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

A viscoelastic model for avascular tumor growth

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.
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
[1]

Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1141-1156. doi: 10.3934/mbe.2015.12.1141

[2]

Shihe Xu, Yinhui Chen, Meng Bai. Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 997-1008. doi: 10.3934/dcdsb.2016.21.997

[3]

Katarzyna A. Rejniak. A Single-Cell Approach in Modeling the Dynamics of Tumor Microregions. Mathematical Biosciences & Engineering, 2005, 2 (3) : 643-655. doi: 10.3934/mbe.2005.2.643

[4]

Ahuod Alsheri, Ebraheem O. Alzahrani, Asim Asiri, Mohamed M. El-Dessoky, Yang Kuang. Tumor growth dynamics with nutrient limitation and cell proliferation time delay. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3771-3782. doi: 10.3934/dcdsb.2017189

[5]

Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Age-structured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 1-17. doi: 10.3934/mbe.2013.10.1

[6]

Gülnihal Meral, Christian Stinner, Christina Surulescu. On a multiscale model involving cell contractivity and its effects on tumor invasion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 189-213. doi: 10.3934/dcdsb.2015.20.189

[7]

Mostafa Adimy, Fabien Crauste. Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 19-38. doi: 10.3934/dcdsb.2007.8.19

[8]

Andrea Tosin. Multiphase modeling and qualitative analysis of the growth of tumor cords. Networks & Heterogeneous Media, 2008, 3 (1) : 43-83. doi: 10.3934/nhm.2008.3.43

[9]

Shinji Nakaoka, Hisashi Inaba. Demographic modeling of transient amplifying cell population growth. Mathematical Biosciences & Engineering, 2014, 11 (2) : 363-384. doi: 10.3934/mbe.2014.11.363

[10]

Elena Izquierdo-Kulich, Margarita Amigó de Quesada, Carlos Manuel Pérez-Amor, Magda Lopes Texeira, José Manuel Nieto-Villar. The dynamics of tumor growth and cells pattern morphology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 547-559. doi: 10.3934/mbe.2009.6.547

[11]

Yang Kuang, John D. Nagy, James J. Elser. Biological stoichiometry of tumor dynamics: Mathematical models and analysis. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 221-240. doi: 10.3934/dcdsb.2004.4.221

[12]

Zejia Wang, Suzhen Xu, Huijuan Song. Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2593-2605. doi: 10.3934/dcdsb.2018129

[13]

Niklas Hartung. Efficient resolution of metastatic tumor growth models by reformulation into integral equations. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 445-467. doi: 10.3934/dcdsb.2015.20.445

[14]

Urszula Ledzewicz, James Munden, Heinz Schättler. Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 415-438. doi: 10.3934/dcdsb.2009.12.415

[15]

Mohammad A. Tabatabai, Wayne M. Eby, Karan P. Singh, Sejong Bae. T model of growth and its application in systems of tumor-immune dynamics. Mathematical Biosciences & Engineering, 2013, 10 (3) : 925-938. doi: 10.3934/mbe.2013.10.925

[16]

Mengli Hao, Ting Gao, Jinqiao Duan, Wei Xu. Non-Gaussian dynamics of a tumor growth system with immunization. Inverse Problems & Imaging, 2013, 7 (3) : 697-716. doi: 10.3934/ipi.2013.7.697

[17]

Heikki Haario, Leonid Kalachev, Marko Laine. Reduction and identification of dynamic models. Simple example: Generic receptor model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 417-435. doi: 10.3934/dcdsb.2013.18.417

[18]

John D. Nagy. The Ecology and Evolutionary Biology of Cancer: A Review of Mathematical Models of Necrosis and Tumor Cell Diversity. Mathematical Biosciences & Engineering, 2005, 2 (2) : 381-418. doi: 10.3934/mbe.2005.2.381

[19]

Fujun Zhou, Shangbin Cui. Well-posedness and stability of a multidimensional moving boundary problem modeling the growth of tumor cord. Discrete & Continuous Dynamical Systems - A, 2008, 21 (3) : 929-943. doi: 10.3934/dcds.2008.21.929

[20]

Junde Wu, Shangbin Cui. Asymptotic behavior of solutions for parabolic differential equations with invariance and applications to a free boundary problem modeling tumor growth. Discrete & Continuous Dynamical Systems - A, 2010, 26 (2) : 737-765. doi: 10.3934/dcds.2010.26.737

 Impact Factor: 

Metrics

  • PDF downloads (1)
  • HTML views (0)
  • Cited by (0)

[Back to Top]