American Institute of Mathematical Sciences

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2007, 4(4): 687-698. doi: 10.3934/mbe.2007.4.687

Mesoscopic model for tumor growth

Elena Izquierdo-Kulich 1, and  José Manuel Nieto-Villar 2,

1. 

Departamento de Ingeniería Química. Facultad de Ingeniería Química. Instituto Superior Politécnico, CUJAE, Havana, Cuba
2. 

Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba

Received  January 2007 Revised  June 2007 Published  August 2007

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.
Keywords: fractal, stochastic model, mesoscopic model, tumor growth, mathematical modeling..
Mathematics Subject Classification: 92C15, 82C31, 92C5.
Citation: Elena Izquierdo-Kulich, José Manuel Nieto-Villar. Mesoscopic model for tumor growth. Mathematical Biosciences & Engineering, 2007, 4 (4) : 687-698. doi: 10.3934/mbe.2007.4.687
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