An eikonal model with re-excitability for fast simulations in cardiac electrophysiology

Precision cardiology based on cardiac digital twins requires accurate simulations of cardiac arrhythmias. However, detailed models, such as the monodomain model, are computationally costly and have limited applicability in practice. Thus, it desirable to have fast models that can still represent the main physiological features presented during cardiac arrhythmias. The eikonal model is an approximation of the monodomain model that is widely used to describe the arrival times of the electrical wave. However, the standard eikonal model does not generalize to the complex re-entrant dynamics that characterize the cardiac arrhythmias. In this work, we propose an eikonal model that includes the tissue re-excitability, which allows to describe re-entries. The re-excitability properties are inferred from the monodomain model. Our eikonal model also handles the tissue anisotropy and heterogeneity. We compare the eikonal model to the monodomain model in various numerical experiments in the atria and the ventricles. The eikonal model is qualitatively accurate in the simulation of re-entries and can be potentially ran in real-time, opening the door to its clinical applicability.