Cardiac dynamics of a human ventricular tissue model with a focus on early afterdepolarizations

This study aims to investigate the computationally complex cardiac dynamics of the well-known human ventricular model of Ten Tusscher and Panfilov from 2006. The corresponding physical system of the cellular model is described by a set of nonlinear differential equations containing various system parameters. If one or a set of specific system parameters crosses a certain threshold, the system is forced to change dynamics, which might result in dangerous cardiac dynamics and can be precursors to cardiac death. To perform an efficient numerical analysis, the original model is revised and simplified such that the modified models perfectly match the trajectory (time-dependent cardiac potential) of the original model. Moreover, it is demonstrated that the reduced models have the same dynamics. Furthermore, using the lowest dimensional model, it is shown by means of bifurcation analysis that combinations of reduced slow and rapid potassium currents and an enhanced calcium current may lead to early afterdepolarizations, which are pathological voltage oscillations during the repolarization or plateau phase of cardiac action potentials and are considered potential precursors to cardiac arrhythmia. Finally, to outline synchronization effects and pattern formation on a larger scale (macro scale), a two-dimensional epicardial monodomain equation is studied.