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

Abstract

The paper is aimed to investigate computationally complex cardiac dynamics of the famous human ventricular model of ten Tusscher and Panfilov from 2006. The corresponding physical system is modeled by a set of nonlinear differential equations containing various of system parameters. In case a specific physical parameter 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. For the performance of an efficient numerical analysis the original model is remodeled and simplified in such a way that the modified models perfectly matches the trajectory of the original model. Moreover, it is demonstrated that the simplified models have the same dynamics. Furthermore, using the lowest dimensional model it is systematically shown by means of bifurcation analysis that combinations of reduced slow and rapid potassium channels and enhanced sodium channel may lead to early afterdepolarizations. Finally, synchronization and the effect of EADs on larger scale (macro scale) is investigated numerically by studying the corresponding monodomain model. To this end we study the pattern formation of an one dimensional network of epi-, mid-myo- and endocardial cells and a two dimensional epicardial monodomain equation.