Математическое моделирование роста ангиогенной опухоли с учётом баланса кислорода и глюкозы
P.N. Lebedev Physical Institute of the Russian Academy of Sciences; 53, Leninskiy Prospekt, Moscow 119991, Russian Federation; email@example.com pp. (accepted)
It is well-known that malignant tumor growth is accompanied by angiogenesis, i.e., the formation of new blood vessels, which increases the nutrient flow to the tumor. This process can be blocked by antiangiogenic therapy (AAT), using of which in clinical practice began a little more than a decade ago. AAT does not stop the flow of nutrients to the tumor completely, but only reduces it, so the usefulness of its applying in every particular case depends on the significance of angiogenesis to a tumor, which is influenced by many factors of different nature. Pre-evaluation of antitumor efficacy of AAT may be realized by means of mathematical modeling. We have developed a spatially distributed multivariable model of tumor progression of "reaction-diffusion-convection" type with the account of AAT, in which the variables are substances concentrations, cell densities and the density of microcirculatory network. The model takes into account two key metabolites – glucose and oxygen, which allows considering both glycolysis and oxidative phosphorylation in metabolism of tumor cells. To establish the relationship between the density of capillary network and the influx of oxygen a separate model of stationary flow in the capillary network was developed and investigated. Numerical study of the tumor progression model showed that anti-angiogenic therapy of diffuse-type tumors reduces the total number of their cells, but has almost no effect on the speed of their invasion into normal tissues. It was found that growth of compact tumors in a fairly wide range of parameters may be non-monotonic. It was demonstrated that in this case AAT stabilizes and significantly inhibits tumor growth rate, and its local-in-time efficiency crucially depends on the time that it begins.