Ikeda N, Tsuruta H, Sato T
Biol Cybern. 1981;42(2):117-28. doi: 10.1007/BF00336729.
As a method for investigating entrainment phenomena found in biological oscillations, a model is presented which is formulated as a set of difference equations on the basis of "phase response curves" of biological oscillators. Properties of the model are discussed and synchronization of cardiac pacemaker cells to the external periodic stimuli is analyzed by use of the model. It is shown that the model is reducible to an equivalent system to the mathematical neuron model of Nagumo et al. under a specific parametric condition of the phase response curve. As an application to the cardiac arrhythmias, the model of ventricular parasystoles studied by Moe et al. is described mathematically in terms of a system of difference equations. In addition, a more comprehensive model of ventricular parasystoles is proposed.
作为一种研究生物振荡中夹带现象的方法，本文提出了一个模型，该模型基于生物振荡器的“相位响应曲线”被公式化为一组差分方程。讨论了该模型的性质，并利用该模型分析了心脏起搏器细胞与外部周期性刺激的同步性。结果表明，在相位响应曲线的特定参数条件下，该模型可简化为与Nagumo等人的数学神经元模型等价的系统。作为对心律失常的应用，用差分方程组对Moe等人研究的心室并行心律模型进行了数学描述。此外，还提出了一个更全面的心室并行心律模型。
