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Departments of Radiology, Applied Mathematics, and Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ

Requests for reprints: Robert A. Gatenby, Department of Radiology, University Medical Center, 1502 North Campbell Avenue, Tucson, AZ 85724. Phone: (520) 626-5725; Fax: (520) 626-9981. E-mail: rgatenby{at}radiology.arizona.edu

Quantitative models from population biology and evolutionary game theory frame the tumor-host interface as a dynamical microenvironment of competing tumor and normal populations. Through this approach, critical parameters that control the outcome of this competition are identified and the conditions necessary for formation of an invasive cancer are defined. Perturbations in these key parameters that destabilize the cancer solution of the state equations and produce tumor regression can be predicted. The mathematical models demonstrate significant theoretical limitations in therapies based solely on cytotoxic drugs. Because these approaches do not alter critical parameters controlling system dynamics, the tumor population growth term will remain positive as long as any individual cells are present so that the tumor will invariably recur unless all proliferative cells are killed. The models demonstrate that such total effectiveness is rendered unlikely by the genotypic heterogeneity of tumor populations (and, therefore, the variability of their response to such drugs) and the ability of tumor cells to adapt to these proliferation constraints by evolving resistant phenotypes. The mathematical models support therapeutic strategies that simultaneously alter several of the key parameters in the state equations. Furthermore, the models demonstrate that administration of cytotoxic therapies will, by reducing the tumor population density, create system dynamics more conducive to perturbations by biological modifiers.

Key Words: mathematical models • tumor therapy • tumor biology • evolutionary models • population biology

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Received 3/17/03; revised 6/17/03; accepted 6/19/03.