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

Luis Miguel De Oliveira Vilaca, Bryan Gómez-Vargas, Sarvesh Kumar, Ricardo Ruiz-Baier, Nitesh Verma

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2 Citations (Scopus)

Abstract

We perform the linear stability analysis of 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 bio-materials. 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.

Original languageEnglish
Pages (from-to)425-446
Number of pages22
JournalApplied Mathematical Modelling
Volume84
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Biomedical applications
  • Biot equations
  • Convection–diffusion-reaction
  • Linear stability analysis
  • Soft poroelastic tissue

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