The dynamics of sustained reentry in a ring model of cardiac tissue

This paper describes the dynamics of circus movement around a fixed obstacle, using a one-dimensional continuous and uniform ring model of cardiac tissue to simulate sustained reentry. The membrane ionic current is simulated by a modified Beeler-Reuter formulation in which the kinetics of the fast sodium current were updated using more recent voltage-clamp data. Changes in the ring length are used to modify the dynamics of reentry. Reentry is stable if the ring length (X) exceeds a critical value (Xcrit) and complete block occurs if X is below a minimum (Xmin). Irregular sustained reentry is observed at intermediate ring lengths, as a narrow range of aperiodic reentry near Xcrit, and a larger range of quasi-periodic reentry at shorter ring lengths. The basic pattern of irregular reentry is an alternation between long and short cycle length, action potential duration (APD), diastolic interval (DIA), wavelength, and excitable gap. In aperiodic reentry cycle length variations are small, APD and DIA fluctuations are of medium amplitude, and conduction velocity over the whole pathway is essentially constant during successive turns. Much larger fluctuations in these various quantities occur during quasi-periodic reentry, and they increase in size as X approaches Xmin. The complexity of quasi-periodic reentry patterns is related to three factors: the slope of the APD versus DIA relation, which is greater than 1, the existence of a zone of slow conduction on the ring when the excitable gap becomes quite short, and the occurrence of triggered waves of secondary repolarization and excitability recovery. In the present model, quasi-periodic reentry with triggered secondary recovery covers most of the range of ring lengths, giving rise to sustained irregular reentry. There is very close agreement between our simulation results and experimental data obtained on rings of cardiac tissue.