A parameterized analysis of the mechanical stress for co-ronary plaque fibrous caps

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J. Biomedical Science and Engineering, 2013, 6, 38-46 JBiSE

http://dx.doi.org/10.4236/jbise.2013.612A006 Published Online December 2013 (http://www.scirp.org/journal/jbise/)

A parameterized analysis of the mechanical stress for

coronary plaque fibrous caps

Ramses Galaz, Catherine Pagiatakis, Emmanuel Gaillard, Rosaire Mongrain*

Department of Mechanical Engineering, McGill University, Montreal, Canada

Email: *[email protected]

Received 31 October 2013; revised 28 November 2013; accepted 8 December 2013

Copyright © 2013 Ramses Galaz et al. This is an open access article distributed under the Creative Commons Attribution License,

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

The fibrous cap is a protective layer of connective

tissue that covers the core of an atherosclerotic

plaque. The rupture of this layer has been commonly

associated with acute myocardial infarctions. The

thickness of the fibrous cap, the percentage of stenos-

ed area, and the stiffness of the core were studied

(commonly associated with vulnerable plaque char-

acteristics) to quantify their effects on the cap’s me-

chanical stress state by performing analyses using

computational fluid-structure interaction (FSI) me-

thods. The mechanical stress levels are significantly

increased within the fibrous cap structure at the up-

stream side of the plaque. As expected, the highest

stresses occurred for a severe stenosis and a thin fi-

brous cap. Interestingly, a weak structural support

such as a soft lipid pool beneath the fibrous cap al-

lowed for the hemodynamic pressure gradient forces

to displace the fibrous cap in the direction of the flow,

resulting in higher strains and thus higher mechani-

cal stresses in the upstream portion of the plaque cap,

potentially increasing the risk of cap rupture. The

peak stress behavior of the most critical cases (thin

fibrous cap and soft lipid core) at various degrees of

stenosis was analyzed. For mid-range stenosis from

43% to 75%, there was a plateau region revealing

that mild and moderate plaques were quickly exposed

to the high stress condition of severe plaques. In con-

clusion, the particular combi nation of a mild to severe

stenosis, a thin fibrous cap and a soft lipid core re-

sulted in the highest mechanical stresses calculated at

the proximal side of the plaque. Mild and moderate

plaques can be subjected to stresses similar to severe

plaques, possibly contributing to their rupture.

Keywords: Coronary Atherosclerotic Plaque; Fibrous

Cap; Stenosis Severity; Lipid Core; Fluid-Structure

Interaction

1. INTRODUCTION

Atherosclerosis is a chronic inflammatory response in the

arterial walls that narrows the lumen of vessels by the

gradual deposition of fatty substances, cholesterol crys-

tals, cellular waste products and calcium minerals, and

the growth of connective tissue [1,2]. These localized

pathological lesions are known as atheromatous plaques.

Covering the plaque’s core is the fibrous cap, which is a

layer of fibrous connective tissue and smooth muscle

cells that prevents the core’s highly thrombogenic con-

tents from coming into contact with blood. The rupture

of the fibrous cap, either by mechanical or by biological

factors, may trigger a biological response of platelet ac-

tivation and subsequently thrombus formation. It is esti-

mated that two thirds to three quarters of all arterial

thrombi are caused by plaque rupture [3]. This event

could potentially occlude the vessel and prevent blood

perfusion downstream, resulting in an acute myocardial

infarction. Clinicians have established from histopatho-

logical studies that ruptured plaques share certain mor-

phological and biological features that would make them

more vulnerable to rupture. Unstable lesions with a large

and soft lipid core, many inflammatory cells, and a thin

fibrous cap are typically associated with acute coronary

syndromes [4-6]. It is now recognized that plaque vul-

nerability leading to rupture is an important cause of

myocardial infarction, and sudden cardiac death.

The characteristics of culprit lesions suggest the con-

tribution of mechanical factors in plaque vulnerability for

rupture. From a mechanical point of view, plaque rupture

would occur when the stresses within the fibrous cap

tissue surpass the ultimate strength of the material.

Therefore, identifying the critical stress state within the

diseased tissue could potentially elucidate plaque me-

chanical failure mechanisms. Numerous studies have

demonstrated that plaque component material properties

*Corresponding author.

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R. Galaz et al. / J. Biomedical Science and Engineering 6 (2013) 38-46 39

and lesion morphology influence the mechanical stress

distribution within the fibrous cap tissue and could play

an important role in plaque rupture [7-11].

While there is an agreement in the scientific community

that mechanical factors influence the site and mode of

tissue failure, it is not yet fully understood to which ex-

tent the different factors, specifically fluid and solid

stresses, affecting the initiation and progression of such

failure. A histopathological study of patients who had

died during physical exertion showed that ruptures were

commonly located in the midcap regions of the plaques

whereas patients who died at rest showed shoulder rup-

ture predominance [12,13]. Changes in cardiac output

induce non-uniform changes in both the fluid and solid

stress states and therefore, these findings suggest that

mechanical factors influence plaque rupture, and that

different rupture mechanisms may occur in different pa-

tient cases as a result of altered stress states. For example,

it has been proposed that lateral plaque shoulder ruptures

are the results of cyclic tensile stress induced by the

pressure wave [13] and that the high shear stress up-

stream of the plaque induces fibrous cap thinning [14].

While significant work has been done in order to

evaluate the stresses within unstable plaques, the quanti-

fication of the relative effect of unstable plaque charac-

teristics (core size and stiffness, fibrous cap thickness,

etc.) on the mechanical stress state of the diseased vessel

has not systematically been done. Therefore, the objec-

tive of this study was to evaluate the role of 3D me-

chanical stress as a factor that might contribute to the

vulnerability of plaques for rupture, emphasizing the

morphological and material property features. The phy-

sical interaction between blood flow and the tissue is

examined by using FSI computational models of syn-

thetic and standardized geometries of coronary arteries

with varying degrees of stenosis. The performed analysis

quantifies the effect of the thickness of the fibrous cap,

the stiffness of the core and the degree of luminal nar-

rowing on the plaque cap mechanical stress. These three

variables have been described by pathologists and clini-

cians as those might increase plaque vulnerability for

rupture [4-6].

2. METHODS

2.1. Geometry of Stenosed Coronary Artery

The simplified synthetic geometry of the coronary artery

was cylindrical, with dimensions corresponding to those

of the proximal third portion of the major epicardial

coronary arteries. This location is where most plaque

ruptures are observed and where the risks of obstructing

blood flow to large regions downstream of the myocar-

dium are the highest [15]. The dimensions of the ideal-

ized stenosed coronary artery were: 3 mm for the lumen

diameter of the artery, 0.5 mm for the artery wall thick-

ness, 20 mm for the total length of the artery segment

and 15 mm for the length of the stenosis at its base

(which corresponds to a slightly diffuse thickening). The

center of the stenosis was coincident with the center of

the segment (see Figure 1).

The stenosis geometry was modeled as an eccentric

blister type protrusion using a symmetrical Gaussian

curve along the longitudinal axis and different heights to

mimic different degrees of stenosis (see Figure 2).

Fibrous Cap

L

c

L

S

D

T

w

T

FC

Lipid Core

Figure 1. Schematic of the idealized stenosed coronary artery.

Lc is the length of the coronary artery segment (here of the

cylinder) (=20 mm), Ls the length of the stenosis (=15 mm), D

the coronary artery lumen diameter (=3 mm), Tw the coronary

artery wall thickness (=0.5 mm), and TFC the fibrous cap thick-

ness.

(a) (b)

19%

28%

36%

43%

51%

59%

67%

75%

83%

91%

Fi gure 2. The ten different stenosis severities used in this study.

(a) Longitudinal view, and (b) Radial view.

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R. Galaz et al. / J. Biomedical Science and Engineering 6 (2013) 38-46

40

2.2. Computational Model for the Structural

Domain

The stresses within the fibrous cap were analyzed using a

standard commercial structural mechanics software

(ANSYS, Canonsburg, PA, USA). Since mechanical de-

formations are not large, linear elastic and isotropic ma-

terial properties were used for both the coronary artery

wall and the fibrous cap. The stiffness of the fibrous cap

was initially assumed to be equal to the stiffness of the

coronary artery wall, Ea, and assigned a value of Ea =

800 kPa for the Young’s modulus (calculated using the

Lame equations for the specified vessel dimensions and a

maximum luminal diameter expansion of 5%). The ma-

terial was assumed to be incompressible due to the high

water content in the tissue; therefore a Poisson’s ratio ν =

0.49 was used.

The necrotic lipid core stiffness, Ec, is modeled with a

very low Young’s modulus Ec ≈ 0 Pa, representing a soft

lipid core, to a very high value, Ec >> Ea, representing

very stiff plaque components such as fibrotic tissue cal-

cifications. In this study, the maximum value of the

plaque core stiffness was taken to be equal to that of the

arterial wall. The ratio between the stiffness of the lipid

core and that of the coronary artery wall was defined as γ,

the stiffness ratio (Eq.1).

c

a

E

E



 (1)

2.3. Computational Model for the Fluid Domain

The fluid domain was modeled using a standard com-

mercial computational fluid dynamics package (ANSYS-

CFX, ANSYS Inc., Canonsburg, PA, USA). The income-

pressible and steady-state Navier-Stokes equations (Eq.2)

were used and the flow was assumed to be Newtonian.

2

0

()p



 

 

u

uu u0

(2)

where ρ is the fluid density, u is the velocity, p is the

pressure and µ is the viscosity. The fluid was assigned a

viscosity of 3.6 MPa and a density of 1050 kg/m3 to

match the properties of blood. Physiological hemody-

namic conditions were applied as boundary conditions

with a fully-developed laminar inlet profile (parabolic)

corresponding to a maximum average phasic coronary

flow of 100 ml/min (Figure 3) [16] and a base inlet

pressure of 100 mmHg [17]. The same flow rate was

used in the different models to study the morphological

and material properties. At the fluid-solid interface, no-

slip boundary conditions were applied.

2.4. Coupling of Structural and Fluid Domains

A unidirectionally-coupled fluid-structure interaction

Inlet Velocity Profile

Radial Position [mm]

−1.5 −1 −0.5 0 0.5 1 1.5

Velocity [cm·s

−1

]

50

45

40

35

30

25

20

15

10

5

0

Figure 3. Fully developed inlet parabolic profile corresponding

to a maximum average phasic coronary flow of 100 mL/min.

(FSI) analysis was performed wherein the pressure gra-

dient results obtained from the fluid analysis were ap-

plied as an external load in the structural analysis. A

structural domain change would translate to a change in

the fluid domain in the same proportion. Due to their

small magnitudes, the changes in the fluid domain and

the corresponding changes in flow field were neglected,

allowing for the treatment of the problem using a unidi-

rectional framework. Both fluid and structural domains

were discretized into approximately 50,000 tetrahedral

elements, which was found to be sufficient based on a

mesh sensitivity analysis.

Using the above procedure, 80 parameterized FSI

analyses were performed for a sensitivity analysis to as-

sess the effect of plaque morphology and material prop-

erties on the magnitude of the mechanical stress within

the fibrous cap. The three main variables investigated

were the stenosis severity, the fibrous cap thickness, and

the stiffness ratio. Four different coronary artery stenosis

severities were selected: 36%, 51%, 75% and 91% and

four fibrous cap thicknesses varying from 200 to 500

microns and five stiffness ratios varying from 0.001 to 1

were taken. The results of the parameterized FSI analy-

ses were used to construct surface plots of the resulting

peak stress values within the plaque. The conditions,

with respect to the fibrous cap thickness and the stiffness

ratio, that produced the critical stress state were identi-

fied and utilized in a separate FSI analysis for the en

stenosis severities displayed in Figure 2, in order to as-

sess the impact of stenosis severity on the plaque’s me-

chanical stress.

3. RESULTS

The influence of plaque geometric features on solid

stresses in the vascular wall and fibrous cap were inves-

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R. Galaz et al. / J. Biomedical Science and Engineering 6 (2013) 38-46 41

tigated. More specifically, parameters that have been

clinically reported to influence plaque vulnerability for

rupture, namely fibrous cap thickness, plaque core com-

position, and stenosis severity were considered. All FSI

computations resulted in a stress concentration in the

arterial wall, at the proximal side of the plaque (Figure

4).

3.1. Effect of Lipid Pool Stiffness and Fibrous

Cap Thickness: Sensitivity Analysis

The results of the sensitivity analysis are provided in

Figure 5. The surface plots display the relationship be-

tween the maximum principal stresses in the fibrous cap

as a function of stenosis severity, fibrous cap thickness

and stiffness ratio. As expected, the highest stresses oc-

curred under the condition of the thinnest plaque cap and

the lowest stiffness ratio for all characteristic plaque se-

verities. Moreover, under this critical condition, as steno-

sis severity increased, the magnitude of the maximum

principal stress also increased.

It can be observed in the surface plots that when the

stiffness ratio is greater than a value of approximately 0.3,

the maximum principal stresses in the fibrous cap appear

to become constant, and therefore independent of stiff-

ness ratio, stenosis severity, and fibrous cap thickness.

Below a stiffness ratio of about 0.3, as both the stiffness

ratio and the cap thickness decrease, the maximum

stresses increase. It is interesting to observe that as the

fibrous cap thickness decreases, the calculated stresses

become more sensitive to changes in stiffness ratio

(steeper variations). In other words, at low cap thickness

(for example, at the minimum value), the results show

that a small decrease in the stiffness of the plaque core

results in significant increase in the maximum principal

Distal

Proximal

Blood Flow Direction

Figure 4. Longitudinal view of a typical mechanical stress

distribution obtained from the FSI analysis. All stenosis sever-

ities resulted in high stress concentrations in the arterial wall,

proximal to the stenosis.

(a)

(b)

(c)

(d)

Figure 5. Maximum principal stresses for four different steno-

sis severities: (a) 36%, (b) 51%, (c) 75%, and (d) 91%.

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R. Galaz et al. / J. Biomedical Science and Engineering 6 (2013) 38-46

42

stresses present in the fibrous cap. When the stiffness

ratio is taken to be constant, a decrease in the plaque cap

thickness results in a more direct increase in stresses to-

wards the maximum value at the minimum plaque thick-

ness. It is important to note that the fibrous cap thick-

nesses considered in this study are above the value for

which plaques have been clinically observed to rupture

(approximately 65 microns) [18].

It can be observed that the magnitude of the stresses in

the fibrous cap appear to be independent of the stenosis

severity, even for severe area reductions, when the stiff-

ness ratio is in the range of 0.1 to 0.3. Moreover, when

the stiffness ratio decreases to a low level such that the

core is essentially a soft lipid pool, the magnitude of the

principal cap stresses still appears to be relatively con-

stant for intermediate stenoses, yet increases significantly

when the area reduction becomes severe.

3.2. Effect of Stenosis Severity

The effect of stenosis severity on the stress state of the

fibrous cap was investigated by performing FSI analyses

for ten different area reductions (ranging from 19% to

91%, Figure 2) under the critical stress condition of

small fibrous cap thickness and low lipid core stiffness

ratio. In Figure 6, the normalized principal stress in the

fibrous cap is plotted as a function of the percent area

reduction for the minimal cap thickness (200 microns)

and the minimal lipid core stiffness ratio (0.001), which

appeared from the sensitivity analysis to be the condition

for which the stresses were most sensitive to percent

stenosis.

The results displayed in Figure 6 show three distinct

regions where stresses increase with different rates as a

function of the area stenosis, which correspond to mild,

Percentage of stenosed area [%]

0 10 20 30 40 50 60 70 80 90 100

1

0.8

0.6

0.4

0.2

0

Normalized principal stress

Figure 6. Normalized principal stress for different stenosis

severities in the case of a fibrous cap thickness of 200 microns

and a stiffness ratio between the lipid core and the coronary

artery wall, γ, of 0.001.

intermediate and severe stenoses, based on the percent

area reduction. For both mild (19% to 43% area reduc-

tion) and severe (greater than 75% area reduction)

stenoses, the rate of increase of the peak stress with in-

creasing area reduction is significant, particularly for

severe stenoses which display a steep slope. However, in

the case of intermediate stenoses (43% to 75% area re-

duction), the plot displays a plateau region where there is

a relatively small increase in peak stress over the range

of lesion severity.

4. DISCUSSION

In previous investigations of the role of mechanical fac-

tors on plaque vulnerability for rupture, much focus has

been put on 2D/3D structural finite element analyses

separate from fluid dynamic analyses. For example, stu-

dies have shown through 2D (cross-sectional views) and

3D finite element models that high stress regions corre-

spond to the culprit (rupture) zones in histopathological

studies and that the magnitudes of these stresses are af-

fected by plaque composition and morphology [19,20].

On the other hand, computational fluid dynamics analy-

ses have also correlated the location of high wall shear

stress to that of plaque ulceration [21].

However, when structural and fluid analyses are con-

sidered separately (and particularly in a 2D model), the

true state of the stress tensor is not fully represented for

either domains and the complex interactions between

plaque morphology, plaque composition and fluid and

solid forces on the global stress state cannot be evaluated.

Therefore, in order to obtain a better understanding of

the true physical events taking place in the diseased ves-

sel, it becomes necessary to use 3D models that incorpo-

rate the interactions between the fluid and structural do-

mains. These models would provide more accurate nu-

merical evidence on the spatial stress distribution and the

longitudinal component of the shear stress caused by

blood flow. Moreover, when combined with localized

anisotropic material properties and a mechanical failure

criterion, the analyses could define the proper orientation

and the extent of rupture propagation. The 3D numerical

results could serve as a basis to compare the spatial loca-

tion of the rupture with clinical evidence that often re-

ports plaque rupture locations, for example, at the up-

stream regions of the stenosis [22,23]. Tang and col-

leagues have developed 3D fluid-structure interaction

(FSI) models based on MRI scans and have displayed

that regions of localized maximum stresses, particularly

solid stresses, correspond well with the location of

plaque ulceration identified from histopathological eva-

luations. The magnitude of the stresses in ulcerated

plaques was also found to be higher than that of stable

plaques, and also displayed a general increasing trend in

unstable plaques with larger lipid pools and thinner

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R. Galaz et al. / J. Biomedical Science and Engineering 6 (2013) 38-46 43

plaque caps [17,24,25].

The idea that mechanical factors play a role in the

rupture of plaques has been agreed upon in the scientific

community although the exact mechanisms by which

these factors, specifically solid and fluid stresses, initiate

plaque damage, are unclear. From a mechanical perspec-

tive, it can be expected that the fibrous cap will rupture

when the solid stresses therein surpass the material’s

ultimate strength (Lee and Loree [26]). Consequently, the

global solid stress state within the fibrous cap is a central

factor in the study of plaque fracture mechanics; it is

affected by the fluid forces (cyclic pressure, pressure

gradients) exerted on and the morphology and material

properties of the tissue. Fluid shear stresses could affect

the surface of the plaque as well as activate endothelial

cells to produce and secrete degrading enzymes that

weaken the structure of the fibrous cap.

A stenosis impedes the flow of blood and induces an

energy loss which is reflected as a pressure drop across

the stenosis. This loss in energy is a result of inertial

pressure losses from geometrical changes, and viscous

effect. It is dissipated from the system in the form of heat

(carried away by flow advection), and in the form of ir-

reversible mechanical deformation, specifically of the

viscoelastic fibrous cap which is the most mechanically

solicited component of the plaque. The hemodynamic

pressure gradient exerts a force on and causes deforma-

tion of the plaque in the direction of the bulk flow, which

results in higher solid stresses at the proximal side of the

fibrous cap, compared to the distal side. This effect is

amplified when the fibrous cap of the plaque is thin and

has a weak structural support underneath it, as was

shown in our study for the case of a soft lipid core which

acts as a weak elastic foundation. This effect has also

been proposed by Doriot [27] and Li [11] using theoreti-

cal and numerical calculations with only 2D longitudinal

models of stenosed arteries.

Our numerical results were consistent with clinical

observations. Fujii et al. [22] have shown that most of

the ulcerated ruptured plaques in culprit lesions of acute

coronary syndrome patients were proximal to site of

minimal lumen dimension based on intravascular ultra-

sound imaging studies. Hiro et al. [23] have also reported

ultrasonographic longitudinal views of ruptured coronary

plaques, and most of them were also located in the

proximal region of the plaque.

4.1. Plaque Cap Principal Stresses

Thin fibrous caps and soft lipid cores have been clini-

cally associated with higher rupture risk. The values ob-

tained in this study for the maximum principal stresses

are consistent with similar studies. In a 2D (cross-sec-

tional) structural analysis, Finet et al. [8] obtained maxi-

mum principal stresses in coronary plaques between 100

kPa and 200 kPa (at a pressure of 110 mmHg, a cap

thickness of 200 microns and a core stiffness of 1 kPa)

for stenoses of approximately 50 - 60 percent area reduc-

tion. Our results gave maximum principal stresses of 85

kPa for similar conditions (baseline pressure of 100

mmHg, a cap thickness of 200 microns and a stiffness

ratio of 0.001). Arterial dimensions in Finet et al. were

greater than those in the present study and can account in

part for the differences in stress magnitude.

Tang et al. [24] performed FSI analyses on coronary

plaques for which the morphology was obtained from ex

vivo MRI of cadaveric samples. For an approximate area

reduction of 80%, a pressure of 100 mmHg the maxi-

mum principal stresses were found to range from 100 -

200 kPa at the interface of the lipid core and the lumen,

which again corresponds well to the 90 - 100 kPa stress

range found in the current study for the thin plaque cap

and the soft lipid core. A similar study by the same au-

thors [28], which also addressed the issue of cyclic bend-

ing, found principal stress values within the plaque cap

within the 50 - 80 kPa range.

4.2. Plaque Cap Thickness and Core Stiffness

Our results showed that plaque cap stresses were found

to be very sensitive to small changes in the core stiffness

at low stiffness ratios. These findings are similar to those

of [8] who showed that for a critical cap thickness of 50

microns, a small change from a core stiffness of 25 kPa

to 1 kPa could destabilize the plaque (specifically, in-

crease the circumferential cap stresses over a predefined

threshold corresponding to rupture initiation).

Virmani et al. [18,29] first introduced a critical cap

thickness below which coronary plaques are at high risk

for rupture. This value was found to be approximately 65

microns and has since been adopted by the American

Heart Association. Through computational studies, a cir-

cumferential fibrous cap stress of 300 kPa has also been

found to correspond to the threshold for coronary plaque

rupture [19] and is consistent with the critical cap thick-

ness. Previous studies have found a curvilinear/exponen-

tial relationship between the cap thickness and the

circumferential stresses [8,30], and that significant in-

crease in principal stress with a small decrease in cap

thickness occurs near this critical value. The results of

this study displayed a more direct relationship between

the stress and the cap thickness which seems to contra-

dict previous findings. It is important to note however,

that the minimum cap thickness considered in this study

is well above the critical value and the corresponding

principal stresses are also below the 300 kPa threshold.

The relative contribution/effect of plaque core compo-

sition and fibrous cap thickness has not been elucidated

thus far yet could have significant clinical implications.

The results of our study suggest that one of these vari-

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R. Galaz et al. / J. Biomedical Science and Engineering 6 (2013) 38-46

44

ables may play a more central role in the initiation of

plaque ulceration. The relatively constant principle

stresses when the stiffness ratio is above 0.3, independent

of both fibrous cap thickness and percent stenosis, sug-

gests that there may be a threshold for plaque stiffness

above the risk of rupture is reduced. Furthermore, the

fact that the maximum principal stresses at the minimum

core stiffness were well below the critical plaque rupture

stress, suggests that the thickness of the plaque cap may

have greater influence on plaque vulnerability for rupture

compared to core stiffness.

4.3. Stenosis Severity

One of the most interesting results of this study was a

quasi-constant region (plateau) of peak principal stress

with increasing stenosis severity for intermediate lesions

(the maximum principal stress was relatively insensitive

to percentage of stenosis). A similar observation was

reported in a clinical investigation by Li et al. [11] in the

carotid artery; they found that the peak principal stress

remained relatively constant for a degree of luminal

stenosis comprised between 40% and 60%, and for a

fibrous cap thickness ranging from 0.2 mm to 1 mm.

The clinical implications of these findings are worthy

of note. For intermediate stenoses, the results suggest

that the vulnerability to rupture may be insensitive to the

severity of the lumen reduction (above and below certain

thresholds) in terms of stress loading and the size of the

lipid pool.

4.4. Limitations

The minimum thickness of the fibrous cap in our model

was 200 microns although pathologists have reported

that the typical thickness at which fibrous caps fail is

around 65 microns [29]. This value facilitated the mesh-

ing of the fibrous cap and allowed to avoid being in a

situation of rupture. However, the computed stress could

be underestimated.

Another limitation of this model was that the me-

chanical properties of the fibrous cap were the same as

those of the artery wall. The mechanical properties of the

fibrous cap are still unknown, and they can vary from

patient to patient. The fact that the fibrous cap is mostly

composed of collagen fibers and some smooth muscle

cells is hint that it is reasonable to assume that its me-

chanical properties are similar to the artery wall. How-

ever, it should be somewhat stiffer since it has a higher

ratio of collagen although it was found in [17] that in-

creasing the stiffness of the fibrous cap by 100% has

minor effects (less than 2%) on the stress state within the

cap.

Finally, in order to obtain a more accurate model in

terms of anatomical structure and physiological condi-

tions, it becomes necessary to analyze realistic geome-

tries of the coronary arteries and include more realistic

material properties such as viscoelasticity and anisotropy

of the connective tissue. Furthermore, it has been shown

that cyclic bending of the arteries can have a significant

effect on the magnitude of the peak principal stresses

[28]. This idea is of particular importance for coronary

arteries which are subjected to such a loading due to the

cyclic contraction of the heart, and must be considered in

order to better understand the relative importance of

plaque morphology (size and cap thickness) and plaque

composition on its vulnerability to rupture.

5. CONCLUSION

Using FSI simulations, the 3D mechanical stress in dis-

eased coronary arteries was calculated for varying plaque

cap thickness, lipid core stiffness and stenosis severity

and evaluated as a factor that might contribute to a

plaque’s vulnerability to rupture. The peak principal

stresses were observed at the proximal side of the plaque

in all FSI analyses which was consistent with pathologi-

cal observations for plaque ulceration locations. The im-

portant findings of this investigation included the fact

that 3D mechanical stresses were observed to be more

sensitive to changes in fibrous cap thickness compared to

changes in core thickness which suggested that cap

thickness could play a more central role in plaque rupture

vulnerability compared to other morphological plaque

characteristics. It was also found that at a critical cap

thickness, a small change in plaque composition could

significantly change the peak principal stresses and thus

the plaque’s vulnerability to rupture. Furthermore, the

peak principal stresses of moderate stenoses (ranging

from 43% to 75% area reductions) were found to be

generally unaffected by stenosis severity (at a particular

cap thickness and core stiffness), displayed by a plateau

in the stresses as a function of severity. This observation

not only suggests that moderate and even mild plaques

could have the same vulnerability to mechanical failure

but that they can be subjected to stresses similar to se-

vere plaques that could contribute to their rupture.

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