On the shape of the common carotid artery with implications for blood velocity profiles
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Physiol. Meas. 32 (2011) 1885–1897
On the shape of the common carotid artery with
implications for blood velocity profiles
Amir Manbachi1,2, Yiemeng Hoi1, Bruce A Wasserman3,
Edward G Lakatta4and David A Steinman1,2
1Biomedical Simulation Laboratory, Department of Mechanical & Industrial Engineering,
University of Toronto, Toronto, ON, Canada
2Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON,
3The Russell H Morgan Department of Radiology and Radiological Sciences, The Johns
Hopkins Hospital, Baltimore, MD, USA
4Laboratory of Cardiovascular Science, Intramural Research Program, National Institute on
Aging, NIH, Baltimore, MD, USA
Received 14 August 2011, accepted for publication 20 September 2011
Published 27 October 2011
Online at stacks.iop.org/PM/32/1885
Clinical and engineering studies typically assume that the common carotid
artery (CCA) is straight enough to assume fully developed flow, yet recent
studies have demonstrated the presence of skewed velocity profiles. Toward
elucidating the influence of mild vascular curvatures on blood flow patterns
and atherosclerosis, this study aimed to characterize the three-dimensional
shape of the human CCA. The left and right carotid arteries of 28 participants
to Atherosclerosis) study were digitally segmented from 3D contrast-enhanced
magnetic resonance angiograms, from the aortic arch to the carotid bifurcation.
Each CCA was divided into nominal cervical and thoracic segments, for
which curvatures were estimated by least-squares fitting of the respective
centerlines to planar arcs. The cervical CCA had a mean radius of curvature of
127 mm, corresponding to a mean lumen:curvature radius ratio of 1:50. The
tilted by a mean angle of 25◦and rotated close to 90◦with respect to that of
the cervical CCA. The left CCA was significantly longer and slightly more
curved than the right CCA, and there was a weak but significant increase in
CCA curvature with age. Computational fluid dynamic simulations carried
out for idealized CCA geometries derived from these and other measured
geometric parameters demonstrated that mild cervical curvature is sufficient to
prevent flow from fully-developing to axisymmetry, independent of the degree
of thoracic curvature. These findings reinforce the idea that fully developed
0967-3334/11/121885+13$33.00© 2011 Institute of Physics and Engineering in MedicinePrinted in the UK 1885
1886 A Manbachi et al
flow may be the exception rather than the rule for the CCA, and perhaps other
nominally long and straight vessels.
carotid artery, blood velocity profile, geometric parameters,
(Some figures in this article are in colour only in the electronic version)
The carotid arteries are the main conduits for blood flow from the heart to the brain. The left
common carotid artery (CCA) typically arises directly from the aortic arch, the right from the
brachiocephalic artery off the arch. Both eventually bifurcate into an internal carotid artery
(ICA), which feeds the brain, and an external carotid artery (ECA), which feeds the rest of
the head. The carotid artery bifurcation has been the subject of intensive anatomical and
hemodynamic study owing to the preferential development of atherosclerosis at this site (e.g.
Giddens et al (1993)). Less well studied are the anatomy and hemodynamics of the CCA, a
vessel which is commonly considered to be straight, or at least straight enough to rationalize
the assumption of fully developed blood flow proximal to the carotid bifurcation (e.g. Carallo
et al (1999)).
An early case study of a healthy volunteer by Caro et al (1992) used magnetic resonance
the cervical CCA, and revealed the presence of secondary velocities characteristic of so-called
Dean-type flow in a planar curved tube. A Doppler ultrasound investigation of 20 healthy
volunteers of various ages reported the presence of skewed velocity profiles irrespective of
age, and which were attributed to ‘slight’ CCA curvatures (Tortoli et al 2003). Recent MRI
investigations have confirmed the common finding of strongly skewed blood velocity profiles
in the CCA (Sui et al 2008, Ford et al 2008).
The dynamics of blood flow in tubes having simple planar curvatures (i.e. Dean flow)
are well understood; however less is known about how and why more complex, shallow
curvatures of vessels such as the CCA produce velocity profile skewing in some cases but
not others. Ultimately, such knowledge may help explain the common finding of eccentric
wall thickening at the CCA (e.g. Boussel et al (2007)), and also overcome errors in Doppler
ultrasound estimations of flow and wall shear rates (e.g. Balbis et al (2005), Krams et al
(2005)) which typically rely on the assumption of fully developed or parabolic (Pantos et al
2007). Toward this ultimate end, the aim of the present study was to conduct the first thorough
survey of the geometry of the human CCA from its thoracic origins to the level of the carotid
2.1. Study subjects and MRI
Data for this study were acquired from the NIA-sponsored VALIDATE (Vascular Aging—The
age is an important determinant of the age-associated increase in atherosclerotic disease.
Specifically, the present study focused on the community-based cohort (i.e. normal vascular
ageing group) recruited from Baltimore Longitudinal Study for Aging (BLSA) participants
(Ferrucci 2008). Written informed consent was obtained from all participants and approval
was given by the institutional review boards.
On the shape of the CCA1887
Figure 1. (a) Maximum intensity projection of a representative 3D CEMRA. (b) Segmented right
CCA viewed normal to best-fit cervical (left) and thoracic (right) planes. Note centerlines, pivot
(P) and cervical (C) and thoracic (T) end points. (c) Best-fit cervical and thoracic circular arcs
(solid lines) compared to original centerline (dotted line). (d) Parametric CCA model derived from
a spline-fit of the indicated circular arc and pivot points, showing good agreement with the original
CCA segmented surface.
As part of a comprehensive MRI survey of the carotid bifurcations, three-dimensional
(3D) contrast-enhanced magnetic resonance angiograms (CEMRA) were acquired coronally
of Willis (figure 1(a)). Owing to the focus on the carotid bifurcations, surface radiofrequency
coils were used, resulting in reduced signal at the CCA’s thoracic origins. As a result, we
considered only those cases acquired using a 3.0 Tesla scanner (Achieva; Philips Healthcare,
Best, The Netherlands), as the CCA thoracic origins were more conspicuous compared to
acquisitions at 1.5 Tesla. Specifically, N = 32 cases were selected for analysis, encompassing
both sexes (13M:19F) and a range of ages (37–85 years; mean ± stdev = 63 ± 12 years).
CEMRA acquisition parameters included 6 cm thick coronal slab partitioned into 1 mm slices
overlapping by 0.5 mm, 33 cm field-of-view acquired with a 408 × 405 acquisition matrix
zero-padded to 512 × 512, and Magnevist (Bayer Schering Pharma AG, Berlin, Germany)
contrast injection of 0.1 mmol kg−1at 2 mL s−1.
2.2. Image segmentation and shape characterization
The left and right CCA lumens were digitally segmented from each 3D CEMRA series using
the computer-assisted fast marching level set method of the open-source Vascular Modeling
ToolKit (VMTK; www.vmtk.org). This requires a user to initialize the surface via interactive
selection of one or more thresholds, but otherwise generates the lumen surface automatically
based on the image gradients. In four cases, either the left or right CCA could not be reliably
segmented down to its origin at the aortic arch or brachiocephalic trunk; these cases were
excluded from further analysis, leaving 28 left/right pairs for geometric characterization. One
quarter (i.e. seven) of the cases were selected randomly for re-segmentation after 1 year, in
order to test the reproducibility of the geometric characterizations.
1888A Manbachi et al
The centerlines of the segmented lumens were generated automatically using VMTK’s
of the maximally-inscribed sphere radius (i.e. minimum radius). In order to truncate the CCA
Specifically, the CCA was truncated one lumen radius proximal to where the CCA splits into
the ICA and ECA, a point referred to as CCA1 (Hoi et al 2010a). These centerline trajectories
and lumen radii were then used exclusively for subsequent geometric characterizations.
As the CEMRA acquisitions, and hence the segmented lumens, were oriented to the
body axes, the total axial length of the CCA could be calculated as the distance along the
superior–inferior axis between the thorax origin and CCA1, points hereafter referred to as T
and C, respectively. As shown in figure 1(b) for a representative case, each CCA was divided
into nominal cervical and thoracic segments at the point of maximum curvature (called the
pivot point, or P) between 50% and 70% of the total CCA length, L. For each of the cervical
and thoracic segments a plane was fitted using a least-squares approach. After projecting each
segment onto its respective plane, a best-fit circular arc (figure 1(c)) was used to characterize
the straight-line distances (SLD) from the respective arc end points and the root-mean-square
(RMS) deviation of the original centerline segments from their respective best-fit planes, as
an estimate of segment non-planarity. The cervical and thoracic planes were each defined
by their normal and tangent vectors, the latter based on the directions of the respective SLD.
The relative orientation of these two best-fit planes was characterized by two angles: the tilt,
calculated from the dot product of the two tangent vectors, and the twist, calculated from the
dot product of the two normal vectors.
2.3. Parametric models and computational fluid dynamics
As illustrated in figure 1(d), idealized models of any specific or statistical CCA could be
constructed from the above-defined geometric parameters as follows. First, each of the planar
cervical or thoracic arc segments was sampled at the arc end point, the arc middle point, and
a point halfway between them. Then, these six points, plus the original pivot point, were
spline-fitted in order to define a new centerline. Finally, the lumen cross-section was assumed
to be circular with a radius equal to the average or nominal radius of the cervical segment.
Computational fluid dynamic (CFD) simulations of pulsatile flow in such parametric
models of the CCA were carried out using a well-validated in-house solver (Ethier et al
1999, 2000, Minev and Ethier 1999). Quadratic tetrahedral-element meshes were generated
by ICEM-CFD (ANSYS, Inc., Canonsburg, PA) with node spacing of 0.3 mm, shown to be
sufficient for resolving the velocity profiles (Manbachi 2010). Fully developed pulsatile (i.e.
Womersley) inlet velocity boundary conditions were prescribed using a representative older
at the outlet. Rigid walls and constant blood viscosity of 0.035 cm2s−1were assumed. Based
numbers were rounded broadly to values of 500 and 3, respectively.
2.4. Statistical analyses
Paired Student’s t-tests were used to test the significance of left versus right and cervical
versus thoracic differences. Linear regression was performed to test for an effect of age on
the various geometric parameters. In all cases significance was assumed for P < 0.05.