Reduced Order Modeling for Real-Time Stent Deformation Simulations of Transcatheter Aortic Valve Prostheses

Abstract

Computational modeling can be a critical tool to predict deployment behavior for transcatheter aortic valve replacement (TAVR) in patients with aortic stenosis. However, due to the mechanical complexity of the aortic valve and the multiphysics nature of the problem, described by partial differential equations (PDEs), traditional finite element (FE) modeling of TAVR deployment is computationally expensive. In this preliminary study, a PDEs-based reduced order modeling (ROM) framework is introduced for rapidly simulating structural deformation of the Medtronic Evolut R valve stent frame. Using fifteen probing points from an Evolut model with parametrized loads enforced, 105 FE simulations were performed in the so-called offline phase, creating a snapshot library. The library was used in the online phase of the ROM for a new set of applied loads via the proper orthogonal decomposition-Galerkin (POD-Galerkin) approach. Simulations of small radial deformations of the Evolut stent frame were performed and compared to full order model (FOM) solutions. Linear elastic and hyperelastic constitutive models in steady and unsteady regimes were implemented within the ROM. Since the original POD-Galerkin method is formulated for linear problems, specific methods for the nonlinear terms in the hyperelastic case were employed, namely, the Discrete Empirical Interpolation Method. The ROM solutions were in strong agreement with the FOM in all numerical experiments, with a speed-up of at least 92% in CPU Time. This framework serves as a first step toward real-time predictive models for TAVR deployment simulations.

Keywords: Finite element analysis; Model order reduction; Predictive computational modeling; Proper orthogonal decomposition; Transcatheter aortic valve replacement.