Dimitrov Alexander G
Centre of Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia 1113, Bulgaria.
J Theor Biol. 2005 Aug 21;235(4):451-62. doi: 10.1016/j.jtbi.2005.01.024.
The current opinion about processes in myelinated axon is that action potential saltatorially propagates between nodes of Ranvier and passively charges internodal axolemma thus causing depolarizing afterpotentials (DAP). Demyelination blocks the conduction that gives additional argument in favor of hypothesis that internode is not able to be activated by the existing internodal sodium channels. The results of our modeling study shows that, when periaxonal space is sufficiently narrow, saltatorial action potential is able to activate internodes. Low density of internodal sodium channels is sufficient to generate active internodal waves that slowly propagate from nodes towards corresponding midinternodes where they collide. The periaxonal width that stops internodal wave propagation (about 400 nm) is significantly larger than the highest value of the physiological range for this parameter (30 nm). Internodal activation is directly manifested as transmembrane internodal potential or as a full-sized action potential in periaxonal space where it can hardly be detected, and only as a small deflection in intracellular space. However, changes in the periaxonal potential cause transmyelin currents that lead to significant DAP. The shape and amplitude of DAP depends on myelin parameters and densities of internodal channels. Several technical parameters affect the results of calculations. Internodal spatial segmentation has to be sufficiently fine (at most 20 microm) for the model to be able to simulate internodal activation. We employ 338 internodal segments as compared with up to 21 used in previous models. Ionic accumulation together with related diffusive and electrical processes alter the calculated DAP amplitude. Inclusion of these processes in calculations demands such increase in the total number of segments that the numerical methods used up to now become unapplicable. To overcome the problem, an iterative implicit approach is proposed. It reduces a matrix of general type in multi-cable models to tridiagonal one and accelerates calculations considerably.
目前关于有髓轴突中过程的观点是，动作电位在郎飞结之间跳跃式传播，并被动地使结间轴突膜带电，从而导致去极化后电位（DAP）。脱髓鞘会阻断传导，这为结间区无法被现有的结间钠通道激活这一假说提供了额外的论据。我们的建模研究结果表明，当轴周间隙足够狭窄时，跳跃式动作电位能够激活结间区。结间钠通道的低密度足以产生从结向相应结间中点缓慢传播并在那里碰撞的活跃结间波。阻止结间波传播的轴周宽度（约400纳米）明显大于该参数生理范围的最高值（30纳米）。结间激活直接表现为跨结间电位，或在轴周间隙中表现为全尺寸动作电位（在该间隙中很难检测到），而在细胞内间隙中仅表现为小的偏转。然而，轴周电位的变化会引起跨髓鞘电流，从而导致显著的DAP。DAP的形状和幅度取决于髓鞘参数和结间通道的密度。几个技术参数会影响计算结果。结间空间分割必须足够精细（最多20微米），以便模型能够模拟结间激活。我们采用了338个结间段，而之前的模型最多使用21个。离子积累以及相关的扩散和电过程会改变计算出的DAP幅度。在计算中纳入这些过程需要增加段的总数，以至于到目前为止使用的数值方法变得不适用。为了克服这个问题，提出了一种迭代隐式方法。它将多电缆模型中的一般类型矩阵简化为三对角矩阵，并显著加速计算。
