A population‐based Bayesian approach to the minimal model of glucose and insulin homeostasis

The minimal model was proposed in the late 1970s by Bergman et al. ( Am. J. Physiol. 1979; 236 (6):E667) as a powerful model consisting of three differential equations describing the glucose and insulin kinetics of a single individual. Considering the glucose and insulin simultaneously, the minimal model is a highly ill‐posed estimation problem, where the reconstruction most often has been done by non‐linear least squares techniques separately for each entity. The minimal model was originally specified for a single individual and does not combine several individuals with the advantage of estimating the metabolic portrait for a whole population. Traditionally it has been analysed in a deterministic set‐up with only error terms on the measurements. In this work we adopt a Bayesian graphical model to describe the coupled minimal model that accounts for both measurement and process variability, and the model is extended to a population‐based model. The estimation of the parameters are efficiently implemented in a Bayesian approach where posterior inference is made through the use of Markov chain Monte Carlo techniques. Hereby we obtain a powerful and flexible modelling framework for regularizing the ill‐posed estimation problem often inherited in coupled stochastic differential equations. We demonstrate the method on experimental data from intravenous glucose tolerance tests performed on 19 normal glucose‐tolerant subjects. Copyright © 2005 John Wiley & Sons, Ltd.