We work to find mechanistic explanations for the genesis and maintenance of cardiac arrhythmias. Cardiac arrhythmias are a major cause of death, particularly self-sustained arrhythmias like fibrillation. The excitation patterns underlying self-sustained arrhythmias are spiral waves (see Fig. 1) and their three-dimensional counterparts, scroll waves.
The dynamics of spiral waves and their interactions are complex. Typically, spiral waves only interact if their tips are close together, and they are then called multiarmed spirals. There are, however, also bound states with a large distance between the tips, as shown in Fig. 2. In this example, one spiral is rotating almost unaffected by the other while the other rotates around the first over time; we call such pairs of spirals master-slave pairs.
Even a single scroll wave is a complex object in itself. Fig. 3 shows a scroll wave and its organizing center, the filament, for a medium with twisted anisotropy. As a result of the anisotropy, the filament assumes a very particular shape that can be characterized as a geodesic in the metric defined by the fiber directions in the volume.