Biomechanical modelling of colorectal crypt formation and in-vitro replication

Nelson, Martin, R. (2011) Biomechanical modelling of colorectal crypt formation and in-vitro replication. PhD thesis, University of Nottingham.

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Abstract

The colon's epithelial lining exhibits a number of invaginations into the underlying tissue, called the crypts of Lieberkühn. Housing stem cells at their bases, these crypts play an essential role in the maintenance of the epithelium; however, the processes by which crypts form are not conclusively understood. This study deploys mathematical and experimental modelling to validate one potential mechanism: that cellular growth in the developing epithelium causes a build up of compressive stresses, resulting in buckling instabilities which initiate crypt formation.

We begin with an extension to the model of Edwards & Chapman (2007), modelling the epithelium as a beam tethered to underlying tissue by a series of springs. Modelling growth parametrically as a sequence of equilibrium configurations attained by beams of increasing length, we demonstrate that competition between lateral supports and stromal adhesion determines buckling wavelength. We show how non-equilibrium relaxation of tethering forces affects post-buckled shapes, and illustrate that growth inhomogeneity has a much weaker influence upon buckled configurations than do variations of mechanical properties.

An in-vitro study, in which we culture intestinal epithelial cells upon a flexible substrate, demonstrates that the cells can exert sufficient force to induce buckling upon reaching confluence. A corresponding one-dimensional model is presented, in which a growing, confluent cell monolayer adheres to a thin compressible elastic beam. The model exhibits buckling via parametric growth. Cell-substrate adhesion and growth inhomogeneity have minimal influence upon configurations. Compressibility is important only in separating bifurcation points; large-amplitude shapes are accurately approximated by incompressible solutions. A two-dimensional analogue of this model, which extends von Kármán plate theory, is then given. Axisymmetric configurations are compared with an alternative shell theory model, highlighting discrepancies arising from constitutive assumptions. Examining configurations of an inhomogeneous plate reveals that generation of multiple crypts by targeted softening alone is difficult; however, attachment to an elastic foundation can bias high frequency configurations.

Item Type:Thesis (PhD)
Supervisors:Jensen, Oliver
King, John
Rose, Felicity
Waters, Sarah
Uncontrolled Keywords:Biomechanics, colorectal crypt, buckling, epithelial cells, tissue engineering, mathematical models
Faculties/Schools:UK Campuses > Faculty of Science > School of Mathematical Sciences
ID Code:1778
Deposited By:Dr Martin R. Nelson
Deposited On:14 Oct 2011 14:05
Last Modified:14 Oct 2011 14:05

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