High-frequency pacing of scroll waves in a three-dimensional slab model of cardiac tissue

Vortices in excitable media underlie dangerous cardiac arrhythmias. One way to eliminate them is by stimulating the excitable medium with a period smaller than the period of the vortex. So far, this phenomenon has been studied mostly for two-dimensional vortices known as spiral waves. Here we present a first study of this phenomenon for three-dimensional vortices, or scroll waves, in a slab. We consider two main types of scroll waves dynamics: with positive filament tension and with negative filament tension and show that such elimination is possible for some values of the period in all cases. However, in the case of negative filament tension for relatively long stimulation periods, three-dimensional instabilities occur and make elimination impossible. We derive equations of motion for the drift of paced filaments and identify a bifurcation parameter that determines whether the filaments orient themselves perpendicular to the impeding wave train or not.