A population based approach to the minimal model

In this work we extend the classical minimal model for glucose and insulin homoestasis to a population based model with the advantage of estimating the metabolic portrait, i.e. the insulin sensitivity, the glucose efficiency and the pancreatic responsiveness, for a whole population. We adopt a Bayesian graphical model to describe a stochastic version of the populations based minimal model, meaning that we do not only consider error terms on the observations, but also on the process increments. 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 modeling 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. tolerance tests performed on 19 normal glucose tolerant subjects.