Constitutive Modelling of Wound Healing

Wound healing is a complex process spanning several temporal and spatial scales and requiring precise coordination of cell populations through mechanical and biochemical regulatory networks. The dermis, which is the load bearing layer of the skin, is rebuilt after injury by fibroblasts through collagen deposition and active contraction. Fibroblast activity is controlled by cytokine gradients established during the initial inflammatory response, as well as by mechanical cues. However, even though we know the individual components of the wound healing system, in particular the factors associated with fibroblast-driven remodeling, we are still unable to achieve perfect skin regeneration and, instead, wounds lead to scars with inferior mechanical properties compared to healthy skin. Computational models offer the unique ability to quantitatively analyze the dynamics of wound healing in order to attain a deeper understanding of this system. Here we show a continuum framework to describe the essential bio-chemo-mechanical couplings during wound healing, together with a finite element implementation of a model problem. We account for nonlinear mechanical behavior and anisotropy of skin through a microstructure-based strain energy function, as well as the split of the deformation gradient into elastic and permanent deformations. These microstructure features evolve in time according to the spatiotemporal evolution of cell and cytokine concentration fields, which obey reaction diffusion differential equations. The model problem exhibits emergent features of wound healing dynamics, such as wound contraction by fibroblasts in the periphery of the injury. Moreover, the proposed framework can be readily extended to more comprehensive regulatory networks and used to simulate other realistic geometries. Thus, we expect that the formulation presented here will enable further advances in wound healing research.