Baker, R. E. and Simpson, M J (2012) Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation & travelling waves. Physica A, 391 (14). pp. 37293750.

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Abstract
Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individuallevel properties of the cell motility mechanism. In this work we provide a new link between individuallevel models, which account for important cell properties such as varying cell shape and volume exclusion, and populationlevel partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individuallevel mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the populationlevel response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to twodimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape.
Item Type:  Article 

Subjects:  A  C > Biology and other natural sciences 
Research Groups:  Centre for Mathematical Biology 
ID Code:  1606 
Deposited By:  Ruth Baker 
Deposited On:  22 Sep 2012 07:30 
Last Modified:  29 May 2015 19:18 
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