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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

Experimental evidence suggests that a tumor's environment may be criticalto designing successful therapeutic protocols: Modeling interactionsbetween a tumor and its environment could improve our understanding oftumor growth and inform approaches to treatment. This paper describes anefficient, flexible, hybrid cellular automaton-based implementation ofnumerical solutions to multiple time-scale reaction-diffusion equations,applied to a model of tumor proliferation. The growth and maintenance ofcells in our simulation depend on the rate of cellular energy (ATP)metabolized from nearby nutrients such as glucose and oxygen. Nutrientconsumption rates are functions of local pH as well as localconcentrations of oxygen and other fuels. The diffusion of these nutrientsis modeled using a novel variation of random-walk techniques.Furthermore, we detail the effects of three boundary updateruleson simulations, describing their effects on computationalefficiency and biological realism. Qualitative and quantitative resultsfrom simulations provide insight on how tumor growth is affected byvarious environmental changes such as micro-vessel density or lower pH,both of high interest in current cancer research.
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Keywords tumor growth; boundary rules.; Mathematical modeling; numerical simulation

Citation: Christopher DuBois, Jesse Farnham, Eric Aaron, Ami Radunskaya. A multiple time-scale computational model of a tumor and its micro environment. Mathematical Biosciences and Engineering, 2013, 10(1): 121-150. doi: 10.3934/mbe.2013.10.121

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