Estimation of beta-cell secretion and insulin hepatic extraction by the minimal modelling technique

Mathematical models are a necessary tool to quantify physiological processes the direct measurement of which is not possible. Pancreatic beta-cell and liver are respectively the secreting and the major degrading site of insulin. To provide a quantitative description of these processes, we have conceived a method which exploits two minimal mathematical models. By using one model the post-hepatic delivery of insulin into the systemic circulation, IDRT(t), is estimated; the other model yields CPST(t), i.e. the secretion rate of C-peptide, which is equimolarly released by the beta-cell with insulin, but is not degraded by the liver. The estimated C-peptide flow rate into plasma is thus representative of that of pre-hepatic insulin. The difference between CPST(t) and IDRT(t) gives the insulin extraction by the hepatocytes. The parameters of the models are estimated in every single subject from the analysis of glucose, insulin, and C-peptide concentration data measured after an intravenous glucose injection. As an example of its usefulness, the method has been applied in patients with liver cirrhosis and in obese non-diabetic subjects, with the purpose of elucidating which mechanism is responsible for the peripheral dynamic hyperinsulinaemia characteristic of such metabolic states. Because mechanism is responsible for the peripheral dynamic hyperinsulinaemia characteristic of such metabolic states. Because of its relative non-invasiveness compared to other techniques this model-based method should prove useful in several other clinical investigations.