bifurcations Computational studies with

143Preliminary data were presented at the 1997 American Society ofMechanical Engineers Bioengineering Conference, Sun RiverOR, June 1997.Reprint requests: David A. Steinman, PhD, John P. RobartsResearch Institute, 100 Perth Drive, P.O. Box 5015, London,Ontario N6A 5K8, Canada.Copyright © 1998 by the Society for Vascular Surgery and Inter-national Society for Cardiovascular Surgery, North AmericanChapter.0741-5214/98/$5.00 + 024/1/87948

Hemodynamics of human carotid arterybifurcations: Computational studies withmodels reconstructed from magneticresonance imaging of normal subjects

Jaques S. Milner, BESc, Jennifer A. Moore, MSc, Brian K. Rutt, PhD, andDavid A. Steinman, PhD, London and Toronto, Canada

Purpose:The precise role played by hemodynamics, particularly wall shear stress, in thedevelopment and progression of vascular disease remains unclear, in large part because ofa lack of in vivo studies with humans. Although technical challenges remain for noninva-sively imaging wall shear stresses in humans, vascular anatomy can be imaged with suffi-ciently high resolution to allow reconstruction of three-dimensional models for compu-tational hemodynamic studies. In this paper we present an entirely noninvasive magneticresonance imaging (MRI) protocol that provides carotid bifurcation geometry and flowrates from which the in vivo hemodynamics can be computed. Maps of average, oscilla-tory, and gradients of wall shear stress are presented for two normal human subjects, andtheir data are compared with those computed for an idealized carotid bifurcation model.Methods:An MRI protocol was developed to acquire all necessary image data in scantimes suitable for patient studies. Three-dimensional models of the carotid bifurcationlumen were reconstructed from serial black blood MR images of two normal volunteers.Common and internal carotid artery flow rate waveforms were determined from MRIphase-contrast velocity imaging in the same subjects and were used to impose fully devel-oped velocity boundary conditions for the computational model. Subject-specific time-resolved velocities and wall shear stresses were then computed with a finiteelement–based Navier-Stokes equation solver.Results:Models reconstructed from in vivo MRI of two subjects showed obvious differ-ences in branch angle, bulb size and extent, and three-dimensional curvature. Maps of avariety of wall shear stress indices showed obvious qualitative differences in patternsbetween the in vivo models and between the in vivo models and the idealized model. Sec-ondary, helical flow patterns, induced primarily by the asymmetric and curved in vivogeometries, were found to play a key role in determining the resulting wall shear stresspatterns. The use of in vivo flow rate waveforms was found to play a minor but notice-able role in some of the wall shear stress behavior observed.Conclusions:Conventional “averaged” carotid bifurcation models mask interestinghemodynamic features observed in realistic models derived from noninvasive imaging ofnormal human subjects. Observation of intersubject variations in the in vivo wall shearstress patterns supports the notion that more conclusive evidence regarding the role ofhemodynamics in vascular disease may be derived from such individual studies. The tech-niques presented here, when combined with subject-specific MRI measurements ofcarotid artery plaque thickness and composition, provide the tools necessary for entire-ly noninvasive, prospective, in vivo human studies of hemodynamics and the relationshipof hemodynamics to vascular disease.(J Vasc Surg 1998;27:143-56.)

From the Imaging Research Laboratories, John P. RobartsResearch Institute (Milner and Drs. Rutt and Steinman); theDepartment of Medical Biophysics, University of WesternOntario, London (Drs. Rutt and Steinman); the Department ofDiagnostic Radiology & Nuclear Medicine, University of West-ern Ontario, London (Dr. Rutt); and the Department ofMechanical and Industrial Engineering, University of Toronto(Moore).Support was provided by the Heart and Stroke Foundation ofOntario (grant NA3197).Despite many hemodynamic studies carried outwith models of arterial bifurcations, especially thecarotid artery bifurcation, the precise role played bywall shear stress in the development and progressionof atherosclerosis remains unclear. Early studies cor-related high,1low,2and oscillatory3shear with thepresence of arterial disease, but later studies postu-lated roles for the temporal4and spatial5gradients ofwall shear stress. The inability to conclusively identi-fy the hemodynamic quantities that influence athero-sclerosismay be attributed in part to the indirectnature of the correlations made between hemody-namics and vascular disease: flow studies are typical-ly carried out in idealized models with averaged flowparameters, and sites predisposed to atherosclerosisare identified from averaged postmortem measure-ments. More direct studies, in which the presence orabsence of disease can be compared with wall shearstress patterns throughout individual carotid bifur-cations, probably are required to remove theseremaining ambiguities.Magnetic resonance imaging (MRI) can producehigh-resolution images of the human carotid bifurca-tion noninvasively and in scan times suitable forpatient studies.6,7Although MRI is also capable ofdirectly measuring blood flow velocity, acquiringvelocity data at spatial and temporal resolutions nec-essary for computing three-dimensional maps of wallshear stress requires scan times sufficiently long topreclude human studies. The studies that have