Schierwagen A K
Karl Marx University, Carl Ludwig Institute for Physiology, Leipzig.
J Theor Biol. 1989 Nov 21;141(2):159-79. doi: 10.1016/s0022-5193(89)80015-3.
A non-uniform equivalent cable model of membrane voltage changes in a passive dendritic tree extending Rall's equivalent cylinder model is presented. It is obtained from a combination of cable theory with the continuum approach. Replacing the fine structure of the branching dendrites by an equivalent, conductive medium characterized by averaged electrical parameters, the one-dimensional cable equations with spatially varying parameters are derived. While these equations can be solved in general only numerically, we were able to formulate a general branching condition (comprising Rall's 3/2 power relationship as a special case) under which analytical solutions can be deduced from those of the equivalent cylinder model. This model allows dendritic trees with a greater variety of branching patterns than before to be analytically treated.
提出了一种扩展拉伊尔等效圆柱体模型的无源树突状树中膜电压变化的非均匀等效电缆模型。它是通过将电缆理论与连续介质方法相结合得到的。用具有平均电学参数的等效导电介质代替分支树突的精细结构，推导出了具有空间变化参数的一维电缆方程。虽然这些方程一般只能用数值方法求解，但我们能够制定一个一般的分支条件（拉伊尔的3/2幂关系作为特殊情况包含在内），在该条件下可以从等效圆柱体模型的解中推导出解析解。该模型允许对具有比以前更多种分支模式的树突状树进行解析处理。
