Modeling and simulation of flow in cerebral aneurysms

134 Pages·2012·4.23 MB·English

MODELING AND SIMULATION
OF FLOW IN CEREBRAL ANEURYSMS
JULIA MIKHAL
Depromotiecommissie:
Voorzitterensecretaris:
Prof.dr.ir.A.J.Mouthaan UniversiteitTwente
Promotoren:
Prof.dr.ir.B.J.Geurts UniversiteitTwente
Prof.dr.ir.C.H.Slump UniversiteitTwente
Leden:
Prof.dr.ing.V.Armenio Universita`degliStudidiTrieste
Prof.dr.S.A.vanGils UniversiteitTwente
Prof.dr.J.G.M.Kuerten UniversiteitTwente
Prof.dr.C.B.L.M.Majoie AcademischMedischCentrumAmsterdam
Prof.dr.A.E.P.Veldman RijksuniversiteitGroningen
Prof.dr.ir.F.N.vandeVosse TechnischeUniversiteitEindhoven
TheresearchpresentedinthisthesiswasdoneinthegroupMultiscaleModelingandSimu-
lation(Dept.ofAppliedMathematics),incollaborationwiththegroupSignalsandSystems
(Dept.ofElectricalEngineering),FacultyEEMCS,UniversityofTwente,TheNetherlands.
ComputingresourcesweregrantedbytheNationalComputingFacilitiesFoundation(NCF),
withfinancialsupportfromtheDutchOrganizationforScientificResearch(NWO).
Modelingandsimulationofflowincerebralaneurysms.Ph.D.Thesis,UniversityofTwente,
P.O.Box217,7500AEEnschede,TheNetherlands. c JuliaMikhal,Enschede,2012.
(cid:13)
PrintedbyWo¨hrmannPrintService,Zutphen,TheNetherlands.
Coverphoto‘LightsandWater’ c JamesAdamson.
(cid:13)
ISBN:978-90-365-3433-8 DOI:10.3990/1.9789036534338
MODELING AND SIMULATION
OF FLOW IN CEREBRAL ANEURYSMS
PROEFSCHRIFT
terverkrijgingvan
degraadvandoctoraandeUniversiteitTwente,
opgezagvanderectormagnificus,
prof.dr.H.Brinksma,
volgensbesluitvanhetCollegevoorPromoties
inhetopenbaarteverdedigen
opvrijdag19oktober2012om12:45uur
door
IuliiaOlegivnaMikhal
geborenop6juni1984
teKharkiv,Oekra¨ıne
Ditproefschriftisgoedgekeurddoordebeidepromotoren:
Prof.dr.ir.B.J.GeurtsenProf.dr.ir.C.H.Slump
To myparents

Contents
1 Introduction........................................................... 1
2 Immersed boundarymethodforthe computationofflow invesselsand
cerebralaneurysms .................................................... 7
2.1 Introduction ....................................................... 7
2.2 Computationalmodelforflowinsidecerebralaneurysms ................. 12
2.2.1 Incompressibleflowincomplexdomains ........................ 12
2.2.2 Numericalmethodforsimulatingincompressibleflowwith an
immersedboundaryapproach.................................. 14
2.2.3 Maskingfunctionstrategy..................................... 18
2.3 ValidationoftheIBmethod.......................................... 22
2.3.1 Flowinstraightvessels ....................................... 23
2.3.2 Flowincurvedvessels........................................ 27
2.3.3 Flowinamodelaneurysm..................................... 29
2.4 Shearstressincurvedvesselandmodelaneurysm ....................... 30
2.4.1 ValidationoftheIBcomputedshearstress ....................... 30
2.4.2 Analysisoftheshearstressdistributioninsidecurvedvesseland
modelaneurysm ............................................. 33
2.5 Concludingremarks ................................................ 36
3 Flowincerebralaneurysmsderivedfrom3Drotationalangiography ........ 39
3.1 Introduction ....................................................... 39
3.2 Computationalmodelforbloodflowincerebralaneurysms ............... 43
3.2.1 Navier-Stokesequationsandimmersedboundarymethod........... 43
3.2.2 Segmentationof3Drotationalangiographydata .................. 45
3.2.3 Elementaryoperationsonthemaskingfunction................... 49
3.3 Flowinarealisticaneurysm.......................................... 52
3.3.1 Motivationanddefinitionofthereferencecase.................... 52
vii
viii Contents
3.3.2 Qualitativeimpressionofflowandforcesinsidetheaneurysm....... 55
3.3.3 Flowinpartiallyfilledcerebralaneurysms ....................... 58
3.3.4 ReliabilityofIBpredictions:agridrefinementstudy............... 61
3.4 Sensitivityofflowpredictionstoelementaryoperationsonmaskingfunction. 64
3.5 Sensitivityofflowpredictionsinboundinggeometries ................... 67
3.5.1 Gridcoarseningandboundinggeometries........................ 68
3.5.2 Numericalboundingsolutions ................................. 70
3.6 Concludingremarks ................................................ 73
4 Transitionofpulsatileflowincerebralaneurysms.......................... 75
4.1 Introduction ....................................................... 75
4.2 Computationalmodelofcerebralpulsatilebloodflow .................... 78
4.2.1 ImmersedBoundarymethodandaneurysmgeometry.............. 78
4.2.2 Flowconditionsandpulsatileforcing ........................... 82
4.2.3 Referencepulsatileflow....................................... 84
4.3 Transitionalpulsatileflow ........................................... 86
4.3.1 Shearstressresponseinnormalandpathologicalflow.............. 86
4.3.2 Robustnessofpulsatiletransition............................... 89
4.3.3 Frequenciesofthepulsatilesolution ............................ 91
4.4 Concludingremarks ................................................ 94
5 ConclusionsandOutlook ............................................... 97
References.................................................................105
Chapter 1
Introduction
There is a growing medical interest in the prediction of flow and forces inside cerebral
aneurysms [48, 103], with the ultimate goal of supporting medical procedures and deci-
sions by presenting viable scenarios for intervention. The clinical background of cerebral
aneurysmsand possible hemorrhagesis well introducedin the literature such as [93, 101].
Thesedays,withthedevelopmentofhigh-precisionmedicalimagingtechniques,thegeome-
tryandstructureofbloodvesselsandpossibleaneurysmsthathaveformed,canbedetermined
forindividualpatients.Todate,surgeonsandradiologistshavetomakedecisionsaboutpos-
sibletreatmentofananeurysmbasedonsize,shapeandlocationcriteriaalone.Inthisthesis
wefocusontheroleofComputationalFluidDynamics(CFD)foridentifyingandclassifying
therapeuticoptionsinthetreatmentofaneurysms.
CFD allows to add qualitative and quantitative characteristics of blood flow inside the
aneurysmtothecomplexprocessofmedicaldecisionmaking.Wecontributetothisbycom-
puting the precise patient-specific pulsatile flow in all spatial and temporal details, using a
so-called‘ImmersedBoundary’(IB)method.Thisrequiresanumberofsteps,frompreparing
therawmedicalimagerytodefinethecomplexpatient-specificflowdomain,totheexecution
ofhigh-fidelitysimulations.Subsequently,detailedinterpretationoftheconsequencesofthe
flow shouldbe givenjointly by medicalexpertsandCFD specialists in termsof flow visu-
alization and quantitative measures of relevance to medical practice. We compute the flow
inside theaneurysmto predicthighandlowstress regions,indicativeofpossiblegrowthof
ananeurysm.Wealsovisualizevorticalstructuresintheflowindicatingthequalityoflocal
blood circulation. We show that, as the size of the aneurysmincreases, qualitative changes
intheflowbehaviorcanarise,whichexpressthemselvesashigh-frequencyvariationsinthe
flow and shear stresses. These rapid variations could be used to quantify the level of risk
associated with the growing aneurysm. Such computationalmodeling may lead to a better
understandingoftheprogressiveweakeningofthevesselwallanditspossiblerupture.
1
2 1 Introduction
Beforepresentingthecontentofthisthesis,wewillbrieflydiscussthemedicalmotivation
oftheproblem,thevariousrolesCFDcanplayandgiveanoverviewofnumericalmethods
beingusedforbloodflowsimulations.Subsequently,thefocuspointsofeachchapterwillbe
presentedandfinallythegeneraloutlineofthisthesiswillbegiven.
Cerebral Aneurysm. Medical motivation. The medical condition known as cerebral
aneurysmisoneofthecardiovasculardiseasesthatinvolvesvesselwallsofcerebralvessels.
Bulgeformationsmightdeveloponthevesselwalls,andovertime,underpermanentpulsat-
ingforces,theaneurysmmaygrowfurtherandevenrupture.Thedegradationofendothelial
cells in the vessel walls is often associated with regions of relatively low shear stress [9]
while locations of relatively high shear stress could be important for initial formation of a
bulge[84].Commonly,cerebralaneurysmsarelocatedinorneartheCircleofWillis[101]–
the centralvesselnetworkforthe supplyofbloodto thehumanbrain.Therisk-areasareat
‘T’and‘Y’-shapedjunctionsinthevessels[34].Treatmentofcerebralaneurysmsoftenin-
volvesinsertionofaslendercoil.Thiscoilingprocedurerepresentsconsiderableriskduringa
surgicalintervention,aswellasuncertaintyaboutthelong-termstabilityofcoiledaneurysms
[86,94].Bloodvesselsandaneurysmsarerathercomplexbytheirstructureandgeometrical
shapes.Thewallsofbloodvesselscontainseverallayersofdifferenttypesofbiologicalcells,
which provide elasticity to the vessels and determine their compliance [76]. The shape of
cerebralaneurysmsdevelopingin patientscanbe inferredbyusingseveraltechniquessuch
asCTA(ComputedTomographicAngiography),DSA(DigitalSubtractionAngiography)and
3DRA (Three-DimensionalRotationalAngiography)[64]. In these proceduresa small part
ofthebrainisscanned,andaneurysmsevenofasizelessthan3mmcanbeobserved[8,95].
These techniques allow a reconstruction of three-dimensional arteries and aneurysms and
hence an approximate identification of the blood vessels and parts of the soft tissue in the
scannedvolume.
ComputationalFluidDynamics.ThetremendouspotentialofCFDinsupportingmedi-
caldecisionsandproposingtherapeuticoptionsinthetreatmentofcerebralaneurysms,was
already anticipatedin [57]. The value of numericalsimulationsfor treating aneurysmswill
likely increase further with better quantitative understanding of hemodynamicsin cerebral
bloodflow.AprimarychallengeforanyCFDmethod,whetheritisabody-fittedmethod[35]
oranIBmethod[37,62,73],istocapturetheflownearsolid-fluidinterfaces.Inthisregion
thehighestvelocitygradientsmayoccur,leadingtocorrespondinglyhighestlevelsofshear
stress, but also potentially highest levels of numerical error. In methods employing body-
fittedgrids,thequalityofpredictionsisdirectlylinkedtothedegreetowhichgrid-linescan
beorthogonaltothesolid-fluidinterfaceandtoeachother.Also,variationinlocalmeshsizes
andshapesofadjacentgridcellsisafactordeterminingnumericalerror.Thegenerationofa
suitablegridisfurthercomplicatedastherawdatathatdefinetheactualaneurysmgeometry