Propagation of Electrical Excitationin a Ring of Cardiac Cells : A Computer Simulation

1 Abstract The propagation of electrical excitation in a ring of cells described by the Noble, Beeler-Reuter (BR), Luo-Rudy I (LR I), and third-order simpliied (TOS) mathematical models is studied using computer simulation. For each of the models it is shown that after transition from steady-state circulation to quasi-periodicity achieved by shortening the ring length (RL), the action potential duration (APD) restitution curve becomes a double-valued function and is located below the original (that of an isolated cell) APD restitution curve. The distributions of APD and diastolic interval (DI) along a ring for the entire range of RL corresponding to quasi-periodic oscillations remain periodic with the period slightly diierent from two RLs. The "S" shape of the original APD restitution curve determines the appearance of the second steady-state circulation region for short RLs. For all the models and the wide variety of their original APD restitution curves, no transition from quasi-periodicity to chaos was observed. 2 Introduction The propagation of an excitation wave in a ring of cardiac excitable cells is a subject of signiicant practical and theoretical importance 1, 2, 3]. The circulation of excitation in atrial tissue is observed during atrium utter and in a ring-shaped preparation of atrial tissue 4]. A one-dimensional ring of excitable cells can be considered as a limiting case of a circle with a hole