Fig. 1: Numerical models of the two self expandable stents to be compared (stent 1 left, stent 2 right).

This study compares the performance of two different stents (see Fig. 1) when deployed in a particular artery. Both stents are self expandable and consist of a shape memory alloy.
Although there exist a number of parameters describing the performance of a stent which are independent of the artery, the real performance can only be assessed by studying the interaction with an artery.
Arterial tissue model. Arterial tissue behaves highly nonlinear and anisotropic. In addition, nonrecoverable deformations appear during therapeutic loadings (e.g. due to angioplasty). This behavior can be described most favourably with the model described in [1], [2] and [4]. It considers three-dimensional morphological data coming from high-resolution magnetic resonance (hrMR) imaging and associated histological analyses of an individual human stenosis. Data from mechanical tests are used to establish constitutive laws, whereas eight different arterial tissues are considered (see [1] and [2]). The constitutive laws represent anisotropic and nonlinear material responses at large strains.
Contact. The contact interaction between stent and artery can lead to serious numerical stability problems or unrealistic solutions regarding the contact pressure (which is of major interest in stenting simulations). To avoid this, a special contact algorithm (see [6]) was used, which satisfies C¹ continuity everywhere in the contact domain, regardless of the structure of the interacting finite-element meshes.
Fluid-Structure Interaction. The stent modifies the arterial configuration considerably. However, also hemodynamic effects influcence the situation after stenting. These effects are considered using a Lagrange multiplier based fictitious domain formulation [7] with a non-Newtonian blood fluid model.
Shape memory alloy. This type of material is used widely, since it provides great advantages during deployment of the stent. In this study it is simulated with a specially developed model capable to replicate the temperatur controlled phase change between austenite and martensite.

Fig. 2: Arterial specimen exploded into eight different tissue layers. The region considered for the present simulation has a length of 5.5 mm and is highlighted in green.

An external iliac artery (male, 68 years) was studied. The axial in situ prestretch, defined as in situ length / ex situ length was obtained as λ_is=1.04. The tissue components were represented by a NURBS model, which served as a basis for an adaptive finite element discretization. The individual components are non-diseased intima I-nos, collagenous cap I-fl (fibrotic part at the luminal border), fibrotic intima at the medial border I-fm, calcification I-c, lipid pool I-lp, nondiseased media M-nos, diseased fibrotic media M-f and adventitia A. The resulting model of the artery is comprised of 8492 hexahedral elements.

Fig. 4: Von Mises stress distribution in axis normal sections of the artery due to deployment of stent 1 (top) and stent 2 (bottom). Black lines indicate borders between tissue components.

The analysis of stress distributions in sections of the arterial vessel provides reasonable insight (see Fig. 4). Parameters to be studied are:

• lumen gain due to stenting
• stress distribution in individual tissue components and along the arterial axis
• stress distribution at the stent edges (where tissue transitions from the stented to the non-stented region)
• prolapse of tissue between stent struts
• turbulence of blood flow due to stent struts
• contact pressure between struts and vessel wall
• pulsatile diameter amplitude and related fatigue of stent material
• several other restenosis related parameters.

These parameters can be used to choose the optimal stent for a praticular artery, but also to optimize stent geometries.

This study considers a number of important aspects in order to compare the performance of two different stent products. These are in particular:

Stress distribution and lumen gain. In general it can be observed that the investigated artery becomes less stressed due to stenting with stent 1 than with stent 2 (except in the contact areas between intima and stent struts, where stent 1 shows higher stresses). However, this is also reflected by a slightly decreased lumen gain of stent 1, when compared with stent 2.
Prolapse. Regarding prolapse, it can be observed that stent 1 leads to a very different behavior in the diseased and in the non-diseased region. That is, in the non-diseased region, the stent struts are deeply sunken into the arterial tissue, which may have advantagous hemodynamic effects (see below). However, in the diseased region, there is a much smaller prolapse seen. The reason for this may be associated with the plaque composition, which gives the arterial wall an increased stiffness. For stent 2, there is almost no prolapse visible, both in the diseased and non-diseased region.
Hemodynamics. The simulation shows that the effects of fluid-structure interaction are significant and can not be neglected. Stent 2 initiates a number of eddies while stent 1 does not. This may be associated with the strut shape and the prolapse.

[1] G. A. Holzapfel, M. Stadler and C. A. J. Schulze-Bauer, A layer specific three-dimensional model for the simulation of balloon angioplasty using magnetic resonance imaging and mechanical testing, Annals of Biomedical Engineering, 30 (2002), 753-767.
[2] G. A. Holzapfel, C. A. J. Schulze-Bauer and M. Stadler, Mechanics of angioplasty: Wall, balloon, and stent. In: Mechanics in Biology, edited by J. Casey and G. Bao. New York: The American Society of Mechanical Engineers, 2000, AMD-Vol. 242; BED-Vol. 46, pp. 141-156.
[3] G. A. Holzapfel and M. Stadler, Changes in the mechanical environment of stenotic arteries during interaction with stents: computational assessment of parametric stent designs, J. Biomech. Eng., 2004, in press
[4] G. A. Holzapfel, T. C. Gasser and R. W. Ogden, A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models, Journal of Elasticity, 61 (2000) 1-48.
[5] Biomechanics of Soft Tissue in Cardiovascular Systems, G.A. Holzapfel and R.W. Ogden (eds.), Springer-Verlag, Wien New York, 2003.
[6] M. Stadler and G.A. Holzapfel, Subdivision schemes for smooth contact surfaces of arbitrary mesh topology in 3D, Int. J. Num. Meth. Eng., 2004, in press.
[7] De Hart, J., Peters, G.W.M., Schreurs, P.J.G., Baaijens, F.P.T., A three-dimensional computational analysis of fluid-structure interaction in the aortic heart valve, J. of Biomechanics, 2001.