A novel numerical method for solving time-fractional models in cardiac electrophysiology

Abstract

• Development of a novel numerical method for time-fractional PDEs. • The method is based on a quadratic spline approximation. • Efficient and accurate solution for cardiac electrophysiology model. • Impact of fractional orders on the transmembrane potential is presented. Time-fractional models in cardiac electrophysiology are well known for capturing cardiac memory, which is a key factor of cardiac electrical activity in both normal and pathological tissues such as alternans. Numerical simulation of these models is computationally demanding and requires accurate time discretization schemes andfine spatial meshes to resolve stiff depolarization and repolarization wave fronts. In the present study, we propose a novel fractional numerical differentiation formula for solving the time-fractional Aliev-Panfilov monodomain model. This method is based on a quadratic spline approximation and it offers high accuracy and efficiency compared to existing classical numerical schemes for time-fractional models. For the space discretization, we employ a second-order finite element method on unstructured meshes. Numerical results demonstrate the convergence and computational efficiency of the proposed method and confirm its effectiveness for modeling cardiac electrical dynamics. Moreover, we present the impact of fractional orders on the transmembrane potential and the action potential duration in a two-dimensional cut of a segmented realistic heart geometry.