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.

翻译：我们提出了一种基于Eikonal方程的新型分区方案，用于模拟心脏电生理中希氏-浦肯野系统与心肌中电信号的耦合传播。该方案首次在基于Eikonal的建模中实现了对病理条件下可能发生的浦肯野网络与心肌之间所有可能信号折返的捕捉。作为所提方案的一部分，我们针对心肌中的Eikonal-扩散问题引入了一种新的伪时间方法，以准确施加来自浦肯野网络的电刺激。我们通过在真实双心室几何结构中进行病理和治疗条件下的心脏电生理数值模拟来测试该方法，验证了其灵活性、鲁棒性和准确性。