Modelling apical constriction in epithelia using elastic shell theory

Gareth Wyn Jones, S. Jonathan Chapman

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    Abstract

    Apical constriction is one of the fundamental mechanisms by which embryonic tissue is deformed, giving rise to the shape and form of the fully-developed organism. The mechanism involves a contraction of fibres embedded in the apical side of epithelial tissues, leading to an invagination or folding of the cell sheet. In this article the phenomenon is modelled mechanically by describing the epithelial sheet as an elastic shell, which contains a surface representing the continuous mesh formed from the embedded fibres. Allowing this mesh to contract, an enhanced shell theory is developed in which the stiffness and bending tensors of the shell are modified to include the fibres' stiffness, and in which the active effects of the contraction appear as body forces in the shell equilibrium equations. Numerical examples are presented at the end, including the bending of a plate and a cylindrical shell (modelling neurulation) and the invagination of a spherical shell (modelling simple gastrulation). © Springer-Verlag 2009.
    Original languageEnglish
    Pages (from-to)247-261
    Number of pages14
    JournalBiomechanics and modeling in mechanobiology
    Volume9
    Issue number3
    DOIs
    Publication statusPublished - Jun 2010

    Keywords

    • Apical constriction
    • Elastic deformation
    • Epithelial tissue
    • Shell theory

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