John C. Dallon: Paper Abstract
A Mathematical Model for Fibroblast and Collagen Orientation
AUTHORS:
John C. Dallon & Jonathan A. Sherratt
Mathematics Institute,
University of Warwick, Coventry CV4 7AL, UK.
ABSTRACT:
Due to the increasing importance of the extracellular matrix in many
biological problems, in this paper we develop a model for fibroblast
and collagen orientation with the ultimate objective of understanding
how fibroblasts form and remodel the extracellular matrix, in
particular its collagen component. The model uses integro-differential
equation to describe the interaction between the cells and fibers at a
point in space with various orientations. The equations are studied
both analytically and numerically to discover different types of
solutions and their behavior. In particular we examine solutions
where all the fibroblasts and collagen have discrete orientations, a
localized continuum of orientations and a continuous distribution of
orientations with several maxima. The effect of altering the
parameters in the system is explored, including the angular diffusion
coefficient for the fibroblasts, as well as the strength and range of
the interaction between fibroblasts and collagen. We find the initial
conditions and the range of influence between the collagen and the
fibroblasts are the two factors which determine the behavior of the
solutions. The implications of this for wound healing and cancer are
discussed including the conclusion that the major factor in
determining the degree of scarring is the initial deposition of
collagen.
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