Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations
Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations
复制标题
心脏动作电位模型中极限循环的周期倍增级联是混沌早期后除极的前兆
作者：
P. Kügler;M. Bulelzai;André H. Erhardt
背景：心脏去极化后（EADs）是心脏动作电位（APs）复极化阶段的病理性电压振荡。EADs是由药物、氧化应激或离子通道疾病引起的，在最近重新定义心脏药物安全范式的尝试中，它们被认为是心律失常的潜在前兆。实验中观察到的EAD的不规则行为先前归因于周期起跳下的混沌EAD动力学，这可能是由于确定性AP微分方程系统的快速子系统中的同斜分岔。结果本文证明了动作电位模型的快速子系统的同斜分叉既不是混沌EADs发生的充分条件也不是必要条件。我们认为，在完整的AP系统中，极限环的周期加倍（PD）分岔级联为各种模型中的混乱EAD动力学铺平了道路，包括a)周期性节律和自发活动的心肌细胞，b)周期性节律和非活动的心肌细胞以及c)无节律和自发活动的心肌细胞。此外，我们的分岔分析表明混沌EAD动力学可以与完全规则AP动力学稳定共存，其中只有初始条件决定显示哪种类型的动力学。结论sead是心律失常的潜在来源，因此从药物心毒性试验和心肌病治疗的角度来看都具有重要意义。本文引入的混沌EADs与极限环周期级联的模型无关关联，为利用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在同质和异质多细胞和心脏组织制备中的同步和传播提供新的思路。
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.
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