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A Multiscale Model for Avascular Tumor Growth

Yi Jiang ^*, Jelena Pjesivac-Grbovic , Charles Cantrell  and James P. Freyer 

^* Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico; Department of Computer Science, University of Tennessee, Knoxville, Tennessee; Department of Material Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts; and Bioscience Division, Los Alamos National Laboratory, Los Alamos, New Mexico

Correspondence: Address reprint requests to Dr. Yi Jiang, Theoretical Division, MS B284, Los Alamos National Laboratory, Los Alamos, NM 87545. Tel.: 505-665-5745; E-mail: jiang{at}lanl.gov.

The desire to understand tumor complexity has given rise to mathematical models to describe the tumor microenvironment. We present a new mathematical model for avascular tumor growth and development that spans three distinct scales. At the cellular level, a lattice Monte Carlo model describes cellular dynamics (proliferation, adhesion, and viability). At the subcellular level, a Boolean network regulates the expression of proteins that control the cell cycle. At the extracellular level, reaction-diffusion equations describe the chemical dynamics (nutrient, waste, growth promoter, and inhibitor concentrations). Data from experiments with multicellular spheroids were used to determine the parameters of the simulations. Starting with a single tumor cell, this model produces an avascular tumor that quantitatively mimics experimental measurements in multicellular spheroids. Based on the simulations, we predict: 1), the microenvironmental conditions required for tumor cell survival; and 2), growth promoters and inhibitors have diffusion coefficients in the range between 10^–6 and 10^–7 cm²/h, corresponding to molecules of size 80–90 kDa. Using the same parameters, the model also accurately predicts spheroid growth curves under different external nutrient supply conditions.

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