A dual adaptive explicit time integration algorithm for efficiently solving the cardiac monodomain equation

TL;DR

This paper introduces a fully explicit, dual adaptive time integration algorithm for the cardiac monodomain equation, enhancing computational efficiency and stability over traditional semi-implicit methods in cardiac excitation simulations.

Contribution

The paper proposes a novel dual adaptive explicit method that overcomes stability limitations, enabling efficient and accurate simulation of cardiac electrical activity.

Findings

Improved computational efficiency over standard methods

Maintains accuracy under physiological conditions

Applicable to pathophysiological cardiac simulations

Abstract

The monodomain model is widely used in in-silico cardiology to describe excitation propagation in the myocardium. Frequently, operator splitting is used to decouple the stiff reaction term and the diffusion term in the monodomain model so that they can be solved separately. Commonly, the diffusion term is solved implicitly with a large time step while the reaction term is solved by using an explicit method with adaptive time stepping. In this work, we propose a fully explicit method for the solution of the decoupled monodomain model. In contrast to semi-implicit methods, fully explicit methods present lower memory footprint and higher scalability. However, such methods are only conditionally stable. We overcome the conditional stability limitation by proposing a dual adaptive explicit method in which adaptive time integration is applied for the solution of both the reaction and diffusion terms. In a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions, results show that our proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting-based methods.