Three-Dimensional Model of Cellular Electrical Activity

Abstract: We present a three-dimensional model of cellular electrical activity. This model takes into account the three-dimensional geometry of biological tissue as well as ionic concentration dynamics, both of which are neglected in conventional models of electrophysiology. The model consists mathematically of a system of partial differential equations with nonlinear evolutionary boundary conditions on membrane boundaries. We use asymptotic and mathematical analysis to study the properties of this model. In particular, this analysis reveals the presence of multiple spatio-temporal scales in the model. A time-implicit numerical method is developed to tackle this difficulty. This modeling methodology is applied to cardiac physiology. Numerical simulations with this model are used to explore the characteristics of a recently observed anomalous mode of cardiac action potential propagation: cardiac propagation without gap junctions.

Refreshments will be served before the seminar in the IAM Lounge, Room 306, please bring your own mug.