A multiple time-scale computational model of a tumor and its micro environment

Christopher DuBois; Jesse Farnham; Eric Aaron; Ami Radunskaya

doi:10.3934/mbe.2013.10.121

Article Contents

2013, Volume 10, Issue 1: 121-150. Doi: 10.3934/mbe.2013.10.121

This issue Previous Article Parameter space exploration within dynamic simulations of signaling networks Next Article On optimal and suboptimal treatment strategies for a mathematical model of leukemia

A multiple time-scale computational model of a tumor and its micro environment

1.
University of California, Irvine, Dept. of Statistics, School of Information and Computer Science, 3019 Bren Hall, Irvine, CA 92617-5100
2.
Princeton University, Dept. of Computer Science, 35 Olden Street, Princeton, NJ 08540-5233
3.
Wesleyan University, Dept. of Mathematics and Computer Science, 265 Church St. Middletown, CT 06459
4.
Pomona College, Dept. of Mathematics, 610 N. College Ave., Claremont, CA 91711

Received: September 2012

Revised: September 2012

Published: November 2012

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Abstract

Experimental evidence suggests that a tumor's environment may be critical to designing successful therapeutic protocols: Modeling interactions between a tumor and its environment could improve our understanding of tumor growth and inform approaches to treatment. This paper describes an efficient, flexible, hybrid cellular automaton-based implementation of numerical solutions to multiple time-scale reaction-diffusion equations, applied to a model of tumor proliferation. The growth and maintenance of cells in our simulation depend on the rate of cellular energy (ATP) metabolized from nearby nutrients such as glucose and oxygen. Nutrient consumption rates are functions of local pH as well as local concentrations of oxygen and other fuels. The diffusion of these nutrients is modeled using a novel variation of random-walk techniques. Furthermore, we detail the effects of three boundary update rules on simulations, describing their effects on computational efficiency and biological realism. Qualitative and quantitative results from simulations provide insight on how tumor growth is affected by various environmental changes such as micro-vessel density or lower pH, both of high interest in current cancer research.

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Mathematics Subject Classification: 92C50, 97M60, 37B15, 68Q80.

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