High-order Discontinuous Galerkin Methods for the Monodomain and Bidomain Models

TL;DR

This paper introduces a high-order Discontinuous Galerkin method with spectral basis for cardiac electrophysiology models, enabling accurate, adaptive simulations of steep wavefronts in monodomain and bidomain equations.

Contribution

It presents a novel DG formulation with spectral basis and semi-implicit time integration for improved modeling of cardiac electrical activity.

Findings

Demonstrates convergence and physiological accuracy of the method.

Successfully simulates realistic electric potential propagation.

Overcomes steep wavefront challenges in cardiac models.

Abstract

This work aims at presenting a Discontinuous Galerkin (DG) formulation employing a spectral basis for two important models employed in cardiac electrophysiology, namely the monodomain and bidomain models. The use of DG methods is motivated by the characteristic of the mathematical solution of such equations which often corresponds to a highly steep wavefront. Hence, the built-in flexibility of discontinuous methods in developing adaptive approaches, combined with the high-order accuracy, can well represent the underlying physics. The choice of a semi-implicit time integration allows for a fast solution at each time step. The article includes some numerical tests to verify the convergence properties and the physiological behaviour of the numerical solution. Also, a pseudo-realistic simulation turns out to fully reconstruct the propagation of the electric potential, comprising the phases of depolarization and repolarization, by overcoming the typical issues related to the steepness of the wave front.