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Mathematical Biosciences and Engineering

2007, Volume 4, Issue 4: 687-698. doi: 10.3934/mbe.2007.4.687
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Mesoscopic model for tumor growth

  • 1.
    Departamento de Ingeniería Química. Facultad de Ingeniería Química. Instituto Superior Politécnico, CUJAE, Havana
  • 2.
    Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana
  • Received: 01 January 2007 Accepted: 29 June 2018 Published: 01 August 2007

  • MSC : 92C15, 82C31, 92C50.

  • In this work, we propose a mesoscopic model for tumor growth to improve our understanding of the origin of the heterogeneity of tumor cells. In this sense, this stochastic formalism allows us to not only to reproduce but also explain the experimental results presented by Brú. A significant aspect found by the model is related to the predicted values for β growth exponent, which capture a basic characteristic of the critical surface growth dynamics. According to the model, the value for growth exponent is between 0,25 and 0,5, which includes the value proposed by Kadar-Parisi-Zhang universality class (0,33) and the value proposed by Brú (0,375) related to the molecular beam epitaxy (MBE) universality class. This result suggests that the tumor dynamics are too complex to be associated to a particular universality class.

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

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  • In this work, we propose a mesoscopic model for tumor growth to improve our understanding of the origin of the heterogeneity of tumor cells. In this sense, this stochastic formalism allows us to not only to reproduce but also explain the experimental results presented by Brú. A significant aspect found by the model is related to the predicted values for β growth exponent, which capture a basic characteristic of the critical surface growth dynamics. According to the model, the value for growth exponent is between 0,25 and 0,5, which includes the value proposed by Kadar-Parisi-Zhang universality class (0,33) and the value proposed by Brú (0,375) related to the molecular beam epitaxy (MBE) universality class. This result suggests that the tumor dynamics are too complex to be associated to a particular universality class.


  • 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. 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
    3. 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
    4. M. A. C. Huergo, M. A. Pasquale, A. E. Bolzán, A. J. Arvia, P. H. González, Morphology and dynamic scaling analysis of cell colonies with linear growth fronts, 2010, 82, 1539-3755, 10.1103/PhysRevE.82.031903
    5. E. Izquierdo-Kulich, I. Rebelo, E. Tejera, J.M. Nieto-Villar, Phase transition in tumor growth: I avascular development, 2013, 392, 03784371, 6616, 10.1016/j.physa.2013.08.010
    6. 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
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  • © 2007 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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