Kinetic approach and estimation of the parameters of cellular interaction between the immunity system and a tumor

A method is suggested to estimate multi component dynamic systems, which permits, with the help of the computer-calculated kinetic curves, to obtain information about the possible mechanisms of the system component interaction. The method is based on the structural and parametrical identification of mathematical models presented in the form of a system of nonlinear differential equations, using a multi-criterial approach. Using experimental data of studies on growth kinetics and regression of multicellular tumor EMT6 line spheroids in the mouse allogenic system and the immune system cell accumulation in spheroids a mathematical model has been developed of the cellular interaction process in a spheroid. It has been stated that the rate of macrophage and neutrophil accumulation in a spheroid depends on the amount of tumor cells and is determined by the hyperbolic law (as analogous to the Michaelis-Menthen kinetics), while the accumulation of immune lymphocytes in a tumor is determined besides that by the three-cellular cooperation of lymphocytes, macrophages and tumor cells. According to the model, the inhibition of the process of neutrophil and lymphocyte (but not of macrophages) accumulation is realized through the auto-suppression mechanism. The numerical values of the process parameters, which characterise the rates of accumulation, cellular death in a tumor and of local cellular interactions intensity are obtained.