Mesoscopic model for tumor growth
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Departamento de Ingeniería Química. Facultad de Ingeniería Química. Instituto Superior Politécnico, CUJAE, Havana
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Department of Physical-Chemistry, Faculty of Chemistry, University of Havana, Havana
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Received:
01 January 2007
Accepted:
29 June 2018
Published:
01 August 2007
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MSC :
92C15, 82C31, 92C50.
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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 $\beta$ 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.
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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Abstract
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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