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Abstract
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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.
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Keywords
three-dimensional cellular
electrophysiology, electrodiffusion, ephaptic transmission,
finite volume method
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Mathematical Subject Classification
Primary: 65M12, 92C30, 92C50
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Milestones
Received: 20 June 2007
Revised: 22 June 2009
Accepted: 24 June 2009
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