Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death process approach.
Biol Cybern
; 58(6): 387-404, 1988.
Article
em En
| MEDLINE
| ID: mdl-3395633
ABSTRACT
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.
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Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
Modelos Neurológicos
/
Condução Nervosa
Tipo de estudo:
Prognostic_studies
Idioma:
En
Revista:
Biol Cybern
Ano de publicação:
1988
Tipo de documento:
Article