PMID: 8971186Dec 15, 1996Paper

A reaction-diffusion model of cancer invasion

Cancer Research
R A Gatenby, E T Gawlinski

Abstract

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 f...Continue Reading

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