Spatiotemporal patterns such as rotating spiral waves have been observed in a variety of experimental chemical and biophysical systems, as well as in mathematical models of excitable reaction-diffusion systems. Applied to cardiac systems, spiral waves are believed to be associated with atrial fibrillation, while for the neocortex, have been connected to seizures including epilepsy. A majority of clinical treatment methods for both fibrillation and seizures/epilepsy employ the use of drugs that affect the electrical properties of heart/nerve cells. Although analytical solutions are very limited for such nonlinear mathematical models, one can make use of numerical simulations to understand the effect of drugs on the system dynamics.

The talk will provide an overview of the simplified mathematical reaction-diffusion equations used to model the electrical conduction properties of heart/nerve cells, including a presentation of some basic concepts for an excitable medium. The concept of reentrant mechanisms associated with spiral waves will be emphasized. The talk will continue with a discussion of spiral wave interaction on thin spherical shells where important self-organizational properties can be found. The significance of these findings, and how they can be related to drug treatment options, will form the final discussions of the talk.

The simulation results presented here were part of my postdoctoral work under the supervision of Dr. Ray Kapral (Chemical Physics Theory Group, University of Toronto) and Dr. Leon Glass (Department of Physiology, McGill University), whose research interests include cardiac physiology.