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On the shape of the common carotid artery with implications for blood velocity profiles

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IOP PUBLISHING

PHYSIOLOGICAL MEASUREMENT

Physiol. Meas. 32 (2011) 1885–1897

doi:10.1088/0967-3334/32/12/001

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,

Canada

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

E-mail: steinman@mie.utoronto.ca

Received 14 August 2011, accepted for publication 20 September 2011

Published 27 October 2011

Online at stacks.iop.org/PM/32/1885

Abstract

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

(63±12years)intheVALIDATE(VascularAging—TheLinkthatBridgesAge

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

thoracicCCAwassignificantlymorecurvedat1:16,withtheplaneofcurvature

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

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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.

Keywords:

Doppler ultrasound

carotid artery, blood velocity profile, geometric parameters,

(Some figures in this article are in colour only in the electronic version)

1. Introduction

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

imaging(MRI)toestimatea1:20curvature(i.e.ratiooflumenradiustoradiusofcurvature)of

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

bifurcation.

2. Methods

2.1. Study subjects and MRI

Data for this study were acquired from the NIA-sponsored VALIDATE (Vascular Aging—The

LinkThatBridgesAgetoAtherosclerosis)study,whichaimstotestthehypothesisthatvascular

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.

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On the shape of the CCA1887

(a)(b) (c)(d)

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

usingacentrick-spaceordering, withafield-of-viewencompassingtheaorticarchtothecircle

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.

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The centerlines of the segmented lumens were generated automatically using VMTK’s

Voronoi-diagram-basedapproach(Antigaetal2008),whichalsoprovideslocalmeasurements

of the maximally-inscribed sphere radius (i.e. minimum radius). In order to truncate the CCA

centerlineatanobjectivelocationproximaltothebifurcation, weusedVMTK’sdefinitionofa

bifurcationcoordinatesystemanddistancesbasedonlumenradii(AntigaandSteinman2004).

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

thesegment’smeanradiusofcurvature(RC).Alsonotedwerethemeansegmentlumenradius,

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

adultflowratewaveform(Hoietal2010b). Traction-freeboundaryconditionswereprescribed

at the outlet. Rigid walls and constant blood viscosity of 0.035 cm2s−1were assumed. Based

onthetypicalflowandheartratesattheCCA(Hoietal2010b), Reynolds(Re)andWomersley

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.