We use high-order approximation schemes for the space derivatives in the nonlinear cable equation and investigate the behavior of numerical solution errors by using exact solutions, where available, and grid convergence. The space derivatives are numerically approximated by means of differentiation matrices. A flexible form for the injected current is used that can be adjusted smoothly from a very broad to a narrow peak, which leads, for the passive cable, to a simple, exact solution. We provide comparisons with exact solutions in an unbranched passive cable, the convergence of solutions with progressive refinement of the grid in an active cable, and the simulation of spike initiation in a biophysically realistic single-neuron model.
Model Type: Neuron or other electrically excitable cell
Cell Type(s): Neocortex L5/6 pyramidal GLU cell; Hodgkin-Huxley neuron
Model Concept(s): Action Potential Initiation; Dendritic Action Potentials; Active Dendrites; Action Potentials; Methods
Simulation Environment: MATLAB
Implementer(s): Omurtag, Ahmet [aomurtag at gmail.com]
References:
Omurtag A, Lytton WW. (2010). Spectral method and high-order finite differences for the nonlinear cable equation. Neural computation. 22 [PubMed]