Vermeulen A, Rospars J P
Laboratoire de Biométrie, Institut National de la Recherche Agronomique, Versailles, France.
J Neurosci Methods. 1998 Aug 1;82(2):123-34. doi: 10.1016/s0165-0270(98)00040-5.
A method is presented for solving the cable equation for a spiking neuron below firing threshold or a nonspiking neuron of arbitrary geometry under constant stimulation. The neuron structure is considered as a tree composed of a set of cylinder cables of three types (terminal, intermediate and branching) characterized by their lengths, diameters and linear membrane properties. The stimulation can result from either a uniform conductance-change over a whole cable segment or a point injection of a current. Other special segments are considered (synapses, voltage clamp, lumped soma). Equations are given for replacing any segment with its Thévenin equivalent, i.e. resistance and electromotive force. The step by step use of these elementary equations allows one to find the Thévenin equivalent of the whole neuron and to determine the steady-state membrane potential at any point.
本文提出了一种方法，用于求解在恒定刺激下低于放电阈值的脉冲神经元或任意几何形状的非脉冲神经元的电缆方程。神经元结构被视为一棵树，由一组三种类型的圆柱电缆（终端、中间和分支）组成，其特征在于它们的长度、直径和线性膜特性。刺激可以由整个电缆段上的均匀电导变化或电流的点注入引起。还考虑了其他特殊段（突触、电压钳、集总胞体）。给出了用其戴维南等效电路（即电阻和电动势）替换任何段的方程。逐步使用这些基本方程可以找到整个神经元的戴维南等效电路，并确定任何点的稳态膜电位。
