Scaling laws for myelinated axons derived from an electrotonic core-conductor model
Scaling laws for myelinated axons derived from an electrotonic core-conductor model
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DOI：
10.1142/s0219635204000427
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发表时间：
2004-06-04
影响因子：
1.8
通讯作者：
Basser, Peter J.
中科院分区：
文献类型：
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作者：
Basser, Peter J.
描述有髓鞘轴突的被动线性（“电紧张”）响应的宏观电缆方程先前是使用Keller的两空间均匀化方法从分段电缆方程导出的[Basser，PJ，Med. and Biol. Comput.，1993年，第31卷，第31页。S87-S92]。在这里，我们使用这个平均电缆方程的空间和长度常数来预测经典的标度律，这些标度律控制轴突髓鞘的内径和外径之间的关系以及Ranvier相邻节点之间的距离。这些定律是通过使沿着轴突的电干扰的特征速度最大化而导出的，即，在节点宽度恒定的约束下，宏观电缆的特征长度与特征时间常数的比值。利用这个结果，也可以证明所有有髓鞘的轴突都具有同样的容错性。在此分析中没有使用自由参数;在这些计算中使用的所有变量和物理常数都来自已发表的实验数据。
A macroscopic cable equation, which describes the passive linear ("electrotonic") response of a myelinated axon, was previously derived from a segmented cable equation using Keller's two-space homogenization method [Basser, PJ, Med. and Biol. Comput., 1993, Vol. 31, pp. S87-S92]. Here we use the space and length constants of this averaged cable equation to predict classical scaling laws that govern relationships among the inner and outer diameters of the axon's myelin sheath and the distance separating adjacent nodes of Ranvier. These laws are derived by maximizing the characteristic speed of an electrical disturbance along the axon, i.e., the ratio of the characteristic length and the characteristic time constants of the macroscopic cable, subject to the constraint that the nodal width is constant. Using this result, it is also possible to show that all myelinated axons are equally fault tolerant. No free parameters were used in this analysis; all variables and physical constants used in these calculations were taken from published experimental data.