| Issue |
Math. Model. Nat. Phenom.
Volume 6, Number 7, 2011
Mathematical modeling in biomedical applications
|
|
|---|---|---|
| Page(s) | 27 - 38 | |
| DOI | https://doi.org/10.1051/mmnp/20116703 | |
| Published online | 15 June 2011 | |
Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy
Department of Theoretical Physics, P.N. Lebedev Physical
Institute, Leninskij prosp.
53, Moscow
119991,
Russia
⋆ Corresponding author. E-mail: apol@lpi.ru
A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that the tumour growth rate depends on the tissue oxygen level in a threshold manner.
Mathematics Subject Classification: 92B05 / 35K40
Key words: tumor growth / proliferation and migration dichotomy / oxygen
© EDP Sciences, 2011
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