SHAPE OPTIMIZATION OF A CORONARY STENT

Nelson Ribeiro (1), João Folgado (1), Hélder Rodrigues (1)

1. IDMEC-IST, Technical University of Lisbon, Portugal

Introduction

One of the most common and widely used

treatments for coronary heart disease is the

deployment of intravascular stents, a minimally

invasive procedure. Balloon expandable stents are

implanted into blood vessels to act as a structural

support in the place of stenosis, holding the artery

open so that blood flow is improved. Despite this

overflow in stent choice, restenosis remains the

principal problem of stenting procedures. Clinical

evidence shows that restenosis is partly related to

vascular injury and non-uniformity of stent strut

distribution. Vascular injury is originated by stent-

artery and balloon-artery interactions, which

depend on the stent design. Therefore, research is

still necessary, in particular to improve the stent

design. The aim of this work was to develop an

optimization model in order to obtain a stent

optimal geometry taking into account our objective,

to minimize the stresses in the artery.

Methods

A shape optimization model was developed and

applied to a 3D model of a generic, non-

commercial stent [Bedoya, 2006]. The design

variables considered in this work were (cf. Fig. 1a):

axial amplitude of the curves in the circumferential

rings (Ac), length of the links between

circumferential rings, or strut spacing (Ll), width of

the curves (wc), width of the links (wl) and the

radius of curvature (c) of the curves. Stent thickness

and radius were kept constant. The goal of this

optimization problem is to obtain stents that are less

likely to provoke restenosis. To avoid that outcome

is essential to reduce the stress change in the

arterial wall caused by stenting. Holzapfel et al.

[Holzapfel, 2005] proposed, among other metrics,

to measure the circumferential stresses. The finite

element procedure used to determine the stresses in

the artery included the following components:

catheter, folded balloon, stent, artery and plaque

(cf. Fig. 1b). The numerical simulations were

executed with quasi-static motions: a pressure was

progressively applied in the inner surface of the

balloon, representative of balloon inflation, and was

followed by balloon deflation. The principal aspects

of the simulation were the presence of material

non-linearities, large deformations, contact, and self

contact in the balloon.

The single objective constrained problem can be

stated as:

y�] Ø#Ù(»� D

A­BÚ >Úª>D#��(��® N »� N #��(�l^DDD� � �� � � � ��

(1)

where #��(��® and #��(�l^are the lower and upper

bounds of design variables »�. The objective

function Ø#Ù( is defined as follows:

Ø#Ù( � Û º¶»ÜÝÛ »ÜÝ

Þ (2)

where º¶ are the circumferential Cauchy stresses in

the artery.

a)

Figure 1: a) Design parameters of the stent; b)

Finite element assembly.

Results

The optimization problem was solved using the

optimization toolbox of MATLAB®. Our first

results generated a design with large strut spacing

comparing with the initial design. The optimal

geometry induced lower stresses over larger areas.

Discussion

As future work we plan to add some inequality

constraints to the optimization formulation,

constraints that are metrics of stent performance,

like radial recoil, flexibility and luminal gain.

References

Bedoya et al, J Biomech Eng, 128:757–765, 2006.

Holzapfel et al, J Biomech Eng,127:166–180, 2005.

b)

S642 Presentation 1758 − Topic 42. Stent mechanics and design

Journal of Biomechanics 45(S1) ESB2012: 18th Congress of the European Society of Biomechanics