Many physical, chemical and biological systems are described by the
reaction-diffusion (RD) equations. One of the most important
phenomena in RD systems is the propagation of non-linear waves.
Notably, such waves initiate the contraction of the heart, and determine
dynamics of many other systems including phase transitions, chemical
reactions, etc. Abnormal regimes of wave propagation, such as vortices,
may cause serious problems. For example, vortices in the heart induce
life-threatening cardiac arrhythmias.
Until now, most studies of non-linear waves and vortices have not
included deformation of the medium, which is an essential component
of the system. In cardiac tissue e.g., the contraction directly affects the
wave propagation in the heart. Such mechano-electrical feedback is
well known in electrophysiology; in extreme situations it can even result
in sudden cardiac death. Despite its importance, the effects of
mechano-electrical feedback on cardiac activity are not yet well
understood.
Very recently, numerical studies of reaction-diffusion-mechanics (RDM)
phenomena have been started at Gent University. Although they
delivered interesting results, the mechanisms of the underlying
phenomena were merely investigated. For, the fundamental
understanding of the main features of coupling of excitation and
deformation in space is nontrivial and cannot rely on numerical studies
all along. It also requires the development of analytical approaches,
which should provide the building blocks or theory of such systems, in
order to explain the observed phenomena. The aim of this project is to
start the development of an analytical description of the RDM system
with application to cardiac and other systems.