A Comparison of Continuum and Cell-based Models of Colorectal Cancer

Walter, Alexander (2009) A Comparison of Continuum and Cell-based Models of Colorectal Cancer. PhD thesis, University of Nottingham.

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Abstract

Colorectal cancer is thought to originate in the epithelial cells that line the colorectal crypt and, in most cases, is associated with a mutation in Wnt-signalling pathway. These mutations cause cells to alter their proliferative behaviour, make their cytoskeleton less deformable and increase their levels of cell-cell and cell-substrate adhesion.

In this thesis we develop three different types of models for the proliferation and movement of epithelial cells in a colorectal crypt. We use these models to investigate how changing the cell adhesion, cytoskeleton and proliferation properties of mutant cells affects their ability to establish a mutant population within the crypt.

First we develop a continuum model of two cell populations, normal and mutant, using a spatially-varying source term to model Wnt-dependent proliferation and using Darcy's law to describe cell movement down pressure gradients. We distinguish between mutant cells and normal cells by assuming the former have a spatially independent source term, representing proliferation, and a different viscosity to normal cells, to model changes in their cytoskeleton and levels of adhesion. The model is solved analytically by an asymptotic expansion of the variables and numerically using a collocation method. The results show that the ability of mutant cells to remain in the crypt depends on the position of the initial mutation and their viscosity: the further up the crypt a cell suffers a mutation the more rigid and adhesive the cell must be for a mutation to persist.

We then consider a discrete cell-centre model based on the work of Meineke et al. (2001). Cell-cell interaction forces are modelled by springs and are balanced by a viscous drag term. Adaptations to Meineke et al. (2001) include unpinning of stem cells from the bottom of the crypt, dependence of cell-drag on cell size, dependence of cell-cell interaction forces on their area of contact and the inclusion of mutant cells. Using agile software engineering techniques, the software environment, CHASTE, is developed and used to solve the model numerically and to reproduce experimental findings such as crypt homoeostasis and monoclonality. The results again reveal that increasing the drag on the mutant cells increases the likelihood of a mutant population establishing itself within the crypt.

The third approach is a discrete cell-vertex model. The model decouples cell-cell adhesion forces from cell deformation forces and movement is determined by a free-energy gradient balanced by a viscous drag term. Numerical simulations show that the model can generate similar results to the cell-centre model, and reveal that increased cell-cell adhesion of the mutant cells increases the likelihood of the mutant population invading the crypt.

Finally the three models are compared in terms of their suitability for modelling epithelial tissue.

Item Type:Thesis (PhD)
Supervisors:Byrne, H. M.
Jensen, O. E.
Uncontrolled Keywords:Colorectal crypt, colorectal cancer, epithelial cell movement, cell-centre, cell-vertex, Darcy.
Faculties/Schools:UK Campuses > Faculty of Science > School of Mathematical Sciences
ID Code:763
Deposited By:Dr Alexander Walter
Deposited On:09 Dec 2009 12:15
Last Modified:09 Dec 2009 12:15

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