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Modelling collective cell behaviour with spatial moment dynamics

Banff International Research Station for Mathematical Innovation and Discovery

Many PDE-based models of collective cell behaviour implicitly assume that the population of cells is ‘well mixed’. This is called a spatial mean-field assumption. In reality, populations often have a more complex spatial structure, such as clusters and/or spatial segregation of cells. This spatial structure is both a cause and an effect of interactions among neighbouring cells and can make a significant difference to model predictions about, for example, cell densities and invasion speeds. I will describe an individual-based model of collective cell behaviour that is based on interactions between pairs of cells. I will show how a neighbour-dependent directional bias can be included in the model and how spatial moment dynamics can be used to give a continuum-level description of the population that retains spatial structure beyond the mean-field.

Mathematics; Partial differential equations; Biology and other natural sciences; Applied analysis / inverse problems

video/mp4

Author affiliation: University of Canterbury

2017-01-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59841

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/