Mathematical modelling of the gastrointestinal epithelium stem cell niche.
by
Sarah Waters (on behalf of Sarah Eastburn)
University of Oxford
Coauthors: Dr Sarah Waters, Dr James Oliver, Prof. Helen Byrne and Dr Felicity Rose

The gastrointestinal tract is lined by a mono-layered epithelium that contains invaginations called the crypts of Lieberkühn. These crypts contain stem cells which are responsible for the regeneration and maintenance of the epithelial lining. The stem cells are thought to reside in a niche at the crypt base. The crypts have a natural hierarchy and transit cells produced by the stem cells, divide, differentiate and migrate towards the intestinal lumen.

Using a number of complementary modelling approaches we investigate the mechanics of the intestinal epithelium and the population kinetics, resulting from, e.g., cell proliferation and cell death. We apply these models to the in vitro experiments carried out in the Tissue Engineering Group at Nottingham, with the aim of determining the spatiotemporal distribution of cell density and stress, and consider the role of different substrate geometries on the morphology of a growing cell aggregate.

We model the tissue mechanics of a growing aggregate of cells using a lattice-free spatial framework. Cells are unrestricted in their position and move in a continuous fashion in response to the resultant force exerted on each cell by its neighbours, with drag balancing the cell-cell interactions which are modelled as springs between neighbouring cells. The model behaviour is captured in one dimensionless parameter, a, the ratio of a typical cell cycle time to the spring relaxation time, with cell cycle times modelled by a simple uniform distribution.

The cell kinetics of the intestinal crypt are modelled via a stochastic branching process model for the evolution of a spatially-homogeneous mixed population of stem, transit and fully differentiated cells. From this model we derive analytic expressions for the expected number and variance of each cell type, and for the total number of crypt cells which are compared with experimental data.

These two models are then coupled together, the kinetic model replacing the original simple cell proliferation assumption in the mechanical model. We investigate how this modified kinetic approach changes the resulting cell densities and stresses. We will present an overview of the modelling techniques used, as well as our key findings from these models.

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Date received: March 10, 2008