Numerical modeling of a mechano-chemical theory for wound contraction analysis

Wound contraction due to traction forces exerted by cells on the underlying extracellular matrix (ECM) brings the wound edges together, effectively reducing the wound size and aiding its healing. It occurs on deep wounds and burns only and plays a central role on fibroplasia related pathologies. In this work, we present a novel model based on the work of Olsen et al. [Olsen, L., Sherratt, J.A., Maini, P.K., 1995. A mechanochemical model for adult dermal wound contraction and the permanence of the contracted tissue displacement profile. Journal of Theoretical Biology 177 (2), 113–128] in which we incorporate a cell differentiation mechanical signaling, a cell mechanical sensing and transmission of traction forces to the ECM and a dynamical change of the ECM mechanical properties with collagen deposition. Along with the mathematical model, we propose a numerical solution of the nonlinearly coupled convection–diffusion-reaction equations based on a finite element analysis with a Newton–Raphson solver and rigorous linearizations of the nonlinear terms. We investigate the effect of wound morphology on the contraction process and analyze the influence of the strength of the dermal attachment to the underlying tissue on contraction.