John Dallon: Paper Abstract
Mathematical Modelling of Anisotropy in
Fibrous Connective Tissue
AUTHORS:
Luke Olsen 1, Philip K. Maini 1, Jonathan A. Sherratt 2,
J.C. Dallon 2
1: Centre for Mathematical Biology, Mathematical Institute,
24-29, St Giles', Oxford OX1 3LB, UK.
2: Department of Mathematics, Heriot-Watt University,
Edinburgh EH14 4AS, UK.
ABSTRACT:
We present two modelling frameworks for studying
dynamic anistropy in connective tissue,
motivated by the problem of fibre alignment in wound
healing. The first model is a system of partial differential equations
operating on a macroscopic scale. We show that a model consisting of a
single extracellular matrix material aligned by fibroblasts via flux and
stress exhibits behaviour that is incompatible with experimental
observations. We extend the model to two matrix types and show that the
results of this extended model
are robust and consistent with experiment. The second model
represents cells as discrete objects in a continuum of ECM. We
show that this model predicts patterns of alignment on macroscopic
length scales that are lost in a continuum model of the cell population.
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