Goldman L, Albus J S
Biophys J. 1968 May;8(5):596-607. doi: 10.1016/S0006-3495(68)86510-5.
For myelinated fibers, it is experimentally well established that spike conduction velocity is proportional to fiber diameter. However no really satisfactory theoretical treatment has been proposed. To treat this problem a theoretical axon was described consisting of lengths of passive leaky cable (internode) regularly interrupted by short isopotential patches of excitable membrane (node). The nodal membrane was assumed to obey the Frankenhaeuser-Huxley equations. The explicit diameter dependencies of the various parameters were incorporated into the equations. The fiber diameter to axon diameter ratio was taken to be constant, and the internode length was taken to be proportional to the fiber diameter. Both these conditions reflect the situation that exists in real, experimental fibers. Dimensional analysis shows that these anatomical conditions are equivalent to Rushton's (1951) assumption of corresponding states. Hence, conduction velocity will be proportional to fiber diameter, in complete agreement with the experimental findings. Digital computer solutions of these equations were made in order to compute a set of actual velocities. Computations made with constant internode length or constant myelin thickness (i.e., nonconstant fiber diameter to axon diameter ratio) did not show linearity of the velocity-diameter relation.
对于有髓纤维，实验已充分证实动作电位传导速度与纤维直径成正比。然而，尚未提出真正令人满意的理论处理方法。为解决这个问题，描述了一种理论轴突，它由被动漏电电缆段（节间）组成，这些节间被短的可兴奋膜等电位片（节点）有规律地中断。假定节点膜服从弗兰克豪泽 - 赫胥黎方程。将各种参数的明确直径依赖性纳入方程中。纤维直径与轴突直径之比被视为常数，节间长度被视为与纤维直径成正比。这两个条件都反映了实际实验纤维中的情况。量纲分析表明，这些解剖学条件等同于拉什顿（1951年）的对应态假设。因此，传导速度将与纤维直径成正比，这与实验结果完全一致。为了计算一组实际速度，对这些方程进行了数字计算机求解。在节间长度恒定或髓鞘厚度恒定（即纤维直径与轴突直径之比不恒定）的情况下进行的计算并未显示速度 - 直径关系的线性。
