Reaction–diffusion waves in cardiovascular diseases

Cardiovascular diseases remain one of the largest causes of death worldwide. The lethal pathologies often occur due to atherosclerosis, clot formation and cardiac arrhythmia. It turns out that all these pathologies can be described using the generic framework of multi-component reaction–diffusion equations. These parabolic partial differential equations sustain waves and pattern formation that are relevant in the study of all those processes. Here we present the first review which combines the description of these fields: atherosclerosis, clot formation and cardiac arrhythmias, and includes classic and recent developments in these areas. We show how mathematical models for the underlying physiological processes have been constructed, and which generic properties follow from their analytical or numerical study. Finally, we discuss the possibility of integrative studies of cardiovascular disease which will include both clot formation and cardiac arrhythmias. Such approach will be highly relevant to atrial fibrillation, a common cardiac arrhythmia whose main complication is clot formation and stroke. © 2019 Elsevier B.V.