¹Perm National Research Polytechnic University, Perm, Russia
²Federal Scientific Center for Medical and Preventive Health Risk Management Technologies, Perm, Russia

Abstract. Investigations focused on how malignant tumors appear and grow in the body are complicated due to multi-level regulation, which makes direct experimental in vivo studies rather difficult. A mathematical model presented in this study describes dynamics of changes in the quantity of abnormal cells taking angiogenesis processes and immune system reactions into account.  The model has been developed within a multi-level approach, which considers interactions between the systems in the body and functional state of various organs. Time lags, which reflect interactions between various components of the system, have been introduced in the model in order to describe spatial organization of oncological processes in various tissues. The suggested approach is based on a prediction model, which considers dynamics of changes in the number of abnormal cells, regulatory pathways and angiogenesis processes. The Monte-Carlo method is employed to analyze possible tumor growth scenarios. The results obtained by numeric experiments reflect both quantitative (growth/decline in cell numbers) and spatial (tumor localization, vessel distribution) changes. We have analyzed impacts exerted on tumor growth by the immune system parameters and characteristics of abnormal cells. Cell division rates, the immune system activity and angiogenesis dynamics are key factors in the process. The suggested model makes it possible to assess the role that belongs to biological factors in tumor growth kinetics and provides necessary data for qualitative understanding of pathways, which determine malignant neoplasm progression. Our findings can be used for further investigations on the role of angiogenesis and immune regulation in tumor growth.

Key words: mathematical modeling, tumor growth, angiogenesis, immune system, neuroendocrine regulation, tumor microenvironment