Modelling the effects of glucagon during glucose tolerance testing

Abstract

BackgroundGlucose tolerance testing is a tool used to estimate glucose effectiveness and insulin sensitivity in diabetic patients. The importance of such tests has prompted the development and utilisation of mathematical models that describe glucose kinetics as a function of insulin activity. The hormone glucagon, also plays a fundamental role in systemic plasma glucose regulation and is secreted reciprocally to insulin, stimulating catabolic glucose utilisation. However, regulation of glucagon secretion by α-cells is impaired in type-1 and type-2 diabetes through pancreatic islet dysfunction. Despite this, inclusion of glucagon activity when modelling the glucose kinetics during glucose tolerance testing is often overlooked. This study presents two mathematical models of a glucose tolerance test that incorporate glucose-insulin-glucagon dynamics. The first model describes a non-linear relationship between glucagon and glucose, whereas the second model assumes a linear relationship.ResultsBoth models are validated against insulin-modified and glucose infusion intravenous glucose tolerance test (IVGTT) data, as well as insulin infusion data, and are capable of estimating patient glucose effectiveness (sG) and insulin sensitivity (sI). Inclusion of glucagon dynamics proves to provide a more detailed representation of the metabolic portrait, enabling estimation of two new diagnostic parameters: glucagon effectiveness (sE) and glucagon sensitivity (δ).ConclusionsThe models are used to investigate how different degrees of pax‘tient glucagon sensitivity and effectiveness affect the concentration of blood glucose and plasma glucagon during IVGTT and insulin infusion tests, providing a platform from which the role of glucagon dynamics during a glucose tolerance test may be investigated and predicted.

Mathematical Model of Glucagon Kinetics for the Assessment of Insulin-Mediated Glucagon Inhibition During an Oral Glucose Tolerance Test

“…The study having more aspects in common with ours is that of Kelly et al. ( 30 ). In that study, a comprehensive model of glucagon kinetics and dynamics was developed for possible clinical applications, i.e., for possible assessment of model parameters in individuals.…”

“…Other studies presented models of glucagon kinetics for possible clinical applications, but they were focused on the analysis of glucagon administered exogenously, or for the analysis of the not common glucagon challenge test (26)(27)(28)(29). The study having more aspects in common with ours is that of Kelly et al (30). In that study, a comprehensive model of glucagon kinetics and dynamics was developed for possible clinical applications, i.e., for possible assessment of model parameters in individuals.…”

“…That model has merits in the details of the physiological phenomena analyzed. For instance, the model allows to address aspects not analyzed in our study, such as the ability of glucagon to promote hepatic glucose production, sometimes denoted in study ( 30 ) as glucagon sensitivity. However, that model, which is to some extent an extension of the traditional Minimal Model ( 50 ), applies to glucose tolerance tests other than the OGTT, such as the IVGTT (consistently with the field of application of the Minimal Model).…”

“…Of note, analyses of model identifiability were not presented. As regards the concept of sensitivity to insulin of glucagon inhibition, which is the focus of our study, it has to be acknowledged that the study ( 30 ) addresses the issue as well, though it does not appear the aspect of major interest in the presented analyses. In fact, one parameter similar our S GLUCA (t) is presented, defined as the maximum rate at which insulin suppresses glucagon secretion.…”

“…Some other studies developed models for the analysis of the glucagon challenge test, which is however not widely used ( 28 , 29 ). The study ( 30 ) had purposes more similar to those of our study, but the developed model analyzed glucagon kinetics during an intravenous glucose tolerance test (IVGTT), or an insulin-infusion test. To our knowledge, no study has been focused on modeling the glucagon kinetics during an oral glucose tolerance test (OGTT), despite the fact that OGTT has remarkable advantages compared to the IVGTT (or other glucose tolerance tests) in terms of simplicity, and hence applicability in the clinical context.…”