(INVITED) 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 eq...

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Bibliographic Details
Published in:Physica. D 2019-12, Vol.399, p.1-34
Main Authors: Panfilov, A.V., Dierckx, H., Volpert, V.
Format: Article
Language:English
Subjects:
Arrhythmia
Atherosclerosis
Cardiovascular diseases
Mathematics
Reaction-diffusion waves
Thrombosis
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Summary: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. •Cardiovascular diseases are reviewed from joint grounds of reaction–diffusion waves.•Atherosclerosis is modeled as chronic inflammation of blood vessel walls.•The state-of-the-art models of thrombus formation are considered.•Cardiac arrhythmia modeling via reaction–diffusion equations is discussed.•Response function perturbation theory for cardiac arrhythmias is presented.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2019.04.001