Coordinated basal-bolus infusion for tighter postprandial glucose control in insulin pump therapy

Abstract

Background: Basal and bolus insulin determination in intensive insulin therapy for type 1 diabetes mellitus (T1DM) are currently considered independently of each other. A new strategy that coordinates basal and bolus insulin infusion to cope with postprandial glycemia in pump therapy is proposed. Superior performance of this new strategy is demonstrated through a formal analysis of attainable performances in an in silico study.

Methods: The set inversion via interval analysis algorithm has been applied to obtain the feasible set of basal and bolus doses that, for a given meal, mathematically guarantee a postprandial response fulfilling the International Diabetes Federation (IDF) guidelines (i.e., no hypoglycemia and 2 h postprandial glucose below 140 mg/dl). Hypoglycemia has been defined as a glucose value below 70 mg/dl. A 5 h time horizon has been considered for a 70 kg in silico T1DM subject consuming meals in the range of 30 to 80 g of carbohydrates.

Results: The computed feasible sets demonstrate that current separated basal/bolus strategy dramatically limits the attainable performance. For a nominal basal of 0.8 IU/h leading to a basal glucose of approximately 100 mg/dl, IDF guidelines cannot be fulfilled for meals greater than 50 g of carbohydrates, independent of the bolus insulin computed. However, coordinating the basal and bolus insulin delivery can achieve this. A decrement of basal insulin during the postprandial period is required together with an increase in bolus insulin, in appropriate percentages, which is meal dependent. After 3 h, basal insulin can be restored to its nominal value.

Conclusions: The new strategy meets IDF guidelines in a typical day, contrary to the standard basal/bolus strategy, yielding a mean 2 h postprandial glucose reduction of 36.4 mg/dl without late hypoglycemia. The application of interval analysis for the computation of feasible sets is demonstrated to be a powerful tool for the analysis of attainable performance in glucose control.

Keywords: glucose control; insulin pump therapy; interval analysis; set inversion; type 1 diabetes mellitus.

Figure 1.

Illustration of inner and outer subpaving for a patient with 1:14 I:C and a 60 g meal. The inner subpaving, corresponding to the collection of rectangles in blue, is guaranteed to contain only solutions of the posed constraint satisfaction problem. Any combination in the blue zone will thus lead to fulfillment of the IDF guidelines in this case. The outer subpaving is given by the blue and red rectangles. Its complementary set (in white) is guaranteed to contain only nonsolutions of the constraint satisfaction problem. Any combination from this set will violate the IDF guidelines in this case. The behavior of combinations in the boundary given by the red rectangles (set difference between outer and inner subpavings) cannot be known a priori. This boundary contains the boundary of the actual solution set X and can be made as thin as wanted with higher computational cost. A lower bound of 0.05 IU/h is considered for basal insulin rate.

Figure 2.

Basics of the SIVIA algorithm: a box in the input space is classified as true if its image under the map f fulfills the constraints defined on the output space for all its elements (in blue); a box is classified as false if its image violates the constraints for all its elements (in white); and a box is classified as indeterminate otherwise. An indeterminate box will be divided into two boxes, with the process repeated for each sub-box.

Figure 3.

Computing the inner and outer subpaving: (A) a box in the input space is classified as true if all the possible glucose responses for all basal–bolus combinations in the box, computed by an interval simulator of the Hovorka model, fulfill the constraint, and (B) a box is classified as false if all the possible glucose excursions violate the constraint as determined by the interval simulator. In any other case (some trajectories fulfill while some others do not), the box is indeterminate. The results shown correspond to a patient with 1:14 I:C after a meal of 60 g of carbohydrates and initial normoglycemia (90.82 mg/dl). International Diabetes Federation guidelines constraints are superimposed in red.

Figure 4.

Postprandial glucose in a 5 h time horizon for a patient with 1:14 I:C after a meal of 60 g of carbohydrates, initial normoglycemia, and different basal–bolus combinations contained (A) in the inner subpaving and (B) outside the outer subpaving. The graph on the left shows the basal–bolus combinations selected. The graph on the right shows the corresponding glucose time profiles coded by color. International Diabetes Federation guidelines constraints are superimposed in red.

Figure 5.

Normalized feasible sets for a meal of 30 to 80 g of carbohydrates and initial normoglycemia. It is considered that bolus insulin is given at mealtime, and basal is kept constant for 5 h. All basal–bolus combinations in the blue region will lead to the fulfillment of the IDF guidelines in a 5 h period, according to the model. Combinations along the solid green line will lead to the same total insulin delivered as the standard strategy. Dotted green lines correspond to total insulin with an excess/defect of 10% the nominal bolus.

Figure 6.

Effect of the duration of the decrement in basal insulin for postprandial control in a 24 h simulation. The nominal basal is 0.8 IU/h, and the I:C is 1:14. A meal of 60 g of carbohydrates is given at time zero. According to the computed feasible set, a bolus 55% greater than the standard is infused simultaneously, and basal is decreased to 20% the nominal value for 2 to 5 h. Constraints considered in the calculation of the feasible sets are superimposed as a thick red line.

Figure 7.

Plasma insulin concentration under the conditions described in Figure 6. Plasma insulin concentration for the standard therapy (nominal basal and nominal bolus) is also shown as a dotted line.

Figure 8.

Comparison of the coordinated basal–bolus and the standard strategy in a three-meal scenario. Breakfast is given at 7:00 (40 g of carbohydrates), lunch at 12:00 (60 g), and dinner at 20:00 (60 g). The top figure shows the obtained glucose profiles for the standard strategy (in red) and the new strategy with basal–bolus coordination (in blue). Meal events are indicated with green triangles. Imposed IDF guidelines are shown as a thick red line. Figures in the middle and at the bottom show the basal infusion profile and bolus insulin dose, respectively. A nominal basal of 0.8 IU/h and a I:C of 1:14 are used for the standard strategy. For basal–bolus coordination, the following selection has been done: nominal basal × 0.4 and nominal bolus × 1.6 for breakfast and nominal basal × 0.2 and nominal bolus × 1.55 for lunch and dinner.