Optimal design of vascular stents using a network of 1D slender curved rods

Abstract

In this manuscript we present a mathematical theory and a computational algorithm to study optimal design of mesh-like structures such as metallic stents by changing the stent strut thickness and width to optimize the overall stent compliance. The mathematical constrained optimization problem is to minimize the “compliance functional” over a closed and bounded set of constraints. The compliance functional is the stent’s overall elastic energy. The constraints are the minimal and maximal strut thickness, and a given fixed volume of the stent material. We prove the existence of a minimizer, thereby proving that the constrained optimization problem has a solution. A numerical scheme based on an iteration procedure is introduced, and implemented within a Finite Element Method framework. Optimal design of three different stent prototypes is considered: (1) a single zig-zag ring, which can be found in many complex stent designs on the US market as a basic cell in the modular stent design, (2) a Palmaz–Schatz type stent consisting of 6 zig-zag rings, and (3) a Cypher(TM) type stent consisting of zig-zag rings with sinusoidal connectors. Several interesting optimization solutions are found, some of which have already been implemented in the design of the currently available stents on the US market. The resulting computational algorithm is compared to a Genetic Algorithm, and it is shown that our computational approach outperforms the Genetic Algorithm in the following three key aspects: (1) computation time, (2) accuracy, and (3) maintaining the symmetry of the solution.