Research of complexity and organization of the physiological system of carbohydrate exchange regulation

Abstract

The article is devoted to an actual methodological issue, that have also the direct practical interest, to clarify the complexity and organization of the physiological system of carbohydrate exchange regulation for selecting an adequate mathematical description of it in a stochastic or deterministic form. It is known that the frequently observed disturbances in this system lead to severe endocrinological disease – Diabetes mellitus. The most widespread form of it – the Diabetes mellitus type II has long latent period, at which, in the absence of treatment, the late dangerous vascular and nervous complications are already developing. To increase radically the level of early diagnostics of the latent Diabetes mellitus on the basis of available for the clinical measurement of the patient data on the periphery, it turned out to be possible only on the basis of the corresponding mathematical model. For a long time, the fundamental question of the complexity and organization of the system of carbohydrate metabolism regulation was solved intuitively in a deterministic form. Only recently this decision was questioned, and an attempt was made to model the carbohydrate exchange system regulation in a stochastic form, however, without proper justification and without obtaining any concrete results. At that, the bases for elaboration of the mathematical model of the system of carbohydrate exchange regulation in the class of stochastic models are obvious. Any complex system in general case is probabilistic in nature, the experimental data, used in its parametric identification, also always contain the measurement errors, that is, they are indeterminate variables. In this article, using the general method for the analysis of the complex Bir-Glushkov systems and the known exactness of glycemia and insulinemia measurings, for the first time the research of the complexity and organization of the physiological system of carbohydrate exchange regulation was carried out. It was shown that this system is very complex and deterministic, that permitted, when modeling the glycemia and insulinemia dynamics in the human body, to limit by the apparatus of the determinated differential equations.