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

### Author information

- 1
- Institute of Applied Mathematics and Statistics, University of Hohenheim, Schloss 1, Stuttgart, 70599, Germany. philipp.kuegler@uni-hohenheim.de.
- 2
- Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, Linz, 4040, Austria. philipp.kuegler@uni-hohenheim.de.
- 3
- Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, Linz, 4040, Austria.
- 4
- Institute of Applied Mathematics and Statistics, University of Hohenheim, Schloss 1, Stuttgart, 70599, Germany.

### Abstract

#### BACKGROUND:

Early 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.

#### RESULTS:

In 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.

#### CONCLUSIONS:

EADs 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.

#### KEYWORDS:

Bifurcation theory; Cardiac action potential; Chaos; Early afterdepolarizations; Nonlinear dynamics

- PMID:
- 28376924
- PMCID:
- PMC5379775
- DOI:
- 10.1186/s12918-017-0422-4

- [Indexed for MEDLINE]