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2009, 2009(Special): 101-108. doi: 10.3934/proc.2009.2009.101

A viscoelastic model for avascular tumor growth

Didier Bresch 1, , Thierry Colin 2, , Emmanuel Grenier 3, , Benjamin Ribba 4, and  Olivier Saut 5,

1. 

Laboratoire de Mathématiques Appliquées, UMR6620, 24 avenue des Landais, 63177 Aubière
2. 

Mathématiques Appliquées de Bordeaux, CNRS ERS 123 et, Université Bordeaux 1, 351 cours de la libération, 33405 Talence cedex
3. 

Unité de Mathématiques Pures et Appliquées, CNRS UMR 5669, Ecole Normale Supérieure de Lyon, 69364 Lyon cedex, France
4. 

Université de Lyon 1, Ciblage Thérapeutique en Oncologie, Faculté de Médecine Lyon-Sud, Oullins, F-69921, France
5. 

Université Bordeaux 1, Institut de Mathématiques, CNRS UMMR 5251, 351 cours de la libération, 33405 Talence Cedex, France

Received  August 2008 Revised  July 2009 Published  September 2009

In this article, we present a new continuous model for tumor growth. This model describes the evolution of three components: sane tissue, cancer cells and extracellular medium. In order to render correctly the cellular division, this model uses a discrete description of the cell cycle (the set of steps a cell has to undergo in order to divide). To account for cellular adhesion and the mechanics which may influence the growth, we assume a viscoelastic mechanical behavior. This model extends the one presented in [18] with a more realistic description of the forces that drive the movement.
Keywords: Avascular tumor growth. Multiscale models. Cell cycle modeling. Fluid dynamics..
Mathematics Subject Classification: Primary: 58A.
Citation: Didier Bresch, Thierry Colin, Emmanuel Grenier, Benjamin Ribba, Olivier Saut. A viscoelastic model for avascular tumor growth. Conference Publications, 2009, 2009 (Special) : 101-108. doi: 10.3934/proc.2009.2009.101
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