John Dallon: Paper Abstract
Biological Implications of a Discrete Mathematical Model for Collagen Deposition and
Alignment in Dermal Wound Repair
AUTHORS:
J.C. Dallon 1, Jonathan A. Sherratt 1, Philip K. Maini 2, Mark Ferguson 3
1: Department of Mathematics, Heriot-Watt University,
Edinburgh EH14 4AS, UK.
2: Centre for Mathematical Biology, Mathematical Institute,
24-29, St Giles', Oxford OX1 3LB, UK.
3: School of Biological Sciences, University of Manchester, Oxford Road, Manchester M13 9PT, UK.
ABSTRACT:
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 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 beta. 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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