Modeling the oral glucose tolerance test in normal and impaired glucose tolerant states: a population approach

Bayesian parameter estimation in the oral minimal model of glucose dynamics from non-fasting conditions using a new function of glucose appearance

BACKGROUND AND OBJECTIVE

The oral minimal model (OMM) of glucose dynamics is a prominent method for assessing postprandial glucose metabolism. The model yields estimates of insulin sensitivity and the meal-related appearance of glucose from insulin and glucose data after an oral glucose challenge. Despite its success, the OMM approach has several weaknesses that this paper addresses.

METHODS

A novel procedure introducing three methodological adaptations to the OMM approach is proposed. These are: (1) the use of a fully Bayesian and efficient method for parameter estimation, (2) the model identification from non-fasting conditions using a generalised model formulation and (3) the introduction of a novel function to represent the meal-related glucose appearance based on two superimposed components utilising a modified structure of the log-normal distribution. The proposed modelling procedure is applied to glucose and insulin data from subjects with normal glucose tolerance consuming three consecutive meals in intervals of four hours.

RESULTS

It is shown that the glucose effectiveness parameter of the OMM is, contrary to previous results, structurally globally identifiable. In comparison to results from existing studies that use the conventional identification procedure, the proposed approach yields an equivalent level of model fit and a similar precision of insulin sensitivity estimates. Furthermore, the new procedure shows no deterioration of model fit when data from non-fasting conditions are used. In comparison to the conventional, piecewise linear function of glucose appearance, the novel log-normally based function provides an improved model fit in the first 30 min of the response and thus a more realistic estimation of glucose appearance during this period. The identification procedure is implemented in freely accesible MATLAB and Python software packages.

CONCLUSIONS

We propose an improved and freely available method for the identification of the OMM which could become the future standardard for the oral minimal modelling method of glucose dynamics.

Population insulin sensitivity from sparsely sampled oral glucose tolerance tests

OBJECTIVE

This work aimed to estimate population-level insulin sensitivity (S_I) from 2-hour oral glucose tolerance tests (OGTT) with less than 7 samples.

RESEARCH DESIGN AND METHODS

The current methodology combines the OGTT mathematical model developed by Dalla Man et al., with nonlinear multilevel (NLML) statistical model to estimate population-level insulin sensitivity (S_I) from sparsely sampled datasets (3 or 4 samples per subject obtained in 120 min). To validate our novel methodology of population S_I estimation, we simulated 50 virtual subjects. We simulated 10 observations per subject over 240 minutes. After estimating their S_I using the OGTT model, the virtual subjects were split into two groups, subjects with S_I above the average and ones with below average. Subsequently, the simulated data were analyzed using statistical software and employing a t-test. The mean estimates of population S_I for the two groups of virtual subjects and their respective 95% CI were compared to the estimates obtained with our novel NLML group S_I estimates obtained using the 3 and 4 time points per subject. To further validate the performance of the novel NLML model, a set of 34 prediabetic and 30 diabetic subjects with T2D was used. As outlined above for the in-silico subjects, differences between the prediabetic and T2D subjects in regard to S_I was assessed using the classical two-stage approach (individual S_I estimation followed by statistical comparison of the two groups). The average estimates obtained with the classical two-stage approach were compared to the group estimated obtained with the NLML approach using 3 (0, 60, and 120 minutes) points per subject obtained in 120 minutes.

RESULTS

Unique and identifiable individual estimates of S_I were obtained for all virtual subjects. In comparison to the subjects with above average S_I (n=25), the subjects with simulated below average S_I (n=25) exhibited significantly lower insulin sensitivity (P<0.001). Our novel NLML population model confirmed these findings (4-point OGTT: P<0.001; 3-point OGTT: P<0.001). In a similar fashion to the one outlined for the virtual subjects, the median insulin sensitivities estimated with the classical two-stage approach were different between the prediabetic (n=34) and T2D subjects (n=32, P=0.004). Using 3 points per subject, our novel NLML model confirmed these findings (P<0.001).

CONCLUSIONS

The population estimates of S_I from OGTT data is an effective tool to assess population insulin sensitivity and assess differences that may not be possible when calculating individual S_I or when less than 7 samples are available.