effect inlet vel profiles

Effect of Inlet Velocity Profiles on Patient-SpecificComputational Fluid Dynamics Simulations of the CarotidBifurcation

Ian C. Campbell(1),*, Jared Ries(1), Saurabh S. Dhawan(2), Arshed A. Quyyumi(2), W. RobertTaylor(1),(2),(3), and John N. Oshinski(1),(4)

(1)Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology andEmory University, Atlanta, GA 30332(2)Division of Cardiology, Department of Medicine, Emory University, Atlanta, GA 30322(3)Cardiology Division, Atlanta VA Medical Center, Decatur, GA 30032(4)Radiology and Imaging Sciences, Emory University, Atlanta, GA 30322

AbstractBackground—Patient-specific computational fluid dynamics (CFD) is a powerful tool forresearching the role of blood flow in disease processes. Modern clinical imaging technology suchas MRI and CT can provide high resolution information about vessel geometry, but in manysituations, patient-specific inlet velocity information is not available. In these situations, asimplified velocity profile must be selected.

Method of approach—We studied how idealized inlet velocity profiles (blunt, parabolic, andWomersley flow) affect patient-specific CFD results when compared to simulations employing a“reference standard” of the patient’s own measured velocity profile in the carotid bifurcation. Toplace the magnitude of these effects in context, we also investigated the effect of geometry and theuse of subject-specific flow waveform on CFD results. We quantified these differences byexamining the pointwise percent error of mean wall shear stress (WSS) and oscillatory shear index(OSI) and by computing the intra-class correlation coefficient (ICC) between axial profiles ofmean WSS and OSI in the internal carotid artery bulb.

Results—The parabolic inlet velocity profile produced the most similar mean WSS and OSI tosimulations employing the real patient-specific inlet velocity profile. However, anatomic variationin vessel geometry and use of non-patient-specific flow waveform both affected WSS and OSIresults more than did choice of inlet velocity profile.

Conclusions—Although careful selection of boundary conditions is essential for all CFDanalysis, accurate patient-specific geometry reconstruction and measurement of vessel flow ratewaveform are more important than choice of velocity profile. A parabolic velocity profileprovided results most similar to the patient-specific velocity profile.

Keywordsbiomechanics

*[email protected].

NIH Public AccessAuthor ManuscriptJ Biomech Eng. Author manuscript; available in PMC 2013 May 01.

Published in final edited form as:J Biomech Eng. 2012 May ; 134(5): 051001. doi:10.1115/1.4006681.

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Introduction/BackgroundThe link between hemodynamics and atherosclerosis is a topic of interest to clinicians andresearchers and has been studied for decades [1, 2]. While a great variety of techniques havebeen employed to understand the pathophysiology of atherosclerosis, among the mostcommonly used tools is computational fluid dynamics (CFD) because of its ability to modelflow conditions in a variety of vascular geometries and in various flow environments. EarlyCFD studies relied on engineering simplifications such as idealized cylindrical geometry asboundary conditions, but advances in computational efficiency and in non-invasive imagingtechnology now allow researchers to study vascular flows in a patient-specific manner [3, 4].Wall shear stress (WSS) and oscillatory shear index (OSI) have emerged as hemodynamicmetrics associated with atherosclerosis localization, aneurysm formation, and other aspectsof vascular disease [4, 5]. As CFD of the vascular system matures, its utility not only as aresearch methodology but also as a clinical diagnostic tool becomes more apparent. As is thecase with all computer models, however, careful characterization of all assumptions thatcondense reality into a mathematical simulation is essential.

Previous studies have investigated the sensitivity of CFD models to assumptions such asrheological constituents, mesh composition, mesh size, the use of flow extensions, and awide range of inlet and outlet boundary conditions [6–13]. Only a small subset of allprevious studies, however, has performed such investigations in a patient-specific manner[13]. Additionally, none of these studies have investigated how direct assignment of inletvelocity profiles influences CFD-simulated hemodynamics in the carotid, and very few haveinvestigated the effect of inlet velocity profiles in other vessels [14, 15]. Although realisticsubject geometry may be derived from a variety of imaging technologies (MRI, CT, X-rayangiography, IVUS, OCT, and others), few of these techniques can provide temporally- andspatially-resolved data on the velocities of flowing blood. Thus, any 3D modeling based onimaging sources without corresponding velocity data must assign an idealized velocityprofile such as a blunt, parabolic, or Womersley flow pattern based on assumed flowconditions [16]. When no flow information whatsoever is available, such as in the case ofCT-derived geometry, researchers must assign a flow waveform acquired from anothersource, which often is derived from a different subject entirely.

In this study, we explored the effect of inlet flow assumptions on patient-specific CFDresults. In human volunteers, we collected each subject’s carotid bifurcation anatomy andpulsatile velocity profile using magnetic resonance angiography (MRA) and phase-contrastmagnetic resonance (PCMR) imaging techniques. This data set enables the firstquantification of how simplified inlet velocity profiles affect CFD-derived wall shear stress(WSS) results in human carotid simulations when compared to a “reference standard” ofusing the subject’s own velocity data. We also compared simulation results obtained fromusing each patient’s own velocity data to simulations based upon a single (non-patient-specific) velocity data set to discern the effect of using “generalized” velocity data. Finally,we compared simulations among subjects using the patient-specific velocity data to discerndifferences in WSS parameters resulting from natural anatomic variation in vessel geometryand flow. We hypothesized that: 1) simulations using simplified velocity profiles willproduce different values of mean WSS and OSI than simulations employing patient-specificvelocity profiles, 2) the differences in mean WSS and OSI between simulations using thepatient-specific and simplified velocity profiles will be less than the difference betweensimulations using the patient-specific velocity waveform and the generalized velocitywaveform, and 3) the differences in mean WSS and OSI values resulting from choice ofsimplified velocity waveform will be less than the differences among patients from naturalvariation in flow and vessel geometry.

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Materials and MethodsImage Acquisition

Magnetic resonance angiography (MRA) was performed on 10 healthy middle-agedvolunteers (mean age ± SD: 60.1 ± 3.6 years) using a 3T MR scanner (Trio, SiemensMedical Solutions, Malvern, PA) employing a four-element phased array carotid coil(Machnet, Maastricht, The NL). We acquired 3D time-of flight (TOF) images consisting of96 slices centered about the carotid bifurcation with spatial resolution 0.47 mm in-plane and1 mm through-plane. Additionally, phase-contrast MR (PCMR) images of through-planeblood velocity were acquired at the inlet of the common carotid artery (CCA) at the samelocation as the proximal slice of the 3D-TOF image stack. PCMR slices were aligned suchthat we acquired perpendicular cross-sections of the vessel. PCMR was acquired at 30 timesteps over the cardiac cycle at a resolution of 0.70 mm in-plane and 4 mm through-plane.

Geometry ExtractionThe 3D geometry of the carotid bifurcation for each patient was contoured and reconstructedfrom the 3D-TOF MR data set using Segment (v1.8 R1172, Medviso AB, Lund, Sweden)[17]. The left carotid was segmented in all except in two patients, where the right carotidwas studied due to imaging artifacts in the left carotid. In all arteries that we segmented, thewall was clearly visible, and there were no imaging artifacts. Light smoothing of thesegeometries was conducted using Geomagic Studio 11 (Geomagic, Inc., Research TrianglePark, NC), and the inlets and outlets were cut perpendicular to vessel walls to ensure axialsimulation of flow in cases of off-axis imaging. The resulting models were meshed usingGambit (v2.4.6, ANSYS, Inc, Cannonsburg, PA) to provide a constant number of elementsper model, ranging between 225,326 and 840,764 elements (mean ± SD: 401,702 ± 175,967elements). The volumes were meshed with a mixture of prism and tetrahedral elements. Aprism boundary layer along the walls was included in all models, which had 6 concentricrows with growth factor 1.11 and outermost element thickness approximately 1% of theCCA diameter.

Velocity Profile ExtractionEach patient’s inlet velocity profile was extracted from the acquired PCMR image datausing custom in-house image processing software implemented in Matlab (R2010a,MathWorks, Natick, MA). We registered the faces of the mesh of the CCA cross-sectionagainst the PCMR-measured velocity data using MR-derived spatial coordinates and linearlyinterpolated the velocity at each element center. Because PCMR data was acquired at 30time steps over the cardiac cycle, we then used cubic splining to temporally interpolate thevelocity at each element center to 600 time steps/cardiac cycle, with the duration of eachtime step based upon the patient’s measured cardiac cycle duration (R-wave to R-wave).Based on this patient-specific flow data, we calculated blunt, parabolic, and Womersleyvelocity profiles normalized to preserve the instantaneous mass flow rate of the realmeasured velocity profile (Figure 1). We additionally generated parabolic velocity profilesfor each patient’s CCA cross-section based upon a published archetypal flow waveform (theaverage of waveforms from 17 volunteers aged 24–34) to provide an independent,generalized non-patient-specific flow waveform [18, 19]. We calculated the parabolic andWomersley velocity profiles based upon a perfect mathematical circle centered at the vesselcross-section’s centroid with radius equal to the vessel’s maximum radius. Trivial linearrescaling was applied to ensure that the instantaneous flow rate remained independent ofvelocity profile to account for any flow loss due to a non-perfect circular cross-section.Womersley velocity profile computer code was validated by comparing the shape and flowrate of computed results against known solutions of Womersley flow [16].

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CFD Simulations3D, pulsatile, CFD simulations of blood flow through the carotid bifurcation wereperformed using Fluent (v6.3.26 and v12.1, ANSYS, Cannonsburg, PA). For each subject’spatient-specific geometry, we performed 4 simulations with identical mesh and CFDparameters except varying only the inlet velocity profile using blunt, parabolic, Womersley,or the real measured profile. We performed a fifth simulation applying a parabolic profilederived from a generalized flow waveform. Velocity profiles were prescribed as inletboundary conditions using a user-defined function (UDF). As an outlet condition, we usedpressure outlets targeting mass flow split between the outlets with 70% exiting the internalcarotid artery (ICA) and 30% exiting the external carotid artery (ECA) [20]. Blood wassimulated as a Newtonian fluid with density 1060 kg/m3 and dynamic viscosity 0.0035 Pa*srespectively [21]. Simulations were performed using Fluent’s pressure-based solver, withthe SIMPLE pressure-velocity coupling scheme and second-order spatial discretization ofpressure and momentum as well as second-order implicit transient formulation. CFDconvergence criteria were set at 0.001 for continuity and velocity residuals. Three cardiaccycles were simulated for each patient (temporally interpolated to 600 time steps/cycle) toeliminate transient model effects, but only the final cardiac cycle data was used for analysis.

Post-processingMean wall shear stress (WSS) and oscillatory shear index (OSI) values on the ICA werecalculated from CFD results and mapped onto a 2D plane using a “virtual en face” techniquewith VMTK software [22, 23]. Briefly, using VMTK, we calculated the bifurcatingcenterline of each vessel in order to automatically determine the extent of the ICA, ECA,and CCA. Then, for each sub-segment, we calculated a circumferential angular metric and aharmonic mapping representing the axial distance along the vessel, Figure 2. Using angularmetric and harmonic mapping as orthogonal coordinates, we mapped these hemodynamicparameters from 3D subject anatomy (Figure 3) into 2D space using linear interpolation ontoan evenly-spaced grid to allow simple, quantitative, spatially registered comparisons amongsubjects (Figure 4). To evaluate differences in the spatial distribution of hemodynamicmetrics, axial WSS profiles were interpolated along a line from the center of the saddle ofthe bifurcation to the ICA outlet (the inner edge) and along another line located one-halfcircumference from that point (the outer edge) for each patient using Matlab software(Figure 5). We used the definition of OSI given by Moore et al. [3]. 3D renderings of CFDresults (Figure 3) were created in Paraview (v3.6.2, Kitware Inc, Clifton Park, NY).

Model ValidationTemporal convergence was confirmed by running each patient’s real measured velocityprofile simulation with 1/10th the time step and confirming that mean WSS was triviallyinfluenced (< 0.3 Pa). Similarly, mesh convergence was confirmed by creating atopologically-identical mesh for each patient by subdividing each element using Fluent’s“mesh adaptation” feature and again confirming that mean WSS was not affected. Ourconvergence threshold was validated by simulating each subject’s PCMR-measured velocityprofile simulation with the residual threshold lowered to 1 × 10−6 and again confirming thatmean WSS was only trivially influenced. To exclude the possibility that our mean WSScriterion was masking changes in the distribution of WSS in all three validations, we alsoexamined our results qualitatively side-by-side to confirm that there was no difference.

Data AnalysisIntraclass correlation coefficient (ICC) between axial profiles was calculated using Rstatistical analysis software (v2.12.1, R Foundation, Vienna, Austria) using the package “irr”to evaluate differences in the spatial distribution of hemodynamic metrics between

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simulations [24]. ICC is a measure of data similarity within predefined groups calculated inpart by quantifying how much each observation differs from its group mean. To evaluatedifferences in the magnitudes of hemodynamic metrics, we computed the pointwise percentdifference between pairs of simulations, considering the entire wall of the ICA rather thanindividual axial profiles (Figure 4). Because the wall of the ICA is not a perfect cylinder, weweighted each point by its normalized arc length as calculated from the point’s distance tocenterline (Equation 1):

(1)

where arci is the arc length traversed by the ith point, RSi is the ith point of the referencestandard, and ICi is the ith point of the inlet condition we are evaluating.

This study had 3 specific hypotheses, and the data analysis was done in 3 ways to answereach of these hypotheses.

Differences from inlet velocity profile—First, to evaluate how mean WSS and OSIwere affected by choice of patient-specific or simplified velocity profiles, we calculated theICC between axial profiles from simulations using the patient-specific (“referencestandard”) velocity profile and either the blunt profile, the parabolic profile, or theWomersley profile. Mean correlation values were computed by averaging the correlationcoefficient for each comparison among patients to yield one mean ICC per inlet condition.We computed the pointwise percent difference between results from the patient-specificprofile simulation and each of the idealized profile simulations. The mean percent differencewas extracted to determine how magnitudes of both OSI and mean WSS varied among allpatients for each inlet velocity condition.

Differences from flow waveform—Second, to evaluate how WSS differences betweenpatient-specific and simplified velocity profiles compared to differences between patient-specific velocity profiles and the generalized velocity profile, we compared simulationsusing the parabolic velocity profile based upon the subject’s own flow waveform and thegeneral non-patient-specific waveform. We computed the ICC from axial profiles extractedfrom these simulations, as well as the pointwise percent difference in mean WSS and OSImagnitudes. We compared these quantitative metrics to results from the first hypothesis. Weused a one-way ANOVA for repeated measures followed by Tukey’s Honestly SignificantDifference post-hoc test implemented in R to analyze the pointwise percent differencebetween all four inlet velocity profiles.

Differences from patient anatomy—Lastly, to evaluate how mean WSS and OSIdifferences from the choice of velocity profile compared to differences between patientsresulting from anatomic variation, we calculated the ICC among axial profiles from allpatients using the patient-specific velocity inlet condition. We also computed the pointwisepercent difference between results from each patient’s simulations using the patient-specificvelocity profile and the group mean WSS and OSI profiles.

Results

Pointwise percent difference results are quantified in Figure 6, and intraclass correlationcoefficients (ICC) are reported in Figure 7. In general, ICC was higher on the outside edge

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of the ICA (where low and oscillatory wall shear stress is present in the carotid bulb) than onthe inside edge (where high wall shear stress dominates the inside edge of the saddle andwhere minimal oscillatory flow is expected). Womersley number ranged between 3.30 and4.69 (mean ± SD 4.07 ± 0.45), and the CCA radius of patients ranged between 2.39 mm and3.40 mm (mean ± SD 2.95 ± 0.33).

Differences from inlet velocity profile—Correlation between the patient-specific andthe parabolic inlet velocity profiles were, on average, the highest of all the simplifiedvelocity profiles (mean ICC: 0.9686 inside, 0.9947 outside). The Womersley profile wasslightly lower on average (mean ICC: 0.9464 inside, 0.9852 outside), and the blunt velocityprofile was the lowest of the simplified velocity profiles (mean ICC: 0.8643 inside, 0.9821outside). Idealized inlet velocity profiles affect calculations of WSS in the carotid bulb onaverage 9.3 ± 4.4%, 13.4 ± 6.2%, and 12.1 ± 4.3% (mean ± SD) for the parabolic,Womersley, and blunt profiles, respectively, while OSI differs on average 4.5 ± 2.5%, 4.0 ±2.0%, and 5.0 ± 2.7% for the parabolic, Womersley, and blunt profiles, respectively. Thepointwise percent difference was not significantly different between any of the threeidealized inlet velocity profiles (p > 0.05) for both WSS and OSI.

Differences from flow waveform—Correlation between simulations using the patient-specific and the non-patient-specific flow waveform (mean ICC: 0.8363 inside and 0.8974outside) were lower than mean ICC values from differences from inlet velocity profiles.Choice of patient-specific vs. non-patient-specific flow waveform affects WSS calculationson average between between 11.4 and 40.7% (mean ± SD = 27.0 ± 11.0%) and OSI between17.0 and 39.1% (mean ± SD = 25.9 ± 7.3%). These differences were significantly greaterthan the differences from each of the idealized inlet velocity profiles (p < 0.002) for bothWSS and OSI.

Differences from patient anatomy—Correlation among simulations of patients due todiffering vessel anatomy (ICC: 0.4101 inside and 0.5926 outside) was lower than mean ICCvalues from differences from inlet velocity profiles. Geometric variation among patientsaffects mean WSS calculations on average between 26.6 and 196.3% (mean ± SD = 71.3 ±50.7%) and OSI between 6.0 and 15.8% (mean ± SD = 9.7 ± 3.5%).

DiscussionWhen computational fluid dynamics is applied to the cardiovascular system, simplifyingassumptions are used either because of computational limitations (inadequate processingpower) or because of data set limitations (specific flow or geometry details are not preciselyknown). In this study, we considered effects when simplified flow profiles are applied toCFD models because of lack of subject-specific velocity data. We found that althoughsimplified inlet velocity profiles do impact mean WSS and OSI, this effect is less than thatfrom use of a non-patient-specific flow waveform and also less than that from differences inpatient anatomy.

The simplified pulsatile velocity profiles (blunt, parabolic, and Womersley) are computedfrom the waveform of a subject’s total flow over the cardiac cycle. In cases where velocitydata are nonexistent, researchers attempting to simulate pulsatile flow must apply boundaryconditions from another source, usually taken from a different subject entirely.Unfortunately, imaging techniques that provide the highest resolution of vascular anatomy(CT, IVUS) are not able to measure velocity profiles, whereas techniques that can measurevelocity (MRI, ultrasound) suffer from comparatively lower spatial resolution [25]. Toframe our comparison of velocity boundary conditions, we investigated the effect ofgeometry on computed hemodynamics and the effect of applying a parabolic velocity profile

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derived from a different subject’s flow waveform. We found that although idealized flowprofiles do affect calculation of mean WSS and OSI (Figure 6), geometry is a greatermodulator of flow than are the differences among velocity profiles. Similarly, the differencein hemodynamics between simulations based upon a subject’s own flow waveform and adifferent subject’s were significantly greater than the differences resulting from choice offlow profile.

Because the patient vessel boundaries were derived from a 3D-TOF MR data set and thevelocity profiles were derived from a PCMR data set, mild underestimation of flow ispossible. The two MR data sets were acquired during a single scanning session where thepatient did not move between sequences, but minor registration error is still possible.Because arteries are compliant, the CCA diameter increases slightly in response to eachpulse, and we were able to see a single-pixel increase in CCA diameter on average in thePCMR data set. However, as we used rigid-wall CFD simulation, our model CCA cross-sections did not increase in diameter with these pulses. At peak systole, our model geometrystill overlaid correctly with the outermost voxel of the CCA PCMR data set, and themeasured velocity in the outer adjacent voxels was nearly zero. We prescribed velocities atthe cell centers of each mesh element face on the CCA, so Fluent was still able to enforcethe no-slip boundary condition. Still, because of the possibility of artifacts, we did notanalyze any WSS or OSI from the CCA region. Additionally, our blunt, Womersley, andparabolic velocity profiles were based upon the flow rate through our rigid-wall modelCCA, so we were self-consistent throughout the study and our comparisons amongwaveforms are still valid.

In simulations where the subject’s own velocity profile is not known, our results suggest thatthere is no significant difference between any of the idealized velocity profiles examined inthis study. However, the parabolic velocity profile produced the lowest mean error for bothWSS and OSI in the majority of simulations. That it produced the lowest mean error isperplexing, as the pulsatile parabolic profile is a variation on Poiseuille flow, a well-knownsolution for fully developed, steady, straight pipe flows [5]. The Womersley profile is asolution of the Navier-Stokes equations, also for fully developed straight pipe flows, butincluding pulsatile effects, and consequently we expected this profile to most closely matcheach subject’s real measured velocity profile [16]. This discrepancy may be best explainedthat the assumption of fully-developed flow probably does not hold for this region of thecommon carotid artery, nor does the assumption that the vessel is a straight pipe. The carotidartery branches off the aortic arch nearly orthogonally, and we measured each patient’s realvelocity profile at a distance equal to only a small number of diameters distal to thisbranching point (4.8 cm proximal to the carotid bifurcation); thus, the assumption of fully-developed flow used in the derivation of both the Womersley and Poiseuille solutions maynot be valid in this situation.

A previous study by Hoi et al. found that in the carotid bifurcation, the effect of inletconditions on disturbed flow is minimal when the common carotid artery is longer thanapproximately 3 times its diameter, as was the case in our simulations [26]. The averageWomersley number, which represents the ratio of pulsatile effects to viscous effects, of oursubjects was 4.1 ± 0.4 (mean ± SD). Smaller values mean that the Womersley velocityprofile more closely approximates the parabolic Poiseuille solution because of the lowerinfluence of pulsatility on hemodynamics. Although the parabolic velocity profile yieldedthe lowest mean error in our simulations, the Womersley profile yielded a similar degree oferror in most cases and was not statistically significantly different. In almost all patients, theaverage difference in hemodynamic outcomes between simulations employing the parabolicand Womersley profiles was less than the difference between simulations using thereference standard profile and any of the simplified profiles. Given the complexity of coding

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the Womersley velocity profile (the authors could locate only one published set of computercode for this task, and this code only produced a single harmonic of the Fourier series; thus,the authors wrote their own computer code), the closeness of the two solutions may notjustify the extra effort in writing this computer code for simulations of the carotidbifurcation [16, 27].

Regardless of which profile is used, when considering which idealized velocity profile toselect, errors in mean WSS between 11.4 and 40.7% may result from using another subject’sflow waveform. However, this source of error is essentially unavoidable when the subject’sown flow waveform is not known. Geometry is a greater modulator of these hemodynamicparameters than differences in the velocity profile, and these findings are in agreement withHoi et al., who investigated the use of assumed flow waveforms on carotid CFD results [28].Both studies found that the relative distribution of OSI for any given bifurcation geometrywas not heavily influenced by inlet flow conditions, although Hoi et al. modulated themagnitude of the flow waveform and we modulated the shape of the velocity profile for agiven flow waveform. Although any error whatsoever is undesirable when simulatinghemodynamics for application to clinical or biological phenomena, careful segmentation ofeach subject’s geometry and selection of flow waveforms that most closely approximate thepatient’s own flow environment will eliminate the majority of these errors.

Because of the desire to understand the effects of boundary condition selection, Moyle et al.considered how WSS and OSI are affected by inlet conditions in the carotid bifurcation [11].However, this study did not directly prescribe velocity profiles as we did—the focus was onthe effects of secondary flow patterns arising from curvature and shape of the commoncarotid artery proximal to the bifurcation. Our findings agree with Moyle et al. thatgeometry is a greater modulator of WSS and OSI than the shape of inlet velocity profiles.Our study found that the magnitude of the mean WSS difference was approximately 3.5 to 4times greater from geometry than from inlet profile. By directly prescribing the velocityprofiles rather than developing secondary flows by modulating upstream anatomy, we areable to specifically isolate the effects of these velocity profile simplifications that arecommonly used in CFD. We build on the findings of Moyle et al. by additionallyinvestigating the effect of selecting a non-subject-specific flow waveform from which toderive these velocity profiles, as is the case in all CFD studies when flow cannot be acquiredwith the same technique as geometry.

Other research groups have investigated the effect of inlet velocity profile on hemodynamicoutcomes in different blood vessels but have come to similar conclusions as the presentstudy. Marzo et al. applied plug, Womersley, and PCMR-measured velocity profiles tointracranial aneurysms [14]. They concluded that geometry rather than velocity profile is agreater modulator of hemodynamics at this site downstream of the vessel considered in ourown study. Myers et al. investigated the effect of parabolic, plug, and Dean flow inletvelocity profiles on CFD results in the right coronary artery [15]. They too concluded thatthe inlet velocity profile had minimal effect on WSS and that geometric factors likecurvature of the vessel are greater modulators of WSS. Further, Marzo et al. similarly agreedthat given the Womersley profile’s complexity of implementation and minimal if anysuperiority in hemodynamic accuracy over other inlet velocity profiles, its use may not benecessary in many cases.

Although we have demonstrated the relative importance of velocity boundary conditions,flow waveform, and vessel geometry, it is important to remember that this study onlyfocused on the carotid bifurcation in humans, where average Womersley number is 4.1 ± 0.4and average radius is 3.0 ± 0.3 mm (mean ± SD). These conclusions may not translate tolarger vessels such as the descending aorta, where Womersley number is approximately 10

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and radius is approximately 15 mm [29]. Additionally, we assumed a constant 70%/30%flow split between the ICA and ECA, respectively [20]. Physiologically, this flow division isnot constant over the cardiac cycle, as the ICA must maintain flow to the brain even near theend of diastole, while the ECA, which supplies blood to the face, may receive a lowerproportion of blood flow depending on available net flow. For the generalized, non-patient-specific flow waveform, we selected a published waveform generated from a youngersubject population (ages 24–34) than the population from which our vessel geometry wasacquired (ages 57–68). We did not consider the effect of age on flow in the present studybecause our volunteers were healthy individuals without evidence of atherosclerosis.

In this study, our “reference standard” velocity profile was based upon through-plane PCMRdata, which only provides axial velocity data. As the CCA is not known for especiallyvortical flows, we assumed that the in-plane velocity components were negligible. Othershave predicted that flow in the CCA is not fully developed, but these conclusions are basedupon PCMR data sets that, like ours, only include through-plane components of velocity[30]. Even without in-plane velocity data, we are still able to measure the total flow in theCCA, and it is upon this flow waveform that we derived the blunt, parabolic, andWomersley velocity profiles in our study. If the true patient-specific velocity profile is notfully developed and does contain in-plane velocity components, then it is likely that thepresent study underestimates the difference between the simplified velocity profiles and thereal profile. In this context, the difference between the three simplified velocity profiles, allof which prescribe only axial flow, is probably even less important.

ConclusionIn cases when patient-specific inlet velocity conditions are not known, simplifyingassumptions must be made for computational fluid dynamics studies of cardiovascular flow.We evaluated three of the most common velocity profile assumptions used historically instudies of the human carotid bifurcation: the blunt profile, the parabolic profile, and theWomersley profile. Although selection of inlet flow profiles affects calculation of wall shearstress and oscillatory shear index, natural variation in vessel geometry among patientsaffects such hemodynamic metrics more, as does the use of the subject’s own flowwaveform over a nonspecific waveform. In cases where an assumption must be made, werecommend use of the pulsatile parabolic profile over the blunt or Womersley profilesbecause it produced the lowest magnitude of error in wall shear stress and oscillatory shearindex. However, because geometry and flow waveform selection are greater modulators ofthese hemodynamic metrics, we first recommend careful reconstruction of vessel anatomyand second recommend acquisition of the subject’s own flow waveform before becomingconcerned with velocity waveform selection.

AcknowledgmentsThe authors would like to thank Jonathan Suever for his invaluable help with Matlab algorithms, and Dr. EmirVeledar for his input on statistical techniques. This material is based upon work supported by an American HeartAssociation Predoctoral Fellowship, by the National Science Foundation Graduate Research Fellowship underGrant No. DGE-0644493, and by the National Institutes of Health Bioengineering Research Partnership underGrant No. R01 HL70531.

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Figure 1.Snapshot at peak systole of the four inlet velocity profiles prescribed at the common carotidartery (CCA). The real measured velocity profile (top left) was derived from direct phase-contrast magnetic resonance (PCMR) imaging of a patient over the cardiac cycle. Thevolume flow rate of this “reference standard” velocity profile was then used to compute theblunt (top right), Womersley (bottom left), and parabolic (bottom right) velocity profiles.Data from subject #4.

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Figure 2.On the reconstructed 3D geometry, centerlines along the carotid bifurcation were detectedusing VMTK software (a) and split into branches (b). Angular metric (c) and distance alongthe centerline were used to map OSI and time-averaged WSS distributions (d) in the internalcarotid artery onto a flat surface to create a “virtual en face” view of hemodynamics (Figure4). Data from subject #4.

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Figure 3.Oscillatory shear index (OSI) in the carotid bulb varies in magnitude and distribution amongCFD simulations employing four different inlet velocity profiles. Data from subject #4.

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Figure 4.Using VMTK software, we mapped hemodynamic parameters from a 3D model (Figure 3)into the 2D plane using techniques in Figure 2. We analyzed the internal carotid arteryaround the carotid bulb and investigated the magnitude and distribution of mean WSS (left)and OSI (right) under varying inlet velocity profile conditions. Mean WSS magnitudes aremore affected by inlet conditions than distribution, while OSI distributions are relativelymore affected by inlet conditions than magnitude. Data from subject #5.

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Figure 5.Extracting axial profiles of mean WSS results in the ICA allows visualization andquantification of spatial and magnitude differences in mean WSS resulting from differentinlet velocity profiles. Profiles aligned with the inner and outer ridge of the ICA (yellowline, in 3D at left and brown [inner] and green [outer] lines in virtual en face at top right) canbe compared visually (bottom right) and using the intraclass correlation coefficient (Figure7). Patient-specific CFD allows researchers to study how local minima and maxima of WSSvary spatially, but inlet flow profile influences this distribution. Data from subject #9.

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Figure 6.Pointwise percent difference of results from simulations using different inlet velocityprofiles. Choice of inlet flow conditions affects WSS and OSI calculations, but not as muchas natural anatomic variation among patients or the use of non-subject-specific flowwaveform to compute the velocity profiles. Error bars shown are standard deviation, and *indicates p < 0.002 relative to other inlet velocity profiles.

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Figure 7.Intraclass correlation coefficient (ICC) calculated between axial profiles of mean WSSextracted from the inside and outside ridges of the internal carotid artery (ICA) as in Figure5. On average, results from simulations using the parabolic velocity profile show the highestcorrelation to results from simulations using the real measured velocity profile, while ICCamong subjects and between simulations using velocity profiles derived from non-subject-specific flow waveforms have lower correlation, demonstrating the strong importance ofpatient anatomy and individual flow waveforms when performing computational fluiddynamics.

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effect inlet vel profiles

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