Re-epithelialization: advancing epithelium frontier during wound healing.

The first function of the skin is to serve as a protective barrier against the environment. Its loss of integrity as a result of injury or illness may lead to a major disability and the first goal of healing is wound closure involving many biological processes for repair and tissue regeneration. In vivo wound healing has four phases, one of them being the migration of the healthy epithelium surrounding the wound in the direction of the injury in order to cover it. Here, we present a theoretical model of the re-epithelialization phase driven by chemotaxis for a circular wound. This model takes into account the diffusion of chemoattractants both in the wound and the neighbouring tissue, the uptake of these molecules by the surface receptors of epithelial cells, the migration of the neighbour epithelium, the tension and proliferation at the wound border. Using a simple Darcy's law for cell migration transforms our biological model into a free-boundary problem, which is analysed in the simplified circular geometry leading to explicit solutions for the closure and making stability analysis possible. It turns out that for realistic wound sizes of the order of centimetres and from experimental data, the re-epithelialization is always an unstable process and the perfect circle cannot be observed, a result confirmed by fully nonlinear simulations and in agreement with experimental observations.