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Zbl 0973.92017
Landman, K.A.; Please, C.P.
Tumour dynamics and necrosis: Surface tension and stability. (English)
[J] IMA J. Math. Appl. Med. Biol. 18, No.2, 131-158 (2001). ISSN 0265-0746

Summary: 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.\par 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.

MSC 2000:: *92C50 Medical appl. of mathematical biology
35Q80 Appl. of PDE in areas other than physics
92C37 Cell biology

Keywords: compaction theory; suspension theory; diffusion; cell motion; multicell spheroids

Cited in: Zbl 1055.92024 Zbl 0996.92013

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