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Computer Methods in Biomechanics and Biomedical

Engineering

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Numerical investigations of the mechanical properties

of a braided non-vascular stent design using finite

element method

Xiao-Yu Ni , Chang-Wang Pan & B. Gangadhara Prusty

School of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing,

Jiangsu Province 210037, P.R. China

Jiangsu Key Laboratory for Design and Manufacture of Micro/Nano Biomedical Instruments

Micro-Tech (Nanjing) Co., Ltd, Nanjing, Jiangsu Province 210096, P.R. China

School of Mechanical and Manufacturing Engineering, The University of New South Wales,

Sydney, NSW 2052, Australia

Published online: 28 May 2014.

To cite this article:

Xiao-Yu Ni, Chang-Wang Pan & B. Gangadhara Prusty (2014): Numerical investigations of the mechanical

properties of a braided non-vascular stent design using finite element method, Computer Methods in Biomechanics and

Biomedical Engineering, DOI:

10.1080/10255842.2013.873420

To link to this article:

http://dx.doi.org/10.1080/10255842.2013.873420

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Computer Methods in Biomechanics and Biomedical Engineering,

2014

http://dx.doi.org/10.1080/10255842.2013.873420

Numerical investigations of the mechanical properties of a braided non-vascular

stent design using ﬁnite element method

Xiao-Yu Ni

Chang-Wang Pan

and B. Gangadhara Prusty

School of Mechanical and Electronic Engineering, Nanjing Forestry University, Nanjing, Jiangsu Province 210037, P.R. China;

Jiangsu Key Laboratory for Design and Manufacture of Micro/Nano Biomedical Instruments Micro-Tech (Nanjing) Co., Ltd, Nanjing,

Jiangsu Province 210096, P.R. China;

School of Mechanical and Manufacturing Engineering, The University of New South Wales,

Sydney, NSW 2052, Australia

(Received

27 May 2013; accepted 5 December 2013)

This paper discusses various issues relating to the mechanical properties of a braided non-vascular stent made of a Ni – Ti

alloy. The design of the stent is a major factor which determines its reliability after implantation into a stenosed non-vascular

cavity. This paper presents the effect of the main structural parameters on the mechanical properties of braided stents. A

parametric analysis of a commercial stent model is developed using the commercial ﬁnite element code ANSYS. As a

consequence of the analytical results that the pitch of wire has a greater effect than other structural parameters, a new design

of a variable pitch stent is presented to improve mechanical properties of these braided stents. The effect of structural

parameters on mechanical properties is compared for both stent models: constant and variable pitches. When the pitches of

the left and right quarters of the stent are 50% larger and 100% larger than that of the central portion, respectively, the radial

stiffness in the central portion increases by 10% and 38.8%, while the radial stiffness at the end portions decreases by 128%

and 164.7%, the axial elongation by 25.6% and 56.6% and the bending deﬂection by 3.96% and 10.15%. It has been

demonstrated by ﬁnite element analysis that the variable pitch stent can better meet the clinical requirements.

Keywords:

braided stent; non-vascular; ﬁnite element method; mechanical properties; parametric analysis

Downloaded by [Politechnika Poznanska] at 12:27 30 November 2014

Introduction

Interventional treatment is a very effective method for

treating vascular and non-vascular stenosis diseases. At

present, the braided stents have been widely applied in the

gastrointestinal, respiratory and other non-vascular sys-

tems to reopen and scaffold the blocked non-vascular

cavities. The braided stent is made of a Ni –Ti alloy wire

wrapped into a helix and interwoven into the straight

tubular pattern, and the wire –wire crossings are not

welded or bonded, but connected only by friction. Due to

the special characteristics of braiding, the braided stents

can maintain original surface conditions and uniform size

(Ni et al.

2012),

which is the main reason to select the

braided structure for the nonvascular stent. However,

studying the overall mechanical properties of braided

stents is quite a complicated issue because of the

interaction between the two crossing wires.

The mechanical properties of some braided stents have

been investigated by some researchers using different

approaches. Jedwab and Clerc (1993) developed a

mathematical model based on the spring theory to describe

the radial and longitudinal stiffness of the stent, but the

model was developed with many assumptions such as the

wires inside the stent structure acted as a number of

independent open-coiled helical springs with ends ﬁxed

against rotation, and that the springs undergo elastic

deformations only. Wang and Ravi-Chandar (2004)

presented a mathematical model to explain the relationship

between the pressure and diameter of the stent based on the

slender road theory. Zahora et al. (2007) derived the

equations of the physical model for the spiral stent to

describe the mutual transformation between the axial force

and the radial pressure. Moon et al. (2009) developed some

mathematical models to predict expansive pressure of three

types of braided stents (bare type, coated type and covered

type). But the interaction between the two crossing wires

due to the characteristic of braiding was not taken into

account in their research. Wang et al. (2011) presented a

method to calculate the radial force of a braided oesophagus

stent based on the ﬁnite element method (FEM). Kim et al.

(2008) developed a mechanical model for designing self-

expandable stents fabricated using braiding technology.

The parameterised analysis is a necessary means for

understanding the inﬂuence of different parameters on

mechanical properties. Zhang et al. (2004) investigated the

effect of structural parameters on the radial compression

performance of braided stents by hanging various weights.

The parametric analysis on the fatigue lives of oesophagus

stents was carried out by Ni et al. (2009).

In addition, several studies have been recently devel-

oped, De Beule et al. (2009), Kim et al. (2010) and Masoumi

et al. (2012) among others performed some experimental and

*Corresponding author. Email:

xyni_luck@163.com

2014 Taylor & Francis

X.-Y. Ni

et al.

Downloaded by [Politechnika Poznanska] at 12:27 30 November 2014

computational simulations or shape optimisations in order to

improve the behaviour and design of braided non-vascular

stents. Indeed, their research results provided very useful and

valuable information that enables to understand the

mechanical properties of the braided stent. However, some

complications still occur in clinical application of these

braided stents, such as tissues hyperplasia (Song et al.

2003;

Shin et al.

2005),

which can foster restenosis or stent

blockage (Orons et al.

2000;

Conti

2007),

ulceration or tissue

necrosis at the end of stents (Acunas et al.

1996;

Dai et al.

1998)

and perforation (Canon et al.

1997;

Khot et al.

2002;

Stewart et al.

2013)

mainly due to the high-contact stress of

the cavity wall caused by over radial stiffness of stents and

the friction between stent and cavity wall caused by over

axial elongation of stents. Reducing the complications is the

main motive to promote the improvement of stents.

Therefore, approaches on the synthesis of optimised

mechanical properties and the relationship between the

structural parameters and the mechanical properties of

braided stents are worthy of more attention.

Taking into account the circumstances described

above, the objective of this research is to propose a

design strategy for a braided stent with a variable pitch.

One reason is to obtain a reasonable radial stiffness to

reduce some complications, such as hyperblastosis or

tissue necrosis caused by over contact stress in the healthy

areas of a cavity. Another reason is to decrease the axial

elongation to facilitate precise positioning (Hussain et al.

2004;

De Beule et al.

2009)

and to reduce friction between

the stent and cavity wall, which also causes hyperblastosis

(Zhang et al.

2004).

With these purposes, the paper is

organised as follows. In Section 2, the model geometry and

the FEM are described. In Section 3, parametric stent

models are analysed under uniform pressure to understand

the effect of structural parameters on the radial stiffness,

axial elongation and ﬂexibility of the stent. The braided

stent with variable pitch is compared with the commercial

constant pitch in Section 4. Finally, a discussion of the

results and some limitations are presented in Section 5.

Figure 1. A photograph of a bare cystic braided stent (a) and

details of structural parameters (b).

According to the clinical requirements, the structural

parameters (see

Figure 1(b))

are various. For example, the

diameter of the stent varies from 6 mm (for biliary) to

20 mm or larger (for oesophagus). In order to study the

inﬂuence of the main structural parameters on the radial

stiffness, axial elongation and ﬂexibility of the stent, the

crown number

the wire diameter

and the pitch of wire (a

space spiral curve)

were various, respectively, see

Table 1.

Therefore, three groups of models were used for the

parametric analysis for a constant stent with the same stent

diameter

and stent length

2.2

The FEM and boundary conditions

2.1

Geometry and FEM

Stent geometry

The straight cylindrical tubular braided stent was taken as

the geometrical basis (see

Figure 1(a)

commercial cystic

stent made by Micro-Tech (Nanjing) Co. Ltd, China).

Table 1.

Group

Three groups with different structural parameters.

Pitch of wire

P(mm)

28,30,35,40,45,50,55,60

Diameter of wire

(mm)

0.18

0.16,0.18,0.20,0.22

0.18

The specialised algorithm was coded using ANSYS

Parameter Design Language and implemented in ANSYS

to generate the geometries and FEMs for the cylindrical

tubular braided stents fast and efﬁciently. A space spiral

curve is determined using

Equation (1)

ﬁrst, and then the

geometric model of the stent can be achieved through

copying and reﬂecting the space spiral curve in a cylindrical

coordinate system.

Z-axis, X-axis

and

Y-axis

are set in the

longitudinal direction, the stent radial direction and the

stent circumferential direction, respectively.

cos

;

sin

;

ð1Þ

;

where

is the stent diameter,

is the pitch of the wire and

is the central angle of the spiral.

Crown number

6,8,10,12

Stent diameter

(mm)

Stent length

(mm)

Computer Methods in Biomechanics and Biomedical Engineering

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model. The material parameters of the Ni– Ti alloy are

taken from Zheng and Zhao (2004) and are presented as:

Young’s modulus

83,000 MPa; density

6450 kg/m

;

yield strength

207 MPa; Poisson’s ratio

0.33.

In general, to ensure that a stent has not any migration

in the body cavity, the diameter of a stent is bigger than

that of the cavity; therefore, the stent will be under short-

term or long-term external loads from the cavity wall.

Radial compression from the cavity wall is the main load

acting on the stent, which can be assumed as a uniform

radial compressive pressure, when the real pressure from

the cavity wall has not been fully known. Furthermore, the

stent may bend because of the natural curve of the body

cavity. Therefore, in order to study the structural

behaviour of the braided stent, including radial stiffness,

axial elongation and ﬂexibility, two kinds of loading

conditions are to be set according to the real working status

of the stent in the body cavity. One is compression

(Figure

3(a))

and the other is bending (Figure

3(b)).

The

radial stiffness and axial elongation of the braided stent

can be examined by uniform compressive pressure, while

the ﬂexibility of the stent can be evaluated by bending.

Figure 2. FEM of a braided stent (a) and contact model of

crossing beams (b).

2.3 Numerical simulation

2.3.1 Radial compression

Radial stiffness characterises the ability of the stent to

resist collapse under short-term or long-term external

loads from the cavity wall. It is one of the most important

properties of the stent. Radial stiffness

deﬁned in Huang

et al. (2008) is expressed in

Equation (3):

;

ð3Þ

The geometric models were meshed with 3D 2-node

(beam188 element) (see

Figure 2(a))

because the beam

element has shear-deformation effects and it is suitable for

analysing slender beam structures. A ﬂexible – ﬂexible and

symmetric contact model was created by using contact

elements (CONTA176 and TARGET170 are contact

elements deﬁned in ANSYS) for the contacts between the

crossing wires. Contact status is detected when two

circular beams touch or overlap each other. The non-

penetration condition for beams with a circular cross

section can be deﬁned as:

ðr

ð2Þ

where

is the radial pressure (N/mm

) and

is the radial

deformation of the stent (mm).

where

and

are the radii of the cross sections of the

beams on the contact and target sides, respectively, and

is the minimal distance between the two beams, which also

determines the contact normal direction. Contact occurs

for negative values of

The contact element real constants

are used to deﬁne the target radius

and the contact radius

on the basis of the wire diameter, see

Figure 2(b).

The Ni –Ti alloy wire of the braided stent undergoes

very little change in its cross-section shape and size; the

total length of the wire remains unchanged. Accordingly,

the strain of the Ni –Ti alloy wires of braided stents should

be in the linear elastic range of the material, and the

mechanical behaviour of the braided stent is modelled

using a linear elastic and isotropic constitutive material

Figure 3. Boundary conditions, uniform pressure (a) and

bending (b).

X.-Y. Ni

et al.

Downloaded by [Politechnika Poznanska] at 12:27 30 November 2014

Figure 4. The deformation of the braided stent under uniform compressive pressure (n

10,

0.18 mm,

10 mm,

60 mm,

0.3,

35 mm) (a) and the experimental phenomenon (b).

As in

Equation (3),

the radial stiffness is inversely

proportional to the radial deformation, hence under the

same

the larger the radial deformation, the stronger the

radial stiffness of the stent. To estimate the sensitivity of

the radial and axial deformation to the structural

parameters of stents, the parametric analysis was carried

out. In this investigation

n, d, P

and the friction coefﬁcient

between two crossing wires were parameterised, while

the stent diameter

and the stent length

are constants.

Because the real radial pressure from the wall of the

cavity is unknown, in order to observe the deformation of

the stent clearly and to avoid the stent collapse due to

overload, the radial compressive pressure was set as 5 kPa.

Figure 4(a)

illustrates the deformation of the braided stent

under uniform radial compressive pressure. Under the same

uniform radial pressure, the braided stents with various

structural parameters have deformation diagrams similar to

that shown in

Figure 4.

It shows that the radial deformation

is non-uniform along the longitudinal direction of the stent.

Obviously, the maximum radial deformation occurs in the

middle of the stent, while the minimum radial deformation

occurs at both ends of the stent, which is consistent with the

experimental phenomenon (see

Figure 4(b)).

This phenom-

enon is also similar to the dogboning phenomenon of the

vascular stent with ball expansion (Wang et al.

2006).

Therefore, the radial stiffness of the stent is non-

uniform along the longitudinal direction of the stent.

Obviously, in the middle of the stent, the radial stiffness is

the weakest, while the radial stiffness is the strongest at

both ends of the stent. The sensibility of deformations,

including the maximum radial deformation, the minimum

radial deformation and the elongation deformation, to

P, d

and

can be understood by comparing the analytical

results. The results of the radial deformation and the axial

elongation of stents obtained from parametric analyses are

presented in

Figures 5

and

respectively.

Although the friction coefﬁcient

between two

crossing wires is not a structural parameter, it may

inﬂuence the overall properties of the stent when the

relative sliding occurs at every contact point. In order to

estimate the sensitivity of deformation to the friction

coefﬁcient

, the parameters of the stent were set as

10,

0.18 mm,

28 mm,

10 mm and

60 mm, and

varies from 0.3 to 0.9. According to

Figure 5(a),

under uniform radial pressure, with

changing, the two deformation (the maximum radial and

the minimum radial) curves of the stent are close to

horizontal straight lines, i.e. that the radial and axial

deformations of the stent cannot be inﬂuenced by

, which

means that the relative rotation but no relative slippage

occurs at the contact points of two crossing wires.

Therefore, the friction coefﬁcient can be set as a constant

0.3 in all subsequent parametric analyses.

Finite element analyses (FEAs) were performed for

several models (Group A) with various

The variation of

radial deformations versus

is shown in

Figure 5(b).

When

is varied from 30 to 45 mm, the maximum radial

deformation increases quickly; while when

50 mm,

the maximum radial deformation increases relatively

slowly. There is a nonlinear relationship between

and the

maximum radial deformation of the stent. When

30 mm, the axial elongation is 10.522 mm and the

maximum radial deformation is 1.429 mm, which are

288.7% and 197.1%, respectively for the case of

60 mm. When

doubles, the maximum radial

deformation increases nearly twice, while the axial

elongation of the stent does not have the same tendency

with the maximum radial deformation and it increases

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