(699e) Pseudo-Blood Insulin and Multiple Disturbance Model For Physiological Modeling of Blood Glucose Under Free-Living Conditions

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 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, a successful modeling methodology in this control context must be capable of producing a cause-and-effect relationship between the manipulated variable, insulin infusion, and the controlled variable, blood glucose concentration (BGC).  Therefore, the objective of this talk is to present a modeling method that is able to achieve this objective via the development of a modeling structure that uses pseudo-blood insulin concentration (BIC) and 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.
                The proposed method extends our Wiener Modeling Method (WMM), that can provide accurate modeling, but is not suited for model-based control applications where cause-and-effect modeling is needed to manipulate insulin flow rate for specific changes in the input variables. Thus, the WMM, while is applicable for monitoring or soft sensor development, it is not well suited for use in the development of an artificial pancreas. This unsuitability exists because after the dynamic transformation of each input separately, the static input contribution, to the level BGC, is additive for carbohydrates and insulin infusion separately. Therefore, under a reduced model of just food and insulin inputs, we set as a minimum acceptability criterion the following: correct phenomenological behavior under zero food input and non-zero insulin input (i.e., dropping glucose concentration with time and approaching zero mg/dL) and zero insulin input and nonzero food input (i.e., growing glucose concentration with time). The WWM cannot meet this criterion because the non-zero input can continue to produce stable BGC levels due to its additive nature.  

Using a physiological type mathematical representation from the literature for the behavior of BGC we developed a modeling structure that meets this criterion. We call it the coupled modeling method (CMM). This structure takes the dynamic insulin input representing unmeasured BIC and feeds it to the blood glucose block or compartment with entering dynamic food input and produces increased BGC with increasing food concentration and decreasing BGC with the product of BIC and BGC. Hence, for the CMM, with zero food input and non-zero insulin input, the BGC response approaches zero with increasing time; conversely, with zero insulin input and non-zero food input, the BGC continues to rise over time. Therefore, the CMM meets our minimum criterion of acceptability. In addition, we set as a target of fitted performance a level comparable to the WMM or greater. This target was met in all 15 modeling cases with the correlation for the measured and fitted BGC (r_fit) averaging about 0.6 on test data sets using only input variables (i.e., no current or previously measured BGC or outputs) , with a best case of r_fit = 0.853.

A critical accomplish achieved by the CMM is a dynamic cause-and-effect relationship where insulin can be manipulated to achieve a targeted BGC level. While the evaluation of this relationship using test subjects in this work was outside the scope of this work, a preliminary evaluation shows very promising results. This evaluation involved deriving a steady state relationship, using the modeling results of one subject, between insulin infusion (x_I) and carbohydrate consumption (x_C) and a constant level of BGC (G). First, these results gave representative x_I values comparable to those used by the subject. Secondly, they indicated that for a fixed value of x_C, how much x_I needs to increase to decrease G to a specific level. Thus, this analysis shows the potential to effectively vary x_I based on the dynamic behavior of BGC, food consumption, and activity levels in a closed loop online subject-specific protocol. That is, it has the potential to critically improve model-based control approaches such as model predictive control or feedforward control for individual insulin dependent subjects.