An integrated glucose homeostasis model of glucose, insulin, C-peptide, GLP-1, GIP and glucagon in healthy subjects and patients with Type 2 diabetes
Oskar Alskär (1), Jonatan I. Bagger (2,3), Jens J. Holst (3), Filip K. Knop (2,3), Mats O. Karlsson (1), Tina Vilsbøll (2), Maria C. Kjellsson (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden (2) Center for Diabetes Research, Gentofte Hospital, University of Copenhagen, Hellerup, Denmark (3) NNF Center for Basic Metabolic Research and Department of Biomedical Sciences, The Panum Institute, University of Copenhagen, Copenhagen, Denmark
Background
The glucose homeostasis is complex and involves several hormones and regulatory systems. Currently available models such as the integrated glucose insulin (IGI) model is capable of describing glucose and insulin during intravenous glucose tolerance tests (IVGTT), oral glucose tolerance tests (OGTT) and meal tolerance tests[1-4]. However, these models have empirical elements, such as the description of glucose absorption and the incretin effect that limits their extrapolation properties. In addition, the models do not provide a description of other important hormones such as glucagon.
Objectives
To develop a mechanism-based pharmacometric model that can describe concentration of glucose, gastric inhibitory polypeptide (GIP), glucagon-like peptide-1 (GLP-1), C-peptide, insulin and glucagon during glucose tolerance tests in healthy individuals and patients with type 2 diabetes (T2D).
Methods
The data used in this analysis originates from a study by Bagger et al [5,6]. The study included eight patients with T2D and eight sex- BMI- and age-matched healthy individuals. The participants were studied at six different occasions; first three OGTTs with the doses 25, 75, and 125 g of glucose were performed. The rate of gastric emptying was monitored by inclusion of 1.5 g of acetaminophen in the oral glucose solutions. On the following occasions, three isoglycaemic intravenous glucose infusions were performed that mimicked the glucose profiles from each of the OGTTs. Blood was frequently sampled during 4 hours (10 samples of glucagon, GIP, GLP-1 and acetaminophen, 15 samples of C-peptide and insulin and 20 samples of glucose). To obtain more information on insulin secretion, insulin data from four previously published IVGTT studies were also included in the analysis[7-10]. Three studies included healthy individuals (totaling 64 individuals) and one included patients with T2D (42 individuals). A bolus glucose dose of 0.25-0.33 g/kg was given and blood frequently sampled up to 180-240 minutes, for determination of glucose and insulin concentrations. In one study of healthy individuals and the study of patients with T2D insulin was infused over five minutes, 20 minutes after the glucose dose.
Model development was divided into four parts, each describing a subset of the data. 1) Paracetamol and glucose, 2) GLP-1 and GIP, 3) C-peptide and insulin, 4) Glucagon and endogenous glucose production. During development of each submodel the observed concentrations of the different biomarkers were used as time varying covariates to reduce runtime and complexity of the model. For GIP, GLP-1 and glucagon half-life were set to literature values. Non-Linear Mixed Effect Models (NONMEM version 7.3) [11] with the first order conditional estimation (FOCE) method and the differential equation solver ADVAN13 was used for the population data analysis. A stringent significance level of 0.1 or 1% was used to avoid over parametrization.
Results
Four submodels were developed describing:
1) Gastric emptying and glucose absorption[12]. After a 5-minute lagtime gastric emptying started and the inhibition of gastric emptying was described by a negative feedback of duodenal glucose. To be able to describe glucose movement through the small intestine it was assumed that the total transit time was 240 minutes and that the duodenum, jejunum and ileum comprised 8%, 37% and 55% of the total length respectively[13]. Saturable absorption of glucose from each intestinal segment was included.
2) Regulation of GIP and GLP-1 secretion[14]. GIP and GLP-1 was described by turnover models with the elimination rate constant fixed, corresponding to literature values. Secretion of GIP was stimulated by duodenal glucose while GLP-1 was stimulated by jejunal glucose.
3) Incretin effect and hepatic extraction of insulin. Secretion of insulin and C-peptide from beta-cells was described by adapting the mathematical beta cell model developed for healthy individuals by Overgaard et al.[10]. Two structural modifications were made to be able to describe the data for patients with T2D. 1) The first-phase secretion of insulin/C-peptide from the passive to the active vesicles was excluded from the model. 2) The fraction of active vesicles was found to be independent of glucose, and thus fixed to the fasting condition. By coupling the shared secretion model with disposition models for C-peptide and insulin it was possible to characterize the hepatic extraction of insulin. The insulinotropic effect of the incretin hormones GIP and GLP-1 was also characterized. Both GIP and GLP-1 were shown to stimulate provision of new insulin/C-peptide and activation of vesicles for healthy individuals. Patients with T2D were assumed to have no effect of GIP in accordance with literature[15] and GLP-1 was shown to mainly affect the activation of vesicles.
4) Regulation of glucagon secretion and endogenous glucose production. During both OGTT and IIGI, glucagon concentrations decrease quickly and stayed suppressed under the baseline throughout the study, even though insulin and glucose returned to baseline. A model where glucose potentiates the inhibitory effect of glucose and insulin on glucagon synthesis over time through a series of transit compartments was estimated to capture the prolonged suppression. This model allows for initial rapid suppression when glucose and insulin concentrations are high, as well as sustained inhibition after the concentrations have returned to baseline. Patients with T2D were shown to have stronger net stimulatory effect of the incretin hormones compared to healthy individuals, explaining the initial hypersecretion of glucagon seen in patients with T2D. The combined effect of glucose, insulin and glucagon on endogenous glucose production was also determined.
All submodels were combined into one comprehensive mechanism-based model capable of simultaneously describing the most important aspects of glucose homeostasis during glucose tolerance tests in healthy individuals and patients with type 2 diabetes, over a wide range of oral and intravenous glucose doses. The approach of developing each submodel conditioned on biomarker observations and then combining the submodels was here show-cased to work well and reduced the complexity of model development considerably.
Conclusion
In conclusion, four submodels each describing different aspects of glucose regulation were successfully combined into a new comprehensive mechanism-based model describing glucose homeostasis. The developed model is covering the most important hormones and mechanisms of glucose homeostasis and may be used to investigate combination treatments, drugs with multiple effects and to improve drug development of new antidiabetic compounds.
References:
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