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Mathematical Biosciences and Engineering

2009, Volume 6, Issue 3: 547-559. doi: 10.3934/mbe.2009.6.547
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The dynamics of tumor growth and cells pattern morphology

  • 1.
    Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana
  • 2.
    Institute of Oncology and Radiobiology, Havana
  • 3.
    Faculty of Physics, University of Havana, Havana
  • 4.
    Faculty of Chemical Engineering, CUJAE, Havana
  • Received: 01 July 2008 Accepted: 29 June 2018 Published: 01 June 2009

  • MSC : 92C15, 82C31, 92C50.

  • 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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  • 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.


  • This article has been cited by:

    1. Morphogenesis and aggressiveness of cervix carcinoma, 2011, 8, 1551-0018, 987, 10.3934/mbe.2011.8.987
    2. Antonio Rafael Selva Castañeda, Erick Ramírez Torres, Narciso Antonio Villar Goris, Maraelys Morales González, Juan Bory Reyes, Victoriano Gustavo Sierra González, María Schonbek, Juan Ignacio Montijano, Luis Enrique Bergues Cabrales, Fabio Rapallo, New formulation of the Gompertz equation to describe the kinetics of untreated tumors, 2019, 14, 1932-6203, e0224978, 10.1371/journal.pone.0224978
    3. Abicumaran Uthamacumaran, Hector Zenil, A Review of Mathematical and Computational Methods in Cancer Dynamics, 2022, 12, 2234-943X, 10.3389/fonc.2022.850731
    4. Yan Fu, Tian Lu, Meng Zhou, Dongwei Liu, Qihang Gan, Guowei Wang, Effect of color cross-correlated noise on the growth characteristics of tumor cells under immune surveillance, 2023, 20, 1551-0018, 21626, 10.3934/mbe.2023957
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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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