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Biomechanical Modelling of Colorectal Crypt Budding and Fission

Bulletin of Mathematical Biology volume 69, pages 1927–1942 (2007)Cite this article

Abstract

This paper presents a biomechanical model for the small pits, called crypts, that line the colon. A continuum approach is adopted, with the crypt epithelium modelled as a growing beam attached to the underlying lamina by cell bonds, which generate tension within the layer. These cell attachments are assumed to be viscoelastic thus allowing for cell progression along the crypt. It is shown that any combination of: an increase in net proliferation (i.e. cell production minus apoptosis), an enlargement of the proliferative compartment, an increase in the strength of the cellular attachment to the underlying lamina, or a change in the rate of cell growth or cell bonding may generate buckling of the tissue. These changes can all be generated by an activating mutation of the Wnt cascade, which is generally accepted to be the first genetic change in colorectal cancer, with subsequent deformation, budding, and crypt fission an observed feature of the adenomatous crypt.

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Affiliations

  1. Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford, OX1 3LB, UK

    Carina M. Edwards

  2. Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford, OX1 3LB, UK

    Carina M. Edwards & S. Jonathan Chapman

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  1. Carina M. Edwards
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  2. S. Jonathan Chapman
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Correspondence to Carina M. Edwards.

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Edwards, C.M., Chapman, S.J. Biomechanical Modelling of Colorectal Crypt Budding and Fission. Bull. Math. Biol. 69, 1927–1942 (2007). https://doi.org/10.1007/s11538-007-9199-8

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  • DOI: https://doi.org/10.1007/s11538-007-9199-8

Keywords

  • Morphogenesis
  • Buckling
  • Colorectal cancer
  • Beam
  • Elasticity
  • Growth