Dynamical analysis of early afterdepolarization patterns in a biophysically detailed cardiac model.

Abstract

Arrhythmogenic early afterdepolarizations (EADs) are investigated in a biophysically detailed mathematical model of a rabbit ventricular myocyte, providing their location in the parameter phase space and describing their dynamical mechanisms. Simulations using the Sato model, defined by 27 state variables and 177 parameters, are conducted to generate electrical action potentials (APs) for different values of the pacing cycle length and other parameters related to sodium and calcium concentrations. A detailed study of the different AP patterns with or without EADs is carried out, showing the presence of a high variety of temporal AP configurations with chaotic and quasiperiodic behaviors. Regions of bistability are identified and, importantly, linked to transitions between different behaviors. Using sweeping techniques, one-, two-, and three-parameter phase spaces are provided, allowing ascertainment of the role of the selected parameters as well as location of the transition regions. A Devil's staircase, with symbolic sequence analysis, is proposed to describe transitions in the ratio between the number of voltage (EAD and AP) peaks and the number of APs. To conclude, the obtained results are linked to recent studies for low-dimensional models and a conjecture is made for the internal dynamical structure of the transition region from non-EAD to EAD behavior using fold and cusp bifurcations and maximal canards.