A model for glucose control of insulin secretion during 24 h of free living

Abstract

The aim of this work was to develop a mathematical model describing the functional dependence of insulin secretion on plasma glucose concentrations during 24 h of free living. We obtained hourly central venous blood samples from a group of healthy volunteers who spent 24 h in a calorimetric chamber, where they consumed standardized meals. Insulin secretory rates were reconstructed from plasma C-peptide concentrations by deconvolution. The relationship between insulin release and plasma glucose concentrations was modeled as the sum of three components: a static component (describing the dependence on plasma glucose concentration itself, with an embedded circadian oscillation), a dynamic component (modeling the dependence on glucose rate of change), and a residual component (including the fraction of insulin secretion not explained by glucose levels). The model fit of the individual 24-h secretion profiles was satisfactory (within the assigned experimental error of glucose and C-peptide concentrations). The static component yielded a dose-response function in which insulin release increased quasi-linearly (from 40 to 400 pmol/min on average) over the range of 4-9 mmol/l glucose. The dynamic component was significantly different from zero in coincidence with meal-related glucose excursions. The circadian oscillation and the residual component accounted for the day/night difference in the ability of glucose to stimulate insulin release. Over 24 h, total insulin release averaged 257 ± 58 nmol (or 43 ± 10 U). The static and dynamic component together accounted for ∼80% of total insulin release. The model proposed here provides a detailed robust description of glucose-related insulin release during free-living conditions. In nondiabetic subjects, non-glucose-dependent insulin release is a small fraction of total insulin secretion.