We are developing and refining mathematical and computational multi-scale models which link macroscopic electrical impulse propagation in the heart to underlying membrane-based sub-cellular ionic currents and other intercellular and intracellular metabolic processes in ways which preserve the anatomical architecture of the heart and avoid the spatial averaging which occurs with bi-domain models. Although much information is now available about the structure of membrane ionic channels and the currents which flow through them, the techniques by which these currents are measured cannot be employed during action potential propagation. By creating propagating models which include these parameters, we seek to create a new understanding of electrical impulse propagation in the heart and in other excitable tissue. In collaboration with Dr. Vasilios Alexiades, an applied mathematician from the UT Knoxville campus, we are applying newer numerical modeling techniques to this field. These techniques bridge across scales and will employ high order explicit time-integrators with adaptive time-stepping so that they can run efficiently using parallel computation on distributed memory clusters of multiprocessors. We are also beginning collaborations with Dr. Jack Dongarra’s group in Knoxville to optimize performance on loosely coupled computational grids. This increased mathematical and computational efficiency will allow for simulations of an entire ventricle or whole heart without averaging out the effects of the discrete cellular nature of the heart and will be particularly useful for modeling regional ischemia. As a proof of concept, we have constructed a model which uses an explicit (DuFort-Frankel) numerical integration scheme and compared the results to a commonly used implicit (Crank-Nicolson) scheme. Using the same explicit techniques, we also compared the effects of increased extracellular potassium on simulated action potential parameters and propagation velocity to published experimental results from our lab*. We found good agreement between our newer techniques and both more traditional modeling methods and previous experimental data. These techniques can also be applied to other excitable tissue such as brain and skeletal and smooth muscle.

*Buchanan, et al (1985) Circulation Research 56:696-703