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: A Journal of the IMA, 18, (2), 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.
|Digital Object Identifier (DOI):||doi:10.1093/imammb/18.2.131|
|Keywords:||compaction theory, suspension theory, diffusion, c|
|Subjects:||Q Science > QA Mathematics
R Medicine > RC Internal medicine > RC0254 Neoplasms. Tumors. Oncology (including Cancer)
Q Science > QH Natural history > QH301 Biology
|Divisions :||University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
|Accepted Date and Publication Date:||
|Date Deposited:||10 May 2006|
|Last Modified:||31 Mar 2016 11:54|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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