TY - JOUR
T1 - A note on stress-driven anisotropic diffusion and its role in active deformable media
AU - Cherubini, Christian
AU - Filippi, Simonetta
AU - Gizzi, Alessio
AU - Ruiz-Baier, Ricardo
PY - 2017/10/7
Y1 - 2017/10/7
N2 - 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.
AB - 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.
KW - Active deformable media
KW - Cardiac dynamics
KW - Electro-Mechanics
KW - Finite elasticity
KW - Reaction-Diffusion
KW - Stress-assisted diffusion
UR - http://www.scopus.com/inward/record.url?scp=85026453019&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2017.07.013
DO - 10.1016/j.jtbi.2017.07.013
M3 - Article
C2 - 28755956
AN - SCOPUS:85026453019
SN - 0022-5193
VL - 430
SP - 221
EP - 228
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
ER -