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.

The role of diastolic outward current deactivation kinetics on the induction of spiral waves.

The mechanism of induced reentry in an initially homogeneous repolarization matrix still remains undefined. In the present study we hypothesized that the slow deactivation rate of the delayed outward current (dIo/dt), which occurs during diastole after complete repolarization, can cause activation failure and facilitate reentry. We modeled the excitation-recovery process using the modified FitzHugh-Nagumo equations in a two-dimensional medium of 128 by 128 cells using the Connection Machine (CM-2), a massively parallel computer that is highly suitable for this class of problem. The model was one cell thick, uniformly excitable, and isotropic. When the rate of Io deactivation was slowed to yield action potential duration (APD) restitution curves similar to experimentally observed arrhythmic ventricular muscle cells ADP restitution curves, premature stimulation (S2) induced nonstationary double spiral waves (Figure 8 reentry). A decrease in dIo/dt increased the radius of the circle around which the tip of the spiral waves rotates and decreased its angular velocity. Wave fronts propagated through areas where the residual diastolic Io was fully inactivated and blocked in areas where its amplitude was high. No such dynamics of wave front propagation could be induced when S2 was applied after the completion of Io deactivation. We conclude that the kinetics of deactivation of the Io during diastole has a profound influence on the dynamics of two-dimensional wave front propagation. The similarities of the APD restitution curve implemented in the computer model with slow deactivation of Io and that observed in our canine model of quinidine induced ventricular tachyarrhythmias suggest that Io deactivation kinetics may play an important role in arrhythmogenesis in the intact ventricle.