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Biophys J. 2005 Dec;89(6):3884-94. Epub 2005 Sep 30.

A multiscale model for avascular tumor growth.

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Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Erratum in

  • Biophys J. 2006 Jul 15;91(2):775.


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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