Multiobjective Nonlinear Shape Optimization of Stent Based on Evolution Principles

The treatment of atherosclerotic stenoses is accomplished by a well-established interventional method called Percutaneous Transluminal Angioplasty (PTA). Generally, this procedure is accompanied with the deployment of small tube shape structure to support the wall of the injured artery and improve the limitations of balloon angioplasty, such as restenosis and abrupt closure. Numerous computational studies have been carried out to investigate the expansion and mechanical behavior of different stent designs. They have limited their analysis to study and compare different commercial and theoretical stent designs using some medical and mechanical criteria, in conjunction with parameters obtained from laboratory test. However, none of them have treated its design as a multi-objective optimization task with different optimization criteria. In this sense, the objective of this work is to present and discuss an evolutionary multiobjective optimization algorithm based on evolution principles and Pareto’s dominance criteria to select, generate and evaluate compromise solutions that generation after generation lead to the optimum (or quasioptimum) external shape of this kind of prosthesis. The main advantage of this approach is that all the different design criteria can be included in one single run. NOMENCLATURE C: strain energy of the structure. D: stent’s diameter at the final deployment load. D: stent’s diameter after balloon deflation (unload). F: set of n>1 objective functions. K: stiffness matrix of the finite element i of the model of the structure. L: initial stent’s length. L: stent’s longitudinal length at the final deployment load. L: stent’s longitudinal length after balloon deflation (unload). P: loading vector of the structure. X: Vector of p designs variables. f(X): objective function. g(X): equality constraint function. h(X): inequality constraint function. l: Number of inequality constraints. m: number of equality constraints. n: number of objective functions. p: number of designs variables. u: displacement nodal vector of the structure. u: displecement vector of the finite element i of the model of the structure.