? Author to whom correspondence should be addressed. E-mail: torquato@matter.princeton.edu -- T. S. Deisboeck, M.D. is also a$liated with the Depart- ment of Neurosurgery, University of Munich (Germany). J. theor. Biol. (2000) 203, 367}382 doi:10.1006/jtbi.2000.2000, available online at http://www.idealibrary.com on Simulated Brain Tumor Growth Dynamics Using a Three-Dimensional Cellular Automaton A. R. KANSAL*, S. TORQUATO*-?, G. R. HARSH IVA, E. A. CHIOCCAB** AND T. S. DEISBOECKB**-- *Department of Chemical Engineering, Department of Chemistry, -Princeton Materials Institute, Princeton ;niversity, Princeton, NJ 08544, ;.S.A., ADepartment of Neurosurgery, Stanford ; niversity Medical School, Stanford, CA 94305, ;.S.A., Neurosurgical Service, BBrain ¹ umor Center, **Molecular Neuro-Oncology ¸aboratory, Massachusetts General Hospital East, Harvard Medical School, Charlestown, MA 02129, ;.S.A. (Received on 20 August 1999, Accepted in revised form on 14 January 2000) We have developed a novel and versatile three-dimensional cellular automaton model of brain tumor growth. We show that macroscopic tumor behavior can be realistically modeled using microscopic parameters. Using only four parameters, this model simulates Gompertzian growth for a tumor growing over nearly three orders of magnitude in radius. It also predicts the composition and dynamics of the tumor at selected time points in agreement with medical literature. We also demonstrate the #exibility of the model by showing the emergence, and eventual dominance, of a second tumor clone with a di!erent genotype. The model incorporates several important and novel features, both in the rules governing the model and in the underlying structure of the model. Among these are a new de"nition of how to model proliferative and non-proliferative cells, an isotropic lattice, and an adaptive grid lattice.  2000 Academic Press 1. Introduction The incidence of primary malignant brain tumors is already 8/100 000 persons per year and is still increasing. The vast majority (80%) consists of high-grade malignant neuroepithelial tumors such as glioblastoma multiforme (GBM) (Fig. 1) (Annegers et al., 1981; Werner et al., 1995). In spite of aggressive conventional and advanced treatments, the prognosis remains uniformly fatal with a median survival time for patients with GBM of 8 months (Black, 1991; Whittle, 1996). The main reason for this grim outcome is not only the rapid tumor growth but especially the fact that, long before the neoplasm can be diag- nosed, it has already grossly invaded the sur- rounding brain parenchyma, rendering surgical removal virtually ine!ective. The proposed se- quence of proliferation, then invasion, followed by proliferation again suggests that invasive cells left behind after an operation not only cause parenchyma destruction, but also eventually tumor recurrence (Suh & Weiss, 1984; Burger et al., 1988; Nazzaro & Neuwelt, 1990; Silbergeld & Chicoine, 1997). Anti-proliferative treatments fail because of poor transport across the 0022}5193/00/080367#16 $35.00/0  2000 Academic Press