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

Area of Science:

• Multiphysics modeling
• Continuum mechanics
• Biophysics

Background:

• Diffusion processes are fundamental in various scientific fields, including biology and materials science.
• Understanding diffusion in deformable and active media is crucial for phenomena like wave propagation in biological tissues.
• Existing models often simplify the interplay between mechanical stress and diffusion dynamics.

Purpose of the Study:

• To introduce a novel theoretical framework for modeling diffusion in active deformable media.
• To investigate how mechanical stress influences diffusion tensor properties.
• To explore the consequences of stress-driven diffusion on wave propagation and biological material behavior.

Main Methods:

• Development of a generalized reaction-diffusion-mechanics model.
• Theoretical analysis of physical properties and mathematical conditions for stress-induced anisotropy.
• Numerical simulations using a mixed-primal finite element method.

Main Results:

• Demonstrated that coupling mechanical stress with diffusion transforms initially isotropic tensors into anisotropic ones.
• Observed significant effects of stress-driven diffusion on anisotropy patterns, drifting, and conduction velocity of excitation waves.
• Validated the model's ability to capture complex diffusion behaviors in deformable media.

Conclusions:

• The proposed model provides a robust framework for understanding stress-influenced diffusion.
• Findings highlight the critical role of mechanical stress in generating anisotropic diffusion.
• The approach is applicable to describing mechano-electric feedback in actively deforming biomaterials, such as cardiac tissue.