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. © 2021 American Physical Society.Ministry of Education and Science of the Russian Federation, Minobrnauka: 075-15-2020-926Our simulations used the Uran cluster of IMM UrB RAS (Ekaterinburg). Research at Sechenov University was financed by the Ministry of Science and Higher Education of the Russian Federation within the framework of state support for the creation and development of World-Class Research Centers, “Digital Biodesign and Personalized Healthcare,” No. 075-15-2020-926