The dynamics of tumor
growth and cells pattern morphology
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1.
Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana
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2.
Institute of Oncology and Radiobiology, Havana
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3.
Faculty of Physics, University of Havana, Havana
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4.
Faculty of Chemical Engineering, CUJAE, Havana
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Received:
01 July 2008
Accepted:
29 June 2018
Published:
01 June 2009
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MSC :
92C15, 82C31, 92C50.
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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 tumorgrowth and cells pattern morphology[J]. Mathematical Biosciences and Engineering, 2009, 6(3): 547-559. doi: 10.3934/mbe.2009.6.547
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Abstract
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.
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