Algorithms for a closed-loop artificial pancreas: the case for proportional-integral-derivative control

Abstract

Closed-loop insulin delivery continues to be one of most promising strategies for achieving near-normal control of blood glucose levels in individuals with diabetes. Of the many components that need to work well for the artificial pancreas to be advanced into routine use, the algorithm used to calculate insulin delivery has received a substantial amount of attention. Most of that attention has focused on the relative merits of proportional-integral-derivative versus model-predictive control. A meta-analysis of the clinical data obtained in studies performed to date with these approaches is conducted here, with the objective of determining if there is a trend for one approach to be performing better than the other approach. Challenges associated with implementing each approach are reviewed with the objective of determining how these approaches might be improved. Results of the meta-analysis, which focused predominantly on the breakfast meal response, suggest that to date, the two approaches have performed similarly. However, uncontrolled variables among the various studies, and the possibility that future improvements could still be effected in either approach, limit the validity of this conclusion. It is suggested that a more detailed examination of the challenges associated with implementing each approach be conducted.

Figure 1.

Comparison of initial PID and MPC studies. (A) PID study 1 conducted at University of California, Los Angeles without meal bolus; studies 2 and 3 conducted at Yale with (semi-closed loop) and without (closed loop) one-third meal bolus (randomized); and study 4 conducted at City of Hope with fixed meal bolus (2 U). (B) Model-predictive control study 1 conducted at University of Virginia, study 2 conducted in Padova,¹⁴ and studies 3 and 4 conducted at Boston University/Massachusetts General Hospital. Breakfast size in study 4 is assumed to be the same as in study 3, as per-day carbohydrate load was reported without delineating separate amounts by meal. (C) Mean and standard deviation of individual breakfast meals shown in (A) and (B). (D) Mean and 95% confidence interval normalized to meal carbohydrate amount. UCLA, University of California, Los Angeles; CL, closed loop; SCL, semi-closed loop; COH, City of Hope; S1, study1; S2, study 2; S3, study 3; S4, study 4; UVA, University of Virginia; BU/MGH, Boston University/Massachusetts General Hospital; SD, standard deviation; CI, confidence interval; CHO, carbohydrate.

Figure 2.

(A) Effect of fat content in closed-loop PID meal response(high-fat dinner shown in green curve, with low-fat dinner with identical carbohydrate shown in blue) together with response obtained with MPC in a study by Russell and coauthors without use of meal boluses (black curve). (B) Same MPC curve from the study by Russell and coauthors shown in panel A (black line) together with MPC curves obtained from studies performed by Hovorka and coauthors^, with open-loop meal boluses. (C) Use of glucagon in closed-loop control fading memory proportional derivative control with and without glucagon (blue and light blue lines) with PID control obtained with insulin feedback and MPC results without meal bolus.S4, study 4; BU/MGH, Boston University/Massachusetts General Hospital; HFD, high-fat dinner; LFD, low-fat dinner; FMPD, fading memory proportional derivative; GN, glucagon; COH, City of Hope; D, dinner; B, breakfast; L, lunch.

Figure 3.

(A) Median and IQR range for dinner and nighttime control effected with PID_IFB algorithm4 superimposed with median and IQR for the enhance control to range eCTR study performed by Breton and coauthors and MD-Logic nighttime-only study performed by Phillip and coauthors. (B) Median and IQR for nighttime glucose values reported in the MD-Logic study by Phillip and coauthors. (C) Standard control-to-range versus eCTR study performed by Breton and coauthors. CI, confidence interval.

Figure 4.

Use of model simulation to compare PID to model-based algorithms (A) PID versus MPC per se and (B) PID versus linear-quadratic-Gaussian control. LQG, linear quadratic Gaussian.

Figure 5.

(A) Differences between model used for simulation (red curve) and model used for control (blue curve) assuming University of Virginia simulation model and low second-order model used for control (blue curve). (B) Residual runs analysis indicating statisticaly significant residuals that may or may not be clinically or control relevant (see text). UVa, University of Virginia.