Numerical approximation of a mechanochemical interface model for skin appendage

TL;DR

This paper develops and analyzes a numerical model for molecular transfer and tissue deformation in skin, coupling complex reaction-diffusion equations with elasticity, and demonstrates its effectiveness through 2D and 3D simulations.

Contribution

It introduces a novel coupled mechanochemical model for skin tissue and proposes advanced numerical methods for its accurate simulation.

Findings

The numerical methods are accurate and robust.

Coupling effects significantly influence molecular transfer and tissue deformation.

Simulations in 2D and 3D illustrate complex interaction dynamics.

Abstract

We introduce a model for the mass transfer of molecular activators and inhibitors in two media separated by an interface, and study its interaction with the deformations exhibited by the two-layer skin tissue where they occur. The mathematical model results in a system of nonlinear advection-diffusion-reaction equations including cross-diffusion, and coupled with an interface elasticity problem. We propose a Galerkin method for the discretisation of the set of governing equations, involving also a suitable Newton linearisation, partitioned techniques, non-overlapping Schwarz alternating schemes, and high-order adaptive time stepping algorithms. The experimental accuracy and robustness of the proposed partitioned numerical methods is assessed, and some illustrating tests in 2D and 3D are provided to exemplify the coupling effects between the mechanical properties and the advection-diffusion-reaction interactions involving the two separate layers.