Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations

Philipp Kügler,M.A.K. Bulelzai,André H. Erhardt

doi:10.1186/s12918-017-0422-4

Abstract

BackgroundEarly afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations.ResultsIn this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed.ConclusionsEADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.

Highlights

Afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs)
As the occurence of chaotic Eearly afterdepolarization (EAD) of the type shown in Fig. 1PP has been attributed in [5, 12] to the steep slope of the action potential duration (APD) restitution curve, see Fig. 2PP, we first wondered
In our attempt to find a common explanation for the chaotic EAD dynamics observed in Figs. 1PP, 1PV and 1UP, we focused on the hypothesis featured in [10, 12,13,14,15] according to which chaotic EADs have their source in a saddle-homoclinic bifurcation in the fast AP subdynamics

Summary

Introduction

Afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). Though biological systems are affected by intrinsic and external stochastic noise, experimentally recorded irregular dynamics in the action potential (the characteristic membrane voltage response to a superthreshold electric stimulus) of cardiomyocytes have still been shown to be of the chaotic nature [2, 3] It has been observed in [2, 3] that by increasing the frequency of the stimulating current (or correspondingly by decreasing the pacing cycle length (PCL)), the 1:1 entrainment of the action potential is lost and a sequence of different m:n rhythms with alterations in the action potential duration (APD) called AP alternans is obtained before the dynamics become irregular. For later reference we emphasize that [2] studied chaotic APD variations in periodically forced cardiac pacemakers cells (i.e., they show spontaneous action potential oscillations in the absence of a stimulus), while [3] studied chaotic APD variations in periodically forced non-spontaneously active Purkinje fibre and ventricular muscle cells

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