Random currents through nerve membranes

✍ Scribed by Henry C. Tuckwell; John B. Walsh

• Publisher: Springer-Verlag
• Year: 1983
• Tongue: English
• Weight: 903 KB
• Volume: 49
• Category: Article
• ISSN: 0340-1200
• DOI: 10.1007/bf00320390

✦ Synopsis

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.