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

TL;DR

This paper introduces a new mathematical model combining chemotaxis, growth, and poromechanics to simulate feather primordia patterning, including stability analysis, nonlinear extensions, and computational examples.

Contribution

It develops a novel coupled model integrating chemotaxis, growth, and poromechanics for feather patterning, extending previous models with nonlinear poroelasticity and computational validation.

Findings

Linear stability analysis identifies key parameters affecting pattern formation.

The extended nonlinear model captures complex tissue deformation behaviors.

Computational examples demonstrate the model's applicability in 2D and 3D simulations.

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.