Coupling chemotaxis and growth poromechanics for the modelling of feather primordia patterning

Abstract

We propose a new mathematical model for the interaction of skin cell populations with fibroblast growth factor and bone morphogenetic protein, occurring within deformable porous media. The equations for feather primordia pattering are based on the work by K.J. Painter et al. [J. Theoret. Biol., 437 (2018) 225--238]. We perform a linear stability analysis to identify relevant parameters in the coupling mechanisms, focusing in the regime of infinitesimal strains. We also extend the model to the case of nonlinear poroelasticity and include solid growth by means of Lee decompositions of the deformation gradient. We present a few illustrative computational examples in 2D and 3D, and briefly discuss the design of tailored efficient solvers.

arXiv comment25 pages, 9 figures

References in corpus (8)

• Firedrake: automating the finite element method by composing abstractions
• An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum
• A Locally Conservative Mixed Finite Element Framework for Coupled Hydro-Mechanical-Chemical Processes in Heterogeneous Porous Media
• Stability analysis for a new model of multispecies convection-diffusion-reaction in poroelastic tissue
• Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media
• Finite element methods for large-strain poroelasticity/chemotaxis models simulating the formation of myocardial oedema
• Numerical approximation of a mechanochemical interface model for skin appendage
• Mechanochemical models for calcium waves in embryonic epithelia