A staggered-in-time and non-conforming-in-space numerical framework for realistic cardiac electrophysiology outputs

TL;DR

This paper introduces a novel numerical framework for simulating cardiac electrical outputs that reduces computational costs by employing a staggered-in-time scheme and non-conforming meshes, validated on realistic geometries.

Contribution

The work presents a new interpolation method at the heart-torso interface enabling non-conforming meshes and a staggered-in-time scheme for efficient cardiac electrophysiology simulations.

Findings

The proposed scheme is reliable and efficient compared to state-of-the-art models.

Non-conforming meshes and interface interpolation impact simulation accuracy.

The framework is applicable to realistic cardiac and torso geometries.

Abstract

Computer-based simulations of non-invasive cardiac electrical outputs, such as electrocardiograms and body surface potential maps, usually entail severe computational costs due to the need of capturing fine-scale processes and to the complexity of the heart-torso morphology. In this work, we model cardiac electrical outputs by employing a coupled model consisting of a reaction-diffusion model - either the bidomain model or the most efficient pseudo-bidomain model - on the heart, and an elliptic model in the torso. We then solve the coupled problem with a segregated and staggered in-time numerical scheme, that allows for independent and infrequent solution in the torso region. To further reduce the computational load, main novelty of this work is in introduction of an interpolation method at the interface between the heart and torso domains, enabling the use of non-conforming meshes, and the numerical framework application to realistic cardiac and torso geometries. The reliability and efficiency of the proposed scheme is tested against the corresponding state-of-the-art bidomain-torso model. Furthermore, we explore the impact of torso spatial discretization and geometrical non-conformity on the model solution and the corresponding clinical outputs. The investigation of the interface interpolation method provides insights into the influence of torso spatial discretization and of the geometrical non-conformity on the simulation results and their clinical relevance.