Wall shear stress at the initiation site of cerebral aneurysms

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Geers, AJ, Morales, HG, Larrabide, I et al. (3 more authors) (2017) Wall shear stress at the
initiation site of cerebral aneurysms. Biomechanics and Modeling in Mechanobiology, 16
(1). pp. 97-115. ISSN 1617-7959
https://doi.org/10.1007/s10237-016-0804-3
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BiomechanicsandModelinginMechanobiologymanuscriptNo.
(willbeinsertedbytheeditor)
Wall shear stress at the initiation site of cerebral aneurysms
1
2 A.J.Geers · H.G.Morales · I.Larrabide ·
3 C.Butakoff · P.Bijlenga · A.F.Frangi
4
5 Received:date/Accepted:date
6 Abstract Hemodynamics are believed to play an important role in the initiation of
7 cerebral aneurysms. In particular, studies have focused on wall shear stress (WSS),
8 which is a key regulator of vascular biology and pathology. In line with the obser-
9 vationthataneurysmspredominantlyoccuratregionsofhighWSS,suchasbifurca-
10 tion apices or outer walls of vascular bends, correlations have been found between
11 the aneurysm initiation site and high WSS. The aim of our study was to analyze
12 the WSS field at an aneurysm initiation site that was neither a bifurcation apex nor
13 the outer wall of a vascular bend. Ten cases with aneurysms on the A1 segment of
14 the anterior cerebral artery (ACA) were analyzed and compared with ten controls.
15 Aneurysmswerevirtuallyremovedfromthevascularmodelsofthecasestomimic
16 thepre-aneurysmgeometry.Computationalfluiddynamics(CFD)simulationswere
17 created to assess the magnitude, gradient, multidirectionality, and pulsatility of the
18 WSS. To aid the inter-subject comparison of hemodynamic variables, we mapped
19 thebranchsurfacesontoatwo-dimensionalparametricspace.Thisapproachmadeit
PreliminaryfindingsfromthisstudywerepresentedattheInternationalSymposiumonBiomechanics
inVascularBiologyandCardiovascularDisease,Montreal,QC,Canada,28–29April2014andatthe
EuropeanSolidMechanicsConference,Madrid,Spain,6–10July2015.
A.J.Geers
CISTIB,UniversitatPompeuFabra,Barcelona,Spain
E-mail:[email protected]
H.G.Morales
Medisys–PhilipsResearchParis,Paris,France
I.Larrabide
PLADEMA-CONICET,UNICEN,Tandil,Argentina
C.Butakoff
PhySense,UniversitatPompeuFabra,Barcelona,Spain
P.Bijlenga
HoˆpitauxUniversitairedeGene`veetFaculte´deme´decinedeGene`ve,Geneva,Switzerland
A.F.Frangi
CISTIB,UniversityofSheffield,Sheffield,UK
2 A.J.Geersetal.
20 possibletoviewthewholebranchatonceforqualitativeevaluation.Italsoallowed
21 us to define a patch for quantitative analysis, which was consistent among subjects
22 and encapsulated all aneurysm initiation sites. To test the reproducibility of our re-
23 sults, CFD simulations were repeated with a second independent observer virtually
24 removingtheaneurysmsandwitha20%higherflowrateattheinlet.Wefoundthat
25 branchesharboringaneurysmswerecharacterizedbyhighWSSandhighWSSgra-
26 dients. Among all assessed variables, the aneurysm initiation site most consistently
27 coincidedwithpeaksoftemporalvariationintheWSSmagnitude.
28 Keywords aneurysminitiation·cerebralaneurysms·computationalfluiddynamics·
29 hemodynamics·image-basedmodeling·flowpulsatility·wallshearstress
1 Introduction
30
31 Cerebralaneurysmsarelocalized,pathologicaldilatationsofcerebralarteries.Their
32 rupture causes subarachnoid hemorrhage and is associated with high rates of mor-
33 bidityandmortality(Hopetal,1997).Betterunderstandingofthemechanismsun-
34 derlying aneurysm initiation is crucial for the development of new preventive and
35 therapeuticstrategies(Jamousetal,2005).
36 Whilesystemicriskfactorssuchashypertensionandconnectivetissuedisorders
37 may weaken the cerebral arteries’ ability to maintain homeostasis, hemodynamic
38 stress appear to be a necessary trigger for the pathological remodeling leading to
39 aneurysm formation (Brown et al, 1990; Stehbens, 1989; Nixon et al, 2010; Penn
40 etal,2011;Dolanetal,2013;Sadasivanetal,2013;Mengetal,2014;Fro¨sen,2014;
41 Turjmanetal,2014).Invivomeasurementsofthesestressesarelimitedbythelow
42 spatialandtemporalresolutionofcurrentimagingtechniques(Markletal,2012)and
43 the rarity of imaging a patient prior to aneurysm formation. Instead, computational
44 fluiddynamics(CFD)techniqueshavebeenemployedtosimulatethehemodynam-
45 ics in vascular geometries with the aneurysm virtually removed to approximate the
46 pre-aneurysmcondition(Manthaetal,2006;Baeketal,2009;Fordetal,2009;Shi-
47 mogonyaetal,2009;Singhetal,2010;Castroetal,2011;Chenetal,2013;Konoand
48 Terada, 2013; Lauric et al, 2014) and in vascular geometries derived from rare pre-
49 aneurysmimages(Doenitzetal,2010;Kulcsaretal,2011;KonoandTerada,2013;
50 Konoetal,2014).CFDsimulationshavealsobeenusedtocomplementhistological
51 analyses of aneurysm formation in animal models (Meng et al, 2007; Metaxa et al,
52 2010).
53 Hemodynamicstudieshavestronglyfocusedonwallshearstress(WSS),which
54 isakeyregulatorofvascularbiologyandpathology(Dolanetal,2013).Inlinewith
55 the observation that aneurysms predominantly occur at high WSS regions such as
56 bifurcationapicesorouterwallsofvascularbends(Kondoetal,1997;Alnaesetal,
57 2007;Piccinellietal,2011;Alfanoetal,2013),manystudieshavefoundcorrelations
58 betweentheaneurysminitiationsiteandhighWSS(Castroetal,2011;Singhetal,
59 2010;Chenetal,2013),especiallyincombinationwithhighpositiveWSSgradients
60 (WSSG)(Mengetal,2007;Metaxaetal,2010;Kulcsaretal,2011;KonoandTer-
61 ada, 2013; Kono et al, 2014). Other studies have found correlations with low WSS
62 (Manthaetal,2006;Doenitzetal,2010),WSSpatternsinvolvingbothhighandlow
Wallshearstressattheinitiationsiteofcerebralaneurysms 3
63 WSS(Baeketal,2009;Lauricetal,2014),orindicesdescribingtheoscillatoryna-
64 tureoftheWSSandWSSG(Manthaetal,2006;Fordetal,2009;Shimogonyaetal,
65 2009; Chen et al, 2013). These apparent inconsistencies among CFD-based studies
66 canbeattributedtothesmalldatasets,varietyofaneurysmlocations,andsubjectivity
67 ofdataanalyses,aspointedoutbyChenetal.(Chenetal,2013),butalsotomissing
68 patient-specificinformationaboutboundaryconditionsandpropertiesofthearterial
69 wall.
70 TheaimofourstudywastoanalyzetheWSSfieldattheaneurysminitiationsite.
71 Allincludedaneurysmswerefromasinglelocation,whichwasneitherabifurcation
72 apex nor the outer wall of a vascular bend. Vascular geometries with the aneurysm
73 removedwerematchedtocontrolsthatneverformedananeurysmatthatparticular
74 locationbutelsewhere.Tostandardizethedataanalysisandsimplifythecomparison
75 of cases, branches of interest were mapped onto the same parametric space. Tests
76 were performed to measure the reproducibility of the computed WSS field with re-
77 spect to the observer virtually removing the aneurysm and the flow rate imposed at
78 theinlet.
2 Methods
79
80 2.1 Caseselection
81 Twenty patients, ten cases and ten controls, were drawn from a large multicenter
82 database created within the EU-funded project @neurIST (Villa-Uriol et al, 2011).
83 Thedatacollectionprotocolwasapprovedbyindividuallocalethicscommittees,and
84 written consent was obtained from patients or, where appropriate, next of kin. The
85 cases were all the patients in the database with an aneurysm on the A1 segment of
86 the anterior cerebral artery (ACA). They were selected because of their remarkable
87 consistencyinaneurysmlocation:allaneurysmswerejustdistaltotheinternalcarotid
88 artery (ICA) bifurcation with nine cases directed posteriorly (cases 1 to 9) and one
89 case directed anteriorly (case 10). Moreover, the location was neither a bifurcation
90 apex nor the outer wall of a vascular bend, which – attributed to being high WSS
91 regions–arethemostcommonaneurysmlocations(Kondoetal,1997;Alnaesetal,
92 2007; Piccinelli et al, 2011; Alfano et al, 2013). The controls were patients with
93 ananeurysmatthemiddlecerebralartery(MCA)bifurcation,hencepredisposedto
94 having aneurysms, that did not form an aneurysm at the studied location on the A1
95 segment of the ACA. They were selected to match cases by patient age (within 2
96 years)andaneurysmhemisphere(leftorright).Nootherinformationwasconsidered
97 duringtheselectionprocess.
98 2.2 Vascularmodeling
99 Patient-specificvascularmodels,representedbytriangularsurfacemeshes,werecon-
100 structed by segmenting three-dimensional rotational angiography (3DRA) images
101 using a geodesic active regions approach (Bogunovic´ et al, 2011). The ophthalmic
4 A.J.Geersetal.
102 artery, anterior choroidal artery, and posterior communicating artery branching off
103 theICAwerepreservedifsuccessfullysegmented.Touchingvesselswereremoved.
104 Models were smoothed using a geometry-preserving smoothing algorithm (Nealen
105 et al, 2006). To ensure consistency in the extent of the vascular models, inlet and
106 outlet branches were clipped at the same location for all cases and controls. Inlet
107 branches were clipped at a manually selected location at the start of the cavernous
108 segment of the ICA and then extruded 10mm to allow for flow to develop. Outlet
109 branches were automatically clipped 10mm from their proximal bifurcation; those
110 shorterthan10mmwerefirstextruded.TheACAhadtobeextrudedonlyforcontrol
111 6.Figure1showsthevascularmodelsofallcasesandcontrols.
112 Aneurysms were virtually removed from the vascular models of the cases to
113 mimicthepre-aneurysmgeometry(Figure1).Triangleremovalandholefillingop-
114 erations were iteratively applied to reconstruct the ACA without aneurysm. Subse-
115 quently,thevascularmodelwassmoothedandinletandoutletbrancheswereclipped
116 asdescribedinthepreviousparagraph.Toassessthereproducibilityofthecomputed
117 WSS field with respect to this manual procedure, two observers independently re-
118 movedtheaneurysmforallcases.
119 Theautomaticselectionofoutletlocationsmadeuseofcenterlinesandbifurca-
120 tion origins generated with the Vascular Modeling Toolkit (VMTK) (Antiga et al,
121 2008; Piccinelli et al, 2009). Manual mesh editing operations were performed in
122 @neuFuse(B3C,Bologna,Italy)(Villa-Urioletal,2011),asoftwareapplicationde-
123 velopedwithin@neurIST.
124 2.3 Bloodflowmodeling
125 UnstructuredvolumetricmesheswerecreatedwithICEMCFD13.0(ANSYS,Canons-
126 burg,PA,USA)usinganoctreeapproach.Mesheswerecomposedoftetrahedralel-
127 ements with a side length of 0.2mm and three prism layers with a total height of
128 0.07mmandasidelengthof0.1mm.Thetotalnumberofelementsrangedfrom2.3
129 to 6.7 million, the density from 3124 to 4076 elements per mm3, depending on the
130 surface-area-to-volumeratioofthecomputationaldomain.Thismeshresolutionwas
131 chosenfollowingpreviouslyperformedmeshdependencytests(Geersetal,2014).
132 CFDsimulationswerecreatedwithCFX13.0(ANSYS),whichisacommercial
133 vertex-centeredfinitevolumesolver.Weusedasecond-orderadvectionschemeanda
134 second-orderbackwardEulertransientscheme.Solutionsconvergeduntilthenormal-
135 izedresidualoftheWSSeverywhereinthecomputationaldomainwas<5×10−4.
136 BloodwasmodeledasanincompressibleNewtonianfluidwithdensityρ=1060kg/m3
137 andviscosityµ =4mPas.Althoughbloodisanon-Newtonianfluid,assumingcon-
138 stantviscosityisappropriateforourproblem(Moralesetal,2013).Vesselwallswere
139 assumedrigidwithano-slipboundarycondition.Aparabolicvelocityprofilewasim-
140 posedattheinlet.
141 Since patient-specific flow information was unavailable, we estimated the flow
142 ratewaveformattheinletandimposedzero-pressureboundaryconditionsatallout-
143 lets. The shape of the flow rate waveform was obtained from Ford et al. who aver-
144 aged the waveform shapes of 17 young, normal volunteers (Ford et al, 2005). The
Wallshearstressattheinitiationsiteofcerebralaneurysms 5
145 time-averaged flow rate, Q, was obtained using the relationship from Cebral et al.:
146 Q=48.21A1.84T−1 whereQisinml/s,Aistheinlet’scross-sectionalareaincm2,
147 andT istheperiodofthecardiaccycleins.Thisrelationshipwasobtainedbyfitting
148 a power-law function through measurements of Q and A of the ICAs and vertebral
149 arteriesof11normalvolunteers(Cebraletal,2008).Reynoldsnumbersattheinlets
150 ranged from 62 to 441 with an average of 152. To assess the reproducibility of the
151 computed WSS field with respect to boundary conditions, we repeated the simula-
152 tionsforallcasesandcontrolswitha20%higherflowrateattheinlet.
153 Thecardiaccyclewasdiscretizedin200uniformlydistributedtimestepsand,to
154 reducetheeffectofinitialtransients,thesecondoftwosimulatedcardiaccycleswas
155 analyzed.Thesesettingswerechosenfollowingpreviouslyperformedtimestepand
156 cycledependencytests(Geersetal,2014).
157 Atotalof50CFDsimulationswerecreated:10casesand10controlsunder‘nor-
158 mal’inflowconditions,10casesand10controlsunder‘high’inflowconditions,and
159 10casesunder‘normal’inflowconditionswiththeaneurysmremovedbythesecond
160 observer.
161 2.4 Hemodynamicvariables
162 AsmentionedintheIntroduction(Section1),differentaspectsoftheWSSfieldare
163 deemedrelevanttotheinitiationofaneurysms.Specifically,weassessedthemagni-
164 tude,gradient,multidirectionality,andpulsatilityoftheWSS,accordingtothedefi-
165 nitionsbelow.
166 GivenWSSvectorτw=τw(x,t)atsurfacepointxandtimet,thetime-averaged
167 WSSmagnitude(TAWSS)isdefinedas
1 T
TAWSS= |τ |dt (1)
w
T Z0
168 whereTistheperiodofthecardiaccycle.
169 ForuseinthedefinitionofotherWSS-relatedvariables,wedefinedunitvectors
170 inthedirectionofandperpendiculartothetime-averagedWSSvector,respectively
171 pˆandqˆ,as
Tτ dt
pˆ= 0 w , qˆ=pˆ×nˆ (2)
RTτ dt
0 w
(cid:12)R (cid:12)
(cid:12) (cid:12)
172 wherenˆ isthesurfacenormal. (cid:12) (cid:12)
173 ForthegradientofTAWSS(TAWSSG),weusedthedefinitionproposedbyMeng
174 andcolleagues(Tremmeletal,2010;Dolanetal,2013),whichdifferentiatesbetween
175 positiveandnegativegradientswithrespecttopˆ,namely,
TAWSSG=∇ (TAWSS)·pˆ (3)
S
176 where∇S isthegradientonthevesselwallsurface.
177 Throughoutthecardiaccycle,theWSSvectormaychangedirectionandnotre-
178 main parallel to pˆ. The changing WSS direction is associated with the concept of
6 A.J.Geersetal.
179 ‘disturbed’ flow. To quantify the multidirectionality of disturbed flow, we used the
180 transverse WSS (transWSS), which was recently proposed by Peiffer et al. in the
181 contextofatherosclerosis(Peifferetal,2013a).ThetransWSSisdefinedasthetime-
182 averagedabsolutevalueoftheq-componentoftheWSSvector,thatis,
1 T
transWSS= |τ ·qˆ|dt (4)
w
T Z0
183 We quantified the temporal variation in the WSS magnitude during the cardiac
184 cycle by calculating the WSS pulsatility index (WSSPI) (Gosling and King, 1974),
185 givenby
max τ − min τ
w w
t∈[0,T] t∈[0,T]
WSSPI= (5)
TAWSS
186 As the WSS magnitude may vary substantially between CFD simulations us-
187 ingeitherpatient-specificorestimatedboundaryconditions,cautionininterpretation
188 mustbeexercised(Karmoniketal,2010;Marzoetal,2011;Jansenetal,2014;Mc-
189 Gahetal,2014).WechosetofocusontheWSSdistributionbynormalizingTAWSS
190 bythespace-averagedTAWSSonthebranch(TAWSSB).Foraneurysms,normalized
191 WSS distributions have been shown to remain relatively unchanged across a range
192 of physiological boundary conditions (Marzo et al, 2011). TAWSSG and transWSS
193 were similarly normalized by TAWSSB. Unless stated otherwise, we will report on
194 normalizedvalues.
195 2.5 Geometricvariables
196 Vascular geometry has a major impact on hemodynamics (Geers et al, 2011) and
197 indeedbifurcationsharboringaneurysmstendtomorestronglydeviatefromtheop-
198 timalityprinciple(Baharogluetal,2014).Tocomplementthehemodynamicanalysis
199 inourstudy,wecharacterizedthevasculargeometryusingtheframeworkpresented
200 by Piccinelli et al. (Piccinelli et al, 2009), which is available as part of VMTK. We
201 willbrieflyoutlinetheprocedure.SomeoftheprocessingstepsareillustratedinFig-
202 ure2.Formoredetails,referto(Piccinellietal,2009).
203 Twocenterlineswerecreated:onefromtheinlettotheMCAoutletandanother
204 fromtheinlettotheACAoutlet.AttheICAbifurcation,thetwocenterlinesdiverged
205 intotheirrespectivebranchesandthecorrespondingbifurcationoriginandplanewere
206 identified. The normal to the bifurcation plane was set to point posteriorly. Center-
207 linesweresplitintobranchescorrespondingtotheICA,MCA,andACA.
208 Foreachbranch,arepresentativecrosssectionalareaAwasdefinedasthemean
209 surface area of two cross sections. These two sections were created one and two
210 maximally inscribed sphere radii away from the bifurcation. The bifurcation’s area
211 ratio(Ingebrigtsenetal,2004)wasgivenby
A +A
ACA MCA
arearatio= (6)
A
ICA
Wallshearstressattheinitiationsiteofcerebralaneurysms 7
212 Vectorspointinginthedirectionofthebrancheswerecreatedandthenprojected
213 ontothebifurcationplane.Thein-planeICA-ACAandICA-MCAangleswerecal-
214 culated.
215 ToquantifythetortuosityoftheACA,weusedthedefinition
L
tortuosity= −1 (7)
D
216 whereListhelengthalongthecenterlineandDistheEuclideandistancebetweenits
217 endpoints.
218 2.6 Branchextractionandparametrization
219 Toaidtheinter-subjectcomparisonofhemodynamicvariablesonthesurfaceofthe
220 ACA,weusedtheapproachproposedbyAntigaetal.(AntigaandSteinman,2004),
221 whichisalsoavailableaspartofVMTK.Briefly,thevesselwallsurfacewassplitinto
222 branches corresponding to the previously split centerlines (Figure 2). As branches
223 are topologically equivalent to cylinders, the ACA could be mapped onto a two-
224 dimensional(2D)parametricspacewithalongitudinalcoordinate,u,andaperiodic
225 circumferentialcoordinate,v.Coordinateurangedfrom0to10mm,increasinginthe
226 direction of the flow. Coordinate v ranged from −π to πrad. The position of v=0
227 was determined by the bifurcation normal parallel transported along the centerline
228 andv>0wassettocorrespondtothesuperiorsideoftheACA.
229 2.7 Datavisualization
230 Contour plots were created to visualize the distribution of hemodynamic variables
231 on the surface of the ACA. Using the 2D parametrization, the branch surface was
232 flattenedontoarectanglesuchthatuandvcorrespondedtotheverticalandhorizontal
233 axes of the plots, respectively (Figure 2). This approach made it possible to view
234 the whole branch at once and more easily compare between subjects. Because the
235 circumferentialcoordinateisperiodic,weslightlyextendedtheplottorangefrom−4
236 to4rad,thusmaintainingavisualcontinuityofthevariabledistributions.Toindicate
237 thelocationoftheaneurysmneck,wecalculatedthedistancefromthesurfacewith
238 aneurysmtothesurfacewithoutaneurysmandplottedacontourlineat0.1mm.The
239 regionenclosedbytheaneurysmneckwillbereferredtoas‘aneurysminitiationsite’.
240 2.8 Statisticalanalysis
241 Inthisstudy,weassessedthereproducibilityofthecomputedWSSfieldwithrespect
242 totheobservervirtuallyremovingtheaneurysmandtotheflowrateimposedatthe
243 inlet. Differences between solutions were quantified by calculating the root-mean-
244 square deviation (RMSD) between TAWSS fields, after linearly interpolating them
245 ontoauniformlyremeshedbranchsurfacewithanominalnodespacingof0.05mm.
246 Solutionsofobserver2wereprojectedontotheremeshedbranchsurfaceofobserver
8 A.J.Geersetal.
247 1. Since normalized TAWSS fields were considered, for which TAWSSB =1, the
248 RMSDwasequaltothecoefficientofvariationoftheRMSD(CVRMSD).CVRMSD
249 willbeexpressedasapercentage.
250 Space-averagedvaluesofvariableswerecalculatedforquantitativeanalysis.Be-
251 sidesanalyzingthewholebranch,wedefineda‘patch’thatencapsulatedallaneurysm
252 initiation sites. This patch was bound by u∈[0,5] and v∈[−π 2,π 2], see Fig-
253 ure 2. For case 10, with the aneurysm directed anteriorly, and its(cid:14)matc(cid:14)hing control,
254 the patch was defined at the opposite side of the branch, bound by u∈[0,5] and
255 v∈[−π,−π 2)∪(π 2,π]. Variables were averaged over the branch, patch, and
256 non-patch(br(cid:14)anchmin(cid:14)uspatch).
257 Totestthesignificanceofthedifferencesbetweenregionsandbetweencasesand
258 controls,weusedtheWilcoxonsigned-ranktestforpairedsamplesandtheWilcoxon
259 rank-sumtestforunpairedsamples.Differenceswereconsideredstatisticallysignifi-
260 cantfor p<0.05.Thefollowingsampleswerecompared:I.patchvs.non-patchfor
261 thecases(paired),II.patchvs.non-patchforthecontrols(paired),III.patchesofthe
262 casesvs.patchesofthecontrols(unpaired),andIV.branchesofthecasesvs.branches
263 ofthecontrols(unpaired).
264 The Wilcoxon rank-sum test was also used to compare geometric variables be-
265 tweencasesandcontrols.Again,differenceswereconsideredstatisticallysignificant
266 for p<0.05.
3 Results
267
268 3.1 Geometry
269 AsmentionedinSection2.1,casesinthisstudywereremarkablyconsistentinloca-
270 tion, which is also confirmed by the location of the aneurysm initiation site in Fig-
271 ure 3. For cases 1 to 9, the circumferential coordinate of the center of the initiation
272 sitewasonaverage2◦ (range:−24to13◦).Forcase10,itwas119◦.Inotherwords,
273 mostaneurysmswereapproximatelyalignedwiththetransportedbifurcationnormal.
274 Table1reportsonthestatisticalanalysisofgeometricvariables.Bifurcationan-
275 gles were very similar among cases and controls. Cross sectional areas of branches
276 tended to be larger for cases, but only for the MCA branch these differences were
277 statisticallysignificant.Arearatioswerenotsignificantlydifferent.Thetortuosityof
278 ACAsshowedanon-significanttrendofbeinglargerforcasesthanforcontrols.
279 3.2 Hemodynamics
280 Figure 3 shows for all cases and controls the non-normalized TAWSS on the ACA.
281 Therewerelargevariationsinspace-averagedTAWSSwithvaluesrangingfrom1.0
282 to11.2Pa(mean:3.5Pa;standarddeviation:2.2Pa).Figure4showsthenormalized
283 TAWSS, highlighting the distribution rather than the magnitude. Overall, cases ap-
284 pearedtohavealargerspatialvariationinTAWSS,coveringawiderrangeofTAWSS
Wallshearstressattheinitiationsiteofcerebralaneurysms 9
285 values.ClosetotheapexofthebifurcationandonthesuperiorsideoftheACA(Fig-
286 ure 2), TAWSS was relatively high for cases. However, some controls showed sim-
287 ilar patterns, e.g. control 3 and control 5, whereas some cases, e.g. case 6, did not.
288 AneurysminitiationsitespartlyoverlappedwithregionsofhighTAWSS,yettended
289 to be near the edge of them. Statistical analysis revealed no significant differences
290 between the patch and the rest of the branch (non-patch) for controls, but did show
291 significant differences between those regions for cases (Table 2). Also, patches of
292 casesexperiencedsignificantlyhigherTAWSSthanthoseofcontrols.Bydefinition,
293 normalizationremoveddifferencesinTAWSSbetweenbranches.
294 Figure 5 shows the distribution of TAWSSG. Cases’ larger spatial variation in
295 TAWSS was reflected by higher positive and negative gradients. Correspondingly,
296 the absolute value of TAWSSG was significantly higher, both for the whole branch
297 andforthepatch(Table2).Althoughmagnitudesvaried,distributionswerefoundto
298 be similar for cases and controls: patches experienced significantly higher absolute
299 TAWSSGthantherestofthebranch.However,therewasnoclearcorrelationbetween
300 eitherpositiveornegativegradientsandtheaneurysminitiationsite.
301 Figure6showsthedistributionoftransWSS.Concentratedregionsofhightran-
302 sWSSwereobserved.WSSvectorschangeddirectionmorestronglyclosertotheICA
303 bifurcation,whichisalsoreflectedbypatcheshavingsignificantlyhighertransWSS
304 thannon-patches(Table2).Onaverage,transWSSwashigherforcasesthancontrols,
305 butonlyforthewholebranchthesedifferencesweresignificant.Noclearcorrelations
306 werefoundbetweenregionsofhightransWSSandtheaneurysminitiationsite.
307 AnimationsoftheWSSfieldduringthecardiaccycleshowedthat,althoughthe
308 WSS magnitude obviously changed over time, the distribution remained relatively
309 unchanged. Please refer to (Geers et al, 2015a) to view the animations online. This
310 meansthatateachpointonthebranchtheWSSmagnitudeovertimeresembledthe
311 shape of a typical flow rate waveform, which motivated our choice for describing
312 the temporal variation with the pulsatility index. Figure 7 shows the distribution of
313 WSSPI.Similarpatternscouldbeobservedamongcasesandcontrols.Nearthebifur-
314 cation, regions of relatively high WSSPI were located on the posterior and anterior
315 side of the ACA and regions of relatively low WSSPI were located on the superior
316 andinferiorside(SeeFigure2Cforalocationguide).Furtherdownstream,WSSPI
317 wasalsorelativelylow.Asaresult,wefoundsignificantdifferencesbetweenpatches
318 andnon-patches(Table2).Themaindifferencebetweencasesandcontrolswasthat
319 WSSPIwasonaveragehigherforcases,asignificantdifferenceforbranchesbutnot
320 forpatches.Judgingfromthecontourplots,however,wedidobserveaclearcorre-
321 lation between WSSPI peaks and the aneurysm initiation site. Additional statistical
322 analysisconfirmedthisobservationbyrevealingthatWSSPIwassignificantlyhigher
323 forjusttheinitiationsitethanforthewholepatch(1.61vs.1.52, p=0.007),which
324 wasnottrueforanyoftheothervariables.Inotherwords,amongtheassessedhemo-
325 dynamicvariables,WSSPImostconsistentlycorrelatedwiththeaneurysminitiation
326 site.
327 Nopatternwasfoundexplainingthedeviatinganeurysmorientationofcase10.
328 Removingthecaseanditsmatchingcontrolfromanalysisdidnotaltertheobserved
329 trends.