Morphogenesis of the tumor patterns

Elena Izquierdo-Kulich; José Manuel Nieto-Villar; Elena Izquierdo-Kulich; José Manuel Nieto-Villar

doi:10.3934/mbe.2008.5.299

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.
- mesoscopic model,
- mathematical modeling.,
- tumor growth,
- fractal,
- stochastic model
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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Abstract

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.
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