Dynamics of Multi-Armed Spiral Waves

Spiral waves in an excitable medium can be so sparse that two or more symmetric arms can rotate stably in a chain, which creates a new type of waves, the hooked multi-arm spiral wave. Such waves were previously observed and simulated but their overdrive pacing has not been studied yet. This paper examines the multi-armed spiral waves in the FitzHugh-Nagumo model. A new variation of S1S2 protocol is proposed to create multi-armed spiral waves. We trace spiral wave's tip trajectories, which enables us to observe the arm symmetry and its spontaneous breakdown. The cycle length maps are shown for different configurations of two-armed spiral cores, including meandering, partial and full core overlap and unhooked spirals. We show how an unstable three-armed spiral wave compresses and becomes stable. The minimum effective pacing period does not depend on the arm number, while the maximum one is determined by the spiral wave period. These results can be valuable for overdrive pacing research since the multi-arm spirals seem to be able to underlie heart arrhythmias.