Section: New Results

Numerical methods for cardiac electrophysiology

Participants : Muriel Boulakia, Jean-Frédéric Gerbeau, Damiano Lombardi, Elisa Schenone.

• In [33] , a reduced-order method based on Approximated Lax Pairs (ALP) is applied to the integration of electrophysiology models. These are often high- dimensional parametric equation systems, challenging from a model reduction stand- point. The method is tested on two and three dimensional test-cases, of increasing complexity. The solutions are compared to the ones obtained by a finite element. The reduced-order simulation of pseudo-electrocardiograms based on ALP is proposed in the last part.

• In [21] , we address the question of the discretization of Stochastic Partial Differential Equations (SPDE) for excitable media. Working with SPDE driven by colored noise, we consider a numerical scheme based on finite differences in time (Euler-Maruyama) and finite elements in space. Motivated by biological considerations, we study numerically the emergence of reentrant patterns in excitable systems such as the Barkley or Mitchell-Schaeffer models.