Theory of reentrant excitation in a ring of cardiac tissue

Abstract

A cardiac pathology, reentrant tachycardia, is caused by the sustained circulation of activation along a reentrant path in cardiac tissue. A new theoretical model for wave propagation in discrete excitable media employing coupled maps with continuous time is used to derive analytical stability criteria for the uni-directional circulation of the excitation pulse on the ring of cardiac tissue. Numerical simulations of the model that incorporate experimentally measurable characteristics of the cardiac tissue reproduce the experimental data quantitatively. The complex oscillations in the cycle length of unstable tachycardia observed experimentally are quasiperiodic oscillations that arise via the multiple Hopf bifurcation in high dimensional maps.