Journal of Mathematical Biology

, Volume 72, Issue 7, pp 1775–1809 | Cite as

An investigation of the influence of extracellular matrix anisotropy and cell–matrix interactions on tissue architecture

  • R. J. Dyson
  • J. E. F. GreenEmail author
  • J. P. Whiteley
  • H. M. Byrne


Mechanical interactions between cells and the fibrous extracellular matrix (ECM) in which they reside play a key role in tissue development. Mechanical cues from the environment (such as stress, strain and fibre orientation) regulate a range of cell behaviours, including proliferation, differentiation and motility. In turn, the ECM structure is affected by cells exerting forces on the matrix which result in deformation and fibre realignment. In this paper we develop a mathematical model to investigate this mechanical feedback between cells and the ECM. We consider a three-phase mixture of collagen, culture medium and cells, and formulate a system of partial differential equations which represents conservation of mass and momentum for each phase. This modelling framework takes into account the anisotropic mechanical properties of the collagen gel arising from its fibrous microstructure. We also propose a cell–collagen interaction force which depends upon fibre orientation and collagen density. We use a combination of numerical and analytical techniques to study the influence of cell–ECM interactions on pattern formation in tissues. Our results illustrate the wide range of structures which may be formed, and how those that emerge depend upon the importance of cell–ECM interactions.


Multiphase model Collagen fibres Cell aggregation Mechanics 

Mathematics Subject Classification

92C10 92C15 92C17 76T30 76Z99 35Q92 



We thank A.M. Soto and C. Sonnenschein (Tufts University) for the initial discussions which led to the development of the model, and D.J. Smith (University of Birmingham) for assistance with aspects of the numerics. RJD gratefully acknowledges the support of the University of Birmingham’s System Science for Health initiative and the hospitality of the School of Mathematical Sciences at the University of Adelaide. JEFG is supported by a Discovery Early Career Researcher Award (DE130100031) from the Australian Research Council. The work of HMB was supported in part by award KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).

Supplementary material

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • R. J. Dyson
    • 1
  • J. E. F. Green
    • 2
    Email author
  • J. P. Whiteley
    • 3
  • H. M. Byrne
    • 3
    • 4
  1. 1.School of MathematicsUniversity of BirminghamBirminghamUK
  2. 2.School of Mathematical SciencesUniversity of AdelaideAdelaideAustralia
  3. 3.Department of Computer ScienceUniversity of OxfordOxfordUK
  4. 4.Mathematical InstituteUniversity of OxfordOxfordUK

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