| Issue |
Math. Model. Nat. Phenom.
Volume 2, Number 3, 2007
Cancer modelling
|
|
|---|---|---|
| Page(s) | 153 - 177 | |
| DOI | https://doi.org/10.1051/mmnp:2007007 | |
| Published online | 15 June 2008 | |
Mathematical model of tumour cord growth along the source of nutrient
Dipartimento di Matematica, Politecnico di Torino,
Corso Duca degli Abruzzi 24, Turin, 10129, Italy
Corresponding author: astanin@calvino.polito.it
A mathematical model of the tumour growth along a blood vessel is proposed. The model employs the mixture theory approach to describe a tissue which consists of cells, extracellular matrix and liquid. The growing tumour tissue is supposed to be surrounded by the host tissue. Tumours where complete oxydation of glucose prevails are considered. Special attention is paid to consistent description of oxygen consumption and growth processes based on the energy balance. A finite difference numerical method is proposed. The level set method is used to track an interface between the tissues. The simulations show localization of the tumour within a limited distance from the vessels and constant expansion velocity along the vessels.
Mathematics Subject Classification: 35R35 / 92C10 / 92B05 / 92C17
Key words: tumour growth / hypoxia / tumour cords / tumour-host interface / mathematical model / mixture theory / finite difference / level set method
© EDP Sciences, 2007
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