The purpose of this work was to determine whether computed temporally coded axonal information generated by Poisson process stimulation were modified during long-distance propagation, as originally suggested by S. A. George. Propagated impulses were computed with the use of the Hodgkin-Huxley equations and cable theory to simulate excitation and current spread in 100-microns-diam unmyelinated axons, whose total length was 8.1 cm (25 lambda) or 101.4 cm (312.5 lambda). Differential equations were solved numerically, with the use of trapezoidal integration over small, constant electrotonic and temporal steps (0.125 lambda and 1.0 microsecond, respectively). 2. Using dual-pulse stimulation, we confirmed that for interstimulus intervals between 5 and 11 ms, the conduction velocity of the second of a short-interval pair of impulses was slower than that of the first impulse. Further, with sufficiently long propagation distance, the second impulse's conduction velocity increased steadily and eventually approached that of the first impulse. This effect caused a spatially varying interspike interval: as propagation proceeded, the interspike interval increased and eventually approached stabilization. 3. With Poisson stimulation, the peak amplitude of propagating action potentials varied with interspike interval durations between 5 and 11 ms. Such amplitude attenuation was caused by the incomplete relaxation of parameters n (macroscopic K-conductance activation) and h (macroscopic Na-conductance inactivation) during the interspike period. 4. The stochastic properties of the impulse train became less Poisson-like with propagation distance. In cases of propagation over 99.4 cm, the impulse trains developed marked periodicities in Interevent Interval Distribution and Expectation Density function because of the axially modulated transformation of interspike intervals. 5. Despite these changes in impulse train parameters, the arithmetic value of the mean interspike interval did not change as a function of propagation distance. This work showed that in theory, whereas the pattern of Poisson-like impulse codes was modified during long-distance propagation, their mean rate was conserved.
摘要
这项工作的目的是确定由泊松过程刺激产生的计算时间编码轴突信息在长距离传播过程中是否如S. A. 乔治最初所提出的那样发生了改变。使用霍奇金 - 赫胥黎方程和电缆理论计算传播的冲动，以模拟直径100微米的无髓轴突中的兴奋和电流传播，其总长度为8.1厘米（25λ）或101.4厘米（312.5λ）。使用梯形积分在小的、恒定的电紧张和时间步长（分别为0.125λ和1.0微秒）上对微分方程进行数值求解。2. 使用双脉冲刺激，我们证实，对于5至11毫秒的刺激间隔，短间隔脉冲对中的第二个脉冲的传导速度比第一个脉冲慢。此外，在足够长的传播距离下，第二个脉冲的传导速度稳步增加，最终接近第一个脉冲的传导速度。这种效应导致了空间上变化的峰峰间隔：随着传播的进行，峰峰间隔增加并最终趋于稳定。3. 在泊松刺激下，传播动作电位的峰值幅度随5至11毫秒的峰峰间隔持续时间而变化。这种幅度衰减是由峰峰间期参数n（宏观钾电导激活）和h（宏观钠电导失活）的不完全弛豫引起的。4. 冲动序列的随机特性随传播距离变得不那么像泊松分布。在传播超过99.4厘米的情况下，由于峰峰间隔的轴向调制变换，冲动序列在事件间隔分布和期望密度函数中出现明显的周期性。5. 尽管冲动序列参数有这些变化，但平均峰峰间隔的算术值并不随传播距离而变化。这项工作表明，理论上，虽然类似泊松的冲动编码模式在长距离传播过程中发生了改变，但其平均速率保持不变。
