A mathematical model of wound healing and subsequent scarring

Wound healing is a complex process involving the delicate interaction between elements that vary widely in nature and size scales, from the nanometre level, such as molecules, to cells measured in micrometres, and fibres with width and length measured on both scales. Hybrid approaches, where each species is represented by a model on an appropriate size scale, have received attention recently. In this study, we provide a review of earlier work on such hybrid models of wound healing. General models for each of the element types involved in dermal wound healing used in this research are described: cells, modelled as discrete individuals; chemicals, modelled as continua; and fibres, modelled with a novel tensorial representation. Techniques for integrating such disparate models are outlined. A six-species model (fibrin, collagen, macrophages, fibroblasts, transforming growth factor-β (TGF-β) and tissue plasminogen activator) of dermal wound healing is presented. The role of the cytokine TGF-β in the healing cascade is investigated using the model, along with its role in the degree of scarring in the healed tissue.