In-silico Analysis of the Role of Boundary Conditions in the Induced Drift of 2D Spiral Waves

Spiral waves are widely spread throughout nature and have been an important research focus in recent decades. The spiral waves in active media (including cardiac tissue) tend to disappear when moving to the domain boundary. The study of the motion of the spiral waves on surfaces without boundaries is of scientific interest. In this paper, we simulated the dynamics of these waves on the following surfaces: a torus, a Mobius strip, and a cylinder. The tissue was simplistically modelled as an isotropic medium with the cell-level model of Aliev-Panfilov; the spiral waves were created using the S1S2 protocol. As a result, we obtained the trajectories of the waves in the absence and presence of external stimulation from a point electrode. Pacing of this kind, called low-voltage cardioversion or defibrillation, is used in clinic to stop paroxysms of dangerous heart rhythm disturbances, such as tachyarrhythmia, fibrillation, or torsade de pointes. An important parameter of the pacing is its period. We found the approximate limits of effective pacing periods and compared them with the results for a square. The spontaneous drift and annihilation of the paired spiral waves were observed.