A reaction-diffusion model of cancer invasion.
We present mathematical analyses, experimental data, and clinical observations which support our novel hypothesis that tumor-induced alteration of microenvironmental pH may provide a simple but complete mechanism for cancer invasion. A reaction-diffusion model describing the spatial distribution and temporal development of tumor tissue, normal tissue, and excess H+ ion concentration is presented. The model predicts a pH gradient extending from the tumor-host interface, which is confirmed by reanalysis of existing experimental data. Investigation of the structure and dynamics of the tumor-host interaction within the context of the model demonstrates a transition from benign to malignant growth analogous to the adenoma-carcinoma sequence. The effect of biological parameters critical to controlling this transition are supported by experimental and clinical observations. Tumor wave front velocities determined via a marginal stability analysis of the model equations are consistent with in vivo tumor growth rates. The model predicts a previously unrecognized hypocellular interstitial gap at the tumor-host interface which we demonstrate both in vivo and in vitro. A direct correlation between the interfacial morphology and tumor wave front velocity provides an explicit, testable, clinically important prediction.
Gatenby
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Department of Diagnostic Imaging, College of Medicine, Temple University, Philadelphia, Pennsylvania 19122, USA.
Gawlinski
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D002294:Carcinoma, Squamous Cell / Q000378:metabolism / Q000473:pathology; D018450:Disease Progression; D006258:Head and Neck Neoplasms / Q000378:metabolism / Q000473:pathology; D006801:Humans; D006863:Hydrogen-Ion Concentration; D008954:Models, Biological; D009361:Neoplasm Invasiveness