MODELING OF HETEROGENEOUS TUMOR DYNAMICS. THE INFLUENCE OF PROTON IRRADIATION ONLY AND IN COMBINATION WITH DNA SYNTHESIS INHIBITOR – ARAC

Interpretation of the growth of a malignant tumor and its response to therapeutic treatment requires consideration of its heterogeneity, taking into account the presence in it of a small subpopulation of tumor stem cells along with ordinary tumor cells. In present work, a mathematical model is proposed that combines two basic concepts of the theory of tumor growth - stochastic growth and the presence of a subpopulation of tumor stem cells. The model is a system of ordinary differential equations that describes the dynamics of subpopulations of tumor cells, taking into account different types of division and transitions between them. An important feature of the system is the maintenance of the equilibrium proportion of tumor stem cells in an unirradiated tumor using feedback. The model was used to interpret experimental data on inhibition of tumor growth after protons irradiation at a dose of 10 Gy only and the combined treatment of irradiation and the inhibitor of DNA synthesis AraC in laboratory mice with grafted melanoma B16. The effect of irradiation only and irradiation in combination with AraC is included in the system using a parameter describing the probability of loss of the cell's ability to successfully divide. As a result, the dependence of tumor volume on time calculated for cases without irradiation, after irradiation and after irradiation with AraC serves as a good approximation of experimental data, which makes it possible to evaluate the parameters of the system.