A Bayesian Approach to Bergman's Minimal Model

The classical minimal model of glucose disposal was proposed as a powerful modeling approach to estimating the insulin sensitivity and the glucose effectiveness, which are very useful in the study of diabetes. The minimal model is a highly ill-posed inverse problem and most often the reconstruction of the glucose kinetics has been done by deterministic iterative numerical algorithms. However, these algorithms do not consider the severe ill-posedness inherent in the minimal model and may only be efficient when a good initial estimate is provided. In this work we adopt graphical models as a powerful and flexible modeling framework for regularizing the problem and thereby allow for estimation of the insulin sensitivity and glucose effectiveness. We illustrate how the reconstruction algorithm may be efficiently implemented in a Bayesian approach where posterior sampling is made through the use of Markov chain Monte Carlo techniques. We demonstrate the method on simulated data.