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Yi Jiang, Jelena Pjesivac, Charles Cantrell and James Freyer, "A Multiscale Model for Avascular Tumor Growth ", Biophysical Journal , vol. 89, pp. 3873--3883, 2005


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 promotors 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.

BibTeX Entry

author = {Yi Jiang and Jelena Pjesivac and Charles Cantrell and James Freyer},
title = {A Multiscale Model for Avascular Tumor Growth },
year = {2005},
urlpdf = {http://math.lanl.gov/~yi/Papers/Jiang_tumorModel_BiophysJ_2005.pdf},
journal = { Biophysical Journal },
volume = {89},
pages = {3873--3883}