Journal Article

Tumour dynamics and necrosis: surface tension and stability

K. A. Landman and C. P. Please

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 18, issue 2, pages 131-158
Published in print June 2001 | ISSN: 1477-8599
Published online June 2001 | e-ISSN: 1477-8602 | DOI: http://dx.doi.org/10.1093/imammb/18.2.131
Tumour dynamics and necrosis: surface tension and stability

More Like This

Show all results sharing these subjects:

  • Applied Mathematics
  • Biomathematics and Statistics

GO

Show Summary Details

Preview

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.

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

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

Full text: subscription required

How to subscribe Recommend to my Librarian

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.