1. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Model Predictive Control for Type 1 Diabetes Based on Personalized Linear Time-Varying Subject Model Consisting of both Insulin and Meal Inputs: in Silico Evaluation Qian Wang, Jinyu Xie Mechanical and Nuclear Engineering Peter Molenaar Human Development and Family Studies Jan Ulbrecht Biobehavioral Health and Medicine, Institute for Diabetes and Obesity The Pennsylvania State University University Park PA, 16802 2015 American Control Conference Chicago July 1 st – 3 rd, 2015 1 of 30MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

2. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsOverview 2 of 30  Background  Modeling  Control Design  Simulation Results  Conclusion MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

3. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Diabetes Mellitus Diabetes mellitus is a group of metabolic diseases characterized by hyperglycemia resulting from defects in insulin secretion, insulin action, or both. 3 of 30 Classificationβ-cell Destruction Insulin Secretion Insulin Resistance Treatment Type 1  MUST inject insulin Type 2  Diet, Exercise, Medication or insulin therapy Other typesGestational, Impaired Glucose Tolerance, etc. - Yes  - No MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

4. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Diabetes Mellitus Diabetes mellitus is a group of metabolic diseases characterized by hyperglycemia resulting from defects in insulin secretion, insulin action, or both. 4 of 30 Classificationβ-cell Destruction Insulin Secretion Insulin Resistance Treatment Type 1  MUST inject insulin Type 2  Diet, Exercise, Medication or insulin therapy Other typesGestational, Impaired Glucose Tolerance, etc. - Yes  - No MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

5. Artificial Pancreas MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions c 5 of 30 A closed-loop solution Patient Glucose Sensor Model and Controller Bio-Mechanical Interface Insulin Pump Dietary Information Insulin Delivery Insulin Command Glucose Measurement The Artificial Pancreas MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

6. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions 6 of 30 Literature Review Literature Review MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015 Challenges:  Insulin bolus is usually served with meal, making the identification of both inputs difficult [8]  Pre-training with insulin and meal served separately is proposed by Percival et al [8]. There are limits of pre-training. Current Control Design Online AdaptingMeal Input Physiological model based [1][2][3] No (fixed parameters, linearized) Yes Empirical model based [4][5][6][7] YesNo Goal of this paper: Design a controller  Taking full advantage of meal information,  Adapted online, pre-training not needed. Our prior work:  An empirical model with both insulin input and meal input has been developed.  Big improvement in glucose prediction has been seen when including meal input.

7. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsModeling 7 of 30 An autoregressive model with time-varying parameters where MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015 The order of the model is chosen as

8. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsModeling 8 of 30 A data-driven model with Time-Varying State-space model where Glucose Autoregression Component Insulin Inputs Meal Inputs MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015 The order of the model is chosen as

9. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsModeling 9 of 30 Finite Impulse Response Filter MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

10. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions 10 of 30 Modeling Parameter Estimation Define the I/O Relationship with MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015 Kalman Filter or Recursive Least Square with Forgetting Factor can be applied to estimate Θ(t).

11. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Control Design 11 of 30 Augmented State Space Representation: where - Control Input = Measured Insulin delivery - Accumulated contribution of carbohydrate intake to blood glucose level MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

12. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Control Design 12 of 30 Augmented State Space Representation: where MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015 ad

13. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Control Design 13 of 30 Control Objective 70~180 mg\dl>180 mg/dl<70 mg/dl HypoglycemiaHyperglycemia Euglycemia Dangerous (could be fatal) Safe Range Chronic Damage BG Level Avoid KeepMinimize MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015 Hard constraint on BG How? Control Objective Penalty in cost function on the deviation from target value

14. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Control Design 14 of 30 Controller Structure BG readings Historical insulin injection data Meal Intake Information Yes Insulin set to 0 No Insulin delivery Optimal Solution MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015 Estimator Insulin Pump Insulin Pump Shut- off Conditions Satisfied? MPC Solver BG Prediction Estimated Parameters

15. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Control Design 15 of 30 Inulin Pump Shut-off Conditions Insulin Pump Shut-off If True MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

16. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Control Design 16 of 30 Model Predictive Control (MPC) Optimization Problem subject to where Solution: MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

17. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsSimulation 17 of 30 Simulation Parameters Controller Design Parameters: Model Parameters Initialization: MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015

18. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsSimulation 18 of 30 FDA – approved UVa/Padova Simulator Subjects: 10 virtual diabetic adults Day 1Day 2 Time6 am 9 am1 pm5:30 pm8 pm9 am1 pm 6pm CHO (g)Start 507090255070 End CHO Rate (g/min)Start2.53.54.51.252.53.5End Simulation Scenario (1.5 Days) MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et alACC 2015 Experiments:  Meal Inputs vs No Meal Inputs  Robustness to meal info error  Empirical vs Physiological  Adding Sensor Noise

19. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsSimulation MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al19 of 30ACC 2015 Meal Inputs vs No Meal Inputs Meal Bolus (MB) + Correction Insulin (CI) Basal CR: Carbohydrate- Insulin Rate CF: Correction Factor * MPC-LTV is the controller we propose.  BB: Basal + Meal Bolus + Correction Insulin  MPC-LTV*: automatic, utilize the meal announcement  MPC-NoCarbLTV: Glucose-Insulin only, no meal inputs  MPC-NoCarbLTV + MealBolus

20. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsResults MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al20 of 30ACC 2015 Meal Inputs vs No Meal Inputs * CHO Rate (meal size/duration time (20 min))

21. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsResults MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al21 of 30ACC 2015 Meal Inputs vs No Meal Inputs

22. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsResults MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al22 of 30ACC 2015 Low BG Index (LBGI) High BG Index (HBGI) Risk Category LBGI≤1.1 -Minimal risk 1.1<LBGI≤2.5HBGI≤4.5Low risk 2.5<LBGI≤54.5<HBGI≤9Moderate risk LBGI>5HBGI>9High risk

23. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsResults MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al23 of 30ACC 2015 Robustness of MPC-LTV with respect to meal intake estimate error Day 1Day 2 9 am1 pm5:30 pm8 pm9 am1 pm η%*50 gη%*70 gη%*90 gη%*25 gη%*50 gη%*70 g

24. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsResults MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al24 of 30ACC 2015 Low BG Index (LBGI)High BG Index (HBGI)Risk Category LBGI≤1.1 -Minimal risk 1.1<LBGI≤2.5HBGI≤4.5Low risk 2.5<LBGI≤54.5<HBGI≤9Moderate risk LBGI>5HBGI>9High risk Robustness of MPC-LTV with respect to meal intake estimate error

25. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsResults MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al25 of 30ACC 2015 Empirical Model vs Physiological Model  MPC-PhysioModel [3] Same shut-off condition and MPC settings; Uses physiological model with fixed model parameters which is the average value among 10 virtual adults.

26. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsResults MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al26 of 30ACC 2015 Adding Sensor Noise  MPC-LTV-CGM-1 Use the CGM measurements Use the same initial parameter values as MPC-LTV  MPC-LTV-CGM-2 Use the CGM measurements Use the pre-trained parameters as the initial values Note: BG in the figure corresponding to noise-free plasma BG.

27. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsConclusion MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al27 of 30ACC 2015  MPC-LTV Controller has been validated, in silico  Advantage of including meal inputs in model  Individualization and adaptation  Robustness w.r.t inaccuracy of meal information Risk Index: 3.7 versus 10.7 BG maintains in Low Risk with ±50% Error of meal information Percentage of BG in safe range Risk Index (HBGI/LBGI) Use plasma BG data83%0.18/3.52 Use CGM data74%1.15/4.13

28. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsReference MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al28 of 30ACC 2015 [1] R. S. Parker, F. J. Doyle, and N. A. Peppas. A model-based algorithm for blood glucose control in type I diabetic patients. IEEE Trans Biomed Eng., 46(2):148–57, 1999. [2] R. Hovorka, F. Shojaee-Moradie, and P. V. Carroll. Partitioning glucose distribution/transport, disposal, and endogenous production during IVGTT. American Journal of physiology, 282(5):992–1007, 2002. [3] Lalo Magni, Davide M Raimondo, Luca Bossi, Chiara Dalla Man, Giuseppe De Nicolao, Boris Kovatchev, and Claudio Cobelli. Model predictive control of type 1 diabetes: an in silico trial. Journal of diabetes science and technology, 1(6):804–812, 2007. [4] Z. Trajanoski and P. Wach. Neural predictive controller for insulin delivery using the subcutaneous route. IEEE Trans Biomed Eng., 45:1122–1134, 1998 [5] R. S. Parker, F. J. Doyle, and N. A. Peppas. A model-based algorithm for blood glucose control in type I diabetic patients. IEEE Trans Biomed Eng., 46(2):148–57, 1999. [6] A. Gani, A. V. Gribok, S. Rajaraman, W. K. Ward, and J. Reifman. Predicting subcutaneous glucose concentration in humans: datadriven glucose modeling. IEEE Trans Biomed Eng., 56(2):246–54, 2009. [7] F. Ståhl and R. Johansson. Diabetes mellitus modeling and short-term prediction based on blood glucose measurements. Math Biosci., 217:101–17, 2009.

29. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results Conclusions Q & A MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al29 of 30ACC 2015

30. MPC for Type 1 Diabetes Based on Personalized LTV Model Consisting of both Insulin and Meal inputs Qian Wang, Jinyu Xie et al Background Modeling Control Design Simulation Results ConclusionsResults MPC for Type 1 Diabetes Based on Personalized LTV ModelQian Wang et al30 of 30ACC 2015 Time-Varying vs Time-Invariant  MPC-LTI Pre-train the model parameters under the training protocol used in [8], and then fix the parameters  MPC-LTV-TrainInit Use the parameters gained by the pre-training as the initial value