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An Integrated Computational/Experimental Model of Tumor Invasion

Departments of ¹ Biomedical Engineering and ² Mathematics, and ³ Beckman Laser Institute, University of California, Irvine, Irvine, California; and ⁴ Departments of Radiology and Applied Mathematics, University of Arizona, Tucson, Arizona

Requests for reprints: Vittorio Cristini, Department of Biomedical Engineering, REC 204, University of California, Irvine, CA 92697-2715. Phone: 949-824-9132; E-mail: cristini{at}math.uci.edu.

The intracellular and extracellular dynamics that govern tumor growth and invasiveness in vivo remain poorly understood. Cell genotype and phenotype, and nutrient, oxygen, and growth factor concentrations are key variables. In previous work, using a reaction-diffusion mathematical model based on variables that directly describe tumor cell cycle and biology, we formulated the hypothesis that tumor morphology is determined by the competition between heterogeneous cell proliferation caused by spatial diffusion gradients, e.g., of cell nutrients, driving shape instability and invasive tumor morphologies, and stabilizing mechanical forces, e.g., cell-to-cell and cell-to-matrix adhesion. To test this hypothesis, we here obtain variable-based statistics for input to the mathematical model from in vitro human and rat glioblastoma cultures. A linear stability analysis of the model predicts that glioma spheroid morphology is marginally stable. In agreement with this prediction, for a range of variable values, unbounded growth of the tumor mass and invasion of the environment are observed in vitro. The mechanism of invasion is recursive subspheroid component development at the tumor viable rim and separation from the parent spheroid. Results of computer simulations of the mathematical model closely resemble the morphologies and spatial arrangement of tumor cells from the in vitro model. We propose that tumor morphogenesis in vivo may be a function of marginally stable environmental conditions caused by spatial variations in cell nutrients, oxygen, and growth factors, and that controlling these conditions by decreasing spatial gradients could benefit treatment outcomes, whereas current treatment, and especially antiangiogenic therapy, may trigger spatial heterogeneity (e.g., local hypoxia), thus causing invasive instability. (Cancer Res 2006; 66(3): 1597-604)

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