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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

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 $\beta$ 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.
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Keywords fractal; stochastic model; mesoscopic model; tumor growth; mathematical modeling.

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


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  • 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, Physica A: Statistical Mechanics and its Applications, 2015, 426, 88, 10.1016/j.physa.2015.01.038
  • 3. 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, Physical Review E, 2010, 82, 3, 10.1103/PhysRevE.82.031903
  • 4. E. Izquierdo-Kulich, I. Rebelo, E. Tejera, J.M. Nieto-Villar, Phase transition in tumor growth: I avascular development, Physica A: Statistical Mechanics and its Applications, 2013, 392, 24, 6616, 10.1016/j.physa.2013.08.010
  • 5. E. Izquierdo-Kulich, J. M. Nieto-Villar, , Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics, 2013, Chapter 48, 657, 10.1007/978-3-642-34070-3_48

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