Giorno V, Lánský P, Nobile A G, Ricciardi L M
Dipartimento di Informatica e Applicazioni, University of Salerno, Italy.
Biol Cybern. 1988;58(6):387-404. doi: 10.1007/BF00361346.
A stochastic model for single neuron's activity is constructed as the continuous limit of a birth-and-death process in the presence of a reversal hyperpolarization potential. The resulting process is a one dimensional diffusion with linear drift and infinitesimal variance, somewhat different from that proposed by Lánský and Lánská in a previous paper. A detailed study is performed for both the discrete process and its continuous approximation. In particular, the neuronal firing time problem is discussed and the moments of the firing time are explicitly obtained. Use of a new computation method is then made to obtain the firing p.d.f. The behaviour of mean, variance and coefficient of variation of the firing time and of its p.d.f. is analysed to pinpoint the role played by the parameters of the model. A mathematical description of the return process for this neuronal diffusion model is finally provided to obtain closed form expressions for the asymptotic moments and steady state p.d.f. of the neuron's membrane potential.
构建了一个单神经元活动的随机模型，它是存在反向超极化电位时生死过程的连续极限。由此产生的过程是一个具有线性漂移和无穷小方差的一维扩散过程，与兰斯基和兰斯卡先前论文中提出的过程有所不同。对离散过程及其连续近似都进行了详细研究。特别地，讨论了神经元放电时间问题，并明确得到了放电时间的矩。然后使用一种新的计算方法来获得放电概率密度函数。分析了放电时间及其概率密度函数的均值、方差和变异系数的行为，以确定模型参数所起的作用。最后给出了该神经元扩散模型返回过程的数学描述，以获得神经元膜电位渐近矩和稳态概率密度函数的封闭形式表达式。
