Buckling of a growing tissue and the emergence of two-dimensional patterns

Nelson, M.R., King, J.R. and Jensen, O.E., 2013. Buckling of a growing tissue and the emergence of two-dimensional patterns. Mathematical Biosciences, 246 (2), pp. 229-241. ISSN 0025-5564

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Abstract

The process of biological growth and the associated generation of residual stress has previously been considered as a driving mechanism for tissue buckling and pattern selection in numerous areas of biology. Here, we develop a two-dimensional thin plate theory to simulate the growth of cultured intestinal epithelial cells on a deformable substrate, with the goal of elucidating how a tissue engineer might best recreate the regular array of invaginations (crypts of Lieberkühn) found in the wall of the mammalian intestine. We extend the standard von Kármán equations to incorporate inhomogeneity in the plate’s mechanical properties and surface stresses applied to the substrate by cell proliferation. We determine numerically the configurations of a homogeneous plate under uniform cell growth, and show how tethering to an underlying elastic foundation can be used to promote higher-order buckled configurations. We then examine the independent effects of localised softening of the substrate and spatial patterning of cellular growth, demonstrating that (within a two-dimensional framework, and contrary to the predictions of one-dimensional models) growth patterning constitutes a more viable mechanism for control of crypt distribution than does material inhomogeneity.

Item Type: Journal article
Publication Title: Mathematical Biosciences
Creators: Nelson, M.R., King, J.R. and Jensen, O.E.
Publisher: Elsevier
Date: 2013
Volume: 246
Number: 2
ISSN: 0025-5564
Identifiers:
NumberType
10.1016/j.mbs.2013.09.008DOI
Rights: © 2013 The Authors. Published by Elsevier Inc. All rights reserved
Divisions: Schools > School of Science and Technology
Depositing User: EPrints Services
Date Added: 09 Oct 2015 11:04
Last Modified: 23 Aug 2016 09:13
URI: http://irep.ntu.ac.uk/id/eprint/22418

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