Minimal modeling of insulin secretion in the perfused rat pancreas: a drug effect case study

The experimental protocol of the perfused rat pancreas is commonly used to evaluate beta-cell function. In this context, mathematical models become useful tools through the determination of indexes that allow the assessment of beta-cell function in different experimental groups and the quantification of the effects of antidiabetic drugs, secretagogues, or treatments. However, a minimal model applicable to the isolated perfused rat pancreas has so far been unavailable. In this work, we adapt the C-peptide minimal model applied previously to the intravenous glucose tolerance test to obtain a specific model for the experimental settings of the perfused pancreas. Using the model, it is possible to estimate indexes describing beta-cell responsivity for first (Phi(D)) and second phase (Phi(S), T) of insulin secretion. The model was initially applied to untreated pancreata and afterward used for the assessment of pharmacologically relevant agents (the gut hormone GLP-1, the potent GLP-1 receptor agonist lixisenatide, and a GPR40/FFAR1 agonist, SAR1) to quantify and differentiate their effect on insulin secretion. Model fit was satisfactory, and parameters were estimated with good precision for both untreated and treated pancreata. Model application showed that lixisenatide reaches improvement of beta-cell function similarly to GLP-1 (11.7-vs. 13.1-fold increase in Phi(D) and 2.3-vs. 2.8-fold increase in Phi(S)) and demonstrated that SAR1 leads to an additional improvement of beta-cell function in the presence of postprandial GLP-1 levels.