Kügler Philipp, Bulelzai M A K, Erhardt André H
Institute of Applied Mathematics and Statistics, University of Hohenheim, Schloss 1, Stuttgart, 70599, Germany.
Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, Linz, 4040, Austria.
BMC Syst Biol. 2017 Apr 4;11(1):42. doi: 10.1186/s12918-017-0422-4.
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.
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.
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.
早期后除极（EADs）是心脏动作电位（APs）复极阶段的病理性电压振荡。EADs由药物、氧化应激或离子通道疾病引起，在最近重新定义心脏药物安全范式的尝试中，它们被视为心脏心律失常的潜在先兆。实验中观察到的EADs的不规则行为先前被归因于周期性起搏下的混沌EAD动力学，这是由微分方程确定性AP系统快速子系统中的同宿分岔所导致的。
在本文中，我们证明动作电位模型快速子系统中的同宿分岔对于混沌EADs的产生既不是必要条件也不是充分条件。我们认为，全AP系统中极限环的倍周期（PD）分岔级联为各种模型中的混沌EAD动力学铺平了道路，这些模型包括：a）周期性起搏和自发活动的心肌细胞，b）周期性起搏和非活动的心肌细胞，以及c）非起搏和自发活动的心肌细胞。此外，我们的分岔分析表明，混沌EAD动力学可能与完全规则的AP动力学以稳定的方式共存，其中只有初始条件决定显示哪种类型的动力学。
EADs是心律失常的潜在来源，因此从药物心脏毒性测试和心肌病治疗的角度来看都具有相关性。本文中引入的混沌EADs与极限环倍周期级联的模型无关关联，为通过分岔控制理论和逆分岔分析研究混沌EADs提供了新的机会。此外，我们的结果可能为混沌EADs在均匀和异质多细胞及心脏组织制剂中的同步和传播提供新的见解。
