Model predictive control of type 1 diabetes: an in silico trial

Abstract

Background: The development of artificial pancreas has received a new impulse from recent technological advancements in subcutaneous continuous glucose monitoring and subcutaneous insulin pump delivery systems. However, the availability of innovative sensors and actuators, although essential, does not guarantee optimal glycemic regulation. Closed-loop control of blood glucose levels still poses technological challenges to the automatic control expert, most notable of which are the inevitable time delays between glucose sensing and insulin actuation.

Methods: A new in silico model is exploited for both design and validation of a linear model predictive control (MPC) glucose control system. The starting point is a recently developed meal glucose-insulin model in health, which is modified to describe the metabolic dynamics of a person with type 1 diabetes mellitus. The population distribution of the model parameters originally obtained in healthy 204 patients is modified to describe diabetic patients. Individual models of virtual patients are extracted from this distribution. A discrete-time MPC is designed for all the virtual patients from a unique input-output-linearized approximation of the full model based on the average population values of the parameters. The in silico trial simulates 4 consecutive days, during which the patient receives breakfast, lunch, and dinner each day.

Results: Provided that the regulator undergoes some individual tuning, satisfactory results are obtained even if the control design relies solely on the average patient model. Only the weight on the glucose concentration error needs to be tuned in a quite straightforward and intuitive way. The ability of the MPC to take advantage of meal announcement information is demonstrated. Imperfect knowledge of the amount of ingested glucose causes only marginal deterioration of performance. In general, MPC results in better regulation than proportional integral derivative, limiting significantly the oscillation of glucose levels.

Conclusions: The proposed in silico trial shows the potential of MPC for artificial pancreas design. The main features are a capability to consider meal announcement information, delay compensation, and simplicity of tuning and implementation.

Keywords: artificial pancreas; diabetes; model predictive control; simulation; virtual patients.

Figure 1

Experiments 1–8: scatter plots of Min_Glycemia vs Max_Glycemia. Each plot compares the results of two experiments. A, C, and E refer to MPC (°, experiment 1; □, experiment 2; +, experiment 3; ×, experiment 4), whereas B, D, and F refer to PID control (°, experiment 5; □, experiment 6; +, experiment 7; ×, experiment 8). Well-regulated patients should stay close to the lower left corner.

Figure 2

Min_Glycemia vs Max_Glycemia during regulation for experiment 2 with the individually tuned values of q (full dot) and with same values of q scaled by the constant factor 0.8 (star-circle).

Figure 3

Box plots for LBGI and HBGI for experiments 1–8 during both commutation (“c”) and regulation (“r”) periods.

Figure 4

Subject 36: experiment 2 (MPC, continuous line) and experiment 6 (PID, dashed line).

Figure 5

Scatter plots of Min_Glycemia vs Max_Glycemia for experiments 2 (•) and 6 (°).