An introduction to mathematical modeling of electrophysiological processes in the myocardium

Summary We discuss major features of modeling cardiac electrophysiology based on the modern concept of an excitable medium such as: general physical mechanisms and energetics of excitability, discrete and continuous aspects of cardiac conduction stemming from its fibrous structure, and anisotropy as another feature of such myocardial structure. We use the propagation velocity as a certain integral measure of the medium excitability and show that the expression for its value always consists of three factors, the scaling factor built out of dimensional constants of the myocardium, and two dimensionless factors, a universal directional factor taking full account of the medium anisotropy, and a dynamical factor that represents balances of all electrical sources and sinks. We describe the minimum, two variable models of an excitable cellular membrane. We show that in the first approximation the effect of the slow inactivation/recovery processes on the propagation velocity can be neglected. The excitation wave becomes in such an approximation a trigger wave of transitions from the resting to the exciting state. Then we discuss the formation of the conduction block at nonzero propagation speed due to the effect of inhibitive (recovery) processes.