Semi-implicit Non-conforming Finite-Element Schemes for Cardiac Electrophysiology: A Framework for Mesh-Coarsening Heart Simulations - Jilberto, Javiera; Hurtado, Daniel E. (Frontiers in Physiology, 2018)
The field of computational cardiology has steadily progressed toward reliable and accurate simulations of the heart, showing great potential in clinical applications such as the optimization of cardiac interventions and the study of pro-arrhythmic effects of drugs in humans, among others. However, the computational effort demanded by in-silico studies of the heart remains prohibitively high, highlighting the need for novel numerical methods that can improve the efficiency of simulations while targeting an acceptable accuracy from a physiological viewpoint, a trade-off typically found in computer simulations. In this work, we propose a semi-implicit non-conforming finite-element scheme (SINCFES) suitable for cardiac electrophysiology simulations. The proposed scheme is assessed by means of numerical simulations of electrical excitation in regular and biventricular geometries, where we show that, based on coarse discretizations, it can predict with high accuracy the wavefront shape and conduction velocity at a fraction of the computing time demanded by standard simulations based on fine discretizations. We further show that the SINCFES allows for coarse discretizations of cardiac domains while being physiologically accurate for simulations of spiral wave dynamics, which are otherwise not feasible using standard finite-element formulations, thus improving the accuracy-efficiency trade-off of cardiac simulations of arrhythmia.