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

## TL;DR

This paper introduces a new model coupling diffusion tensors to mechanical stress in active deformable media, demonstrating how stress influences anisotropic diffusion patterns and wave propagation, with potential applications in bio-materials like the heart.

## Contribution

It presents a novel theoretical framework and experimental validation for stress-driven anisotropic diffusion, advancing understanding of mechano-electrical feedback in deformable biological tissues.

## Key findings

- Stress couples to diffusion tensors, creating anisotropy.
- Numerical simulations show effects on wave conduction and drift.
- Experimental results support the model's predictions.

## Abstract

We propose 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 use diffusion tensors directly coupled to mechanical stress. A proof-of-concept experiment and the proposed generalised reaction-diffusion-mechanics model reveal 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 experiment, the model, and the numerical results obtained using a mixed-primal finite element method, clearly support relevant consequences of stress-assisted 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-electrical feedback in actively deforming bio-materials such as the heart.