# Mathematical model of tumour cord growth along the source of nutrient

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 2, Issue: 3, page 153-177
- ISSN: 0973-5348

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topAstanin, S., and Tosin, A.. "Mathematical model of tumour cord growth along the source of nutrient." Mathematical Modelling of Natural Phenomena 2.3 (2010): 153-177. <http://eudml.org/doc/222323>.

@article{Astanin2010,

abstract = {
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.},

author = {Astanin, S., Tosin, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {tumour growth; hypoxia; tumour cords; tumour-host interface; mathematical model;
mixture theory; finite difference; level set method; mixture theory},

language = {eng},

month = {3},

number = {3},

pages = {153-177},

publisher = {EDP Sciences},

title = {Mathematical model of tumour cord growth along the source of nutrient},

url = {http://eudml.org/doc/222323},

volume = {2},

year = {2010},

}

TY - JOUR

AU - Astanin, S.

AU - Tosin, A.

TI - Mathematical model of tumour cord growth along the source of nutrient

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/3//

PB - EDP Sciences

VL - 2

IS - 3

SP - 153

EP - 177

AB -
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.

LA - eng

KW - tumour growth; hypoxia; tumour cords; tumour-host interface; mathematical model;
mixture theory; finite difference; level set method; mixture theory

UR - http://eudml.org/doc/222323

ER -

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