A Multiscale Model for Avascular Tumor Growth
(Yi Jiang, Los Alamos National Laboratory)

Tumor complexity gives rise to experimental models to describe their microenvironment, multicellular spheroid being the primary example. We present a mathematical model for tumor growth and death in a spheroid system. The model consists of three scales: at the subcellular level, a Boolean network regulates protein expression that controls the cell cycle; at the cellular level, a lattice Monte Carlo model describes cell dynamics; and at the extracellular level, reaction-diffusion equations describe the chemical dynamics. 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 survival microenvironment conditions for tumor cells; and that 2) growth factors and inhibitors have their diffusion coefficients in the range between $10^{-6}$ and $10^{-7}$ $cm^2/hr$, corresponding to molecules of size 80-90 kD.  The model also "postdicts" the spheroid growth results under different chemical conditions.