V. Alexiades - UTK and ORNL
Propagation of cardiac Action Potentials

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.

  • Typical action potentials generated by the cable equation with the Luo-Rudy ionic model,
      in   10 mm cable ,   and   50 mm cable.

  • Comparison of time-steppers on 50mm cable:   (note that CPU timings are in minutes!)   serial parallel

  • Li, Alexiades, Comparison of time-stepping schemes on the cable equation , EJDE conf.19, 2010.  
  • 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, Proceedings of Dynamic Systems and Applications 6: 241-247, 2012.
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