredin-vivo.Since there wasa nearly perfectcorrelationbetweenpressuredropscalculatedusingeither inletprofilecondition,usingapluginletprofilemightbesufficient forpredictionofunphysiologicallyhighpressuredrops.However, anadjustmentoftheclinicalthresholdmightbenecessarytotake theoverpredictingbiasintoaccount.

Theaverageturbulentkineticenergywassignificantlyincreased usingthepatient-specificvelocityinletprofilecomparedtotheplug profile.Thisfindingwastobeexpected,sincethepatient-specific profilesusuallyfeatureadistinctvelocitymaximumandthusbig- gervelocitygradients,whilethereisnovelocitygradientinthe plugvelocityprofileatall.Recentstudiesfoundlowerturbulence withinphysiologichemodynamicscomparedtopathologicones [10].Whilepredictionofturbulenceaftertreatmentmightbedesir- able,noclinicalthresholdsanddefinitionsofpathologicaldegrees ofturbulenceareestablishedasofyet.Furthermore,itisdifficultto obtainreliablein-vivodataofturbulencebecauseoflimitedaccess andmeasurementtechniques.Howsoever,thisstudysuggeststhat thevelocityinletprofilehasanimpactonpredictionofturbulence, whichmightnotbenegligible.

An important finding was that velocity magnitude profiles extractedimmediatelydownstreamof theaorticvalveprosthe- sesrevealeddistinct differencesinallbut threepatients.While generalflow orientationanddisplacementwasnotsignificantly differentusingeithervelocity inletcondition,hemodynamicsin theimmediatevicinityoftheaorticvalveprosthesesweresubstan- tiallydifferent.Here,alimitationofthemethodusedbecomesclear.

Valveprostheseswereassumedtobeideallyopened,regardlessof pressureandflowpatternsbeforethevalveorthepressuredistri- butionwithinthevalve.Eventhoughvalveprosthesesaredesigned tofullyopenduringpeaksystole,itispossiblethatthecleardif- ferencesofthebloodflowwithintheimmediatevicinityofthe prosthesesmightleadtoalterationsinopeninganglesofleaflets ofmechanicalprosthesesorleafletgeometriesofbiologicalpros- theses.Themethodusedwithinthisstudyisnotabletoincorporate theseinfluencesofhemodynamicsontheprosthesisgeometry.It maybepossiblethatleafletanglesandthereforetheeffectiveori- ficeareaofvalveprosthesesmightbealteredbythechosenvelocity

inletprofile.However,accordingtheISO5840,theseprosthesesare testedin-vitrowithinastraighttube.Eventhoughanon-patient- specificfloworananatomicgeometryisusedforthesetest,the prostheses’leafletsdoopenfullyundertheseconditions.Nonethe- less,additionalresearchontheimpactofdifferentvelocityinlet profilesonfunctiononprosthesesseemswarranted.Here,fluid- structure-interactionmodelsorimmersedboundaryapproaches mightbesuited.

Ideally,resultsobservedusingthismethodshouldbevalidated againstrealclinicalmeasuresobtainedafteraorticvalvereplace- ment.However,validationofsimilarlysimplifiedpatient-specific simulationsofaortichemodynamicsagainstclinicalmeasurements wasalreadyperformed[19]andmodelassumptionswereshown tohaveonlyaminorimpactoncalculatedhemodynamics[17,18].

Furthermore,alargersamplewouldbeofgreatinterest,because it would allowtoevaluateeffects of biological and mechanical prosthesesseparately.Sincebiologicalprosthesesarenearlyrota- tionallysymmetric,itmightbeassumedthattheyaremorerobust tochangesinthevelocityinletprofilewithintheLVOT.

Finally,thisstudyfocusedontheuncertaintiesintroducedby onlyoneaspectoftheprocesspipelineofimage-based,cardiovas- cularmodelling: thepatient-specificvelocityinletprofile.There are,ofcourse,severalotherpossiblesourcesoferrors,asforexam- plethereconstructionofthepatient-specificanatomyfromMRI imagedataortheuncertaintiesintroducedbymodelassumptions, asforexampleneglectingtheelasticityoftheaorticwallorused turbulencemodels.Furthermore,thepatient-specificMRIinflow profileitselfis affectedbyerrors due toimageacquisition.The impactoftheseuncertaintiesisintensivelyinvestigatedinseveral studies[4,12,13,33].However,notonlythemaineffectsbutalso theinteractioneffectsofthoseuncertaintiesonthepredictionof hemodynamicoutcomeareofinterest.Astudy,inwhichmultiple uncertaintiesintroducedduringtheprocesspipelinearecompared, isdesirable.Suchastudywouldallowtoidentify,whichaspectsare mostrelevantforareliableoutcomepredictionofcardiovascular interventionastheheartvalvereplacement.

5. Conclusions

In-silicomethodsand4D-flow-MRIallowassessment ofspa- tiallyresolvedaswellas averagedparameters,which mightbe correlatedtoapositiveoutcomeofavalvereplacementprocedure withinthefuture.However,thesemethodsarerelativelynoveland haveyettobetranslatedtoclinicalroutine.Parameterscorrelated tothehelicityoftheascendingaorticbloodflow,suchastheSFD, arediscussedtobeassociatedwithdilationoftheascendingaorta.

Theseparameterswererobustagainstchangesinthevelocityinlet profile.Therefore,itmightbepossibletousesimplifiedvelocity inletprofiles,suchasaplugprofile,asboundaryconditionwithin patient-specifictreatment-planningprocedureusingCFD.

Thiswouldbedesirable,becauseitallowstocircumventtwo majorproblemsregarding patient-specificsimulations.Thefirst oneisthatusingapatient-specificvelocityinletprofilerequires4D- flow-MRIdata,whichisnotalwaysavailable.Aplugprofilecouldbe usedwhilethevolumeflowratecouldbeestimatedusinggeneral patientcriteriasuchasage,weight,heightandgender.Thesecond problem,whichcouldbecircumvented,isthatthereplacementof theaorticvalvewillmostlikelyresultinachangeoftheventricular functionandthusapossiblechangeofthevelocityprofilegener- atedwithintheLVOT.Thereisnowaytopredictthischangeasof yet.Modelsthatincorporatetheventricularmotionmightallow thispredictioninthefuture.However,theirapplicationremains challengingduetotheirhighcomputationalcost.Sincemultiple interventionsorsurgerieshavetobesimulatedtodeterminethe