(373d) Robust Predictive Control Strategies for Glycemic Regulation in Insulin Dependent Diabetes Mellitus Patients

The problem of Insulin Dependent Diabetes Mellitus (IDDM) management is very complex due to the great inter- and intra-patient variability in physiology. A variety of factors that may cause fluctuations in the glucose metabolism, such as variability in the meal and exercise profiles, as well as human intervention in implementing the control strategies, may further complicate this problem. In this work, robust model based strategies are proposed to regulate the glycemic levels within normal physiological ranges using both the intravenous (IV) and subcutaneous (SC) insulin infusion routes. Both the strategies are validated on simulation studies of diabetes patients under various patient-model mismatch and multi-meal scenarios. In order to generate patient data a detailed physiological patient model is developed and the validation of the model is accomplished using the triple-tracer data published by Man et al. (2007).

In the case of critically ill patients treated in an intensive care unit (ICU), the availability of continuous variable flow-rate insulin pumps and high frequency blood glucose measurements facilitates the application of advanced control algorithms such as model predictive control involving dynamic optimization every sampling time (Parker et al., 2001). However, model-based predictive control of the insulin infusion system requires a compensation mechanism for mismatch in patient behavior and model predictions resulting from inter- and intra- patient variability in terms of insulin-glucose metabolism and in terms of the daily meal and exercise profiles. For glycemic control in critically ill patients using IV infusion, an input-output data based modeling approach is adopted with a state estimation based offset-free model predictive controller (MPC/SE: Ricker, 1990&1991). Also presented is an MPC/SE with zone control algorithm which mimics the natural feedback involved in glycemic control of healthy subjects by employing a range for set-point (Gonzalez and Odloak, 2009; Lez et al., 2009). The offset-free MPC/SE algorithm effectively improved the meal disturbance rejection properties in the presence of patient-model mismatch. The MPC/SE with zone control showed similar disturbance rejection properties as that of offset-free MPC/SE, however, the total amount of insulin dispensed into the patient via IV route was minimized. MPC/SE with zone control algorithm also demonstrated better meal-to-meal decoupling and lower number of insulin pulses as compared with offset-free MPC/SE.

In case of diabetic patients undergoing critical insulin infusion therapy while carrying out their daily routine, the control algorithms requiring frequent blood glucose measurements and continuous insulin infusion may be difficult to adapt for glycemic control (Palerm et al., 2007a&b). In order avoid the problems posed by the infrequent blood glucose measurements (three to six per day) and limited number of insulin infusions (four per day) an adaptive optimal control algorithm was proposed. At the end of each day, using the available information of (pre- and post-prandial) blood glucose measurements, the meal timing and qualitative description of the meal quantity and the dosage and timing of insulin infusions, the subset of control relevant patient model parameters are re-identified to describe the current patient behavior. This re-identified control relevant patient model is used in estimating the optimal basal and bolus insulin doses for the day ahead. The robustness of this control algorithm for patient-model mismatch, variability in meal sizes, meal amounts, number and sampling times of blood glucose measurements is demonstrated in simulation case studies. From these robustness analysis studies, it was demonstrated that, this control algorithm can effectively handle the complex variability involved in a day-to-day routine and human intervention in implementing glycemic regulation. In addition to efficient disturbance rejection characteristics, the digital nature of this control algorithm enables potential implementation onto to a microprocessor chip, which makes it possible to be integrated onto a hand-held glucometer as an insulin dose advisor.

REFERENCES

Gonzalez, A.H., and Odloak, D., 2009. A stable MPC with zone control. Journal of Process Control, 19(1), 110-122.

Lez, A.H.G., Marchetti, J.L., and Odloak, D., 2009. Robust model predictive control with zone control. Institution of Engineering and Technology: Control Theory & Applications, 3(1), 121-135.

Man, C.D., Rizza, R.A., and Cobelli C., 2007. Meal simulation model of the glucose-insulin system, IEEE Transactions of Biomedical Engineering, 54(10), 1740-1749.

Palerm, C.C., Zisser, H., Bevier, W.C., Jovanovic°, L., and Doyle III, F.J., 2007a. Prandial insulin dosing using run-to-run control: application of clinical data and medical expertise to define a suitable performance metric, Diabetes Care, 30(5), 1131?1136.

Palerm, C.C., Zisser, H., Jovanovic°, L., and Doyle III, F.J., 2007b. A run-to-run framework for prandial insulin dosing: handling real-life uncertainty, Int. J. Robust Nonlin. 17(13), 1194?1213.

Parker, R.S., Doyle, F.J. III, and Peppas, N.A., 2001. The intravenous route to blood glucose control. IEEE Engineering in Medicine and Biology, 20:65?73.

Ricker, N.L., 1991. Model-predictive control: state of the art. In: Chemical Process Control?CPC IV, Fourth International Conference on Chemical Process Control, edited by Y. Arkun, and W.H. Ray. Amsterdam: Elsevier, 271-296.

Ricker, N.L., 1990. Model predictive control with state estimation. Industrial & Engineering Chemistry Research, 29(3):374-382.