Wound healing is a complicated orchestration of cells and biological signals that changes over the life of the wound. Chronic wounds, such as pressure ulcers or the foot sores of diabetics, are breaches in the skin that often refuse to heal. In this talk, we present a mathematical model of chronic wounds that incorporates the interactions of different type of cells, chemicals and the extracellular matrix (ECM) that are involved in the healing process.
The model consists of a coupled system of partial differential equations in the partially healed region, with the wound boundary as a free boundary. The ECM is assumed to be viscoelastic, and the free boundary moves with the velocity of the ECM at the boundary. The model variables include the concentration of oxygen, PDGF and VEGF, the densities of macrophages, fibroblasts, capillary tips and sprouts, and the density and velocity of the ECM. Simulations of the model demonstrate how oxygen deficiency may limit macrophage recruitment to the wound-site and impair wound closure. The results are in general agreement with experimental findings in an animal model.