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

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

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

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

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

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

Sensitivity to Noise Need to use optimal estimation techniques…

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

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

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

State Estimation Results Can achieve better KF results…

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

State Estimation Results – Revised KF

Hypoglycemia Prediction Choleau et al. (2002)

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

Hypoglycemia Prediction Using our Kalman Filter-based approach

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

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.

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

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

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

Improved Meal Effect Prediction (ramp)

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

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)

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

Estimation – More Complex

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

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

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

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

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