A note on stress-driven anisotropic diffusion and its role in active deformable media

JOURNAL OF THEORETICAL BIOLOGY

卷:430

Article

Cherubini, Christian^1,2  Filippi, Simonetta^1,2  Gizzi, Alessio¹  Ruiz-Baier, Ricardo³ 

[1] Univ Campus BioMed Rome, Dept Engn, Unit Nonlinear Phys & Math Modeling, Via A del Portillo 21, I-00128 Rome, Italy

[2] Univ Campus BioMed Rome, Int Ctr Relativist Astrophys, Via A del Portillo 21, I-00128 Rome, Italy

[3] Univ Oxford, Math Inst, Radcliffe Observ Quarter, A Wiles Bldg,Woodstock Rd, Oxford OX2 6GG, England

关键词: Active deformable media;    Stress-assisted diffusion;    Reaction-Diffusion;    Electro-Mechanics;    Finite elasticity;    Cardiac dynamics;   

DOI  :  10.1016/j.jtbi.2017.07.013

来源: Elsevier

【 摘 要 】

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. (C) 2017 Published by Elsevier Ltd.

【 授权许可】

Free