Journal Article

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

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 17, issue 4, pages 379-393
Published in print January 2000 | ISSN: 1477-8599
Published online January 2000 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/17.4.379
Biological implications of a discrete mathematical model for collagen deposition and alignment in dermal wound repair

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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 β. 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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Subjects: Applied Mathematics ; Biomathematics and Statistics

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