Joint consideration of reaction-diffusion equations with continuum mechanics for tissue deformations showed that deformation can induce the breakup and drift of spiral waves.
Incorporating tissue mechanics into reaction-diffusion models reveals that deformation can induce spiral wave breakup and drift, offering new insights into the mechanisms of cardiac arrhythmias.
Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction-diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by substantial deformations of the medium. Here, we show that joint consideration of the RD equations with the equations of continuum mechanics for tissue deformations (RD-mechanics systems), yield important effects on spiral wave dynamics. We show that deformation can induce the breakup of spiral waves into complex spatiotemporal patterns. We also show that mechanics leads to spiral wave drift throughout the medium approaching dynamical attractors, which are determined by the parameters of the model and the size of the medium. We study mechanisms of these effects and discuss their applicability to the theory of cardiac arrhythmias. Overall, we demonstrate the importance of RD-mechanics systems for mathematics applied to life sciences.
Panfilov et al. (Fri,) conducted a other in Cardiac arrhythmias. Reaction-diffusion-mechanics systems vs. Reaction-diffusion equations alone was evaluated on Spiral wave dynamics (drift and breakup). Joint consideration of reaction-diffusion equations with continuum mechanics for tissue deformations showed that deformation can induce the breakup and drift of spiral waves.