Using parametric model order reduction for inverse analysis of large nonlinear cardiac simulations

Abstract

Predictive high-fidelity finite element simulations of human cardiac mechanics commonly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90% of the computation time is spent solving linear systems of equations. We propose to reduce the structural dimension of a monolithically coupled structure-Windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom, while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. Following a brief comparison of subspace interpolation methods, we demonstrate how projection-based model order reduction can be easily integrated into a gradient-based optimization. We demonstrate the performance of our method in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting.

Keywords: cardiac mechanics; inverse analysis; parametric model order reduction; proper orthogonal decomposition.