29-09-2012, 11:25 AM
Step Change in Design: Exploring Sixty Stent Design Variations Overnight
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Abstract
Traditionally, computer analysis has been used to verify the structural performance of a proposed stent design. The stent deployment process consists of multiple stages (e.g. crimping, springback, expansion etc.) which is highly non-linear inducing material plasticity and load transfer via component contact. A single structural verification assessment would require a couple of days to compute on a PC. This paper investigates how recent developments in Computer Aided Engineering (CAE) and computer hardware combine to facilitate the rapid exploration of many stent design variations. It is demonstrated that by utilising these technologies, over sixty stent design variables can be assessed overnight provides valuable design sensitivity information and an optimum stent geometry configuration. On an example baseline geometry considered the radial stiffness was significantly enhanced with an improvement in structural performance. This represents a step change in the CAE assessment of a stent design.
Introduction
Due to the complex nature of a coronary stent deployment (Figure 1), CAE has been utilised as a design verification tool to assess the structural performance of the process. This activity was extremely time consuming requiring a couple of day‟s computer time to simulate a stent deployment process which consisted of a number of stages (e.g. crimp down, deployment, fatigue cases etc.). These stages induce both non-linear material and geometric behaviour into the stent structure.
It was decided to investigate how recent enhancements to CAE software and computer hardware could impact stent design. For a baseline stent configuration, a number of design variables and their corresponding upper and lower bound limits can be defined (e.g. number of crowns in a circumference, strut height, strut width etc.). Typically for this complex non-linear system, five design variables will require around sixty individual finite element analyses to adequately explore the design space.
Base Simulation
Before optimization technology is applied, it is important to obtain a comprehensive understanding of the baseline stent design subjected to crimp, expansion and in service loading (pressure and bending cases). The non-linear implicit solver, LS-DYNA [2] is used to simulate the deployment.
The model is of one half of a single stent section with symmetry boundary conditions applied at the cut planes. The complete model consists of 14,232 ten noded tetrahedral elements, 10,368 eight noded solid elements and 27,158 nodal points (Figure 2).
Design Variables
The design variables consist of five geometric shape variables which are used to vary the geometry of the stent (Table 1). Each design variable can be varied independently within defined bounds in order to generate a different stent design. The nominal shape for each variable corresponds to the baseline stent design while the extremes of each variable correspond to a pre-defined percentage increase or decrease in shape.
The shape change given by the design variables is approximately ±25% for all the design variables except for the strut length at ±20%. Some of the design variables could not be changed independently whilst maintaining a feasible design. For this reason the radius variable also encompasses a small change in length and the length variable causes a slight change in angle. Also it is possible that combinations of the design variables (for example radius and length) can lead to the individual upper or lower limit value being exceeded for one of those variables.
Non-linear Optimization
Each design variable has lower and upper bounds specified (Table 1), this defines a multi-dimensional design space. A typical point in this space is defined by specific values for all five design variables which corresponds to a unique stent geometry. The first stage in the non-linear optimization process is to sample the system‟s response (i.e. design objective and design constraints) at pre-defined locations within this multi-dimensional design space. The pre-defined locations are selected by HyperStudy to ensure a uniform sampling within the design space. A Hammersley Sampling Method is used.
The optimization considers sixty discrete locations within the design space. This was considered adequate for a concept assessment. Each of these sixty combinations of design variables is output from HyperStudy as an analysis input deck. LS-DYNA simulations are performed to determine the radial stiffness and the maximum tensile principal stresses in the weld region of the stent during the in service loading conditions. The total CPU time to run the sixty case was 130 hours which on a sixteen CPU cluster was completed in eight hours.
Conclusions
It has been successfully demonstrated that stent designs may be optimized efficiently, through use of cluster computing technology and the efficiency of LS-DYNA. A three dimensional LS-DYNA (Implicit) model has been developed that allows the reliable simulation of the crimp, expansion, pressure and bending steps within a single analysis. This model has enabled the use of design optimization. Altair HyperStudy has been used to create run matrices utilizing a parameterized form of the LS-DYNA input deck. Key to the ability to do this was the utilization of three dimensional stent shape variables developed in HyperMorph.
The computational time required for sixty runs using LS-DYNA was 130 hours; in real terms this meant that the optimization could be completed overnight using a multi-node Linux cluster, Altair OptiBox. Consequently, the optimization was able to efficiently assess a large range of combinations of Stent geometry.