Andrietti F, Bernardini G
Biophys J. 1984 Nov;46(5):615-23. doi: 10.1016/S0006-3495(84)84060-6.
The linear cable theory has been applied to a modular structure consisting of n repeating units each composed of two subunits with different values of resistance and capacitance. For n going to infinity, i.e., for infinite cables, we have derived analytically the Laplace transform of the solution by making use of a difference method and we have inverted it by means of a numerical procedure. The results have been compared with those obtained by the direct application of the cable equation to a simplified nonmodular model with "equivalent" electrical parameters. The implication of our work in the analysis of the time and space course of the potential of real fibers has been discussed. In particular, we have shown that the simplified ("equivalent") model is a very good representation of the segmented model for the nodal regions of myelinated fibers in a steady situation and in every condition for muscle fibers. An approximate solution for the steady potential of myelinated fibers has been derived for both nodal and internodal regions. The applications of our work to other cases dealing with repeating structures, such as earthworm giant fibers, have been discussed and our results have been compared with other attempts to solve similar problems.
线性电缆理论已应用于一个模块化结构，该结构由n个重复单元组成，每个重复单元由两个具有不同电阻和电容值的亚单元构成。对于n趋于无穷大的情况，即对于无限长电缆，我们利用差分法解析推导了解的拉普拉斯变换，并通过数值方法对其进行了反演。我们将结果与通过将电缆方程直接应用于具有“等效”电学参数的简化非模块化模型所得到的结果进行了比较。我们还讨论了我们的工作在分析真实纤维电位的时间和空间过程中的意义。特别是，我们已经表明，简化的（“等效”）模型在稳定状态下以及在肌肉纤维的各种条件下，对于有髓纤维的节点区域的分段模型是一种非常好的表示。我们已经推导了有髓纤维在节点和节间区域的稳定电位的近似解。我们还讨论了我们的工作在处理重复结构的其他情况（如蚯蚓巨纤维）中的应用，并将我们的结果与解决类似问题的其他尝试进行了比较。
