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: [email protected]
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
4
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.
5
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
6
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;
7
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
11
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.
14
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
27
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
32
33
34
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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