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Tetrahedral and Polyhedral Mesh Evaluation for Cerebral Hemodynamic Simulation - a Comparison

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Martin Spiegel at Friedrich-Alexander-University of Erlangen-Nürnberg
Martin Spiegel
Thomas Redel at Siemens Healthare GmbH
Thomas Redel
  • Siemens Healthare GmbH
Y. Jonathan Zhang
Y. Jonathan Zhang
Y. Jonathan Zhang
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Tobias Struffert
Tobias Struffert
Tobias Struffert
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Abstract

Computational fluid dynamic (CFD) based on patient-specific medical imaging data has found widespread use for visualizing and quantifying hemodynamics in cerebrovascular disease such as cerebral aneurysms or stenotic vessels. This paper focuses on optimizing mesh parameters for CFD simulation of cerebral aneurysms. Valid blood flow simulations strongly depend on the mesh quality. Meshes with a coarse spatial resolution may lead to an inaccurate flow pattern. Meshes with a large number of elements will result in unnecessarily high computation time which is undesirable should CFD be used for planning in the interventional setting. Most CFD simulations reported for these vascular pathologies have used tetrahedral meshes. We illustrate the use of polyhedral volume elements in comparison to tetrahedral meshing on two different geometries, a sidewall aneurysm of the internal carotid artery and a basilar bifurcation aneurysm. The spatial mesh resolution ranges between 5,119 and 228,118 volume elements. The evaluation of the different meshes was based on the wall shear stress previously identified as a one possible parameter for assessing aneurysm growth. Polyhedral meshes showed better accuracy, lower memory demand, shorter computational speed and faster convergence behavior (on average 369 iterations less).
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Tetrahedraland PolyhedralMesh EvaluationforCerebral
HemodynamicSimulation-aComparison
MartinSpiegel,ThomasRedel,Y.JonathanZhang,TobiasStruffert,JoachimHornegger,
RobertG.Grossman,Arnd Doerflerand ChristofKarmonik
Abstract—Computationalfluid dynamic (CFD)basedon
patient-specificmedicalimagingdatahasfound widespread use
forvisualizing and quantifyinghemodynamicsin cerebrovas-
culardiseasesuchascerebralaneurysmsorstenotic vessels.
This paper focusesonoptimizingmesh parametersforCFD
simulationofcerebralaneurysms.Valid blood flowsimulations
strongly depend onthemesh quality.Mesheswithacoarse
spatialresolutionmay leadto aninaccurateflowpattern.
Mesheswithalargenumber ofelementswill result in un-
necessarily highcomputationtimewhichis undesirable should
CFDbeusedforplanningin theinterventionalsetting.Most
CFDsimulationsreportedforthesevascularpathologieshave
usedtetrahedralmeshes.Weillustratetheuseofpolyhedral
volume elementsin comparisontotetrahedralmeshing ontwo
differentgeometries,asidewall aneurysmof theinternalcarotid
artery and abasilarbifurcationaneurysm.Thespatialmesh
resolutionrangesbetween5,119 and 228,118 volume elements.
The evaluationof thedifferentmesheswasbasedonthewall
shearstress previously identifiedasa onepossible parameter for
assessing aneurysmgrowth.Polyhedralmeshes showed better
accuracy,lower memorydemand,shorter computationalspeed
and faster convergence behavior(onaverage369 iterationsless).
I.INTRODUCTION
Advancesin hardware and softwarehave enabledthe
application ofCFDin variousclinicalfields,e.g.cardiology
[1]orneuroradiology [2].Differentaspectshavebeenana-
lyzedlikepatient-specifichemodynamicsimulation [3],[4],
correlation ofwall shearstress (WSS)patternwiththerisk
of ruptureofcerebralaneurysms[5],[6]orhemodynamic
characteristicspertaining tothe angleofthe aneurysmbulb
relativetotheparentartery[7].OtherCFDstudiesconsid-
eredthegeometricfactorsofaneurysms[8],[9],[10],e.g.
lesion size oraspectratiotoassess therisk ofananeurysm
M.Spiegel iswithFriedrich-AlexanderUniversityErlangen-Nuremberg
(FAU),DepartmentofComputerScience,ChairofPatternRecogni-
tion,Germany and FAU,DepartmentofNeuroradiology and Siemens
AG HealthcareSector,Forchheim, Germany and theErlangenGrad-
uateSchool inAdvancedOpticalTechnologies(SAOT),Germany
martin.spiegel@informatik.uni-erlangen.de
T.Redel iswithSiemensAG HealthcareSector,Forchheim, Germany
J.Zhang isaninterventionalneuroradiologistand vascularsurgeon with
TheMethodistHospital,Houston,TX,USA
T.Struffert isaninterventionalneuroradiologistwithFAU,Department
ofNeuroradiology,Erlangen,Germany
J.HorneggeriswithFAU,DepartmentofComputerScience,Chairof
PatternRecognition (Head)and SAOT,Erlangen,Germany
RG GrossmanisChairman oftheDepartmentofNeurosurgeryand
DirectoroftheNeurologicalInsitute,TheMethodistHospital,Houston,
TX USA
A.DoerfleriswithFAU,DepartmentofNeuroradiology (Head),Erlan-
gen,Germany
C.KarmonikisaResearchScientistwithTheMethodistHospital
ResearchInstitute,Houston,TX,USAckarmonik@tmhs.org
rupture.In[11],different inflowconditionswereinvestigated
toassess itsdependence totheWSSdistribution inthe
vicinity ofthree basilartipaneurysms.WSSpatternsplaya
major roleforassessing pathologicalvesselsystemswithin
theCFDblood flowcommunity.
Mostofthesesimulationsutilizedtetrahedralmeshes.More
advancedmeshing techniquesarenowavailableinturn-key
commercialCFDsoftwarepackageswhichmayleadtoare-
duction incomputing timeby reducing theoverall numberof
volume elementswhilemaintaining accuracy.While accurate
meshing isessential to obtainmesh-independentresults,ade-
ficiencyinthemeshmay notbeobviousand mayleadto non-
validresultsasotherincorrectsimulation parameters,such
asimproperinletconditionsintermsofmass orblood flow
speed,varying blood densityand viscosity,blood modeledas
Newtonianfluid.Mesh deficienciesinclude cellswith high
skewness factorand a coarsespatialresolution thatmaylead
toimprecision computation oflocalvelocity orWSSpattern.
While assessmentofthemesh qualityistime-consuming,it is
nevertheless averyimportant task.Two distinctapproaches
formeshsuitability verification havebeenintroduced[12]:
1)Comparison ofthenumericalsimulation resultswith
experimentaldata and 2)generation ofasetofmeshes
withincreasing numberofcontrolelementsalsocalledmesh
independence analysis.Phase-contrastMRImeasurements
deliversuitableresultstocompareMRvelocity valuesorpri-
mary blood flowpatternswithCFDsimulation results[13].
Meshindependence analysisisconsideredthe established
method forverifying meshaccuracytosimulate arterialflow.
Itrequiresasetup ofdifferentmeshespervesselgeometry
fromlowto high resolution.
Thegoalofthis study wastoexploreintheframework of
meshindependence analysiswhetherpolyhedralmesheswith
fewervolume elementsthancomparabletetrahedralmeshes
will result in betteraccuracywithshortercomputation time
using patient-specificimaging data.Twocerebralaneurysm
geometrieswereinvestigated:oneinternalcarotidand one
basilartipaneurysm,respectively(see Fig.1).Asetof
varying meshresolutionswas systematicallycreatedasa
benchmarkforspatialmeshresolutionsneededto obtain
accurate,mesh-independentWSSpatternsorblood flow
velocity.
II.METHODS
3-Ddigitalsubtraction angiography (DSA)imagedata
[14]ofthetwocerebralaneurysms(see Fig.1)were ac-
quired during endovascularinterventionsusing abiplane
2787
31st Annual International Conference of the IEEE EMBS
Minneapolis, Minnesota, USA, September 2-6, 2009
978-1-4244-3296-7/09/$25.00 ©2009 IEEE
TABLE I
SET OFMESHES-CASE1AND CASE2.TE T.AND POLY.ABBREVIATE TETRAH EDRALAND POLYHEDRALRES PECTIVELY.PA AND ITE R.DENOT E
PASCALAND ITERATION S.
#Tet.CellsAngleGrowthMax./Min.TriangleTet.#Iter.#Poly.CellsPoly.#Iter.Tet.WSS(Pa)Poly.WSS(Pa)
Case1 13841 25 1.2 6 /0.001 153 5119 63 9.52 10.33
26702 14 1.2 3.6/0.001 180 7283 81 11.66 11.88
52374 14 1.1 1.8/0.001 296 12467 108 13.37 13.15
76493 6 1.2 1.2/0.001 306 17695 122 14.53 13.80
86621 12 1.1 0.4/0.001 1633 18681 142 14.43 13.92
106010 12 1.1 0.36 /0.001 1291 22297 185 14.76 13.99
115014 10 1.1 0.3/0.001 451 25540 154 14.71 14.32
228118 10 1.1 0.25 /0.001 -43487 583 -15.58
Case2 31696 17 1.2 0.42 /0.001 242 8814 111 5.91 5.26
43063 17 1.17 0.37 /0.001 378 10843 176 7.18 6.20
56176 15 1.12 0.34 /0.001 365 13280 185 7.06 6.51
75469 13 1.10 0.32 /0.001 437 16795 202 7.33 6.84
98399 10 1.10 0.3/0.001 462 21108 211 7.43 7.15
114227 10 1.10 0.28 /0.001 496 23846 230 7.47 7.23
148625 8 1.09 0.25 /0.001 714 30167 269 7.62 7.45
174225 6 1.10 0.24 /0.001 626 35665 254 7.48 7.57
(a) (b)
Fig.1.Three dimensionalreconstruction ofthe evaluatedaneurysms:(a)
Case1 depictsainternalcarotidaneurysm(b)Case2illustratesabasilartip
aneurysm
flat-panelsystemSiemensC-ArmSystem(dBA,Siemens
AG HealthcareSector) inErlangen(Germany)and Houston
(USA).3-Dimagereconstructionsofbothaneurysmsledto
animagevolumeforCase1 of138.24×138.24×57.72mm
withavoxelspacing of0.27×0.27×0.13mm and forCase2
97.28×97.26×66.43mm (voxelspacing 0.19×0.19×0.1mm)
respectively.Formesh generation and smoothing,theMarch-
ing Cubes[15]and aLaplacian-basedsmoothing algorithm
(VTK KitwareInc.)wasappliedasanaddtionalstep.The
imagedatawas storedasastereolithographicfile(STL)pro-
viding theinputdataforthe commercialmeshing software
GAMBIT(ANSYSInc.).
TheGAMBITcurvaturesize function [16]wasusedtoeasily
generatedifferentsurface meshesexhibiting agranularity
fromcoarsetofine.Thisfunction constrainsthe anglebe-
tween outward-pointing normalsforany twoadjacentsurface
triangles.That isparticularly useful inthe caseofhighly
curvedsurfaceslike aneurysmgeometries.Hence,regions
with high curvature aremeshedinmoredetail thanthose
withlowercurvature.Fourparametersdefinethe curvature
size function i.e.anglein degree,growthin percentage,max.
and min.trianglesize.TableIcontainsadetailed overview
ofthe appliedcurvaturesize function parameters.Givena
certain geometryand certain parametervalues,themeshing
algorithmwill automaticallychoosethefinalnumberof
trianglesforthesurface mesh.
Thenumberoftetrahedralmeshelementsforthewhole
volumedependson theresolution ofthegivensurface mesh
-thelargerthenumberoftriangles,representing thesurface,
thelargerthenumberoftetrahedralmeshelements.
Mesheswereimportedintothesimulation softwareFluent
(ANSYSInc.).Foreachtetrahedralmesha corresponding
polyhedralmeshwasgenerated by a conversion algorithm
partoftheFluentCFDsolver.Thesurface ofthe aneurysm
and theparentarteryweremodeledasrigid-wallsand no
slipas shearcondition.Blood wasmodeledasanincom-
pressibleNewtonianfluidwithadensity of1050kg/m3and
aviscosity of0.004 N/m2s[17].Theboundaryconditions
forall conductedsimulationswere asfollows: theinletwas
consideredasavelocityinletand all outletsweremodeled
aspressureoutletzero.Aconstant inflowrateof0.5m/s
wasappliedinthesteady simulations.We considereda
steady-statesimulation asconverged,iftherelativeresiduals
fallsunder0.001 (i.e.the absolutevaluesoftheresiduals
werereduced by three ordersofmagnitude).Aseriesof
steady-statesimulationswereperformedaccording tothe
meshes shownintableIin ordertoeliminatetheissueof
unsuitableCFDmeshesand tocomparetheresultsgiven
frompolyhedraland tetrahedralmeshes.Figure2 gives
an overviewabout thesimulation resultsconcerning WSS
distribution.TheArea-Weighted-AverageWSSdistribution
wasusedtoanalyze theWSSdifferencesbetween polyhedral
and tetrahedralmeshesintermsofnumbers.It isdefinedas
1
AZφdA=
1
A
n
X
i=1
φi|Ai|(1)
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whereAdenotesthetotalarea being consideredand φi
describesthewall shearstress associatedwiththefacetarea
Ai.
III.RESULTS
Thesimulation series showstwofindings.1)theWSS
pattern ofpolyhedralmesheslook morehomogeneousthan
theonesofthetetrahedralmeshesasindicated by theyellow
circlesinfigure2.TableI (columns9and 10)depictstheval-
uesofthe averageArea-Weighted-AverageWSSdistribution
considering onlythe aneurysmarea asillustratedinfigure
2.Thedifferencesbetween bothmeshtypesarenegligible
considering thefact thatpolyhedralmeshesexhibit farless
cell elementsthantetrahedralmeshes.2)tetrahedralmeshes
exhibit afarworse convergence asthepolyhedralones(see
tableIcolumn 6 and 8).Onaverage,tetrahedralmeshes
need 369 iterationsmorethanthepolyhedralmeshes.The
highestresolvedtetrahedralmesh(case1 228118 tetrahedral
elements)did notconverge according tothe applied boundary
condition asdescribedinthemethod section.
IV.DISCUS SIO N
Acertainmeshresolution isneededtoresolvetheWSS
distribution on avalid base.TheWSSpatternis similar for
tetrahedral(whenconverged)and polyhedral.However,it
changeswithincreasing spatialresolution and convergesat
a certainlevel(see figure2and tableI).Polyhedralmeshes
can be consideredasaviable alternativetotetrahedral
meshesbecausethey do notonlyshowbettercomputational
convergence [18].Theyare alsoabletoresolvetheWSS
patternwithfarless controlvolumespermeshinamoreho-
mogeneousmannerthanthetetrahedralmeshes.Thereason
forthisliesinthewaytheWSSmagnitudeiscalculated
which dependson twomajoraspects:1)onlythose cell
elementsare consideredwhichactuallyshare a face with
thevesselboundary.Notall tetrahedralelementslocatedat
thevesselboundarysharenecessarilyanentireface withthe
boundary-somemaytouchtheboundarywithitscorner.
While all polyhedralelementslocatedat thewall share an
entireface withtheboundaryitself.2)Thedistancesofthe
consideredtetrahedralcentersarenotequal tothevesselwall
leading toamoreinhomogeneousWSSappearance.
Froma clinicalperspective,the convergence aswell asthe
computation speed ofCFDsimulationsare crucialaspects
regarding future clinicalCFD-based diagnostic and treatment
tools.It isnotfeasibleforthetreating physicianto have
tochangesimulation parametersto optimize convergence
behavior.Ourevaluation has shownthat thepolyhedral-based
meshesaremorestable and fasterand should beusedina
futurestandardizedclinicalsimulation workflow.
Theresultsobtained during this study may be affected
duetoseveral limitations.Ourassumptionsconcerning the
conductedCFDexperimentsdiffer fromtheinvivostatein
termsof rigid vesselwalls,Newtonian-based blood fluidand
thedetermination oftheboundaryconditions,respectively.
Theoutflowsofthepatient-specificmodelsaredefinedas
pressureoutletzerowhich doesnothavetomatchwiththe
realenvironment.Theremightbenaturalresistancesat the
outflows.Aswith othercomputationalstudies,it isassumed
that theselimitationshaveonlyminoreffectson theresulting
flowpattern[19].However,futurework hastofocuson the
reduction oftheselimitation inthesenseofvalidation against
invivomeasurements.
V.CO NCLUSIO N
This study representsthefirstmeshindependencyanalysis
inthefield ofcerebralblood flowsimulation togetherwith
a comparison ofpolyhedraland tetrahedral-basedmeshes.
Here,weput thefocusfromthe actualflowpatternwithin
aneurysmsoritscorresponding WSSpatterntothe evaluation
oftheCFDmesh.Our resultsillustratetheimportance ofa
well-foundedmesh granularityevaluation beforestarting a
blood flowsimulation in orderto getreliableblood flow
simulation resultstosupport the clinicaldecision making.
Thisapproachservesasafirstkeysteptowardsafuture
clinicalCFDapplication wherethemesh generation process
hasto be automatedasmuchaspossible.Furthermore,
theresultswill allowto deviaterequirementsto geometric
modelaccuracyacquired by modernimaging methodsand
to optimize CFDcomputation timewithout loss ofaccuracy.
VI.ACKNOWLED GMENTS
The authorswouldliketothank Dr.RalfKroeger (ANSYS
Germany GmbH) forhisadvice and simulation support.
The authorsgratefullyacknowledgefunding oftheErlangen
GraduateSchool inAdvancedOpticalTechnologies(SAOT)
by theGermanNationalScience Foundation (DFG)inthe
framework ofthe excellence initiative.
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Case1
Polyhedral Tetrahedral
5119
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13841
86621
115014
Case2
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8814 31696
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35665 174225
0.0 Pascal 58.6 Pascal
0.0 Pascal 121.3 Pascal
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... It has been found that trimmer mesh requires less memory compared to polyhedral mesh on small gap overset problems (CD-Adapco 2015). The polyhedral mesh generating method was chosen for the rest of the system for smaller number of cells (CD-Adapco 2015), higher accuracy, and faster convergence (Spiegel et al. 2009). Local refinement was performed in disc rotation regions. ...
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... Tetrahedral or polyhedral elements are commonly used to discretize the volume. 46 To accurately address high velocity radial gradients in the vicinity of the wall, and thus to accurately estimate the WSS, three to five layers of prismatic boundary layer elements are required in near-wall regions. 13,47,48 Unstructured meshes in the context of aneurysm flow modeling are commonly comprised of elements of 0.1-0.2 ...
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  • Jan 2020
  • J BIOMECH
We discuss a computationally-efficient numerical Reduced Order Model (ROM) for patient-specific cerebral aneurysms, which can be used to examine the rupture-related hemodynamic parameters over a range of relevant physiological flow parameters, rapidly. The ROMs were derived using a Proper Orthogonal Decomposition (POD) technique, which also took advantage of the method of Snapshot POD. Initially a series of Computational Fluid Dynamics(CFD) training runs were performed, which were subsequently improved using a QR-decomposition technique to satisfy the various boundary conditions in physiological flow problems. We used the obtained ROMs to study the influence of Pulsatility Index (PI) on a patient-specific aneurysm's Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI). In addition, we discuss how each of the obtained high-energy POD modes represents a separate significant flow pattern that is believed to influence the aneurysm's WSS and OSI.
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Numerical Simulation of a Check Valve Closure Induced by Pump Shutdown
Article
  • Dec 2018
High pressure surges induced by the sudden closure of check valves can cause severe damage to mechanical and hydraulic facilities. A three-dimensional unsteady numerical simulation of a dual disc check valve closure induced by upstream pump shutdown was performed and validated experimentally. An overset mesh was applied to achieve a full closure of the check valve discs and capture pressure surges accurately. The velocity field graphs improve the understanding of the flow field evolution during the transient event. The impact of system outlet pressure, initial flow rate, and pump shutdown speed on pressure surges was investigated to explore factors that affect the amplitude of pressure surges. This work improves the understanding of check valve closure behavior, which is beneficial to check valve design, selection, and operation. Additionally, this work proves that overset mesh technology could be applied to other similar flow domain breaking cases.
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Untangling polygonal and polyhedral meshes via mesh optimization
Article
  • Jul 2014
We propose simple and efficient optimization-based untangling strategies for 2D polygonal and 3D polyhedral meshes. The first approach uses a size-based mesh metric, which eliminates inverted elements by averaging element size over the entire mesh. The second method uses a hybrid quality metric, which untangles inverted elements by simultaneously averaging element size and improving element shape. The last method using a variant of the hybrid quality metric gives a high penalty for inverted elements and employs an adaptive sigmoid function for handling various mesh sizes. Numerical experiments are presented to show the effectiveness of the proposed untangling strategies for various 2D polygonal and 3D polyhedral meshes.
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Marching Cubes: A High Resolution 3D Surface Construction Algorithm
Article
Full-text available
  • Aug 1987
  • Comput Graph
We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.
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Simulation of cardiac motion on non-Newtonian, pulsating flow development in the human left anterior descending coronary artery
Article
Full-text available
  • Oct 2008
This study aimed at investigating the effect of myocardial motion on pulsating blood flow distribution of the left anterior descending coronary artery in the presence of atheromatous stenosis. The moving 3D arterial tree geometry has been obtained from conventional x-ray angiograms obtained during the heart cycle and includes a number of major branches. The geometry reconstruction model has been validated against projection data from a virtual phantom arterial tree as well as with CT-based reconstruction data for the same patient investigated. Reconstructions have been obtained for a number of temporal points while linear interpolation has been used for all intermediate instances. Blood has been considered as a non-Newtonian fluid. Results have been obtained using the same pulse for the inlet blood flow rate but with fixed arterial tree geometry as well as under steady-state conditions corresponding to the mean flow rate. Predictions indicate that myocardial motion has only a minor effect on flow distribution within the arterial tree relative to the effect of the blood pressure pulse.
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Image-Based Computational Simulation of Flow Dynamics in a Giant Intracranial Aneurysm
Article
Full-text available
  • May 2003
Blood flow dynamics are thought to play an important role in the pathogenesis and treatment of intracranial aneurysms; however, hemodynamic quantities of interest are difficult to measure in vivo. This study shows that computational fluid dynamics (CFD) combined with computed rotational angiography can provide such hemodynamic information in a patient-specific and prospective manner. A 58-year-old woman presented with partial right IIIrd cranial nerve palsy due to a giant carotid-posterior communicating artery aneurysm that was subsequently coiled. Computed rotational angiography provided high resolution volumetric image data from which the lumen geometry was extracted. This and a representative flow rate waveform were provided as boundary conditions for finite element CFD simulation of the 3D pulsatile velocity field. CFD analysis revealed high speed flow entering the aneurysm at the proximal and distal ends of the neck, promoting the formation of both persistent and transient vortices within the aneurysm sac. This produced dynamic patterns of elevated and oscillatory wall shear stresses distal to the neck and along the sidewalls of the aneurysm. These hemodynamic features were consistent with patterns of contrast agent wash-in during cine angiography and with the configuration of coil compaction observed at 6-month follow-up. Anatomic realism of lumen geometry and flow pulsatility is essential for elucidating the patient-specific nature of aneurysm hemodynamics. Such image-based CFD analysis may be used to provide key hemodynamic information for prospective studies of aneurysm growth and rupture or to predict the response of an individual aneurysm to therapeutic options.
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Computational Simulation of Therapeutic Parent Artery Occlusion to Treat Giant Vertebrobasilar Aneurysm
Article
Full-text available
  • Feb 2004
We applied computational fluid dynamics (CFD) analysis to assess 3D digital subtraction angiography findings in a patient with a giant vertebrobasilar aneurysm to simulate and compare the consequences of left and right vertebral artery occlusion. The balloon occlusion test suggested that occlusion of the right vertebral artery is the better way to treat this patient's aneurysm from the point of view of aneurysmal thrombosis and isolation from the circulation. The computer simulation supported this conclusion, at the same time indicating that from the point of view of pressure distribution on the wall of the aneurysm, the right vertebral occlusion may be also accompanied by an undesirable effect. A high-pressure area on the aneurysm wall in systole was revealed. This high pressure potentially could lead to subsequent aneurysmal growth, which indeed occurred, as was revealed by a follow-up examination 6 months later. This study is a good example of possible future applications of CFD in patients with cerebrovascular disease before therapeutic intervention.
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Is the Aspect Ratio a Reliable Index for Predicting the Rupture of a Saccular Aneurysm?
Article
  • Apr 2001
The present retrospective study was undertaken to prove the reliability of the aspect ratio (aneurysm depth to aneurysm neck width) for predicting an aneurysmal rupture. The aspect ratio is considered a better geometric index than aneurysm size for determining the intra-aneurysmal blood flow. We measured the aspect ratios and the sizes of aneurysms, as determined by examining angiographic films magnified 1.4x, in 129 patients with ruptured aneurysms and in 72 patients with 78 unruptured aneurysms. After categorizing the aneurysms into four groups on the basis of their locations (aneurysms of the anterior communicating artery, middle cerebral artery, internal carotid artery-posterior communicating artery [ICA-PComA], and other aneurysms), a statistical analysis of ruptured and unruptured aneurysms was performed. The mean aneurysm size was found to be statistically significant in the aneurysms at the ICA-PComA and in locations excluding the anterior communicating artery, the middle cerebral artery, and the ICA-PComA. However, the mean aspect ratio was statistically significant at all four locations. In patients with ruptured aneurysms, no ruptured aneurysms with an aspect ratio of less than 1.0 were found. The distribution of the ruptured group versus the unruptured group with an aspect ratio of less than 1.6 at each location was 13 versus 79%, respectively, at the anterior communicating artery, 11 versus 58% at the middle cerebral artery, 11% versus 85% at the ICA-PComA, and 7 versus 81% at other locations. The aspect ratio between ruptured aneurysms and unruptured aneurysms was found to be statistically significant, and almost 80% of the ruptured aneurysms showed an aspect ratio of more than 1.6, whereas almost 90% of the unruptured aneurysms showed an aspect ratio of less than 1.6. This study therefore suggests that the aspect ratio may be useful in predicting imminent aneurysmal ruptures.
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Requirements for Mesh Resolution in 3D Computational Hemodynamics
Article
  • May 2001
Computational techniques are widely used for studying large artery hemodynamics. Current trends favor analyzing flow in more anatomically realistic arteries. A significant obstacle to such analyses is generation of computational meshes that accurately resolve both the complex geometry and the physiologically relevant flow features. Here we examine, for a single arterial geometry, how velocity and wall shear stress patterns depend on mesh characteristics. A well-validated Navier-Stokes solver was used to simulate flow in an anatomically realistic human right coronary artery (RCA) using unstructured high-order tetrahedral finite element meshes. Velocities, wall shear stresses (WSS), and wall shear stress gradients were computed on a conventional "high-resolution" mesh series (60,000 to 160,000 velocity nodes) generated with a commercial meshing package. Similar calculations were then performed in a series of meshes generated through an adaptive mesh refinement (AMR) methodology. Mesh-independent velocity fields were not very difficult to obtain for both the conventional and adaptive mesh series. However, wall shear stress fields, and, in particular, wall shear stress gradient fields, were much more difficult to accurately resolve. The conventional (nonadaptive) mesh series did not show a consistent trend towards mesh-independence of WSS results. For the adaptive series, it required approximately 190,000 velocity nodes to reach an r.m.s. error in normalized WSS of less than 10 percent. Achieving mesh-independence in computed WSS fields requires a surprisingly large number of nodes, and is best approached through a systematic solution-adaptive mesh refinement technique. Calculations of WSS, and particularly WSS gradients, show appreciable errors even on meshes that appear to produce mesh-independent velocity fields.
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Is aspect ratio a reliable predictor of intracranial aneurysm rupture?
Article
  • Jul 2004
This study was undertaken to assess the reliability of the aspect ratio (AR) (i.e., aneurysm depth to aneurysm neck) in predicting aneurysm rupture. It has been shown that the AR is a key factor in predicting intraaneurysmal blood flow and aneurysm rupture. Seventy-five patients with subarachnoid hemorrhage and multiple aneurysms were studied. The sizes of the aneurysms and their ARs were determined by examining the angiographic films. By comparing the difference between ruptured and unruptured aneurysms in the same individual, each patient in effect served as his or her own control. Each ruptured aneurysm was confirmed during surgery. There were 75 ruptured and 107 unruptured aneurysms. The mean AR was 2.70 for ruptured aneurysms, compared with 1.8 for unruptured aneurysms. This difference between the ARs was statistically significant (P < 0.001). The difference in aneurysm sizes in the two groups also was significant (P < 0.001). AR on its own is as reliable a variable as the size of the aneurysm for predicting aneurysm rupture.
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