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

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. We perform a set of numerical examples where cardiac propagation is simulated under physiological and pathophysiological conditions. Results show that the proposed method presents preserved accuracy and improved computational efficiency as compared to standard operator splitting-based methods.

Automated summary

The study proposes a fully explicit method for decoupling the reaction and diffusion terms in the monodomain model. Compared to semi-implicit methods, this approach offers lower memory footprint and higher scalability, albeit with conditional stability. The conditional stability limitation is overcome by introducing a dual adaptive explicit method which applies adaptive time integration for both the reaction and diffusion terms.