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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.
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
January 1954,
Arkhiv anatomii, gistologii i embriologii,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
March 1947,
The Anatomical record,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
January 1976,
Arkhiv patologii,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
January 1896,
The Journal of experimental medicine,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
October 2009,
Mathematical biosciences,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
January 1897,
The Journal of experimental medicine,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
January 1952,
Arkhiv patologii,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
February 1976,
Journal of the National Cancer Institute,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
January 1960,
Borgyogyaszati es venerologiaia szemle,
L Olsen, and
P K Maini, and
J A Sherratt, and
J Dallon
January 1978,
Archivum immunologiae et therapiae experimentalis,
