Stationary Pulses and Wave Front Formation in an Excitable Medium

In an excitable medium, the method of phase plane analysis of ODE reductions is often used to separate suprathreshold disturbances that collapse from disturbances that expand andresult in a propagating front. Following this approach, we stud y here pulse formation in 1-Dimensional (1-D) and2-D med ia andd erive closedform (1-D) andapproximate (2-D) expressions for a critical pulse structure, which is stationary but unstable. This critical structure, called a stationary pulse, can be modulated by altering (e.g. adding a constant to) the reaction portion of the reaction-diffusion equation, suggesting a mechanism for extinguishing the initial expanding phase of front formation or for steering a front. We have also studied analytically andnumerically the onset of “recovery”, lead ing from a single wavefront to an ordinary action potential wave. Possible applications of these ideas to the development of practical strategies for controlling cardiac arrhythmia are discussed.