Suppression of expanding vortex rings in systems with negative filament tension by pulsed electric fields

Scroll waves are the three-dimensional counterparts of spiral waves in excitable media, and their filaments can form closed loops known as vortex rings. In systems with negative filament tension, such vortex rings tend to expand and may develop into Winfree turbulence, which is regarded as one of the key mechanisms underlying fibrillationlike activity in cardiac tissue. Therefore, controlling the formation and evolution of scroll-wave vortex rings is crucial for treatment of fibrillation. Motivated by recent advances in pulsed electric field (PEF) ablation for fibrillation therapy, we numerically investigate how PEF modulates the dynamics of free scroll-wave vortex rings in the three-dimensional Barkley model. By systematically varying pulse amplitude, pulse duration, pulse number, and field orientation, we show that when the PEF is applied opposite to the natural drift direction of the vortex ring, sufficiently strong and long pulses can reverse ring expansion and induce collapse, thereby suppressing the onset of turbulence. We further propose a kinematic model that combines intrinsic filament dynamics with the electric-field-induced drift of two-dimensional spiral waves to explain the observed transition from expansion to contraction. These results clarify how pulsed electric forcing can control scroll-wave filaments in media with negative filament tension and may provide mechanistic insight for electrical control of cardiac reentry.