Investigation of the effects of angiogenesis on tumor growth using a mathematical model

Abstract

A mathematical model of tumor growth has been developed that takes angiogenesis into account. Malignant cells under metabolic stress produce vascular endothelial growth factor, which stimulates angiogenesis and, thus, increases nutrient influx into a tumor. The model takes into account migration-proliferation dichotomy in malignant cells that depends on the nutrient concentration. Convective fluxes that occur upon active tumor-cell proliferation in a compact dense tissue have been also considered. The computational investigation of the model demonstrated that the diffusive tumor growth rate does not depend on angiogenesis, while for noninvasive tumors angiogenesis could significantly alter tumor growth, although it is not able to stop it completely. The causes and significance of the results for the estimation of the antitumor efficacy of antiangiogenic therapy are discussed.