• Previous Article
    Finite-difference and pseudo-spectral methods for the numerical simulations of in vitro human tumor cell population kinetics
  • MBE Home
  • This Issue
  • Next Article
    A spatial model of tumor-host interaction: Application of chemotherapy
2009, 6(3): 547-559. doi: 10.3934/mbe.2009.6.547

The dynamics of tumor growth and cells pattern morphology

1. 

Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba

2. 

Institute of Oncology and Radiobiology, Havana, Cuba

3. 

Faculty of Physics, University of Havana, Havana, Cuba

4. 

Faculty of Chemical Engineering, CUJAE, Havana, Cuba

Received  July 2008 Revised  November 2008 Published  June 2009

The mathematical modeling of tumor growth is an approach to explain the complex nature of these systems. A model that describes tumor growth was obtained by using a mesoscopic formalism and fractal dimension. This model theoretically predicts the relation between the morphology of the cell pattern and the mitosis/apoptosis quotient that helps to predict tumor growth from tumoral cells fractal dimension. The relation between the tumor macroscopic morphology and the cell pattern morphology is also determined. This could explain why the interface fractal dimension decreases with the increase of the cell pattern fractal dimension and consequently with the increase of the mitosis/apoptosis relation. Indexes to characterize tumoral cell proliferation and invasion capacities are proposed and used to predict the growth of different types of tumors. These indexes also show that the proliferation capacity is directly proportional to the invasion capacity. The proposed model assumes: i) only interface cells proliferate and invade the host, and ii) the fractal dimension of tumoral cell patterns, can reproduce the Gompertzian growth law.
Citation: 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
[1]

Elena Izquierdo-Kulich, José Manuel Nieto-Villar. Mesoscopic model for tumor growth. Mathematical Biosciences & Engineering, 2007, 4 (4) : 687-698. doi: 10.3934/mbe.2007.4.687

[2]

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

[3]

Guanqi Liu, Yuwen Wang. Pattern formation of a coupled two-cell Schnakenberg model. Discrete & Continuous Dynamical Systems - S, 2017, 10 (5) : 1051-1062. doi: 10.3934/dcdss.2017056

[4]

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

[5]

Michael Grinfeld, Harbir Lamba, Rod Cross. A mesoscopic stock market model with hysteretic agents. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 403-415. doi: 10.3934/dcdsb.2013.18.403

[6]

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

[7]

T.L. Jackson. A mathematical model of prostate tumor growth and androgen-independent relapse. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 187-201. doi: 10.3934/dcdsb.2004.4.187

[8]

J. Ignacio Tello. On a mathematical model of tumor growth based on cancer stem cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 263-278. doi: 10.3934/mbe.2013.10.263

[9]

Hyun Geun Lee, Yangjin Kim, Junseok Kim. Mathematical model and its fast numerical method for the tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1173-1187. doi: 10.3934/mbe.2015.12.1173

[10]

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

[11]

Marcelo E. de Oliveira, Luiz M. G. Neto. Directional entropy based model for diffusivity-driven tumor growth. Mathematical Biosciences & Engineering, 2016, 13 (2) : 333-341. doi: 10.3934/mbe.2015005

[12]

Kentarou Fujie. Global asymptotic stability in a chemotaxis-growth model for tumor invasion. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 203-209. doi: 10.3934/dcdss.2020011

[13]

Shaoyong Lai, Yulan Zhou. A stochastic optimal growth model with a depreciation factor. Journal of Industrial & Management Optimization, 2010, 6 (2) : 283-297. doi: 10.3934/jimo.2010.6.283

[14]

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

[15]

Cristina Anton, Alan Yong. Stochastic dynamics and survival analysis of a cell population model with random perturbations. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1077-1098. doi: 10.3934/mbe.2018048

[16]

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

[17]

Amy H. Lin. A model of tumor and lymphocyte interactions. Discrete & Continuous Dynamical Systems - B, 2004, 4 (1) : 241-266. doi: 10.3934/dcdsb.2004.4.241

[18]

Ali Ashher Zaidi, Bruce Van Brunt, Graeme Charles Wake. A model for asymmetrical cell division. Mathematical Biosciences & Engineering, 2015, 12 (3) : 491-501. doi: 10.3934/mbe.2015.12.491

[19]

Julien Dambrine, Nicolas Meunier, Bertrand Maury, Aude Roudneff-Chupin. A congestion model for cell migration. Communications on Pure & Applied Analysis, 2012, 11 (1) : 243-260. doi: 10.3934/cpaa.2012.11.243

[20]

Krzysztof Fujarewicz, Krzysztof Łakomiec. Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1131-1142. doi: 10.3934/mbe.2016034

[Back to Top]