biomechanical factors in coronary vulnerable plaque risk ...xuan lianga, michalis xenosa,e, yared...

Biomechanical factors in coronary vulnerable plaque risk ofrupture: intravascular ultrasound-based patient-specificfluid–structure interaction studiesXuan Lianga, Michalis Xenosa,e, Yared Alemua, Suraj H. Rambhiaa, Ifat Lavic,d,Ran Kornowskid, Luis Grubergb, Shmuel Fuchsd, Shmuel Einava,c

and Danny Bluesteina

Objectives The aim of this study was to elucidate the

mechanisms and underlying biomechanical factors that

may play a role in the risk of rupture of vulnerable plaques

(VPs) by studying patient-based geometries of coronary

arteries reconstructed from intravascular ultrasound

(IVUS) imaging utilizing fluid—structure interaction (FSI)

numerical simulations.

Background According to recent estimates, coronary

artery disease is responsible for one in six deaths in the

USA, and causes about one million heart attacks each year.

Among these, the rupture of coronary VPs followed

by luminal blockage is widely recognized as a major

cause of sudden heart attacks; most importantly,

the patients may appear as asymptomatic under

routine screening before the occurrence of the index

event.

Materials and methods FSI simulations of patient-based

geometries of coronary arteries reconstructed from IVUS

imaging were performed to establish the dependence of

the risk of rupture of coronary VP on biomechanical factors,

such as the fibrous cap thickness, presence of

microcalcification in the fibrous cap, arterial anisotropy, and

hypertension.

Results Parametric FSI simulations indicated that

mechanical stresses (von Mises stresses) increase

exponentially with the thinning of the fibrous cap as well as

with increasing levels of hypertension. The inclusion of a

microcalcification in the fibrous cap considerably increases

the risk of rupture of VP , with an Btwo-fold stress increase

in the VP stress burden. Furthermore, the stress-driven

reorientation and biochemical degradation of the collagen

fibers in the vessel wall because of atherosclerosis

(studied with an anisotropic fibrous cap 658 fiber

reorientation angle) results in a 30% increase in the stress

levels as compared with simulations with isotropic material

models, clearly indicating that the latter, which are

commonly used in such studies, underestimate the risk of

rupture of VP.

Conclusion The results indicate that IVUS-based patient-

specific FSI simulations for mapping the wall stresses,

followed by analysis of the biomechanical risk factors, may

be used as an additional diagnostic tool for clinicians to

estimate the plaque burden and determine the proper

treatment and intervention. Coron Artery Dis 24:75–87 �c2013 Wolters Kluwer Health | Lippincott Williams & Wilkins.

Coronary Artery Disease 2013, 24:75–87

Keywords: anisotropic fiber orientation, coronary vulnerable plaque,fibrous cap, fluid–structure interaction, hypertension, microcalcification,patient-based geometry

aDepartment of Biomedical Engineering, Stony Brook University, bDepartment ofMedicine, Division of Cardiovascular Medicine, Stony Brook University Hospital,Stony Brook, New York, USA, Departments of cBiomedical Engineering,dCardiology, Rabin Medical Center, Petah Tikva and the Sackler School ofMedicine, Tel Aviv University, Tel Aviv, Israel and eDepartment of Mathematics,University of Ioannina, Ioannina, Greece

Correspondence to Danny Bluestein, PhD, Department of Biomedical Engineer-ing, Stony Brook University, HSC T18-030, Stony Brook, NY 11794-8181, USATel: + 1 631 444 2156; fax: + 1 631 444 6646;e-mail: [email protected]

Received 16 July 2012 Revised 30 September 2012Accepted 21 October 2012

IntroductionCardiovascular disease is the primary cause of death in

developed countries. According to recent estimates, B62

million Americans have single or multiple types of

cardiovascular diseases [1–3]. Vulnerable plaque (VP) is

typically composed of a large necrotic lipid pool covered

by a thin fibrous cap that may trigger rapid thrombosis

upon rupture and cause a severe heart attack. Luminal

thrombosis resulting from plaque rupture may be caused

by erosion of the thin fibrous cap and stress concentra-

tions that arise from calcified spot inclusions in the

fibrous cap [4–7]. Fibrous cap formation occurs as a result

of accumulation from an inflammatory cell-rich fatty

streak lesion [8,9]. Over 50% of fibrous caps are

distributed in the proximal artery and most frequently

in the left anterior descending artery [10]. Virmani

et al. [2,11] defined VPs as those with a thin fibrous cap

(23±19 mm), aggressively penetrated by macrophage,

T cells, and an underneath necrotic core. Dhume

et al. [12] reported that the mean thickness of the fibrous

cap from asymptomatic (before the index event) plaques

was 129±10 mm, whereas it was 35±3 mm in symptomatic

Pathophysiology and natural history 75

0954-6928 �c 2013 Wolters Kluwer Health | Lippincott Williams & Wilkins DOI: 10.1097/MCA.0b013e32835bbe99

Copyright © Lippincott Williams & Wilkins. Unauthorized reproduction of this article is prohibited.

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cases. Stable plaques can be diagnosed and treated by

interventional techniques. However, it is the asympto-

matic plaques that carry greater risk of rupture, leading to

higher rate of morbidity and mortality [13,14]. A cap

thickness of 65 mm was established as a criterion for the

assessment of plaque vulnerability because the mean cap

thickness for 95% of the caps actually measured less than

64 mm in arteries with ruptured plaque [9].

It has been suggested that early calcification formation in

coronary arteries is an active process, and results from

calcification of smooth muscle cell organelles [15]. In

addition, pulse pressure is a well-recognized biomarker

routinely used for the risk assessment of cardiovascular

diseases [16,17]. For instance, hypertension has been

considered to play a role in the pathogenesis and risk of

rupture of abdominal aortic aneurysm [18]. However, the

influence of hypertension on coronary VP is not well

established. Coronary calcifications correlate with plaque

burden [2,5,6,11]. The precise mechanism that augments

critical stresses was initially unclear, as macrocalcifica-

tions underlying or adjacent to a lipid-rich necrotic core

have been proposed previously to have a stabilizing

effect [19,20]. However, Vengrenyuk et al. [5] have shown

that stress-induced debonding of microcalcification (micro-

Ca) embedded in a fibrous cap can trigger the rupture of

thin-cap fibroatheroma. These micro-Ca are dangerous if

they lie near the region of high peak circumferential

stress (aka ‘hoop stress’). The spherical inclusion, with

sizes typically ranging from 10 to 20 mm, intensifies the

local stress up to 545 kPa (considered to be a threshold

for the fibrous cap rupture) or higher when the cap

thickness is less than 65 mm [4].

In the early stage of pathogenesis, patches of arterial

endothelial cells start to secrete adhesion molecules,

which can bind to leukocytes, and the expression of these

molecules is characterized as a response to vascular injury

that eventually develops atheroma [21]. Macrophages

accumulate within regions of high stress, usually at the

shoulders of the fibrous plaque, and express the multi-

domain enzyme MMP-9. These enzymes contribute

toward the vulnerability of the plaque by slowly degrad-

ing collagen type I fibers and elastin, decreasing the

tensile strength of the tissue, allowing it to be more prone

to rupture. Macrophages are the cells predominantly

occurring at the immediate site of either rupture or

superficial erosion of the fibrous cap [22]. The resulting

orientation of the collagen fibers in the subendothelial

layer is not uniform throughout the vessel wall [23].

In this study, fluid—structure interaction (FSI) simula-

tions were conducted in patient-based geometries of

coronary arteries reconstructed from intravascular ultra-

sound (IVUS) imaging datasets. Our main goal is to

elucidate the role of biomechanical factors in the risk of

rupture of VP by establishing the correlation and

dependence of stress/strain distributions on parameters

such as the fibrous cap thickness, hypertension, the

presence of micro-Ca in the fibrous cap, and arterial

anisotropy. Our studies suggest that IVUS-based FSI

numerical simulations can provide insights into the

location and magnitude of critical stresses for the

potential rupture location in coronary VP assessment.

Materials and methodsIntravascular ultrasound imaging protocol

IVUS is a minimally invasive, catheter-based imaging

technique for the evaluation of coronary plaque, lumen,

and vessel dimensions. IVUS can measure lumen, plaque,

and vessel area as well as morphological features of the

vessel. Calcified regions and dense fibrous tissues appear

bright and homogeneous because of a good reflection of

the ultrasound energy. IVUS has the ability to localize

plaques and quantify plaque burden with a spatial

resolution of B150 mm when using a 20 MHz phase array

and a 2.9 F catheter. In this study, we have used Virtual

Histology (VH), an advanced IVUS imaging technique

(IVUS-VH) for tissue characterization of plaques using

spectral analysis of the radiofrequency data (Eagle Eye;

Volcano Corporation, Rancho Cordova, California, USA).

The VH technique provides quantitative assessment of

the wall morphology and maps the various plaque

components. IVUS-VH, which is based on spectral and

amplitude analysis of the IVUS backscatter signals, allows

reliable characterization of the mechanical and acoustic

properties of various vascular tissues [24–26]. The raw

signals from reflection of ultrasound waves are transduced

into a color-coded representation of plaque components

and their composition properties.

Three-dimensional reconstruction of the vulnerable

plaque structures

A three-dimensional (3D) mesh of the arterial anatomy

and the complex plaque geometry was reconstructed by

collecting the IVUS-VH cross-section images along the

path of the center of the catheter. The segmented

contours were imported to Avizo (version 6.1.1; VSG,

Merignac Cedex, France) and a surface was generated for

each tissue. The Avizo software package allowed us to

thoroughly examine the generated surface by enabling a

high-end rendering. A dedicated application written in

Matlab (MathWorks Inc., Natick, Massachusetts, USA)

was used to evaluate the plaque area and its component

characteristics on the basis of the IVUS-VH images.

Morphological operations have been applied to obtain

smoother IVUS-VH images. An edge detector generated

boundary lines for the various plaque components, and

automatic labeling defined the region of each tissue. The

rendered composite 3D geometry, including the fluid

domain and the various components of the VP solid

domain, was then converted into triangular finite

elements mesh using a mesh generation package

(Gambit; Ansys Inc., Canonsburg, Pennsylvania, USA).

The solid domain consisted of the fibrotic artery wall,

76 Coronary Artery Disease 2013, Vol 24 No 2


calcium, necrotic core, and media (Fig. 1a). The FSI

simulations were performed using the ADINA FSI

software package (ADINA R&D Inc., Watertown,

Massachusetts, USA).

Four IVUS-based patient-specific coronary plaques with

various fibrous cap thicknesses were reconstructed and

incorporated into the analysis. Specifically, the fibrous cap

thickness varied from 400 to 150 mm for case I, from 250

to 150 mm for case II, and from 600 to 300 mm for case III

(all visualized with current IVUS resolution). For case IV,

we have studied the effect of VP fibrous cap thickness by

artificially incorporating a thin fibrous cap with a uniform

thickness of 65 mm, which is considered the threshold

thickness of an unstable plaque. The reconstructed

coronary vessel (case I) is shown in Fig. 1a, composed

of the vessel wall (silver), the necrotic core (red), and

macrocalcifications (white).

To study the contribution of a calcified spot toward the

fibrous cap stress burden, a rigid spherical inclusion with

10 mm diameter was placed distal to the plaque shoulder

within the thin region of the fibrous cap [5,6]. Both global

and local von Mises stresses were compared. Local stress

is defined as the stress distribution directly in the region

where the micro-Ca were embedded (as opposed to the

global maximum stress showing the overall peak stress

value in the VP structure). The local stress concept was

used to study the effect on the stress distribution within

the fibrous cap with or without micro-Ca inclusion by

comparing the local stress for both baseline and micro-Ca

cases. This facilitated better differentiation of the local

Fig. 1

130(a) (b)

(c)

Pressure

Flow velocity

PressureVelocity

Time (s)

Cauchy stress

Pre

ssur

e (m

mH

g)

120

110

100

90

Vesselwall

Microcalcification

LumenCase l

Necroticcore

80

70

60

50

400 0.2 0.4

1.3

1.2

1.1

1.0

400

�2

�θ

200

01.0

1.1

1.2

1.3

0.6 0.8 10

0.1

0.2

0.3

Flow

vel

ocity

(m/s

)

0.4

0.5

(a) Reconstructed coronary artery (case I): this geometry is composed of the arterial wall (silver), macrocalcification (white), and the necrotic core(red). (b) Pressure and mean flow velocity were extracted from patient coronary measurement and were applied at the outlet and inlet of the vessel,respectively [27]. (c) Three-dimensional representation of the axial and circumferential Cauchy stress over corresponding stretches for a fibrous capwith a 65o collagen fiber orientation angle.

IVUS-based patient-specific FSI studies Liang et al. 77


impact of the micro-Ca on stress distributions within the

fibrous cap. A similar concept has been used by us

previously in micro-CT-based VP studies [4,7]. Hyper-

tension was represented by elevating the physiologically

normal pressure by 25% for the entire cardiac cycle (e.g.

the peak systolic pressure was increased from 122 mmHg

for the normal blood pressure (BP) case to 152.5 mmHg

in the hypertensive case).

Material modelsIsotropic material models for vessel and fibrous cap

A nonlinear, modified Mooney–Rivlin isotropic material

model was used to characterize the material property of

the coronary vessel, including arterial wall, the necrotic

core, and calcification. The isochoric elastic response of

the strain energy function (per unit volume), c, for the

isotropic Mooney–Rivlin model, without the hydrostatic

pressure term, – pI, is shown in Eqs (1) and (2).

c¼C1ðI1�3ÞþC2ðI2�3ÞþD1½expðD2ðI1�3ÞÞ�1�; ð1Þ

I1¼trðCijÞ; I2¼1

2I2

1�CijCij

� �; J¼l1l2l3¼ det F;

ð2Þ

In an incompressible material formulation, the arbitrary

hydrostatic pressure work, – pI, commonly known as

reaction stresses, is always considered in the stress

representation. Scalar p is chosen to maintain incompres-

sibility, which means that det F is equal to 1 and is

separately interpolated. Where I1 and I2 are the first and

the second strain invariant of the strain tensor, the

isotropic strain energy function shown in Eq. (1) can be

used to calculate the second Piola–Kirchhoff stress tensor,

S, by taking the derivative of the function with respect to

right Cauchy–Green tensor, C. With the calculated stress

tensor, the Cauchy stress obtained through the relation

r = FSFT, where F is the deformation gradient, can be

used to fit the experimental data to generate material

constants [28]. The material constants, Ci and Di, were

taken from a previous experiment [29,30]. All values used

in the simulations can be found in Table 1.

Anisotropic material model for the fibrous cap

An anisotropic material model was applied to examine the

high degree of anisotropy of the fibrous cap material. The

anisotropic strain energy function, c (per unit volume;

without the hydrostatic pressure term – pI) is shown in

Eqs (3) and (4).

c¼C1ðI1�3ÞþD1ðeD2ðI1�3Þ�1Þþ k1

2k2

ðek2ðI4�1Þ2�1Þ; ð3Þ

I1¼trðCijÞ; I4¼CijðnaÞiðnaÞj: ð4Þ

This model is a combination of the Holzapfel anisotropic

material formulations, which describe the arterial wall as

fiber-reinforced tissues, with a Fung-type material [31],

where I4 is the pseudoinvariant of the strain tensor,

incorporating the fiber angle into the function, and k1 and

k2 are material constants that are specifically associated

with anisotropic characteristics. na is the angle between

the collagen fiber and the circumferential direction in the

vessel; thus, it acts as a geometrical parameter [19,32,33].

Various fiber angles, for example 5, 65, and 851, were used

to represent both healthy and diseased fiber directions. A

651 fiber angle represented a VP with a fully developed

fibrous cap according to the literature [33]. The 3D

representation of the axial and the circumferential

Cauchy stresses over corresponding stretches (Fig. 1c)

shows the general stress behavior of the above anisotropic

material model ranging from small to large strain

conditions applied for the case of a fibrous cap with a

651 fiber orientation. It serves to illustrate the unique

stress stiffening behavior of anisotropic material models

that generate a lower stress within most of the stretch

range (compared with isotropic models such as Mooney–

Rivlin-type models), but increase exponentially under

higher stretch range conditions (characteristic of the VP

rupture range).

Fluid–structure interaction methodology

The FSI VP patient-based reconstructed models were

used to study the blood flow and stress/strain distribu-

tions on the wall in the vessel. Blood flow (density and

viscosity of 1.050 g/cm3 and 3.5 cP, respectively) was

assumed to be laminar, Newtonian, viscous, and incom-

pressible. The governing Navier–Stokes equations were

solved in the FSI scheme using an arbitrary Lagrangian–

Eulerian formulation. In coronary circulation, there is a

typical 721 phase lag between the coronary peak pressure

and the resulting flow (Fig. 1b). This is partially because

of the fact that the coronaries are mostly compressed

during the vigorous left ventricle systolic contraction,

resulting in most of the coronary perfusion delivered

during diastole [27]. Pressure boundary dynamic wave-

form condition was applied at the outlet of the vessel and

the mean flow velocity waveform was applied at the inlet

(waveforms shown in Fig. 1b). For the vessel wall, both

the inlet and the outlet were constrained to move only in

the axial direction [31], and 10% prestretching was

applied to the vessel [34–37]. Natural traction equili-

brium and no-slip conditions were applied at all inter-

faces. Displacements that the fluid and solid domains

underwent were equalized and fully compatible [31,32].

Table 1 Material parameters determined for the material modelused in our simulations

Model C1 (kPa) D1 (kPa) D2 k1 (kPa) k2 Fiber angle

Vessel wall 28.14 1.31 11.5 – – –Necrotic core 0.5 0.5 0.5 – – –Calcification 281.4 13.1 11.5 – – –Anisotropic fibrous tissue 8.29 0.907 3.1 8.824 3.7 51, 651, 851



For FSI, both solid and fluid domains of the VP model

were simulated numerically using the ADINA FSI

package (ADINA R&D Inc.), using a first order finite

element scheme to solve the set of motion and fluid

equations [6,31,32]. A direct numerical approach was

used for the integration of the highly nonlinear coupled

system of equations.

Grid independence studies and computational capacity

Mesh was locally refined at the boundaries of the distinct

components of each plaque. Computational mesh size

was considered grid independent when less than a 4%

solution difference was achieved between different mesh

sizes. A 1 mm elemental size was used to mesh the

embedded micro-Ca to capture the finer details of stress

distribution around them in the fibrous cap [32]. The

final luminal blood flow domain contained 17 367, 34 781,

82 319, and 48 984 elements for cases I, II, III, and IV,

respectively. The solid domain, which was composed of

the vessel wall, the necrotic core, macrocalcification, and

embedded micro-Ca, had 184 244, 231 605, 816 529, and

196 185 elements in cases I–IV, respectively. The domain

was initially pressurized for 1 s to reach a physiological

pressure of B90 mmHg. Then, two complete cardiac

cycles, initially with 100 time steps for each cycle (initial

Dt = 0.01 s), were simulated. Automatic time stepping

control was applied to obtain a optimized converged

solution by subdividing the time step until the solution

reached convergence [31,32]. The FSI simulations were

conducted on a high-capacity computing cluster com-

posed of four quad core Xeon CPUs with a shared

memory of 64 GB RAM. The CPU time for each

simulation was B4 days for the finest grid.

ResultsIn this study, we combined IVUS-VH with FSI simula-

tions to determine the biomechanical factors that play a

role in the risk of rupture of coronary VPs, including

hypertension, vascular calcification, and fibrous cap

anisotropy.

Patient-specific baseline models

Four IVUS-based patient-specific coronary plaques de-

scribed in the Materials and methods section were

studied with various cap thicknesses. The typical

characteristics of these four vessels are presented

in Table 2. They were chosen as baseline samples, with

normal pressure applied, with no micro-Ca inclusions in

the fibrous cap, and with the fibrous cap modeled as an

isotropic material. Calculated Reynolds numbers at the

inlet of the fluid domain at peak flow were 458 in case I,

247 in case II, 459 in case III, and 339 in case IV. Wall

shear stresses (WSSs) at peak flow were 157, 125, 310,

and 96 dyn/cm2, in cases I–IV, respectively. WSS remained

high throughout the entire cardiac cycle, and the maximal

flow velocity was found during diastole due to the phase

lag that characterizes coronary flow and confers the

maximum perfusion during diastole (Fig. 2, for case I).

Specifically, high WSS and high blood flow velocity also

occurred at mean arterial pressure (MAP), defined as the

pressure at diastole plus one-third of the sum of systolic and

diastolic pressures: MAP¼Pdiastoleþð1=3ÞðPdiastole�PsystoleÞ.Elevated and higher peak wall stress concentration regions

characterized the fibrous cap, mostly at the thinner portion

of the fibrous cap, which is considered mechanically weaker

(Fig. 3). As a normal pressure waveform was applied to the

vessels in all four cases, this verified that the highest stress

is most likely to occur at where the coronary fibrous cap was

the thinnest. This was the location of the maximal von

Mises stresses, peaking at 77, 172, 82, and 267 kPa during

diastole, and MAP stresses were 66, 130, 33, and 210 kPa for

the four cases, respectively (Table 3).

The effect of hypertension

Following a 25% simulated BP increase and compared

with the corresponding normal BP, the von Mises stress

concentrations along the fibrous cap increased by 32, 34,

34, and 30% for cases I–IV, respectively. The wall stresses

corresponding to MAP were 83, 170, 45, and 254 kPa,

respectively (Fig. 4). WSS were 152, 156, 340, and

124 dyn/cm2, for cases I–IV, respectively. For the case I

hypertensive case, where the vessel is B60% stenosed,

the peak velocity somewhat decreased (from 1.94 to

1.82 m/s) because of dilation of the vessel compared with

the normal BP case. In the other three cases, the peak

velocities remained almost the same (Table 3).

Effect of microcalcification

The inclusion of a micro-Ca in the fibrous cap, modeled

as a sphere with 10 mm diameter, has been shown to

further burden the VPs by markedly increasing the local

stress distribution around the lesion. The local maximal

von Mises stresses increased from 43 to 103 kPa for case I,

Table 2 Diseased arteries and plaque characterizations

Participants RepresentationMaximum diameter

(cm)Minimum diameter

(cm)Fibrous cap thickness

(mm) Length of the vessel (cm)Large

calcificationNecrotic

pool

Case I 0.36 0.21 150–350 3.04 + +

Case II 0.23 0.20 150–250 3.60 + +

Case III 0.16 0.14 > 300 1.75 – +

Case IV 0.21 0.20 65 3.10 – +

+ / – , present/not present.



153 to 408 kPa for case II, 60 to 154 kPa for case III, and

232 to 510 kPa for case IV as compared with the baseline

models. The highest stresses occurred at the interface

between the fibrous cap and the micro-Ca. These values

represent 2.4-, 2.6-, 2.5-, and 2.2-fold local increases

(Table 3).

The effect of anisotropy of the fibrous cap

Anisotropic FSI simulations with varying fiber orienta-

tions were studied to delineate the effect of tissue

anisotropy on the rupture risk. Maximum circumferential

stress values of anisotropic FSI simulations with 5, 65,

and 851 fibrous cap fiber angles were 250, 265, and

Fig. 2

Diastole Systole MAP

WSS

Velocity (m/s)

14.0013.0012.0011.0010.009.008.007.006.005.004.003.002.001.00

1.0500.9750.9000.8250.7500.6750.6000.5250.4500.3750.3000.2250.1500.0750.000

Maximal flow

Fluid wall shear stress (WSS) and velocity profiles at four different stages of the cardiac cycle for case I. (Top: from left to right): Flow waveform atdiastole, systole, peak flow rate, mean arterial pressure, and overlapped pressure and flow waveform showing a phase-shifted condition. Themaximum WSS and velocity are observed in the region of maximum stenosis (60%). WSS and velocity are relatively low at systole and are converselyhigher at diastole because of the phase lag. MAP, mean arterial pressure.



244 kPa, respectively (Table 4). These values show a 23,

30, and 20% increase compared with the 204 kPa

circumferential stress value predicted in the isotropic

baseline model. The simulation results presented

in Table 4 with different fiber angles predicted higher

stress with increasing degree of fiber anisotropy, with the

651 fiber angle producing the highest value – previously

identified ex vivo as an angle characterizing atherosclero-

tic vessels [33]. In the simulation with a micro-Ca

inclusion in the fibrous cap and anisotropic tissue model

with a 651fiber angle, von Mises stress peaked at 626 kPa,

increasing by 23% as compared with its isotropic counter-

part. This translated into a 2.35-fold increase in von

Mises stress in the fibrous cap in the presence of micro-

Ca for the anisotropic fibrous cap case, as compared with

the 2.2-fold reported for the isotropic case.

Fig. 3

Case I

Case II

Case III

Case IV

Maximal stress (77 kPa)




SMOOTHEDEFFECTIVESTRESSRST CALCTIME 1,400




240000

5875055000512504750043750400003635032500287502500021250175001375010000

25006250

22000020000018000016000014000012000010000080000600004000020000

72000660006000054000480004200036000300002400018000120006000

1175001100001035005000087500800007250045000575005000042500350002750020000125005000

Von Mises stress distributions (isotropic material model). All four cases show higher stress regions in their fibrous caps. Stress values increaseconsiderably and respond exponentially with the thinning of the fibrous cap. On average, the fibrous cap thickness reduces from case I to case IV.



Table 3 Summary of maximal von Mises stress, mean arterial pressure stress, peak velocity, peak wall shear stress, and circumferentialstress

Maximal stress global (kPa) Maximal stress local (kPa) MAP stress (kPa) Peak velocity (m/s) Peak wall shear stress (dyn/cm2)

Case IBaseline model 77 43 66 1.94 157Hypertension 102 (32%) – 83 (26%) 152Micro-Ca 103 (34%) 103 (140%) 84 (27%) 153

Case IIBaseline model 172 153 130 0.96 125Hypertension 230 (34%) – 170 (31%) 156Micro-Ca 408 (137%) 408 (167%) 386 (197%) 118

Case IIIBaseline model 82 60 33 0.86 310Hypertension 110 (34%) – 45 340Micro-Ca 154 (88%) 154 (157%) 41 310

Case IVBaseline model 267 232 210 1.02 96Hypertension 348 (30%) – 254 (21%) 124Micro-Ca 510 (92%) 510 (120%) 372 (77%) 95

MAP, mean arterial pressure; micro-Ca, microcalcification.

Fig. 4

Physilogical pressure Hypertensive Stress (Pa)

Case II

Case I

Case III

Case IV

Maximum (77 kPa) Maximum (102 kPa)

96000880008000072000640005600048000400003200024000160008000

12533311466710400093333826677200061333506674000029333186678000

8640081000756007020064800594005400048600432003780032400270002160018200108005400

230000210000190000170000150000

110000

7000050000

1000030000

90000

130000


Maximum (82 kPa)


Maximum (110 kPa)

Zoom-in view of the von Mises stress distributions along the fibrous cap from four hypertensive simulations. Hypertension increases the stressconcentration in the fibrous cap in a close to linear relationship.



DiscussionFSI simulations were carried out using a coronary artery

model reconstructed from IVUS-VH imaging data. The

methodology of combining FSI simulation and recon-

struction of clinical imaging data from IVUS-VH that

enables one to assess the plaque morphology and

progression, for example, as parametrically studied with

varying degrees of fibrous cap anisotropy that is related to

the disease progression, has already shown its versatility

and usefulness in studying various vascular pathologies

such as carotid artery disease [38], abdominal aortic

aneurysm, and coronary plaques [6,30]. In this study, it

was shown that by combining advanced patient-based FSI

numerical simulations with IVUS-VH, it is possible to

study parametrically various biomechanical aspects that

promote VPs and their risk of rupture.

Previous studies have confirmed that VP rupture leads to

immediate thrombosis and total arterial occlusion

[2,9–11,39]. Biomechanical factors that are typically

considered in VP biomechanical analysis include fibrous

cap thickness, vessel anisotropy, macrocalcification and

micro-Ca in the vulnerable region, cyclic bending caused

by constant cardiac motion, and cap erosion because of

biochemical degradation of the vessel [4,6,30,33,40]. In

our study, the effects of cap thickness, material anisotropy,

the presence of macrolevel and microlevel calcified spot

inclusions in the fibrous cap, and hypertension on plaque

vulnerability were systematically assessed and analyzed in

terms of the critical stress/strain distribution in the various

VP components that may contribute toward its risk of

rupture. The hemodynamic burdens created by patholo-

gical atherosclerotic flow patterns are captured by our FSI

simulations. These contribute toward increased inflamma-

tory cell activity, leading to the infiltration and accumula-

tion of a necrotic lipid pool inside the vessel wall, and may

lead to alteration of the lesion by enlarging the volume

ratio of necrotic core and the fibrous cap underneath [41].

As shown in Fig. 3, the baseline models (normal pressure,

no micro-Ca, and isotropic model) showed that reduced

cap thickness increases the stress concentration in the

lesion corresponding to stress values that increase

exponentially with a thinner fibrous cap [13,40].

In hypertension studies, the results shown in Fig. 3

indicate that stress values increased by 32, 34, 34, and

30% following this 25% simulated increase in BP (cases I–

IV, respectively), indicating that the stress distributions

developed in the fibrous cap respond almost linearly to

the pressure elevation for all cases and appear to be

independent of the cap thickness [40]. Considerable

increases in both maximal stress and MAP stress

distributions along the fibrous cap show that coronary

plaque patients who also have hypertension appear to be

at a higher risk of plaque rupture compared with

nonhypertensive patients and, thus, fibrous cap vulner-

ability because of such elevated BP can be predicted by

the IVUS-FSI methodology.

Previous studies using finite element methods to

determine the contribution of VP morphological features,

such as cap thickness and necrotic pool size on cap

vulnerability, seem to have failed to predict the actual

rupture location. Specifically, some of these studies

cannot explain why close to 40% of actual ruptures

occurred in the middle of the fibrous cap instead of its

shoulders, where simulations would predict the highest

stress region. An analytical model described by Vengre-

nyuk et al. [5], and later confirmed by the same group

with finite element methods simulations, proposed that

interfacial debonding because of microcalcified inclusions

(10–20 mm in diameter) can be accounted for many

inexplicable fibrous cap ruptures [4]. Following these

studies and collaborating with this group, our group

studied the effects of micro-Ca by embedding micro-Ca

in an idealized coronary model using FSI simulations,

confirming these results [6,7]. In the present work, we

have examined the impact of micro-Ca on cap stability

both locally and globally, where the local stress directly

measures the stress developed at the same location in the

fibrous cap with and without micro-Ca. The presence of a

spherical microcalcified spot of 10 mm diameter increased

the von Mises stresses 2.4-, 2.6-, 2.5-, and 2.2-fold (Fig. 5)

for cases I–IV, respectively (Table 3). This observation is

in close agreement with the hypothesis proposed by

Vengrenyuk and colleagues [4,5,7] that a significant

increase in local circumferential stress would be observed

if micro-Ca are embedded in the region of high

circumferential stress in the VP fibrous cap. This is clearly

shown in case IV, where the fibrous cap has a uniform

thickness of 65mm. Although the fibrous cap thickness at

the location of the embedded micro-Ca in case II is much

thicker (150mm), the appearance of micro-Ca still

increased the stress considerably. Although none of the

cases with isotropic models exceeds the reported stress

threshold for rupture plaques [42], we have restricted the

simulations to the upper limit of VP fibrous cap thickness

(65mm) for only case IV (cases I, II, and III had much

thicker 150–600mm fibrous caps). In addition, we observed

that generally, large calcifications do not affect the stress

distribution and may stabilize the cap if these macro-

calcifications are located at the shoulders of the fibrous cap

[4,5]. Among several proposed mechanisms, macrophage

Table 4 Summary of maximal von Mises and circumferentialstresses for anisotropic studies

Case IV:anisotropic fibrous cap

Maximalcircumferential

stress (kPa)Maximal von Mises stress

(kPa) with micro-Ca embedded

Baseline model 204 51051 Fiber angle 250 (23%) –651 Fiber angle 265 (30%) 626851 Fiber angle 244 (20%) –

Micro-Ca, microcalcification.



and smooth muscle cell apoptosis is considered to be

responsible for the formation of vascular calcification, and

it is well established that necrosis and apoptosis are

prevalent in atherosclerosis [43]. Accordingly, detection of

the micro-Ca in the fibrous cap and taking them into

account in FSI coronary VP studies represents a more

reliable model of the disease that would not underestimate

the risk of rupture of VP.

Fig. 5

Maximum(43 kPa)

52000480004400040000360003200028000240002000016000120008000

163333153333143333133333123333113333103333933338333373333633335333343333333332333313333

48000450004200039000360003300030000270002400021000180001500012000900060003000

18666717333316000014666713333312000010666793333800006666753333400002666713333

Case IV

Case III

Case II

Case IMaximum(103 kPa)

With micro-Ca No micro-Ca Stress (Pa)

Maximum(408 kPa)

Maximum(154 kPa)

Maximum(510 kPa)

Maximum(232 kPa)

Maximum(60 kPa)

Maximum(153 kPa)

Cross-sectional view of the vessels; local (background) stress distributions show the effects of the micro-calcifications (micro-Ca) in the fibrous cap(with isotropic material properties). Localized 2.4-, 2.6-, 2.5-, and 2.2-fold increase of von Mises stress can be observed where the micro-Ca arelocated, compared with the local stresses at the same cross-section without micro-Ca.



We have further studied the effect of the inherent

anisotropy of vascular tissues and its different stress–

strain response as compared with isotropic materials

under hemodynamic loading conditions. Most available

constitutive models describing arterial walls were derived

on the basis of unidirectional mechanical testing

data [23,33,44,45]. Unfortunately, mechanical testing on

coronary artery specimens, especially components such as

the VP fibrous cap, proved difficult, resulting in paucity

of data in the literature. The 3D modified Mooney–Rivlin

model proposed by Tang and colleagues, based on ex-vivo

biaxial mechanical testing of coronary artery specimen,

considers the tissue anisotropy by incorporating collagen

fiber orientations [29,30,38]. In parametric FSI simula-

tions examining tissue anisotropy, a distinct layer of

fibrous cap in case IV was modeled with different fiber

angles, varying from 5 to 851. Our results indicate that

tissues with 651 fiber angles produce the highest

circumferential stress values among all the angles used

(Table 4). Anisotropic tissue models with a 651 fiber

orientation predicted a stiffer response in both axial and

circumferential directions (in terms of Cauchy–Green

stresses on the basis of the modified Mooney–Rivlin

material model). This particular angle was clinically

found to be characteristic of patients with coronary

atherosclerosis [33]. One possible explanation for this

adaptation response is the biomechanical stress-driven

reorientation of the fibers. Kuhl et al. [46] pointed out

that the collagen fibers in biological tissues undergoing

remodeling would allow for a continuous reorientation to

eventually align in the direction of the maximum

principal strain. Much higher von Mises stress was

observed in the simulation that combined the effects of

micro-Ca and anisotropic fibrous cap, increasing by 23%

(from 510 to 626 kPa) with the micro-Ca inclusion in the

anisotropic fibrous cap with a 651 fiber angle. It is well

established that isotropy of biological material may be

assumed at the small strain range, and that sudden

increases in stress (characteristic of an anisotropic

response) are observed once the material is stretched

beyond the small strains range threshold [47,48].

Our FSI simulations were carried out using physiological

pressure and flow waveforms with a 721 phase lag. This is

because of the fact that the bulk of coronary flow is

delivered during diastole because of the vigorous

contraction of the left ventricle during systole that

almost blocks the perfusion through the compressed

coronaries (seen as a sharp dip in the coronary flow rate

waveform during peak systole). Our simulation results

show that this phase lag of coronary maximal flow after

the pressure peak prolongs the duration of high stresses

experienced by the wall throughout the cardiac cycle.

Specifically, the flow-induced WSS remains at a higher

level for a longer duration, and larger MAP stress is

observed as compared with simulation results using

synchronized pressure and flow waveforms (Fig. 2).

By analyzing the effects of the above-mentioned biome-

chanical factors systematically and parametrically, better

understanding of the underlying mechanisms affecting

the risk of rupture of the coronary VP was gained. Fibrous

cap thickness, micro-Ca in the lesion, anisotropic material

properties, and hypertension may contribute significantly

toward the fibrous cap vulnerability. However, certain

limitations are inherent to our study. Detailed geome-

trical features of the fibrous cap, such as thickness and

direct detection of micro-Ca, cannot be easily captured

because of limited imaging resolution. IVUS-VH allows

for the assessment of atherosclerotic plaque morphology

by using radiofrequency analysis of ultrasound signals;

however, its spatial resolution of 150 mm is well above the

thickness considered for an unstable fibrous cap (65 mm)

and cannot be visualized directly by this modality.

Accordingly, we had to assume this VP fibrous cap

thickness for the case IV studied, and in this way were

able to show the effect of such a likely scenario of fibrous

cap thinning. Furthermore, IVUS-VH is unlikely to detect

subtle changes in plaque composition that occur over

small distances because of ultrasound beam cross-

sectional thickness. In the FSI simulations, laminar blood

flow was assumed (justified by the relatively low

Reynolds numbers). The arterial wall was modeled as a

uniform entity and not layer specific. Further studies

incorporating individual patient-specific pressure and

flow patterns, and adding layer-specific modeling of the

vessel components may provide better predictions of

plaque rupture, although necessarily more computation-

ally intensive. The present work combining IVUS-VH

imaging with FSI simulations represents a useful

contribution to coronary VP studies by systematically

studying the effects of major biomechanical factors that

contribute toward the VP burden and stability, and are

needed to be able to predict its rupture potential.

Conclusion

This study incorporates several major biomechanical

factors associated with coronary VP risk assessment. It

shows that IVUS-based patient-specific FSI approach can

be effective for elucidation of the biomechanics of VPs

and estimation of their rupture potential. Parametric FSI

simulations indicated that von Mises stresses increase

exponentially with the thinning of the fibrous cap, as well

as with increasing levels of hypertension where a linear

response to the elevation of BP was established. This

finding implies that plaque stability can be predicted as a

function of the degree of hypertension in coronary VP

patients. Furthermore, it showed that micro-Ca em-

bedded in the fibrous cap, which were observed in VP

patients, considerably destabilize the fibrous cap and

increase its risk of rupture. Stress-driven reorientation

and biochemical degradation of the collagen fibers in the

vessel wall, as shown with a typical anisotropic fibrous cap

with 651 fiber angle orientation, further contributed

toward the stress levels in the fibrous cap. FSI



simulations reconstructed from patients’ IVUS images

were found to be an effective approach for quantification

of the stress burden of VPs and the contribution of

various biomechanical factors toward its risk of rupture.

This methodology can be used as an additional diagnostic

tool to help clinicians determine the rupture risk and the

need for intervention.

AcknowledgementsThis study was supported in part by a research grant from

the Rothschild–Caesarea Foundation, Israel.

Conflicts of interest

There are no conflicts of interest.

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