Key result
Novel numerical method solves 3D cellular electrical models using implicit time and finite volume discretization.
Why the study?
A numerical scheme for cellular electrophysiology models is challenging due to stiffness from differing time scales of membrane potential diffusion and ionic diffusion.
The proposed numerical method successfully addresses the stiffness of electrodiffusion equations in cellular electrophysiology models.
Implicit time discretization stabilizes stiff cardiac cell models with ion dynamics; leaves open clinical translation pending validation.
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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Mori et al. (2009) studied Cellular electrophysiology (computational model). Numerical method based on electrodiffusion equations was evaluated. The authors present a numerical method using implicit time discretization and finite volume spatial discretization to solve a three-dimensional model of cellular electrical activity.
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