Meal Detection and Meal Size Estimation for Type 1 Diabetes: a Variable State Dimension Approach 2015 DSCC Columbus Oct. 30 Jinyu Xie, Prof. Qian Wang Department of Mechanical and Nuclear Engineering The Pennsylvania State University, University Park

Outlines Motivation Modeling Variable State Dimension Approach Meal Detection and Meal Size Estimation Simulation Results Conclusion 2 of 24

Motivation Controllers with meal or manual meal bolus showed larger amount of time in target range (70 – 180 mg/dL) than fully automated controllers [1] [2]. A study by Burdick et al[3]: a group of young patients aged from 7 to 20 missed 2 mealtime boluses per week on average. Artificial Pancreas Patient Glucose Sensor Model and Controller Bio-Mechanical Interface Insulin Pump Meal Announcement (Feed-forward) Insulin Delivery Insulin Dosage Glucose Measurement Data Processing Insulin Bolus = Meal/IC Ratio Meal Detection & Estimation 3 of 24

Literature Review 4 of 24

General idea Insulin Meal Internal Factors (Renal, Liver, etc.) Blood Glucose (BG) Measurement = Insulin Effect Meal Intake Effect + + Noise + Same Insulin Injection History A general glucose dynamic model: For models without meal input, meal detection is possible while meal size estimation is not available. The accuracy of meal size estimation depends on the quality of the model. 5 of 24

- Glucose Autoregressive Component - Insulin Regression Component - Carbohydrate Regression Component Modeling Model Parameters: ζ : True Blood Glucose (BG) y : BG Measurement v : Filtered Insulin Input w: Filtered Carbohydrate Input η : Process Noise (model noise) ξ : Measurement Noise 6 of 24 A linear regressive model

Modeling FIR Filter for Insulin/Carbohydrate Absorption Profile Unit Impulse Response General Shaping. Each patient can be personalized by 7 of 24

Modeling Parameter Training Scenario, suggested by Parcival et al [9] Data generated by the FDA approved UVa/Padova Simulator 8 of 24

StateInsulin EffectMeal Effect State Space Representation are assumed to be White Gaussian Noise. ζ : True Blood Glucose (BG) y : BG Measurement v : Filtered Insulin Input w: Filtered Carbohydrate Input η : Process Noise ξ : Measurement Noise Parameters obtained by the training. 9 of 24

Monitoring the innovation (residual) Variable State Dimension (VSD) Quiescent Model Maneuvering Model Maneuver Detected Maneuver Terminated - An Adaptive Estimation Algorithm Linear Kalman Filter is run and switched between the two models. Monitoring the augmented disturbance 10 of 24

Algorithm Overview Monitoring a sliding window of data. Quiescent Model. Monitoring the innovation Maneuvering Model. Monitoring the augmented disturbance Meal occurrence time is assumed to be at the beginning of the sliding window. Meal Size Estimation starts right after the meal is detected, and evolves as new observation comes. 11 of 24

Meal (Maneuver) Detection Monitoring the innovation Hypothesis Test : is White Gaussian Process. Rectangular Weighted Window Exponential Weighted Window Test Statistics with sliding window Window Length = s - Fading Factor Effective Window Length where 12 of 24 where

Meal (Maneuver) Detection (cont’d) is rejected, if, where c is the confidence level. Hypothesis Test : is White Gaussian Process. If is true, Quiescent Maneuvering H 0 rejected H 0 accepted 13 of 24 Meal is detected when H 0 is rejected

Kalman Filter Initialization at Maneuvering Stage Maneuver Detected Assumed maneuver onset time - Estimation with quiescent model - Estimation with maneuvering model of 24 Estimated State and State Covariance Initialization:

Kalman Filter Initialization at Maneuvering Stage (cont’d) 15 of 24 State Variance Initialization:

Meal Size Estimation Assumptions: Only one meal for one maneuver (multiple meals will be considered as one meal) The meal is an impulse lasting only one time step Meal Effect Γ(w(t)) Disturbance d(t) = 16 of 24

Maneuver Termination Monitoring the augmented disturbance state Hypothesis Test H 0 : is a White Gaussian Process If is true, H 0 is accepted, if, where c is the confidence level. where Effective Window Length Maneuvering Quiescent H 0 rejected H 0 accepted 17 of 24 Maneuver is terminated when H 0 is accepted

Simulation Platform Data generated by the FDA approved UVa/Padova simulator: Noise-free Plasma Blood Glucose (Plasma) Glucose measured by Continuous Glucose Monitor (CGM) 18 of patients, 48 hour

Simulation Results - Plasma Adolescent #005 - Plasma Equal trust on the model and the measurement. Without meal information With meal information 19 of 24 VSDIGIMG 0.52 (0.34)0.28 (0.52)0.45 (0.43) All 30 subjects Mean (Standard Deviation) Red - No meal information, Black – full meal information

Simulation Results - CGM Adolescent #005 - CGM Relying more on the model (due to the sensor noise) Without meal information With meal information 20 of 24 VSDIGIMG 0.35 (0.34)-0.07 (0.77)0.37 (0.44) All 30 subjects Mean (Standard Deviation) Red - No meal information, Black – full meal information

Meal Detection Performance Dassau et al (CGM) [4] Lee & Bequette (Not known) [6] Cameron & Niemeyer (CGM) [8] VSD (Plasma) VSD (CGM) Meal detection time since a meal starts (min) (±10)34(±19) Meal detection time since meal onset* (min) -3181(±10)8(±19) Sensitivity -82%-97%95% False alarm rate -7.6%-10%17% * Meal onset is defined as the time when the glucose level rises by 4mg/dL after meal [6]. For our data, average meal onset time: 21 min (Plasma), 26 min (CGM) Sensitivity = TP/(TP+FN) Patient had a mealPatient did not have a meal Detector says yesTrue Positive (TP)False Positive (FP) Detector says noFalse Negative (FN)True Negative (TN) False alarm rate = FP/(TP+FP) 21 of 24

Meal Size Estimation Performance 22 of 24

Conclusion and Future Work A Kalman Filter switches between quiescent state model and maneuvering state model (an adaptive estimator) 86% increase in goodness of fit (R 2 ) compared to Kalman Filter without model switching (both no meal information available) Better or comparable detection performance <13% meal size estimation error rate Future work on online estimation and control Possible extension to detect and estimate physical activities 23 of 24

Reference [1] Doyle, Francis J., Lauren M. Huyett, Joon Bok Lee, Howard C. Zisser, and Eyal Dassau. "Closed-loop artificial pancreas systems: engineering the algorithms." Diabetes care 37, no. 5 (2014): [2] Wang, Q., J. Xie, P. Molenaar, and J. Ulbrecht. “Model predictive control for type 1 diabetes based on personalized linear time-varying subject model consisting of both insulin and meal inputs: an in silico evaluation.” Journal of Diabetes Science and Technology, 9(4) (2015): [3] Burdick, Jonathan, H. Peter Chase, Robert H. Slover, Kerry Knievel, Laura Scrimgeour, Aristides K. Maniatis, and Georgeanna J. Klingensmith. "Missed insulin meal boluses and elevated hemoglobin A1c levels in children receiving insulin pump therapy." Pediatrics 113, no. 3 (2004): e221-e224. [4] Dassau, Eyal, B. Wayne Bequette, Bruce A. Buckingham, and Francis J. Doyle. "Detection of a Meal Using Continuous Glucose Monitoring Implications for an artificial β-cell." Diabetes care 31, no. 2 (2008): [5] Lee, Hyunjin, and B. Wayne Bequette. "A closed-loop artificial pancreas based on model predictive control: Human-friendly identification and automatic meal disturbance rejection." Biomedical Signal Processing and Control 4.4 (2009): [6] Lee, Hyunjin, Bruce A. Buckingham, Darrell M. Wilson, and B. Wayne Bequette. "A closed-loop artificial pancreas using model predictive control and a sliding meal size estimator." Journal of diabetes science and technology 3, no. 5 (2009): [7] Cameron, Fraser, Günter Niemeyer, and Bruce A. Buckingham. "Probabilistic evolving meal detection and estimation of meal total glucose appearance."Journal of diabetes science and technology 3.5 (2009): [8] Fraser Cameron and Gunter Niemeyer. Predicting blood glucose levels around meals for patients with type i diabetes. In ASME 2010 Dynamic Systems and Control Conference, pages 289–296. American Society of Mechanical Engineers, [9] Matthew W Percival, Wendy C Bevier, Youqing Wang, Eyal Dassau, Howard C Zisser, Lois Jovanoviˇc, and Francis J Doyle. Modeling the effects of subcutaneous insulin administration and carbohydrate consumption on blood glucose. Journal of diabetes science and technology, 4(5):1214–1228, of 24

Online Basal-Bolus Control 25 of 24