Diffusion Reaction Eikonal Alternant Model: Towards Fast Simulations of Complex Cardiac Arrhythmias

Abstract

Reaction-diffusion (RD) computer models are suitable to investigate the mechanisms of cardiac arrthymias but not directly applicable in clinical settings due to their computational cost. On the other hand, alternative faster eikonal models are incapable of reproducing reentrant activation when solved by iterative methods. The diffusion reaction eikonal alternant model (DREAM) is a new method in which eikonal and RD models are alternated to allow for reactivation. To solve the eikonal equation, the fast iterative method was modified and embedded into DREAM. Obtained activation times control transmembrane voltage courses in the RD model computing, while repolarization times are provided back to the eikonal model. For a planar wave-front in the center of a 2D patch, DREAM action potentials (APs) have a small overshoot in the upstroke compared to pure RD simulations (monodomain) but similar AP duration. DREAM conduction velocity does not increase near boundaries or stimulated areas as it occurs in RD. Anatomical reentry was reproduced with the S1-S2 protocol. This is the first time that an iterative method is used to solve the eikonal model in a version that admits reactivation. This method can facilitate uptake of computer models in clinical settings. Further improvements will allow to accurately represent even more complex patterns of arrhythmia.