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

Abstract

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.

Keywords: Glucose appearance; Insulin sensitivity; Oral minimal model; Variational Bayesian analysis.