Abstract
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 challenging, highlighting the need of novel numerical methods that can improve the efficiency of simulations while targeting an acceptable accuracy. In this work, we propose a semi-implicit non-conforming finite-element scheme (SINCFES) suitable for cardiac electrophysiology simulations. The accuracy and efficiency of the proposed scheme are assessed by means of numerical simulations of the electrical excitation and propagation in regular and biventricular geometries. We show that the SINCFES allows for coarse-mesh simulations that reduce the computation time when compared to fine-mesh models while delivering wavefront shapes and conduction velocities that are more accurate than those predicted by traditional finite-element formulations based on the same coarse mesh, thus improving the accuracy-efficiency trade-off of cardiac simulations.
Highlights
Computer simulations of the electrical activity of the heart have increasingly gained attention in the medical community, as they have steadily shown potential in the study of cardiac diseases and in the design of novel cardiac therapies
Computational models of the heart have shown promise in assisting the design of effective therapies for terminating atrial fibrillation (Trayanova et al, 2018). While these examples can only confirm the tremendous relevance of computational models in advancing the semi-implicit non-conforming finite-element scheme (SINCFES) for Cardiac Electrophysiology field of cardiology, they share the fundamental challenge of being highly demanding in terms of wall-clock time needed in computer simulations
Finite-element simulations using Q1, Q2, and Q1NC element formulations were implemented for the FI and SI timeintegration schemes described in the previous section in an enhanced version of FEAP (Taylor, 2014)
Summary
Computer simulations of the electrical activity of the heart have increasingly gained attention in the medical community, as they have steadily shown potential in the study of cardiac diseases and in the design of novel cardiac therapies. Current models of the human heart are able to represent the complex three-dimensional anatomical structure of the heart chambers, incorporating key functional features such as the Purkinje network and the cardiomyocyte orientation (Vadakkumpadan et al, 2009) Such advanced representation of the heart has enabled novel in-silico studies of undesired pro-arrhythmic effects of drugs in patients (Sahli Costabal et al, 2018), potentially reducing the number of subjects needed in a clinical trial by aiding the experiment design. Current simulations of the heart typically employ mesh sizes in the range of tens to hundreds of micrometers for domains with lengths in the order of centimeters, which translates into large systems of equations with several millions of DOFs that need to be solved at each time step Such high dimensionality renders the solution of heart simulations extremely challenging for personal computers, and calls for improving their implementation in highperformance computing (HPC) platforms (Niederer et al, 2011a; Vazquez et al, 2011)
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