A note on stress-driven anisotropic diffusion and its role in active deformable media. (7th October 2017) - Cherubini, Christian; Filippi, Simonetta; Gizzi, Alessio; Ruiz-Baier, Ricardo
Highlights: A model is introduced for the anisotropic diffusion of species within active deforming media. Mechanical stress influences directly the propagating patterns of the diffusing species in the context of nonlinear couplings. Physical and mathematical properties of the proposed set of governing equations are discussed in detail. Numerical tests reveal important consequences of stress-assisted diffusion in the drifting and conduction velocity of excitation waves. Abstract: We introduce a new model to describe diffusion processes within active deformable media. Our general theoretical framework is based on physical and mathematical considerations, and it suggests to employ diffusion tensors directly influenced by the coupling with mechanical stress. The proposed generalised reaction-diffusion-mechanics model reveals that initially isotropic and homogeneous diffusion tensors turn into inhomogeneous and anisotropic quantities due to the intrinsic structure of the nonlinear coupling. We study the physical properties leading to these effects, and investigate mathematical conditions for its occurrence. Together, the mathematical model and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-driven diffusion into anisotropy patterns, drifting, and conduction velocity of the resulting excitation waves. Our findings also indicate the applicability of this novel approach in the description of mechano-electric feedback in actively deforming bio-materials such as the cardiac tissue.