Coupled Eikonal problems to model cardiac reentries in Purkinje network and myocardium

TL;DR

This paper introduces a novel partitioned Eikonal-based scheme to accurately model electrical signal propagation and reentries between the Purkinje network and myocardium in cardiac electrophysiology, capturing complex pathological behaviors.

Contribution

It presents the first Eikonal-based model capable of simulating all possible reentries between the Purkinje system and myocardium, incorporating a new pseudo-time method for myocardium signal propagation.

Findings

Successfully simulates cardiac reentries in real geometries

Demonstrates robustness under pathological conditions

Accurately models electrical stimuli from Purkinje network

Abstract

We propose a novel partitioned scheme based on Eikonal equations to model the coupled propagation of the electrical signal in the His-Purkinje system and in the myocardium for cardiac electrophysiology. This scheme allows, for the first time in Eikonal-based modeling, to capture all possible signal reentries between the Purkinje network and the cardiac muscle that may occur under pathological conditions. As part of the proposed scheme, we introduce a new pseudo-time method for the Eikonal-diffusion problem in the myocardium, to correctly enforce electrical stimuli coming from the Purkinje network. We test our approach by performing numerical simulations of cardiac electrophysiology in a real biventricular geometry, under both pathological and therapeutic conditions, to demonstrate its flexibility, robustness, and accuracy.