Collaborators: Chuan Li (UTK) , Jack Buchanan (UT Memphis)
Electrical propagation in excitable tissue, such as nerve fibers and
heart muscle, is described by a parabolic PDE
of diffusion-reaction type for the transmembrane voltage,
known as the cable equation.
The source term, representing the sum of ionic currents
across the cell membrane, is modeled by complicated ionic models
appropriate to the tissue.
One of the successful ionic models for cardiac myocytes is the Luo-Rudy I (1991) model (available at cellML). It involves 7 ODEs for the "gate" variables, with highly nonlinear coefficients (functions of voltage).
We are trying to find ways to speed up the computations, which turn out to be extremely demanding, even in 1D, due to very high diffusivity (low resistance) and very steep gradients. We use low and high order, explicit and implicit, non-adaptive and adaptive time-stepping schemes, and parallelization on distributed multiprocessors (with MPI library).
We implemented parallel methods in space only, in time only, and in time-and-space, which achieves excellent scaling.