A New Meal Absorption Model for Artificial Pancreas Systems

Abstract

Background: Artificial pancreas (AP) systems reduce the treatment burden of Type 1 Diabetes by automatically regulating blood glucose (BG) levels. While many disturbances stand in the way of fully closed-loop (automated) control, unannounced meals remain the greatest challenge. Furthermore, different types of meals can have significantly different glucose responses, further increasing the uncertainty surrounding the meal.

Methods: Effective attenuation of a meal requires quick and accurate insulin delivery because of slow insulin action relative to meal effects on BG. The proposed Variable Hump (VH) model adapts to meals of varying compositions by inferring both meal size and shape. To appropriately address the uncertainty of meal size, the model divides meal absorption into two disjoint regions: a region with coarse meal size predictions followed by a fine-grain region where predictions are fine-tuned by adapting to the meal shape.

Results: Using gold-standard triple tracer meal data, the proposed VH model is compared to three simpler second-order response models. The proposed VH model increased model fit capacity by 22% and prediction accuracy by 12% relative to the next best models. A 47% increase in the accuracy of uncertainty predictions was also found. In a simple control scenario, the controller governed by the proposed VH model provided insulin just as fast or faster than the controller governed by the other models in four out of the six meals. While the controllers governed by the other models all delivered at least a 25% excess of insulin at their worst, the VH model controller only delivered 9% excess at its worst.

Conclusions: The VH Model performed best in accuracy metrics and succeeded over the other models in providing insulin quickly and accurately in a simple implementation. Use in an AP system may improve prediction accuracy and lead to better control around mealtimes.

Keywords: artificial pancreas; automated insulin delivery; blood glucose control; meal prediction; model predictive control; triple tracer.

Figure 1.

Triple tracer studies of carbohydrate turnover for meals of varying compositions.

Figure 2.

Modeling framework of proposed Variable Hump (VH) Model: After the peak, two models are used to capture different meal shapes.

Figure 3.

Some curves are better described by a decay behavior (left), whereas others a drop behavior (right). The left panel shows the least-squares fits to Meal 2, while the right panel shows fits to Meal 4. Absorption has units of µmol/kg (FFM)/min. FFM: fat free mass.

Figure 4.

Evolution of predicted meal size $\left(\mathrm{\mu }\pm 1\mathrm{\sigma }\right)$ over time into the meal. Errors are single dots and symmetric confidence bounds are lines (dash-dotted: Model 1, dash: Model 2, dotted: Model 3, solid: VH Model). The VH Model adapts to the meal while other models either fail to (Meal 4) or overestimate (Meal 3). VH: Variable Hump.

Figure 5.

Residuals of estimated model-absorption peak time from time of true absorption peak (blue dot: Model 1, gray +: Model 2, red x: Model 3, black arrowhead: VH Model, #: Assumed constant peak time of 32 minutes). An arrow connects the assumed constant peak time (32 minutes) to the VH Model estimated peak time. VH: Variable Hump.

Figure 6.

Agreement between symmetric confidence intervals of a theoretical width with the actual percentage of readings within the interval.

Figure 7.

Since underestimation of meal sizes is preferred to overestimation, one may choose to deliver insulin assuming a meal size determined from the lower bound of predicted meal size (µ-1σ). Compensation for 75% of the meal is shown on the left axis and as blue data. The total insulin compensation is shown on the right axis and as red data.