Fibroblast migration and collagen deposition during dermal wound healing: mathematical modelling and clinical implications

The extent to which collagen alignment occurs during dermal wound healing determines the severity of sear tissue formation. We have modelled this using a multiscale approach, in which extracellular materials, for example collagen and fibrin, are modelled as continua, while fibroblasts are considered as discrete units. Within this model framework, we have explored the effects that different parameters have on the alignment process. and we have used the model to investigate how manipulation of transforming growth factor-beta levels can reduce scar tissue formation. We briefly review this body of work, then extend the modelling framework to investigate the role played by leucocyte signalling in wound repair. To this end, fibroblast migration and collagen deposition within both the wound region and healthy peripheral tissue are considered. Trajectories of individual fibroblasts are determined as they migrate towards the wound region under the combined influence of collagen/fibrin alignment and gradients in a paracrine chemoattractant produced by leucocytes. The effects of a number of different physiological and cellular parameters upon the collagen alignment and repair integrity are assessed. These parameters include fibroblast concentration, cellular speed, fibroblast sensitivity to chemoattractant concentration and chemoattractant diffusion coefficient. Our results show that chemoattractant gradients lead to increased collagen alignment at the interface between the wound and the healthy tissue. Results show that there is a trade-off between wound integrity and the degree of scarring. The former is found to be optimized under conditions of a large chemoattractant diffusion coefficient. while the latter can be minimized when repair takes place in the presence of a competitive inhibitor to chemoattractants.