TY - JOUR
T1 - Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue
AU - De Oliveira Vilaca, Luis Miguel
AU - Gómez-Vargas, Bryan
AU - Kumar, Sarvesh
AU - Ruiz-Baier, Ricardo
AU - Verma, Nitesh
PY - 2020/8
Y1 - 2020/8
N2 - 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.
AB - 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.
KW - Biomedical applications
KW - Biot equations
KW - Convection–diffusion-reaction
KW - Linear stability analysis
KW - Soft poroelastic tissue
UR - http://www.scopus.com/inward/record.url?scp=85087787502&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2020.04.014
DO - 10.1016/j.apm.2020.04.014
M3 - Article
AN - SCOPUS:85087787502
SN - 0307-904X
VL - 84
SP - 425
EP - 446
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
ER -