From a cellular automaton model of tumor-immune interactions to its macroscopic dynamical equation: A drift-diffusion data analysis approach

  • Authors:

  • K. Patanarapeelert;T. D. Frank;I. M. Tang

  • Affiliations:

  • Department of Mathematics, Faculty of Science, Silpakorn University, Nakorn Pathom 73000, Thailand;Department of Psychology, Center for the Ecological Study of Perception and Action, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269, USA;Department of Physics, Faculty of Science, Mahidol University, Rama VI Road, Bangkok 10400, Thailand and ThEP Center, Commission of Higher Education, 328 Si Ayutthaya Road, Bangkok 10400, Thailand

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2011

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Abstract

Several models of tumor growth have been developed from various perspectives and for multiple scales. Due to the complexity of interactions, how the macroscopic dynamics formed by such interactions at the microscopic level is a difficult problem. In this paper, we focus on reconstructing a model from the output of an experimental model. This is carried out by the data analysis approach. We simulate the growth process of tumor with immune competition by using cellular automata technique adapted from previous studies. We employ an analysis of data given by the simulation output to derive an evolution equation of macroscopic dynamics of tumor growth. In a numerical example we show that the dynamics of tumor at stationary state can be described by an Ornstein-Uhlenbeck process. We show further how the result can be linked to the stochastic Gompertz model.