Wave block formation in homogeneous excitable media following premature excitations: Dependence on restitution relations

Spiral wave formation and disorganized activity in excitable media require the existence of broken waves and are related to partial wave block. The determinants of wave block in excitable systems are incompletely understood, especially for cardiac excitable tissue. Previous work in one-dimensional cardiac models has suggested that wave break of a premature excitation (PE) requires critical timing and that the conditions for broken waves are improbable. We analyzed the mechanism of unidirectional wave block that occurs when two consecutive PEs interact with a normal plane wave in a generic one-dimensional spatial excitable medium. A nondimensional coupled-map model built from mesoscopic characteristics of the substrate (the velocity and action potential duration restitution functions) shows that block can occur over a large interval of timing between the two PEs and leads to wave break in two-dimensional media. This mechanism may be an important determinant of spiral wave formation by the response to premature excitations.