具有反射边界和诱导搏动的心肌细胞随机相位模型
A stochastic phase model with reflective boundary and induced beating for the cardiac muscle cells
摘要：
本文研究了心肌细胞群体效应的随机相位模型。该模型是随机积分-点火模型的推广，在该模型中我们引入了跳动后的不可逆性、诱导跳动和不可逆性。我们重点研究了（同步）心跳间隔的期望和方差。特别地，对于单个孤立细胞，我们得到了搏动间隔的封闭形式的期望和方差，并且我们发现方差系数（CV）有上限$\sqrt{2/3}$。对于两个耦合细胞，我们推导了预期的同步拍频间隔和相位分布密度的偏微分方程。此外，我们还考虑了传统的Kuramoto模型的两个和$N$ -细胞模型，其中我们建立了一个新的分析使用随机微积分获得的“同步”的跳动间隔的CV，并作出了一些改进的文献工作。
英文摘要：
We consider the stochastic phase models for the community effect of cardiac muscle cells. The model is the extension of the stochastic integrate-and-fire model in which we incorporate the irreversibility after beating, induced beating and refractory. We focus on investigating the expectation and variance of (synchronized) beating interval. In particular, for the single-isolated cell, we obtain the closed-form expectation and variance of the beating interval, and we discover that the coefficient of variance (CV) has upper limit $\sqrt{2/3}$. For two-coupled cells, we derive the partial differential equations (PDEs) for the expected synchronized beating intervals and the distribution density of phase. Moreover, we also consider the conventional Kuramoto model for both two- and $N$-cells models, where we establish a new analysis using stochastic calculus to obtain the CV of the ''synchronized'' beating interval, and make some improvement to the literature work.
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