flow patterns at the stenosed carotid

Annals of Biomedical Engineering,Vol. 28, pp. 415–423, 2000 0090-6964/2000/28~4!/415/9/$15.00Printed in the USA. All rights reserved. Copyright © 2000 Biomedical Engineering Society

Flow Patterns at the Stenosed Carotid Bifurcation: Effectof Concentric versus Eccentric Stenosis

DAVID A. STEINMAN,1,2 TAMIE L. POEPPING,1,2 MAURO TAMBASCO,1,2 RICHARD N. RANKIN ,1,3,4

and DAVID W. HOLDSWORTH1,2,3

1Imaging Research Labs, The John P. Robarts Research Institute Departments of2Medical Biophysics and3Diagnostic Radiology &Nuclear Medicine, University of Western Ontario, and4Division of Radiology, London Health Sciences Center London,

Canada

(Received 28 June 1999; accepted 8 February 2000)

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Abstract—Carotid stenosis severity is a commonly used incator for assessing risk of stroke. However, the majorityindividuals with severe carotid artery disease never suffestroke, and strokes can occur even with only mild or moderstenosis. This suggests local factors~other than stenosis seveity! at or near the carotid artery bifurcation may be importandetermining stroke risk. In this paper we investigate the effof stenosis geometry on flow patterns in the stenosed carbifurcation, using concentrically and eccentrically stenosedthropomorphic carotid bifurcation models having identicstenosis severity. Computational simulations and experimeflow visualizations both demonstrate marked differencesflow patterns of concentric and eccentric stenosis modelsmoderately and severely stenosed cases, respectively. Inticular, we identify post-stenotic recirculation zone size alocation, and spatial extent of elevated wall shear stress asfactors differing between the two geometries. As these arekey biophysical factors promoting thrombogenesis, we propthat the stenosed carotid bifurcation geometry—or the induflow patterns themselves—may provide more specific inditors for those plaques that are vulnerable to enhanced thrboembolic potential, and hence, increased risk of ischestroke. © 2000 Biomedical Engineering Society.@S0090-6964~00!00504-X#

Keywords—Stroke, Blood flow velocity, Model studiesThrombogenesis, Wall shear stress, Thromboemboli.

INTRODUCTION

Recent clinical trials have shown that the riskstroke increases with carotid lesion severity, resultinga considerable effort to develop techniques to characize carotid stenoses. The North American~NASCET!and European~ECST! carotid surgery trials have showa surgical benefit for symptomatic stenosis greater t70%.4,6,20,21 However, carotid plaque is a common ocurrence, so the presence of carotid lesions alone is n

Address correspondence to David A. Steinman, PhD, Imagingsearch Labs, John P. Robarts Research Institute, 100 Perth Dr.,Box 5015, London, Ontario N6A 5K8, Canada. Electronic [email protected]

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good indicator of subsequent stroke risk. Although ab60% of individuals aged 65–74 exhibit carotatherosclerosis,7 the absolute risk of stroke in the asymtomatic population is low~2.1% over three years5!.Among symptomatic individuals, the risk of major ofatal stroke ipsilateral to a severe carotid stenosis is 1over two years.20 Although this risk is significant, it alsoindicates that the majority of individuals with carotidisease do not suffer stroke, and that grading of stenseverity with respect to linear reduction of lumen diameter is only a surrogate measure of stroke risk with retively poor specificity. Clearly, other mechanisms mube at work to make a subgroup of individuals with crotid plaque more vulnerable to cerebral embolus pduction.

For many years the most commonly proposed mecnism for cerebrovascular accident was a reductionlarge-artery flow due to the pressure drop across a ccal stenosis, the so-called ‘‘hemodynamic’’ stroke.2 Thistheory led naturally to diagnostic indicators based onsize of the patent carotid lumen, such as x-ray anggraphic measurements.9 However, our understanding ostroke has evolved in the last two decades, and curtheories stress plaque morphology~composition andform! and local hemodynamics as factors that contribto artery-to-artery embolization. Hemodynamic factoare important, contributing to both thrombus formatioand the rupture of unstable plaque in diseased indivials. Shear rate is particularly important, as high sheapartially occluded arteries is known to initiate platelactivation and platelet–platelet binding events that plakey role in thrombosis.12 Although blood flowingthrough arterial stenoses is subject to high shear for stimes, in vitro experiments indicate that exposure to hishear for as little as 7 ms can activate procoagulphospholipids.29 High-speed flow through the stenosalso leads to high-shear regions on the fibrous cap, w

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the resulting mechanical stress contributing to plaqrupture and dislodged material.11

Several aspects of lumen geometry may vary witindividual plaques, even for lesions with the same stesis severity. Lesions at the carotid bifurcation can ocwith equal deposition of plaque on both the inner aouter walls~concentric or axisymmetric plaque! or withplaque preferentially deposited on the outer wall~eccen-tric or asymmetric plaque!. Although there is a greatetendency for eccentric plaque development, both cfigurations are possible. Plaque eccentricity can havsignificant effect on the distal velocity field, independeof the degree of stenosis.In vitro studies usingpulsatile17 and steady30 flow indicate that plaque eccentricity increases turbulent intensity, producing highpressure drops than with concentric plaque. Since ioften difficult to estimate plaque eccentricityin vivo, it isnot clear whether the hemodynamic effects of eccenplaque result in greater stroke risk; however, in ostudy of coronary artery disease it was found that ecctric stenoses were more likely than concentric stenoseprogress to myocardial infarction.26

Although the carotid bifurcation has been the focusmany hemodynamic studies, surprisingly little is knowabout the hemodynamic patterns of moderately andverely stenosed bifurcations. Several carotid bifurcatmodels have also been studied in the past, althoughhave usually been constructed with no disease14–16,31 orvery mild disease,10,22,28 in order to study the initiationand progression of carotid plaque. A recently developgeometric model defines an idealized shape forstenosed carotid bifurcation,23 leading to the possibilityof controlled in vitro and numerical investigations ohemodynamic factors in varying geometries. In this stuwe investigate the effect of lesion geometry~concentricversus eccentric! on post-stenotic recirculating flow anwall shear stress, using both computational fluid dynaics ~CFD! and digital particle image~DPI! flow visual-ization. Both moderately and severely stenosed carbifurcations are studied, with DPI providing data—in thcase of turbulent flow—that is unavailable with CFD.

METHODS

Pulsatile flow in 30% concentrically and eccentricastenosed carotid bifurcation models was computed uspreviously validated, in-house CFD software. The goerning Navier–Stokes and continuity equations were dcretized via the finite element method, using isoparamric ten-node~quadratic! Taylor–Hood tetrahedral finiteelements. The convective terms were decoupled fromunsteady Stokes equations using a first order operaintegration-factor time-splitting approach.18 The convec-tive terms were solved using fourth order Runge–Kuintegration, while the generalized Stokes equations w

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solved using a preconditioned conjugate gradient Uzamethod.1 Further details of the solver are provideelsewhere.3 ~CFD studies were not carried out in th70% models, owing to the anticipated presence of turlence.! The three-dimensional geometries were costructed using computer-aided design software~DDN;ICEM CFD Engineering, Berkeley, CA!, based upon thegeometric descriptions of anthropomorphic stenosedrotid bifurcation models provided by Smithet al.23 Avolume-filling tetrahedral finite element mesh was geerated for each model using an automated mesh gentor ~TETRA; ICEM CFD Engineering!. Owing to theinherent symmetry of the geometry, only one halfeach model was constructed, and filled with appromately 30,000 second-order isoparametric finite ements, corresponding to approximately 60,000 nodThe finite element mesh for the 30% eccentric stenomodel is shown in Fig. 1~a!.

For pulsatile flow studies, a representative normalrotid bifurcation wave form was imposed at the commcarotid artery~CCA! inlet of the models, with mean anpeak flow rates of 6 and 23.6 ml/s.13 Combined with anassumed blood viscosity of 3.5 cStokes and CCA diaeter of 8 mm, these resulted in mean and peak Reynnumbers of 275 and 1073, and a Womersley numbe5.6 ~assuming a heart rate of 65 beats-per-minute!. Fullydeveloped Womersley velocity profiles computed frothe first 13 Fourier coefficients of this flow rate wavform were imposed at the model~CCA! inlet. To pro-duce a representative constant flow split of 56:44tween the internal~ICA! and external~ECA! carotid ar-tery branches, fully developed velocity profiles were a

FIGURE 1. „a… Finite element mesh of the 30% eccentricstenosis geometry used for the CFD studies. The orientationaxis at the top left identifies the direction of positive „z…flow. „b… Acrylic flow-through model of the 70% concentricstenosis model used for the DPI studies. CCA Äcommon ca-rotid artery; ICA Äinternal carotid artery; ECA Äexternal ca-rotid artery. Also used in this study but not shown are the30% symmetric stenosis finite element mesh and the 70%eccentric flow-through model.

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417Flow Patterns at the Stenosed Carotid Bifurcation

applied at the ECA outlet, while traction-free boundaconditions were applied at the ICA outlet. For the vadation study comparing CFD and DPI visualizations, vlocity boundary conditions were imposed based onFourier coefficients of the CCA and ICA flow rate wavforms measured directly from the DPI experimenstudy as described later.

All blood flow simulations were carried out on a Indigo 2 workstation~Silicon Graphics Inc., Mountainview, CA!. The carotid flow wave form was discretizein 480 uniformly spaced time steps, and the solution wcarried out for two cardiac cycles to damp initial trasients owing to the zero-velocity initial conditions. Thfinite element mesh densities and time-step size usethe current study were deemed sufficient based onprevious experience with pulsatile flow studies in tcorresponding normal carotid bifurcation model.19 Thepulsatile simulations were considered converged wthe maximum absolute difference between velocity vtors at corresponding time steps from the current aprevious cycles was less than 1025. Each pulsatile flowsimulation required approximately 40 CPU h. Velocidata was post-processed and visualized using bothhouse and Tecplot~Amtec Engineering, Bellevue, WA!software.

DPI Flow Visualization

DPI studies were carried out in 70% concentricaand eccentrically stenosed carotid bifurcation modelswell as a 30% concentrically stenosed model for coparison with the CFD studies. The DPI system consisof two 5 mW He–Ne lasers~Melles Griot, Carlsbad,CA! lasers producing 1-mm-thick fanbeams, which illminated the center plane of the vessel model uniformfrom opposite sides. A charge coupled device cam~Panasonic, Seacaucus, NJ! was used to record the flowof small ~;400 mm diameter! reflective particles seedeinto a 2:1 volume mixture of water-glycerol flui~viscosity53.2 cStokes!. ECG-gated 6403480 digitalimages of the central plane of the vessel model wcaptured with 16 ms temporal resolution onto an Inworkstation~Silicon Graphics Inc., Mountainview, CA!.

Life-sized ~8 mm CCA diameter! anthropomorphicflow-through models were designed and constructedour laboratory using a transparent polyester resin. Tgeometries were fabricated using the geometric desctions provided by Smithet al.,23 and details of the modeconstruction are provided elsewhere.24 A photograph ofthe 70% concentric stenosis model is shown in Fig. 1~b!.

A computer-controlled pump~R. G. Shelley, Ltd.,North York, ON! was programed with the same realisflow-rate wave form described earlier for the CFD stuies. Downstream flow resistors were used to achieveICA:ECA flow division independent of the stenosis s

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verity of the particular model being used. Owing to thcompliant tubing connecting the flow-through modelthe pump, the flow wave form at the model inlet wslightly different than the programed wave form prduced at the pump outlet. To facilitate the comparisonDPI and CFD results for the 30% concentric stenocase, the wave forms at the model CCA inlet and ICoutlet were measured directly using an electromagnflow meter~Carolina Medical Electronics, King, NC!. ATTL logic signal provided by the computer-controllepump allowed for the ECG-gated acquisition of both tDPI images and the flow meter recordings.

RESULTS

30% Concentric Stenosis: CFD vs DPI

As Fig. 2 demonstrates, CFD and DPI studies of30% concentric stenosis model reveal similar centplane flow patterns. Specifically, at peak systole, bshow: ~1! a high-speed jet impacting the outer wallthe ICA; ~2! a large recirculation zone along the innwall of the ICA; ~3! a smaller recirculation zone on thouter wall of the ICA; and~4! the re-establishment oaxial flow along the inner wall of the ICA. Excellenagreement is seen in both the size and location of thkey flow features.

FIGURE 2. „a… DPI image of peak systolic flow in the 30%concentric stenosis model. „b… Simulated DPI image basedon the CFD modeling of the same geometry and flow condi-tions. To simulate the appearance of the DPI image, particleswere seeded randomly at the inlet of the CFD model, andadvected through the computed pulsatile velocity field.Streak length and spacing were determined from the shutterspeed and frame rate of the DPI acquisition. Labeled arrowsidentify key flow features in the ICA: „1… stenotic jet; „2… innerwall recirculation zone; „3… outer wall recirculation zone; and„4… re-establishment of axial flow along the inner wall.

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FIGURE 3. Still frames from streakline animations of the CFD-computed flow field in both 30% stenosis models at selectedphases of the cardiac cycle. Streak length and color intensity are proportional to z velocity: red streaks identify forward flow,blue streaks identify regions of reverse flow, and white streaks correspond to slow flow. Streak length and spacing werecalculated assuming a 60 Hz frame rate and 1 Õ60 s shutter speed, as described elsewhere. 25 As each image represents aprojection through the model with the center plane furthest from the eye, streaks closest to the walls are superimposed onstreaks closer to center plane flow. Note the labeled arrows in panel „a…, identifying the same key flow features as in Fig. 2.Panel b identifies the location of the zÄ1, 2, and 3 cross sections plotted in Fig. 4.

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30% Concentric and Eccentric Stenosis: CFD Studie

CFD studies of the 30% concentric and eccenstenosis models show a dynamic and highly comphemodynamic environment in both models. As illustratin Fig. 3, the post-stenotic region of both modelsdominated by a high-speed jet surrounded by coun

rotating recirculation zones. In both models these reculation zones are mobile and dynamic, appearing npeak systole, persisting throughout early diastole, aappearing again in late diastole during periods of flodeceleration. As seen in Fig. 2, a large recirculation zoextends approximately three CCA diameters alonginner wall of the ICA, while a smaller, counter-rotatin


FIGURE 4. CFD-computed flow patterns in the ICA of both 30% concentric and eccentric stenosis models at selected phases ofthe cardiac cycle. Each panel shows contours of the z-velocity magnitude and corresponding in-plane „x – y … velocity vectors atslices approximately 1, 2, and 3 CCA diameters downstream of the bifurcation apex. Thick solid contour lines separate regionsof forward and reverse z velocity. Note the contour lines and reference velocity vector in panel „a….

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recirculation zone is present on the opposite wall. Foreccentric model, however, both the size and locationthese regions are markedly different: the recirculatzone on the outer wall now fills much of the posstenotic region, while recirculation on the inner walldisplaced downstream compared to its concentric mocounterpart.

A more detailed view of the post-stenotic fluid dnamic in the ICA is provided in Fig. 4. For the concetric model, retrograde flow is present around the encircumference atz51 beginning during systole@panels~a!–~b!#. During flow deceleration@panels~c!–~d!#, thisretrograde flow regime divides, producing the distininner and outer wall recirculation zones observed.peak systole~panel b!, retrograde flow also appearsz52 along the inner wall as a characteristic mushroo

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shaped, Dean-type vortex, which persists distathroughout much of the early diastolic deceleration phof the cardiac cycle@panels~c!–~d!#. Further inspectionof the in-plane velocity vectors reveals that fluid is tranported from the outer to the inner recirculation zonesthe secondary flow. This can also be inferred from tpresence of slow flow~as manifested by short, whitstreaks! superimposed on the high-speed~bright red! jetin Figs. 3~a! and 3~b!.

For the eccentric model, the fluid dynamics of thpost-stenotic region are markedly different than thosethe concentric model. During acceleration~panel a!, alarge region of retrograde flow is present only semiccumferentially on the outer wall of the ICA. The seconary velocities in panel~c! also reveal the presence otwo, counter-rotating vortices, compared to the sin

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FIGURE 5. Maps of CFD-computed peaksystolic „a–b… and time-averaged „c–d …wall shear stress magnitudes in the 30%concentric and eccentric stenosis mod-els. Note the different contour levels usedfor peak systolic and time-averaged shearmaps.

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vortex in the concentric case. The high-speed flow ofstenotic jet is also observed to remain midway betwethe inner and outer walls, and is separated by thereverse flow regions, for a distance of two CCA diameters. In contrast, for the concentric stenosis model,high-speed jet is largely confined to the outer wall.

As Fig. 5 shows, both concentric and eccentric 30stenosis models are subject to elevated wall shear s~.200 dyn cm22 at peak systole! at the throat of thestenosis, as expected. Both models also demonstraregion of elevated wall shear stress~.100 dyn cm22 atpeak systole! along the outer wall of the ICA just downstream of the post-stenotic dilatation, owing to the ipact of the stenotic jet. Regions of low wall shear strecorrespond to the observed locations of the recirculazones. Compared to the concentric model, however,eccentric model exhibits an extended region of elevawall shear stresses along the inner wall of the ICA fodistance of approximately two CCA diameters dowstream of the stenosis throat.

Surface elevation maps of the central-plane wall shstresses along the inner and outer walls of the Ishown in Fig. 6 further highlight the differences betwethe two models. Along the outer wall of the ICA, theccentric model experiences a more elevated butspatially extensive region of peak wall shear stress atstenosis throat than the concentric stenosis model. Cversely, a much larger region of elevated wall shestress is seen approximately two diameters downstrof the stenosis in the concentric model. Along the innwall of the ICA the differences are even more dramaSpecifically, the concentric model experiences relativhigh peak wall shear stresses localized largely tothroat of the stenosis, while the eccentric model shomore modest peak wall shear stresses extending netwo diameters along the inner wall. Distal to thesegions, the wall shear stresses are largely similar.

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70% Concentric and Eccentric Stenosis Models:DPI studies

DPI studies in corresponding 70% concentric andcentric stenosis models are shown in Fig. 7. As seen wthe 30% stenosis models, flow patterns are markedifferent between the two geometries. For the concencase, the recirculation zone on the outer wall is notiably larger than for the corresponding 30% concenstenosis model, and the axial extent of the inner wrecirculation zone is obviously increased. For the ecctric case, however, the post-stenotic region appears tofilled with a single recirculation zone, although the fielof-view prevented us from detecting what may have bea second recirculation zone further downstream inmodel.

DISCUSSION AND CONCLUSIONS

In this study we have characterized the hemodynamof moderately and severely stenosed carotid bifurcatioBoth concentric and eccentric stenosis models demstrate dynamic and complex flow patterns composedhelical Dean-type vortices, dual mobile recirculatiozones, and asymmetric distribution of wall shear stresin the post-stenotic region. By altering stenosis geomewhile maintaining stenosis severity, we have identifimarked differences in these hemodynamic factors. Sdifferences were observed for both moderate~30%! andsevere ~70%! stenoses. Comparison of correspondi30% and 70% stenosed models reveals the same geflow characteristics. The presence of a severe stenserves to increase the size and extent of the recirculazones, and introduces turbulence in the post-stenoticgion; this is in broad agreement with other studie8

From this we infer that the marked differences in flopatterns we have observed between the concentric


FIGURE 6. Surface elevation maps showing the spatial and temporal variations of center-plane wall shear stress along the outer„a…–„b… and inner „c…–„d… walls of the ICA. The elevation corresponds to the value of wall shear stress „WSS, in dyn cm À2

… alongthe local tangent direction. Contour levels are spaced in increments of 25 dyn cm À2 according to the legend in Fig. 5 „a…; the levelat 100 dyn cm À2 is explicitly labeled. The other axes represent the time, normalized to the period of the cardiac cycle, and thedistance along the wall, normalized to the diameter of the CCA „with 0 corresponding to the stenosis throat …. For the time axis,only the first half of the cardiac cycle is shown in the interest of clarity. For the distance axis, the range †À3,6‡ correspondsroughly to the left and right extent of the models shown in Fig. 5. Note that, along the inner wall, maps are only defined startingat the apex of the bifurcation, which is just upstream of the stenosis throat.

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As these hemodynamic factors are importantthrombogenesis, our results provide intriguing prelimnary evidence for the more direct role that stenosisometry and induced hemodynamics—rather than stenseverity alone—may provide more specific cluesidentifying patients at risk of thromboembolic evenAlthough it is intuitively obvious that the presence ofstenosis will invariably produce elevated shear rates,

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time-dependent nature of shear-activation suggeststhe post-stenotic shear environment may also be of ccal importance in determining whether activation occuIn our study, the eccentric stenosis model has a mmore extensive region of elevated shear, perhaps incring the likelihood of post-stenotic shear activation. Athough the observed differences in post-stenotic recirlation patterns do not necessarily imply that residentimes between the two models would be significandifferent, the presence of an extended region of hshear in the eccentric stenosis model does suggest

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platelet aggregation may be enhanced for this case.ther studies are also clearly needed to determine if shactivation and thrombogenesis can indeed occur unthese conditions.

As with any model study, we have made some siplifications. The stenosed carotid bifurcation models uhere, although based upon measurements from paangiograms, are admittedly idealized: the model is symetric about the plane of the bifurcation; the vesselscircular in cross section; and the internal branchstraight. ~Recent work by Milneret al.19 have, for ex-ample, demonstrated that curvature at the carotid bication can have a dramatic impact on the amountsecondary flow compared to an idealized model, whin turn would impact both wall shear stress and florecirculation patterns.! However, for the purposes of tesing the hypothesis that stenosis geometry plays anportant role in determining local flow patterns, the athropomorphic model we have used is ideally suited,it allows us to effectively fix confounding factors~suchas stenosis severity and other geometrical factors!. Wehave also assumed a constant ICA:ECA flow division56:44 which, although representative of the normal hman carotid bifurcation,27 is a simplification that ignoresthe fact that the flow division varies throughout the cdiac cycle.15 In a previous study, however, we observonly minor differences in normal carotid bifurcation flopatterns when using a constant versus subject-spetime-varying ICA:ECA flow division.19 We are thereforeconfident that our conclusions regarding the effect

FIGURE 7. DPI images of flow in the 70% „a… concentric and„b… eccentric stenosis models during early diastolic flow de-celeration. Refer to caption Fig. 2 for definition of numberedlabels.

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stenosis geometry on local hemodynamics would remvalid even in the presence of more physiological geoetry and/or flow boundary conditions.

We conclude by encouraging further studies to detmine how local factors—such as stenosis geometryinduced flow patterns—are related to thromboemboactivity, and whether as-yet undetermined geometrichemodynamic factors may provide more specific indictors of stroke risk due to thrombus formation. Althougretrospective studies of patient angiograms to compoutcome to stenosis geometry may be possible, itlikely that only prospective studies of carotid artery gometry and flow patterns will help identify more specifilocal factors that are important in identifying a vulneable plaque. If hemodynamic risk factors are ultimateidentified, it is not inconceivable that, with advancesthree-dimensional magnetic resonance and Doppler usound velocity imaging techniques, hemodynamicwell as morphological factors will be considered in adiagnoses of carotid stroke risk.

ACKNOWLEDGMENTS

The authors thank Jaques Milner for technical asstance. Financial support for this work was providedHeart & Stroke Foundation of Ontario Grant NoNA3632 ~D. W. H.! and Medical Research Council oCanada Group Grant No. GR-14973~D. A. S.!. D. A. S.and D. W. H. are supported by Research Scholarshfrom the Heart & Stroke Foundation of Canada.

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