The Model of the Glycemic Level Self-Regulation for Extracting the Information From the Glucose Tolerance Tests Data

Abstract

The paper provides a brief critical review of the original mathematical models of the carbohydrate exchange regulation system from historically first works to its most advanced model. Their significant deficiencies were mentioned. To eliminate them, it was carring out the construction of the most minimal, but the universal, structural and functional mathematical model of this physiological system, for the program-model extraction of the diagnostic information from the glycemic data of the glucose tolerance tests. The model presents itself a differential equation of the first order with delayed argument relative to the glycemic level in the periphery, through which all the significant factors of the carbohydrate exchange regulation are expressed, including insulin. This model is convenient for numerical analysis, in which it ultimately reduces to a simple recurrent formula. A definite physiological sense was given to the parameters of this model. This model firstly universally describes the dynamics of glycemia with arbitrary exogenous glucose load under the standard oral and intravenous glucose tolerance tests, as well as under the oral glucose tolerance test with double load, according Staub - Tragott. At that, the new model for the first time describes the well-known phenomenon of insulin suppression of the second rise of the normal glycemic level.