Mulitistabilities And Oscillations In Cardiac Tissues: Model Study

Abstract

In this paper, we perform phase-plane bifurcation analyses to characterize arrhythmogenic states in an excitable tissue as a function of a steady depolarizing current I,. The excitable tissue is schematically represented by a ring containing excitable cells in a circular fashion. Cell-to-cell coupling is modelled by a cable model, while each cell in the ring is modelled by a Beeler-Reuter type ionic model. Our analysis reveals the existence of five distinct multi-stable phases as I,, increases: (1) Bistability between a rotor and a quiescent state, (2) three stable states coexisting among repolarized quiescent state, rotor, and ectopic beats, (3) bistability between rotor and ectopic beats, (4) three stable states coexisting among depolarized state, rotor, and ectopic beats, and (5) bistability between ectopic beats and depolarized state. Depending on the stengh of Iapp (i.e., depending on the whereabout on the bifurcation dagram), external impulses exert very interesting effects, such as initiation of circus movement from a quiescent tissue, annihilation of ectopic beating to quiescence, and reentry to ectopic beating.