Mathematical model of glucagon kinetics during an oral glucose tolerance test based on a dual regulation mechanism

Glucagon is a hormone secreted by the pancreatic alpha cells and plays a key role in glucose homeostasis and in the pathophysiology of type 2 diabetes (T2D). Different mechanisms are involved in its regulation, but exact mechanisms are still largely unknown. This study aimed to propose a model describing glucagon inhibition during an oral glucose tolerance test (OGTT), accounting for a double regulation mechanism. The model has been developed starting from a model previously proposed by our group that includes two differential equations, one for plasma glucagon and one for C-peptide (marker of insulin at pancreatic level). In the new model, in addition to plasma C-peptide, plasma glucose is included as model input. The model provides two parameters of possible clinical relevance, namely SGLUCA and kG (alpha-cell insulin and glucose sensitivity, respectively) and has been validated on mean literature data of healthy subjects and subjects affected by T2D (CNT and T2D, respectively). Model analysis yielded SGLUCA estimates ranging from -0.1515 to 0.7629 and from -5.5602 to 1.1067 (ng of glucagon·nmol of C-peptide-1) in CNT and T2D groups, respectively; according to the 95% confidence intervals (CIs), SGLUCA was significantly different from zero in 4 and in 0 out of 8 time points, in CNT and T2D. Estimates for kG were equal to 2.8302 (95% CIs: 1.1973-4.4632) and 0.9913 (95% CIs: -0.5559-2.5386) ng of glucagon·mmol of glucose-1. Thus, results suggest both insulin (represented by C-peptide) and glucose significantly contributes to glucagon inhibition in healthy subjects, but not in T2D. In conclusion, the proposed model may help to describe different mechanisms acting on glucagon inhibition in the single individuals.