'Sphere': A Dedicated Bifurcation Aneurysm Flow-Diverter Device

14 Pages·2014·4.7 MB·English

CardiovascularEngineeringandTechnology,Vol.5,No.4,December2014((cid:3)2014)pp.334–347
DOI:10.1007/s13239-014-0188-4
The ‘Sphere’: A Dedicated Bifurcation Aneurysm Flow-Diverter Device
THOMASPEACH,1 J. FREDERICK CORNHILL,2,3 ANH NGUYEN,2,3HOWARD RIINA,2,3,4 and YIANNIS VENTIKOS5
1InstituteofBiomedicalEngineering,DepartmentofEngineeringScience,OxfordUniversity,Oxford,UK;2MinimallyInvasive
New TechnologiesProgram, Weill-Cornell MedicalCollege, NewYork, NY, USA; 3New YorkPresbyterian Hospital,New
York, NY, USA; 4Departmentof Neurosurgery, NYU LangoneMedical Center,New York, NY,USA; and 5Departmentof
Mechanical Engineering,University College London,London, UK
(Received29January2014;accepted15July2014;publishedonline26August2014)
AssociateEditorAjitP.Yoganathanoversawthereviewofthisarticle.
Abstract—Wepresentflow-basedresultsfromtheearlystage INTRODUCTION
design cycle, based on computational modeling, of a proto-
typeflow-diverterdevice,knownasthe‘Sphere’,intendedto The frequency of intracranial aneurysms in the gen-
treat bifurcation aneurysms of the cerebral vasculature. The eralpopulationisconsideredtobebetween1and5%.47
deviceisavailableinarangeofdiametersandgeometriesand
In the vast majority of cases, these aneurysms are
is constructed from a single loop of NITINOL(cid:2) wire. The
asymptomatic, posing no health risk to the patient. In
‘Sphere’reducesaneurysminflowbymeansofahigh-density,
patterned, elliptical surface that partially occludes the aneu- some cases,an aneurysmwill rupture, causing a poten-
rysmneck.Thedeviceissecuredinthehealthyparentvessel tially life-threatening hemorrhage. The risk of rupture
by two armatures in the shape of open loops, resulting in canbedependentonaneurysmsizeandgeometrybutis
negligible disruption of parent or daughter vessel flow. The
typically only a few percent for small aneurysms,
device is virtually deployed in six anatomically accurate
increasing to up to 50% for giant (>25 mm diameter)
bifurcation aneurysms: three located at the Basilar tip and
three located at the terminus bifurcation of the Internal lesions.49Intracranialaneurysmruptureisamajorcause
Carotid artery (at the meeting of the middle cerebral and of stroke, resulting in hemorrhagic stroke or subarach-
anterior cerebral arteries). Both steady state and transient noidhemorrhage.Aneurysmrupturecanleadtosignif-
flowsimulationsrevealthatthedevicepresentswitharange
icant brain damage and even death in around 25% of
of aneurysm inflow reductions, with mean flow reductions
hemorrhage cases.8 As diagnostic imaging use becomes
falling in the range of 30.6–71.8% across the different
geometries. A significant difference is noted between steady more widespread, an increasing number of asymptom-
stateandtransientsimulationsinonegeometry,whereazone aticaneurysmsarebeingidentifiedduringimagingscans
of flow recirculation is not captured in the steady state (CT, MRI) requested for other conditions.47 This has
simulation. Across all six aneurysms, the device reduces the
lead to marked increase in the need for effective treat-
WSS magnitude within the aneurysm sac, resulting in a
ment options to stabilize the ever-increasing number of
hemodynamicenvironmentclosertothatofahealthyvessel.
We conclude from extensive CFD analysis that the ‘Sphere’ aneurysms identified as being at risk of rupture or
device offers very significant levels of flow reduction in a complications.Treatmentsfocusonreducingtherupture
number of anatomically accurate aneurysm sizes and loca- risk by excluding the aneurysm from the circulation,
tions, with many advantages compared to current clinical
which induces stable thrombus formation within the
cylindrical flow-diverter designs. Analysis of the device’s
aneurysmsac,andultimately,vascularremodeling.
mechanicalpropertiesanddeployabilitywillfollowinfuture
publications. Flow-diverters (FDs) were first proposed in the late
1990s15 as a potential treatment for cerebral aneu-
Keywords—Minimallyinvasive,Neurovascular,Thrombosis, rysms,whichwouldpotentiallyeliminatetheproblems
Stent, CFD, Medical devices, SILK, PED, WEB, WSS, associated with the placement of coils (e.g., coil
Shearstress. migration, mass effect, puncture of aneurysm dome,
etc.) and achieve aneurysm stabilization by decreasing
the blood flow into the aneurysm sac. Flow-diverter
treatment aims to reconstruct the parent vessel with a
low porosity stent that reduces intra-aneurysmal flow,
Address correspondence to Yiannis Ventikos, Department of
leading to stable thrombus formation in addition to
MechanicalEngineering,UniversityCollegeLondon,London,UK.
Electronicmail:[email protected] allowing neointimal and endothelial growth on the
334
1869-408X/14/1200-0334/0(cid:3)2014TheAuthor(s).ThisarticleispublishedwithopenaccessatSpringerlink.com
A DedicatedBifurcation AneurysmFlow 335
reportedin41cases,inthefiveremainingcases(10.9%)
completeocclusionofthedaughtervesselwasreported,
which resulted in the death of one patient.
Alternative concepts to the conventional cylindrical
flow-diverterhavebeenproposedtobetteraddress the
treatment of bifurcation aneurysms and reduce treat-
ment morbidity and mortality. The most significant
alternative is the WEB device (Sequent Medical, Aliso
Viejo, CA) The WEB device is capable of treating a
bifurcation aneurysm without daughter vessel occlu-
sion by morphing a NITINOL(cid:2) mesh, similar to con-
ventional cylindrical FDs, into a collapsible ball that
may be deployed within the aneurysm dome.20,32 The
deviceisthensecuredwithintheaneurysmsacitselfby
expandingtoopposethevesselwallinasimilarmanner
FIGURE1. Conventional cylindrical FD treatment of an
internal carotid artery (ICA) sidewall aneurysm (left) and the to conventional coiling. Whether or not a relatively
same FD deployed to treat an ICA bifurcation aneurysm, high radial force device deployed inside the aneurysm
resultingintheocclusionofonedaughtervessel(right). domealtersanyriskofaneurysmweakening,enlarging
orruptureisunknown,asistheeffectofsuchforceson
wide-neckandgiantaneurysmsinparticular.
stent surface.30 A typical flow-diverter of a cylindrical Inthisstudyweproposeanoveldesignforadevice
design,placedtotreatasidewallaneurysm,isshownin with flow-diverting functionality, intended to specifi-
Fig. 1 (left). A similar design of flow-diverter was first cally treat bifurcation aneurysms. The device, known
usedinapatientin2006,25and fromearly experiences as the ‘Sphere’, is a NITINOL(cid:2) spherical frame that
of the devices’ usage on a variety of clinical cases, the presents a high-density face to the aneurysm neck in
outcomes have been positive with good aneurysm order to reduce inflow. It is secured by ‘legs’ in the
occlusion rates at times of follow up.5,24,25,27 Many form of multiple open hoops that form part of the
authors have shown low flow-diverting effects experi- spherical frame, which are deployed in the parent
enced by small side branches and perforators of a vessel distal to the aneurysm. Thus, all bifurcation
vessel after FD deployment, suggesting there is little daughter vessels remain uncompromised following
risk of secondary infarction following treatment in treatment, unlike some interventions using conven-
territories with rich collaterals.21 However, the result tional cylindrical FDs. In addition, the device is
oflargevesselocclusionbyflow-diverters,especiallyat secured in a non-diseased portion of the artery where
bifurcations, remains unknown. high radial force, of the order of conventional cylin-
Therearecurrentlytwocylindricaldesignsofcerebral dricalFDs,isnotaconcernandnoportionoftheflow-
flow-diverteronthemarketthatareapprovedforusein diverterentersthedelicateaneurysmdome.Wepresent
patients: the PIPELINE EMBOLIZATION DEVICE, an analysis of one of the ‘Sphere’ device designs, of
known as the PED (Covidien/ev3, Irvine, CA) and the whichthereareseveral,deployedinsixpatient-specific,
SILK flow-diverter (Balt Extrusion, Montmorency, anatomically accurate aneurysm geometries.
France), with another four or five in various stages of
development. Clinical experience of both the PIPE-
LINE24,27 and the SILK21,25 report good aneurysm LITERATURE REVIEW
occlusioninmanydifferentsacsizesandgeometries.The
Flow-Diverter Devices
body of research detailing clinical experience with both
designsofflow-divertercontinuestogrow,withatotalof A broad spectrum of stent designs has been studied
over800interventionsrecordedintheliterature. using computationalfluid dynamics (CFD) modeling in
While such flow-diverter designs present an elegant the literature, ranging from the very abstract to designs
treatmentsolutionforsidewallaneurysms,treatmentof thatarecommerciallyavailable.Fromthesestudies,itis
bifurcation aneurysms with FDs remains problematic. clear that when considering variations in flow-diverter
Theclosed-cellcylindricalnatureofcurrentFDdesigns geometry, porosity has been most widely investigated,
makes the jailing of all but one daughter vessel inevi- with the general and intuitive assumption that lower
table during treatment. This is illustrated in Fig. 1 porositydevicesinhibitflowtogreaterdegree.Itiswidely
(right). A study conducted by Saatchi et al.36 included heldthataporosityofaround70%isoptimalforflow-
46 ‘uncoilable’ aneurysms that originated at vessel diverting stents.9,23,42 Exploring beyond the effect of
branches.AlthoughsuccessfultreatmentwithPEDwas porosity,Lieberetal.22reportedtheeffectofstrutsizeon
336 PEACHet al.
intra-aneurysm flow. The study concluded that at a Blood flow in the small-diameter vessels that feed
constant porosity, decreasing the filament diameter and the brain typically has a Reynolds number that is less
therefore increasing the number of struts across the than 1000, suggesting little risk of turbulent transition
aneurysm neck reduced inflow more. Fu et al.11 consid- for the surface roughness of such a vessel.11,19
ered the role of stent geometry and surface pattern on Thepulsatilityeffectsofbloodflowwereextensively
aneurysm inflow, with strut cross-section (circular, rect- studiedbyWomersley,whoshowedthatpulsatilepipe
angular, and concave) and overall pattern of the stent flow adopts an increasingly non-parabolic flow profile
(zig-zagorhelical)beingvaried.Thegreatestreductionin with increasing flow frequency.13,50 The tendency for
inflowandwallshearstress(WSS)wasseenwithadesign flow to depart from the steady-state profile and adopt
havingstrutswitharectangularcross-sectionarrangedin a plug profile increases with the Womersley number,
azig-zagpattern.Inapaperdiscussingmeshoptimisation defined in (Eq. 2).
strategies,Appanaboyinaetal.2modeledstentswithboth
lrffixffiffiffiqffiffiffi
zig-zag and hexagonal cell designs, finding the greatest a¼ ; ð2Þ
2 l
reductionininflowfromthezig-zagdesign.
Current commercially available flow-diverters are
where a is the Womersley number, q the fluid density
dominated by the SILK/SILK + (Balt Extrusion, (kg m(cid:2)3), x the angular frequency of flow oscillations
Montmorency, France) and PED (EV3/Covidien, (x = 2p/T, s(cid:2)1), l the length scale (pipe diameter, m)
Irvine, CA). Both devices have a cylindrical shape
and l the dynamic viscosity (Pa s)
composed of a rhomboid-shaped mesh that is woven
This effect is small at a Womersley number typical
from NITINOL(cid:2) wires of approximately 30 lm
of the small blood vessels supplying the brain (when
diameter. The mesh is woven from 48 strands of wire
a (cid:3) 1.0–2.0). Flow profiles for the ICA and similar
resulting in mesh pore diameters in the range of 110–
sized vessels have been validated with 3D Doppler
250 lm. The devices are available in a similar range
measurements and show little departure from a para-
of diameters (typically 2.5–5 mm) and lengths (10– bolic flow distribution.18,33 Hence, most studies in the
40 mm) resulting in a device porosity of around 70%
literature model the inlet of a vessel geometry as a
regardless of device size or manufacturer.
parabolic velocity profile consistent with steady, pres-
TheWEB/WEBIIdevice(SequentMedical,AlisoVie-
sure driven flow in a pipe (Poiseuille flow).
jo, CA) is the only other commercially available flow-
Typical mesh independent CFD solutions vary in
divertingdeviceapprovedforuseinEurope,butnotthe
size across the literature due to different percentage
US,todate.TheWEBresemblesacylindricalflowdiverter
levels of required fidelity to the true solution, to the
withbothopenendscrimpedclosedtocreateasmallmesh
increase in mesh fineness required to capture compli-
ballthatmaybeexpandedinsidetheaneurysmsac.The
cated patient-specific geometries when compared to
deviceisavailableindiametersbetween5and11 mmand
more idealized models, or due to different mesh
isconstructedfromabraidedmeshcomprising108or144
requirements and behavior by different solvers—the
wires,dependingonthedevicesize.Twolayersofmeshare
latter being of particular importance since it depends
employed,oneinsidetheother,resultinginflowresistance
directly on the nominal accuracy and numerical fea-
from a total of 216 or 288 wires. The largest mesh pore
tures of the solution algorithm employed. Idealized
diameters observed are in the range of 106–181 lm,
models often are reported utilising meshes of 50,000–
depending on device size.31 The device has a variable 500,000 elements,41 whereas geometries based on
porosityacrossthefaceintendedtofilltheaneurysmneck
patient-specific data sometimes necessitate 3,000,000–
due to the gathering of the woven mesh at the device’s 10,000,000 + elements for mesh independence.6,16,39
center.Consequently,thedevice’sporosityvariesfrom0%
Introducing a low-porosity stent with small mesh
atthedevicecenterto78%attheedges.20
openingsintosuchgeometriesalmostinvariablyresults
in finer grid requirements for the same level of mesh
Computational Modeling independence.Stuhneetal.41concludedthattoreduce
randomnoiseintheflowandtofullyresolveWSSnear
Animportantparameter inpatient-specificvascular
to stent struts, the diameter of a mesh element should
modeling is the Reynolds number (Eq. 1).
be less than 1/3 of the strut radius.
qul
Re¼ ; ð1Þ
l Aneurysm Treatment and Risk of Rupture
where Re is the Reynolds number, q the fluid density Many authors have linked a reduction in either
(kg m(cid:2)3),uthemeanvelocity(m s(cid:2)1),lthelengthscale aneurysm inflow (Q ) or a reduction in mean aneu-
in
(pipe diameter, m) and l the dynamic viscosity (Pa s) rysm sac velocity to stable thrombus formation.11,17,22
A DedicatedBifurcation AneurysmFlow 337
Another measurement linked to thrombus formation aneurysm and three examples of an ICA terminus
and frequently given in the literature is the turnover bifurcation aneurysm. The geometries are segmented
time before and after FD placement (turnover from MRA data in OsiriX (OsiriX v.4.1.1, Freeware)
time = aneurysm sac volume/inflow rate), which al- and converted to STL format before being imported
lows comparisons between aneurysms with different into Blender (Stichting Blender Foundation, Amster-
sac geometries.16 Finally, Sadasivan et al.37 modeled dam,TheNetherlands).Thegeometriesaretrimmedto
aneurysm inflow in the two distinct components of result in vessel lengths of around five vessel diameters
diffusion and convection. Under this regime, resident distal and proximal to the aneurysm location, as
times of the aneurysm inflow may be calculated with shown in Fig. 2.
dramatic increases in flow residence time associated The‘Sphere’deviceisaself-expandingflow-diverter
withthrombusformation.Suchamodelgivesa‘virtual that may be deployed by micro-catheter unsheathing.
contrast’ capability to CFD simulations, allowing The device is sized with a diameter between 4.50 and
direct comparison of results with patient angiograms. 6.50 mm depending on aneurysm neck size and is
Risk of aneurysm rupture is a complex phenome- constructed from a continuous NITINOL(cid:2) wire of
non, which remains poorly understood. Both elevated 102 lm (0.004¢¢) diameter. See Fig. 3 (left). The cap-
and reduced WSS have been linked to aneurysm for- like dense portion of the device is placed at the aneu-
mation and increased rupture risk.1,12,38 A study by rysm neck, which is in turn secured by the two device
Chen et al.7 suggested that a number of shear-stress- legsthatarepositionedintheparentvesselproximalto
based metrics (WSS, OSI, GON etc.) may have a the aneurysm neck. The cap-like portion of the device
substantial role in aneurysm enlargement or rupture, usedinthissimulation,whichblocksaneurysminflow,
but the biochemical basis of such hypotheses remains hasaporosityof54%.The‘Sphere’hasbeendesigned
almost entirely unknown. in several configurations with varying geometric
TheWSSdistributionseeninananeurysmispatient- designsandfacedensities.A‘Sphere’deviceisvirtually
specific but has been found to correlate with aneurysm sized to both the aneurysm neck and parent vessel
aspect ratio (height of aneurysm divided by aneurysm diameters before being virtually deployed. A typical
neckdiameter):studieshavelinkedanaspectratiogreater device placement is shown in Fig. 3 (right).
than1.6withanincreasedriskofrupture,attributedtoan The aneurysm geometries, with and without the
elevatedWSSinthedomeduetothejettingeffectofthe device deployed, are imported into CFD-VisCART
geometry.43Flowvelocityinsidetheaneurysm,andcon- (ESIGroup,Paris,France)tobemeshed.Themeshing
sequentlyWSSdistribution,isinverselycorrelatedtothe of each geometry is completed with a Projected Single
squareoftheaneurysmneckmaximumdiameter.38Thus, Domaincon-conformingmesh,anOmnitreeCartesian
prediction of aneurysm rupture by size, which is com- treetype,andthreenear-wallCartesianlayerstogivea
monlyheldtobethestrongestmetricofrupture(especially smooth and well-resolved boundary definition.
in the clinical setting), supports the high-WSS theory of Themeshesareimportedintothemultiphysicssuite
rupture. Regardless of competing high or low WSS-in- CFD-ACE + (ESI Group, Paris, France).
ducedaneurysmgrowthandrupturetheories,itiswidely
acceptedintheliteraturethataWSSmagnitudearound
2 Paistypicalofhealthyarterialwallsthatwillretaintheir
structure.26 Any large variation from a WSS of around
2 Pa can therefore be considered detrimental and may
leadtoanincreasedriskofaneurysmgrowthorrupture.
Pressure changes within an aneurysm and the sur-
rounding vasculature may also influence aneurysm
growthandrupturerisk.Cebraletal.6linkedanincrease
inaneurysmpressureandpressuregradientwithrupture,
following treatment with a flow-diverter in a study
comparingCFDsimulationsandinvivopatientdata.
METHODOLOGY
Governing Equations and Solution Procedure
FIGURE2. Summaryofthesixgeometriessimulated:three
Six anatomically accurate, bifurcation aneurysm
Basilar tip aneurysms (Upper: BA_01-03) and three ICA
geometriesareselected:three examples ofaBasilartip bifurcationaneurysms(Lower:ICA_01-03).
338 PEACHet al.
Althoughbloodisingeneralnon-Newtonian,ithas incompressible fluid with unsteady 3D Navier–Stokes
been shown that the non-Newtonian effects can be governing equations that are solved following the
assumed secondary in arteries with a diameter greater control (or finite) volume approach, with a Central
than0.5 mm.29Non-Newtonianeffects have alsobeen Differencing scheme for spatial differentiations and
shown to be small inside the aneurysm dome. A neg- interpolations, as well as a Crank–Nicholson second
ligible difference is seen in flow, pressure and WSS order scheme for time-marching. The SIMPLE-Con-
distributions between Newtonian and non-Newtonian sistent (SIMPLEC) pressure correction method28,46
models with non-Newtonian models suggesting more and an algebraic multigrid method for convergence
stable flow regimes where oscillations are damped by acceleration48 are used.
increased viscous forces.44 Thus, in this study the The periodic variation of the mean inlet velocity of
blood fluid is assumed incompressible and Newtonian each vessel is scaled to fit volumetric flow curves gen-
withadensityof1000 kg m(cid:2)3andadynamicviscosity erated from a 1D model of the arterial tree.34 Typical
of0.004 Pa s.Arigidarterialwallisassumed,asithas flow profiles for the ICA and BA parent vessels over
been shown to have little effect on the flow patterns the cardiac cycle are shown in Fig. 4 and have mean
seen when compared to simulations with elastic flow rates over the cardiac cycle of 230 and 120 mL/
compliant walls.10 Blood flow is modeled as an min respectively. Steady state tests are run with mean
FIGURE3. The‘Sphere’deviceinitsunconstrainedconfiguration(left)andthetypicaldeployedpositioninanICAbifurcation
aneurysm(right).
FIGURE4. TransientmeshindependencetestresultsforgeometriesICA_02andBA_02plottingpercentageinflowreductiondue
todevicedeploymentwithincreasingmeshfineness.Bothgeometriesshowgoodconvergenceofpercentageflowreductioninthe
twofinestmeshes.Theindependencecriterionof<1%variationinflowreductionbetweenconsecutivemeshesismetforthemean
inflowreductionandsalientpointsinthecardiaccycle(P1,P2etc.)forbothgeometriesatmesheswithacelldensitygreaterthan
~4000elements/mm3(indicatedingreen).
A DedicatedBifurcation AneurysmFlow 339
flow of 230 mL/min for the ICA geometries and over a single cardiac cycle. Three full cardiac cycles
120 mL/min for the BA geometries. Poiseuille flow is were simulated with results measured from the final
assumed and a parabolic, radially symmetric inflow cycle in order to remove transient effects. The study
profileprescribed.InletReynoldsnumbersintherange suggests mesh independence at meshes with a typical
of274–392areseenacrossthesteadystatesimulations minimum cell density larger than 4000 elements/mm3
of the six geometries. as shown in Fig. 4. Additionally, at this level, the
Transient studies are run with the same meshes but number of mesh elements in each geometry measure-
atime-varyinginflowbasedontheprofilesofFig. 4.A mentplaneexceedstherecommendationofJouetal.17
radially symmetric inlet velocity profile is prescribed to fully resolve flow features.
andscaledtoresultinthesamemeanflowofthesteady Similarmeshindependencetestswereperformedon
statestudywhenaveragedovertheentirecardiaccycle. all six aneurysm geometries, with and without the de-
This results in transient simulations with mean inlet vice deployed, but for steady-state simulation only.
Reynoldsnumbersof274–323 (rangeofinstantaneous The simulationswere runwith aninlet velocity typical
Re:189–403)fortheBAvesselsand306–392(rangeof ofthemeanvelocityseenacrossthecardiaccycleinthe
instantaneous Re: 169–980) for the ICA vessels. A ICA and BA respectively. The steady-state mesh
parabolic inlet velocity profile is used as the relatively independence test suggested a similar independent cell
small Womersley number of the inflow (1.68–2.72) density (4000 elements/mm3) in five of the geometries.
suggests little departure in velocity profile from a No convergent solution was found in the steady state
Poiseuille solution. for the ICA_01 geometry, possibly due to intrinsic
The option to include outflow boundary conditions strong unsteady flow patterns emerging due to flow
derived from either experimentally measured flows or instabilities, as reported by both Valen-Sendstad
pressures, values originating from 1D models, or sim- et al.45 and Baek et al.3 at high and low frequencies
ple fixed pressure values was available to the authors. respectively. This extensive mesh independence ana-
Given that the goal of this study was to compare lysis resulted in mesh size selections that vary between
conditions between untreated and treated vessels, and 3.41 and 6.52 million elements across the geometries
that access to measurements for the particular aneu- for both transient and steady state tests and for cases
rysms studied was not available, the simplest possible with and without the device implanted.
outlet boundary condition was chosen to avoid spuri- Theindependenceofthetransientflowsolutionwith
ous assumptions of downstream flow conditions after time-stepsizewasalsoinvestigated.Simulationsrunat
device deployment. Hence, in both the steady and a time-step(Dt) of 0.05, 0.01 and 0.005 s respectively
transientcomputationsanoutflowboundarycondition indicated that Dt = 0.01 s offered both good conver-
of fixed pressure is prescribed at all daughter vessel gence of solution, unlike Dt = 0.05 s, and no signifi-
outlets.Althoughsuchaconditionmaybelessrealistic cant change in flow pattern when compared to
than pulsatile 1D analogue models and not fully cap- Dt = 0.005 s. Such a choice of time-step is consistent
ture the different back-pressures of the circulatory with similar CFD studies.17,23,45
branches, the relative proportions of outflow in each Aneurysm inflow is measured through a plane
daughter vessel observed in this study do not differ defined at the aneurysm neck. The plane must be
substantially frominvivoresultsrecorded elsewhere in placed as close to the natural neck of the aneurysm
the literature.14,35 without falling too close to the device, which can lead
tospurious results from localvorticity, asobserved by
Kimetal.19Forthepurposeofouranalysis,thisplane
Mesh Independence
alsodefinestheboundarybetweentheaneurysmdome
Transient flow mesh independence tests are per- and parent vessel.
formedononeaneurysmgeometryfromeachlocation,
with and without a device deployed (in this case
geometries BA_02 and ICA_02). The grid indepen-
RESULTS
dencetestmetricemployedisthemeanvolumetricflow
at the aneurysm neck. Meshes are generated at Transient simulations are run with a time-step of
increasing levels of fineness with minimum cell densi- 0.01 s for three cardiac cycles at 75 BPM, totaling
tiesintherangeof1–50,000elements/mm3.Thesolution 2.40 s.The simulationsare runon up to 32,2.93 GHz
is assumed mesh independent when the discrepancy cores with each time-step converging to five orders of
between twoconsecutive meshes falls below 1%ofthe magnitude residual reduction in around 50–100 itera-
total inflow. Aneurysm inflow is measured at salient tionsinatypicalsolutiontimeof40 minpertimestep.
pointsinthecardiaccycle(peaksystole,dicroticnotch Steadysimulationsarerunonupto8,2.93 GHzcores
etc.) as well as computing a mean aneurysm inflow with a typical solution time around 20 hours to the
340 PEACHet al.
same residual. No convergent steady-state solution at
meanparentvesselflowratewasfoundfortheICA_01
geometry. An entry plane meeting the criteria previ-
ously set out is projected across each aneurysm neck,
and the aneurysm inflow at each time step of the
transient solution and for the steady state solution is
calculated. For both the steady state and transient
solutions, the aneurysm inflow before and after device
placement are compared to give a percentage flow
reduction for a given time step.
Thesteadystatemeaninflowwithadevice,without
a device, and the subsequent flow reduction for each
geometry, excluding ICA_01, are plotted in Fig. 5 in
red. The mean (over one cardiac cycle) inflow with a
device, without a device and the subsequent flow
reduction of a transient simulation is found by taking
the mean of the flow reduction from each time-step
and isplotted inFig. 5inblue foreachgeometry. The
range of inflow and flow reduction seen over the car-
diaccycleforeachgeometryisalsoindicatedinFig. 5,
but in black.
ThemeanflowenteringtheaneurysmsacintheBA
geometries is similar to the mean flow in the parent
vessel(120 mL/min),suggestingalmostalloftheblood
flowing in the parent vessel enters the aneurysm. The
pattern in the ICA geometries is quite different. Al-
though the mean flow in the ICA geometry parent
vesselsisalmosttwicethatoftheBAcases,at230 mL/
min, the mean flow entering the aneurysm sac in the
ICA geometries is equal or substantially less than for
the BA cases. The ICA_03 geometry shows a mean
aneurysm inflow of approximately half the parent
vessel mean flow while the flow entering the aneurysm
sacintheICA_01and ICA_02 cases isonly 5–20%of
the parent vessel flow.
Asimilarpatternisobservedafterdeviceplacement,
as shown in the center graph of Fig. 5. Again the
aneurysm inflow in the BA geometries exceeds that of
the ICA geometries despite the substantially higher
parent vessel flow in the ICA cases. Both ICA_01 and
ICA_02 also experience a very low level of aneurysm
inflow after device placement, which, in the ICA_02
case, corresponds to a mean inflow of less than 5% of FIGURE5. Aneurysminflowwithoutdevice(top);aneurysm
the parent vessel flow. inflowwithdevice(centre);percentagereductionofaneurysm
inflow due to device deployment (bottom) for all six geome-
As previously discussed, no convergent solution for
triesmodeledforbothsteadystateandtransientbloodflow.
the ICA_01 geometry was reached for a steady state Resultsofsteadystatesimulationsforflowreductionatmean
simulationofmeanparentvesselflow.Thesteadystate parentvesselflowareshowninred.Themeanandrangeof
flow reduction over the cardiac cycle observed in transient
simulations of the five other geometries give similar
simulationsareshowninblueandblackrespectively.
results to the mean result of the corresponding tran-
sient simulations with the exception of the BA_01 ‘‘no
device’’andBA_03‘‘withdevice’’cases.Boththemean
and maximum aneurysm inflow with no device pre- Anexplanationforthisphenomenonisdiscussedinthe
dictedbythetransientsimulationofBA_01areofnote following section and elucidated in Fig. 8.
in that they appear non-physical, exceeding the corre- Figure 6 shows typical lines tangent to the instan-
spondingmeanandmaximumparentvesselflowrates. taneous velocity vectors at a point of mean parent
A DedicatedBifurcation AneurysmFlow 341
dissipating into a vortex. In all three geometries the
device reduces the aneurysm inflow velocity at this
meanparentvesselflowconditiontotypicallylessthan
0.25 ms(cid:2)1.
Figure 7 shows typical lines tangent to the instan-
taneous velocity vectors for the ICA geometries with
and without a device deployed. The mean flow reduc-
tionforeachgeometryisalsoindicatedinbothfigures.
TheflowpatternswithintheaneurysmsacfortheICA
cases are also dominated by a single vortex with a
small amount of, possibly, chaotic mixing.40 The flow
patternsappearlesscomplexthanfortheBAcasesbut
a large variation (almost 40%) in inflow reduction
after device deployment is still seen. Flow velocities in
the aneurysm sac are greatly reduced after placement
of the device but the flow pattern of a single vortex
appears unchanged, although this is less clear in the
ICA_01 and ICA_02 cases with very low aneurysm
inflow after device deployment. The post-device
reduction in flow velocity entering the aneurysm sac
at mean parent vessel flow is greater than in for the
BA cases, with inflow reduced to approximately
0–0.15 ms(cid:2)1.
Further detail of the flow regime in the aneurysm
sac of the BA_01 geometry for both steady and tran-
sient computations is shown in Fig. 8, which is dis-
cussed at length in the following section. Broadly, a
zoneofflowrecirculationattheaneurysmneckresults
in aneurysm inflows that exceed the instantaneous
parent vessel flow rate.
Finally, distributions of WSS magnitude are shown
FIGURE6. Linestangenttotheinstantaneousvelocityvec- inFig. 9.WSSmagnitudeisviewedfromthefrontand
torsacrossallthreeBAaneurysmgeometrieswithandwith-
back of each geometry and both with and without the
out a ‘Sphere’ device deployed. The streamlines shown are
taken from a time step in the transient solution with mean device deployed. WSS plots are shown for maximum
parent vessel flow. The percentage reduction in aneurysm inflow at peak systole, and although the magnitude of
inflow after device deployment is also indicated for each
the WSS varies, the WSS distribution remains
geometry.
approximately the same across the cardiac cycle.
Across all geometries the ‘Sphere’ device reduces the
vessel flow in each transient simulation for the BA overall WSS magnitude within the aneurysm dome.
geometries with and without a device deployed. In all Peaks in WSS magnitude correspond to areas of flow
three geometries, flow in the aneurysm sac before and impingement or jets with high velocity fields near the
after device placement is dominated by a single vortex wall (see Figs. 6, 7) and the reduction in flow jetting
with a small degree of, possibly, chaotic mixing.40 A after device deployment is also apparent in the WSS
reduction in this mixing and both the mean and peak distributions and is especially pronounced across the
flow velocity in the aneurysm sac are seen after device Basilar geometries and in ICA_03.
deployment. The BA_02 geometry experiences the
greatestreductioninaneurysminflowandalsoappears
toretain the simplest flow regime (a single vortex with DISCUSSION
little jetting) both before and after device deployment.
ThejettingseenintheBA_01andBA_03caseswithno Fromtheaneurysminflowwith‘nodevice’shownin
device is substantially reduced after ‘Sphere’ deploy- thefirstgraphofFig. 5,itisclearthattheBAandICA
mentbuttheflowreductionseenissome20%lessthan geometries behave very differently with a much higher
for the BA_02 case. A more complex flow pattern aneurysminflowrateintheBAcasesdespitethelower
remains after device deployment in these two cases parent vessel flow rate of the basilar artery. This phe-
with flow violently striking the aneurysm wall before nomenon may be due to the anatomical differences in
342 PEACHet al.
FIGURE7. Lines tangent to the instantaneous velocity vectors across all three ICA aneurysm geometries with and without a
‘Sphere’devicedeployed.Thestreamlinesshownaretakenfromatime-stepinthetransientsolutionwithmeanparentvesselflow.
Thepercentagereductioninaneurysminflowafterdevicedeploymentisalsoindicatedforeachgeometry.
the BA and ICA termination bifurcations; in the BA seen at the peak systole and the dicrotic notch
cases each aneurysm isrelatively wide-necked, with an respectively. Consistently across the geometries the
aneurysm neck diameter larger than the parent vessel greatest reduction in inflow is observed at the point of
diameter,whereastheICAcasesarerelativelynarrow- lowest parent vessel flow (dicrotic notch) and the least
necked and typically have an aneurysm neck smaller reduction in inflow is observed at the highest parent
than the parent vessel. Consequently, the resistance to vessel flow (peak systole). In the BA_01 and BA_03
flow entering the aneurysm in the BA cases is much geometries there is a discrepancy between the mean of
lower than in the ICA cases, which may explain the the transient prediction of flow reduction (blue) and
reduced flow entering the aneurysms in the ICA the steady state flow reduction prediction (red) but
geometries despite a much higher parent vessel flow otherwise the steady state predictions of mean flow
rate than the BA geometries. This hypothesis is also reduction are very accurate for the remaining three
supportedbythehigherpeakandmeanvelocityofthe geometries for which steady state solutions exist.
flowintheaneurysmsacoftheBAgeometries,despite InboththeBA_01‘withoutdevice’andBA_03‘with
similar parent vessel velocities between the two vessel device’ cases, the steady simulation appears to have
types. underestimated the aneurysm inflow. An explanation
FromthetransientresultsshowninFig. 5(bottom), for this discrepancy is suggested in Fig. 8. The tran-
itcanbeseenthatthe‘Sphere’deviceproducesalarge sient simulation of BA_01 reveals recirculation
variation of flow reduction across the six geometries, behavior in the right-hand portion of the aneurysm
with a range of 30.6–71.8% in mean reduction and dome with flow both exiting and re-entering
flowreductionsaslow as19.1% andashigh as87.5% the aneurysm neck. This can be clearly seen when
A DedicatedBifurcation AneurysmFlow 343
appearstobereducingthemomentumoftheaneurysm
inflowsufficientlytopromoteaflowpatternwherethe
vortexisweakerandisrotatingaboutanaxiscloserto
that inthesteady state prediction asseen Figs. 8b, 8d,
8f, 8h. This also explains the seemingly non-physical
result shown intheBA_01 ‘withoutdevice’casewhere
a mean aneurysm inflow of 137 mL/min is calculated
despiteameanparentvesselflowofonly120 mL/min.
The additional 17 mL/min results from the recircula-
tionofflowexitingandre-enteringtheaneurysmneck.
The same effect is present in the BA_03‘with device’
geometry but to a lesser extent.
Considering Figs. 6 and 7, it appears the action of
the ‘Sphere’ is to reduce the velocity and intensity of
theflowenteringtheaneurysmsacwithlittlechangein
the general flow pattern within the aneurysm, with the
exception of BA_01 as previously discussed. In all
geometries with no device deployed, the flow in the
aneurysm sac appears to be dominated by a single
vortex accompanied by a small degree of chaotic
mixing, where the inflow jet first strikes the aneurysm
wall, as also observed by Butty et al.4 Such mixing
appears less prevalent in the BA_02 and ICA_02
geometries,whichbothsawflowreductioninexcessof
50% after device deployment. The ICA_01 geometry,
however, which also saw a substantial flow reduction,
has a flow pattern dominated by mixing that was
subsequently reduced to a very slow moving single
vortex after device deployment.
As previously discussed, the precise mechanisms of
FIGURE8. Comparison of steady state (a, b) and transient high or low WSS-induced aneurysm growth and rup-
(c–h) simulations at the same instantaneous parent vessel
ture are still hotly debated; in this case, the ‘Sphere’
flow rate of 120mL/min for the BA_01 geometry with and
without the ‘Sphere’ device deployed. A radically different device appears to promote a healthier hemodynamic
flowpatternisvisibleinthetransient‘nodevice’casesatall environment within the aneurysm sac by reducing the
points of the cardiac cycle (c, e, g) when compared to the
peaks of the WSS distribution to a more physiologi-
steadyprediction(a).
cally normal value (~2 Pa) as shown in Fig. 9. The
larger ICA flow rate results in increased blood flow
comparing the steady and transient ‘without device’ velocity and hence higher WSS in the ICA cases. This
simulationsinFig. 8:thesteadysimulation(a)suggests is particularly noticeable in the ICA_01 geometry,
a flow pattern with a large low-velocity vortex, in the which has a below-average vessel diameter (<3 mm)
right-hand portion of the aneurysm dome, with the resultingisverylargevelocities(Fig. 7)andhencehigh
axis of rotation coincident with the centerline of the WSS magnitude throughout the geometry. This effect
parentvessel,whereasthetransientsimulation(c,e,g) islikelytobelessenedphysiologicallywithmoreelastic
indicatesasimilarsizedlow-velocityvortexinthesame deformationofthelargerICAvessels,inturnreducing
approximate location but rotating about a perpendic- the WSS magnitude.
ular axis. The vortex seen in the transient case As previously discussed, the geometries that expe-
encourages substantial flow recirculation in the aneu- rience the greatest flow reduction after device deploy-
rysmwithflowbrieflyexitingontheright-handsideof ment appear to have less flow impingement/jetting in
the aneurysm, before being drawn back into the the aneurysm sac prior to device placement. This is
aneurysm close to the centre of the aneurysm neck. reinforcedbytheWSSdistributionsofboththeBA_02
This recirculation appears to be the source of the and ICA_02 geometries where no high WSS (>5 Pa)
discrepancy between the steady and transient BA_01 regions caused by flow jets occur in the aneurysm
resultsseeninthe‘withoutdevice’graphofFig. 4.The dome. Conversely, the three geometries that perform
discrepancy does not appear as dramatic for the same less favorably in terms of device flow reduction
geometry with the ‘Sphere’ deployed, as the device (BA_01, BA_03 and ICA_3) also have high WSS