Stability analysis for a new model of multispecies convection-diffusion-reaction in poroelastic tissue

TL;DR

This paper conducts a linear stability analysis of a novel poromechanical model with inertia, revealing parameter conditions for spatio-temporal instabilities and exploring how deformations influence pattern formation in biomaterials.

Contribution

It introduces a new coupled model for poromechanics with inertia and provides stability analysis and computational examples relevant to brain mechanobiology.

Findings

Identified parameter regions causing instabilities.

Showed deformation patterns influence chemical wave dynamics.

Demonstrated relevance to brain tissue modeling.

Abstract

We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes convected in the medium. We find parameter regions that lead to spatio-temporal instabilities of the coupled system. The mutual dependences between deformation and diffusive patterns are of substantial relevance in the study of morphoelastic changes in biomaterials. We provide a set of computational examples in 2D and 3D (related to brain mechanobiology) that can be used to form a better understanding on how, and up to which extent, the deformations of the porous structure dictate the generation and suppression of spatial patterning dynamics, also related to the onset of mechano-chemical waves.