BRESCH, Didier; COLIN, Thierry; GRENIER, Emmanuel; RIBBA, Benjamin; SAUT, Olivier

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BRESCH, Didier
Laboratoire de Mathématiques [LAMA]

COLIN, Thierry
Institut de Mathématiques de Bordeaux [IMB]
Modélisation, contrôle et calcul [MC2]

GRENIER, Emmanuel
Unité de Mathématiques Pures et Appliquées [UMPA-ENSL]

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Ce document a été publié dans

SIAM Journal on Scientific Computing. 2010, vol. 32, n° 4, p. 2321-2344

Society for Industrial and Applied Mathematics

Résumé en anglais

In this paper, we present a mathematical model for avascular tumor growth and its numerical study in two and three dimensions. For this purpose, we use a multiscale model using PDEs to describe the evolution of the tumor cell densities. In our model, cell cycle regulation depends mainly on micro-environment. The cancer growth of volume induces cells motion and tumor expansion. According to biology, cells grow against a basal membrane which interacts mechanistically with the tumor. We use a level set method to describe this membrane and we compute its influence on cell movement thanks to a Stokes equation. The evolution of oxygen, diffusing from blood vessel to cancer cells and used to estimate hypoxia, is given by a stationary diffusion equation solved with a penalization method. The model has been applied to investigate the therapeutic benefit of anti-invasive agents and constitutes now the basis of a numerical platform for tumor growth simulation.< Réduire

Mots clés en anglais

Avascular tumor growth. Multiscale models. Cell cycle modeling. Fluid dynamics. Level-set methods.

Avascular tumor growth. Multiscale models. Cell cycle modeling. Fluid dynamics. Level-set methods

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Institut de Mathématiques de Bordeaux (IMB) - UMR 5251