[Investigation of the Influence of Angiogenesis on Tumor Growth with the Use of a Mathematical Model].

Abstract

A mathematical model of tumor growth is developed taking into account angiogenesis. Malignant cells under metabolic stress produce vascular endothelium growth factor that stimulates angiogenesis, increasing nutrient influx in tumor. The model takes into account the migration and proliferation dichotomy in the malignant cells depending on nutrient concentration. Convective fluxes originated due to active tumor cell proliferation in compact dense tissue are also considered. The computational analysis of the model has demonstrated that diffusive tumor growth rate does not depend on angiogenesis while for non-invasive tumors angiogenesis can significantly alter tumor growth, although it is not able to stop it completely. The causes and significance of the result for estimation of the antitumor efficacy of antiangiogenic therapy are discussed.