Mitchell Colleen C, Schaeffer David G
Department of Mathematics, Duke University and Center for Nonlinear and Complex Systems, Durham NC 27708, USA.
Bull Math Biol. 2003 Sep;65(5):767-93. doi: 10.1016/S0092-8240(03)00041-7.
In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it useful in numerical simulations, especially in two or three spatial dimensions where numerical efficiency is so important. (2) It can be understood analytically without recourse to numerical simulations. This allows us to determine rather completely how the parameters in the model affect its behavior which in turn provides insight into the effects of the many parameters in more realistic models. (3) It naturally gives rise to a one-dimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenon--subcritical alternans--that does not occur for the commonly used exponential map.
在本文中，我们介绍并研究了一种仅包含内向电流和外向电流的心脏膜电活动模型。该模型有三个方面的用途：（1）它的简单性与菲茨休 - 纳古莫模型相当，这使得它在数值模拟中很有用，特别是在二维或三维空间中，数值效率非常重要。（2）无需借助数值模拟就可以进行解析理解。这使我们能够较为全面地确定模型中的参数如何影响其行为，进而深入了解更现实模型中众多参数的作用。（3）它自然地产生了一个一维映射，该映射将动作电位持续时间指定为前一个舒张期间隔的函数。对于某些参数值，此映射表现出一种新现象——亚临界交替现象——这在常用的指数映射中不会出现。
