Choosing the optimal stent - numerical strategies
Clinical studies have identified factors such as the stent design and the deployment technique that are one cause for the success or failure of angioplasty treatments. In addition, the success rate may also depend on the stenosis type. Hence, for a particular stenotic artery, the optimal intervention can only be identified by studying the influence of factors such as stent type, strut thickness, geometry of the stent cell, and stent-artery radial mismatch with the wall. We propose a methodology that allows a set of stent parameters to be varied, with the aim of evaluating the difference in the mechanical environment within the wall before and after stenting. Novel scalar quantities attempt to characterize the wall changes in form of the contact pressure caused by the stent struts, and the stresses within the individual components of the wall caused by the stent. These quantities are derived numerically and serve as indicators, which allow the determination of the optimal size and type of the stent for each individual stenosis. In addition, the luminal change due to angioplasty may be computed as well. The methodology is demonstrated by using a full three-dimensional geometrical model of a postmortem specimen of a human iliac artery with a stenosis using imaging data. To describe the material behavior of the artery, we considered mechanical data of eight different vascular tissues, which formed the stenosis. The constitutive models for the tissue components capture the typical anisotropic, nonlinear and dissipative characteristics under supra-physiological loading conditions. Three-dimensional stent models were parameterized in order to fit into the numerical device-optimization process. For the three-dimensional stent-artery interaction we use a contact algorithm based on smooth contact surfaces of at least C1-continuity, which prevents numerical problems known from standard facet-based contact algorithms. The proposed methodology has the potential to provide a scientific basis for optimizing treatment procedures and stent geometries and materials, to help stent designers examine new stent designs ‘virtually’, and to assist clinicians in choosing the most suitable stent for a particular stenosis.
Arterial model

An external iliac artery (female, 65 year old) was harvested during autopsy within 24 hours from death. The investigated artery has an atherosclerotic lesion of type V, according to Stary et al., which contains mainly reparative smooth muscle cells and fibrous tissue and additionally two or more lipid pools of unequal size separated from each other by cells and fibrous tissue. Two cross-sectional macroscopic views of the stenotic iliac artery are provided in Fig. 1, Sections A-A and C-C. The axial in situ pre-stretch, defined as the ratio of in situ length to ex situ length, was calculated to be 1.052. Use of autopsy material from human subjects was approved by the Ethics Committee, Medical University Graz, Austria.

Fig. 1: Sections of the analyzed external iliac artery. Section B-B is the region with the smallest lumen diameter. The tissue components are: adventitia (A), non-diseased media (M-nos), non-diseased intima (I-nos), fibrous cap (I-fc), lipid pool (I-lp), calcification (I-c), fibrotic intima at the medial border (I-fm) and diseased media (M-f). The regions for the analysis of edge effects, are denoted by the areas with dotted frames (Section D-D).

In order to detect the three-dimensional geometry for reconstruction purposes, we use hrMRI. For this lesion eight different tissue types were considered: the non-diseased intima I-nos, fibrous cap I-fc (fibrotic part at the luminal border), fibrotic intima at the medial border I-fm, calcification I-c, lipid pool I-lp, non-diseased media M-nos, diseased fibrotic media M-f and adventitia A. This classification has resulted in a separation of the diseased vessel wall (compare with Fig. 1) that is (solid) mechanically representative and that covers the gross histological composition of the stenosis. This separation is also physically feasible using surgical instruments.

For each scanned image-based cross-section the borders of the arterial components were traced automatically by a set of points. These points were then fitted by NURBS curves using a least-square fitting procedure. Finally, the curves were combined along the arterial axis in order to get the boundary surfaces of the different tissue components. NURBS representations have the advantage that they enable discretizations of different mesh densities to be based on a single smooth surfaces. They provide a suitable basis for mesh adaption procedures that allow mesh refinement with respect to the (original) reference geometry, and for error estimation.

Stent parameterization
Fig. 2 : Three different stent geometries described by a number of (geometrical) parameters, denoted by lower case letters (upper panels). The cell types are based on products that are (or were) available commercially: (a) Multi-Link Tetra™ stent (Guidant): S1, (b) NIROYAL™-Elite stent (Boston-Scientific): S2, (c) InFlow-Gold-Flex™ stent (InFlow Dynamics): S3. The lower panels show the generated 3D views of the different stents.

Parametric design is a useful technique in engineering practice when products are tailored to fit specific customer needs or when numerical optimization is used to generate the optimal design of a product. Both requirements are to be addressed for the design of novel stents regarding their geometric structure. Basically, the parameterization of a stent involves the geometry of the stent cells, the geometry of the stent struts, which may vary across the stent length, and the nominal stent diameter and the length. Local changes in the geometries of the stent cells and struts are useful, for example, to specify different stiffnesses at the ends of a stent in order to avoid edge effects.
In this study we investigate three different types of stent cells, which are based on products that are (or were) available commercially. In particular, for our study we employ shapes of stent cells used in products such as (a) the Multi-Link-Tetra™ stent (Guidant), (b) the NIROYAL™ Elite stent (Boston-Scientific) and (c) the InFlow™-Gold-Flex stent (InFlow Dynamics). For subsequent use we will refer to these stent types as S1, S2 and S3, respectively. The geometries of the stent cells were traced from photographs.

We developed a software, which is able to parameterize (i) the geometry of the stent cells, (ii) the geometry of the struts (with width, measured in the circumferential direction, and with thickness, measured in the radial direction), and (iii) the overall dimensions of the stent (i.e. nominal diameter, number of cells in the axial direction and in the circumferential direction refers to the stent diameter achieved at any axial position, while the balloon is fully inflated). For the parameterization of the stent cell the software requires information about: (i) the cell type (S1, S2, S3), (ii) the geometrical quantities to be parameterized (see the upper panels of Fig. 2; each dimension, denoted by lower case letters, represents a parameter), and (iii) a set of rules describing how the parameters depend on each other.The lower panels of Fig. 2 show the generated 3D views of the different stents. The software also allows to generate a finite element mesh for the individual parameterized stent.

Fig. 3 : Circumferential Cauchy stress distributions in the arterial wall before (a), and after stenting for stent S1 at (b). The only load applied in both configurations is the mean arterial pressure of 100 mmHg.

We study the effect of different stent geometries S1, S2, S3 on the stenotic iliac artery.
As a representative example, Fig. 3 shows the numerical results in form of circumferential Cauchy stress distributions. The cutting planes indicate stresses before (see Fig. 3(a)) and after stenting (see Fig. 3(b)) at locations, where changes in stress due to stenting are most pronounced. For the image shown in Fig. 3(b) the stent S1 was used. As can be seen, stenting induces large stress concentrations in the non-diseased area, while the diseased area remains largely unchanged. Within the diseased part, the fibrous cap (I-fc) becomes extensively stressed. High stress in this plaque component may lead to tissue failure and to an increased risk of thrombus formation.

Numerical indicators. In the following we characterize the mechanical effect after deployment and expansion of the stent by the numerical indicators D1 and D2. Thereby D1 quantifies the pressure between stent and arterial wall, D2 quantifies the overall circumferential stress in the arterial wall. Both quantities can be linked to adverse effects such as restenosis (i.e. large values of D1 and D2 lead to higher risk of restenosis). As a purely geometric quantity of stenting success, we introduce LG, which describes the lumen gain due to stenting. The study is based on a variation of (i) the strut thicknesses for the entire stent, (ii) the strut thicknesses for the end cells of the stent only, and (iii) of the stent cell geometry. These parameter studies are performed for four different values of mismatch DM between stent and lumen diameter. The smallest value is such that the diameter of the expanded stent is smaller than the lumen diameter of the healthy arterial region, while for the largest value of mismatch DM, the expanded stent diameter is larger than the healthy lumen, and hence over-stretches the artery significantly.

Fig. 4 : Influence of mismatch and the modified geometries of stents S1, S2, S3 on the three indicators D1, D2, LG . Solid lines indicate the ‘original cell geometry’ (orig cg). Dashed lines indicate the results by modifying the cell geometry (modif cg) (the original width of all stent cells is increased by 30%). For each stent type, arrows indicate the change from ‘orig cg’ to ‘modif cg’-data.

A large number of studies is possible based on the previous concept. Here we only show how the three stents performed in the described artery (solid lines in Fig. 4). Clearly, stent S3 (thinnest solid line) leads to the largest values of D1 and D2 for the present stenosis and hence shows a higher risk of restenosis than S1 and S2.
As an additional study shown here, we increase the cell length of the stents by 30% and analyze their performance again (dashed lines in Fig. 4). Clearly, S3 (thinnest solid line) can be improved most significantly with this modification when used for the present artery, since D1 and D2 is reduced drastically, while the lumen gain (LG) is almost not affected.


We have developed a method to evaluate indicators for the stenting procedure, which can be linked to the risk of restenosis. These indicators also allow a judgement of the performance of stents used for a specific artery. Numerical studies allow the determination of changes of these indicators as a function of certain parameters such as stent cell type, geometry of stent strut and stent cell, and the mismatch between the smallest lumen diameter in the stenosis and the expanded stent diameter, a crucial parameter in clinical practice. The indicators are measures for the mechanical stresses produced during the expansion, which should be as small as possible, and for the lumen gain, which should be as large as possible.

This research was supported by the FWF - Austrian Science Foundation. More information about this research project can be found here.


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