Simulation Software for Assessment of Nonlinear and Adaptive Multivariable Control Algorithms: Glucose - Insulin Dynamics in Type 1 Diabetes

Abstract

A simulator for testing automatic control algorithms for nonlinear systems with time-varying parameters, variable time delays, and uncertainties is developed. It is based on simulation of virtual patients with Type 1 diabetes (T1D). Nonlinear models are developed to describe glucose concentration (GC) variations based on user-defined scenarios for meal consumption, insulin administration, and physical activity. They compute GC values and physiological variables, such as heart rate, skin temperature, accelerometer, and energy expenditure, that are indicative of physical activities affecting GC dynamics. This is the first simulator designed for assessment of multivariable controllers that consider supplemental physiological variables in addition to GC measurements to improve glycemic control. Virtual patients are generated from distributions of identified model parameters using clinical data. The simulator will enable testing and evaluation of new control algorithms proposed for automated insulin delivery as well as various control algorithms for nonlinear systems with uncertainties, time-varying parameters and delays.

Keywords: benchmark testbed process; biomedical application; multivariable simulator; nonlinear and adaptive model predictive control; time-varying uncertain nonlinear system.

Figures

Figure A - 1.

Comparison of the effects of exercise intensity on the exercise state variables for the proposed model and the reference model [97]: (a) three different levels of heart rate represent different exercise intensities; the E1(t) state variable to characterize the immediate effects of physical activity; and (c) the E2(t) state variable to describe the prolonged effects of physical activity. The exercise session is conducted over the first hour followed by several hours of post-exercise recovery period.

Figure 1.

The input-output framework of the multivariable simulator (mGiPsim) for T1D. Meal, insulin, and physical activity are user-specified inputs to the multivariable simulator that affect the simulated glucose dynamics and physiological variables. The mGiPsim software generates physiological variables that are measured by wearable sensors for use in mAP systems. Red text (dash-dot lines) indicates new features unique to the multivariable simulation environment, blue text (dashed line) is the typical metabolic simulation environment, and green text (dotted line) is the insulin and rescue carbohydrates manipulated by the control algorithm to regulate the simulated glucose dynamics.

Figure 2.

Main menu screen of the mGIPsim software graphical user interface. Buttons for meals (carbohydrate consumption), insulin, and exercise are used to access submenus and specify the relevant information for the simulation scenarios.

Figure 3.

Summary of the CGM, HR, and Basal Insulin Data Collected During the Clinical Experiments (MED: Median, IQR: Interquartile Range)

Figure 4.

The glucose kinetics, insulin action, and exercise subsystems including the immediate and long-lasting effects of physical activity on the glycemic dynamics. The blue circles denote the previously existing compartments in the reference glucose-insulin model [56], the orange circles are the augmented exercise compartments, and the orange dashed lines indicated the physical activity effects on glucose streams.

Figure 5.

Optimization results of the glucose-insulin model for a select subject (#2) with T1D involving diverse meals and physical activities throughout three days of clinical experiments.

Figure 6.

Optimization results for the physiological heart rate model for a select subject (#2) with T1D involving bouts of diverse exercises throughout three days of clinical experiments (treadmill – pink, bicycle – orange).

Figure 7:

Weighted Residuals for the Original Hovorka’s Model and the Proposed Extended Hovorka’s Model with Explicit Consideration of Physical Activity in the Glucose-Insulin Dynamics

Figure 8.

Blood glucose variations in response to meals and bouts of treadmill and stationary bike exercises for all virtual subjects in mGIPsim. The solid line in the top plot represents the mean of the glucose trajectories, and the shaded area denotes the standard deviation. The dashed line in the bottom plot represents the average basal insulin and the solid bars in the bottom plot represent the average bolus insulin administered to the virtual subjects.

Figure 9.

Comparison of actual and predicted EE for (a) treadmill and (b) stationary bike exercise.

Figure 10.

Comparison of actual and predicted ST for (a) treadmill and (b) stationary bike exercise.

Figure 11.

Mean and SD (shaded area) of the variations in glycemic dynamics for 20 virtual subjects caused by (a) different intensities of running at the same exercise duration, (b) different durations of running at the same exercise intensity, (c) different intensities of biking at the same exercise duration, and (d) different durations of biking at the same exercise intensity. Different running intensities are simulated with treadmill speeds of 3, 4, and 5 mph and an incline grade of 2% for 40 mins in duration. Different running durations are simulated with treadmill durations of 20 (cyan shaded area), 40 (cyan and yellow shaded areas), and 60 mins (cyan, yellow, and magenta shaded areas) and a speed and incline grade of 4 mph and 2%. Different biking intensities are simulated with stationary bike power of 40, 80, and 120 W for 40 mins in duration. Different biking durations are simulated with stationary bike durations of 20, 40, and 60 mins and a cycling power of 80 W. All exercise sessions are initiated at 09:00 from the same initial conditions.

Figure 12.

Mean and SD (shaded area) of the variations in heart rate dynamics for 20 virtual subjects caused by (a) different itensities of running at the same exercise duration, (b) different durations of running at the same exercise intensity, (c) different intensities of biking at the same exercise duration, and (d) different durations of biking at the same exercise intensity. Different running intensities are simulated with treadmill speeds of 3, 5, and 7 mph and an incline grade of 2% for 40 mins in duration. Different running durations are simulated with treadmill durations of 20 (cyan shaded area), 40 (cyan and yellow shaded areas), and 60 mins (cyan, yellow, and magenta shaded areas) and a speed and incline grade of 5 mph and 2%. Different biking intensities are simulated with stationary bike power of 40, 80, and 120 W for 40 mins in duration. Different biking durations are simulated with stationary bike durations of 20, 40, and 60 mins and a cycling power of 80 W. All exercise sessions are initiated at 09:00 from the same initial conditions.