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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 2: 299-313. doi: 10.3934/mbe.2008.5.299
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Morphogenesis of the tumor patterns

  • 1.
    Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana
  • Received: 01 November 2007 Accepted: 29 June 2018 Published: 01 March 2008

  • MSC : 92C15, 82C31, 92C50.

  • The mathematical modeling of tumor growth allows us to describe the most important regularities of these systems. A stochastic model, based on the most important processes that take place at the level of individual cells, is proposed to predict the dynamical behavior of the expected radius of the tumor and its fractal dimension. It was found that the tumor has a characteristic fractal dimension, which contains the necessary information to predict the tumor growth until it reaches a stationary state. This fractal dimension is distorted by the effects of external fluctuations. The model predicts a phenomenon which indicates stochastic resonance when the multiplicative and the additive noise are correlated.

    Citation: Elena Izquierdo-Kulich, José Manuel Nieto-Villar. Morphogenesis of the tumor patterns[J]. Mathematical Biosciences and Engineering, 2008, 5(2): 299-313. doi: 10.3934/mbe.2008.5.299

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  • The mathematical modeling of tumor growth allows us to describe the most important regularities of these systems. A stochastic model, based on the most important processes that take place at the level of individual cells, is proposed to predict the dynamical behavior of the expected radius of the tumor and its fractal dimension. It was found that the tumor has a characteristic fractal dimension, which contains the necessary information to predict the tumor growth until it reaches a stationary state. This fractal dimension is distorted by the effects of external fluctuations. The model predicts a phenomenon which indicates stochastic resonance when the multiplicative and the additive noise are correlated.


  • This article has been cited by:

    1. E. Izquierdo-Kulich, J. M. Nieto-Villar, 2013, Chapter 48, 978-3-642-34069-7, 657, 10.1007/978-3-642-34070-3_48
    2. J.A. Llanos-Pérez, A. Betancourt-Mar, M.P. De Miguel, E. Izquierdo-Kulich, M. Royuela-García, E. Tejera, J.M. Nieto-Villar, Phase transitions in tumor growth: II prostate cancer cell lines, 2015, 426, 03784371, 88, 10.1016/j.physa.2015.01.038
    3. J.A. Llanos-Pérez, J.A. Betancourt-Mar, G. Cocho, R. Mansilla, José Manuel Nieto-Villar, Phase transitions in tumor growth: III vascular and metastasis behavior, 2016, 462, 03784371, 560, 10.1016/j.physa.2016.06.086
    4. Sheyla Montero, Reynaldo Martin, Ricardo Mansilla, Germinal Cocho, José Manuel Nieto-Villar, 2018, Chapter 8, 978-1-4939-7455-9, 125, 10.1007/978-1-4939-7456-6_8
    5. Elena Izquierdo-Kulich, Esther Alonso-Becerra, José M Nieto-Villar, Entropy Production Rate for Avascular Tumor Growth, 2011, 02, 2153-1196, 615, 10.4236/jmp.2011.226071
    6. Abicumaran Uthamacumaran, Hector Zenil, A Review of Mathematical and Computational Methods in Cancer Dynamics, 2022, 12, 2234-943X, 10.3389/fonc.2022.850731
    7. Luiza M.S. Miranda, Andre M.C. Souza, Fractality in tumor growth at the avascular stage from a generalization of the logistic-Gompertz dynamics, 2023, 03784371, 128664, 10.1016/j.physa.2023.128664
    8. A. Guerra, J. A. Betancourt-Mar, J. A. Llanos-Pérez, R. Mansilla, J. M. Nieto-Villar, 2024, Chapter 4, 978-1-0716-3576-6, 45, 10.1007/978-1-0716-3577-3_4
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  • © 2008 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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