1

Toward hemodynamic diagnosis of carotid artery stenosis based on ultrasound image

data and computational modeling

Luísa C. Sousa (corresponding author)

Instituto de Engenharia Mecânica (IDMEC-Polo FEUP),

Faculdade de Engenharia, Universidade do Porto,

Rua Dr. Roberto Frias, s/n, 4200 - 465 PORTO, PORTUGAL

E-mail: lcsousa@fe.up.pt

Phone: +351 962186383

Fax: +351 225081445

Catarina F. Castro

Instituto de Engenharia Mecânica (IDMEC-Polo FEUP),

Faculdade de Engenharia, Universidade do Porto,

Rua Dr. Roberto Frias, s/n, 4200 - 465 PORTO, PORTUGAL

Carlos C. António

Instituto de Engenharia Mecânica (IDMEC-Polo FEUP),

Faculdade de Engenharia, Universidade do Porto,

Rua Dr. Roberto Frias, s/n, 4200 - 465 PORTO, PORTUGAL

André Miguel F. Santos

Instituto de Engenharia Mecânica e Gestão Industrial,

Faculdade de Engenharia, Universidade do Porto,

Rua Dr. Roberto Frias, s/n, 4200 - 465 PORTO, PORTUGAL

Rosa Maria dos Santos

Departamento de Neurologia, Hospital São João,

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Faculdade de Medicina, Universidade do Porto,

Alameda Professor Hernâni Monteiro, 4200-319, PORTO, PORTUGAL

Pedro Miguel A. C. Castro

Departamento de Neurologia, Hospital São João,

Faculdade de Medicina, Universidade do Porto,

Alameda Professor Hernâni Monteiro, 4200-319, PORTO, PORTUGAL

Elsa Azevedo

Departamento de Neurologia, Hospital São João,

Faculdade de Medicina, Universidade do Porto,

Alameda Professor Hernâni Monteiro, 4200-319, PORTO, PORTUGAL

João Manuel R. S. Tavares

Instituto de Engenharia Mecânica e Gestão Industrial,

Faculdade de Engenharia, Universidade do Porto,

Rua Dr. Roberto Frias, s/n, 4200 - 465 PORTO, PORTUGAL

Number of words of Manuscript: 7566

Number of words of the abstract: 199

Number of figures: 10

Number of tables: 1

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Toward hemodynamic diagnosis of carotid artery stenosis based on ultrasound image

data and computational modeling

Abstract

The ability of using non-expensive ultrasound (US) image data together with computer fluid

simulation to access various severities of carotid stenosis was inquired in this study. Subject-

specific hemodynamic conditions were simulated using a developed finite element solver.

Individual structured meshing of the common carotid artery (CCA) bifurcation was built from

segmented longitudinal and cross-sectional US images; imposed boundary velocities were based

on Doppler US measurements. Simulated hemodynamic parameters such as velocities, wall

shear stress (WSS) and derived descriptors were able to predict disturbed flow conditions which

play an important role in the development of local atherosclerotic plaques. Hemodynamic

features from six individual CCA bifurcations were analysed. High values of time average WSS

(TAWSS) were found at stenosis site. Low values of TAWSS were found at the bulb and at the

carotid internal and external branches depending on the particular features of each patient. High

oscillating shear index (OSI) and relative residence time (RRT) values assigned highly

disturbed flows at the same artery surface regions that correlate only moderately with low

TAWSS results. Based on clinic US examinations, results provide estimates of flow changes

and forces at the carotid artery wall towards the link between hemodynamic behaviour and

stenosis pathophysiology.

Keywords: Carotid artery bifurcation; image-based analysis; 3D reconstruction; computational

hemodynamics; finite element method; WSS descriptors

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1 Introduction

Diagnostic ultrasound of the carotid arteries is prognosis-oriented towards identifying patients at

risk for stroke [35]. A simple, inexpensive and noninvasive carotid artery ultrasound (US) of the

neck can be used as a preliminary diagnostic tool for artery disease as an alternative to the

expensive computed tomographic (CT) or magnetic resonance imaging (MRI) diagnosis [1].

Our long term goal is to contribute towards the design of a computer-aided tool based on

parameters estimated from common US examinations in order to accurately characterize and

identify patients with high probability for developing cerebral vascular events. This work aims

at developing a computer-based methodology with the purpose of helping physicians to further

inspect and interpret carotid US data.

The carotid system is quite superficial, thus it can be examined with a high-frequency

transducer yielding B-mode images with high spatial resolution, useful to identify the course of

the vessels and their walls [16]. While scanning the carotid arteries, the blood flow in

longitudinal orientation can be examined using continuous spectra obtained with Doppler

ultrasounds by sampling at short intervals. By looking at Doppler ultrasound images and

velocity spectra, medical doctors identify patients with possible problematic stenosis. In most

cases, carotid stenosis occurs along the internal carotid artery starting at the segment just in

front of the bifurcation [18, 46]. At practice, grading an internal carotid stenosis considers

basically two complementary methods: one uses specific patient residual lumen measurements

and the other important hemodynamic features [2, 40]. Usually, such information altogether

determines the choice of treatment that individual patients receive. Endarterectomy carries a

non-negligible risk for the patient as well as significant costs for the patient, hospital and health

system in general [41]. Trial studies performed in symptomatic and asymptomatic patients

indicate that the degree of stenosis does not always accurately predict patients who will develop

symptomatic lesions, as low-grade stenosis may also result in cerebrovascular events [32, 44].

Regarding the asymptomatic lesions, the majority of asymptomatic patients with highly stenotic

plaques remained asymptomatic [15]. Thus, the identification of asymptomatic patients that will

develop symptoms in the follow-up remains an important challenge.

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The analysis of anatomically realistic blood flow simulations has the potential to enhance

our understanding of how hemodynamic factors are involved in atherosclerotic disease. Studies

showed that the genesis and progression of atherosclerosis are correlated with hemodynamics

and suggested that disturbed flow environment promotes atherogenesis [11, 18]. The effect of

blood flow mechanics in human arteries and the relation between vessel geometry and the

presence of atherosclerotic plaques has been addressed by different authors [46, 23]. Although

large quantitative uncertainties may exist among these works, qualitative blood flow patterns are

remarkably robust as highlighted by Lee et al. [22].

Intensive research has been performed during the past decades based on carotid US, MRI or

CT imaging [36, 46, 42]. Expensive CT or MRI imaging analysis is unreachable for the

common subject in community clinic setting. Nevertheless, CT and MRI based research is

priceless to access carotid data analysis [4, 9]. US image-based hemodynamic simulations of

carotid bifurcation have been carried out using reconstructed vascular geometry and typical

volumetric flow and pressure waves [21]. For an accurate study, subject-specific waveform flow

collected in clinical practice yields a more accurate assessment of flow characteristics [14, 47].

3D ultrasound reconstruction of carotid artery considering stenosed carotid bifurcations and

stenosis-free cases enables to extend clinical studies of the atherosclerotic disease. Reported

studies showed considerable inter-individual variation in arterial geometry and variation in

arterial flow patterns between the studied subjects [22, 24]. Morphology plays an important role

on the hemodynamic behavior of the carotid artery bifurcation, and it is imperative to include

subject-specific morphology and individual flow behavior in modeling blood streams that are

related to potential risk factors [28]. Computer fluid dynamics (CFD) based on US patient-

specific data is expected to contribute towards pathologic findings. Hemodynamic CFD

parameters such as wall shear stress (WSS) are extremely important since plaque ulceration is

related to the existence of high WSS at the upstream region of the plaque and on the contrary,

regions exposed to low WSS are most prone to develop atherosclerotic plaques [13, 43].

Surgical planning and therapy outcomes for atherosclerotic carotid bifurcation would benefit

from a US based diagnosis assistance platform. The present research was partially done in the

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scope of a project with a public hospital and aims at early detect vessels at risk and to predict

further atherosclerotic disease progression.

2 Methods

In this paper, a platform for US data analysis of patient-specific carotid bifurcation is proposed,

and clinical related indicators of artery stenosis are addressed. In order to improve the link

between hemodynamic changes and stenosis pathophysiology, six carotid artery bifurcations

with various severities were reconstructed from Doppler ultrasound scans. Intravascular flow

patterns were predicted using an efficient blood flow simulator [37-39] with a fine structured

mesh and a Newtonian viscosity model under pulsatile conditions.

The developed computational pipeline includes four steps: acquisition of ultrasound

morphological and blood flow velocity data of patient´s carotid artery cervical segments,

surface reconstruction, blood flow simulation and hemodynamic analysis. In this study,

ultrasound data from six CCA bifurcations, referred in this study as patients P1 to P6, were

analyzed. Patient ages ranged between 50 and 84 years old. The important criterion for

selecting the small sample presented in this study was the possibility of US examination to

identify and record the full extent of carotid bifurcation starting at the common carotid artery at

the base of the neck and by moving the probe distally the internal and external carotid arteries.

The present research was approved by the institutional ethical committee, and all subjects gave

informed consent.

2.1 Data acquisition

The first step involved in developing the stenosis model was data acquisition. Ultrasound

imaging examinations were performed by an experienced certified sonographer dedicated to

neurovascular ultrasound at the Neurosonology Unit of the Department of Neurology of São

João Hospital Centre, in Portugal. For each volunteer, a set of B-mode and pulsed-wave

Doppler images of the CCA, its bifurcation and proximal segments of internal (ICA) and

external (ECA) carotid arteries, was acquired. A high-resolution ultrasound scanner (Vivid e;

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GE, Milwaukee, WI, USA) equipped with a linear array transducer probe (GE 8L-RS) was used

to examine the extracranial carotid arteries. This system with spectrum analysis capabilities

provides high-resolution ultrasonic images with 256 level of gray scale and pulsed-wave

Doppler. To allow the correct reconstruction of the carotid bifurcation luminal surface, the

acquired B-mode longitudinal and transversal images of each carotid vessel were registered at

end-diastole to control physiologic variations of vessel diameter along cardiac cycle. In order to

minimize flow modeling inaccuracies, tracking of the US probe was done by marking positions

along the artery bifurcation relying on the ability to manually guide the US probe.

Six carotid arteries obtained during routine medical examinations were part of this report.

During acquisition procedure ICA stenosis was measured according to European Carotid

Surgery Trial (ECST), the percentage of luminal diameter narrowing at the most stenotic region.

Using pulsed-wave mode, blood flow velocity spectral waveforms were obtained at several

specific locations identified on B-mode imaging, from approximately 2 cm before CCA

bifurcation, until post-bulbar ICA and ECA, including the bifurcation entrance (APEX). Angle

correction was activated as appropriated, always with angle of insonation <= 60° [12].

Ultrasound images were stored to hard disc, for later offline analysis.

2.2 Ultrasound image segmentation

Medical ultrasound images are a huge challenge to automatic segmentation since they are

extremely noisy and diseased arteries bring additional difficulties [25]. B-mode images were

segmented to produce smooth lumen and plaque contours by using an image segmentation

propose-developed MATLAB (The Mathworks Inc. Natick, MA, USA) algorithm [33, 34]. The

referred algorithm for the automatic segmentation of the lumen and bifurcation boundaries of

the carotid artery in ultrasound B-mode images uses the hypoechogenic characteristics of the

lumen and bifurcation of the carotid artery. Each input image is initially processed with the

application of an anisotropic diffusion filter for speckle removal, and morphologic operators are

employed in the detection of the relevant ultrasound data regarding the artery. The information

obtained is then used to define smooth contours, one corresponding to the lumen and the other

8

regarding the bifurcation boundaries, by application of the Chan-Vese level set segmentation

model [5, 19, 33, 34]. Figure 1 presents two examples of segmented cross-sectional B-mode

images considered for surface reconstruction of carotid bifurcation (patient P4).

2.3 Geometrical 3D surface reconstruction

In order to build the lumen surface all acquired longitudinal and transversal images were

segmented. In the plaque region two contours were delineated for each cross-section image,

corresponding to the inner arterial wall beneath the plaque and to the interface between the

lumen and the plaque (Figures 1a) and 1b)). Then 2D smooth lumen contours were stacked in

the axial direction according to each image location obtained during data acquisition. Figure 1c)

presents the assembling of cross-sectional lumen contours. The reconstructed lumen surface was

smoothed in order to reduce misalignment errors due to patient´s involuntary movements during

scan.

The obtained polygonal surface is not directly usable for generating a suitable computational

mesh. It is desirable to impose boundary conditions proximally and distally to the reconstructed

region. Cylindrical flow extensions with a length of four times the local diameters were added at

the inlet and outlet locations, in the direction of the centerlines.

<insert Figure 1 around here>

2.4 Blood flow model

Pulsatile 3D hemodynamics was simulated for each of the six carotid bifurcation geometries

using a self-developed CFD code already validated in previous studies [37,38]. The required

discretization of the domain of interest and blood flow simulation specific features are described

in the following two sections.

2.4.1. Structured mesh generation

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A structured hexahedral mesh of the lumen of the carotid bifurcation was built using grid

generation software. Hexahedral meshes are generally more difficult to generate and time

consuming [3, 8]. On the other hand, for the same accuracy of the result, computer simulations

using hexahedral meshes compared to tetrahedral/prismatic meshes converge better, require less

computational time, and allow a better calculation of the WSS [3, 42].

<insert Figure 2 around here>

Figure 2 illustrates the mesh generation method showing a coarse mesh for the carotid

bifurcation of patient P4. The generation of the volume mesh with hexahedral elements started

by defining three confining cross-sections created as artificial separations of the CCA, ECA and

ICA branches at the bifurcation. Then, the domain was divided into six parts, and mesh

definition was performed maintaining finite elements continuity at each contact surface: first, a

2D quadrilateral mesh was considered in the three confining sections; then, by sweeping or

extruding a 2D mesh of a section (quadrilateral) along a path, a volume mesh was generated

(hexahedrons). Blood motion in vessels is highly directional and the use of computational

meshes with well-organized elements along the main flow direction assures faster convergence

and more accurate numerical solutions [2, 3, 7, 29].

2.4.2. Computational fluid dynamics

Considering isothermal conditions, the time dependent incompressible blood flow is governed

by the Navier-Stokes equations given as:

(

) (1)

where and are the velocity and the stress fields, the blood density and f the volume force

per unit mass of fluid. The components of the stress tensor are defined by the Stokes’ law

( ) (2)

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where p is the pressure, I the unit tensor, he dynamical viscosity ( ) the strain rate tensor

and S the deviatoric stress. Given appropriate boundary and initial conditions, the equation

system Eq. (1) can be solved for the velocity and the pressure. In this study the biochemical and

mechanical interactions between blood and vascular tissue were neglected. The innermost lining

of the arterial wall in contact with the blood is a layer of firmly attached endothelial cells and it

appears to be reasonable to assume no slip at the interface with the rigid vessel wall; at the flow

entrance (host artery) Dirichelet boundary conditions are considered prescribing the Womersley

velocity profile for the time dependent value of the velocity on the portion of the

boundary ( ) ( ) . At an outflow boundary ГN the condition describing

surface traction force h is assumed. This can be described mathematically by the condition:

( (

))

(3)

where nj are the components of the outward pointing unit vector at the outflow boundary. The

numerical procedure for the discretization in space uses the Galerkin-finite element

interpolation of mixed type [37-39].

Blood is a complicated non-Newtonian fluid with shear thinning and viscoelastic properties,

especially when the shear rate is low. The flow field of the carotid bifurcation usually covers a

wide range of shear rate. However, studies suggest that since shear rate in most regions of the

carotid bifurcation is typically between 250 and 450 s-1

averaged over the cardiac cycle, blood

exhibits mainly Newtonian property [22]. Perktold et al. [31] and Fan et al. [10] numerically

compared non-Newtonian and Newtonian models in the human carotid artery bifurcation. They

concluded that blood can be considered as a Newtonian fluid with good approximation. Due to

available levels of geometric precision, and uncertainties related to the inlet boundary

conditions, the assumption of Newtonian rheology is reasonable in the sense that it has been

shown to have only a minor effect on the resulting carotid bifurcation flow dynamics [7, 8, 22,

28, 36]. Furthermore non-Newtonian fluid simulations require greater CPU effort and storage

requirements compared to Newtonian fluid simulations due to the calculation of the diffusion

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matrix at every time step. In this work blood was considered as a isotropic, incompressible,

homogeneous, Newtonian viscous fluid, with a specific mass value equal to 1060 kg/m3 and a

constant dynamic viscosity value equal to 0.0035 kg/(m.s) [38, 39]. Considering all the studied

patients, the Reynolds numbers

based on the CCA inlet mean velocity V and diameter

D were approximately between 750 and 1100 for peak flow rates. In order to solve the

nonlinear system of equations derived from the discretization of the flow equations on the

computational grid, the upwinding method was applied and the backward Euler implicit time

integration scheme was implemented to obtain the solution at each time step of the transient

analysis.

Inlet and outlet flow conditions were available from the Doppler image sets of the six

bifurcations under study. At the flow entrance, CCA inlet Womersley velocity profiles were

imposed [45]. As for the outlets, a common approach was applied by imposing Dirichlet

velocity conditions at ICA (Womersley profiles) and stress-free boundary condition at the ECA

section [14, 17, 23, 27]. Patient-specific CCA and ICA Womersley velocity profiles were

derived from the pulsatile velocity waveforms obtained by pulsed Doppler images and imported

as input data into the FEM software to simulate the fluid dynamics.

The approach introduced by Womersley on pulsatile flow in arteries [45] uses concepts from

fluid mechanics including Poiseuille flow. In order to obtain the longitudinal velocity of a

incompressible fluid in a circular pipe with radius R as a function of the distance r from the axis

and of the time t, ( ), Womersley expresses the pressure gradient as a periodic function of

time using Fourier series. Then the longitudinal velocity is given by

( )

(

( ⁄

)

( )

) (4)

where is the Bessel function, the Womersley number and the term

is the

pressure gradient. Substituting in the previous equation the measured velocity at the center

velocity , ( ) and as J0(0)=1 one obtains

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( )

(

( ⁄

)

( )

)

( (

⁄ )

( )

) (5)

Approximating the measured axial velocity ( ) by a Fourier cosine series, ( )

( ) with k and being the magnitude and the phase, |A| can be obtained:

| | | ( )| |

( )

( ⁄ ) | (6)

and by the product of complex numbers

( ) ( ( )) (

[

( )

( ⁄ ) ]) (7)

Finally, as the true pressure gradient is the real part of the complex pressure gradient:

| | ( ( )) (8)

Figure 3 depicts the selected ultrasound image used to calculate the inlet CCA Womersley

velocity profile for patient P1. Similar images were acquired and analyzed for all six patients to

determine individual boundary conditions at CCA inlet and ICA and ECA outlets.

<insert Figure 3 around here>

To ensure mass conservation, outlet blood flow velocities were corrected using the

instantaneous ratio ICA to ECA flow division and maintaining the CCA flow. The need to solve

instantaneous flow discrepancies was due to uncertainties in measurements or small branches

and the assumption of rigid wall in the simulations. However, distensible arteries might still

produce instantaneous flow mismatches at the bifurcation [14].

Mesh and time-step refinements were performed using the prescribed inlet and outlet

boundary conditions [38]. A mesh sensitivity analysis was considered under steady conditions

to assure grid independence. The grid distribution was not uniform to allow a finer mesh at the

bifurcation, near the stenosis and the walls. In order to enhance calculation precision at the

boundary layer, as wall shear stress and derived quantities are directly linked to carotid

13

hemodynamics, gradually finer grids were employed in the radial direction, near the vessel wall

elements are aligned with the local orientation of the boundary surface [2, 3, 7, 29]. This was

obtained with a locally refined mesh creating one or more layers of prismatic elements having

smaller thickness. Temporal convergence was studied with transient analysis. Refinement of

both spatial and temporal resolutions was performed until changes in predicted velocities and

WSS became insignificant (1.5%). Mesh density with between 60 and 70 thousand hexahedra,

depending on the subject, and constant time-step equal to 2.5x10-3

s were deemed sufficient for

the purposes of characterizing velocities and wall shear stress (WSS) patterns.

2.5 Statistical analysis and WSS-based hemodynamic descriptors

To assess the acceptability of the proposed modeling, an agreement analysis was addressed [20].

Concordance correlation coefficient was calculated using simulated and Doppler systolic

velocities at specific locations corresponding to sites explored during ultrasound examination.

Hemodynamic forces, particularly WSS, play an important role in the development and

progression of vessel wall pathologies. It has been demonstrated that low mean shear stress and

marked oscillations in the direction of WSS may be critical factors in the localization and

development of atherosclerotic plaques [18, 22, 24, 28]. The most widely used wall shear stress

(WSS) based descriptors are the time averaged WSS (TAWSS), the oscillating shear index

(OSI) and the relative residence time (RRT). These descriptors have been found to be the best

metrics for measuring low and oscillating shear at the carotid bifurcation [4, 18]:

( )

∫ | ( )|

(9)

( ) [ (|∫ ( ) |

∫ | ( )|

)] (10)

( )

( )

|∫ ( )

| (11)

where T is the total time of the cardiac cycle, s is the location on the vessel wall and t is the

time.

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TAWSS index is used to evaluate the total shear stress exerted on the wall throughout a

cardiac cycle, and OSI is used to identify regions on the vessel wall subjected to highly

oscillating WSS values during the cardiac cycle. OSI is a dimensionless quantity reaching a

maximum value of 0.5 in regions with the high oscillating shear stress corresponding to a

greater susceptibility to these regions to develop atherosclerosis. Both metrics are related to the

amount of shear stress distributed across the carotid wall. RRT is inversely proportional to the

magnitude of the TAWSS vector which is equal to the term in the numerator of the OSI

formula. The residence time of particles near the wall is proportional to a combination of OSI

and TAWSS, and RRT index has a tangible connection to the biological mechanisms underlying

atherosclerosis [24].

3 Results

Pulsatile hemodynamics was computed for six patients (age 50 to 84 years; 4 males and 2

females). For each analyzed bifurcation, a segmented longitudinal image, patient’s

identification, age, gender and ECST grading of stenosis measured during examination is shown

in Figure 4. For patient P3, no ICA plaque was observed, and for the others, ICA stenosis

varying from 30 to 70% was registered. Patients P4 to P6 presented the highest degree of

stenosis.

The accuracy of results was validated by a statistical analysis performed using simulated and

Doppler systolic velocities at specific locations where Doppler ultrasound measurements were

made. Considering the total sample of systolic velocity pairs (simulated/Doppler) presented in

Table 1, Lin’s concordance correlation coefficient analysis demonstrated an almost perfect

strength of agreement (c = 0.9978) between ultrasound data and numerically calculated values.

<insert Table 1 around here>

Velocity contour plots of various cross-sections for all six cases are shown in Figures 5 and 6

at two time instants of the cardiac cycle, systolic peak and mid deceleration (instants are

15

detailed in Figure 3 for patient P1). For all patients, a stagnation zone was detected near the

outer bulb wall, opposite to the bifurcation divider wall. This stagnation zone was larger during

deceleration phase, as expected. For most patients, a strongly skewed axial velocity in proximal

ICA due to the enlarged bulb region was observed. At systole, patients P2 to P4 exhibited the

highest velocities at ECA as compared to the other patients, which present higher velocities at

ICA; for patients P3 and P4 these high velocity gradients are probably due to the sharp

unevenness of the ECA vessel wall as seen in Figures 5 and 6. At ICA, the highest velocity

gradients were detected during peak systole for patients P1, P5 and P6. For each patient,

simulated velocity values were used to calculate the intra-stenotic peak systolic velocity (PSV)

and the ratio between PSV and CCA peak systolic velocity (ICA/CCA) as depicted in Figure 4.

<insert Figures 4,5 and 6 around here>

Figure 7 presents anterior (left) and posterior (right) side WSS contours at near peak systole

instant for all carotid arteries (P1 to P6). The main features expected from fluid dynamics, such

as low WSS values in the bulb region of the ICA and high WSS at the bifurcation APEX, were

successfully captured. For the non-stenotic bifurcation P3, low WSS patches in CCA were

contiguous with the carotid bulb low WSS region, and a high WSS value of 22 Pa was found at

the carina of bifurcation. All other stenotic patients attended higher values for systolic peak

WSS. Also located at the carina of the bifurcation, maximum values of 32 and 35 Pa of WSS

were calculated for mild stenotic patients P1 and P2, respectively. For the other patients

presenting higher stenosis degree, the highest peak systolic WSS values were computed within

the throat of ICA stenosis. Although in this sample, patient P6 presents the highest stenotic

degree (70%), the maximum value (42 Pa) for near systolic peak WSS was detected for patient

P4 (50% stenosis).

<insert Figure 7 around here>

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The distributions of the WSS-based descriptors obtained on the luminal surface of all

volunteers are shown in Figures 8 to 10. A common feature that can be seen is that TAWSS

(low values) and OSI and RRT (high values) mainly captured apparent flow disturbances at the

same sites: ICA origin and the carotid bulb. Regions of high OSI values up to 0.5 were found at

the ICA origin for all bifurcations and downstream stenosis for patients P4 to P6 presenting the

highest degree of stenosis. WSS-based parameters were also able to capture flow disturbances at

ECA branches for patients P3 to P6.

<insert Figure 8 to 10 around here>

4 Discussion

A noninvasive approach for quantifying a variety of hemodynamic parameters as indicators of

CCA bifurcation problems was presented. Inter-individual variation in flow dynamics was

analyzed considering six individual bifurcations based on ultrasound morphologic and

velocimetric acquisitions.

One of the possible outcomes of Doppler-based hemodynamic simulations is the possibility

of assessing a stenosis diagnosis when grade is so high that aliasing renders determination of the

PSV impossible or irregular calcified plaques obscure the true lumen (space) of the carotid

artery. In order to quantify a stenosis, the ICA/CCA ratio has been considered as a kind of

normalization with ratio >1.5 for high-grade (> 70-80%) stenosis [1]. Our finds agreed with this

classification: for all mild-stenosed patients with ECST graded lower than 70% the maximum

ratio was equal to 1.43 and only for patient P6 presenting an ECST grade of 70% the ICA/CCA

ratio is higher than 1.5 (equal to 3.45).

Considering the total sample of systolic velocity pairs (simulated/Doppler) presented in

Table 1, the calculated Lin’s concordance correlation coefficient was equal to c = 0.9978; This

analysis demonstrated an almost perfect strength of agreement between ultrasound data and

numerically calculated values. Analyzing separately each patient´s model, the concordance

17

analysis for systolic velocity values suggested an almost perfect strength of agreement for

patients P1, P2 and P4 and a substantial degree of agreement for patients P3 and P5.

Different patients exhibited different velocity patterns associated with their morphology and

hemodynamic patient-specific conditions. For patients P2, P3 and P4 during systolic peak, high

velocity gradients were detected at ECA, while for the others, maximum velocity gradients

occurred at ICA; these variations were mainly associated with reduction in lumen section. When

atherosclerotic plaques did not cause relevant stenosis as in patients P1 and P2, maximum

velocities at ICA appeared more distally, and similarly to P3, the non-stenotic case, while for

patients P4 to P6, maximum velocities were detected within stenosis, presenting high gradients.

Two different view angles of WSS distributions near peak systole are shown in Figure 7 for

all the volunteers. Again, different WSS field behaviors were found for the six volunteers.

Furthermore, for all stenosed ICAs, low WSS values were found in the outer wall downstream

stenosis identifying abnormal flow and as expected, high peak systolic WSS values were

observed within the stenosis.

TAWSS distributions obtained for all volunteers are shown in Figure 8. Although low values

were concentrated at the outer walls of the common carotid bifurcations, the patterns were

different: for the non-stenosed ICA (P3), low values were contiguous with bulb region, as for

the other patients, low TAWSS were found at the outer wall downstream stenosis identifying

abnormal flow. Abnormally high TAWSS (higher than 40 Pa) values can cause direct

endothelial injury and increase the risk of getting thrombosis [26]. Such high values of TAWSS

were not identified at any of the analyzed bifurcations. More in depth, for the non-stenosed

bifurcation the highest TAWSS values (7 Pa) were detected at the apex of divider wall of the

bifurcation, as for the severe stenosed bifurcation P6, the highest TAWSS values (from 7 to 9.5

Pa) were found at the throat of the ICA stenosis territory.

In this study, areas of high OSI lying within areas of low TAWSS were located on the outer

wall of ICA (Figure 9), which correspond to recirculation zones consistent with other studies

[24, 27, 28].

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Results shown in Figure 10 also confirm that the RRT distribution captured the main features

of both TAWSS and OSI presenting high values at ICA origin for all patients and downstream

stenosis for patients P4 to P6. Recent studies recommended the relative residence time (RRT) as

a robust single metric of low and oscillatory shear stress [24, 27, 28]. Overall, TAWSS, OSI and

RRT distributions presented in Figures 8 to 10 hint at the correlations among patched regions of

assigned disturbed flows. Low values of TAWSS and high values of OSI and RRT were

assigned to all six bifurcations under analysis, identifying ICA origin as the region of flow

disturbances. Areas of high OSI (higher than 0.3) are predisposed to endothelial dysfunction and

atherogenesis [6, 18]. Low TAWSS values (lower than 0.4 Pa) [26] and high RRT (higher than

10 m2/N) [24, 27] are also known to promote an atherogenic endothelial phenotype. The

distributions of the WSS descriptors for each of the six carotid bifurcations were analyzed in

order to identify whether the sites of extremes for one descriptor would be reflected in the sites

of extremes for another descriptor. Considering a Spearman rank correlation coefficient (r) and

a significance (p-value), correlations having p<0.05 were deemed strong for |r|>0.9, weak for

|r|<0.5, and moderate in between. The correlation coefficient results indicate a strong correlation

for OSI and RRT regions of extreme values for all six bifurcations. Correlation analysis for

TAWSS and OSI (or TAWSS and RRT) suggests a strong correlation for P1, P2 and P6 and a

moderate correlation for P3, P4 and P5. So, in this small patient-specific data sample (P1 to P6),

if regions of low TAWSS values are identified as sites of low and oscillatory shear, then RRT

(or OSI) does not seem such as a robust single metric. Other than plaque induced, patient-

specific hemodynamic conditions might contribute towards disturbed flows, being responsible

for the moderate correlation found among half of the analyzed bifurcations. This discrepancy

can be explained by the fact that WSS descriptors are unable to distinguish between uniaxial

and multidirectional flows [30].

For the normal carotid bifurcation P3 and for the moderately grade stenosis P5, flow

disturbances were captured by the three descriptors at extended sites of ECA branch. This might

be associated to branch geometry and tortuosity occurring at proximal ECA inner wall for P3

and outer wall for P5, leading to high OSI values where blood jet impinges on the wall [23]. On

19

the other hand, for the moderate and high-graded stenosed carotid bifurcations P4 and P6, WSS-

based descriptors capture abnormal flow at less extended areas of ECA wall; whether these

findings are significant in the context of atherosclerosis is to be clarified.

Although the hemodynamic analysis presented here seems to be consistent with previous

works on normal carotid bifurcations [23, 24, 28], real artery morphology and patient-specific

flow velocities were employed, and an obvious question arises if variations were attributable to

morphology or flow velocity differences or both. The analyzed bifurcations indicate that

morphology, as the curvature of the in vivo models, may play a key role in determining wall

shear stress patterns. These findings could help to explain why some individuals develop more

pronounced ICA stenosis than others, although cardiovascular risk factors may be similar and

future further research applicable to large-scale studies of hemodynamic factors in

atherosclerosis should be enforced.

This study indicates that lumen surfaces exposed to significant disturbed flow can be

identified by WSS descriptors, and that morphology plays an important role on the

hemodynamic behavior of the carotid artery bifurcation. It is imperative to include subject-

specific morphology and flow waveform in modeling. This methodology might help to

understand the relationship between hemodynamic environment and carotid wall lesions, and

have a future impact in carotid stenosis diagnosis and management.

5 Conclusions

Patient-based hemodynamic analysis predicts a complex hemodynamic environment with flow

and WSS variations that occur rapidly. A full understanding of hemodynamic changes caused

by the carotid bifurcation and stenosis is meaningful for clinical decisions. In this study, we

presented a noninvasive approach for simultaneously quantifying subject-specific flow patterns

and wall shear stress distributions of human carotid bifurcation using a combination of US data

and CFD modeling. Application of this approach to a normal volunteer and five subjects with

atherosclerosis demonstrated WSS-based descriptors to be correlated and extremely sensitive to

variation in geometry and able to capture flow disturbances due to stenotic plaques. High values

20

of TAWSS were found at carina and stenosis sites of all bifurcations. For the analyzed high-

graded stenosis (ECTS grade of 70%) the highest value of TAWSS was found at ICA stenosis.

For the mild-graded stenosis low values of TAWSS were found at the carotid bulb, ICA and

ECA depending on the hemodynamic features of each patient. The two WSS-based descriptors,

OSI and RRT, assigned highly disturbed flows at the same artery surface regions that correlate

only moderately with low TAWSS indications. One interesting area for further research is to

develop a diagnosis procedure incorporating medical video and 3D ultrasound images. Multiple

views given by medical video allow an improved 3D reconstruction of the carotid artery.

Specifically, video segmentation of the carotid artery may be used to estimate the motion, find

and track the boundaries of the plaque, classifying the motion of the plaque in normal or

abnormal, and thus finding normal and abnormal plaques. Since disturbed hemodynamics

might be important in assessing the prognostic of further progression of the atherosclerotic

disease, the hemodynamic modeling incorporating non-rigid walls will be better suited at

evaluating the tensile stresses within a vulnerable plaque. Subject specific identification of the

link between hemodynamic behavior and stenosis pathophysiology might allow testing

hypotheses and to address important clinical vascular problems, improving diagnostic and

therapy treatment or surgical planning. Further larger prospective studies are required to

validate the use of WSS and its derived parameters before widespread application takes place in

daily medical practice.

Acknowledgment This work was partially done in the scope of project PTDC/SAU-

BEB/102547/2008, “Blood flow simulation in arterial networks towards application at

hospital”, financially supported by Fundação para a Ciência e a Tecnologia (FCT) in Portugal.

Conflict of interest statement

All authors hereby declare no conflicts of interest.

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FIGURE CAPTIONS

Fig. 1 Details for surface reconstruction of carotid bifurcation: segmented cross-sectional B-

mode images - section S1, proximal bifurcation (left), section S2, distal bifurcation (center) and

assembling scheme (right).

Fig. 2 Carotid artery bifurcation mesh: 2D quadrilateral meshes (left), central structure to

connect the three branches (center) and structured mesh obtained by extruding each 2D mesh

along each branch (right)

Fig. 3 Inlet CCA velocity flow for patient P1: pulsed-wave Doppler image (left) and pulsatile

velocity waveform used to set the Womersley approach (right)

Fig. 4 Segmented longitudinal images and identification of patients P1 to P6

Fig. 5 Velocity field (cm/s) at systolic peak (top) and mid deceleration phases (bottom) for

patients P1 to P3

Fig. 6 Velocity field (cm/s) at systolic peak (top) and mid deceleration phases (bottom) for

patients P4 to P6

Fig. 7 WSS contours (Pa) near peak systole for carotid bifurcations P1 to P6: anterior (left) and

posterior (right) side of the carotid artery

Fig. 8 TAWSS descriptor for all patient-specific models: anterior (left) and posterior (right) side

of the carotid artery

Fig. 9 OSI descriptor for all patient-specific models: anterior (left) and posterior (right) side of

the carotid artery

Fig. 10 RRT descriptor for all patient-specific models: anterior (left) and posterior (right) side

of the carotid artery

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28

29

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Ultrasound Image Identification and Data

P1 Age: 73 Gender: Male ECST grade: 30% PSV: 75.0 cm/s ICA/CCA=0.99

P2 Age: 50 Gender: Male ECST grade: 40% PSV: 68.9 cm/s ICA/CCA=1.13

P3 Age: 63 Gender: Male ECST grade: none

P4 Age: 57 Gender: Male ECST grade: 50% PSV: 70.0 cm/s ICA/CCA=1.43

P5 Age: 78 Gender: Female ECST grade: 55% PSV: 92.5 cm/s ICA/CCA=1.40

P6 Age: 84 Gender: Female ECST grade: 70% PSV: 169.5 cm/s ICA/CCA=3.45

Fig. 4 Segmented longitudinal images and identification of patients P1 to P6

31

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Table 1 Simulated/Doppler measured systolic velocities (cm/s) at locations explored during

ultrasound examination of patients P1 to P6. For each individual, Lin’s concordance correlation

coefficient value (c) is shown at the last row

Location P1 P2 P3 P4 P5 P6

Within

stenosis 70.6/71.5 62.2/69 - 65.4/63.5 90.5/89.9 170/190

Distal ICA 102.6/103.4 68.9/68.2 38.0/33.2 99.3/104.6 94.5/87.5 153.5/160.0

Bulb 26.8/27.6 25.6/25.0 13.5/13.7 - - -

At carina 55.3/57.1 96.6/95.9 39.1/38.4 490/478 47.9/47.5 -

Proximal

ECA 74.4/73.6 100.9/101.7 57.9/59.6 91.4/93.0 52.1/42.3 -

Individual

c 0.9990 0.9934 0.9871 0.9992 0.9620 -

36