Mathematical models of wound healing

• Main Author: Sherratt, Jonathan Adam
• Published: University of Oxford 1991
• Subjects: 510; Pure mathematics
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.291720

The complex mechanisms responsible for mammalian wound healing raise many biological questions that are amenable to theoretical investigation. In the first part of this thesis, we consider the role of mitotic auto-regulation in adult epidermal wound healing. We develop a reaction-diffusion model for the healing process, with parameter values based on biological data. The model solutions compare well with experimental results on the normal healing of circular wounds, and we analyse the solutions in one spatial dimension as travelling waves. We then use the model to perform 'mathematical experiments' on the effects of adding mitosis-regulating chemicals and of varying the initial wound shape. Recent experiments suggest that in embryos, epidermal wound healing occurs not by lamellipodial crawling as in adults, but rather by contraction of a cable of filamentous actin at the wound edge. We focus on the formation of this cable as a response to wounding, and develop and analyse a mechanical model for the post-wounding equilibrium in the microfilament network. Our model reflects the well-documented phenomenon of stress-induced alignment of actin filaments, which has been neglected in previous mechanochemical models of tissue deformation. The model solutions reflect the key aspects of the experimentally observed response to wounding. In the final part of the thesis, we consider chemokinetic and chemotactic control of cell movement, which play an important role in many aspects of wound healing. We propose a new model which reflects the underlying receptor-based mechanisms, and apply it to endothelial cell movement in the Boyden chamber assay. We compare our model with a simpler scheme in which cells respond directly to gradients in extracellular chemical concentration, and for both models we use experimental data to make quantitative predictions on the values of the transport coefficients.