Anticipating Meals with Behavioral Profiles: Towards Stochastic Model Predictive Control of T1DM
Modeling and Control in Biomedical Systems, Volume # 7 | Part# 1
Authors
Patek, Stephen D.; Hughes, Colleen; Breton, Marc; Kovatchev, Boris
Identifier
10.3182/20090812-3-DK-2006.00007
Index Terms
Endocrine and metabolic systems; Disease control and critical care,; Control of physiological and clinical variables,
Abstract
The delay associated with subcutaneous glucose sensing and insulin infusion actuation significantly complicates the design of control algorithms for regulating blood glucose in patients with Type 1 Diabetes Mellitus (T1DM). Model predictive control (MPC) is one strategy for mitigating delay, where optimal insulin infusions can be given in anticipation of future meal disturbances. Unfortunately, exact prior knowledge of meals can only be assured in a clinical environment, and uncertainty about when and if meals will arrive could lead to catastrophic outcomes. In this paper we develop an MPC-like control law that can anticipate meals given a probabilistic description of the patient's eating behavior in the form of a random meal (behavioral) profile. Preclinical in silico trials using the oral glucose meal model of Dalla Man et al. show that the control strategy provides a convenient means to account for uncertain prior knowledge of meals without compromising patient safety, even in the event that anticipated meals are skipped.
References
[1] A. Bensoussan and J. L. Menaldi. Stochastic hybrid control. J of Math Anal and App, 249(1):261–288, 2000. [2] B. W. Bequette. A critical assessment of algorithms and challenges in the development of a closed-loop artificial pancreas. Diab Technol Ther, 7:28–47, 2005. [3] M. Breton and B. Kovatchev. Analysis, modeling, and simulation of the accuracy of continuous glucose sensors. J Diab Sci Tech, 2(5):1–10, 2008. [4] L. Campo and Y. Bar-Shalom. Control of discrete-time hybrid stochastic systems. IEEE Trans Automatic Control, 37(10):1522–1527, 1992. [5] P. E. Cryer. Hypoglycemia is the limiting factor in the management of diabetes. Diabetes Metab Res Rev, 15:42–46, 1999. [6] C. Dalla Man, D. M., Raimondo, R. A. Rizza, and C. Cobelli. GIM, simulation software of meal glucose-insulin model. J Diabetes Sci Technol, 1(3):323–330, 2007. [7] C. Dalla Man, R. A. Rizza R.A., and C. Cobelli. Meal simulation model of the glucose-insulin system. IEEE Trans Biomed Eng, 54:1740–1749, 2007. [8] Diabetes Control and Complications Trial Research Group. The effect of intensive treatment of diabetes on the development and progression of long-term complications of insulin-dependent diabetes mellitus. N Engl J Med, 329:978–986, 1993. [9] A. E. Gold, B. M. Frier, K. M. Macleod K.M., and I. J. Deary. A structural equation model for predictors of severe hypoglycemia in patients with insulin-dependent diabetes mellitus. Diabet Med, 14:309–315, 1997. [10] R. Hovorka, V. Canonico, L. J. Chassin, U. Haueter, M. Massi-Benedetti, M. O. Federici, T. R. Pieber, H. C. Schaller, L. Schaupp, and T. Vering. Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Phys. Meas., 25:905–920, 2004. [11] B. Kouvaritakis, M. Cannon, and V. Tsachouridis. Recent developments in stochastic mpc and sustainable development. Ann Rev Control, 28:23–35, 2004. [12] B. P. Kovatchev, M. Breton, C. Dalla Man, and C. Cobelli. In silico preclinical trials: A proof of concept in closed loop control of type 1 diabetes. J Diab Sci Tech, 3(1):44–55, 2009. [13] L. Magni, D. M. Raimondo, C. Dalla Man, G. De Nicolao, B. Kovatchev, and C. Cobelli. Model predictive control of glucose concentration in sub jects with type 1 diabetes: an in silico trial. In 17th IFAC World Congress, pages 4246–4251, 2008. [14] L. Magni, D. M. Raimondo, C. Dalla Man, M. Breton, S. Patek, G. De Nicolao, C. Cobelli, and B. P. Kovatchev. Evaluating the efficacy of closed-loop glucose regulation via control variability grid analysis. J Diab Sci Tech, 2(4):630–635, 2008. [15] C. Owens, H. Zisser, L. Jovanovic, B. Srinivasan, D. Bonvin, and F. J. Doyle III. Run-to-run control of blood glucose concentrations for people with type 1 diabetes mellitus. IEEE Trans Biomed Eng, 53:996–1005, 2006. [16] C.C. Palerm, H. Zisser, W.C. Bevier, L. Jovanovic, and F. J. Doyle III. Prandial insulin dosing using run-to-run control: application of clinical data and medical expertise to define a suitable performance metric. Diabetes Care, 30:1131–1136, 2007. [17] C.C. Palerm, H. Zisser, L. Jovanovic, and F. J. Doyle III. A run-to-run control strategy to adjust basal insulin infusion rates in type 1 diabetes. J Process Control, 18:258–265, 2008. [18] R. S. Parker, F. J. Doyle III, and N. A. Peppas. A model-based algorithm for blood glucose control in type I diabetic patients. IEEE Trans Biomed Eng, BME-46:148–157, 1999. [19] S. Patek, M. Breton, C. Cobelli, C. Dalla Man, and B. Kovatchev. Adaptive meal detection algorithm enabling closed-loop control in type 1 diabetes. In Proc. Diab Technology Meeting, 2007. [20] UK Prospective Diabetes Study Group (UKPDSG). Intensive blood-glucose control with sulphonylureas or insulin compared with conventional treatment and risk of complication in patients with type 2 diabetes. Lancet, 352:837–853, 1998. [21] H. Zisser, L. Jovanovic, F. J. Doyle III, P. Ospina, and C. Owens. Run-to-run control of meal-related insulin dosing. Diab Technol Ther, 7:48–57, 2005.
