Abramovich-Sivan S, Akselrod S
Abramson Institute of Medical Physics, Sackler Faculty of Exact Sciences, Tel Aviv University, Israel.
J Theor Biol. 1998 Jun 21;192(4):567-79. doi: 10.1006/jtbi.1998.0684.
This study introduces a simple mathematical model for a pacemaker cell affected by an external parasympathetic and/or sympathetic input. The model presented is based on the two most important functional properties of the cardiac pacemaker cells. The first property is the intrinsic pacemaker cycle length, an "internal" parameter of the cell. The second basic property is the phase response curve (PRC), a function which reflects the various interactions of the pacemaker cell with the outside world (i.e. interaction with surrounding cells, external stimulus). The vagal stimulus is simulated as affecting the pacemaker cycle length via a PRC, while the sympathetic input is expressed in the model as a continuous reduction in the pacemaker cycle length. When combined vagal and sympathetic activation is allowed, our model shows that autonomic systems are also capable of interacting. First, we studied the entrainment phenomena resulting from a repetitively applied vagal stimulus. Various complex patterns of dynamic interaction between the pacemaker cell and the vagal input were simulated. The PRC parameters appear to be an important factor in the prediction of the entrainment phenomena. Specifically, they permit a quantitative description of the limits of a 1:1 synchronization zone. Next, we apply this model to qualitatively investigate the phenomenon of "accentuated antagonism" between parasympathetic and sympathetic autonomic branches. We examined the various options for this interaction in regulating the pacemaker periodicity. Although this model is a simplified reflection of the biological system, we conclude that it can mimic many aspects of the dynamic autonomic control and of the possible interactions between vagal and sympathetic stimulation of a pacemaker cell.
本研究介绍了一种受外部副交感神经和/或交感神经输入影响的起搏器细胞的简单数学模型。所提出的模型基于心脏起搏器细胞的两个最重要的功能特性。第一个特性是固有起搏器周期长度，这是细胞的一个“内部”参数。第二个基本特性是相位响应曲线（PRC），该函数反映了起搏器细胞与外界的各种相互作用（即与周围细胞的相互作用、外部刺激）。迷走神经刺激被模拟为通过PRC影响起搏器周期长度，而交感神经输入在模型中表现为起搏器周期长度的持续缩短。当允许迷走神经和交感神经联合激活时，我们的模型表明自主神经系统也能够相互作用。首先，我们研究了重复施加迷走神经刺激所导致的同步现象。模拟了起搏器细胞与迷走神经输入之间各种复杂的动态相互作用模式。PRC参数似乎是预测同步现象的一个重要因素。具体而言，它们允许对1:1同步区的界限进行定量描述。接下来，我们应用该模型定性研究副交感神经和交感神经自主分支之间的“强化拮抗”现象。我们研究了这种相互作用在调节起搏器周期性方面的各种选项。尽管该模型是生物系统的简化反映，但我们得出结论，它可以模拟动态自主控制的许多方面以及起搏器细胞迷走神经和交感神经刺激之间可能的相互作用。
