Multiscale modeling of angiogenic tumor growth, progression, and therapy

Abstract

A mathematical model of angiogenic tumor growth in tissue with account of bevacizumab therapy was developed. The model accounts for convective flows that occur in dense tissue under active division of tumor cells, as well as the migration and proliferation dichotomy of malignant cells, which depends on the concentrations of major metabolites, such as oxygen and glucose. Tumor cells wich are in a state of metabolic stress produce vascular endothelial growth factor, which stimulates angiogenesis. To establish the relationship between the capillary network density and oxygen supply, a separate model of stationary blood flow in the capillary network was developed and investigated. A numerical study of the tumor-growth model showed that antiangiogenic bevacizumab treatment of tumors of the diffuse type reduces the total number of their cells, but practically does not affect the rate of their invasion into normal tissues. At the same time, it was found that the growth of dense tumors may be non-monotonic in a rather wide range of parameters. It was shown that in this case bevacizumab therapy stabilizes and significantly inhibits tumor growth, while its local-in-time efficiency is sensitive to the time that it begins.