An integrated glucose-insulin minimal model for IVGTT
A. Largajolli (1), A. Bertoldo (1), C. Cobelli (1), P. Denti (2)
(1) Department of Information Engineering, University of Padova, Italy (2) Division of Clinical Pharmacology, University of Cape Town, Cape Town, South Africa
Objectives: The glucose and insulin regulatory system following an intravenous glucose injection (IVGTT) can be investigated through the so-called minimal models (MM) [1,2], quantifying insulin sensitivity and release. However, these approaches suffer from the limitation of analysing the two signals separately, by using one as known input to predict the other, and vice versa. Although this procedure has been shown to have a small impact on parameter estimation [3], it limits the simulation capabilities of the models and may not be as robust with sparse data. We propose an integration of the glucose and insulin MM by using nonlinear mixed effect modelling.
Methods: The dataset is composed of 204 healthy subjects [4] (118 M /86 F, mean age 55.53 ± 21.66, mean BMI 26.62 ± 3.39 kg/m^2) that underwent an insulin-modified IVGTT. The model building strategy (NONMEM using FOCE with INTERACTION) focused first on the two subsystems separately, to then proceed to the integration and simultaneous fit. Allometric scaling was used for CL and V terms and correlations were investigated between the model parameters.
Results: The original glucose minimal model (GMM) was revised with the use of a two compartment model as in [1] and by adding transit compartment input [5] to cater for the glucose kinetic in the first minutes of the experiment, previously customarily discarded. The original insulin minimal model (IMM) [2] was modified with the addition of a transit model to capture the delay in the onset of insulin release and a second compartment to better describe the kinetics. The model adequately fits both glucose and insulin and the VPC shows a better description when compared to the VPCs obtained from the separate models, with tighter simulated CIs around the observed data percentiles. The fixed effects estimates have an average normalized discrepancy value of 15% from the estimates obtained on the separated models. The size of BSV in the parameter estimates is reduced and strong correlations were detected between the insulin sensitivity and action (79%), and insulin and glucose delay (67%).
Conclusions: This integrated model, while providing parameter estimates compatible with the traditional MM approaches, allows the simultaneous characterization of the glucose-insulin regulation system. Unlike the GMM and IMM this integrated model provides full simulation capabilities and can be used as a framework to explore disease and drug effects. The model could be further improved by integrating C-peptide kinetics.
References:
[1] Minimal model Sg overestimation and Si underestimation: improved accuracy by a Bayesiam two-compartment model. Cobelli C, Caumo A, Omenetto M. 1999, AM J Physiol Endocrinol Metab, vol. 277, pp. 481-488.
[2] A minimal model of insulin secretion and kinetics to assess hepatic insulin secretion. Toffolo G, Campioni M, Basu R, Rizza A, Cobelli C. 2005, Am J Phyisiol Endocrinol Metab, vol. 290, pp. E169-E176.
[3] Diabetes: Models, Signals, and Control. Cobelli C, Dalla Man C, Sparacino G, Magni L, De Nicolao G, Kovatchev B P. 2009, IEEE Reviews in Biomedical Engineering, vol. 2, pp. 54-96.
[4] Effects of age and sex on postprandial glucose metabolism: differences in glucose turnover, insulin secretion, insulin action, and hepatic insulin extraction. Basu R, Dalla Man C, Campioni M et al. 2006, Diabetes, vol. 55, no. 7, pp. 2001-14.
[5] Implementation of a transit compartment model for describing drug absorption in pharmacokinetic studies. Savic RM, Jonker DM, Kerbusch T, and Karlsson MO. 2007, Journal of pharmacokinetics and pharmacodynamics, vol. 34, no. 5, pp. 711–26.
