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ATP Production and Necrosis Formation in a Tumour Spheroid Model

A. Bertuzzi, A. Fasano, A. Gandolfi, C. Sinisgalli (2010)

Mathematical Modelling of Natural Phenomena

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...

Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy

A.V. Kolobov, V.V. Gubernov, A.A. Polezhaev (2011)

Mathematical Modelling of Natural Phenomena

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...

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