Subject-Specific Multiple Input Block-Oriented Glucose Modeling of Several Type 1 Diabetic Subjects

Type 1 diabetics often experience extreme variations in glucose concentrations which can have adverse long- and short-term effects such as severe hypoglycemia, hyperglycemia and organ degeneration. Studies have established that there is a need to maintain the glucose levels within a normal range to avoid complications caused by diabetes. However, initial attempts to regulate blood glucose levels using insulin infusion, multiple injections or a combination of the two have had limited success as they lack the ability to decide the appropriate rate and/or amount of insulin infusion based on the current metabolic state of the body. An “artificial pancreas” consisting of a continuous glucose monitor, an insulin infusion pump, and a control algorithm has the potential to improve glucose regulation by intelligently deciding the proper amount of insulin delivery at the proper time. However, a critical key in the success of the electro-mechanical pancreas is the ability to effectively model and use this model to improve closed-loop control. Thus, the objective of this talk is to propose a modeling method that takes into account the simultaneous and multiple effects of food, activity, stress and their interactions in developing subject-specific models for several type 1 diabetic subjects.

This talk will present the results on 10 to 15 type 1 diabetic subjects where food (3 variables), activity (7 variables), insulin infusion (2 variables), and time of day (TOD) (a total of 13 variables) are collected for two weeks and modeled using the Wiener block-oriented method of Rollins et al. (2010). The data sets are split two ways. One way is into training and validation sets of 1 week each. The second way is into training (1 week), validation (4 days) and testing (3 days). The method of Rollins et al. is modified to use an approach that determines dynamic parameters separately from the static parameters such that consistency in the fitted models are maintained over all the data sets to guard against over-fitting the data. Three types of models are compared: input only (Model 1), input/output (Model 2), and output only (Model 3). Results are given for forecast predictions K-steps ahead (KSA) from 5 minutes to 3 hours. Model 1 uses only the 13 input variables for prediction and technically it is not a KSA forecast model. Model 2 is a pre-whitened model for forecasting one step ahead and uses measured glucose and the 13 input variables. Model 3 is an auto-regressive-integrated moving average (ARIMA) model that forecasts KSA using only glucose measurements. The results show that Model 2 approaches Model 1 as k increases and that this approach can vary considerably from subject to subject. They also show that Model 3 consistently performs worse that Model 2 but its decay in performance as k increases can also vary considerably from subject to subject. For each data set, results are given for models with only food variables, only activity variables and only insulin variables. Results showing the importance of modeling interactions between input variables are also given.

Rollins, D. K., N. Bhandari, J. Kleinedler, K. Kotz, A. Strohbehn, L. Boland, M. Murphy, D. Andre, N. Vyas, G.Welk and W. Franke, "Free-living inferential modeling of blood glucose level using only noninvasive inputs," Journal of Process Control 20 95-107 (2010).