Assessing insulin sensitivity, glucose effectiveness, and β-cell responsivity using an integrated glucose, insulin, and C-peptide minimal model
Edoardo Faggionato (1); Anna Largajolli (2); Alessandra Bertoldo (1); Chiara Dalla Man (1); Paolo Denti (3)
(1) Department of Information Engineering, University of Padova, Padova, Italy; (2) Certara, Princeton, New Jersey, USA; (3) Division of Clinical Pharmacology, University of Cape Town, Cape Town, South Africa
Objectives:
Intravenous glucose tolerance tests (IVGTT) have been widely used to investigate the glucose-insulin interaction in subjects with and without diabetes, using the glucose (GMM) [1], and the insulin and C-peptide minimal models (IMM, CMM) [2]. The identification of these models is usually performed at individual level, and separately for each entity. This is done by employing a forcing function strategy, where one measured profile is assumed to be an input of the system, known without error. Although this approach avoids unidentifiability in parameter estimates, it may lead to incorrect propagation of the measurement error and, in turn, to biased parameter estimates. Moreover, the separate identification precludes the estimation of correlations among parameters, which may rather be physiologically relevant. Using nonlinear mixed-effects (NLME) modelling, as opposed to fitting at individual level, one can overcome these limitations, as in [3], where GMM and IMM were integrated. Here, we aimed to further extend the model by incorporating also the CMM, since C-peptide and insulin are secreted in a 1:1 ratio, but, unlike insulin, C-peptide is not extracted by the liver and therefore is a better marker of insulin secretion. Integrating the three models, we could assess insulin sensitivity (SI) and glucose effectiveness (GE) as in [3], plus the first (Φ1) and second phase (Φ2) β-cell responsivity to glucose.
Methods:
The dataset is a frequent collection of glucose, insulin, and C-peptide measures gathered from 204 non-diabetic subjects (118M/86F, age=65[27,71]years, body weight, BW=79[69,87]kg) who underwent an insulin-modified IVGTT (IM-IVGTT), consisting of a constant intravenous injection of glucose (0.330g/kg) for 2 min from time 0, followed by a constant insulin infusion (0.02U/kg) for 5 min from time 20 min. Intensive blood sampling was performed for 4h and glucose, insulin, and C-peptide concentrations were determined.
Parameters were estimated with the SAEM algorithm in NONMEM [4], plus the IMP algorithm to calculate the exact likelihood of the data. The modelling approach consisted in the integration and possible expansion of the models presented in [1] and [2]. At variance with the original models, model equations were reparametrized to use amounts instead of concentrations as state variables and clearances instead of transfer rates. Second, we modelled the infusion of glucose and insulin with a variable duration and a subject-specific lag time between the start of infusion and the appearance in plasma to account for delay and variability introduced by the pump and the attending clinician. We also investigated the expansion of the GMM and IMM to a two-compartment disposition kinetics to better describe the profile of the analyzed substances. Finally, fixed allometric scaling was used to describe part of the variability associated with distribution volumes and clearances using easily accessible covariates.
Results:
Kinetics of glucose and insulin were best described by two-compartment disposition models. The model assumed a full covariance matrix of random effects, with exception to those describing lag and duration of infusion. Fat-free mass (calculated as in [5]) scaled GE, the peripheral distribution volume of glucose, and its intercompartmental clearance. BW scaled all other volumes and clearances.
Precision of model parameters was good. All estimates lay within physiological ranges. Relevant estimates were SI=1.76∙10-4L/(pmol∙min), GE=2.3dL/min, Φ1=115∙10-9min-1, and Φ2=9.4∙10-9min-1. Strong correlations were found between IMM parameters and their CMM counterparts. Relevant correlations were found between Φ2 and SI (ρ=-0.62) as in [6], and Φ2 and basal insulin (ρ=0.73) as in [7]. The visual predictive check showed satisfactory fit for all analytes.
Conclusions:
In this work, we integrated the widely used GMM, IMM, and CMM in an NLME framework and built a model that can simultaneously provide precise estimates of SI, GE, and β-cell function in healthy subjects during an IM-IVGTT. The model provided a complete characterization of the joint parameter distribution of a healthy population. Further work will focus on exploring the covariate in the model, integrating the secretion of IMM and CMM to assess also the hepatic extraction, and extending the usability of the model in diabetic populations.
References:
[1] R N Bergman et al., “Quantitative estimation of insulin sensitivity,” Am J Physiol, 236(6):E667–77, 1979.
[2] G Toffolo et al., “A minimal model of insulin secretion and kinetics to assess hepatic insulin extraction,” Am J Physiol Endocrinol Metab, 290(1):E169–76, 2006.
[3] A Largajolli et al., “An integrated glucose-insulin minimal model for IVGTT,” 22nd PAGE meeting, Abstr 2762, http://www.page-meeting.org/?abstract=2762, 2013.
[4] RJ Bauer, “NONMEM users guide. Introduction to NONMEM 7.5.0,” ICON plc. Gaithersburg, MD, USA, 2017–2020.
[5] S Janmahasatian et al., “Quantification of lean bodyweight,” Clin Pharmacokinet, 44(10):1051–65, 2005.
[6] C Cobelli et al., “Assessment of beta-cell function in humans, simultaneously with insulin sensitivity and hepatic extraction, from intravenous and oral glucose tests,” Am J Physiol Endocrinol Metab, 293(1):E1–E15, 2007.
[7] MMA Ibrahim et al., “The integrated glucose insulin minimal model: An improved version,” Eur J Pharm Sci, 15(134):7–19, 2019.
