We present a numerical method for solving the system of equations of a model of cellular electrical activity that takes into account both geometrical effects and ionic concentration dynamics. A challenge in constructing a numerical scheme for this model is that its equations are stiff: There is a time scale associated with "diffusion" of the membrane potential that is much faster than the time scale associated with the physical diffusion of ions. We use an implicit discretization in time and a finite volume discretization in space. We present convergence studies of the numerical method for cylindrical and two-dimensional geometries for several cases of physiological interest.
|Original language||English (US)|
|Number of pages||50|
|Journal||Communications in Applied Mathematics and Computational Science|
|State||Published - Jan 1 2009|
- Ephaptic transmission
- Finite volume method
- Three-dimensional cellular electrophysiology