Random currents through nerve membranes. I. Uniform poisson or white noise current in one-dimensional cables.
The linear cable equation with uniform Poisson or white noise input current is employed as a model for the voltage across the membrane of a one-dimensional nerve cylinder, which may sometimes represent the dendritic tree of a nerve cell. From the Green's function representation of the solutions, the mean, variance and covariance of the voltage are found. At large times, the voltage becomes asymptotically wide-sense stationary and we find the spectral density functions for various cable lengths and boundary conditions. For large frequencies the voltage exhibits "1/f3/2 noise". Using the Fourier series representation of the voltage we study the moments of the firing times for the diffusion model with numerical techniques, employing a simplified threshold criterion. We also simulate the solution of the stochastic cable equation by two different methods in order to estimate the moments and density of the firing time.
D000200:Action Potentials; D000818:Animals; D003712:Dendrites / Q000502:physiology; D004594:Electrophysiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D013223:Statistics as Topic; D013997:Time Factors