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Title: 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
Silpakorn University
University of Connecticut
Mahidol University
Commission on Higher Education
Keywords: Computer Science;Mathematics
Issue Date: 1-Jan-2011
Citation: Mathematical and Computer Modelling. Vol.53, No.1-2 (2011), 122-130
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. © 2010 Elsevier Ltd.
ISSN: 08957177
Appears in Collections:Scopus 2011-2015

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