Geodesic
Mathematical model of tumour cord growth along the source of nutrient
S. Astanin1 ; A. Tosin1
1 Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, 10129, Italy
Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 153-177

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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.
DOI : 10.1051/mmnp:2007007

S. Astanin 1 ; A. Tosin 1

1 Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Turin, 10129, Italy 
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S. Astanin; A. Tosin. Mathematical model of tumour cord growth along the source of nutrient. Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 153-177. doi: 10.1051/mmnp:2007007

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