Rinzel J
Mathematical Research Branch, NIDDK, National Institutes of Health, Bethesda, Maryland 20892.
Ann N Y Acad Sci. 1990;591:51-61. doi: 10.1111/j.1749-6632.1990.tb15080.x.
We have discussed two classes of mechanisms that can lead to propagation with nonconstant velocity, and to disruption of temporal patterning of action potentials. Inhomogenieties along the cable due to geometrical change or to altered cell coupling can result in conduction delays, with the possibility of block or reflection. Such conduction irregularities have been considered relevant to cardiac reentry phenomena. Our simulations with a discrete number of excitable cells, coupled by gap junctions, showed that the underlying mathematical structure of a saddle point threshold in an ionic model also contributes in an important way to creating a long delay. Such threshold behavior, although not yet demonstrated for some of the most well-studied models of excitability, should not be viewed as extraordinary; we have seen it in models other than those of references 6 and 7, and have produced it in the Hodgkin-Huxley model with reasonable parameter variations (but have not yet checked for reflections with these modifications). We are unaware of any computations with theoretical models of cardiac membrane that yield robust reflection behavior. Perhaps modifications of these models will be necessary in order to obtain adequate delays for reflection. The mechanism we have described here may serve as a guideline for additional features to seek in such parametric tuning. A different class of factors that contribute to interferring with action potential timing include the effects of previous activity on propagation speed. These influences may be described in terms of the dispersion relation, c(T), the dependence of speed on time between action potentials. The form of this function, for large T, reflects the exponential behavior of the action potential's return to rest. Supernormal conduction reveals itself in the dispersion relation when there is an overshoot of excitability in the return to rest, either a single overshoot or an alternating sequence of over- and undershoots (as seen in some nerve membrane models). A simple kinematic recipe was described for quantitatively predicting timing changes during propagation without having to solve the full cable equations. To apply these concepts to cardiac models it will be necessary to compute the dispersion relation for these models. By studying the dependence of c(T) and the waveform trajectory (including conductances as well as membrane potential) on various parameters one may gain insight into the ionic basis for experimentally observed supernormal conduction.
我们已经讨论了两类可能导致非恒定速度传播以及动作电位时间模式破坏的机制。由于几何形状变化或细胞耦合改变而沿电缆出现的不均匀性可导致传导延迟，并可能出现传导阻滞或反射。这种传导不规则性被认为与心脏折返现象有关。我们用通过缝隙连接耦合的离散数量的可兴奋细胞进行的模拟表明，离子模型中鞍点阈值的潜在数学结构也在很大程度上有助于产生长时间延迟。这种阈值行为，尽管在一些研究得最充分的兴奋性模型中尚未得到证实，但不应被视为异常；我们在参考文献6和7之外的模型中也看到过这种情况，并且在霍奇金 - 赫胥黎模型中通过合理的参数变化也产生过这种情况（但尚未检查这些修改是否会产生反射）。我们不知道有任何关于心脏膜理论模型的计算能产生稳健的反射行为。也许为了获得足够的反射延迟，有必要对这些模型进行修改。我们在此描述的机制可作为在这种参数调整中寻找其他特征的指导原则。另一类导致干扰动作电位时间的因素包括先前活动对传播速度的影响。这些影响可以用色散关系(c(T))来描述，即传播速度对动作电位之间时间的依赖性。对于较大的(T)，这个函数的形式反映了动作电位恢复到静息状态的指数行为。当恢复到静息状态时兴奋性出现超调，无论是单次超调还是超调与欠调交替出现的序列（如在一些神经膜模型中所见），超常传导就会在色散关系中表现出来。描述了一种简单的运动学方法，用于在无需求解完整电缆方程的情况下定量预测传播过程中的时间变化。为了将这些概念应用于心脏模型，有必要计算这些模型的色散关系。通过研究(c(T))以及波形轨迹（包括电导和膜电位）对各种参数的依赖性，人们可以深入了解实验观察到的超常传导的离子基础。
