Comprehensive Geometric Parameterization and Computationally Efficient 3D Shape Matching Optimization of Realistic Stents

Abstract Flexible and compact shape representation schemes are essential for design optimization problems. Current shape representation schemes for coronary stent designs concern predominantly idealized or independent ring (IR) designs, which are outdated and only consider a small number of core design variables (such as strut width, height, and thickness) and ignore clinically critical design characteristics such as the number of connectors. No reports exist on the geometry parameterization of the latest helical stents (HS) that have more complex geometric designs than IR stents. Here, we present two new shape parameterization schemes to fully capture the 3D designs of contemporary IR and double-helix HS stents. We developed a 3D stent geometry builder based on 17 (IR) and 18 (HS) design variables, including strut width, thickness, height, number of connectors and rings, stent length, and strut centerline shape. The shape of the strut centerline was derived via a combination of NURBS, PARSEC, quarter circle, and straight line segments. Shape matching for complex 3D geometries, such as the contemporary stents within limited function evaluations, is not trivial and requires efficient parameterization and optimization algorithms. We used shape matching optimization with a limited function evaluation budget to test the proposed parameterization and two surrogate-assisted optimization algorithms relying on predictor believer and an expected improvement maximization formulation. The performance of these algorithms is objectively compared with a gradient-based optimization method to highlight their strengths. Our work paves the way for more realistic, full-fledged stent design optimization with structural and hemodynamic objectives in the future.