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.
We are trying to find ways to speed up the computations,
which turn out to be extremely demanding, even in 1D, due to
extremely high diffusivity (low resistance).
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.
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).
in
10 mm cable ,
and 50 mm cable.
Li-Alexiades, Time Stepping for the cable equation,
Part 1: Serial performance , pp.241-246,
Li-Alexiades, Time Stepping for the cable equation,
Part 2: Parallel performance, pp.247-251,
in
Proceedings of Neural, Parallel, and Scientific Computations, Vol.4,
editors GS Ladde, NG Medhin, C Peng, M Sambandham,
Dynamic Publishers, Aug. 2010.
Li-Alexiades-Buchanan,
Robustness of Action Potentials in Cardiac Myocytes
