Assessing Glucagon Kinetics through Nonlinear Mixed Effects Modeling
Edoardo Faggionato (1); Marcello C. Laurenti (2); Adrian Vella (2); Chiara Dalla Man (1)
(1) Department of Information Engineering, University of Padova, Padova, Italy; (2) Division of Endocrinology, Diabetes & Metabolism, Mayo Clinic College of Medicine, Rochester, MN.
Objectives:
A concomitance of both defective insulin secretion and impaired glucagon suppression leads to the development of impaired glucose tolerance in patients with prediabetes. However, compared to insulin, dysfunction on glucagon secretion is still understudied in the investigation of the pathogenesis of type 2 diabetes.
The state-of-the-art method to assess insulin secretion in vivo employs deconvolution of plasma C-peptide measurements and a population model of the hormone kinetics. The lack of a model of glucagon kinetics precluded so far the possibility to apply the same methodology to estimate glucagon secretion. In a recent work by Laurenti et al. [1], population parameters of glucagon kinetics were derived using a standard-two-stage approach. Using that approach, the best model describing glucagon kinetic data was a single-compartment one. However, a two-compartment model performed satisfactorily in a nonnegligible percentage of the analyzed subjects (39 out of 51).
The aim of this work was to assess whether a two-compartment model for glucagon kinetics can be identified in a population framework employing nonlinear mixed effects (NLME) modeling.
Methods:
The database was a collection of glucagon pharmacokinetic data gathered from 53 healthy subjects (age=54±13 years, weight=81±15 kg). Volunteers underwent a constant infusion of somatostatin (60 ng/kg/min), starting at t=0 min, to suppress endogenous insulin and glucagon production, and a variable infusion of insulin to restore normal insulin values. After 120 min, glucagon was infused with a constant rate (65 ng/kg/min). Plasma glucagon concentration was frequently sampled from 120 to 300 min. The study was performed after approval of the Mayo Institutional Review Board (Mayo Clinic College of Medicine, Rochester, MN).
The NLME model for glucagon kinetics consisted of a structural model describing the individual response and a stochastic model describing the variability of the kinetic parameters. The structural model was a two-compartment model parametrized with clearance, CL, central and peripheral volumes of distribution, V1 and V2 respectively, and intercompartmental clearance, Q. In addition, a zero-order delay, t0, was added to account for the time lag introduced by the pump used to infuse glucagon. The stochastic model of parameter variability assumed a log-normal distribution for every kinetic parameter. Finally, the error model describing residual unexplained variability was fixed to that used in [1].
Monolix [2] was used for model identification. Data below the level of detection were accounted in estimating the maximum likelihood of model parameters. Some prior information was employed for estimating t0. Five models were tested to assess possible correlation between the random effects of CL, V1 and V2. They were validated in terms of residual distribution and relative standard error (RSE) of the estimates. Models that performed satisfactorily were then compared using a Bayesian information criterion (BIC), and the model that scored the lowest BIC was selected as the best one.
Results:
Residual distribution was satisfactory for every tested model. Models providing at least one parameter estimated with a RSE>50% were discarded. Among the remining models, the one scoring the lowest BIC was the one including the correlation between the random effects of CL and V1.
All population parameters were within physiological ranges and in agreement with those estimated in [1] for a one compartmental model: CL=1.25 L/min (RSE=3%), V1=5.11 L (7%), V2=5.23 L (42%), Q=0.49 L/min (10%) and t0=10.7 min (7%). Standard deviations of the random effects were 0.22 (10%), 0.39 (12%), 2.44 (15%), 0.45 (17%) and 0.47 (10%) for ωCL, ωV1, ωV2, ωQ and ωt0 respectively. Correlation between ηCL and ηV1 was 0.68 (20%). Visual predictive check plot was also satisfactory.
Conclusions:
In this work, a two-compartment model describing glucagon kinetics in plasma has been developed in a NLME framework. This is a further improvement towards the knowledge of glucagon kinetics, which to date has been modelled with a one-compartment model. The model can be employed for the estimation of glucagon secretion via deconvolution as currently done for insulin. Moreover, this model can also be incorporated in diabetes simulator platforms to test therapies employing exogenous glucagon administration. Future work includes adding a covariate model or allometric scaling to the presented NLME model.
References:
[1] Laurenti MC et al., “Assessment of individual and standardized glucagon kinetics in healthy humans,” Am J of Physiol Endocrinol Metab, 2021; 320(1): E71-E77.
[2] Monolix, version 2020 R1, ©Lixoft, Antony, France. Documentation avalable at https://monolix.lixoft.com/
