Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair
Dallon J., Sherratt J., Maini P., Ferguson M.
We develop a novel mathematical model for collagen deposition and alignment during dermal wound healing. We focus on the interactions between fibroblasts, modelled as discrete entities, and a continuous extracellular matric composed of collagen and a fibrin based blood clot. There are four basic interactions assumed in the model: fibroblasts orient the collagen matrix, fibroblasts produce and degrade collagen and fibrin and the matrix directs the fibroblasts and determines the speed of the cells. Several factors which influence the alignment of collagen are examined and related to current anti-scarring therapies using transforming growth factor β. The most influential of these factors are cell speed and, more importantly for wound healing, the influx of fibroblasts from surrounding tissue.