Zone model predictive control: a strategy to minimize hyper- and hypoglycemic events

Abstract

Background: Development of an artificial pancreas based on an automatic closed-loop algorithm that uses a subcutaneous insulin pump and continuous glucose sensor is a goal for biomedical engineering research. However, closing the loop for the artificial pancreas still presents many challenges, including model identification and design of a control algorithm that will keep the type 1 diabetes mellitus subject in normoglycemia for the longest duration and under maximal safety considerations.

Method: An artificial pancreatic beta-cell based on zone model predictive control (zone-MPC) that is tuned automatically has been evaluated on the University of Virginia/University of Padova Food and Drug Administration-accepted metabolic simulator. Zone-MPC is applied when a fixed set point is not defined and the control variable objective can be expressed as a zone. Because euglycemia is usually defined as a range, zone-MPC is a natural control strategy for the artificial pancreatic beta-cell. Clinical data usually include discrete information about insulin delivery and meals, which can be used to generate personalized models. It is argued that mapping clinical insulin administration and meal history through two different second-order transfer functions improves the identification accuracy of these models. Moreover, using mapped insulin as an additional state in zone-MPC enriches information about past control moves, thereby reducing the probability of overdosing. In this study, zone-MPC is tested in three different modes using unannounced and announced meals at their nominal value and with 40% uncertainty. Ten adult in silico subjects were evaluated following a scenario of mixed meals with 75, 75, and 50 grams of carbohydrates (CHOs) consumed at 7 am, 1 pm, and 8 pm, respectively. Zone-MPC results are compared to those of the "optimal" open-loop preadjusted treatment.

Results: Zone-MPC succeeds in maintaining glycemic responses closer to euglycemia compared to the "optimal" open-loop treatment in te three different modes with and without meal announcement. In the face of meal uncertainty, announced zone-MPC presented only marginally improved results over unannounced zone-MPC. When considering user error in CHO estimation and the need to interact with the system, unannounced zone-MPC is an appealing alternative.

Conclusions: Zone-MPC reduces the variability of control moves over fixed set point control without the need to detune the controller. This strategy gives zone-MPC the ability to act quickly when needed and reduce unnecessary control moves in the euglycemic range.

Figure 1.

Proposed protocol that facilitates the separation of meal and insulin effects on blood glucose.

Figure 2.

Insulin and meal inputs are mapped through second-order transfer functions and, as a result, are spread and separated. (A) Typical input data collected from T1DM subjects: meals and insulin are assigned as pulses over relatively close discrete time instances. (B) Result of transformed inputs, where each pulse becomes a prolonged time response.

Figure 3.

Illustration of zone-MPC in the context of diabetes; zone-MPC is typically divided into three different zones. The permitted range is the control target and is defined by upper and lower bounds. For example, green dots indicate predicted glycemic values in the permitted range. The upper zone represents undesirable high predicted glycemic values, which are represented by orange dots. The lower zone represents undesirable low predicted glycemic values that represent the hypoglycemic zone or a prehypoglycemic protective area that is a low alarm zone. Zone-MPC optimizes predicted glycemia by manipulating insulin CM to stay in the permitted zone under specified constrains.

Figure 4.

Model prediction structure in zone-MPC includes two parts. First is second-order transfer function that is unvaried over the different subjects. Second is an individualized discrete model that predicts glycemia given mapped input data. The overall prediction is a result of raw data containing past outputs, inputs, and future manipulated CM going through transfer functions and mapped into new states (I_map, M_map) into the individualized discrete model to give the glycemia prediction.

Figure 5.

Comparison between experiments 1 to 4 as applied to subject #5 of the UVa\Padova metabolic simulator. Experiments 1 to 4 are represented by gray triangles and red, blue, and black circles, respectively. Glycemic response (A) and insulin administration (B) are depicted. The dashed black line indicates 60 and 180 (mg/dl). Insulin administration is presented in a semilogarithmic scale to include open-loop bolus treatment and controller insulin administrations in a single plot.

Figure 6.

Population result of experiments 1 to 4, (A) to (D), respectively, on 10 UVa\Padova metabolic simulator subjects. Gray area bounds are minimum and maximum points at each given time instant, the green solid line is the mean glycemic response, and dashed red lines are mean glycemic ± SD at each time instant. Glucose distribution for experiments 1 to 4 is presented in the histogram plots.

Figure 7.

Comparison among experiments 1, 5, 6, and 7 when applied to subject #5 of the metabolic simulator. Experiments 1, 5, 6, and 7 are represented by gray triangles and red, blue, and black circles, respectively. Glycemic response (A) and insulin administration (B) are depicted. Insulin administration is presented in a semilogarithmic scale to include open-loop bolus treatment and controller insulin administrations in a single plot.

Figure 8.

Population result of experiments 1, 5, 6, and 7 on 10 UVa\Padova subjects. Gray area bounds are minimum and maximum points at each given time instant, the green solid line is the mean glycemic response, and dashed red lines are mean glycemic ± SD at each time instant. Glucose distribution for experiments 1, 5, 6, and 7 is presented in the histogram plots.

Figure 9.

Population result of experiments 2, 8, and 9 on 10 UVa\Padova subjects. Gray area bounds are minimum and maximum points at each given time instant, the green line is the mean glycemic response, and dashed red lines are mean glycemic ± SD at each time instant. Glucose distribution for experiments 2, 8, and 9 is presented in the histogram plots.