A Multiscale Model for Avascular Tumor Growth

Biophys J. 2005 Dec;89(6):3884-94. doi: 10.1529/biophysj.105.060640. Epub 2005 Sep 30.


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.

Publication types

  • Comparative Study
  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Animals
  • Cell Adhesion
  • Cell Culture Techniques / methods*
  • Cell Line, Tumor
  • Cell Proliferation
  • Cell Survival
  • Computer Simulation
  • Humans
  • Mammary Neoplasms, Experimental / blood supply
  • Mammary Neoplasms, Experimental / pathology*
  • Mammary Neoplasms, Experimental / physiopathology*
  • Mice
  • Models, Biological*
  • Neovascularization, Pathologic / physiopathology
  • Spheroids, Cellular / physiology*