Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

Abstract

Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of $\sim$1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations.