Tuckwell H C, Wan F Y, Wong Y S
Biol Cybern. 1984;49(3):155-67. doi: 10.1007/BF00334461.
The firing time of a cable model neuron in response to white noise current injection is investigated with various methods. The Fourier decomposition of the depolarization leads to partial differential equations for the moments of the firing time. These are solved by perturbation and numerical methods, and the results obtained are in excellent agreement with those obtained by Monte Carlo simulation. The convergence of the random Fourier series is found to be very slow for small times so that when the firing time is small it is more efficient to simulate the solution of the stochastic cable equation directly using the two different representations of the Green's function, one which converges rapidly for small times and the other which converges rapidly for large times. The shape of the interspike interval density is found to depend strongly on input position. The various shapes obtained for different input positions resemble those for real neurons. The coefficient of variation of the interspike interval decreases monotonically as the distance between the input and trigger zone increases. A diffusion approximation for a nerve cell receiving Poisson input is considered and input/output frequency relations obtained for different input sites. The cases of multiple trigger zones and multiple input sites are briefly discussed.
采用多种方法研究了电缆模型神经元在白噪声电流注入下的放电时间。去极化的傅里叶分解导致了放电时间矩的偏微分方程。通过微扰法和数值方法求解这些方程，所得结果与蒙特卡罗模拟结果高度吻合。发现对于短时间，随机傅里叶级数的收敛非常缓慢，因此当放电时间较短时，直接使用格林函数的两种不同表示来模拟随机电缆方程的解效率更高，一种表示在短时间内快速收敛，另一种表示在长时间内快速收敛。发现峰峰间隔密度的形状强烈依赖于输入位置。不同输入位置获得的各种形状类似于真实神经元的形状。随着输入与触发区之间距离的增加，峰峰间隔的变异系数单调减小。考虑了接收泊松输入的神经细胞的扩散近似，并获得了不同输入位点的输入/输出频率关系。简要讨论了多个触发区和多个输入位点的情况。
