Halter J A, Clark J W
Division of Restorative Neurology and Human Neurobiology, Baylor College of Medicine, Texas.
J Theor Biol. 1991 Feb 7;148(3):345-82. doi: 10.1016/s0022-5193(05)80242-5.
This paper presents a new model for the characterization of electrical activity in the nodal, paranodal and internodal regions of isolated amphibian and mammalian myelinated nerve fibers. It differs from previous models in the following ways: (1) in its ability to incorporate detailed anatomical and electrophysiological data; (2) in its approach to the myelinated nerve fiber as a multi-axial cable; and (3) in the numerical algorithm used to obtain distributed model equation solutions for potential and current. The morphometric properties are taken from detailed electron microscopic anatomical studies (Berthold & Rydmark, 1983a, Experientia 39, 964-976). The internodal axolemma is characterized as an excitable membrane and model-generated nodal and internodal membrane action potentials are presented. A system of describing equations for the equivalent network model is derived, based on the application of Kirchoff's Current Law, which take the form of multiple cross-coupled parabolic partial differential equations. An implicit numerical integration method is developed and the numerical solution implemented on a parallel processor. Non-uniform spatial step sizes are used, enabling detailed representation of the nodal region while minimizing the number of total segments necessary to represent the overall fiber. Conduction velocities of 20.2 m sec-1 at 20 degrees C for a 15 microns diameter amphibian fiber and 57.6 m sec-1 at 37 degrees C for a 17.5 microns diameter mammalian fiber are achieved, which agrees qualitatively with published experimental data at similar temperatures (Huxley & Stämpfli, 1949, J. Physiol., Lond. 108, 315-339; Rasminsky, 1973, Arch, Neurol. 28, 287-292). The simulation results demonstrate the ability of this model to produce detailed representations of the transaxonal, transmyelin and transfiber potentials and currents, as well as the longitudinal extra-axonal, periaxonal and intra-axonal currents. Also indicated is the potential contribution of the paranodal axolemma to nodal activity as well as the presence of significant longitudinal currents in the periaxonal space adjacent to the node of Ranvier.
本文提出了一种新模型，用于表征分离的两栖动物和哺乳动物有髓神经纤维的结区、旁结区和结间区的电活动。它与以前的模型在以下方面有所不同：（1）能够纳入详细的解剖学和电生理学数据；（2）将有髓神经纤维视为多轴电缆的方法；（3）用于获得电位和电流的分布式模型方程解的数值算法。形态测量特性取自详细的电子显微镜解剖学研究（Berthold & Rydmark，1983a，Experientia 39，964 - 976）。结间轴膜被表征为可兴奋膜，并给出了模型生成的结区和结间膜动作电位。基于基尔霍夫电流定律的应用，推导了等效网络模型的描述方程组，其形式为多个交叉耦合的抛物型偏微分方程。开发了一种隐式数值积分方法，并在并行处理器上实现了数值解。使用了非均匀空间步长，能够详细表示结区，同时最小化表示整个纤维所需的总段数。对于直径为15微米的两栖动物纤维，在20℃时传导速度为20.2米/秒；对于直径为17.5微米的哺乳动物纤维，在37℃时传导速度为57.6米/秒，这与在相似温度下已发表的实验数据定性相符（Huxley & Stämpfli，1949，J. Physiol., Lond. 108，315 - 339；Rasminsky，1973，Arch, Neurol. 28，287 - 292）。模拟结果表明，该模型能够详细表示跨轴突、跨髓鞘和跨纤维的电位和电流，以及纵向轴外、轴周和轴内电流。还指出了旁结轴膜对结区活动的潜在贡献，以及在靠近郎飞结的轴周空间中存在显著的纵向电流。
