Biomechanical Modelling of Colorectal Crypt Budding and Fission |
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Authors: | Carina M Edwards S Jonathan Chapman |
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Institution: | (1) Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford, OX1 3LB, UK;(2) Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, 24–29 St Giles’, Oxford, OX1 3LB, UK |
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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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Keywords: | Morphogenesis Buckling Colorectal cancer Beam Elasticity Growth |
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