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IMA Journal of Mathematical Control and Information 2000 17(4):379-393; doi:10.1093/imamci/17.4.379
© 2000 by Institute of Mathematics and its Applications
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Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair

JOHN DALLON, JONATHAN SHERRATT, PHILIP MAINI and MARK FERGUSON

Department of Mathematics, Brigham Young University Provo, UT 84602–6539, USA
Department of Mathematics, Heriot-Watt University Edinburgh EH14 4AS, UK
Centre for Mathematical Biology, Mathematical Institute, University of Oxford 24–29 St Giles', Oxford OX1 3LB, UK
School of Biological Sciences, University of Manchester Oxford Road, Manchester M13 9PT, UK

We deveiop 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 matrix 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 ß. The most influential of these factors are cell speed and, more importantly for wound healing, the influx of fibroblasts from surrounding tissue.


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