Mathematical modelling of anisotropy in fibrous connective tissue

Luke Olsen, Philip K. Maini, Jonathan A. Sherratt, John Dallon

Research output: Contribution to journalArticle

44 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)145-170
Number of pages26
JournalMathematical Biosciences
Volume158
Issue number2
DOIs
Publication statusPublished - May 1999

Keywords

  • Dynamic anisotropy
  • Matrix alignment
  • Scar tissue
  • Wound healing

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