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9
Carotid Plaque Stresses
Samuel Alberg Kock1 and Jens Vinge Nygaard2
1Aarhus
University Hospital Skejby, 2Aarhus University: iNANO
Denmark
1. Introduction
Cardiovascular atherosclerotic disease is the leading cause of death and severe disability
worldwide (Rosamond et al., 2007; WHO and CDC, 2004; Yusuf et al., 2001). Carotid
atherosclerotic plaques are a major cause of cerebrovascular thromboembolic events
including transitory ischemic attacks and strokes (Virmani et al., 2006; Redgrave et al., 2006;
Nighoghossian et al., 2005; Carr et al., 1996).
1.1 Current Carotid Risk Assessment
In current clinical practice, selection for surgical removal of the carotid plaque (carotid
endarterectomy) is determined by the degree of luminal narrowing known as the degree of
stenosis (Rothwell et al., 2003a). The operation has been determined beneficial in patients
with symptomatic, severe stenosis in two large, randomized trials; the North American
Symptomatic Carotis Endarterectomy Trial (NASCET, 1991) and the European Carotid
Surgery Trial (ECST, 1998). To determine the degree of stenosis, NASCET and ECST used
measurements based on x-ray digital subtraction angiographies. Today, Doppler ultrasound
is used in clinical practice for determination of the degree of stenosis (Nederkoorn et al.,
2003; Titi et al., 2007). This technique does not rely on direct measurements of the degree of
stenosis but uses determination of maximum peak systolic and end diastolic blood flow
velocities as well as the spectral composition of these velocities to assess the degree of
stenosis. The ultrasound Doppler techniques, though in universal clinical use, are
problematic due to problems with the insonation angle affecting the Doppler equation (Tola
and Yurdakul, 2006; Claudon et al., 2001), inter- and intra-observer variations (Mead et al.,
2000; Lui et al., 2005), and interpretation in the presence of complex geometries (Clevert et
al., 2006; Clevert et al., 2007).
Preventive treatment of patients with carotid plaques but no symptoms (asymptomatic
patients) would be preferable but is controversial, since trials have shown only marginal
effect of treatment from current risk stratification, and total mortality after five years is
unchanged in treated vs. untreated groups (Halliday et al., 2004; Redgrave et al., 2006). To
prevent a single stroke, the number needed to treat for symptomatic patients is seven
(Rothwell et al., 2003a) rising to forty for asymptomatic patients (Halliday et al., 2004).
Using the current risk assessment algorithm, the majority of patients operated are thus
needlessly exposed to peri-operative risks. Further, atherosclerotic plaques tend to grow
outwards initially, which may result in normal luminal size belying substantial plaque
volumes, a process known as arterial remodeling (Glagov et al., 1987; Glagov et al., 1988;
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Pasterkamp and Smits, 2002) making risk assessment based on the degree of stenosis
problematic. In addition, most ruptured plaques are less than 50% stenosed, the current
limit at which carotid endarterectomy is offered (Casscells et al., 2003; Falk et al., 1995).
Thus, the decision of whether or not to operate is based on scientifically problematic
methodologies. A great need therefore exists for improved methods of selecting patients
with carotid atherosclerosis who may benefit from operation.
1.2 Vulnerable Plaque Features
Histological examinations have determined the hallmarks of plaques at risk of rupture
(vulnerable plaques) to be large lipid-rich, necrotic cores covered with thin fibrous caps
(Virmani et al., 2006; Gronholdt et al., 1998; Falk, 2006; Naghavi et al., 2003; Casscells et al.,
2003; Virmani et al., 2000; Stary et al., 1995). Many studies have shown that inflammation
and the subsequent immune response contribute to atherosclerosis. Further, blood pressure
is known to influence the incidence of strokes (Kario et al., 2003; Staessen et al., 1997; Dart
and Kingwell, 2001; Rothwell et al., 2003b).
1.3 Plaque Imaging
Through the advent of high-resolution in-vivo imaging techniques such as intravascular
ultrasound (Sipahi et al., 2007; Imoto et al., 2005), optical coherence tomography (Huang et
al., 1991; Yabushita et al., 2002), and magnetic resonance imaging (MRI) (Yuan and Kerwin,
2004), detailed morphologic and structural characterization of atherosclerotic plaques has
been enabled. In particular, MRI has proven a valuable modality for imaging carotid
plaques with the capability of non-invasively imaging necrotic cores (Yuan et al., 1997; Yuan
et al., 2001), fibrous caps (Hatsukami et al., 2000; Yuan et al., 2002; Mitsumori et al., 2003),
and presence of intraplaque hemorrhage (Chu et al., 2004). Indeed, the characterization of
atherosclerotic lesions using MRI approaches histological definitions (Cai et al., 2002).
Recently, semi-automated tissue segmentation has been enabled (Liu et al., 2006).
Furthermore, MRI has the ability to measure blood velocities through phase-contrast
imaging (Firmin et al., 1990; McDonnell, III et al., 1994) and deformations using cine MR
imaging (Draney et al., 2002; Metafratzi et al., 2002).
1.4 Computational Simulations of Plaque Stresses
Since plaque rupture by definition represents a structural failure of the protective fibrous
cap, it seems reasonable to assume that plaque morphology as well as biomechanical
properties of the atherosclerotic lesion may influence the plaque vulnerability. To estimate
stress levels in the fibrous cap, fluid structure interaction analysis has emerged as a tool
combining blood flow simulation through computational fluid dynamics combined with
finite element analysis of the corresponding stress levels in the surrounding tissues. Thus, a
number of studies have been performed investigating intraplaque stresses as a potential risk
marker of vulnerable plaques (Li et al., 2006a; Imoto et al., 2005; Kaazempur-Mofrad et al.,
2004; Chau et al., 2004; Steinman, 2002; Huang et al., 2001; Li et al., 2006b; Tang et al., 2004;
Zhao et al., 2002). Indeed, in vitro studies of coronary arteries have shown markedly
elevated fibrous cap stresses in ruptured coronary lesions compared to stable lesions (Cheng
et al., 1993) and a recent publication found carotid fibrous cap stress levels in symptomatic
patients to be nearly twice those of asymptomatic patients (Li et al., 2007).
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In principle, 3D simulations of fibrous cap stresses would be preferable since they inherently
provide more information than 2D sections. However, the computational demands for
performing 3D fluid structure interaction simulations are great requiring substantial
solution times. Thus, simulations in 2D cross-sections corresponding to either histological
data (Cheng et al., 1993) or MRI scans (Li et al., 2006a) have been suggested. Though the use
of cross-sectional data matches the orientation of the available morphologic data, this
approach precludes fluid structure interaction analysis and necessitate assumptions
regarding the longitudinal blood pressure distribution used to load the blood/vessel wall
interface. We have recently developed a novel semi-automated method of creating
longitudinal 2D models from transverse MRI scans allowing simulations of longitudinal
stress distributions including the effects of fluid structure interactions and determination of
correct blood pressure distribution enabling predictions of plaque rupture risk and
examinations of correlations between local stress variation and morphology.
To investigate the clinical usefulness of the method, we performed fluid-structure
interaction simulations of an idealized carotid artery based on the geometry of a
symptomatic patient. We investigated the impact of different known markers of plaque
vulnerability, i.e. propensity for rupture, namely degrees of luminal stenosis, fibrous cap
thicknesses, lipid core sizes, and lipid core positions to determine their effect on plaque
stress levels and risk of plaque rupture.
2. Morphology Generation
A variety of imaging modalities have been employed for generating morphology suitable
for computational fluid dynamics simulations including magnetic resonance imaging (Li et
al., 2006a; Tang et al., 2004), intravascular ultrasound (Wentzel et al., 2003; Ramaswamy et
al., 2006), computed tomography (Jin et al., 2004), and optical coherence tomography (Chau
et al., 2004). In particular, magnetic resonance imaging has gained widespread usage as the
method-of-choice for producing computational fluid dynamic models given the modality’s
excellent soft tissue contrast and inherent capability of obtaining velocity images alongside
the morphological imagery. In addition, dynamic deformational images may be obtained
allowing for evaluations of the computational simulations with regards to induced
deformations. In the present work, magnetic resonance imaging was used to scan a a male
patient (age 69) with a 70% stenosed carotid artery, awaiting surgery for carotid
atherosclerosis who gave informed written consent before participation. The protocol was
approved by the local ethics committee.
2.1 Plaque Morphology
The critical plaque components to be identified include lipid-rich necrotic cores, fibrous
caps, and intraplaque hemorrhages. Histological studies have demonstrated that plaque
tissue components often exist in a mixture state, especially in advanced lesions. Thus lipidrich necrotic cores largely consist of cholesterol esters, free cholesterols, and triglycerides,
which all contribute differently to the MRI signal based on their physical states (Yuan et al.,
2001; Small and Shipley, 1974). In addition, signal features of intraplaque hemorrhage may
change depending on the evolution stage (Chu et al., 2004). A single contrast weighting is
thus insufficient for characterizing plaque tissues. Therefore, noninvasive visualizations of
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carotid plaque morphology mainly rely on multispectral (or multicontrast) weighted MRI
techniques to characterize atherosclerotic lesions.
A well-validated MRI multicontrast protocol has been developed for the noninvasive
detection and characterization of atherosclerotic plaques in carotid arteries employing T1weighted (T1W), T2-Weighted (T2W), Proton Density Weighted (PDW), and Time Of Flight
(TOF) scans (fig. 1) (Yarnykh and Yuan, 2003; Yuan and Kerwin, 2004; Cai et al., 2002).
A
B
Figure 1. Custom Matlab toolbox for measuring time-resolved deformation. A: Crosssectional B-TFE MRI scan with contour of CCA outlined in red. B: Top left: Deformation as a
function of time and radial angle. Top right: mean deformation as a function of radial angle.
Bottom left: Mean radial deformation overlaid the MRI scan. Bottom right: Mean (solid line),
maximal (dashed line), and minimal (dotted line) deformation
Though current state of the art MRI protocols for carotid plaque imaging have an accuracy
proven to approach histological AHA classifications of plaque morphology (Cai et al., 2002),
current spatial resolution of the employed sequences is only 0.6x0.6x2 mm. The critical
fibrous cap thickness is typically thought to be below 0.25 mm in the carotid artery, and
below 0.1 mm in the coronaries (Bassiouny et al., 1997; Li et al., 2006b; Imoto et al., 2005).
Increasing spatial resolution of MRI scans to enable visualization of very thin fibrous caps of
0.25 mm or below in thickness could thus prove of importance. Moving towards scanners
with higher field strengths (Yarnykh et al., 2006) or switching from 2D to 3D acquisitions
(Koktzoglou and Li, 2007) may facilitate this.
Presently, complete morphological imaging of the carotids requires scans with a total
duration of approximately 45 minutes. Though shortened scan times would be desirable in
terms of clinical feasibility, signal-to-noise ratios will thereby be negatively impacted. The
conflicting demands of time requirements and signal-to-noise ratio must be considered, and
compromises reached. The increased signal-to-noise ratio of scanners with higher field
strengths and 3D acquisitions may also be used for shorter scan durations instead of
increased resolution.
The carotid arteries are superficial structures whose length is greater than their distance
from the surface, a configuration well suited for the use of phased-array coils consisting of
several adjacent small surface coils from which data are collected simultaneously (Hayes et
al., 1996; Botnar et al., 2001; Roemer et al., 1990). Such coils have been reported to increase
signal-to-noise ratio by 37% and would be preferable for carotid imaging (Yuan and Kerwin,
2004).
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2.2 Velocity Measurements
Phase-contrast MRI scans may be used to measure time-resolved blood velocities in the
internal (ICA), external (ECA), and common (CCA) carotid arteries over a cardiac cycle. The
accuracy of phase-contrast MRI is generally considered high, even in unsteady flows as
present in patients with severe degrees of stenosis (Frayne et al., 1995).
The measured velocities were applied at the ICA and ECA as parabolic flow profiles.
Previous studies have shown non-parabolic velocity profiles in the carotid arteries affecting
the WSS distributions (Perktold and Rappitsch, 1995). However, since stress levels are
mainly the result of pressure distributions rather than effects of blood flow adjacent to the
vessel walls, these are thought to be less affected thereby.
2.3 Vessel Deformation
Vessel deformation can be monitored using a cine MRI Balanced True Field Echo sequence
(B-TFE). A custom Matlab toolbox (fig. 1) was constructed allowing semi-automatically
measurements of deformations as a function of time and radial position. An initial circle
surrounding the carotid vessel was drawn, the center of mass found, and a polar image
constructed of the carotid vessel. Using thresholding, the vessel outline was detected and
transformed back to a Cartesian space. Snakes were used to generate smooth outlines
surrounding the vessel (Yuan et al., 1999).
The measured deformations can be used for tuning material parameters of the tissue
surrounding the carotids to ensure deformations in the computational simulations matches
the in-vivo measurements.
2.4 Segmentation
As previously stated, atherosclerotic tissues may exhibit heterogeneous signal levels
necessitating the use of multicontrast protocols. Table displays the appearance of typical
plaque features on the different contrast weightings. Given this heterogeneity,
reproducibility of the segmentations might have been expected to be low. However, the
opposite holds true, studies have shown excellent reproducibility of MRI-based
segmentations of carotid plaque morphological features.(Yuan et al., 1998; Shinnar et al.,
1999) Further, all the scans presented in I, II, and III were validated by an experienced
reviewer at the Vascular Imaging Lab at the University of Washington, USA. Recently, an
approach utilizing computational morphology enhanced probability maps was described
allowing for fully automated segmentation of carotid plaque morphology.(Liu et al., 2006)
MR Contrast Weighting
Plaque Component
TOF
T1W
PDW
T2W
Recent intraplaque hemorrhage
+
+/0
-/0
-/0
lipid-rich necrotic cores
0
+
-/0
-/0
Intimal calcifications
-
-
-
-
Table 1. Magnetic resonance imaging criteria used to identify plaque tissue components
(Yuan et al., 2001). The intensities listed are relative to the adjacent sternocleidomastoid
muscle
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2.5 Computational Model Generation
The segmented data describing the spatial distribution of plaque components in each MRI
slice were exported as a collection of spline curves. These were imported into Matlab®
R2006b (The MathWorks Inc., Natick, MA, USA) and converted to 2D grayscale images (fig.
2). From the 2D images, a region-of-interest was selected and collected into a single 3D
matrix describing the spatial distribution of segmented tissue within the scanned volume.
The dataset was resampled using linear interpolation to obtain an isotropic voxel size of
0.3125x0.3125x0.3125 mm3 followed by Gaussian smoothing.
Figure 2. (A) Four MRI weightings were performed in order to enable segmentation into
blood, vessel wall, and lipid-rich necrotic core. PDW=Proton Density Weighted image,
T2W=T2 Weighted image, T1W=T1 Weighted image, TOF=Time Of Flight scan. (B) Greyscale images were constructed from the segmented MRI images and used for constructing
logical images oft he plaque morphological distribution. Visible features include blood
stream (red), vessel wall (purple), and lipid-rich necrotic cores (yellow)
From the isotropic dataset, isosurfaces surrounding each component were created (fig. 3A).
To create a longitudinal 2D model, the 3D isosurface model was sectioned along
skeletonization points by a Non-Uniform Rational B-Spline (NURBS) (Piegl and Tiller, 1997)
surface (fig. 3A), yielding a final 2D model to be analyzed (fig. 3B). To minimize boundary
effects the model was extended linearly 5 cm up- and downstream, corresponding to
approximately five times the CCA diameter.
The close proximity of blood lumen and lipid-rich necrotic cores, with fibrous cap
thicknesses of 0.25 mm or below may cause problems with overlapping isosurfaces in some
patients, necessitating manual adjustment of interpolation and smoothing parameters.
Further, due to the slice thicknesses of 2 mm employed in the MRI scans, the flow divider
was seldom depicted and the resulting longitudinal model had a distinct flattened profile at
this location. Thus manual adjustment of the area surrounding the flow divider from
longitudinal MRI scans was needed.
Initially, the patient was scanned using the aforementioned magnetic resonance protocol
which was used to generate an initial model using the described methodology. In order to
suppress local effects of uneven vessel wall borders, a simplified longitudinal model was
created using the previously generated curves as guidelines. A cosine function was used to
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generate the walls surrounding the plaque, initially calculated horizontally before being
rotated using the plaque angle (-65.5°).
(1)
where f = horizontal plaque height, S = degree of stenosis in percent, MS = amplitude at
100% degree of stenosis, mS = amplitude at 0% degree of stenosis (negative), and l = length
of stenosis. User-selected amplitudes (S) were applied to simulate models with 95%, 90%,
80%, and 70% degrees of stenosis, measured using the NASCET standard (Rothwell et al.,
2003a). Lipid pools were generated as ellipsoids with varying sizes (6x3 mm, 4x2 mm, and
2x1 mm) inside the plaque area at specified locations to generate models with
proximal/distal lipid core position and decreasing fibrous cap thicknesses (0.5, 0.2, 0.1, and
0.05 mm).
Figure 3. (A) A 3D skeletonization was performed on the blood-stream and a NURBS
surface constructed intersecting the center of the blood stream throughout the model. (B)
Intersections between NURBS surface and the iso-surfaces delineating the plaque tissues
were used to derive a longitudinal 2D model which was embedded in a slab of surrounding
tissue. External boundary conditions are also presented, rollers at top and bottom with fixed
boundaries at either side. ICA = Internal Carotid Artery, ECA = External Carotid Artery,
CCA = Common Carotid Artery, VICA = Velocity at ICA, VECA = Velocity at ECA, PCCA =
Pressure at CCA
2.6 Boundary Specifications
Blood flow was simulated as Navier-Stokes flow and treated as an incompressible,
homogeneous, Newtonian, viscous fluid with a density of 1050 kg/m3 and dynamic
viscosity of 0.0035 Pa·s. The two outflows were specified as parabolic velocity outlets using
the phase-contrast MRI measured mean blood flow velocities of the patient at the internal
and external carotids (fig. 3B). A no-slip boundary condition was applied along the bloodstream/vessel wall interface, and an Arbitrary Lagrangian-Eulerian (ALE) formulation was
used to couple the fluid forces to the structural deformation and vice versa along the vessel
wall/blood-stream interface. Reynold’s number in the normal healthy carotid is insufficient
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to warrant turbulence modeling, however flow fields in carotid phantoms with large
degrees of stenosis are more accurately depicted using κ-ω models than both laminar flow
and κ-ε turbulence models (Banks and Bressloff, 2007). If blood flow is modeled as being
turbulent, recent research suggests that the κ-ω model is superior with regard to flow field
depiction (Banks and Bressloff, 2007), thus this model was chosen.
A carotid pulse pressure profile was measured noninvasively using the applanation
tonometry technique (Chen et al., 1996; Zhao et al., 2002) with a high-fidelity external
pressure transducer (SPT-301, Millar Instruments Inc., Texas, USA) applied to the skin
above the common carotid artery. The pulse pressure profile was scaled using the systolic
and diastolic blood pressures of the patient and applied as the inlet boundary condition at
the common carotid inlet.
The model was embedded in a rectangle of surrounding tissue the width of which was
determined from cross-sectional MRI scans. Left and right boundaries were fully
constrained and top and bottom boundaries (excluding the fluid boundaries) constrained in
the Z-direction. The boundary between the top surrounding tissue block and vessel wall
was also fully constrained (fig. 3B).
Using MRI phase contrast scans, fluid velocities were measured at both outlets in the patient
with 70% degree of stenosis. To account for the change in velocities caused by the varying
degree of stenosis, the internal carotid artery was modeled as a Venturi tube:
(2)
where Q = volumetric flow rate, C = coefficient of discharge (0.77), D1 = diameter of normal
internal carotid artery (after the stenosis), D2 = diameter of internal carotid artery at
maximal point of constriction, Δp = pressure difference, and ρ = mass density of blood (1050
kg/m3).
Initial conditions were specified using the diameters and flow measured in the patient to
estimate the pressure difference. Subsequently, the D2 diameter was changed to that of the
individual degrees of stenosis, and the resulting flows (Q) were used to calculate the
velocities in the internal carotid artery in each of the models. To preserve common carotid
flow rate, the loss in internal carotid flow was assigned to the external carotid. Laminar,
parabolic velocity profiles were assigned at both outlets using the calculated velocities. The
systolic blood pressure of the patient was prescribed at the inlet (160 mmHg ≈ 21.300 Pa).
The blood was initialized using the inlet blood pressure and mean external outlet velocity.
Although a simplification, blood was simulated as a Newtonian fluid with a constant
viscosity. Due to the content of formed elements within the bloodstream shear thinning
occurs in vivo and the viscosity is not constant. However, recent research (Lee and
Steinman, 2007) suggests that the use of Newtonian models for simulations of blood flow
are reasonable in the carotid artery.
2.7 Material Properties
Tissues were simulated as isotropic homogenous entities. To account for the non-linear
stress/strain dependency of human tissues, a computationally efficient Neo-Hookean
hyper-elastic model was used to specify the material properties of the tissues using the
following strain energy function (W):
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Carotid Plaque Stresses
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(3)
where µ designate the initial shear modulus and is the first deviatoric strain invariant, J is
the ratio of the deformed elastic volume over the undeformed volume, and K is the bulk
modulus calculated as follows:
(4)
where C1 and C2 are the material constants in the Mooney-Rivlin hyper-elastic model (the
Neo-Hookean model can be considered a subset of the Mooney-Rivlin model with C1 = 0
and C2 = µ / 2), ν represents Poisson’s ratio, assigned to be 0.495 to mimic the almost
incompressible human tissues. The initial bulk modulus K was thus set to 100 times that of
the initial shear modulus. The initial shear modulus µ was set to 6 MPa for the vessel wall
(COMSOL AB, 2005). Lipid was treated as an isotropic material with Young’s modulus set
to 1/100th that of the equivalent Young’s modulus of the vessel wall (Young’s modulus =
1E5 Pa, Poisson’s ratio = 0.45) (Tang et al., 2004). The initial shear modulus of the
surrounding tissue was adjusted until the deformation near the common carotid inlet
matched that measured by MRI B-TFE scans as measured by the change in vessel diameter
between diastole and systole.
The Neo-Hookean model is considered to be valid for the moderate deformations present in
atherosclerotic plaques and was validated with a geometry similar to a previously
described model (Li et al., 2006b). Other researchers have used linear orthotropic models
(Imoto et al., 2005), modified Mooney-Rivlin models (Chau et al., 2004; Tang et al., 2004),
and Ogden hyperelastic models (Li et al., 2007; Versluis et al., 2006; Antheunis et al., 2006).
Since different hyperelastic models and material specifications may substantially affect
resulting stress levels, comparison of stress levels between different models should be
interpreted with caution.
To simplify the present finite element analysis, the materials were assumed to be isotropic,
incompressible, and uniform solids. By assuming that plaques, lipids, and normal arterial
walls could each be characterized by a single set of structural variables, spatial and
interspecimen variations within a particular component were not considered (Holzapfel et
al., 2004). However, these assumptions have been widely accepted as allowable for the
assessment of biomechanical properties of atherosclerotic lesions (Loree et al., 1992; Cheng
et al., 1993; Imoto et al., 2005).
2.8 Solving the FSI model
The coupled fluid–structure interaction simulations were performed using COMSOL, a
commercially available finite element solver (COMSOL 3.4, COMSOL Inc, Stockholm,
Sweden). Streamline diffusion was applied to artificially stabilize the solution.
3. Results
Two examples of velocity fields, first principal stress distributions, and velocity streamlines
are presented in fig. 4. A 90% degree of stenosis model with a proximal 6x3 mm lipid core
and minimal fibrous cap thickness of 0.2 mm yielded maximal principal stresses of 674.4 kPa
occurring at the area of minimal fibrous cap thickness (fig. 4A, red arrowhead). Immediately
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adjacent to the area with maximal first principal stresses equal to tensile stresses, was a
pressure zone with negative first principal stresses of -101.4 kPa (fig. 4A, white arrowhead).
A second model with 80% degree of stenosis, a distal 4x2 mm lipid core, and minimal
fibrous cap thickness of 0.2 mm is presented in fig. 4B. The velocities in the internal carotid
artery were higher in this model due to the Venturi calculations, generating a large zone of
recirculating blood above the plaque (fig. 4B, yellow asterisk). Again, maximal (fig. 4B, red
arrowhead) and minimal (fig. 4B, white arrowhead) first principal stresses were found to be
adjacent and located at the area of minimal fibrous cap width, with a magnitude of 429.1/89.5 kPa, respectively.
Figure 4. Examples of the results generated from the simulations. Arrowheads mark the
location of maximal/minimal first principal stresses, red/white respectively. Insets depicts
areas of maximal/minimal stress levels. (A) Carotid with 90% stenosis, proximal 6x3 mm
lipid pool, and minimal fibrous cap width of 0.2 mm. (B) Carotid with 80% stenosis, distal
4x2 mm lipid pool, and minimal fibrous cap width of 0.2 mm. A large zone of recirculating
blood was present above the plaque (yellow asterisk)
The combined effects of degrees of stenosis, fibrous cap thicknesses, lipid core size, and lipid
core location on peak principal stress levels are depicted in fig. 5. Stresses are seen to
increase with decreasing fibrous cap thickness, and increasing degrees of stenosis. However,
the degree of stenosis mainly affects peak principal stresses in models with fibrous caps
below 0.2 mm in width. This is evident by the observation that the variation in peak
principal stresses increases as the fibrous cap width decreases. Lipid core sizes have a
marked influence on peak principal stress levels. Peak principal stress in a model with 95%
degree of stenosis, a proximal lipid core, and fibrous cap thickness of 0.1 mm varied from
1861.2 kPa with a 6x3 mm lipid core to 445.6 kPa with a 2x1 mm lipid core.
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Figure 5. Effects of fibrous cap thickness, degree of stenosis, lipid core size, and lipid core
position on peak principal stress levels
The longitudinal position of the lipid core did not affect peak principal stress levels in this
model, as shown in fig. 5. Also evident in fig. 5 are the effects of decreasing lipid core sizes
producing substantial reductions in median peak principal stress levels.
I
Figure 6. Principal stress levels and deformations as a function of lipid core position in a
model with 90% degree of stenosis, 0.5 mm fibrous cap thickness, and 6x3 mm lipid core
size
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n another model with a 90% degree of stenosis employing the original flow values measured
in the patient with a 70% degree of stenosis instead of using the Venturi calculations, lipid
core position was seen to influence peak principal stress levels substantially, as presented in
fig. 6. Using this model, peak principal stresses were 323.4 kPa, 335.0 kPa, and 64.6 kPa in
the proximal, central, and distal lipid core simulation, respectively.
4. Discussion
Currently, carotid risk assessment is based on measuring the degree of stenosis to determine
if carotid endarterectomy should be offered symptomatic patients (NASCET, 1991; ECST,
1991; Rothwell et al., 2003a). However, there is growing evidence that morphological
composition rather than degree of luminal stenosis may be the deciding factor in
determining plaque vulnerability (Virmani et al., 2006; Gronholdt et al., 1998; Falk, 1992). In
particular, large lipid cores with thin fibrous caps have been determined to be the hallmark
of unstable plaques at high risk of rupture. Through the advent of high-resolution MR
imaging combined with computational analysis, in-vivo estimations of mechanical stresses
in the fibrous cap have been enabled (Li et al., 2007; Tang et al., 2004; Zhao et al., 2002).
In a recent study by Li et al. (Li et al., 2006b), the effect of stenosis severity and fibrous cap
thickness on resulting mechanical stress levels was investigated. This study showed that
plaques with a degree of stenosis at 70% or above all gave rise to high fibrous cap stress
levels regardless of fibrous cap width. Plaques with lower degrees of stenosis also reached
high stress levels depending on the thickness of the fibrous cap. However, to simplify the
computational analysis a straight tube without bifurcation was used and the plaque was
modeled as a large homogeneous lipid core covered by a fibrous cap of varying thickness.
In our study, we used an idealized bifurcation model based on geometry obtained from a
patient awaiting carotid endarterectomy. Ellipsoidally shaped lipid cores were used to
create heterogeneous plaques with varying position of the lipid cores allowing for
examinations of the effects of lipid core size and position in addition to the effects of the
degree of stenosis and fibrous cap width. To account for the effect of increasing degrees of
stenosis on fluid flows, the internal carotid artery was modeled as a Venturi tube, and the
velocities adjusted accordingly.
The findings of Li et al. (Li et al., 2006b) were confirmed; increasing degrees of stenosis and
decreasing fibrous cap thicknesses were found to affect peak principal stress levels severely
(fig. 5). Though decreases in fibrous cap width was by far the most influential parameter on
fibrous cap stress levels it cannot stand alone. Lipid core sizes also impacted mechanical
stress levels significantly (fig. 5) and a comprehensive approach towards fibrous cap
mechanical stress estimations is deemed important.
In an angiographic study of plaque ulceration, Lovett (Lovett and Rothwell, 2003)
determined ulcerations to be asymmetrically distributed longitudinally with the majority
occurring upstream to the plaque rather than downstream. To investigate if this
phenomenon could be attributed to mechanical stress levels, symmetrical simulations were
performed with lipid cores placed proximally and distally inside the plaque. However, no
significant differences were found between models with proximal cores vs. distal cores,
indeed the stress levels were virtually identical except for very small lipid cores (fig. 5). This
effect may be due to the modeling of the internal carotid artery as a Venturi tube keeping
the pressure difference across the stenosis constant. Thus a second round of simulations was
performed using the original flow values measured in the patient with a 70% degree of
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Carotid Plaque Stresses
159
stenosis instead of adjusting these using the Venturi calculations. These revealed vast
increases in stress levels if the fibrous cap was thinnest on the proximal side of the plaque,
compared with the distal side. These results thus agree with the findings of Lovett (Lovett
and Rothwell, 2003), and principal stress levels may be the cause of the asymmetrical
longitudinal distribution of plaque rupture with the majority occurring proximally to the
plaque.
Previous studies have used principal stress levels in excess of 300 kPa to be predictive of
plaques at high risk of rupture (Cheng et al., 1993; Li et al., 2006b; Li et al., 2007). However,
the choice of material model and parameters may substantially affect simulated stress levels
(Li et al., 2006a). Care should thus be taken comparing absolute stress levels across different
simulations employing different material models, and the choice of an absolute level at
which the plaques are considered to be at risk of rupture may be problematic.
Currently, state-of-the-art MRI scans employ typical in plane spatial resolutions of 0.5 – 0.6
mm (Yuan and Kerwin, 2004; Crowe et al., 2005). Stress levels increased dramatically with
decreasing fibrous cap widths, particularly below 0.2 mm. Increasing spatial resolution to
enable visualization of very thin fibrous caps could thus prove of vital importance. Moving
towards scanners with higher field strengths (Yarnykh et al., 2006) or switching from 2D to
3D acquisitions (Koktzoglou and Li, 2007) may facilitate this.
5. Conclusion
The new technique of obtaining longitudinal 2D computational models of the carotid artery
was systematically investigated using idealized carotid bifurcation geometry with variables
thought to be linked to risk of carotid plaque rupture; degree of stenosis, fibrous cap
thickness, and lipid core size, all of which affected stress levels severely. Numerous
histopathological studies have indicated lipid pool size and fibrous cap thickness to be key
determinants of plaque vulnerability. Principal stresses may be of additional merit, since
this parameter combines effects of fibrous cap thickness, lipid pool size, degree of stenosis,
and blood pressure into a single comprehensive risk assessment marker. With the advent of
fast computational techniques for obtaining in-vivo stress levels, assessing risk of plaque
rupture using peak principal stress levels is enabled which may lead to improved reliability
of carotid risk assessment in the future.
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Modelling and Simulation
Edited by Giuseppe Petrone and Giuliano Cammarata
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