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

A viscoelastic model for avascular tumor growth


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


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


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


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


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.
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

Christina Surulescu, Nicolae Surulescu. Modeling and simulation of some cell dispersion problems by a nonparametric method. Mathematical Biosciences & Engineering, 2011, 8 (2) : 263-277. doi: 10.3934/mbe.2011.8.263


Wenbin Yang, Yujing Gao, Xiaojuan Wang. Diffusion modeling of tumor-CD4$ ^+ $-cytokine interactions with treatments: asymptotic behavior and stationary patterns. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021090


Qi Deng, Zhipeng Qiu, Ting Guo, Libin Rong. Modeling within-host viral dynamics: The role of CTL immune responses in the evolution of drug resistance. Discrete & Continuous Dynamical Systems - B, 2021, 26 (7) : 3543-3562. doi: 10.3934/dcdsb.2020245


Mats Gyllenberg, Jifa Jiang, Lei Niu, Ping Yan. On the classification of generalized competitive Atkinson-Allen models via the dynamics on the boundary of the carrying simplex. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 615-650. doi: 10.3934/dcds.2018027


Joel Fotso Tachago, Giuliano Gargiulo, Hubert Nnang, Elvira Zappale. Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting. Evolution Equations & Control Theory, 2021, 10 (2) : 297-320. doi: 10.3934/eect.2020067


Dugan Nina, Ademir Fernando Pazoto, Lionel Rosier. Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system. Evolution Equations & Control Theory, 2013, 2 (2) : 379-402. doi: 10.3934/eect.2013.2.379


Rama Ayoub, Aziz Hamdouni, Dina Razafindralandy. A new Hodge operator in discrete exterior calculus. Application to fluid mechanics. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021062


Nadezhda Maltugueva, Nikolay Pogodaev. Modeling of crowds in regions with moving obstacles. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021066


Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565


Eduardo Casas, Christian Clason, Arnd Rösch. Preface special issue on system modeling and optimization. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021008


Haibo Cui, Haiyan Yin. Convergence rate of solutions toward stationary solutions to the isentropic micropolar fluid model in a half line. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2899-2920. doi: 10.3934/dcdsb.2020210


Cicely K. Macnamara, Mark A. J. Chaplain. Spatio-temporal models of synthetic genetic oscillators. Mathematical Biosciences & Engineering, 2017, 14 (1) : 249-262. doi: 10.3934/mbe.2017016


Fernando P. da Costa, João T. Pinto, Rafael Sasportes. On the convergence to critical scaling profiles in submonolayer deposition models. Kinetic & Related Models, 2018, 11 (6) : 1359-1376. doi: 10.3934/krm.2018053


Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817


Matthias Ebenbeck, Harald Garcke, Robert Nürnberg. Cahn–Hilliard–Brinkman systems for tumour growth. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021034


John Villavert. On problems with weighted elliptic operator and general growth nonlinearities. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021023


Ronald E. Mickens. Positivity preserving discrete model for the coupled ODE's modeling glycolysis. Conference Publications, 2003, 2003 (Special) : 623-629. doi: 10.3934/proc.2003.2003.623


Xu Zhang, Xiang Li. Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 393-403. doi: 10.3934/naco.2015.5.393


Brandy Rapatski, James Yorke. Modeling HIV outbreaks: The male to female prevalence ratio in the core population. Mathematical Biosciences & Engineering, 2009, 6 (1) : 135-143. doi: 10.3934/mbe.2009.6.135


Andrey Kovtanyuk, Alexander Chebotarev, Nikolai Botkin, Varvara Turova, Irina Sidorenko, Renée Lampe. Modeling the pressure distribution in a spatially averaged cerebral capillary network. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021016

 Impact Factor: 


  • PDF downloads (80)
  • HTML views (0)
  • Cited by (0)

[Back to Top]