The Mathematical Institute, University of Oxford, Eprints Archive

Comparing a discrete and continuum model of the intestinal crypt

Murray, P J and Walter, A and Fletcher, A G and Edwards, C. M. and Tindall, M. J. and Maini, P. K. (2011) Comparing a discrete and continuum model of the intestinal crypt. Physical Biology, 8 (2). 026011 (11 pages. ISSN 1478-3975



The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1055
Deposited By: Philip Maini
Deposited On:22 Mar 2011 07:46
Last Modified:29 May 2015 18:44

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