Embedded Model Predictive Control for a Wearable Artificial Pancreas

Abstract

While artificial pancreas (AP) systems are expected to improve the quality of life among people with type 1 diabetes mellitus (T1DM), the design of convenient systems that optimize the user experience, especially for those with active lifestyles, such as children and adolescents, still remains an open research question. In this work, we introduce an embeddable design and implementation of model predictive control (MPC) of AP systems for people with T1DM that significantly reduces the weight and on-body footprint of the AP system. The embeddable controller is based on a zone MPC that has been evaluated in multiple clinical studies. The proposed embedded zone MPC features a simpler design of the periodic safe zone in the cost function and the utilization of state-of-the-art alternating minimization algorithms for solving the convex programming problems inherent to MPC with linear models subject to convex constraints. Off-line closed-loop data generated by the FDA-accepted UVA/Padova simulator is used to select an optimization algorithm and corresponding tuning parameters. Through hardware-in-the-loop in silico results on a limited-resource Arduino Zero (Feather M0) platform, we demonstrate the potential of the proposed embedded MPC. In spite of resource limitations, our embedded zone MPC manages to achieve comparable performance of that of the full-version zone MPC implemented in a 64-bit desktop for scenarios with/without meal-disturbance compensations. Metrics for performance comparison included median percent time in the euglycemic ([70, 180] mg/dL range) of 84.3% vs. 83.1% for announced meals, with an equivalence test yielding p = 0.0013 and 66.2% vs. 66.0% for unannounced meals with p = 0.0028.

Keywords: Artificial pancreas; biomedical control; control applications; convex optimization; embedded systems; model predictive control; safety-critical control.

Fig. 1:

Periodic zone for embedded zone MPC. The orange shade depicts the glucose zone in the day time (7AM to 11PM) and the blue shade depicts the zone at night (11PM to 7AM).

Fig. 2:

Feasible combinations of the maximum number of iterations N and the tuning parameter τ for the [A] FAMA algorithm, [B] FADMM algorithm.

Fig. 3:

Architecture of hardware-in-the-loop evaluation.

Fig. 4:

In silico protocols for performance evaluation. The protocols start at 4 PM on Day 1 and end at 9 AM on Day 3. A 75 g CHO dinner accompanied with a 40 g CHO is provided on Day 1. Day 2 features a hypoglycemia challenge together with breakfast, lunch and dinner of [60, 75, 75] g CHO, respectively. The meal boluses are carbohydrate contents of the meals in g-CHO, and the percentages indicate what percent of the meal carbohydrate content is announced.

Fig. 5:

Results for announced meals. Blue, green and purple triangles denote meals of 40 gCHO, 60 gCHO, and 75 gCHO, respectively, and the orange triangle denotes a 2-unit unannounced insulin bolus. The mean values for the 10 patients are plotted using continuous red and blue curves for the embedded zone MPC and the MATLAB-implemented zone MPC proposed in [39], while the corresponding one standard deviations are plotted using dotted red and continuous purple curves.

Fig. 6:

Results for unannounced meals. Keys are the same as Fig. 5.