A REACTION-DIFFUSION MODEL OF CANCER INVASION

We present mathematical analyses, experimental data, and clinical obse rvations which support our novel hypothesis that tumor-induced alterat ion of microenvironmental pH may provide a simple but complete mechani sm for cancer invasion, A reaction-diffusion model describing the spat ial distribution and temporal development of tumor tissue, normal tiss ue, and excess H+ ion concentration Is presented, The model predicts a pH gradient extending from the tumor-host interface, which is confirm ed by reanalysis of existing experimental data, Investigation of the s tructure and dynamics of the tumor-host interaction within the context of the model demonstrates a transition from benign to malignant growt h analogous to the adenoma-carcinoma sequence, The effect of biologica l parameters critical to controlling this transition are supported by experimental and clinical observations. Tumor wave front velocities de termined via a marginal stability analysis of the model equations are consistent with in vivo tumor growth rates. The model predicts a previ ously unrecognized hypocellular interstitial gap at the tumor-host int erface which we demonstrate both in vivo and in vitro, A direct correl ation between the interfacial morphology and tumor wave front velocity provides an explicit, testable, clinically important prediction.