  A spiral wave is a macroscopic dynamic of excitable media that plays an
important role in several distinct systems, including the Belousov-Zhabotinsky
reaction, seizures in the brain, and lethal arrhythmia in the heart. Because
spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise
quantification can be challenging. Here we present a hybrid geometric and
information-theoretic approach to quantifying spiral wave dynamics. We
demonstrate the effectiveness of our approach by applying it to numerical
simulations of a two-dimensional excitable medium with different numbers and
spatial patterns of spiral waves. We show that, by defining information flow
over the excitable medium, hidden coherent structures emerge that effectively
quantify the information transport underlying spiral wave dynamics. Most
importantly, we find that some coherent structures become more clearly defined
over a longer observation period. These findings validate our approach to
quantitatively characterize spiral wave dynamics by focusing on information
transport. Our approach is computationally efficient and is applicable to many
excitable media of interest in distinct physical, chemical and biological
systems. Our approach could ultimately contribute to an improved therapy of
clinical conditions such as seizures and cardiac arrhythmia by identifying
potential targets of interventional therapies.
