1. Blood/Subcutaneous Glucose Dynamics Estimation Techniques
Blood Glucose Monitoring and Control based on Subcutaneous Measurements
Motivation
Subcutaneous Sensor, Desire Blood Glucose Values
Blood/Subcutaneous Glucose Dynamics
Estimation Techniques
Model and Controller Design
Unique Challenges: Meal Disturbance Rejection
B. Wayne Bequette

2. Disclaimer Personal Background and Biases
Chemical Engineering
Process Control Focus
Chemical Process Applications
Estimation, Model Predictive Control
Biomedical Applications
Drug infusion during critical care
View of Glucose Sensing, Monitoring, Control
Focus has been on the “hard work” (developing a sensor)
Much less effort on applying advanced estimation and control

3. Blood/Subcutaneous Dynamics
Compartmental Model
Plasma
ISF
Rebrin et al. (1999)

4. Blood/Subcutaneous Glucose Dynamics
Rebrin et al. (1999)
Diffusion
Reaction
Schmidtke et al. (1998)
Standard first-order ODE

5. Response – “Lag”
After Rebrin et al. (1999)

6. Estimate Blood Glucose (Rebrin et al.)
Solve for u (blood glucose)
based on y (s.c. glucose)
Finite differences

7. Sensitivity to Noise
Need to use optimal estimation techniques…

8. State Estimation: Basic Concept
s.c. glucose
measurement
State estimates:
s.c. glucose
blood glucose
observer
gain
dynamic
model + _
s.c. glucose
estimate
sensor
model

9. Optimal Estimation - Kalman Filter
Measurement noise vs. process noise (disturbances)
Which is causing a particular measurement change?
If little measurement noise
Trust measurement more than model
If much measurement noise
Trust model more than measurement
Estimate unmeasured states
Blood glucose based on s.c. measurement, for example

10. Kalman Filter w/Augmented State
5/3/2019
Kalman Filter w/Augmented State
noise
s.c. glucose
blood glucose
Augmented state (includes
blood glucose)
Measured
s.c. glucose
Predictor-corrector equations:
Aug. state
estimate
Kalman gain
Measured s.c. glucose

11. State Estimation Results
Can achieve better KF results…

12. Ramp Change in Blood Glucose
5/3/2019
Ramp Change in Blood Glucose
s.c. glucose
noise
blood glucose
change in bg
augmented state (includes
blood glucose and its
rate of change)
measured
s.c. glucose

13. State Estimation Results – Revised KF

14. Hypoglycemia Prediction
Choleau et al. (2002)

15. Prediction of Blood Glucose and Detection of Hypoglycemia
Solve for time to reach critical glucose
(with proper reality checks…)

16. Hypoglycemia Prediction
Using our Kalman Filter-based approach

17. Automated Feedback Control
glucose setpoint
controller
pump
patient
Sensor (Therasense)

18. Model Predictive Control
Find current and future insulin infusion rates that best meet a desired future glucose trajectory. Implement first “move.”
Correct for model mismatch (estimate states), then perform new optimization.

19. MPC Issues Type of Model Model Update
Linear differential equations
Model Update
Additive “correction”?
Explicit disturbance (meal) or parameter estimation?
Error Due to Disturbance or Noise?
Future Prediction?
Classical MPC - assume constant for future
Sensors & Estimation
Measure subcutaneous, control blood glucose

20. Constant Disturbance Assumption (Classical)
Additive step
output
Glucose
conc.
Additive step
input
Insulin
infusion

21. Simulation Study Simulated Type I Diabetic
Minimal Model - Bergman (3-state)
Lehman and Deutsch (1992) Meal Model
Absorption into circulation
Gastric
emptying

22. Improved Meal Effect Prediction (ramp)

23. Blood/Subcutaneous Glucose Dynamics Estimation Techniques
Summary
Blood/Subcutaneous Glucose Dynamics
Compartmental model
Estimation Techniques
“Inversion” vs. Kalman Filter
Model and Controller Design
Unique Challenges: Meal Disturbance Rejection

24. MPC Literature Review Dogs, Venous Blood, Glucose+Insulin Delivery
Kan et al. (2000)
Simulation, s.c. Sensor + Delivery, ANN
Trajanoski and Wach (1998)
Simulation, i.v.-i.v., EFK-based MPC
Parker et al. (1999)
Simulation, i.v.-s.c., EKF-based MPC
Lynch and Bequette (2002)
Simulation, s.c.-s.c., EKF-based MPC
Lynch (2002)

25. Optimal Estimation - Kalman Filter
Measurement noise vs. process noise (disturbances)
If little measurement noise
Trust measurement more than model
If much measurement noise
Trust model more than measurement
Estimate unmeasured states
Blood glucose based on s.c. measurement, for example

26. Estimation – More Complex

27. Simulation Study Using s.c. Sensor
Simulated Type I Diabetic
19 Differential Equations (Sorenson, 1985) - Extended
Model for Estimator/Controller
Modified Bergman “minimal model”
Parameters fit to Sorenson response
Augmented equation for meal disturbance

28. Simulation Results - s.c. Sensor Degradation
Motivates use of additional blood capillary measurement for s.c. sensor calibration
50% sensor sensitivity decrease over 3 days

29. Simulation results: Sensor compensation
5% s.c. noise (s.d. = 3.8 mg/dl) 2% capillary blood noise (s.d. =1.6 mg/dl)
Sensor degradation (50% over 3 days)
Sensitivity estimate

30. Summary Kalman Filter (estimation)-based MPC
Disturbance (meal) estimation
Improved disturbance prediction
Low-order linear model, high-order patient
State estimation: measure s.c., estimate blood glucose
Estimate sensor sensitivity with capillary blood measurement
Dual rate Kalman Filter
Future
Multiple Models

31. Kalman Filter w/Augmented States
5/3/2019
Kalman Filter w/Augmented States
Augmented state (includes meal disturbance)
Predictor-corrector equations:
Insulin infusion
Aug. state
estimate
Kalman gain
Measured s.c. glucose