Conference publications

Abstracts

XXII conference

Tumor growth modeling with account of angiogenesis and anti-angiogenic therapy

Kolobov A.V., Kuznetsov M.B.

P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53, Leninskiy Prospekt, Moscow, 119991.

It is well-known that when a malignant tumor reaches the size of several millimeters in diameter, its exponential (by number of cells) growth decelerates due to the lack of nutrients for cell division in its core. Under metabolic stress tumor cells produce different chemical mediators, particularly vascular endothelial growth factor, or VEGF, which stimulate the process of new blood vessels formation – angiogenesis, that increases the nutrient supply. In 1970 J. Folkman suggested a new type of antitumor therapy – the anti-angiogenic one (AAT). Unlike traditional types of tumor treatment, AAT aims not at killing proliferating cells – both cancer ones and specialized cells of organism, but at blocking of neovascularization, thus it doesn’t have the set of side effects, which are typical for chemo- and radiotherapy. However, as it is shown by clinical essays, the successful inhibition of angiogenesis doesn’t always lead to the significant deceleration of tumor growth and progression. The answer to the question, when AAT will be effective and when it will be not, can be given by mathematical modeling.

To answer this question a mathematical model taking into consideration the growth of different tumor cell types in the tissue, angiogenesis and the effect of AAT as well was developed. The model is built accounting for the dichotomy of migration and proliferation of malignant cells. Native motility of the cells and their convection in the tissue are considered. The physiological distinctions of the newly-formed capillaries from the pre-existing ones and the degradation of vessels inside the tumor are also incorporated in the model.

The resulting system of partial differential equations of parabolic and hyperbolic types was analyzed numerically. The results of modeling adequately present the structure of tumor and vascular density in normal and malignant tissues. It was shown that under high individual motility of malignant cells the angiogenesis practically does not influence tumor growth, and that agrees the experimental results well.

For tumor with low individual cell motility an analysis of angiogenic parameters influence on its growth was performed as well as an estimation of AAT effectiveness in the case of treatment with bevacizumab, which is a monoclonal antibody to VEGF. The range of effective dosages is found, the comparison with real clinical values is drawn.

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