Translation between two models; Application with integrated glucose homeostasis models

Aims: Both the Integrated Glucose Insulin model (IGI) and the Integrated Minimal Model (IMM) have been proposed to characterize simultaneously glucose-insulin regulation system following intravenous glucose tolerance test (IVGTT) [1, 2]. Though with different structure, these models provide full simulation capabilities that allow their use as a platform to quantify disease status as well as analysis of treatment effects in clinical drug development. Here we investigated the translation of information between the two models in terms of parameters' identifiably and precision, as well as mapping two key parameters for clinical diagnosis, glucose effectiveness and insulin sensitivity available in IMM with parameters in the IGI model.

Methods: To investigate the parameter precision and ability of the model to simulate data mimicking real glucose homeostasis data, three sources of data were used: 1) a bootstrap (n=100) of real data, 2) 100 simulated datasets from point estimates of the IMM and 3) 100 simulated datasets from point estimates of the IGI model. Each source of data was analysed with the two models. The point estimates for each model used in the simulations and the bootstrap came from two previously published IVGTT studies performed in healthy subjects with one of the studies being insulin-modified [3, 4] with measurements of glucose and insulin plasma concentration. In total, for each of the models 300 sets of parameters were obtained. To map the clinically important parameters of the IMM with their corresponding parameter in the IGI, a large dataset was simulated using the IGI and analysed with the IMM. A generalized additive model (GAM) was used to evaluate differences between simulated and estimated individual parameters. .

Results: Comparing the parameter precision of the three sources for the two models, unsurprisingly the precision is the highest when the same model is used for simulation and estimation. Additionally, the lowest precision is seen in the opposite situation, i.e. IMM generated data analysed with the IGI model and vice versa. When data was generated by the IGI model, bias was observed in 26% of the IMM parameters ranging from 10.9% to 30.6%, while data generated by the IMM, resulted in 75% of the IGI model parameters being biased, ranging from 13% to 4859%. For the GAM, the strongest parameter correlations across models were found for: insulin dependent glucose clearance (IGI) – insulin sensitivity (IMM); insulin independent glucose clearance (IGI) – glucose effectiveness (IMM); and rate constant related to insulin effect on glucose clearance (IGI) – insulin action (IMM).

Conclusion: The results of this translation between two models of glucose homeostasis indicate that when analyzed with the IMM, real data and data simulated with the IGI model gave similar results. When analyzed with the IGI model, real data and data simulated from the IMM gave different results. The poor estimation of the rate constant related to suppression of endogenous glucose production indicate that the reason could be a model misspecification in the implicit description of hepatic glucose production. The clinically important parameters in the IMM were successfully mapped to the expected IGI model parameters.

Acknowledgment: This work was supported through the IDeAl project (FP7-HEALTH-2013-602552)

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