BIOPHYSICAL THEORY AND MODELING |
A Multiscale Model For Avascular Tumor Growth
Yi Jiang 1*, Jelena Pjesivac-Grbovic 2, Charles Cantrell 3 and James Freyer 1
1 Los Alamos National Laboratory
2 University of Tennessee
3 MIT
* To whom correspondence should be addressed. E-mail: jiang{at}lanl.gov.
Submitted on February 3, 2005
Revised on May 17, 2005
Accepted on 13 September 2005
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Abstract |
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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/hr, corresponding to molecules of size 80-90 kD. Using the same parameters, the model also accurately predicts spheroid growth curves under different external nutrient supply conditions.
Key Words:
cancer, cell cycle arrest, mathematical model, microenvironment, multicellular tumor spheroid, necrosis
