ATP Production and Necrosis Formation in a Tumour Spheroid Model
Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 30-46
Cet article a éte moissonné depuis la source EDP Sciences
Mathematical models of tumour spheroids, proposed since the early seventies, have been generally formulated in terms of a single diffusive nutrient which is critical for cell replication and cell viability. Only recently, attempts have been made to incorporate in the models the cell energy metabolism, by considering the interplay between glucose, oxygen and lactate (or pH). By assuming glucose and lactate as the only fuel substrates, we propose a simple model for the cell ATP production which takes into account the main reactions that occur in the glycolytic and the oxidative pathway. Under the assumption that cell death occurs when ATP production falls below a critical level, we have studied the free boundary problem for the concentration of glucose, lactate and oxygen inside the spheroid viable rim. We show that the existence of a necrotic core is guaranteed for a sufficiently large size of the spheroid.
Affiliations des auteurs :
A. Bertuzzi 1 ; A. Fasano 2 ; A. Gandolfi 1 ; C. Sinisgalli 1
@article{10_1051_mmnp:2007002,
author = {A. Bertuzzi and A. Fasano and A. Gandolfi and C. Sinisgalli},
title = {ATP {Production} and {Necrosis} {Formation} in a {Tumour} {Spheroid} {Model}},
journal = {Mathematical modelling of natural phenomena},
pages = {30--46},
year = {2007},
volume = {2},
number = {3},
doi = {10.1051/mmnp:2007002},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007002/}
}
TY - JOUR AU - A. Bertuzzi AU - A. Fasano AU - A. Gandolfi AU - C. Sinisgalli TI - ATP Production and Necrosis Formation in a Tumour Spheroid Model JO - Mathematical modelling of natural phenomena PY - 2007 SP - 30 EP - 46 VL - 2 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007002/ DO - 10.1051/mmnp:2007002 LA - en ID - 10_1051_mmnp:2007002 ER -
%0 Journal Article %A A. Bertuzzi %A A. Fasano %A A. Gandolfi %A C. Sinisgalli %T ATP Production and Necrosis Formation in a Tumour Spheroid Model %J Mathematical modelling of natural phenomena %D 2007 %P 30-46 %V 2 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007002/ %R 10.1051/mmnp:2007002 %G en %F 10_1051_mmnp:2007002
A. Bertuzzi; A. Fasano; A. Gandolfi; C. Sinisgalli. ATP Production and Necrosis Formation in a Tumour Spheroid Model. Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 30-46. doi: 10.1051/mmnp:2007002
Cité par Sources :