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| HAL : inria-00148610, version 3 |
| Fiche détaillée |  Récupérer au format |
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| SIAM Journal on Scientific Computing (2009) |
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| Versions disponibles : | v1 (23-05-2007) | v2 (23-11-2007) | v3 (21-04-2009) | v4 (14-12-2009) |
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| Computational modeling of solid tumor growth: the avascular stage |
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| Didier Bresch 1Thierry Colin 2, 3 |
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| (2009) |
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| 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. |
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| 1 : | Laboratoire de Mathématiques (LAMA) |
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CNRS : UMR5127 – Université de Savoie |
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| 2 : | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| 3 : | MC2 (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR |
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| 4 : | Unité de Mathématiques Pures et Appliquées (UMPA-ENSL) |
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CNRS : UMR5669 – École Normale Supérieure - Lyon |
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| 5 : | Ciblage thérapeutique en Oncologie (EA3738) |
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Université Claude Bernard - Lyon I |
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| Domaine | : | Informatique/Modélisation et simulation Mathématiques/Equations aux dérivées partielles Physique/Mécanique/Mécanique des fluides Sciences de l'ingénieur/Mécanique/Mécanique des fluides Sciences du Vivant/Cancer |
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| Avascular tumor growth. Multiscale models. Cell cycle modeling. Fluid dynamics. Level-set methods. |
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| Liste des fichiers attachés à ce document : | |||||
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| inria-00148610, version 3 | |
| http://hal.archives-ouvertes.fr/inria-00148610 | |
| oai:hal.archives-ouvertes.fr:inria-00148610 | |
| Contributeur : Olivier Saut | |
| Soumis le : Mardi 21 Avril 2009, 15:11:53 | |
| Dernière modification le : Mardi 21 Avril 2009, 15:57:21 | |
