Geometry-driven dynamics in reaction-diffusion systems

The cardiac monodomain equations can be formulated as a set of parabolic differential equations of the reaction-diffusion type. Most of our theoretical results apply to the wide class of reaction-diffusion equations, only the existence of stable traveling waves or vortices needs to be assumed.

Therefore, our findings also apply to other reaction-diffusion systems, such as active diffusion of substances across the cell membrane, pattern formation on animal furs, signaling waves at the cellular of multicellular level, oxidation waves, and oscillating chemical reactions (e.g. the Belousov-Zhabotinsky (BZ) reaction).

One of our theoretical predictions on the drift of scroll waves in a medium of stepwise thickness, inspired by a cardiac application, was shortly thereafter experimentally verified in the BZ reaction by Steinbock et al:

H. Ke, Z. Zhang, and O. Steinbock, “Scroll Wave Drift Along Steps, Troughs, and Corners”, Chaos 25, 064303, 1-7, 2015 pdf

Spiral wave chimeras

Spiral wave chimeras are emergent structures in oscillatory media, with spatial coexistance of synchronized and asynchronized regions. The first chimeras were found in non-locally coupled media (i.e. with action-at-a-distance), but in collaboration with B.W. Li, we showed that also a classical reaction-diffusion system can generate spiral wave chimeras.

Cover image generated by Dall-E 3.