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Journal of Biomechanics 41 (2008) 10531061

Effects of different stent designs on local hemodynamics

in stented arteries

Rossella Balossino, Francesca Gervaso, Francesco Migliavacca, Gabriele Dubini

Laboratory of Biological Structure Mechanics, Department of Structural Engineering, Politecnico di Milano,

Piazza Leonardo da Vinci, 32, 20133 Milan, Italy

Accepted 3 December 2007

Abstract

Following the deployment of a coronary stent and disruption of an atheromatous plaque, the deformation of the arterial wall and the

presence of the stent struts create a new fluid dynamic field, which can cause an abnormal biological response. In this study 3D

computational models were used to analyze the fluid dynamic disturbances induced by the placement of a stent inside a coronary artery.

Stents models were first expanded against a simplified arterial plaque, with a solid mechanics analysis, and then subjected to a fluid flow

simulation under pulsatile physiological conditions. Spatial and temporal distribution of arterial wall shear stress (WSS) was investigated

after the expansion of stents of different designs and different strut thicknesses. Common oscillatory WSS behavior was detected in all

stent models. Comparing stent and vessel wall surfaces, maximum WSS values (in the order of 1 Pa) were located on the stent surface

area. WSS spatial distribution on the vascular wall surface showed decreasing values from the center of the vessel wall portion delimited

by the stent struts to the wall regions close to the struts. The hemodynamic effects induced by two different thickness values for the

same stent design were investigated, too, and a reduced extension of low WSS region (o0.5 Pa) was observed for the model with a

thicker strut.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Stent; Computational fluid dynamic; Wall shear stress; Numerical modeling

Introduction

Many forms of vascular arterial disease can affect the

flow of blood through arteries near or farther away from

the heart. Coronary arteries are the most subjected ones to

atherosclerosis, the end result of atheromatous plaques

accumulation within the walls of the arteries. In case of

partial or total lumen obstruction, a medical intervention is

mandatory to restore the normal blood flow and avoidfurther complications. Stenting shows some advantages

compared to other possible treatments, as it does not

require any surgical operation and has less complications,

pain and a more rapid recovery (Mullany, 2003).

Since the first implantation of stents in humans in

1986, many improvements, changes and discoveries have

occurred to make them safer and more functional. The

presence of a non-biological device inside an artery causes

an inevitable inflammation response and influences the

fluid dynamic behavior in the regions next to the arterial

wall. Parts of the stent struts protruding into the lumen

may induce the formation of vortices and stagnation zones

which affect wall shear stress (WSS) spatial and temporal

distribution. These effects depend on the stent configura-

tion, its global length, the delivery system, the struts

dimension, shape, spacing and many others (Tominagaet al., 1992; Rogers and Edelman, 1995). Moreover, low-

mean shear stress, oscillating shear stress, high particle-

residence times, and non-laminar flow have all been

shown to occur in the locations where early intimal

thickening is the greatest (Ku et al., 1985; Jin et al., 2004;

LaDisa et al., 2005; Katritsis et al., 2007). In particular,

a correlation exists between low-WSS values less than

0.5 Pa (Ku, 1997; Henry, 2000), sites of intimal thicken-

ing and non-uniform spatial distribution, which appear to

represent important initiating factors for the development

ARTICLE IN PRESS

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0021-9290/$ - see front matterr 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jbiomech.2007.12.005

Corresponding author. Tel.: +39 02 2399 4283; fax: +3902 23994286.

E-mail address: rossella.balossino@polimi.it (R. Balossino).

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of atherosclerosis. Conversely, moderate and high WSS do

not seem to contribute to neointima hyperplasia (Malek

et al., 1999; Ku, 1997; LaDisa et al., 2004). In vivo and

in vitro studies have revealed that stent structure influences

restenosis and thrombus formation between struts

(Tominaga et al., 1992; Rogers and Edelman, 1995;

Kleinstreuer et al., 2001). The evaluation of fluid dynamiceffects caused by stent geometric parameters is thus

important to optimize the stent design. Computational

fluid dynamic (CFD) techniques have the advantage of a

greater flexibility and easiness of using with respect to the

experimental or in vivo methods. They can provide detailed

information on critical local flow parameters near the stent

struts and the arterial wall, at least during the acute stage

of the implantation. Many computational studies in the

literature dealt with the influence of stent physical

parameters on fluid dynamic changes correlated with the

restenosis process (Henry, 2000; LaDisa et al., 2004; Berry

et al., 2000). Stent strut spacing, thickness and number of

struts were found to influence the distribution of low and

high shear stress values (Wentzel et al., 2001). LaDisa et al.

(2003 and 2004) studied the localized alterations in

coronary WSS by performing different CFD studies on

3D stent geometries with different struts number, width

and thickness. The highest WSS values were found over the

surface of the stent, decreasing modestly with subsequent

struts. Lower values were instead detected before and after

each stent strut and at transition between the vessel and the

stent. Most studies considered the artery as a simple

symmetrical and cylindrical model, neglecting the circum-

ferential vascular deformation after stent implantation that

alters the WSS distribution. A first attempt to consider thiseffect was done by LaDisa et al. (2005) by comparing two

3D models of vessel and stent. The artery had a circular

cross-section in the former whereas it was conformed to the

stent geometry in the latter, thus resulting polygonal or

straightened shape. Circumferential straightening intro-

duced areas of high WSS among stent struts that were

absent in the stented vessel model with circular cross-

section. Stent profile or strut height was found to

significantly influence neo-intimal thickness (Barth et al.,

1996). Sullivan et al. (2002) compared a Clemson stent with

a Palmaz one and showed that the former, due to its

thicker struts, creates a 1020% greater degree of intimal

thickening for the same degree of vessel injury. The new

generation stents showed a less regular design compared to

old stents (e.g. PalmazSchatz) with multiple links that

provide higher flexibility and consequently a lower chance

to be perfectly symmetric after their expansion (Isenbarger

and Resar, 2005).

The novelty of the present study resides in the numerical

simulation of the expansion of models resembling a

number of commercially available stents inside a vessel in

the presence of an atherosclerotic plaque. A solid mechanic

analysis was combined with a fluid dynamic one.

A preliminary step was performed in which the stent was

expanded against a stenosed artery, and then the deformed

configuration was used to carry out fluid dynamic

simulations. The basic idea was to compare different stent

models in a configuration as close as possible to the real-life

one. By varying the stent design or strut thickness and

keeping the same boundary conditions, stents models were

compared to suggest possible technical prescriptions to

improve their performances.

Methods

Four different coronary stent designs were taken into consideration.

They resemble four commercial intravascular stents: PalmazSchatz

(Johnson & Johnson Interventional System, Warren, NJ, USA), Cordis

BX Velocity (Johnson & Johnson Interventional System, Warren, NJ,

USA), Sorin Carbostent (Sorin Biomedica S.p.A., Saluggia (VC), Italy)

and Jostent Flex (JOMED AB, Helsingborg, Sweden). The four models

will be referred to as STENT A, STENT B, STENT C and STENT D for

Cordis BX velocity, Jostent flex, Sorin Carbostent and PalmazSchatz,

respectively. The internal diameter, thickness, length and the number of

struts of the simulated models are reported in Table 1. Apart from the

PalmazSchatz, the other designs are considered new generation stents astheir structures incorporate the presence of tubular-like rings and bridging

members (links).

Fig. 1 depicts the four stent models in their unexpanded configuration

and the single unit used in the numerical simulations. Actually, a stent is

pre-crimped in order to be mounted on the balloon catheter, so the

unexpanded configuration refers to the configurations immediately before

the crimping process. To obtain the dimensions of the models, the stents

were analyzed by means of a Nikon SMZ800 stereo microscope (Nikon

Corporation, Tokyo, Japan) when they were available, otherwise the

models were constructed on the basis of images and data available in the

literature (Serruys and Kutryk, 2000).

Plaque and artery were modelled as simple, coaxial, hollow cylinders

(Fig. 2a). The former (inner) is shorter and has rounded extremities; the

latter has a length of 11.68 mm, an internal diameter of 2.15mm, which

becomes 3 mm after a pressurization of 100mmHg, and a thickness of

0.5mm. The plaque is a symmetric plaque with a length of 3.68mm, an

internal diameter of 1.25 mm, which becomes 1.46mm after a pressuriza-

tion of 100 mmHg, and a thickness of 0.45mm. It corresponds after

pressurization to a stenosis of 76% in terms of area reduction in the

central cross-section.

The methodology adopted to simulate the expansion of each stent

inside the artery is described in a previous work ( Migliavacca et al., 2007).

Briefly, the stent expansion was simulated with large deformation analyses

by means of the commercial code ABAQUS (Abaqus Inc., Pawtucket, RI,

USA) based on the finite element method. The mechanical behavior of

both artery and plaque was described with hyperelastic isotropic

constitutive models. The outer cross-sections of the artery were

constrained in the longitudinal direction to simulate the fact that the

considered model is not a stand-alone segment, but is part of a whole

coronary artery. Furthermore, three nodes forming the vertices of an

equilateral triangle were constrained in the tangential direction in an axial

section located in the center of the artery, to avoid the rotation of the

structure. These conditions allowed the radial expansion of the artery.

ARTICLE IN PRESS

Table 1

Main geometrical characteristics of the stent models

Models Dint(mm) Thi ckn ess

(mm)

Length

(mm)

Strut

number

STENT A 0.9 0.15 13 6

STENT B 1 0.05 16 10

STENT C 0.95 0.075 16 10

STENT D 1 0.1 16

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With regard to the stent, boundary conditions were applied which

constrain the three nodes forming the vertices of an equilateral triangle in

the medial cross-section of the stent in the longitudinal and tangential

directions.

A single unit of stent, covering the entire stenosis length, was expanded

under displacement control until a diameter of 3 mm was reached

(Fig. 2b). Once the deformed configurations of artery, plaque and stent

were obtained, the fluid domain geometry delimited by the internal arterial

and stent surfaces, was created using Rhinoceros 2.0 Evaluation CAD

program (McNeel & Associates, Indianapolis, IN, USA). Each deployed

configuration was imported into the CAD program as a point cloud and

then the surfaces and the volumes were rebuilt ( Fig. 2c). Since the stent

was discretized using shell elements in the solid mechanic analysis, a

thickness was prescribed for the stent according to the data reported in

Table 1 to take into account the actual protrusion of the stent struts into

the lumen. The geometry was then imported into the commercial code

Gambit (ANSYS Inc., Canonsburg, PA, USA) to enable the mesh

generation for the fluid domain. A mixed grid was created by means of

tetrahedral elements for the stented portion of the model and brick

elements for the unstented one. A very fine discretization was prescribed in

the region of interest, which is the stent imprint and the arterial wall within

the stent struts (Fig. 2d), to guarantee an accurate evaluation of the

significant quantities. In the unstented portion a coarser mesh was

generated (Fig. 2e). A grid-sensitivity analysis was conducted on six

different meshes with increasing number of elements (102,540, 130,700,

203,200, 325,000, 654,000, and 689,000, respectively). The area weighted

average WSS was calculated separately over the stent imprint and the

vessel region around the stent struts. The values were compared according

to the relative error, calculated as:

y 1

x

s21 s22 s

2n

1=2

n 1,

where s is the standard deviation, n is the number of the different

considered meshes and x is the WSS arithmetic mean. The relative errors

were below the 5% for each mesh and the last three meshes showed no

significant differences in spite of the considerable increase in cell number.

The choice was for the mesh with 654,000 cells and 160,000 nodes.

ARTICLE IN PRESS

Fig. 1. Stents models (left) and particular of the single stent units (right)

used in the simulations.

Fig. 2. 3D CAD geometry of the plaque and the artery (a); deformed configuration after stent expansion (b); fluid domain (c); particular of the fine

discretization in the vessel area within the stent struts (d) and of the coarser mesh in the area outside the stented region.

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The flow simulations were carried out by numerically solving the

continuity and NavierStokes momentum equations for a pulsatile blood

flow, using the commercial package Fluent (ANSYS Inc., Canonsburg,

PA, USA), based on the finite volume method. A three-dimensional

double-precision, segregated and laminar solver was used with first-order

time implicit scheme employed to discretize the governing equations.

Under-relaxation factors of 0.3 for pressure, 1 for density, and 0.7 for

momentum were used. Standard discretization was followed for pressure

with a PISO algorithm chosen for pressure-velocity coupling. A second-

order upwind scheme was adopted for the discretization of momentum.

Convergence criterion for continuity and velocity residuals was kept at

104, an order of magnitude lower than the recommended value.

The adopted inlet blood-flow velocity waveform was taken from the

literature (LaDisa et al., 2005), which was obtained from a canine

coronary artery under normal resting conditions and the data were

sampled obtaining a final step function. A time-varying velocity boundary

condition with a parabolic profile was imposed at the inlet with a user-

defined subroutine (with a Womersley number equal to 2.87). A no-slip

condition was specified on the wall which makes all velocity components

equal to zero. The arterial wall was specified as rigid, a reasonable

assumption in the stented portion even though questionable in the other

parts of the domain. At the outlet, a zero-gauge pressure boundary

condition was specified. Four cardiac cycles were simulated to guarantee a

stable solution and the results referred to the last cycle.

Results

The WSS results are reported with reference to the

luminal side of the strut surface (stent area) and to the

luminal side of the bare vascular wall surface (vessel area).

Fig. 3 illustrates the stent area (a) and the vessel area (b)

above defined for the STENT A. Six time instants are

properly selected inside the cardiac cycle to report the

temporal changes.

Stent design

Based on the suggestions in the literature indicating a

threshold of 0.5 Pa as a critical WSS value to consider a

region prone to restenosis, the corresponding artery wall

and stent percentage area was evaluated to compare the

performances of the four stents.

Fig. 4 shows the histograms of the vessel area

percentage with a WSS magnitudeo0.5 Pa for each stent

model in the six selected time instants. A miniature of the

time course of inlet velocity is also represented to help the

reader to localize the time instants in the cardiac cycle.

Low and high values alternate during the entire cardiaccycle. At blood-flow peaks i.e. at time instants 0.16 s

(diastolic perfusion) and 0.40 s (systolic heart ejection

phase) the percentage area with WSSo0.5 Pa is around

30% for all stent models. It increases significantly in the

other time instants of the cycle, when blood flow is either

decelerating or minimum. Such a behavior is common for

all models with only slight differences for STENT D, that

shows an increase in the area percentage in the last timeinstant (0.52 s) if compared to the slight decrease showed

by the other three models. Comparing the four stent

models, STENT B shows the highest percentage of area

with low WSS values during the cardiac cycle, except for

time points 0.16 s and 0.40 s, when area percentage is higher

for STENT A.

Fig. 5a shows the comparison in terms of maximum

WSS values on the stent area and vessel area at the six

selected time points in the cardiac cycle. The histograms

illustrate the trend for STENT A only, being the same for

the other ones. Comparing the vessel area and the stent

area, the maximum values are located on the stent area.

They remain above 1 Pa during the entire cardiac cycle and

reach the maximum in the diastolic perfusion phase with a

value of around 5 Pa. Fig. 5b reports the comparison in

terms of maximum WSS values on the stent area. It can be

noted that STENT A has the highest values along the

cardiac cycle, whereas the other three models have

ARTICLE IN PRESS

Fig. 3. Fluid domain regions used to describe the results: the luminal side of the strut surface, named stent area (a) and the luminal side of the bare

vascular wall surface, named vessel area (b).

0

20

40

60

80

%o

fvesselarea