A Novel Insulin Delivery Approach Capable of Substantially Tight Variation of Blood Glucose Level

The potential for successful automatic insulin delivery has entered a new era due to recent technological advancements of insulin pumps and blood glucose sensors. However, for full automation and control twenty four hours a day/seven days a week (24/7) the control algorithm must be capable of tight control for major disturbances such as meals, activity and stress. Theoretically, the superiority of feedforward control (FFC) over all other control systems is that corrective action can be taken proactively to completely eliminate the effects of measured disturbances on the control variable. Thus, FFC has the potential to completely cancel the effect of any disturbance that it models. More specifically, in this FFC approach the objective is the development of an automatic insulin delivery system (AIDS) that nullifies the effects of eating, activity and stress. Accomplishing this goal will substantially reduce the variation in BGC.

While FFC has great potential, it is quite difficult to accomplish. From a search in the literature, FFC has seen very limited application in real processes in general and our work appears to be the only AIDS approach. Successful FFC starts with the ability to obtain an accurate causative model for inputs only. This is quite difficult to achieve for real data, especially in the use of free-living data, because of high cross correlation of inputs and changing levels of unmeasured disturbances. Our work takes a unique approach in the use of transfer function dynamic structures with physically interpretable parameters that are highly nonlinear in the models. Through published work were have demonstrated the superiority of our modeling approach causatively over all other methods theoretically as well as experimentally. In addition, our approach is quite efficient in capturing the variation in the response due to the measured inputs with large variations in unmeasured inputs, even those highly correlated with measured inputs that are modeled.

Even with an accurate FFC model, an effective FFC algorithm is needed for its implementation into a control system. Traditional FFC decomposes each input into a separate FFC and adds the output from each controller to obtain controller output or in this case the insulin rate to compensate for the model input changes. To obtain this value the model must be linearized and the final equations can be a highly complex high order differential equation. This work will present a simple control law that does not decompose or linearize the model. Thus, it keeps all the properties of the FFC model in its determination of FFC output.

In this work, 11 cases of two weeks of free living data collection on subjects with type 1 diabetes is modeled. The study was done in two parts. The first part takes a Wiener modeling approach which allows each input to have separate dynamic behavior. However, while the Wiener network (WN) is an excellent choice for the input transfer function model, in the response space, it is limited in representing the interaction of insulin and glucose in the blood. This drawback limits the ability to develop an accurate fit for insulin infusion rate, which is critical to controller performance. However, to model blood insulin and glucose interaction, one needs BIC at the sampling rate of BGC (i.e., every five minutes with the glucose sensor used in our studies). There is no such sensor in existence currently. To circumvent this need, we developed a semi-coupled network (SCN) for BIC and BGC that was inspired by the compartment modeling work of researchers in the literature. This led to the development of an unmeasured “pseudo” BIC variable. To our knowledge, this is the first use of such a variable in this context of subject-specific clinical modeling of BGC consisting only of inputs in free-living data collection. This novel change made a substantial advancement in obtaining a better phenomenological model and in providing a dynamic relationship between insulin infusion rate, consumed nutrients, and BGC.

This work consists of 13 input variables of three (3) food nutrients, seven (7) activity variables including one to measure stress, 24-hour clock time for circadian rhythm, and two (2) for insulin infusion. The activity variables were collected using the SenseWear^® Pro3 Body Monitoring System (BodyMedia Inc., Pittsburgh, Pennsylvania), which is worn on the triceps of the subject's arm.

For a FFC model, the premier measure of performance is the correlation of the measured BGC and the fitted BGC (r_fit). The results of splitting the data sets into 1 week of training, 4 days of validation, and 3 days of testing are reported here. The average r_fit values of the 11 cases for the WN for training, validation and testing were 0.58, 0.59, and 0.59, respectively. The average r_fit values of the 11 cases for the \SCN for training, validation and testing were 0.64, 0.63, and 0.61, respectively. The closeness of the values for each of the three sets is an indication that the models did not significantly over-fit the data on unmeasured disturbances. Given that the values for each approach are close, this is an indication that both methods explained about the same amount of variation. While the SCN values are slightly higher they are not substantially higher, which seems to suggest that about all the variations due to the measured inputs were captured by both models. Thus, given this result, the superiority of the SCN is not revealed by r_fit but in its ability to capture or reveal true static and dynamic behavior.

Our static evaluation consisted of examining the steady state relationships of carbohydrates (x_C), insulin infusion rate (x_I) and BGC level (G). This evaluation consisted of using the SCN results of one subject and plotting x_I versus x_C with lines of constant G. First, the numbers for these variables were in the ranges used by the subject. Secondly, for a constant value of x_C (e.g., 60 gms), as G decreased (e.g. from 300 to 100 mg/dL), x_I increased indicating that it would take more insulin to maintain a lower BGC, which makes phenomenological sense.

The dynamic evaluation consisted of setting x_C to zero or setting x_I to zero for a selected subject's model. With x_C set to zero, the WN BGC shifted down slightly but the SCN BGC dropped to zero, as it should. Conversely, with x_I set to zero, the WN BGC shifted up slightly but the SCN BGC continued to rise over time, as it should. Thus, these static and dynamic evaluations support the SCN over the WN on grounds of phenomenological soundness.

An r_fit value around 0.6 may not seem very high, but this value does not need to be extremely high to make a significant difference in tightening glucose control. This amount may represent nearly all the variation in the response that is due to the set of inputs models. In this case the model did an exceptional job in capturing all the variation that could be captured and whatever this level is, the FFC has the potential to nullify all the measured inputs.

To understand the potential impact of a particular FFC model in this work we use its fit to illustrate how the variation would be reduced under the proposed FFC approach. More specifically, the variability is substantially reduced, with the standard deviation dropping from 73.9 to 8.7 mg/dL, a decrease of 88.3%. This improvement results in a level of variation similar to a person without diabetes. Thus, this AIDS has the potential to control BGC as well as the body does for people without diabetes.

Key words: Artificial Pancreas, Insulin Delivery System