Geometric optimization of vascular stents modeled as networks of 1D rods

Abstract

We develop a novel mathematical and computational framework for geometric optimization of mesh-like devices such as stents, based on modeling mesh-like structures as networks of one-dimensional curved rods. To simplify calculations, the curved rods are approximated by piecewise straight rods. Constrained optimization problems for different cost functionals are stated and mathematically analyzed. The cost functionals considered include: (1) stents' compliance, (2) L2 norm of displacement, (3) L2 norm of contact moment (which is related to fatigue), and (4) multicriteria optimization in which stents are optimized to achieve maximal radial stiffness and minimal bending rigidity. The optimization parameters are stent's vertices, namely, the location of points where the stent struts meet. Existence of solutions to the mathematically posed optimization problems is obtained, and a numerical method based on the gradient descent algorithm is proposed to find the solutions. Three representative stents' geometries are numerically analyzed to show that the optimization algorithms provide tangible solutions. The stent geometries considered are those of Palmaz type stents, single zig-zag stent rings, and Express type stents. Interesting findings are obtained, including several new stent designs. Several optimized stents are presented, including an optimized Palmaz stent with a reduction in contact moment of 30%, and optimized Express and Palmaz stents with a reduction in compliance by more than 70%.