CYBERNETIC ONE-COMPARTMENT MODEL OF GLYCEMIA DYNAMICS IN GLUCOSE HOMEOSTASIS DISORDERS
Keywords:Diabetes mellitus, system of carbohydrate exchange regulation, dynamics of glycemia, mathematical model.
The medical and social problems of Diabetes mellitus caused by disorders in the system of carbohydrate exchange regulation have led to a deep level of its research, sufficient to describe it in mathematical modelling terms. The models, which have so far been developed, refer only to separate manifestations of the behaviour of this system.
The carbohydrate exchange regulation system minimal mathematical model is proposed in the form of the one-compartment model of glycemic dynamics with indirect regard to insulinemia. This model at an arbitrary glucose load, without reconstructing its structure and without changing the values of its main parameters for the first time fully describes the glycemic curves of all existing glucose tolerance tests and allows solving practical questions of objective diagnosis.
The paper uses the generalization of Wiener's method for clarification the structure of the studied complex system in the form of negative feedback connection according to its response to a given input signal. The investigation used clinical data of glucose tolerance tests and the analytical view of the function of intravenous and oral intake of exogenous glucose into the blood.
The new model represent the differential equation of the first order with delayed argument, which, in numerical analysis is reduced to a recurrent formula. To parameters of the model are given the physiological meaning. Their values are unambiguously found when the model is individualized to the patient according to clinical data in the process of parametric identification while minimizing the objective function of the discrepancy between the calculated and clinical values of glycemia.
The parameters of the model, individualized to the patient according to his clinical data, can be used as diagnostic.
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