A viscoelastic model for avascular tumor growth

Pages: 101 - 108, Issue Special, September 2009

 Abstract        Full Text (235.4K)              

Didier Bresch - Laboratoire de Mathématiques Appliquées, UMR6620, 24 avenue des Landais, 63177 Aubière, France (email)
Thierry Colin - Mathématiques Appliquées de Bordeaux, CNRS ERS 123 et, Université Bordeaux 1, 351 cours de la libération, 33405 Talence cedex, France (email)
Emmanuel Grenier - Unité de Mathématiques Pures et Appliquées, CNRS UMR 5669, Ecole Normale Supérieure de Lyon, 69364 Lyon cedex, France (email)
Benjamin Ribba - Université de Lyon 1, Ciblage Thérapeutique en Oncologie, Faculté de Médecine Lyon-Sud, Oullins, F-69921, France (email)
Olivier Saut - Université Bordeaux 1, Institut de Mathématiques, CNRS UMMR 5251, 351 cours de la libération, 33405 Talence Cedex, France (email)

Abstract: 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

Received: August 2008;      Revised: July 2009;      Published: September 2009.