Understanding the effects of parametric uncertainty and correlation structure of the parameters is important to the performance of Internal Model Control (IMC). Results of simulated control of blood sugar in both healthy and type-I diabetics is presented. The simulated patient is described using the models presented by the Cinar Group at IIT, titled GlucoSim(1). This is a compartmental pharmacokinetic model, derived primarily from the work of Puckett (2), that predicts dynamic blood-sugar and blood insulin levels, with inputs of activity and meals. The controller is a simple IMC structure, constructed using one of either the simple Bergman model (3) or the simple Ackerman model (4). The correlation structure of the parameters where obtained by performing multiple Monte Carlo simulations on the regression of the parameters of the models used.

As others have shown (5), IMC works reasonably well for this simulated system. However, the role of parameter uncertainty and parameter correlation is important, and can be significant under realistic scenarios. Typical uncertainty levels in experimental (clinical) data can produce enough variation in model dynamics to substantially degrade IMC controller performance.

(1) http://216.47.139.196/glucosim/index.html, accessed April 1, 2006. Also "Glucosim: a simulator for education on the dynamics of diabetes mellitus" by Erzen, F.C. Birol, G. Cinar, A. Engineering in Medicine and Biology Society, Proceedings of the 23rd Annual International Conference of the IEEE 2001 4(4), 3163- 3166 (2001).

(2) W. R. Puckett. Dynamic Modeling of Diabetes Mellitus. PhD thesis, University of Wisconsin-Madison, Department of Chemical Engineering, (1992).

(3) R.N. Bergman, L.S. Phillips, and C. Cobelli, “Physiologic Evaluation of Factors Controlling Glucose Tolerance in Man: Measurement of Insulin Sensitivity and β-Cell Glucose Sensitivity from the Response to Intravenous Glucose,” Journal of Clinical Investigation, 68, 1456-1467, (1981).

(4) L. Gatewood, E. Ackerman, J.W. Rosevear, and G.D. Molnar, “Modeling Blood Glucose Dynamics,” Behavioral Science, 15, 72-87, (1970).

(5) Parker RS, Doyle FJ "Control-relevant modeling in drug delivery" Advanced Drug Delivery Reviews 48(2-3) 211-228 (2001).