Tumour dynamics and necrosis: surface tension and stability

Landman, K.A. and Please, C.P. (2001) Tumour dynamics and necrosis: surface tension and stability Mathematical Medicine and Biology, 18, (2), pp. 131-158. (doi:10.1093/imammb/18.2.131).


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A model is developed for the motion of cells within a multicell spherical tumour. The model allows either for the intercellular forces to be in compression and cells to be compacted to a fixed number density, or for the cell number density to fall and cells to become isolated from each other. The model develops necrotic regions naturally due to force balances rather than being directly attributable to a critical oxygen concentration. These necrotic regions may result in a gradual reduction in local cell density rather than jump to a completely dead region.
Numerical and analytical analysis of the spherically symmetric model shows that the long time behaviour of the spheroid depends on any surface tension effects created by cells on the outer surface. For small surface tension the spheroid grows linearly in time developing a large necrotic region, while for larger surface tension the growth can be halted. The linear stability to spherically symmetric perturbations of all the possible resulting steady states is revealed.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1093/imammb/18.2.131
ISSNs: 1477-8599 (print)
Keywords: compaction theory, suspension theory, diffusion, c

ePrint ID: 29255
Date :
Date Event
1 June 2001Published
Date Deposited: 10 May 2006
Last Modified: 16 Apr 2017 22:23
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/29255

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