Purkinje和心室心肌细胞模型中的复杂动力学
On complex dynamics in a Purkinje and a ventricular cardiac cell model
摘要：
心肌细胞可以表现出复杂的模式，包括不规则的行为，如混乱或（混乱）早期后去极化（EAD），这可能导致心脏猝死。合适的数学模型及其分析有助于预测这种现象的发生并解码其机理。本文的重点是研究由常微分方程描述的心肌细胞动力学。这通常通过研究浦肯野细胞模型和改良的心室细胞模型来进行。我们发现在浦肯野细胞模型中的泄漏电流的混沌动力学，以及在心室细胞模型中的快速钾电流减少和钙电流增强的EAD和混沌--这些特征已经在实验中观察到，并且已知存在于某些模型中，但是对于目前考虑的模型来说是新的。我们还调查了这两个系统的相关单域模型，以研究与所发现的功能有关的宏观尺度上的细胞的同步和行为。该模型定性地表现出与实验观察到的行为相同的行为。然而，对于某些参数设置，动态发生在非生理范围内。
英文摘要：
Cardiac muscle cells can exhibit complex patterns including irregular behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which can lead to sudden cardiac death. Suitable mathematical models and their analysis help to predict the occurrence of such phenomena and to decode their mechanisms. The focus of this paper is the investigation of dynamics of cardiac muscle cells described by systems of ordinary differential equations. This is generically performed by studying a Purkinje cell model and a modified ventricular cell model. We find chaotic dynamics with respect to the leak current in the Purkinje cell model, and EADs and chaos with respect to a reduced fast potassium current and an enhanced calcium current in the ventricular cell model -- features that have been experimentally observed and are known to exist in some models, but are new to the models under present consideration. We also investigate the related monodomain models of both systems to study synchronisation and the behaviour of the cells on macro-scale in connection with the discovered features. The models show qualitatively the same behaviour to what has been experimentally observed. However, for certain parameter settings the dynamics occur within a non-physiological range.
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