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A Bayesian Approach to Bergman's Minimal Model

Kim Emil Andersen and Malene Højbjerre

Aalborg University, Denmark

The classical minimal model of glucose disappearance (Bergman et al., 1979) was proposed as a powerful modelling approach to estimating insulin sensitivity and glucose effectiveness during a standard frequently sampled intravenous glucose tolerance test (IVGTT) or a tolbutamide- or insulin-modified IVGTT. The standard frequently sampled IVGTT consists in administering a single intravenous injection of glucose over a small period of time and measuring in plasma the resulting glucose and insulin concentrations. Two mathematical non-linear models are used to model the dynamics of plasma glucose and the kinetics of plasma insulin. Highly computer intensive deterministic iterative numerical algorithms exist for reconstructing the glucose kinetics and thereby obtain estimates for the insulin sensitivity and glucose effectiveness. However, these algorithms are only efficient when a good initial estimate is provided. In this work we present a Bayesian approach to estimating the insulin sensitivity and glucose effectiveness by adopting graphical models as a powerful and flexible modelling framework. We demonstrate how the reconstruction algorithm may be efficiently implemented through the use of Markov chain Monte Carlo methods.

Bergman, R.N., Ider, Y.Z., Bowden, C.R. and Cobelli, C.:Quantitative Estimation of Insulin Sensitivity, American Journal of Physiology, 236 (1979), E667-77.