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2009, 6(3): 547-559. doi: 10.3934/mbe.2009.6.547

The dynamics of tumor growth and cells pattern morphology

Elena Izquierdo-Kulich 1, , Margarita Amigó de Quesada 2, , Carlos Manuel Pérez-Amor 3, , Magda Lopes Texeira 4, and  José Manuel Nieto-Villar 1,

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.
Keywords: pattern cell morphology., mesoscopic model, fractal, stochastic model, tumor growth.
Mathematics Subject Classification: 92C15, 82C31, 92C5.
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
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