Termination of spiral wave breakup in a Fitzhugh-Nagumo model via short and long duration stimuli

Abstract

Rotating spiral waves have been observed in a variety of nonlinear biological and physical systems. Spiral waves are found in excitable and oscillatory systems and can be stationary, meander, or even degenerate into multiple unstable rotating waves (a process called "spiral wave breakup"). In the heart, spiral wave breakup is thought to be the underlying mechanism of cardiac fibrillation. The spatiotemporal complexity of multiple unstable spiral waves is difficult to control or terminate. Here, the mechanisms of the termination of spiral wave breakup in response to global stimulation are investigated. A modified Fitzhugh-Nagumo model was used to represent cellular kinetics to study the role of the fast (activation) and slow (recovery) variables. This simplified model allows a theoretical analysis of the termination of spiral wave breakup via both short and long duration pulses. Simulations were carried out in both two-dimensional sheets and in a three-dimensional geometry of the heart ventricles. The short duration pulses affected only the fast variable and acted to reset wave propagation. Monophasic pulses excited tissue ahead of the wave front thus reducing the amount of excitable tissue. Biphasic shocks did the same, but they also acted to generate new wave fronts from the pre-existing wave tails by making some active regions excitable. Thus, if the short duration stimuli were strong enough, they acted to fill in excitable tissue via propagating wave fronts and terminated all activity. The long duration wave forms were selected such that they had a frequency spectrum similar to that of the pseudoelectrocardiograms recorded during fibrillation. These long duration wave forms affected both the recovery and activation variables, and the mechanism of unstable multiple spiral wave termination was different compared to the short duration wave forms. If the long duration stimuli were strong enough, they acted to alter the "state" (i.e., combination of fast and slow variables) of the tissue throughout 1.5 cycles, thus "conditioning" the tissue such that by the end of the stimuli almost no excitable tissue remained. The peak current, total energy, and average power of stimuli required to terminate spiral wave breakup were less for the long duration wave forms compared to the short duration wave forms. In addition, closed loop feedback via stimulation with a wave form that was the difference of the pseudoelectrocardiogram and a strongly periodic chaotic signal was successful at terminating spiral wave breakup. These results suggest that it may be possible to improve cardiac defibrillation efficacy by using long duration wave forms to affect recovery variables in the heart as opposed to the traditional brief duration wave forms that act only on the fast variables. (c) 2002 American Institute of Physics.