3D Hybrid Cellular Automata for Cardiac Electrophysiology: A Concept Study

Abstract

A heartbeat is the emerging collective behavior of billions of cells. However, if this synchronization fails, lethal arrhythmias can appear. Mathematical and computational models offer an ethical alternative to in-vivo analyses of cardiac electrophysiological properties. However, the inherent multiscale complexity of the underlying nonlinear dynamics still limits model applicability and predictability. In previous contributions, we implemented a unidirectional Hybrid Cellular Automata (HCA) model reproducing cardiac cell cables and introducing the concept of a statistically distributed cell-cell resistance. Here, we generalize the theoretical framework by considering a bidirectional coupling and simulate physiological and pathological conditions in three-dimensional domains. The work compares two HCA approaches reproducing critical spatiotemporal phenomena and contrasts them with well-established model formulations. We discuss the limits and applicability of discrete vs. continuum approaches in view of improved numerical performances.