Action potential duration restitution and electrical excitation propagation in a ring of cardiac cells

The propagation of electrical excitation in a ring of cells described by the Noble, Beeler-Reuter, Luo-Rudy I, and third-order simplified mathematical models is studied using computer simulation. For each of the models it is shown that after transition from steady-state circulation to quasiperiodicity 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 along a ring for the entire range of RL corresponding to quasiperiodic oscillations remain periodic with the period slightly different from two RLs. The sigmoidal 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 quasiperiodicity to chaos was observed.