Preliminary data were presented at the 1997 American Society of
Mechanical Engineers Bioengineering Conference, Sun River
OR, June 1997.
Reprint requests: David A. Steinman, PhD, John P. Robarts
Research 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 American
0741-5214/98/$5.00 + 0
Hemodynamics of human carotid artery
bifurcations: Computational studies with
models reconstructed from magnetic
resonance imaging of normal subjects
Jaques S. Milner, BESc, Jennifer A. Moore, MSc, Brian K. Rutt, PhD, and
David A. Steinman, PhD, London and Toronto, Canada
Purpose: The precise role played by hemodynamics, particularly wall shear stress, in the
development and progression of vascular disease remains unclear, in large part because of
a 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 magnetic
resonance imaging (MRI) protocol that provides carotid bifurcation geometry and flow
rates 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, and
their 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 scan
times suitable for patient studies. Three-dimensional models of the carotid bifurcation
lumen were reconstructed from serial black blood MR images of two normal volunteers.
Common and internal carotid artery flow rate waveforms were determined from MRI
phase-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 finite
element–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 a
variety of wall shear stress indices showed obvious qualitative differences in patterns
between 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 vivo
geometries, were found to play a key role in determining the resulting wall shear stress
patterns. 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 interesting
hemodynamic features observed in realistic models derived from noninvasive imaging of
normal human subjects. Observation of intersubject variations in the in vivo wall shear
stress patterns supports the notion that more conclusive evidence regarding the role of
hemodynamics in vascular disease may be derived from such individual studies. The tech-
niques presented here, when combined with subject-specific MRI measurements of
carotid artery plaque thickness and composition, provide the tools necessary for entire-
ly noninvasive, prospective, in vivo human studies of hemodynamics and the relationship
of hemodynamics to vascular disease. (J Vasc Surg 1998;27:143-56.)
From the Imaging Research Laboratories, John P. Robarts
Research Institute (Milner and Drs. Rutt and Steinman); the
Department of Medical Biophysics, University of Western
Ontario, London (Drs. Rutt and Steinman); the Department of
Diagnostic Radiology & Nuclear Medicine, University of West-
ern Ontario, London (Dr. Rutt); and the Department of
Mechanical and Industrial Engineering, University of Toronto
Support was provided by the Heart and Stroke Foundation of
Ontario (grant NA3197).
Despite many hemodynamic studies carried out
with models of arterial bifurcations, especially the
carotid artery bifurcation, the precise role played by
wall shear stress in the development and progression
of atherosclerosis remains unclear. Early studies cor-
related high,1low,2and oscillatory3shear with the
presence of arterial disease, but later studies postu-
lated roles for the temporal4and spatial5gradients of
wall shear stress. The inability to conclusively identi-
fy the hemodynamic quantities that influence athero-
sclerosis may be attributed in part to the indirect
nature of the correlations made between hemody-
namics and vascular disease: flow studies are typical-
ly carried out in idealized models with averaged flow
parameters, and sites predisposed to atherosclerosis
are identified from averaged postmortem measure-
ments. More direct studies, in which the presence or
absence of disease can be compared with wall shear
stress patterns throughout individual carotid bifur-
cations, probably are required to remove these
Magnetic resonance imaging (MRI) can produce
high-resolution images of the human carotid bifurca-
tion noninvasively and in scan times suitable for
patient studies.6,7Although MRI is also capable of
directly measuring blood flow velocity, acquiring
velocity data at spatial and temporal resolutions nec-
essary for computing three-dimensional maps of wall
shear stress requires scan times sufficiently long to
preclude human studies. The studies that have
JOURNAL OF VASCULAR SURGERY
144 Milner et al.
Fig. 1. A custom bilateral phased-array radio-frequency coil, indicating the multiple transla-
tional and rotational degrees of freedom. The inset shows the position of a volunteer in the coil.
in the derived ECA flow rate waveforms; this effect
was most pronounced in model I. Although it is
possible that even small errors in the extraction of
the ICA and CCA flow rate data (from which ECA
flow was derived) may account for this finding,
reverse flow in the ECA has been reported by
Aldrete et al.30,31The findings suggest that the
effects of such negative flow, most apparent in the
elevated OSI and reduced average shear stresses in
the ECA of the in vivo models, may be genuine and
significant. Further careful studies are needed to
confirm the finding of transient reverse flow in the
ECA of normal human volunteers.
In the absence of a reliable and noninvasive stan-
dard, it is difficult to directly assess the absolute
accuracy of the in vivo geometry and flow rate wave-
form reconstructions in normal subjects. When we
used an in vitro carotid bifurcation model imaged
under conditions admittedly more ideal than those
in this study (e.g., higher signal-to-noise ratio, no
motion artifacts), we found that our reconstruction
technique can accurately reproduce the true hemo-
dynamics of a known complex arterial geometry.15
Qualitative features of the wall shear stress patterns
remained even in the presence of modest recon-
struction errors. The reconstructed flow rate wave-
forms compare favorably in terms of magnitude and
overall shape with ultrasound measurements in nor-
mal subjects.32,33Phenomena that might have been
attributed to measurement error (e.g., reverse flow
in the ECA) were found to have precedents in the
literature, and results of our flow waveform sensitiv-
ity studies in the idealized model indicated only
moderate differences in wall shear stress patterns
induced by a large change in the applied flow rate
waveform. We therefore conclude that it is extreme-
ly unlikely that errors in flow rate or geometry
reconstruction could explain the pronounced quali-
tative differences observed in the hemodynamics of
the models studied. However, we also believe that
extension of this novel combined vascular imaging
and modeling paradigm from the qualitative to the
quantitative realms will require rigorous accuracy
and precision studies.
In summary, we have shown that the distribu-
tions of wall shear stress variables hypothesized to
play a role in development and progression of vascu-
lar disease can vary from subject to subject. This
finding supports the notion that more conclusive
evidence regarding the role of hemodynamics in vas-
cular disease may be derived from studies in individ-
ual subjects. The techniques developed and applied
in this study, when combined with concomitant in
vivo measurements of plaque distribution and com-
position (possibly derived from the same MR images
used to reconstruct the geometry), provide the
means necessary to carry out such studies. The
observation that geometry plays a key role in deter-
mining local wall shear stress patterns in principle
supports the notion of a “geometric risk factor” in
atherosclerosis.34-36Idealized models were found to
mask interesting and potentially important in vivo
hemodynamic behavior. Although such models have
in the past proved invaluable for providing hemody-
namic measurements with which pathologic data
could be correlated, further advances in our under-
standing of the complex relationship between hemo-
dynamics and vascular disease will probably come
only when individual subjects are studied in a
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Submitted Aug. 21, 1997; accepted Dec. 3, 1997.
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