Assessing Insulin Secretion by Modeling in Multiple-Meal Tests

Abstract

We developed a mathematical model of the glucose control of insulin secretion capable of quantifying β-cell function from a physiological meal test. The model includes a static control, i.e., a secretion component that is a function of plasma glucose concentration (the dose-response function), and a dynamic control, i.e., a secretion component that is proportional to the positive values of the glucose concentration derivative. Furthermore, the dose-response function is assumed to be modulated by a time-varying potentiation factor. To test the model, nine nondiabetic control subjects and nine type 2 diabetic patients received three standardized mixed meals over a period of 14–15 h. Blood samples were drawn for the measurement of glucose, insulin, and C-peptide concentration. The dose-response function, the parameter of the dynamic control, and the potentiation factor were determined by fitting the model to glucose and C-peptide concentrations. In diabetic patients, the dose-response function was shifted to the right (glucose concentration at a reference insulin secretion of 300 pmol · min⁻¹ · m⁻² was 11.7 ± 1.1 vs. 7.2 ± 0.7 mmol/l; P < 0.05), and decreased in slope (53 ± 15 vs. 148 ± 38 pmol · min⁻¹ · m⁻² · mmol⁻¹ · l; P < 0.05) and the parameter of the dynamic control was decreased (220 ± 67 vs. 908 ± 276 pmol · m⁻² · mmol⁻¹ · l; P < 0.05) compared with the nondiabetic control subjects. Furthermore, potentiation was markedly blunted and delayed: maximum potentiation was observed at the first meal in normal subjects and at the second meal (about 4 h later) in diabetic subjects; the mean time for the potentiation factor was higher (7.1 ± 0.2 vs. 5.9 ± 0.2 h; P < 0.01), and the size of potentiation was reduced (2.6 ± 0.5 vs. 7.2 ± 1.5 fold increase; P < 0.005). In conclusion, our model of insulin secretion extracts multiple indexes of β-cell function from a physiological meal test. Use of the model in patients with type 2 diabetes retrieves known defects in insulin secretion but also uncovers new facets of β-cell dysfunction.