Strings, Branes and Twistons: Topological Analysis of Phase Defects in Excitable Media Such as the Heart

Several excitable systems, such as the heart, self-organize into complex spatiotemporal patterns that involve wave collisions and rotating vortices. The dynamics between these structures are incompletely understood. Here we establish a comprehensive topological framework in three spatial dimensions. Conduction blocks are identified as phase defect surfaces, on which three types of closed curves move and carry a topological vector charge. Our framework not only sheds new light on twistons and hybrid reentry but also predicts new states: a Möbius scroll wave and conduction block surfaces that can split, branch, or contain multiple filaments. We hypothesize that the latter play a role in cardiac arrhythmias.