There is great interest in modeling propagation of electrical impulses in heart tissue. Normal operation of the heart requires orderly propagation of electrical impulses (depolarization waves) through the entire heart muscle. Disturbances in this propagation are at the root of "sudden cardiac death," which is the condition causing people to suddenly lose effective cardiac pumping and (usually) die. This is, of course, one of the leading killers in the Western World. Cardiac electrical modeling can be used both to aid in understanding of sudden cardiac death, and to attempt to prototype therapies. Many models have represented the molecular basis of cardiac conduction, but these models are extremely slow and therefore impractical for large-scale processes (like sudden death).

A more promising approach is based on rigorous analysis of heart muscle as an excitable medium, and therefore mathematically determining the behavior of electrical propagation waves. I will demonstrate that very efficient models can be constructed by mathematically constraining the model behavior and then modeling the macroscopic wave propagation in heart tissue, rather than attempting to model the microscopic cellular currents, as is normally done. This approach allows practical, whole-heart simulations for studying electrical disease.

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2000-2001 Program: Mathematics in Multimedia