Plane Thermoelastic Waves in Infinite Half-Space Caused

FACTA UNIVERSITATIS

Series: Mechanical Engineering

https://doi.org/10.22190/FUME201211051B

Original scientific paper

NUMERICAL INVESTIGATION OF THE INFLUENCE OF THE

LINK POSITIONING IN THE CORONARY STENT INSIDE THE

NORMAL ARTERY: A COMPARATIVE STUDY OF TWO

COMMERCIAL STENT DESIGNS

Chandrakantha Bekal1, Satish Shenoy1, Ranjan Shetty2

1Department of Aeronautical & Automobile Engineering, Manipal Institute of Technology,

Manipal Academy of Higher Education (MAHE) Manipal, India
2Manipal Hospitals, Bangalore, India

Abstract. This paper investigates the performance of two commercial stent designs

inside the normal artery for induced Von Mises Stress and radial displacement pattern.

Investigation focuses on identifying the key design feature of the stent structure

responsible for varied stress and displacement pattern. Two commercial stent designs,

Supraflex (Stent S) and Yukon Choice (Stent T),are modeled using micro CT images

and MIMICS® while idealized models are used for investigation. ANSYS Workbench is

used to numerically expand the stent inside an idealized normal artery with inflation

pressure. The stent and the artery are modeled using elastic-plastic and hyperelastic

material models, respectively. The results suggest crucial influence of the link

positioning in inducing an area of higher Von Mises Stress and stress gradient. The

locations of a higher stress gradient are those in line with unbound stent crowns. Also,

higher and uniform arterial displacement can be observed in the locations in line with

the bound crown. Results also suggested a considerable difference in arterial

distortion induced by two designs, causes for which can also be attributed to the

differences in the link placement. The study suggests that the link connections play a

crucial role in setting up stress field/radial displacement. Suitable modification of the

link positioning can reduce the higher stress gradient and arterial distortion, which

probably can reduce arterial injury.

Key Words: Coronary Stents, Finite Element Analysis, Arterial Stress, Artery Radial

Displacement, Arterial Distortion

Received December 11, 2020 / Accepted May 28, 2021

Corresponding author: Satish Shenoy B

Department of Aeronautical & Automobile Engineering,

Manipal Institute of Technology, Manipal Academy of Higher Education (MAHE) Manipal, India

E-mail: satish.shenoy@manipal.edu

2 C. BEKAL, S. SHENOY

1. INTRODUCTION

It has been reported that Cardiovascular Disease (CVD) is a major cause of mortality

(about 30%) world over [1-2]. Stenosis of the coronary artery is a major health issue

involving accumulation of fatty deposits thereby narrowing the lumen area leading to

Myocardial Infraction (MI). Stenosis is conveniently treated using coronary stents [3].

Percutaneous Coronary Intervention (PCI) has revolutionalized the treatment of stenosis

and there has been tremendous increase in the number of stents being used worldwide [1],

[4]. Mechanical interaction between the stent and the artery plays a crucial role in setting

up a non-physiological stress field. It is reported that higher arterial stress can lead to

greater intimal thickening [5]. Smooth muscle cell proliferation and stent migration

immediately post stenting can lead to narrowing of vessel, the condition known as In-

Stent Restenosis [6]. Clinicians are encountered with a variety of stent designs to choose

from with a variety of geometrical configurations [7]. Measuring immediate stress field

post stenting is experimentally nonviable. Data about comparative

advantages/disadvantages of different stent designs are seldom available since assessment

of long-term efficacy of implanted stent needs a long clinical trial period. Hence a

promising alternative for predicting the performance of the coronary stent is numerical

investigation which has been successfully utilized to investigate different generic as well

as realistic stent designs [8-10], also supported by clinical implications of design

parameters [11-13]. Azaouzi et al [14], investigated the effect of ‘link’ on bending and

torsional capabilities without considering the artery interaction and suggested that

bending and torsion are greatly affected by the link shape and placement. Bukala et al

[15] investigated for expansion of the stent inside the stenotic artery and discussed the

mechanical interaction between stent/artery surface highlighting stress and strain pattern.

Chua et al [16] investigated interaction between the stent and the balloon during

expansion and discussed stress distribution on the stent surface. A paper by Bedoya et al

[17] investigated the effect of the stent design parameters such as curvature radius, axial

strut spacing and amplitude on biomechanical responses. Martin et al [18] investigated the

influence of the balloon folding configuration on arterial stress and suggested that the

balloon configuration significantly affects the stress on the stent and the artery.

Though researchers investigated stress and displacement pattern, the rationale for a

particular stress field and displacement pattern as well as identification of the key design

feature responsible for the same are rarely reported. In this study, we tried to identify the

key components of the stent design crucial for inducing a stress field and displacement

pattern. Our study investigates the comparative performance of two different stent designs

using commercial Finite Element Analysis (FEA) software ANSYS workbench (Ansys

Inc.). This paper involves realistic modeling of stent models in order to identify the

geometrical arrangements of stent struts and links, and a numerical analysis of the

expansion of the idealized stent model inside the idealized normal artery. The main

outcome of the investigation is identification of the key design feature, which is

responsible for differences in induced arterial Von Mises Stress (VMS) and differences in

the arterial displacement pattern. The investigation findings are expected to serve as a

qualitative tool to underscore the importance of the key design feature in the construction

of the stent design and its clinical implications.

Numerical Investigation of Influence of Link Positioning in Coronary Stents Inside Normal Artery... 3

2. METHODS AND MATERIALS

2.1 Geometry

2.1.1 Stent

Idealized geometry of stents, SupraflexTM (Sahajanand Medical Technologies Pvt.

Ltd, INDIA), hereafter referred as Stent S, and Yukon Choice PC (Translumia

Therapeutics, INDIA), hereafter referred as Stent T, are modeled using 3D image

reconstructed using Micro Computed Tomography (Xradia versa XRM500, IISc,

Bangalore) and Materialize Mimics® Innovation Suite. The main dimensions of the stent

models in crimped form are tabulated (Table 1).

Table 1 Crimped stent dimensions (Diameters are actual values as measured on the

models)

Stent Inner radius

(mm)

Outer radius

(mm)

Length

(mm)

Strut thickness

(mm)

Stent S 0.36 0.46 4 0.1

Stent T 0.46 0.56 4 0.1

Reconstructed models from Mimics® and idealized stent models (created by wrapping

stent profile) (simplified as a rectangle section) are as shown in Figs. 1 and 2,

respectively.

Fig. 1 3-Dimensional realistic geometry from MIMICS, Stent S (a) and Stent T (b)

Fig. 2 Idealized geometry of Stent S (a) and Stent T (b)

4 C. BEKAL, S. SHENOY

2.1.2 Artery

A healthy artery is modeled as a straight cylinder with a representative dimension of

1mm inner radius and 0.4mm thickness [19]; the artery length is taken to accommodate an

unstented region into its value (1mm each on each side). The stent models are centrally

placed as concentric with the artery model as shown in Fig. 3.

Fig. 3 Concentrically placed stent/artery meshed model (mesh size: artery-0.2mm, stent-

0.05mm)

2.2 Material

Medical grade stainless steel (AISL316L) is extensively used for manufacturing a

balloon expandable stent. Bilinear Elastic-Plastic material model is assumed for this class

of material with properties listed in Table 2 [20-21].

Table 2 Bilinear elastic-plastic material constants used for stent modeling

Stent

material

Young’s

modulus

Yield

strength

Poison’s

ratio

Tangent

modulus

Density

AISL316L 196GPa 205MPa 0.3 692MPa 7850kg/m3

The artery is modeled as hyperelastic with 5 parameter Mooney-Rivlin model with

constants as tabulated in Table 3 [22].

Numerical Investigation of Influence of Link Positioning in Coronary Stents Inside Normal Artery... 5

Table 3 5-parameter Mooney-Rivlin hyperelastic material constants

Material

Model

Constants Values(KPa)

Artery

3rd order 5

parameter

Mooney

Rivlin

C10 18.9

C01 2.75

C20 85.72

C11 590.43

C02 0

2.3 Simulation conditions

The crimped stent model is expanded in the first load step (subsequent removal of

pressure in the second load step to simulate final condition, achieving final diameter of

stent in the range of 1.6mm to 1.7mm) inside the idealized normal artery by 2MPa

inflation pressure directly applied to the internal surface of the stent in radially outward

direction [15-16]. Rigid body motion of the stent is prevented by restricting few nodes of

approximately central section of the central stent cell in longitudinal and tangential

direction allowing only radial movement. A Frictional contact with coefficient 0.2 is

defined between the stent and the artery surface [23]. The artery ends are tethered in all

directions (longitudinal, tangential and radial) to prevent a rigid body movement. A large

deformation option is activated to perform a nonlinear analysis. Augmented Lagrangian

contact formulation with penetration tolerance of 0.1 and normal stiffness 0.1 is used

(These values specify the maximum penetration and stiffness allowed when contacts are

encountered during simulation). Intraluminal pressure caused by pressurized blood and

in-vivo longitudinal prestretch are neglected in this study.

In post processing, percentage of luminal surface subjected to critical von Mises

Stress (VMS) level is identified. These critical stress level (class I>545KPa and class

III>475KPa) are adapted from Ref. [17]. Apart from this, a plot of VMS gradient (Ratio

of difference between VMS between two consecutive nodal points and the difference in

distance between those two points) on the arterial inside surface along arbitrary paths are

plotted to identify the locations of a high stress gradient [24]. Variations of radial

displacement of the arterial surface through the same paths are plotted. The plots of radial

displacement of the arterial inside surface at different sections, particularly to highlight

the displacements near the link locations, identify distortion of the arterial inside surface

post expansion. Arterial distortion is presented as difference between maximum to

minimum radial displacement of the artery surface across left, central and right stent

sections.

2.4 Mesh density test

Mesh density test result (Table 4) suggested a large variation in the peak VMS on the

artery surface but the maximum radial displacement is unaffected by element size. We

choose radial displacement as criterion for a mesh density test since the peak VMS is

observed only at few nodal locations, whereas the maximum radial displacement on the

artery surface prevailed over larger nodal locations. For the chosen criterion, though

6 C. BEKAL, S. SHENOY

found to be independent of the mesh size, we chose a mesh size of 0.05mm for stent and

0.2mm for artery, respectively, with a linear tetrahedron element. Fig. 4 shows two of

such meshes used for this study.

Table 4 Summary of mesh sensitivity test on artery expansion

Artery

Mesh

size

(mm)

Stent

mesh

size

(mm)

Peak

VMS

artery

(MPa)

Peak

VMS

artery

(elemental

mean)

(MPa)

Peak

VMS

stent

(MPa)

Peak

VMS

stent

(elemental

mean)

(MPa)

Artery

displacement

(max)

(mm)

Stent inside

Displacement

(Max/Min)

(mm)

Number of

Nodes/Elements

0.4 0.1 0.20 0.27 263.6 254.1 0.26 0.80/0.70 83852/15519

0.2 0.1 0.39 0.50 263.8 252.9 0.27 0.81/0.70 101784/25494

0.1 0.1 0.65 0.94 263.7 252.9 0.26 0.81/0.70 173631/66601

0.08 0.05 0.88 1.35 291.5 291.1 0.26 0.80/0.70 285783/130363

Fig. 4 Different meshes used for mesh density study Artery-0.1mm, Stent 0.1mm (a);

Artery 0.08mm, Stent -0.05mm (b)

Fig. 5 plots the radial displacement of the luminal surface for a default mesh and a

mesh of the chosen element size.

Fig. 5 Radial displacement of artery inside surface default mesh (a); and refined mesh (b)

Numerical Investigation of Influence of Link Positioning in Coronary Stents Inside Normal Artery... 7

3. RESULTS AND DISCUSSION

The following section discusses the results of investigations in the form of plots, tables

and graphs.

Fig. 6 VMS distribution on artery luminal surface (Class I-0.545MPa to 0.658MPa and

Class III- 0.475MPa to 0.545MPa) for Stent S at 2MPa inflation pressure (legend unit,

MPa)

Fig. 7 VMS distribution on artery luminal surface (Class I-0.545MPa to 1.65MPa and

Class III- 0.475MPa to 0.545MPa) for Stent T at 2MPa inflation pressure (legend unit,

MPa)

Table 5 Percentage of luminal surface of arterial tissues subjected to class III critical

stress level

Stent Percentage of luminal surface above 475kPa at 2MPa

inflation pressure

Stent S 0.27

Stent T 9.1

We have observed VMS concentration predominantly on the internal surface of artery

segments, with a diminishing stress across section, suggesting a large percentage volume

of the artery remaining much below non-physiological stress (above class III). Figs. 6 and

8 C. BEKAL, S. SHENOY

7 show contour plots of VMS distribution on the inside surface of artery for Stent S and

Stent T, respectively. It suggests that the artery segment in line with the stent crown is the

area more susceptible for restenosis (Class I stress level). Stent S induced considerably a

smaller area of critical stress region (Table 5). This can be attributed to a lower

stent/artery contact area (3.77mm2) compared to that of Stent T (5.5mm2). For Stent S, the

critical stress region is observed along the stent-artery contact region while majority of the

stented surface remained much below the critical stress (between 0MPa-0.475MPa). For

Stent T, approximately the entire stented region is subjected to critical stress state

(between 0.475MPa-1.65MPa).

Fig. 8 Distribution of class I and class III stress level. Stent crown unbound by link (thick

circle) and stent crown bound by link (thin circle) for Stent S(a), Stent T (b)

A closer look at the location of critical stress level (Fig. 8) shows that higher VMS

areas (Class I) are essentially located near the stent crowns unbound by connecting links,

while near the bound crown a more distributed stress pattern is observed. This can be

attributed to the fact that the stent crown unbound by links is more likely to open up and

penetrate into the artery during expansion which is also evident from Fig. 9 showing

prolapse of arterial tissues through the stent struts at these locations.

Fig. 9 Artery and stent surface after expansion, indicating larger tissue prolapse through

stent struts at location without link (a) and no prolapse at location with link (b) (legend

unit, mm)

A plot of VMS gradient on the inside surface of the artery along artery length (Figs.

10 and 11) suggests the existence of certain high stress gradient points. Plot essentially

Numerical Investigation of Influence of Link Positioning in Coronary Stents Inside Normal Artery... 9

shows the VMS gradient calculated along two random longitudinal paths (path 1 and path

2) on the internal surface of the artery. Incidentally, path 1 passes through the location

where it encounters the stent crown unbound by link. Interestingly, the locations of high

VMS gradient happened to be on path 1 promptly suggesting consequence of tissue

prolapse as discussed previously. Stent T induced a comparatively higher stress gradient

(5MPa/mm) in comparison with Stent S (3MPa/mm). In Stent T, the links are connected

at the center of the stent struts unlike in Stent S where the links are connected to the stent

crown, which would have resulted in a greater number of high gradient points for Stent T.

High stress and stress gradient stimulate the regrowth of arterial tissue through the stent

strut. This phenomenon is called re-stenosis which makes revascularization inevitable.

Fig. 10 VMS gradient on artery inside surface along artery length for Stent S at 2MPa

inflation pressure

Fig. 11 VMS gradient on artery inside surface along artery length for Stent T at 2MPa

inflation pressure

10 C. BEKAL, S. SHENOY

The following plots (Figs. 12 and 13) show radial displacement of the arterial inside

surface at three circular sections at left, right and central region stented portion of the

artery. Incidentally, the left and right sections happened to pass through the linked region

while the central section passes through a region devoid of links. Plots indicates more

uniform(circular) displacement for the central section compared to the left and right

sections. At the left and right regions, maximum displacement is observed at the locations

of links (2 diametrically opposite locations for Stent S and 3 locations at 1200 apart for

Stent T). This finding suggests the influence of the links in achieving higher radial

displacements.

Fig. 12 Radial displacement of arterial inside surface at left, center and right sections for

Stent S at 2MPa inflation pressure (legend unit, mm)

Fig. 13 Radial displacement of arterial inside surface at left, center and right sections for

Stent T at 2MPa inflation pressure (legend unit, mm)

For Stent S, the difference between maximum and minimum radial displacement is

found to be 0.11mm for both the left and right sections while in the central section the

difference is found to be 0. 05mm. For Stent T the difference is found to be 0.15mm at

Numerical Investigation of Influence of Link Positioning in Coronary Stents Inside Normal Artery... 11

left ,0.13mm at right and 0.05mm at central section, thus rightfully suggesting the

necessity of a closed cell stent design (more links) to achieve circular expansion [25].

Fig. 14 Variation radial displacement of artery inside surface along artery length for Stent

S at 2MPa inflation pressure

Fig. 15 Variation radial displacement of artery inside surface along artery length for Stent

T at 2MPa inflation pressure

Non-uniformity of radial displacement is observed along longitudinal direction as well

for both stent designs. The plot (Figs. 14 and 15) shows the variation of radial

displacement of the arterial inside surface along longitudinal direction of the artery.

Radial displacement is plotted through two longitudinal paths, path 1 and path 2, so that

these paths pass through the locations of the stent crown. Interestingly, path 2 encountered

12 C. BEKAL, S. SHENOY

a pair of stent crown bound by the links. The plots suggest that the radial displacements

increase gradually from the ends of the artery through the stented region. The maximum

displacement value is located near the stent crown for both path 1 (0.26 mm) and path 2

(0.29 mm) for Stent S. Larger maximum radial displacement for path 2 propose the

influence of the link. The links not only achieved larger maximum displacement at this

location but also contributed to higher displacement in the vicinity of the stent crown.

Similar trend is observed for Stent T. For Stent T the maximum radial displacements

observed are 0.29 mm for path 1 and 0.34 mm for path 2.

Fig. 16 below takes a closer look on displacement of the luminal surface near the stent

crown with and without link for Stent S. It is observed that the stent crown unbound by

links is bound to misalign when expanded and may result in twisting of the artery surface

damaging endothelium surface.

Fig. 16 Radial displacement of arterial inside surface near stent crown without link (a);

and with link (b) for Stent S (legend unit, mm)

4. CONCLUSION, LIMITATIONS AND SCOPE FOR FUTURE STUDY

This study investigates the performance of two commercial stent designs inside the

normal artery particularly highlighting an induced stress field, an arterial displacement

pattern and the factor affecting it. The result suggests that the link contributes crucially to

maintaining a uniform stress field in the stented region. The presence of the link reduced

the VMS gradient and maintained uniform arterial displacements as well. Uniformity of

expansion is greatly affected near the stent crown unbound by link. The link also

contributed to lesser tissue prolapse and lesser misalignment. The results suggest that

stent designs with bound stent crowns can induce diffused stress pattern and uniform

arterial displacement. It can also result in minimal arterial distortions thereby minimizing

detrimental effect arising from non-native biomechanical environment on tissues.

3-Dimensional idealized geometry is used in this investigation with simplifications

(round edges of the strut are avoided). Using realistic models directly for investigation

can simulate the effect of surface irregularities caused by drug coating and crimping

process. Idealized artery geometry used here can certainly help in differentiating

performance of different designs but realistic stenosed artery obtained from imaging

techniques such as Intra Vascular Ultra Sound IVUS [26] can improve the investigation

results in terms of applicability of stent design for specific lesion type. The boundary

conditions used for avoiding rigid body motions of artery and stents in this study are

Numerical Investigation of Influence of Link Positioning in Coronary Stents Inside Normal Artery... 13

simplified. It is assumed that few nodes of central stent cells move only in radial

direction. In actual case, all the points on stent surface move in longitudinal and tangential

directions. Hence, the boundary conditions that are more realistic can improve the validity

of numerical investigation and translation of numerical inferences into clinical

applications will be accomplished. Though we reported the values of stress and stress

gradients in this study, these values are to be considered with almost care as mesh density

study suggests considerable variation in maximum Von Mises Stress for different mesh

sizes. Nevertheless, the pattern of stress and stress gradient can be certainly relied upon.

Acknowledgements: This work is supported by TA Pai PhD Scholarship Program

(MU/DREG/MUSCHOLAR/PHD/2014), from Manipal Academy of Higher Education (MAHE).

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