The Artificial Pancreas: Current Situation and Future Directions 0128156554, 9780128156551

Table of contents :
Cover
The Artificial Pancreas:

Current Situation and Future
Directions
Copyright
Dedication
Contributors
About the contributors
Foreword
References
Preface
1 Feedback control algorithms for automated glucose management in T1DM: the state of the art
1.1 Introduction
1.2 Proportional-integral-derivative control
1.2.1 Insulin delivery using PID control
1.2.2 Glucagon delivery using PID control
1.3 Logic-based control
1.4 Model predictive control
1.4.1 Unconstrained MPC with safety checks
1.4.2 Multiple model adaptive MPC
1.4.3 Zone MPC
1.4.4 Set-point-based enhanced MPC design
1.4.5 Multiple model probabilistic predictive control
1.4.6 Adaptive generalized predictive control and MPC design
1.4.7 Bihormone adaptive generalized predictive control
1.4.8 Policy-based stochastic MPC
1.5 Switched linear parameter varying control
1.6 Personalization and adaptation
1.6.1 Run-to-run approaches
1.6.2 Iterative learning control
1.6.3 Moving average approach
1.7 Machine-learning-based control
1.7.1 Reinforcement-learning-based approach
1.7.2 Gaussian process MPC
1.7.3 Deep learning-assisted control
1.8 Summary
Acknowledgments
References
2 Getting IoT-ready
2.1 Introduction
2.2 IoT-enabled AP ecosystems
2.2.1 The changing face of AP systems
2.2.2 AP research platforms: past and present
2.3 Interfacing with additional signals from the IoT
2.3.1 Activity sensors
2.3.2 Location sensors
2.3.3 Multimedia
2.3.4 Electronic health records
2.3.5 Crowdsourcing
2.3.6 Calendar data
2.4 Rewiring controllers for an IoT-enabled AP
2.4.1 PID
2.4.2 MPC
2.5 Case study: efficient resource utilization in an MPC-based embedded AP
2.6 Case study: IoT-enabled autonomous bolus assist via deep learning based zone MPC
2.7 High-level adaptation from big IoT data
2.7.1 The interplay of cloud, fog, and edge computing
2.7.2 An AP that learns from big data
2.8 Conclusions
Acknowledgments
References
3 Multivariable AP with adaptive control
3.1 Introduction
3.2 Preliminaries
3.2.1 Adaptive and personalized PIC estimator
3.2.2 Recursive subspace-based system identification
3.3 Adaptive PIC cognizant MPC algorithm
3.3.1 Integrating insulin compartment models with subspace identification
3.3.1.1 Set-point modification during exercise and recovery period
3.3.1.2 Glycemic risk index
3.3.1.3 Plasma insulin risk index
3.3.1.4 Feature extraction for manipulating constraints
3.3.1.5 Plasma insulin concentration bounds
3.3.1.6 Hypoglycemia detection and carbohydrate suggestion
3.3.2 Adaptive MPC formulation
3.4 Results
3.5 Conclusions
3.A
Acknowledgments
References
4 The ARG algorithm: clinical trials in Argentina
4.1 Introduction
4.2 Control-oriented models
4.3 ARG algorithm
4.3.1 Switched LQG regulator
4.3.2 SAFE layer
4.3.3 Auxiliary modules
Hypoglycemia-related module (Hypo-RM)
Hyperglycemia-related module (Hyper-RM)
4.4 Simulations
4.5 Clinical trials
4.5.1 Hardware and software
4.5.2 Clinical procedures
4.5.3 Results
4.6 Conclusions
Acknowledgments
References
5 Use of intraperitoneal insulin delivery for artificial pancreas
5.1 Bedside artificial pancreas: the birth of a concept
5.2 Prioritization of subcutaneous insulin delivery in the development of a wearable artificial pancreas (AP)
5.3 Rationale for using intraperitoneal insulin delivery
5.4 Clinical experience with continuous intraperitoneal insulin infusion
5.5 Closed-loop experience with IP insulin delivery
5.5.1 AP with IV glucose sensing and IP insulin delivery
5.5.2 AP with SC glucose sensing and IP insulin delivery
5.5.2.1 IP insulin delivery: closed-loop vs. open-loop
5.5.2.2 Closed-loop control with IP vs. SC insulin delivery
5.6 Perspectives for IP insulin use in AP
5.7 Declaration of interests
References
6 Physiological models for artificial pancreas development
6.1 Role of physiological models
6.2 The University of Virginia/Padova T1D simulator
6.2.1 A serendipitous beginning
6.2.2 Accelerating AP research: the FDA-accepted T1D simulator
6.2.3 Further developments of the UVA/Padova T1D simulator
6.3 The oral glucose minimal model
6.3.1 The model
6.3.2 Insulin sensitivity: diurnal pattern
6.3.3 Insulin sensitivity: simple vs. complex carbohydrates
6.4 Models of new molecules
6.4.1 Inhaled insulin
6.4.2 Subcutaneous UltraFast acting insulin analog
6.4.3 Modeling of pramlintide: in silico assessment of optimal pramlintide to insulin ratio
6.5 Modeling subcutaneous glucose sensor delay
6.6 The UVA/Padova T1D simulator for nonadjunctive use of glucose sensors
6.7 Adaptive AP algorithms
6.7.1 Run-to-Run strategy for adaptive MPC tuning
6.7.2 In silico testing
6.8 Conclusions
6.A
6.A.1 UVA/Padova T1D simulator model equation
Glucose subsystem
Insulin subsystem
Glucose rate of appearance
Endogenous glucose production
Glucose utilization
Renal excretion
External insulin rate of appearance
Subcutaneous insulin kinetics
Intradermal insulin kinetics
Inhaled insulin kinetics
Subcutaneous glucose kinetics
Glucagon kinetics and secretion
Subcutaneous glucagon kinetics
Acknowledgments
References
7 Deployment of modular MPC for type 1 diabetes control: the Italian experience 2008-2016
7.1 Introduction
7.2 AP hardware
7.2.1 APS: the in-patient hardware platform
7.2.2 DiAs: the out-patient hardware platform
Config. A: Omnipod and Dexcom SEVEN PLUS
Config. B: t:slim and G4 Platinum
Config. C: Accu-Chek Combo and G4 Platinum
7.3 Telemedicine
7.4 AP control algorithm
7.4.1 Safety layer
7.4.2 Control layer
7.4.2.1 Hyperglycaemia Mitigation System
7.4.2.2 Model Predictive Control
Model
Cost function
Constraints
Meal announcement and feed-forward action
7.4.3 Adaptation layer
7.4.3.1 Adaption rules
7.4.3.2 Real-life algorithm
7.5 In-patient studies
7.5.1 Study design
7.5.2 Data analysis
7.5.3 Results
7.5.4 H2MS and mMPC
7.5.5 Further inpatient studies testing the mMPC
7.5.6 Concluding remarks
7.6 Out-patient studies
7.6.1 Study design
7.6.2 Data analysis
7.6.3 Results
7.6.3.1 H2MS, DiAs configuration A [28]
7.6.3.2 mMPC, DiAs configuration A [29]
7.6.3.3 mMPC, DiAs configuration C [21]
7.6.4 Concluding remarks
7.7 Real-life testing
7.7.1 Evening & night use of mMPC
7.7.2 Day & night use of mMPC
7.7.3 Adaptive mMPC
7.8 Concluding remarks
7.9 Conclusions
Acknowledgments
References
8 Integrating the clinical and engineering aspects of closed-loop control: the Virginia experience
8.1 Introduction
8.2 Overview of the technology
8.3 Early outpatient AP studies (2011-16)
8.4 Pediatric studies
8.5 Ongoing clinical trials (2016-)
8.6 Conclusion
References
9 Strategies to mitigate hypoglycaemia in the artificial pancreas
9.1 Introduction
9.2 Safety monitoring systems and hypoglycaemia prediction
9.3 Control strategies for insulin infusion limitation
9.4 Feedforward actions in exercise-informed systems
9.5 Carbohydrate intake suggestions as counterregulatory control action
9.6 Glucagon as counterregulatory control action
9.7 Conclusions
Acknowledgments
References
10 Multiple-signal artificial pancreas systems
10.1 Introduction
10.2 Improving control of physical activity and exercise
10.2.1 Quantitative models of exercise and T1D
10.2.2 Physical activity as a cue to modified artificial pancreas operation
10.2.3 Adapting AP operation by quantifying the effect of physical activity and exercise inputs
10.3 Improving control of meals and snacks
10.4 Improving control of blood glucose overnight
10.4.1 Detecting sleep
10.4.2 Detected sleep as a cue to modified artificial pancreas operation
10.5 Enhancing patient safety and security
10.5.1 Remote patient monitoring for emergency services
10.5.2 Context awareness: pros and cons
10.6 Conclusions
References
11 Artificial pancreas in pediatrics
11.1 Introduction
11.2 Effect on children of hypoglycaemia and hyperglycaemia
11.3 Overview of AP development in pediatrics
11.4 Threshold suspend and predictive low glucose suspend in pediatrics
11.5 Managing expectations about AP use among families and diabetes providers
11.6 Hybrid closed-loop systems in pediatrics
11.7 Fully closed-loop systems
11.8 Understanding differences in AP tuning in pediatrics
11.9 Use of AP systems in young children
11.10 Skin care issues impacting device use
11.11 Psychological and social considerations for AP in pediatrics
11.12 Role of automated decision support in pediatrics and short-term AP use in the developing world
11.13 Long-term needs and future improvements
11.14 Conclusions and summary
References
Index
Back Cover

Citation preview

The Artificial Pancreas

The Artificial Pancreas Current Situation and Future Directions Edited by

Ricardo S. Sánchez-Peña ITBA & CONICET Departmento de Investigación y Doctorado Buenos Aires, Argentina

Daniel R. Cherñavvsky University of Virginia Center for Diabetes Technology Charlottesville, VA, USA

Series editor

Edgar Sánchez

Academic Press is an imprint of Elsevier 125 London Wall, London EC2Y 5AS, United Kingdom 525 B Street, Suite 1650, San Diego, CA 92101, United States 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom Copyright © 2019 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-12-815655-1 For information on all Academic Press publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Mara Conner Acquisition Editor: Chris Katsaropoulos Editorial Project Manager: Ana Claudia A. Garcia Production Project Manager: Nirmala Arumugam Designer: Matthew Limbert Typeset by VTeX

This book is dedicated to Pedro and Sandra, the new lights in my life Ricardo S. Sánchez-Peña This book is affectionally dedicated to my wife Kim and children Cata, Liza, and Spencer, who inspire me every day Daniel R. Cherñavvsky

Contributors Stacey M. Anderson University of Virginia Center for Diabetes Technology, Charlottesville, VA, USA University of Virginia Division of Endocrinology and Metabolism, Charlottesville, VA, USA Ananda Basu University of Virginia School of Medicine, Department of Endocrinology, Charlottesville, VA, USA Rita Basu University of Virginia School of Medicine, Department of Endocrinology, Charlottesville, VA, USA Fernando Bianchi Instituto Balseiro, Comisión Nacional de Energía Atómica, Bariloche, Argentina CONICET, Argentina Jorge Bondia Instituto Universitario de Automática e Informática Industrial, Universitat Politècnica de València, Valencia, Spain Centro de Investigación Biomédica en Red de Diabetes y Enfermedades Metabólicas Asociadas (CIBERDEM), Madrid, Spain Rachel Brandt Department of Biomedical Engineering, Illinois Institute of Technology, Chicago, IL, USA Marc D. Breton University of Virginia Center for Diabetes Technology, Charlottesville, VA, USA Sue A. Brown University of Virginia Center for Diabetes Technology, Charlottesville, VA, USA University of Virginia Division of Endocrinology and Metabolism, Charlottesville, VA, USA Ankush Chakrabarty Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

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Contributors

Daniel R. Cherñavvsky University of Virginia Center for Diabetes Technology, Charlottesville, VA, USA Center for Diabetes Technology, University of Virginia, Charlottesville, VA, USA Ali Cinar Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL, USA Department of Biomedical Engineering, Illinois Institute of Technology, Chicago, IL, USA Claudio Cobelli University of Padova, Department of Information Engineering, Padova (PD), Italy University of Padova, Dep. of Information Engineering, Padova (PD), Italy Patricio Colmegna University of Virginia, Charlottesville, VA, USA CONICET, Argentina Chiara Dalla Man University of Padova, Department of Information Engineering, Padova (PD), Italy Eyal Dassau Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA Hernán De Battista Universidad Nacional de La Plata, Buenos Aires, Argentina CONICET, Argentina Mark DeBoer University of Virginia Center for Diabetes Technology, Charlottesville, VA, USA University of Virginia Department of Pediatrics, Charlottesville, VA, USA Simone Del Favero University of Padova, Dep. of Information Engineering, Padova (PD), Italy Sunil Deshpande Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA Francis J. Doyle III Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

Contributors

Anne Farret Department of Endocrinology, Diabetes, Nutrition, University Hospital of Montpellier, Montpellier, France Institute of Functional Genomics, CNRS, INSERM, University of Montpellier, Montpellier, France Gregory P. Forlenza Barbara Davis Center for Childhood Diabetes, University of Colorado Denver, Denver, CO, USA Fabricio Garelli Universidad Nacional de La Plata, Buenos Aires, Argentina CONICET, Argentina Iman Hajizadeh Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL, USA Nicole Hobbs Department of Biomedical Engineering, Illinois Institute of Technology, Chicago, IL, USA Boris P. Kovatchev University of Virginia Center for Diabetes Technology, Charlottesville, VA, USA David M. Maahs Division of Pediatric Endocrinology, Stanford University/Lucile Packard Children’s Hospital, Palo Alto, CA, USA Lalo Magni University of Pavia, Dep. of Civil Engineering and Architecture, Pavia (PV), Italy Laurel H. Messer Barbara Davis Center for Childhood Diabetes, University of Colorado Denver, Denver, CO, USA Stephen D. Patek Charlottesville, VA, USA Jerôme Place Institute of Functional Genomics, CNRS, INSERM, University of Montpellier, Montpellier, France Mudassir Rashid Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL, USA

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Eric Renard Department of Endocrinology, Diabetes, Nutrition, University Hospital of Montpellier, Montpellier, France Clinical Investigation Centre INSERM 1411, Montpellier, France Institute of Functional Genomics, CNRS, INSERM, University of Montpellier, Montpellier, France Sediqeh Samadi Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL, USA Ricardo S. Sánchez-Peña Instituto Tecnológico de Buenos Aires, C.A.B.A., Argentina CONICET, Argentina Michele Schiavon University of Padova, Department of Information Engineering, Padova (PD), Italy Mert Sevil Department of Biomedical Engineering, Illinois Institute of Technology, Chicago, IL, USA Dawei Shi Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA Tara Sowrirajan Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA Chiara Toffanin University of Pavia, Dep. of Electrical, Computer and Biomedical Engineering, Pavia (PV), Italy Josep Vehí Institut d’Informàtica i Aplicacions, Universitat de Girona, Girona, Spain Centro de Investigación Biomédica en Red de Diabetes y Enfermedades Metabólicas Asociadas (CIBERDEM), Madrid, Spain Roberto Visentin University of Padova, Department of Information Engineering, Padova (PD), Italy Stamatina Zavitsanou Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

About the contributors Stacey M. Anderson is Medical Director of the UVA Center for Diabetes Technology, a multidisciplinary group of research academicians with specialties in Endocrinology, Behavioral Medicine, Systems Engineering, Mathematics and Statistics, working collaboratively for the advancement of technology for the treatment of type 1 diabetes. As part of the International Artificial Pancreas (IAP) Study Group, she conducted several of the first international artificial pancreas trials conducted initially in the hospital and hotel settings. Subsequently, Dr. Anderson was Principal Investigator of a JDRF-funded multicenter international study that deployed one of the first ambulatory artificial pancreas systems at home for 1 month. Additionally, Dr. Anderson is co-PI of UC4 grant from the NIH to conduct pivotal long-term use studies of the artificial pancreas at home in 10 sites around the globe. As a clinical closedloop expert, Dr. Anderson has received grants from both Animas Corporation and Medtronic Diabetes Care to study their artificial pancreas technology and a grant support from JDRF to train other clinical sites on closed-loop research. Dr. Anderson is an adult endocrinologist and Certified Diabetes Technology Clinician and has personally conducted numerous hospital-, hotel-, and home-based clinical trials, including over 150 hyperinsulinemic clamp procedures involving algorithmic blood glucose control. In her clinical practice, she has expertise in diabetes technology and treats patients with insulin pumps, insulin pens, CGMs, and closed-loop technologies in the UVA Advanced Diabetes Management Clinic. Ananda Basu, MD, FRCP (UK), is Harrison Professor of Medicine in the Division of Endocrinology at the University of Virginia. Dr. Basu is currently Principal Investigator of two NIH funded projects that are designed to better understand the physiology of type 1 diabetes. These include: i) NIDDK-DP3-106785, which attempts to recreate a truly electronic beta cell by infusing insulin and amylin (hormones released by the normal beta cell) in a closed-loop system to test the safety and efficacy of the combination therapy in those with type 1 diabetes; ii) NIDDK-R01-085516, which seeks to understand the altered physiology of the alpha cell by using stable nonradioactive isotopes of glucagon as truly innovative probes to understand the dynamics of glucagon secretion and its metabolism in humans with and without type 1 diabetes. Dr. Basu is also a coinvestigator in NIH and Industry funded projects with Dr. Rita Basu MD as Principal Investigator. He is also a consultant in a project that seeks to introduce the first indigenous artificial pancreas for patients with type 1 diabetes in India. Rita Basu, MD is a tenured Professor in the Division of Endocrinology, department of Medicine at the University of Virginia. Dr. Basu is currently Principal Investigator on projects that are both NIH and Industry funded. These include: 1) NIDDKR01-029953, which probes the mechanisms of hepatic and peripheral insulin resistance in humans with type 2 diabetes and prediabetes using state-of-the-art isotope

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dilution methods coupled with organ catheterization (splanchnic and leg balance), which she helped develop and validate (e.g., triple tracer techniques for estimation of glucose and cortisol turnover in humans), critical insights into the mechanisms of organ and system-specific dysfunctions that lead to insulin resistance have been delineated; 2) Investigator-initiated industry sponsored clinical trial of a novel therapy for patients with Non-Alcoholic Steatohepatitis (NASH/NAFLD) that targets hepatic fat and secondarily improves hepatic insulin action; iii) Industry-sponsored Phase III study to understand the effects of a faster acting insulin analog on glucose turnover in type 1 diabetes; iv) Industry-sponsored study to determine the physiology of glucose sensing in the intraperitoneal space in humans and type 1 diabetes. Dr. Basu is also a coinvestigator in NIH sponsored projects with Dr. Ananda Basu MD as Principal Investigator. She also collaborates extensively with investigators outside of UVA at prestigious institutions such as Harvard Medical School, Joslin Diabetes Center, UTHSCSA, Mayo Clinic, amongst others. Fernando Bianchi received the B.S. and Ph.D. degrees in electronic engineering from the National University of La Plata (UNLP), La Plata, Argentina, in 1999 and 2005, respectively. From 1999 to 2006, he was a Ph.D. Student and a Postdoctoral Fellow at LEICI, UNLP, La Plata, Argentina. From 2006 to 2010, he was Postdoctoral Researcher at the Technical University of Catalonia (UPC), Barcelona, Spain. From 2010 to 2017, he was Scientific Researcher at the Power Electronics and Electric Power Grids Group, Catalonia Institute for Energy Research (IREC), Barcelona, Spain. In 2017, he joined the Institute Balseiro as Professor and CONICET as Senior Researcher working in the Telecommunications Department, Centro Atomico Bariloche (CNEA), Argentina. His research interests include robust control and linear parameter-varying systems and their applications in the control of renewable energies and other systems. Jorge Bondia holds a Ph.D. in Computer Science (2002) from Universitat Politècnica de Valencia (UPV) under the program of Automation and Industrial Computing. He has been lecturing in the Department of Systems Engineering and Control of the UPV since 1995 in the areas of control engineering and biomedical engineering. He is Full Professor since 2017. He carries out his research at the Instituto Universitario de Automática e Informática Industrial of the UPV, where in 2004 he started his research line in diabetes technology and the artificial pancreas. Currently, he is coordinator of the Spanish Consortium on Artificial Pancreas and Diabetes Technology, which joined in 2018 the Spanish excellence diabetes research center Centro de Investigación Biomédica en Red en Diabetes y Enfermedades Metabólicas Asociadas (CIBERDEM). He has authored more than 60 journal articles in the area of the artificial pancreas and more than 120 conference contributions. He is a member of the IFAC Technical Committee TC 8.2 Biological and Medical Systems since September 2010 and a member of the Spanish Diabetes Society. Rachel Brandt received the B.Sc. degree in Biomedical Engineer from the University of Texas at San Antonio, San Antonio, TX, USA in 2016. She is currently working toward the Ph.D. degree in the Department of Biomedical Engineering at

About the contributors

the Illinois Institute of Technology, Chicago, IL, USA. Her research interests include artificial pancreas systems, the dawn phenomenon, the effects of sleep on glycemic control, and sleep and sleep stage detection. Marc D. Breton is Associate Director for Research at the Center for Diabetes Technology at the University of Virginia. Dr. Breton’s research is centered on bringing engineering techniques such as mathematical modeling, simulation, signal processing, and automatic control into the field of medicine and clinical practice. Dr. Breton has been successful at applying these techniques to the field of diabetes technology, in particular the assessment and control of glucose levels in type 1 diabetes mellitus. Dr. Breton has participated in the design of the first (and to date only) simulation environment accepted by the US Food & Drugs Administration as replacement for animal studies in preclinical assessment of insulin treatment strategies and is now in charge of its update and further development. Dr. Breton has been the principal investigator on numerous projects joining engineering development and clinical trials aimed at testing new insulin delivery strategies in diabetes, avoiding hypoglycemia and reducing hyperglycemia, including systems linking continuous glucose monitors and subcutaneous insulin injection (Artificial Pancreas). Dr. Breton has participated in both the design of the dosing logic and the hardware platform. Dr. Breton is one of the founders of the Center for Diabetes Technology at UVA and has mentored graduate students, post doctoral fellows, and junior researchers. Sue A. Brown is Associate Professor of Medicine at the University of Virginia in the Division of Endocrinology and is an integral member of the multidisciplinary group at the Center for Diabetes Technology. Dr. Brown has focused on novel treatment options for patient with diabetes since 2009. Dr. Brown is active as Principal Investigator or coinvestigator of clinical trials related to automated insulin delivery (Artificial Pancreas or AP) technology funded primarily by the NIH and JDRF and conducted within the Center for Diabetes Technology. Dr. Brown has been the sponsor of Investigational Device Exemptions (IDEs) for multiple AP trials approved by the FDA. Dr. Brown is currently the lead investigator of a multicenter clinical trial (7 sites) that represents the pivotal trial of an AP technology. Dr. Brown has been the PI and lead clinician at UVA on several multicenter NIH projects involving longterm use of AP systems overnight as well as the development of real-time adaptation of an automated insulin delivery system. Dr. Brown has also directed studies investigating additional inputs to glucose variability such as exercise and the menstrual cycle. Dr. Brown is the co-PI on an NIH grant investigating glucagon alterations in relatives of individuals with type 1 diabetes. In addition to research, Dr. Brown is an active endocrinologist with an academic clinical practice and one of the core teaching faculty for endocrinology fellows. Dr. Brown’s efforts are directed at creating novel treatment options for patients with diabetes, particularly type 1 diabetes, and working toward pivotal trials required for bringing advance decision support and automated insulin delivery techniques to patients at home. Ankush Chakrabarty received a B.E. with first-class honors from Jadavpur University, India (2011), and the Ph.D. from Purdue University, West Lafayette, USA

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(2016), both in Electrical Engineering. Since 2018, he is Visiting Research Scientist in the Control and Dynamical Systems Group at Mitsubishi Electric Research Laboratories (MERL), prior to which he was Postdoctoral Fellow at Harvard University, working on developing control algorithm for next-generation artificial pancreas systems. His work leverages artificial intelligence and approximation/relaxation methods to provide computationally efficient and provably safe solutions to challenging problems arising in control and estimation, with special emphasis on model predictive control and unknown input estimation. Daniel R. Cherñavvsky is Assistant Professor of Research in the Center for Diabetes Technology at the University of Virginia. The Center for Diabetes Technology is a multidisciplinary group of research academicians with specialties in Pediatrics, Endocrinology, Behavioral Medicine, Systems Engineering, Mathematics, and Statistics, working collaboratively for the advancement of technology for the treatment of type 1 diabetes. Currently, Dr. Cherñavvsky is leading several artificial pancreas studies in pediatric and young adult populations. In addition, Dr. Cherñavvsky collaborates with the International Artificial Pancreas (iAP) Study Group, which joins investigators from Italy, France, Israel, Argentina, and the USA. He had conducted the first-ever outpatient clinical study of a cell phone-based artificial pancreas system and performed US and international outpatients-based trials with different generations of the Artificial Pancreas system. Dr. Cherñavvsky’s funded studies include summer and winter camps with adolescents evaluating the effect of exercise and type 1 diabetes. Dr. Cherñavvsky, a pediatric nephrologist and pediatric intensive care specialist graduate from the University of Buenos Aires, has conducted and designed clinical research projects for over 15 years in the USA. Since September 2016, he joined TypeZero Technologies, Inc., as a part time chief medical officer. Now he divides his time between academia, continuing his clinical research activities, and industry, where he is moving forward technological products aiming to optimize treatment for people with type 1 diabetes. Ali Cinar received the Ph.D. degree in chemical engineering from Texas A&M University, College Station, TX, USA. He is currently Professor of chemical engineering and biomedical engineering in the Illinois Institute of Technology, Chicago, IL, USA. Since 2004, he has been Director of the Engineering Center for Diabetes Research and Education. He has published three books and more than 200 technical papers in refereed journals and conference proceedings. His research interests include agentbased techniques for modeling, supervision, and control of complex and distributed systems, modeling of diabetes, angiogenesis, and tissue formation, and adaptive control techniques for artificial pancreas systems for people with diabetes. Dr. Cinar is Fellow of AICHE. and Senior Member of IEEE. Claudio Cobelli is Full Professor of Biomedical Engineering at University of Padova since 1981. From 2000 to 2011 he has been Chairman of the Graduate Program in Biomedical Engineering and of the Ph.D. Program in Bioengineering at the University of Padova. His main research activity is in the field of modeling and identification of physiological systems, especially the glucose system in diabetes. His research is

About the contributors

currently supported by NIH, JDRF, and European Comunity. He has published 489 papers in internationally refereed journals, is a coauthor of 8 books and holds 11 patents with an h-index of 91. He is currently Associate Editor of IEEE Transaction on Biomedical Engineering and Journal of Diabetes Science & Technology. He is on the Editorial Board of Diabetes Technology & Therapeutics. Dr. Cobelli has been Chairman (1999–2004) of the Italian Biomedical Engineering Group, Chairman (1990–1993 and 1993–1996) of IFAC TC on Modeling and Control of Biomedical Systems and member of the IEEE EMBS AdCom (2008–2009). In 2010, he received the Diabetes Technology Artificial Pancreas Research Award. He is Fellow of IEEE and BMES. Patricio Colmegna received the engineering degree from the University of Quilmes (UNQ) in 2010 and the doctoral degree in engineering from the Buenos Aires Institute of Technology (ITBA) in 2014. He focused his doctoral research on applying optimal, robust, and switched control algorithms to an artificial pancreas (AP), which aimed to not only mitigate glucose excursions, but also patient burden. In 2017, he was named as a research assistant at the National Scientific and Technical Research Council (CONICET) and was part of the team that performed the first clinical AP trial in Latin America. Dr. Colmegna joined the Center For Diabetes Technology, University of Virginia in early 2018, and is currently working on the development of a next generation simulation facility for diabetes. This effort involves the design of new and more computationally efficient platforms for multimodel, multidisease modeling and simulation. Chiara Dalla Man was born in Venice, Italy, on March 2, 1977. She graduated cum laude in Electronics Engineering at the University of Padova in 2000 and received the Ph.D. degree in Biomedical Engineering from the University of Padova and City University London, in 2005. She has been Post-Doctoral Research Fellow with the Department of Information Engineering of Padova University from 2005 to 2007. In 2007, she became Assistant Professor at the University of Padova. Since January 2015, she is Associate Professor in Bioengineering at University of Padova. Her research activity, carried out in collaboration with Italian and foreign investigators, regards mainly mathematical modeling of physiological systems, in particular metabolic and endocrine systems. She is the author of more than one hundred and twenty publications on international journals and two international patents. Eyal Dassau is Director of the Biomedical Systems Engineering Research Group and Senior Researcher in Biomedical Engineering in the Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University. He is also Adjunct Senior Investigator with the Sansum Diabetes Research Institute, Santa Barbara, CA, and an Adjunct faculty at the Joslin Diabetes Center, Boston, MA. He received his B.Sc., M.Sc., and Ph.D. degrees in Chemical Engineering from the Technion Israel Institute of Technology, Haifa, Israel in 1999, 2002, and 2006, respectively. Dr. Dassau’s research is focused on the development medically inspired control algorithms for people with type 1 diabetes mellitus. He is directing and supervising the research and development efforts to develop an artificial pancreas from algorithm design to

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bench evaluation and clinical studies. His work matured from theoretical developments (bench testing) to clinical evaluation in humans to commercial implementation. Hernán De Battista was born in La Plata, Argentina, in 1968. He received the M.S.Eng. degree with highest honors in 1994 and the Ph.D. degree in 2000, both from La Plata National University, Argentina. Currently he is Full Professor at the Faculty of Engineering of La Plata National University and Principal Researcher of the National Research Council of Argentina (CONICET). His main research interests are in nonlinear control and its applications to renewable energies and biological systems. HDB coauthored two books and 65 journal articles. He received the E. Galloni award from the Argentine Academy of Exact, Physical, and Natural Sciences in 2002 and the S. Gershanik award from the Buenos Aires Academy of Engineering in 2006. Mark DeBoer is Professor of Pediatrics at the University of Virginia and a member of the Center for Diabetes Technology. As a pediatric endocrinologist and a clinical investigator, Dr. DeBoer has a focus on the treatment of children and adolescents with type 1 diabetes (T1D). Dr. DeBoer has assisted in the Pediatric AP Program efforts, including assessment of AP use in summer camps and ski camps, and evaluation of AP use in adolescents during exercise. Dr. DeBoer secured funding for a trial of AP use among young 5–7 years old children and assessing the AP in adolescents after missing insulin for food and during exercise, and obtained an NIH grant to assess of additional diabetes analytics in improving pediatric diabetes control. Simone Del Favero received his M.S. degree (cum laude) in control systems engineering and his Ph.D. in Information Engineering from University of Padova, Padova, Italy in 2007 and 2010. From 2010 to 2016 he served as Post-Doc Researcher at the same university in the Bioengineering group, working to the international Artificial Pancreas (AP) project. Since 2016, he is Assistant Professor at University of Padova. His research interests include estimation, learning, and dynamical-system identification applied to the automated blood-glucose control and the clinical testing of this technology. He served as an engineer and coordinated more than 15 clinical trials testing the AP in adults, adolescents, and children both in- and outpatient. Sunil Deshpande received the B.Tech. degree in electronics and instrumentation engineering from Vellore Institute of Technology, India, in 2007, the M.S. and Ph.D. degrees in electrical engineering from Arizona State University, USA, in 2011 and 2014, respectively. Since January 2016, he has been with the Harvard John A. Paulson School of Engineering and Applied Sciences as Postdoctoral Fellow in bioengineering. He has previously held appointments at Arizona State University and the University of California, Santa Barbara. His research interests are in feedback systems, constrained control, system identification, experiment design, and their applications in biology and medicine. Francis J. Doyle III is the John A. Paulson Dean of the Paulson School of Engineering and Applied Sciences at Harvard University. Prior to that, he was Mellichamp Professor at UC Santa Barbara. He received the B.S.E. degree from Princeton, C.P.G.S. from Cambridge, and Ph.D. from Caltech, all in Chemical Engineering. He

About the contributors

has been recognized as Fellow of multiple professional organizations including IEEE, IFAC, AIMBE, and the AAAS. In 2005, he was awarded the Computing in Chemical Engineering Award from the AIChE for his innovative work in systems biology, and in 2015, he received the Control Engineering Practice Award from the American Automatic Control Council for his development of the artificial pancreas. In 2016, he was inducted as a Fellow into the National Academy of Medicine for his work on biomedical control. His research interests are in systems biology, network science, modeling and analysis of circadian rhythms, and drug delivery for diabetes. Anne Farret is the M.D. and Ph.D. She holds a position of Senior Clinical Research investigator at Montpellier University Hospital in the Department of Endocrinology, Diabetes, and Nutrition. She has a broad expertise in the evaluation of medical devices dedicated to diabetes monitoring, therapy, and control, including insulin pumps, CGM systems, and artificial pancreas in outpatients. Gregory P. Forlenza, M.D., is Assistant Professor of pediatrics at the Barbara Davis Center at the University of Colorado Denver. His research focus is on developing and improving technology to care for patients with type 1 diabetes. He has been involved in the pivotal trials for all of the current and emerging automated insulin delivery systems. He is also involved in research focused on glycemic control in special populations of children such as bone marrow transplant recipients and those with cystic fibrosis related diabetes. In addition, he is passionate about his work with diabetes camps. Fabricio Garelli is currently Full Professor at the National University of La Plata (UNLP) and Official Member of the National Research Council of Argentina (CONICET). He is the author of an awarded Ph.D. Thesis, IET book, and more than a hundred journal or conference papers. His research work focuses on constrained automatic control and estimation via sliding mode techniques, with application to industrial processes/bioprocesses, robotics, and biomedical engineering (artificial pancreas). Iman Hajizadeh received the B.Sc. and M.Sc. degrees from Sharif University of Technology, Tehran, Iran, in 2011 and 2013, respectively, both in chemical engineering, with a primary focus on process control. He is currently working toward the Ph.D. degree in the Chemical and Biological Engineering Department, Illinois Institute of Technology, Chicago, IL, USA. His research interests include process control, estimation, system identification, fault-tolerant control, and optimization. Nicole Hobbs received the B.Sc. degree in Biomedical Engineering at Illinois Institute of Technology in Chicago, IL, with a specialization in cell and tissue engineering. She is currently pursuing the Ph.D. in Biomedical Engineering at the same university. Her research interests include system identification, optimization, and process modeling. Her current research is focused upon blood glucose variations in people with type 1 diabetes during exercise with reference toward artificial pancreas systems. Boris P. Kovatchev is Professor at the University of Virginia (UVA) School of Medicine, Adjunct Professor at UVA’s School of Engineering and Applied Science,

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and the founding Director of the UVA Center for Diabetes Technology. He received his Ph.D. in Mathematics from Sofia University “St. Kliment Ohridski,” Bulgaria, in 1989. Kovatchev has a 25-year track record in mathematical modeling and computing, with primary focus on diabetes technology since 1996. Currently, Dr. Kovatchev is Principal Investigator of several projects dedicated to the development and testing of closed-loop control and decision support systems for diabetes, including the large-scale NIH/NIDDK International Diabetes Closed-Loop Trial (grant UC4 DK 108483), Project “Nightlight” (NIH grant RO1 DK 085623), and the University of Virginia’s PrIMeD Project (Precision Individualized Medicine for Diabetes). Dr. Kovatchev is the author of over 195 peer-reviewed publications and holds 85 patents. In 2008, he received the U.S. Diabetes Technology Leadership Award; in 2011, he was named the UVA’s Edlich-Henderson Inventor of the Year, and in 2013, he was the recipient of JDRF’s Gerold and Kayla Grodsky Award presented for outstanding scientific contributions to diabetes research. David M. Maahs is Professor of Pediatrics and Division Chief of Pediatric Endocrinology at Stanford University and the Lucile Packard Children’s Hospital. He is the author or coauthor of over 250 research publications. His multidisciplinary research has been funded by the JDRF, the National Institutes of Diabetes and Digestive and Kidney Diseases, the American Diabetes Association, the Helmsley Charitable Trust, and the National Science Foundation. He is Associate Director for the recently formed and NIDDK P30 funded Stanford University Diabetes Research Center (https://sdrc.stanford.edu). Lalo Magni received the masters degree in 1994 and the Ph.D. degree in 1998, both from the University of Pavia, Italy. Since that time, he has been with the University of Pavia, where he is now Full Professor of automatic control and dean of Engineering Faculty. His current research interests include nonlinear control, predictive control, robust control, process control, and the artificial pancreas. Laurel H. Messer (RN, MPH, CDE) is Senior Instructor at the Barbara Davis Center for Childhood Diabetes and the University of Colorado School of Medicine. She is also a PhD candidate studying factors related to uptake of diabetes technology in type 1 diabetes self-management. Ms. Messer is a research investigator and manager of the Pediatric Artificial Pancreas Research projects at the Barbara Davis Center for Diabetes. She received her BSN from Quinnipiac University and MPH from the Colorado School of Public Health, and has been a Certified Diabetes Educator for 10 years. Stephen D. Patek (Ph.D. 1997 MIT; SMEE 1994 MIT; BSEE 1991 U. Tennessee) has been active in research and development in diabetes technology since 2007. He was a faculty member and Professor at the University of Virginia in 1998–2018, where he worked on control systems “broadly construed.” In 2013, he cofounded TypeZero Technologies, Inc., which was acquired by Dexcom, Inc., in 2018. He has authored or coauthored more than 80 peer reviewed publications. Jerôme Place is an M.Sc. and a research engineer at the Institute of Functional Genomics, UMR CNRS 5203/INSERM U1191/ University of Montpellier, Montpellier,

About the contributors

working in the team led by Prof. Renard. He is the coordinator of many clinical studies dedicated to diabetes technology and has developed remote monitoring systems used for the investigation of outpatients testing artificial pancreas systems. He is also data manager of multicenter clinical studies of insulin delivery and CGM systems and holds ability of statistical analyses. Mudassir Rashid is Senior Research Associate in the Department of Chemical and Biological Engineering at the Illinois Institute of Technology in Chicago, Illinois. He obtained his B.Eng. and Ph.D. from McMaster University (Hamilton, CA) in 2011 and 2016, respectively. His research interests are in the general area of process systems engineering, with emphasis on system identification, process monitoring and fault diagnosis, model predictive control, fault tolerant control, and optimization. He has published more than 26 manuscripts in referred journals and conference proceedings. Eric Renard received a Doctorate in Medicine (MD) at Montpellier Medical School in 1987, performed a Research Fellowship (Arthur Sachs Scholarship) at Joslin Diabetes Center, Harvard Medical School, Boston, MA, USA, in 1992, and received Ph.D. in Biochemistry & Molecular Biology from the University of Montpellier in 1995. He holds a Chair of Professor of Endocrinology, Diabetes & Metabolism at the Medical School of University of Montpellier, France, since 1999 and heads the Department of Endocrinology, Diabetes and Nutrition at Lapeyronie University Hospital in Montpellier since 2010. Eric Renard is also Head of the INSERM Clinical Research Center at Montpellier University Hospital since January 2010. He served as Medical Director of Clinical Research at Montpellier University Hospital from 2008 to 2018. He leads a research team focusing on “Determinants and correction of the loss of insulin secretion in diabetes” at the Institute of Functional Genomics, UMR CNRS 5203/INSERM U1191/ University of Montpellier, since 2012. Sediqeh Samadi received the B.Sc. degree from the University of Tehran, Tehran, Iran, and the M.Sc. degree from Sharif University, Tehran, Iran, both in chemical engineering. She is currently working toward the Ph.D. degree in chemical engineering at the Illinois Institute of Technology, Chicago, IL, USA. Her research interests include mathematical modeling of chemical and biological systems based on soft computing and artificial intelligence methods. Her current research focuses on modeling and detection of different events and disturbances on blood glucose variation in people with type 1 diabetes. Ricardo S. Sánchez-Peña received the Electronic Engineer degree from the University of Buenos Aires (UBA, 1978) and the M.Sc. and Ph.D. from the California Institute of Technology (1986, 1988), both in Electrical Engineering. In Argentina, he worked since 1977 in different research institutions. He collaborated with NASA, the German (DLR) and Brazilian (CTA/INPE) space agencies. He was (Plenary) Full Professor at UBA (1989–2004), ICREA Senior Researcher at the UPC (2005–2009, Barcelona) and visiting Prof./Researcher at several Universities in the USA and EU. He consulted for companies in the USA, Spain, and Argentina. He published four

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books and more than 160 journal and conference papers. He received awards from NASA, IEEE, and the National Academy of Exact, Physical, and Natural Sciences of Argentina. He is Director of the Research and Ph.D. Program at the Buenos Aires Institute of Technology (ITBA) and Investigador Superior from CONICET. He has applied identification and control to acoustical, mechanical, aero, and astronautical engineering and currently to type 1 diabetes and neurobiology. Michele Schiavon was born in Chioggia (VE), Italy, on December 28, 1985. He received the Doctoral degree in bioengineering from the University of Padova, Padova, Italy, in 2010, and the Ph.D. degree in bioengineering from the University of Padova, Padova, Italy, in March 2014. He is currently Postdoctoral Researcher at the University of Padova. His current research interests include mathematical modeling and identification and simulation of physiological, especially endocrine-metabolic systems. On these topics, he published more than 15 papers in international peerreviewed journals and more than 40 contributions in national and international conference abstracts and proceedings. Mert Sevil received his B.Sc. degree in electrical engineering and the double major B.Sc. degree in computer engineering with primary focus on control algorithm design in 2013 and 2015, respectively, and the M.Sc. degree in control and automation engineering from Yildiz Technical University Istanbul, Turkey, in 2015. He is currently working toward the Ph.D. degree in the Biomedical Engineering Department, Illinois Institute of Technology, Chicago, IL, USA. His research interests include algorithm development for stress and exercise detection, energy expenditure estimation, control systems, communication of electronic devices, fuzzy logic estimation, artificial neural network, and artificial intelligence algorithms. Dawei Shi received the B.Eng. degree in electrical engineering and its automation from the Beijing Institute of Technology, Beijing, China, in 2008, the Ph.D. degree in control systems from the University of Alberta, Edmonton, AB, Canada, in 2014. In December 2014, he was appointed as Associate Professor at the School of Automation, Beijing Institute of Technology. Since February 2017, he has been with the Harvard John A. Paulson School of Engineering and Applied Sciences as Postdoctoral Fellow in bioengineering. His current research focuses on learning-based multitimescale parameter adaptation of artificial pancreas for patients with type 1 diabetes. He was selected to the National “1000-Youth Talent Program” of China in 2018. Tara Sowrirajan did her B.S. in Computer Science at the California Institute of Technology, graduating in 2016. She is currently pursuing her Ph.D. in Computer Science at Harvard University. Chiara Toffanin obtained the masters degree (cum laude) in computer science engineering (automation curricula) in 2009 and the Ph.D. degree in electronics, computer science, and electrical engineering in 2013, both from the University of Pavia, Italy. Since then, she has been with the Identification and Control Systems Laboratory of

About the contributors

the University of Pavia as Postdoctoral Fellow. In 2015, she won a one-year Postdoctoral Fellow at the Oxford university related to a computational research project on the analysis of high-throughput screen data, in the context of a broader scientific collaboration. Since 2017, she is Assistant Professor at the University of Pavia, and her research interests include identification and control techniques of linear systems, model predictive control, physical system modeling, and supervised machine learning techniques, mostly applied to the artificial pancreas development. Josep Vehí is a Professor of Electrical and Biomedical Engineering at the University of Girona, Spain and Research Associate at the Girona Biomedical Research Institute. Since 2013, he is Head of the Department of Electrical and Electronic Engineering. Professor Vehi has been researching in technologies for diabetes and artificial pancreas since 2004, including the prediction of glucose in conditions of uncertainty and intrapatient variability, the optimization of insulin therapy, the development of closed loop control algorithms for type 1 diabetic patients, fault detection in continuous glucose monitors and insulin pumps, patient monitoring, and decision support systems. Currently, he leads the University of Girona team within the Spanish Consortium on Artificial Pancreas and Diabetes Technology, which joined in 2018 the Spanish excellence diabetes research center Centro de Investigación Biomédica en Red en Diabetes y Enfermedades Metabólicas Asociadas (CIBERDEM). Roberto Visentin was born in Sacile (PN), Italy, on March 3, 1984. He received the Doctoral degree in bioengineering from the University of Padova, Padova, Italy, in 2010, and the Ph.D. degree in bioengineering from the University of Padova, Padova, Italy, in March 2016. He is currently Postdoctoral Researcher at the University of Padova. His current research interests include mathematical modeling, identification and simulation of physiological systems, with particular focus on glucose metabolism in healthy and diabetic subjects and on silico and in vivo testing of artificial pancreas closed-loop control algorithms. On these topics, he published more than 20 papers in international peer-reviewed journals and tens of other contributions in conference abstracts and proceedings. Stamatina Zavitsanou received the B.E. and M.Sc. in Chemical Engineering from National Technological University of Athens (NTUA), Greece (2009), and the Ph.D. from Imperial College London, London, UK (2015), in Process Systems Engineering. Since then, she is Postdoctoral Fellow at Harvard University working on the development of an artificial pancreas (AP) system for people with type 1 diabetes. Her research interests include the development of optimal control strategies for drug delivery systems, physiologically based mathematical modeling, and clinical translation of the developed AP systems.

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Foreword From Research to Reality: a decade of artificial pancreas research, development, and delivery The Beginning of the JDRF Artificial Pancreas Project In the fall of 2004, I was thrilled to be hired at JDRF as a Scientific Program Manager focusing on diabetes complications. The position was well suited for my background as a molecular biologist, and I had a strong desire to focus on a disease that had already impacted my family tremendously. My younger brother Stephen was diagnosed with type 1 diabetes in 1977 at the age of three, and I was diagnosed at the age of 13 in 1984. Diabetes treatment at the time was still very crude. When Steve was diagnosed, we measured urine glucose levels and gave two to three injections of animal insulin a day. When I was diagnosed, we used colorimetric glucose strips and a lancet device that we not-so-affectionately called the guillotine. My goal upon joining JDRF was to apply my background as a scientist to the advance the type 1 diabetes cause and play a part in making life with diabetes better. The very first conference I attended as the newest JDRF staff scientist was the annual Diabetes Technology Society (DTS) meeting in Philadelphia in October of 2004. The JDRF Artificial Pancreas project began for me at a DirecNet study group at that DTS meeting. JDRF and NIH are strong partners, and my first assignment when I joined JDRF was to represent us at the meeting. This important consortium focused on testing new diabetes technologies in the pediatric population. At this meeting, we were piloting the new and not-yet-FDA-approved Abbott Navigator continuous glucose monitor. It was at DTS that I met for the first time many individuals, whom to this day I hold in the highest esteem: the Stanford team – Drs. Bruce Buckingham and Darrel Wilson and Jen Block; Dr. Peter Chase and Laurel Messing from the Barbara Davis Center; Drs. Bill Tamborlane and Stu Weinzimer from Yale; Dr. Roy Beck and Katrina Ruedy from the Jaeb Center; and many others. They were kind and invited me right into the discussion. I was thrilled! Would this new CGM work and was it ready for further testing in kids? Personally, I could not believe that, after so many years of finger sticks, a CGM could be a reality – we had hoped for such a tool for so many years. After being outfitted with the sensors on day one, we waited for the warm up period of ten hours to be complete, and then the data started to flow. The initial response was positive! It was incredibly exciting. The meeting proceeded, and there really seemed to be something special there. I could not wait to get back to JDRF. It was at the end of the meeting that another fortuitous connection was made: I crossed paths with and met Jeffrey Brewer for the first time. Jeffrey was attending the meeting as a JDRF International Board member and father of a recently diagnosed son (Sean). These two meetings were the seed from which the JDRF Artificial Pancreas Project began.

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Launch of the JDRF Artificial Pancreas Project In 2004, JDRF did not formally support research into diabetes devices. The only work that we funded at the time was a component of the JDRF Center at Yale University with Drs. Tamborlane and Weinzimer in partnership with the Medtronic team, Drs. Garry Steil and Kerstin Rebrin. Upon arriving back in New York from the DTS meeting, I reported that a new tool existed, that the DirecNet group was testing a novel CGM, and that it held the potential to reduce hypoglycemia through real-time glucose alerts. I must admit that there was some skepticism. Of course, we in the diabetes community had been hearing about potential continuous glucose monitors for years, and none had reached the market and shown efficacy. In a tag-team effort, Jeffrey Brewer and I argued to the JDRF Research leadership and the JDRF International Board and made the case that JDRF could help accelerate the first artificial pancreas systems to the market and that by doing so we would help people be healthier as we drove to a biological cure for diabetes. We showed that JDRF could play an important role in supporting research to drive the science and clinical testing forward, and we could address what appeared to be business barriers such as FDA approvals and reimbursement for the devices. The JDRF Board of Directors agreed, and the JDRF Artificial Pancreas Project was launched in 2005. The JDRF Artificial Pancreas Project consisted of two “Tracks.” Track One focused on demonstrating the safety and effectiveness of continuous glucose monitors. Track Two focused on addressing gaps in the science of artificial pancreas system development and broadening the community of researchers working in the field. It was shortly after this time that two things occurred that were critical to the success of the project. First, JDRF hired Cynthia Rice. Cynthia brought extensive policy experience to the table. Second, JDRF partnered with the Helmsley Charitable Trust (HCT). Working with David Panzirer and Dana Ball, JDRF was able to hire additional staff and further increase efforts on the project. Figs. 0.1 and 0.2 represent slides from that time highlighting the composition of the original funded consortium. The JDRF CGM Study [1] is often cited as a landmark trial that “bent the curve” for CGM adoption and access, initially across the United States and ultimately around the globe. The study demonstrated conclusively that CGM was superior to fingersticking alone in patients who consistently wore the device. In fact, it told us even more. It crystalized the concept of “Time in Range” and highlighted the significant amount of time that people with diabetes spend both hyper- and hypoglycemic every single day. It showed that this was a better way to look at diabetes control. Crucially, it changed reimbursement policy for the better. At the time of the publication of the study, no large insurer in the United States formally covered CGM devices. After the publication, nearly all of private insurers had formal policies in place and the leading clinical guidelines recommended CGM for people with T1D. It was clear from that moment on that CGM worked and it was here to stay! The beginning of Track 2 was also highly successful. From the beginning it was clear that this project would require alignment and contribution from an exceptional diversity of stakeholders. The consortium consisted of multiple institutions and partnered with industry, regulators, governments, payers, and clinical organizations. The

Foreword

FIGURE 0.1 January 2007 Slide via Weinzimer/Tamborlane et al. demonstrating hybrid closed-loop proof of concept.

background of the group was equally diverse: clinicians, engineers, biologists, physiologists, computer scientists, people living with the disease, government officials, and so on... The original funding for artificial pancreas studies included seven institutions and coordination from the Jaeb Center in Tampa Florida. It is very important to note the incredible contributions John Lum at the Jaeb Center and Drs. Marlon Pragnell and Sanjoy Dutta made to drive “Track 2” forward. It was also in 2006 that JDRF partnered with the FDA and the artificial pancreas was listed as a Critical Path Initiative. In March 2006, the FDA made the development of an artificial pancreas one of its “critical path opportunities”: these are top-priority research projects that the agency believes have the greatest potential to speed new medical discoveries for patients. By putting a closed-loop artificial pancreas on this list, the FDA in effect committed to helping advance its development by promoting the public- and privatesector collaboration necessary to reach this goal. It is amazing looking back at that original consortium and fast-forwarding to today to see what an important role each of the sites played in moving the field forward. Fig. 0.3 is a slide from a talk that I gave in early 2007 highlighting what was published in [2]. The first hybrid closed-loop patient—amazing! So much work happened in between 2006 and today. In the early years of the research, blood glucose testing was required frequently, including overnight. The patients were poked and prodded, they wore multiple devices, they and clinical teams spent days in hospital rooms, and

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FIGURE 0.2 Original slide representing JDRF CGM Trial Consortium. Note that the convergence of lines represent the JAEB Center in Tampa Florida. The Coordinating Center for the trial.

the work moved slowly. That said, it laid the foundation that concluded convincingly that these systems could work safely and were ready to be tested in outpatient trials. Incredible leadership was shown by Drs. Boris Kovatchev and Claudio Cobelli from UVA and U Padova, Drs. Frank Doyle, Howard Zisser, and Eyal Dassau from USCB/Sansum Institute, Drs. Bill Tamborlane and Stu Weinzimer, Dr. Roman Hovorka, and Drs. Ed Damiano and Steven Russell, to name just a few of the numerous in the field who worked tirelessly to push it forward. There have been many important milestones that marked the progress of the JDRF Artificial Pancreas Project. Importantly, the Helmsley Charitable Trust and the NIDDK both began to provide significant additional funds. The JDRF has contributed over $100M to the field to date. The HCT and NIDDK support has easily more than doubled that amount. I am proud of the paper I published that illustrated a roadmap to incrementally more automated AP systems [3]. JDRF worked closely with the FDA, and, in 2012, the FDA issued guidance on the development of AP systems, which paved the way for commercial development in the United States (the Content of Investigational Device Exemption (IDE) and Premarket Approval (PMA) Applications for Artificial Pancreas Device Systems (FDA, 2012). Furthermore, the Industry worked closely with the teams to provide devices that would communicate and be used in studies, which could receive IDEs and could be tested. Medtronic,

Foreword

FIGURE 0.3 Original slide representing the first iteration of the JDRF Artificial Pancreas Consortium.

DexCom, Insulet, Tandem, Roche, Dana, and others all provided significant support, without which progress could not have been made. Bryan Mazlish, who came from a banking background but wanted more for his wife and son, also provided significant help by helping break the need for wired systems with the “Mazlish Sleeve,” an elegantly engineered Bluetooth communicator, which allowed for wireless studies to be performed before Bluetooth-enabled devices were readily available. The past decade has brought incredible advancements thanks to the authors of this book and to many others. We have seen multiple high-impact manuscripts published in the most prestigious journals (see References for important examples). The safety and efficacy of closed-loop systems has been demonstrated convincingly (see Fig. 0.4). The first systems have been approved in many countries globally (Reference: 670g, Tandem, Diabeloop), a monumental achievement! It is important to note that a thriving “do it yourself” community has also arisen. On social media the hashtag #wearenotwaiting speaks to the urgency that people with diabetes feel and how these tools are providing benefit (full discloser: my brother and I have both been using DIY systems for two years). I often say “there are means” and there are “ends.” The key to the JDRF Artificial Pancreas project and to all of the incredible research and development in the artificial pancreas field is that we never lost sight of the ends. The ends are better diabetes outcomes! Of course, the outcomes that first comes to mind is the A1c. The A1c is critical, but they also include other important outcomes

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FIGURE 0.4 Original JDRF six-step artificial pancreas roadmap [4].

including less hypoglycemia, more time in range, better sleep, less anxiety and worry, and better quality of life! The story is still being told. More systems will come to the market, they will improve further, and they will reach more people with diabetes. Along the way, research will push these advances forward and, that is, the means. The means are critical. The authors of this book and countless others will continue to write the story and change the lives of people with diabetes. My brother and I thank you, the JDRF families thank you, and people with diabetes around the world thank you and will benefit from this tireless effort. I am thrilled that I could live through this exciting time and tell a piece of this incredible story! Aaron Kowalski, PhD Chief Mission Officer at JDRF December 2018

References [1] G. Tamborlane, W.V. Beck, R.W. Bode, B.W. Buckingham, et al., JDRF CGM study, Continuous glucose monitoring and intensive treatment of type 1 diabetes, N. Engl. J. Med. 359 (2008) 1464–1476. [2] S.A. Weinzimer, G.M. Steil, K.L. Swan, J. Dziura, N. Kurtz, W. Tamborlane, Fully automated closedloop insulin delivery versus semiautomated hybrid control in pediatric patients with type 1 diabetes using an artificial pancreas, Diabetes Care 31 (2008) 934–939.

References

[3] A.J. Kowalski, Can we really close the loop and how soon? Accelerating the availability of an artificial pancreas: a roadmap to better diabetes outcomes, Diabetes Technol. Ther. 11 (2009) S113–S119. [4] A.J. Kowalski, Pathway to artificial pancreas systems revisited: moving downstream, Diabetes Care 38 (2015) 1036–1043. [5] R.M. Bergenstal, S. Garg, S.A. Weinzimer, B.A. Buckingham, B.W. Bode, W.V. Tamborlane, F.R. Kaufman, Safety of a hybrid closed-loop insulin delivery system in patients with type 1 diabetes, JAMA 316 (2016) 1407–1408. [6] P. Cheng, P.C. Hindmarsh, F.M. Campbell, S. Arnolds, T.R. Pieber, M.L. Evans, D.B. Dunger, R. Hovorka, Home use of an artificial beta cell in type 1 diabetes, N. Engl. J. Med. 373 (2015) 2129–2140. [7] S. Del Favero, D. Bruttomesso, F. Di Palma, G. Lanzola, R. Visentin, A. Filippi, R. Scotton, C. Toffanin, M. Messori, S. Scarpellini, P. Keith-Hynes, B.P. Kovatchev, J.H. Devries, E. Renard, L. Magni, A. Avogaro, C. Cobelli, AP@home Consortium, First use of model predictive control in outpatient wearable artificial pancreas, Diabetes Care 37 (2014) 1212–1215. [8] F.H. El-Khatib, C. Balliro, M.A. Hillard, K.L. Magyar, L. Ekhlaspour, M. Sinha, D. Mondesir, A. Esmaeili, C. Hartigan, M.J. Thompson, Home use of a bihormonal bionic pancreas versus insulin pump therapy in adults with type 1 diabetes: a multicentre randomised crossover trial, Lancet 389 (2017) 369–380. [9] M. Phillip, T. Battelino, E. Atlas, O. Kordonouri, N. Bratina, S. Miller, T. Biester, M.A. Stefanija, I. Muller, R. Nimri, T. Danne, Nocturnal glucose control with an artificial pancreas at a diabetes camp, N. Engl. J. Med. 368 (2013) 824–833. [10] S.J. Russell, F.H. El-Khatib, M. Sinha, K.L. Magyar, K. McKeon, L.G. Goergen, C. Balliro, M.A. Hillard, D.M. Nathan, E.R. Damiano, Nocturnal glucose control with an artificial pancreas at a diabetes camp, N. Engl. J. Med. 371 (2014) 313–325. [11] Z.A. Stewart, M.E. Wilinska, S. Hartnell, R.C. Temple, G. Rayman, K.P. Stanley, D. Simmons, G.R. Law, E.M. Scott, R. Hovorka, H.R. Murphy, Closed-loop insulin delivery during pregnancy in women with type 1 diabetes, N. Engl. J. Med. 375 (2016) 644–654. [12] M. Tauschmann, H. Thabit, L. Bally, J.M. Allen, S. Hartnell, M.E. Wilinska, Y. Ruan, J. Sibayan, C. Kollman, P. Cheng, R.W. Beck, C.L. Acerini, M.L. Evans, D.B. Dunger, D. Elleri, F. Campbell, R.M. Bergenstal, A. Criego, V.N. Shah, L. Leelarathna, R. Hovorka, Closed-loop insulin delivery in suboptimally controlled type 1 diabetes: a multicentre, 12-week randomised trial, Lancet 392 (2018) 1321–1329. [13] H. Thabit, M. Tauschmann, J.M. Allen, L. Leelarathna, S. Hartnell, M.E. Wilinska, C.L. Acerini, S. Dellweg, C. Benesch, L. Heinemann, J.K. Mader, M. Holzer, H. Kojzar, J. Exall, J. Yong, J. Pichierri, K.D. Barnard, C. Kollman, P. Cheng, P.C. Hindmarsh, F.M. Campbell, S. Arnolds, T.R. Pieber, M.L. Evans, D.B. Dunger, R. Hovorka, Closed-loop insulin delivery in suboptimally controlled type 1 diabetes: a multicentre, 12-week randomised trial, N. Engl. J. Med. 373 (2015) 2129–2140.

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Preface Diabetes is a problem that is affecting millions of patients around the world and is projected to keep increasing in the upcoming years. Although the notion of an Artificial Pancreas (AP) was conceptualized about 60 years ago when Professor E.P. McCullaguh from Cleveland Clinic demonstrated the possibility of creating an implantable endocrine pancreas, it was not until 2006 when the Juvenile Diabetes Research Foundation (JDRF) formally introduced the AP project and outlined a clear road map that AP has been a true possibility. The last two decades have seen an important set of scientific and technological research advances. Today several multidisciplinary research groups led by physicians and engineers, mainly in the United States and Europe, but also with groups in Israel, Australia, and Latin America, have reported quality results that have led to creative solutions and options to provide better treatment for patients with diabetes. This book outlines the current activities and developments in the discipline of AP and describes the results of research of these multidisciplinary teams. Our intention in this publication is to present different views and approaches that have been taken and, particularly, to maintain a balance between the engineering and medical aspects of the Artificial Pancreas project. For that reason, it has been crucial for the editors in the selection of the chapters to present, not only the results obtained in silico, simulated results, but also the rich experience and knowledge gained by performing clinical trials. The latter have been covered in groups of all ages: children, adolescents, and adults. In this book a wide regional experience is presented by discussing both, simulated and clinical trials performed in France, Italy, Spain, different centers in the United States of America (California, Colorado, Illinois, Massachusetts, Virginia), and in Argentina. We expect this book to be a reference for engineers and physicians that want to gain knowledge in the current and future state of research and development of an Artificial Pancreas. Both editors would like to thank Dr. Edgar N. Sánchez for proposing this idea and the Elsevier group lead by Chris Katsaropoulos, Anna Valutkevich, and Ana Claudia Abad García, who guided us through the whole procedure. A special mention to all the authors that have contributed to this book making it an excellent example of worldwide collaboration. Thanks to all the patients and families that had participated in an immense amount of clinical trials voluntarily and with the only goal to help discover and advance the best treatment option for diabetes while awaiting cure. Finally, we are eternally thankful to our families for their constant support, patience, and encouragement. Ricardo S. Sánchez-Peña, PhD and Daniel R. Cherñavvsky, MD Buenos Aires and Charlottesville December 2018

xxxvii

CHAPTER

Feedback control algorithms for automated glucose management in T1DM: the state of the art

1

Dawei Shi, Sunil Deshpande, Eyal Dassau, Francis J. Doyle III Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

1.1 Introduction Feedback control algorithms play a central role in artificial pancreas (AP) systems to achieve safe and effective glucose regulation for people with type 1 diabetes mellitus (T1DM) [1–3]. With the availability of subcutaneous (SC) continuous glucose monitoring (CGM) and continuous SC insulin infusion (CSII), feedback control algorithms are designed to achieve maximized time spent within the euglycemic safe range of [70, 180] mg/dL, minimization of hypoglycemic events, and prevention of postprandial hyperglycemia with minimized patient intervention [1]. A closed-loop glucose control system is comprised of several basic modules with different functionalities (see Fig. 1.1). Generally, it consists of a sensor module, a pump module, and a feedback control module and treats the glucose metabolic process of a patient as the controlled process. The controlled variable (CV) of this system is usually the blood glucose concentration, but other physiological parameters can also be considered or controlled. The insulin infusion dose at each time instant is usually the default manipulated variable (MV); in certain systems, however, glucagon and pramlintide can be chosen as MVs as well. To obtain the information of CV, the sensor module can have one or more CGM sensors, and it can also have additional sensors to monitor other physiological parameters (e.g., heart rate, accelerometry, skin temperature) [4]. Depending on the choice of MVs, the pump module can have one or more CSII pumps containing the chosen MVs (e.g., insulin or glucagon). With technological developments, the intraperitoneal (IP) space has shown improved sensing and control characteristics and is a potential alternative site for delivery [5,6]. The feedback control module processes the sensor measurements through a signal processing unit, the outcome of which is further used by the controller to calculate the doses of MV at discrete time instants. In many cases, a model obtained based on either physiological principles or data-driven methods is needed to compute certain intermediate parameters, which are used to generate the MV dose [7]. The reference The Artificial Pancreas. https://doi.org/10.1016/B978-0-12-815655-1.00010-7 Copyright © 2019 Elsevier Inc. All rights reserved.

1

2

CHAPTER 1 Feedback control algorithms for glucose management

input to the system is usually the desired glucose concentration, which can either be formulated as a fixed/time-varying set-point or a constant/changing zone. The system is also subject to external treatment actions from patients or physicians (e.g., meal announcements, meal boluses, hypoglycemia treatments, patient-specified correction boluses); in certain cases, these external inputs can be used to perform open-loop feedforward control actions for improved glucose regulation performance. In this sense, the overall AP control system is sometimes said to be “hybrid” [8] as it has combined feedforward and feedback strategies. Control algorithm design for AP systems faces several critical challenges. First, asymmetric risks of hyperglycemia and hypoglycemia have to be dealt with. Hyperglycemia can cause severe and incurable health problems over long term (e.g., premature cardiovascular diseases, nephropathy, and neuropathy [9,10]), whereas hypoglycemia may cause immediate life-threatening consequences (e.g., seizures, coma, and even death). Second, severe actuation limitations exist in glucose regulation. Insulin can only be administered in a narrow therapeutic window where underdelivery can cause hyperglycemia whereas overdelivery can cause hypoglycemia. For SC delivery, an inevitable time delay composed of combined deadtime and dynamical lag associated with insulin pharmacokinetics exists before the insulin infused starts to take effect. Therefore, insulin on board (IOB), namely, insulin units that are still active in the human body, has to be carefully taken into account to prevent overdelivery. Third, the insulin-glucose metabolic dynamics is a high-order nonlinear process determined by a considerable number of parameters that change with patient’s growth/aging and lifestyle; thus it is difficult to obtain an accurate model based only on glucose and insulin information. To overcome these challenges, several types of feedback controllers have been developed and successfully tested in clinical studies (see [11] for an up-to-date database of AP clinical trials using different control algorithms). In this chapter, we provide a systematic overview of the designed control algorithms, with the aim of presenting the state-of-the-art feedback control algorithms for automated glucose regulation. We will start with simpler yet effective proportional-integral-derivative and fuzzy logic controllers, and then continue with the more advanced model predictive control, which is the main focus of our chapter as this approach has been clinically evalu-

FIGURE 1.1 Feedback control loop for automated glucose management. In this figure, the core elements in feedback control of the AP are illustrated. Note that some of the blocks may be optional in certain AP systems.

1.2 Proportional-integral-derivative control

ated by multiple research groups. We also cover a linear parameter-varying approach, which provides an alternative model-based possibility to consider the performance and safety requirements in an AP. Considering the need of long-term usage of the AP at home, controller personalization and adaptation approaches over a longer time scale are presented as well. Finally, we briefly introduce a few machine learning (ML) based control approaches, as ML has shown great potential in understanding and revealing complicated relationships that hide underneath physiological data during the recent years [12,13]. In the remainder of this chapter, the notation and nomenclature used in the original developments in the literature are adapted into a unified form for a clearer description.

1.2 Proportional-integral-derivative control The proportional-integral-derivative control or PID control is perhaps the most common strategy of implementing negative feedback control [14]. In its classical form, the PID control law consists of summation of three distinct terms or components: the proportional or P-term that captures the current tracking error (e(t), difference between the current CV and the desired set-point), the integral or I-term that captures historical accumulation of the error, and the derivative or D-term that captures anticipated change of the error. In continuous time, the PID control law can be mathematically written in terms of its three components as follows; in terms of gain parameter for each term:  t de(t) u(t) = Kc e(t) + KI e(t) + KD , (1.1) dt 0 or equivalently in terms of a common (proportional) gain parameter and time constants for the integral and derivative terms:    de(t) 1 t u(t) = Kc e(t) + e(t) + τD , (1.2) τI 0 dt where proportional gain Kc , integral gain KI , derivative gain KD , and integral and derivative times τI and τD , respectively, are the tunable parameters [14,15]. In general, while increasing Kc , KI , KD , τD or decreasing τI results in a more aggressive response to the error, this could lead to oscillations and instability. Further, the proportional term cannot always provide zero steady-state error, which is provided for by the integral term even in the presence of uncertainties and nonlinearities. Finally, while the derivative term can respond to changes in the error, it can be sensitive to noise and hence typically needs filtering before derivative action is implemented. Due to its simplicity and effectiveness, PID controllers are found ubiquitously in many natural and engineered systems [14–16]. In the following subsections, PID control approaches developed in the existing AP literature are reviewed, which have been evaluated in clinical studies. Section 1.2.1

3

4

CHAPTER 1 Feedback control algorithms for glucose management

describes the approaches for delivery of insulin using PID control, and Section 1.2.2 describes the approaches for delivery of glucagon using PID control.

1.2.1 Insulin delivery using PID control Other than its computational simplicity, it has been argued that PID control can be used to emulate the pancreatic β-cell biphasic insulin response and thus can be designed for a more physiological insulin delivery [17]. Together with the proportional component, the rapid first phase response can be achieved using the derivative component, whereas the sustained second phase response can be achieved using the integral component [17,18]. One of the formulations for automated closed-loop insulin delivery using PID control has been developed by Steil and coauthors as part of development of the AP at Medtronic Diabetes [8,19,20]. The PID control law used can be written in discrete time as follows: e(n) := SG(n) − target, P (n) = Kc e(n), I (n) =

K c Ts τI

n 

(1.3) (1.4)

e(k),

(1.5)

k=1



 e(n) − e(n − 1) D(n) = Kc τD , Ts P I D(n) = P (n) + I (n) + D(n),

(1.6) (1.7)

where SG is the sensor glucose, target is the desired glucose concentration, n represents the most recent sample, e(n) is the tracking error, Ts is the sample time, and the gain Kc can be set proportional to the subject’s daily insulin requirements, whereas τI and τD can be chosen as per desired glycemic response [19]. To avoid controller-induced hypoglycemia following an aggressive response to a meal, the PID control algorithm can be refined so that insulin delivery is decreased as the plasma insulin levels rise to mimic mechanism in pancreatic β-cells where insulin inhibits its own secretion. Since the actual insulin concentration cannot be currently measured in real-time, a compartment model can be used to estimate insulin concentration. The update to the PID insulin delivery algorithm with insulin feedback [20,21] can be written as I D(n) = P I D(n) − γ Iˆp (n),

(1.8)

where P I D(n) is the insulin input suggested by the classical PID controller, γ is the insulin feedback parameter, I D(n) is the final insulin delivery adjusted for insulin feedback Iˆp (n), which is the estimated insulin concentration. The addition of this insulin feedback term to the PID control can also be interpreted as a cascaded control system or an additional compensator, and typically the PID parameters have to

1.2 Proportional-integral-derivative control

be retuned to achieve the original basal response [21]. Insulin delivery by PID control through the IP route, which results in faster insulin absorption than SC insulin delivery, can result in further improvement in glycemic regulation [22]. To incorporate pancreatic β-cell response that plateaus after sustained hyperglycemia, a fading memory proportional derivative (FMPD) control has been proposed by Ward and coauthors [23–25]. The algorithm weights recent errors more than errors occurring in the distant past in cumulative terms consisting of proportional and derivative components as follows: I D(n) = K0

m  k=0

W0 (k)e(n − k) + K1

m  k=0

W1 (k)

de (n − k), dt

(1.9)

where K0 and K1 are weights, Wi (k) is an exponentially decaying function, m is the number of samples over which the summation is taken, de dt (·) is an estimate of the glucose rate-of-change, and the basal insulin is added to I D(n) for the final recommended value [25]. By keeping track of IOB the algorithm has built-in logic that turns off insulin infusion if the IOB reaches a predetermined value of the subject’s estimated total daily insulin [24,25]. In other works, PID control augmented with safety layer utilizing IOB to prevent controller-induced hypoglycemia has been proposed in [26]. A robust PID controller for a fully implantable intraperitoneal AP with insulin feedback and antireset windup strategy has been proposed in [5]. In an alternative approach, a bioinspired controller based on a mechanistic subcellular model of insulin secretion incorporating dynamics of readily releasable pool of insulin, along with insulin feedback, has been proposed and evaluated in [27–29].

1.2.2 Glucagon delivery using PID control Whereas insulin increases glucose disposal causing drop in glucose levels, glucagon has the counter-regulatory effect by increasing glucose levels by stimulating endogenous glucose production. Thus, other than treating with rescue carbs, glucagon delivery is required in order to correct for occurring hypoglycemia or to prevent impending hypoglycemia. The trigger of glucagon delivery is desired when there is a significant decreasing trend of glucose values and the two algorithms discussed in this section use a proportional-derivative (PD) formulation for glucagon delivery. The glucagon delivery Gdose in the bihormonal AP (also see Section 1.4.7) is through a PD controller [30], which can be written as follows:   SG(n − 1) − SG(n) Gdose (n) = Kc (target − SG(n)) + KD − Gpending (n) Ts (1.10) under the constraint 0 ≤ Gdose (n) ≤ Gmax , where Gmax is the maximum glucagon dose and Gpending (n) is the estimate of glucagon still active in the body [30].

5

6

CHAPTER 1 Feedback control algorithms for glucose management

The FMPD controller is also proposed for glucagon delivery using the control law shown in (1.9) with no additional basal glucagon infusion rate. To avoid glucagon overdelivery, the algorithm features a refractory period during which glucagon was not delivered if the delivered glucagon reached a maximum limit. The insulin rate was also modulated after delivery of a maximal glucagon pulse [24,25].

1.3 Logic-based control Unlike methods in the previous section, which rely on a dynamical representation of glycemic regulation, the closed-loop algorithms using fuzzy logic use specially designed dosing rules to incorporate expert clinical knowledge in diabetes decision making [31,32]. A fuzzy-logic-based controller has three main stages [15,33]: 1. Input fuzzification. The first stage maps the input x, e.g., glucose or its rate of change, using input membership functions μ(x) to a value in [0, 1] to denote its degree of membership. 2. Fuzzy inference. The second stage combines the fuzzy inputs from the first stage and a set of R fuzzy rules to determine the degree of activation αk of output membership functions, e.g., as αk = min(μAk (xA ), μBk (xB ))

(1.11)

for each rule k, where xA , xB , and μAk , μBk are inputs and input membership functions, respectively. 3. Output defuzzification. The third stage determines the final output u for the given time by calculating center of mass of the clipped output membership functions, e.g., as R αk uk u = k=1 , (1.12) R k=1 αk where uk is the center of output membership function k. Although the dosing logic is composed using discrete components, the final insulin delivery is uniformly continuous, and thus any variation in glucose is always responded by a small variation in insulin [34]. In the following, the two fuzzy control approaches, which have been evaluated in clinical studies, are reviewed. One fuzzy-logic-based AP system is known as MD-Logic Artificial Pancreas (MDLAP) developed by researchers at Schneider Children’s Medical Center of Israel [31]. The closed-loop algorithm consists of two control modules: control to range module (CRM), which aims to keep glucose in 80–120 mg/dL range, and control to target module (CTM), which aims to keep glucose at a specific target. The CRM houses the fuzzy logic controller that uses inputs consisting of current and future glucose levels and of past and future glucose trends while generating two outputs, change in subject’s basal rate and portion of insulin bolus. The initial output from

1.4 Model predictive control

CRM is used as an input to CTM, which also utilizes IOB and a meal detection logic to determine the final insulin basal and bolus dose. Another controller designed based on the fuzzy logic approach is known as FL controller, which has been developed by Mauseth and coauthors [32,34]. The closedloop algorithm requires three inputs: current glucose (mg/dL), rate of change of glucose (mg/dL/min), and acceleration of glucose (mg/dL/min/min), whereas the output variable is the insulin micro-bolus dose for each time. The recommended insulin dose is then multiplied by the personalization factor to account for inter- and intrasubject variability. Whereas both fuzzy-logic-based controllers discussed above rely on using dosing rule codified by clinicians and Mamdani-type fuzzy logic rules, the main differences between the two systems is that while FL recommends insulin doses, MDLAP modulates both basal and bolus insulin. The MDLAP also requires prediction of glucose and its rate of change, whereas the FL controller relies only on the current glucose information [31,32].

1.4 Model predictive control Model predictive control (MPC) is one of the most widely used approaches to advanced control system design in academia and industry [35] due to its ability to directly handle practical constraints and multiple inputs and outputs, formulate control objectives into a constrained optimization problem, and find the optimal control inputs by solving the optimization problem in a receding-horizon fashion. So far, this approach has been successfully utilized in the development of AP systems by different research groups [1,11,36]. In the context of AP systems, the aim of adopting MPC is to explicitly enforce safety constraints, penalize asymmetric risks of hyper- and hypoglycemia, optimize glucose trajectories under disturbances, and predict impending hypoglycemic episodes. Generally speaking, MPC identifies the optimal control trajectories by solving a constrained optimization problem at each controller update time instant n: min

u0 ,...,uNu −1

s.t.

J (x0 , u0 , . . . , uNu −1 )

(1.13)

xk+1 = f (xk , uk ), k = 0, 1, . . . , Np − 1, g(xk , uk ) ≤ 0, k = 1, 2, . . . , Np ,

where each element is defined as follows: • An objective function J (x0 , u0 , . . . , uNu −1 ) quantifies the importance of different control objectives. For notational brevity, we denote J (x0 , u0 , . . . , uNu −1 ) as J (·) in the remainder of this section. Generally, J (·) is a convex function with respect to the optimization parameters, and depending on the goal of MPC, it can be defined to penalize glucose trajectories toward a set-point or zone.

7

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CHAPTER 1 Feedback control algorithms for glucose management

FIGURE 1.2 Flow diagram for MPC. Here we use xn instead of xk to denote that state of the process under control. xˆ n denotes an estimate of xn . Note that the truncation module takes the first element u∗0 of the optimizer.

• A prediction model xk+1 = f (xk , uk ) predicts the future behavior of the controlled system within the prediction horizon Np . In an AP, this model normally describes the insulin-glucose dynamics and can be linear or nonlinear depending on the level of modeling approximation; a switching model can also be used by defining a number of submodels and a law of deciding the “active” submodel at each k. For implementation consideration, discrete-time models are usually utilized in MPC, but continuous-time models can be utilized as well. • A set of inequality constraints g(xk , uk ) ≤ 0 describe the limitations of system operation. In the context of AP, the constraints normally include upper and lower bounds on the insulin infusion at each time instant. In particular, constraints that ensure patient’s safety against controller-induced hypoglycemia can be incorporated as well. For a clearer description, we use n to denote instants in real time and k to denote instants within an MPC iteration, and we denote the starting point of the prediction at all time instants n as k = 0. At each controller update time instant n, MPC solves problem (1.13) and obtains the optimal control sequence {u∗0 , . . . , u∗Nu −1 }. The first element u∗0 is executed, and the rest of sequence is ignored for most cases. This procedure is performed in a receding horizon fashion with the increment of time n. Also note that the state predictions are built on the knowledge of x0 , which is usually not known as only the sensor measurements {yn } are available. Thus it is necessary to estimate x0 based on {yn } utilizing a state observer or estimator. This procedure is also illustrated in Fig. 1.2. The optimization problem in (1.13) can be either solved online through off-theshelf numerical optimization tools or offline explicitly combined with an online lookup-table algorithm [37,38], depending on the problem size and available computation resources. If no inequality constraint is considered, the prediction model is linear, and the cost function is quadratic, then the closed-form expression of a constant controller

1.4 Model predictive control

FIGURE 1.3 Features of MPC for glucose regulation. The key features of MPC developed for the AP are summarized, the detailed description of which is provided in the remainder of this section.

gain can be obtained by solving a quadratic problem with linear equality constraints [39]. In the following subsections, various MPC approaches developed in the existing AP literature are reviewed, most of which have been extensively evaluated through clinical studies. In particular, the approach in Section 1.4.1 featured a high-order linearized model and an unconstrained solution; the approaches in Sections 1.4.2, 1.4.6, and 1.4.7 adopted adaptive model parameter estimation and set-point references with different safety precautions; the approach in Section 1.4.3 penalized the glucose trajectories toward a zone, whereas that in Section 1.4.4 respectively utilized quadratic and exponential penalties for hyper- and hypoglycemia, both of which considered IOB constraints in the MPC optimization problem. The approach in Section 1.4.5 featured a risk-dependent cost function and a probabilistic switching prediction model. The approach in Section 1.4.8 adopted policy optimization instead of sequence optimization. It is also worth noting that the approaches in Sections 1.4.1, 1.4.2, 1.4.3, and 1.4.7 have been evaluated in large- or long-term clinical trials. Due to space limitations, not all the results on MPC design for the AP in the literature have been discussed; the idea here, however, is to discuss the key features in MPC design for AP systems, which are also briefly summarized in Fig. 1.3.

1.4.1 Unconstrained MPC with safety checks An unconstrained MPC approach was developed by Cobelli, Magni, and coauthors [40], which has been evaluated through clinical trials in outpatient and free-living conditions [40–42]. The controller considered a quadratic cost function of the form J (·) :=

Np −1  k=0

  Px , q · (yk − yref,k )2 + (uk − uref,k )2 + xN Np p

(1.14)

where yk denoted the glucose predictions from the basal glucose value, uk denoted insulin delivery from basal rate ubasal,k , and yref,k and uref,k denoted the reference trajectories for yk and uk , respectively. The cost function had a terminal cost term

9

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CHAPTER 1 Feedback control algorithms for glucose management

 Px xN Np with P obtained by solving the Riccati equation corresponding to the linear p quadratic regulator [40]. In this approach, a high-dimensional linear state-space model was utilized for state and glucose prediction:

xk+1 = Axk + Buk + Mdk , yk = Cxk ,

(1.15)

where dk represented the meal. This model was obtained by linearizing the nonlinear Dalla Man model reported in Magni and coauthors [43], and a Kalman filter was utilized to estimate the state xk . As no constraints were considered for this MPC, the control law can be explicitly calculated in a closed-form:  

u∗k = 1 0 . . . 0 −Kx xk − Kd Dk + KYref Yref,k + KUref Uref,k , where Kx , Kd , KYref , KUref denoted gain matrices [40], and Dk , Yref,k , and Uref,k were lumped vectors for dk , yref,k , and uref,k , respectively. For real-time implementation, an initial control input was first calculated using this control law, based on which safety constraints, including meal bolus limitation, insulin constraint, pump shutoff avoidance, and insulin variation constraints, were further incorporated to generate the final control input. In a recent paper [44], an updated version of the unconstrained MPC was proposed, for which integral action was introduced by adding an integral error term in the MPC cost function and an augmented state space model, which described the original system dynamics together with the integral action.

1.4.2 Multiple model adaptive MPC A multiple-model MPC approach was developed by Hovorka and coauthors [45,46]. Different versions of this control algorithm have been tested in multiple clinical trials [47–51]. This approach featured a reference-based objective function  Np  1 (uk − uk−1 )2 , (yk − yref,k )2 + kagr (1.16) J (·) := k=1 where kagr > 0 was a tuning parameter that adjusted the aggressiveness of the controller. To consider asymmetric risks of high- and low-glucose events, different target trajectories yref,k were adopted, which were characterized by a slow (linear) decline from hyperglycemia and rapid (exponential) recovery from hypoglycemia toward the targeted glucose value (e.g., 108 mg/dL [45]). Glucose predictions of this approach were obtained on the basis of the nonlinear Hovorka model [52]. Several competing models with different rate of subcutaneous insulin absorption and action and CHO absorption profile were run in parallel, and a stochastic model-selection approach was adopted to determine a model with best glucose fittings [46]. The models were initialized using subject’s weight, total daily insulin and basal insulin profile, and two model parameters (glucose flux and CHO

1.4 Model predictive control

bioavailability) were updated in real time using a Kalman filter approach with glucose measurements. Kalman filter was also adopted for present glucose and insulin estimates. In an earlier paper [45], the authors also reported that a Bayesian parameter estimation approach was taken to identify the model parameters by optimizing a cost function that included a weighted sum of squares of residues and a regulation penalty due to the distance from the prior distributions for different learning windows. In [45], the authors reported that upper and lower bounds on insulin delivery were used inside MPC, but “safety checks” were also performed before the MPC-requested insulin was delivered, including [46]: • a maximum infusion rate limitation that was 2–5 times of the subject’s basal rate, depending on the current glucose level, time elapsed from previous meals, and CHO content of the meal; • compulsory pump-suspension operation when glucose level was 77 mg/dL; • reducing insulin delivery rate when glucose level was decreasing rapidly; • limiting the maximum infusion rate to basal rate if a “pump occlusion” event was inferred.

1.4.3 Zone MPC As euglycemia is defined as a range of blood glucose values instead of a single value [53], Doyle, Dassau, and coauthors [54–57] developed a zone MPC approach to blood glucose management, which is less sensitive to small glucose variations (e.g., due to sensor measurement noises) and leads to less abrupt control trajectories. This approach has been extensively evaluated in inpatient and outpatient clinical studies [58–61]. Zone MPC featured the penalization of the distance of predicted glucose trajectories from a prespecified time-varying safe zone; mathematically, this time-dependent distance for a glucose prediction y were defined as 

Z(y, n) := arg min α 2 |y − α ∈ [ˇz(n), zˆ (n)] ,

(1.17)

α∈R

where n denoted time of day, and zˆ (n) and zˇ (n) denoted the upper and lower bounds of the safe zone. In earlier versions of zone MPC, a constant zone was utilized to achieve the goal of “control to range” [54,62], whereas more delicate periodic and time-dependent zones were proposed later to emphasize the safety against overnight hypoglycemia and consider metabolic circadian rhythm [56,57]. A simple zone MPC objective function could be written as [54] J (·) :=

 Ny

k=1 [Z(yn , n + k)] + R

Nu −1 k=0

u2k ,

(1.18)

where uk denoted the deviation from basal rate ubasal,k . More recently, an advanced objective function was proposed as [57]

11

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CHAPTER 1 Feedback control algorithms for glucose management

J (·) :=

 Ny

ˆ

k=1 [min(Z(yn , n + k), 0) + Q(vk ) max(Z(yk , n + k), 0) + Dvk ] Nu −1 + k=0 [Rˆ max(uk , 0)2 + Rˇ min(uk , 0)2 ],

(1.19) where deviations above and below the safe zone [ˇz(n), zˆ (n)] were separately weighted by 1 and Q(vk ) to emphasize the asymmetric risks of hypoglycemia and ˆ k was included to further counhyperglycemia, a glucose velocity penalty term Dv teract hyperglycemia, and the control actions above and below basal rate (which is denoted as 0 in (1.19) as uk is defined as the deviation from basal rate ubasal,k ) were also separately penalized to enhance safety. Note that different forms of objective functions have been utilized in zone MPC design, and the form in (1.19) corresponds to the most recent version and has been recently evaluated in a 12-week outpatient clinical study [61]. Recent versions of zone MPC [56,57] were built on a linear control-relevant statespace model [7] xk+1 = Axk + Buk , yk = Cy xk , vk = Cv xk , (1.20) ⎡ ⎤ p1 + 2p2 −2p1 p2 − p22 p1 p22   ⎣ A := 1 0 0 ⎦ , B := K 1 0 0 , 0 1 0 1800F (p1 − 1)(p2 − 1)2 , p1 := 0.98, p2 := 0.965, u   TDI   Cy := 0 0 1 , Cv := 0.1 0 −0.1 , K :=

where the model gain K was personalized to the subject utilizing the total daily insulin (TDI) uTDI and a safety factor F . Since the proposed MPC was based on state-feedback and only CGM readings were available, an estimate of the state xk was generated utilizing a Luenberger observer with observer gain designed according to a steady-state Kalman filter [63]. The obtained estimate was further used by the zone MPC for glucose prediction and optimization. Two types of constraints on control input sequences {uk } were considered in a zone MPC. The first type of constraints specified a time-dependent upper bound u¯ k of allowable insulin dose uk + ubasal,k for each k, where ubasal,k denotes the basal rate. The second type of constraints was the so-called insulin-on-board (IOB) constraint [64], which captured the difference between amount of insulin needed and the IOB that had already been infused subcutaneously but had not yet become active. IOB was estimated by evaluating the IOB caused by meal boluses and IOB induced by closed-loop control according to different insulin decay curves. Note that the possibility to incorporate the circadian rhythm of insulin sensitivity (IS) into an IOB constraint has also been considered [65]. Another major consideration in zone MPC design was control parameter personalization and adaptation. To capture the mismatch between the linear prediction model utilized and the underlying nonlinear insulin-glucose metabolic dynamics,

1.4 Model predictive control

a trust index was incorporated in zone MPC to adaptively adjust controller parameters based on the precision of the prediction model in recent history [66]. In an effort to implement zone MPC on embedded devices, event-triggered controller update strategies were introduced to adaptively reduce the amount of computation power required [67,68]. An extreme-seeking-based adaptive mechanism was developed to identify the personalized optimal zone boundaries of a zone MPC for an individual by optimizing the relative regularized glycemic penalty index [69]. More recently, a glucoseand velocity-dependent control penalty parameter adaptation approach was proposed by constructing an explicit map from glucose prediction and glucose rate-of-change to control penalty parameters [70].

1.4.4 Set-point-based enhanced MPC design Aside from the zone MPC approach, Doyle, Dassau, and coauthors also worked on a set-point MPC approach to address AP design challenges. Specifically, a set-pointbased enhanced MPC (eMPC) [71] was recently proposed to consider inter- and intraindividual variations in insulin sensitivity, the asymmetry in the effects of hyper and hypoglycemia, and controller-induced hypoglycemia after rescue CHO ingestion following prolonged pump suspension. The eMPC featured an asymmetric hybrid objective function that applied a quadratic penalty on glucose predictions above the set-point but an exponential penalty on excursions below the set-point: Ny  J (·) := k=1 max(yk , yref )2 + exp (a min(yk , yref )2 )  u −1 2 2 ˆ ˇ + N (1.21) k=0 [R max(uk , 0) + R min(uk , 0) ]. Similar to the zone MPC, the control actions above and below basal rate (which is denoted as 0 in (1.21)) were also separately penalized to consider the asymmetric effects of hyper- and hypoglycemia. The eMPC utilized a prediction model with identical structure and eigenvalues as that in (1.20), except that the model gain K was modified according to subject’s TDI and more importantly, the subject-specific basal profile. Specifically, K := 0.4f (uTDI )/ubasal,k ,

(1.22)

where f (uTDI ) was a function of uTDI specified either according to that in van Heusden et al. [7] or by the subjects according to the correction factor. This choice allowed the change of glucose response according to the change of insulin sensitivity. Similar to zone MPC, eMPC also adopted upper bound constraints on allowable insulin dose and IOB constraints. In particular, to reduce the potential controllerinduced hypoglycemia without affecting controller’s activeness in reacting against hyperglycemia, an enhanced dynamic IOB strategy was incorporated in eMPC. Basically, the revised IOB calculation algorithm modified any series of q or more consecutive steps of zero insulin delivery (pump suspension) in the previous N steps

13

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CHAPTER 1 Feedback control algorithms for glucose management

in history with ubasal,k . This led to a larger value of IOB and thus brought in a tighter IOB constraint that limited over-aggressive insulin delivery and alleviated controllerinduced hypoglycemia.

1.4.5 Multiple model probabilistic predictive control A scenario-dependent multiple model MPC approach was proposed by Cameron, Bequette, and coauthors [72–74] to achieve consistent and strong filtering of sensor noise and fast adaptation for disturbances; the controller has been tested in a recent clinical study without meal announcements [75]. Different from other approaches, this MPC took future glycemic risks into account by considering risk-dependent cost functions. Specifically, a risk-based cost function was proposed as [73] J (·) :=



∈{0,±1.25,±2.5} exp(−

−1 

2)

∈{0,±1.25,±2.5} exp(−

2)

· risk(g  (u0 , . . . , uNu )). Here g  (u0 , . . . , uNu ) := g(u0 , . . . , uNu ) + σ , with g(u0 , . . . , uNu ) denoting the predicted glucose trajectories given a insulin delivery sequence {u0 , . . . , uNu }, and σ being the estimated standard deviation sequence of the predicted glucose. The risk Np risk(g i ) with function risk(g) was defined as risk(g) := i=1  risk(g) := a · g + b ·

c(d − g)3 0

if g ≤ d, otherwise,

(1.23)

where a, b, c, d were parameters. To obtain the optimal insulin delivery rate, the MPC relied on a multiple model probabilistic algorithm that predicted not only future mean glucose but also glucose measurement uncertainty [72]. The probabilistic prediction algorithm was based on a 7-state linear model of the glucose dynamics for a subject with T1DM. On the basis of a stable random walk process that modeled the unforced glucose dynamics, the actual glucose response was calculated by considering meal and insulin inputs captured by second-order impulse responses. Sensor noise was modeled as a stable random walk as well. Multiple versions of this model were used, each of which was propagated by a Kalman filter; these candidate models were then weighted based on prior probabilities and the data fitting. As time went by, the prediction algorithm selectively included, merged, and removed candidate models to keep the available model set relevant. According to [73], upper and lower bounds on insulin delivery were considered in the MPC optimization algorithm. A detailed and combined summary of the probabilistic model and the MPC can be found in [74].

1.4 Model predictive control

1.4.6 Adaptive generalized predictive control and MPC design With the goal of ultimately eliminating the need of meal and activity announcements, Cinar and coauthors have focused on an adaptive predictive control approach to the AP design, together with different parameter identification techniques [76–80]. The results developed were verified in clinical trials [76,81]. In earlier results [76], a generalized predictive control (GPC) approach was utilized, based on a cost function of the form similar to (1.16) but with separate prediction and control horizons J (·) :=

 Np

k=2 (yk

− yref,k )2 +

 Nu

k=1 wk (uk

− uk−1 )2 ,

(1.24)

where uk denoted predicted insulin delivery. In this approach, an autoregressive moving average model with exogenous input (ARMAX) A(q −1 )yk =

3

i=1 Bi (q

−1 )u i,k

+ C(q −1 )ek

(1.25)

was utilized for glucose predictions, where u1,k , u2,k , and u3,k denoted infused insulin, measured energy expenditure, and galvanic skin response, respectively. The model parameters were obtained by minimizing a mean square error cost function. The physiological signals (measured energy expenditure and galvanic skin response) were used as external inputs for the prediction model. For the GPC optimization problem, constraints on maximum and minimum insulin infusion rates were considered. After the optimal insulin input u∗t was obtained, the final insulin delivery rate was obtained by comparing u∗t with the predicted IOB value. In recent developments [78–80], an MPC approach that accounted for plasma insulin concentration (PIC) was proposed, together with a PIC estimation technique based on the Hovorka model [45]. The cost function utilized was almost identical to that in (1.24), but with different choices of Np and Nu . Glucose predictions were based on a time-varying linear state-space model, with one of the states being estimated PIC; the model parameters were updated using predictor-based subspace identification algorithm [79]. In addition to bounds on insulin infusion rates, PIC constraints were also considered in the MPC optimization problem. The results, however, are yet to be tested clinically.

1.4.7 Bihormone adaptive generalized predictive control Damiano, El-Khatib, and coauthors developed an adaptive generalized predictive control approach [30,82,83], with the applicability to bihormone (insulin and glucagon) AP systems [84]. The results were tested in animal tests and clinical studies [30,82,85–87]. This approach was firstly developed to determine insulin infusion microboluses, utilizing a cost function of the form in (1.24) with small prediction and control hori-

15

16

CHAPTER 1 Feedback control algorithms for glucose management

zons. In [83], the authors discussed the use of a cost function that also penalized insulin accumulation in the subcutaneous depot on top of the terms in (1.24). Predictions were made by using an ARMAX model, with inputs being insulin and glucagon doses and output being glucose deviation from set-point, but only insulin was considered as the control input in GPC. The model parameters were updated recursively to ensure the precision of glucose predictions. When penalization of insulin accumulation in the subcutaneous depot was considered, a discrete-time model that captured the relationship between insulin doses and insulin concentration in the subcutaneous depot qt was also built: qt = −α1q qt−1 − α2q qt−2 + b1q ut−dq + b2q ut−dq −1 .

(1.26)

This equation was then combined with the ARMAX model to obtain the augmented model for GPC. An unconstrained GPC was used in [30,82], for which the optimal control law could be analytically calculated. In [83], it was mentioned that input constraints on minimum and maximum doses together with their rate of change could be considered. In [84], the authors mentioned that apart from the PD control approach to glucagon infusion calculation introduced in Section 1.2.2, it was also possible to compute glucagon doses through a GPC cost function similar to that in (1.24). The actual commanded dose could be further calculated through different but easy-toimplement ways on the basis of estimated accumulation of exogenously insulin and glucagon. The glucagon accumulation could be directly penalized in the cost function as well, with a mathematical model estimating the accumulated exogenous glucagon.

1.4.8 Policy-based stochastic MPC To consider the uncertainty associated with future food and exercise disturbances, an MPC scheme based on stochastic programming that incorporated policy optimization was proposed by Goodwin and coauthors [88]. This approach considered different meal and exercise scenarios through a probabilistic model. Preliminary numerical evaluation results were available. To take food and exercise patterns of a subject into account, a stochastic MPC cost function was proposed: J (·) := Ed 1 ,...,d m j

l



Np k=1 



yk (dj1 , . . . , dlm ), uk (dj1 , . . . , dlm ), yref,k

 ,

(1.27)

where dj1 , . . . , dlm denoted a disturbance sequence that described random meal and exercise events. The prediction horizon was set to be relatively long (e.g., 24 hours [88]) to consider lifestyle disturbances. As the number of disturbance scenarios increase exponentially with the cardinality of the disturbance sequence, computation was the major challenge to this approach.

1.5 Switched linear parameter varying control

A linear impulse response prediction model was utilized in this MPC, which had the form  N u d (1.28) yk = y s + N l=1 hl dk−l − l=1 hl uk−l , where y s and dk denoted steady-state glucose concentration and disturbance sequence, respectively, and the model parameters hdl and hul were obtained based on data from a real patient. As in other approaches, constraints on control inputs were considered. Noticeably, limitations on lower and upper bounds of disturbed glucose levels were imposed as well to ensure the robustness of the obtained control policy. In addition, causality equality constraints were adopted to ensure that the control policy was a function of the actual disturbances that had appeared in the past and the set of all possible disturbances in the future.

1.5 Switched linear parameter varying control Another approach to closed-loop glucose regulation is to separately design subcontrollers with simpler forms for specific symptoms/scenarios (e.g., hyperglycemia, hypoglycemia, meal, exercise) and to select the appropriate subcontroller based on a dynamic switching mechanism. With this idea, Sánchez-Peña and coauthors [89,90] developed a switched linear parameter varying (LPV) control approach, for which in silico results were obtained. In [89], an LPV controller that switched between two subcontrollers was proposed, with one controller dealing with large and persistent hyperglycemic excursions and the other responsible for glucose control at all other scenarios. The subcontrollers were designed on subject-specific transfer models with different model gains: Gj (z) = −

(1 − z−1 p

Fj crz−3 , j = 1, 2, −1 −1 1 )(1 − z p2 )(1 − z p3 )

(1.29)

where F1 relied on the subject’s body weight and carbohydrate ratio, F2 was designed to be smaller than F1 to obtain a more aggressive control law for high and rising glucose levels, r reflected the effect of total daily insulin, and the parameters c, p1 , p2 , and p3 were constant for all subjects. The LPV controller was designed based on Matlab Robust Control Toolbox with stability guarantees. Two signals θ1 (t) and θ2 (t) were selected as time-varying parameters, with θ1 (t) inversely proportional to glucose level y(t), and θ2 (t) related to current plasma insulin level ipe (t) and basal plasma insulin level ipb (t): θ1 (t) = 110/y(t), θ2 (t) = ipe (t)/ipb (t).

(1.30)

Estimation of ipe (t) was performed through the subcutaneous insulin model in [91, 92]. To switch between different subcontrollers, a switching signal σ (t) ∈ {1, 2} was

17

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CHAPTER 1 Feedback control algorithms for glucose management

designed based on CGM processed through noise-spike and Savitzky–Golay filters, which was further fed into hyperglycemia detector and switching signal generator blocks. The overall switching controller was executed according to   Kσ (t) (θ (t)) = v=1 η (t)Kσ (t) (θ ), θ (t) = v=1 η (t)θ , (1.31) where {η (t)} were the polytopic coordinates of θ (t), and {θ } were the vertices of the underlying polytopic system. The controller was evaluated utilizing the adult cohort of the complete UVA/Padova metabolic simulator [91,92] for two in silico protocols without meal announcements. In [90], this approach was further extended to consider the scenario of physical activity (PA). An additional “conservative” subcontroller was introduced in the LPV control scheme to deal with postprandial PA control. The control performance was evaluated through an ad hoc simulator developed based on the distribution version of the UVA/Padova model by further including the effect of PA.

1.6 Personalization and adaptation This section is devoted to control algorithms for parameter personalization and adaptation in the AP under longer time-scales (e.g., days or weeks, as opposed to 5–15 minutes). As the glucose metabolic process and lifestyle changes consistently throughout the lifetime of patients, the AP should have the ability to adapt with the growth and aging of patients. In fact, the interest on this problem precedes the advent of CGM and CSII, the focus of which was to adaptively update basal rate and meal bolus sizes [39,93]. With the development of an AP based on CGM-driven feedback control algorithms, this interest has been recently enhanced with the goal of achieving long-term home-use-safe glucose regulation.

1.6.1 Run-to-run approaches Run-to-run control was the earliest approach utilized in parameter adaptation for glucose regulation, as this approach is suitable to applications that lack in situ measurements for the controlled variable y of interest [94]. Roughly speaking, a run-to-run control algorithm has the recursive form of [94] u(k) = αu(k − 1) − r(k),

(1.32)

where u denotes the manipulated variable, α is a forgetting factor, and r is the updating law for run-to-run. An example for r can be r(k) = K[y ∗ − y(k − 1)], where K is a gain matrix, and y ∗ denotes the reference value. In earlier results [39,93], run-to-run parameter adaptation algorithms were proposed to adjust meal-related insulin dose and basal rate based on sparse glucose measurements, respectively. A run-to-run approach was also proposed to achieve MPC parameter tuning in [95]. This approach was recently revisited in [96], in which

1.6 Personalization and adaptation

the basal insulin delivery was adapted at night and the carbohydrate-to-insulin ratio was adjusted during the day, based on performance metrics extracted from subcutaneous CGM data.

1.6.2 Iterative learning control Iterative learning control (ILC) can be regarded as a two-timescale enhancement of the run-to-run approach that builds on the availability of measurements of the controlled variable y on a faster timescale n [94]. Parameter adaptation, however, is performed on a slower timescale k. Similar to (1.32), a typical ILC algorithm can be mathematically described as u(t, k) = αu(n, k − 1) − r(n, k).

(1.33)

The objective is to design r(n, k) to ensure a small tracking error y ∗ − y(n, k). Obviously, the availability of CGM makes ILC an attractive approach to adapt AP parameters along a longer timescale. In [97,98], an ILC-based approach was proposed to achieve MPC adaptation for glucose regulation. This approach exploited the 24-h circadian rhythm of insulin sensitivity and life style by iteratively updating either the reference trajectory or the cost function of MPC, so that the control performance could be gradually improved from day to day. The resultant ILC-MPC was tested through a pilot clinical study recently [99]. In [100], an iterative learning process was proposed to tune a mixed feedback and feedforward controller through day-by-day automated analysis of glucose response to insulin infusion, which was tested through in silico experiments.

1.6.3 Moving average approach As part of a bihormone glucose level control scheme composed of a glucagon controller, a basal insulin controller, a corrective insulin controller, and a priming insulin controller, a moving average approach was introduced to achieve long-term adaptation of a nominal basal infusion rate and meal bolus rate to accommodate patient’s needs during growth, sickness, hormonal fluctuations, physical activity, and aging [84]. In [84], the authors suggested two methods of adapting nominal basal infusion rate μ¯ k in a receding horizon fashion: α k μj , N  j =k−N β k μ¯ k+1 = μ¯ k N j =k−N μ¯ k+1 =

(1.34) μj μ¯ j

 ,

(1.35)

where μj denoted the instantaneous basal infusion rate at time instant k ≥ N . In a similar fashion, an adaptation law for instantaneous dynamic meal-time bolus Bkm of

19

20

CHAPTER 1 Feedback control algorithms for glucose management

meal m on day k was suggested as  m = β m Bkm Bk+1

1 k N j =k−N+1

Bjm Bjm +Cjm

−1 ,

(1.36)

where β m ∈ (0, 1) denoted a safety factor, Cjm denoted insulin that was given by the control system for meal m over a certain prandial and post prandial-time interval, and Bkm could be split into a number of doses. Adaptation laws in continuous time were also provided. Notice that the bihormone glucose level control scheme has been tested through multiple clinical trials [30,86,87].

1.7 Machine-learning-based control The abundance of data from CGM and CSII, together with the availability of measurements from additional sensors (e.g., heart rate and flux, skin temperature, 2D acceleration [101]) have made machine learning (ML) approaches attractive in glucose management for T1DM. Machine learning approaches are capable of directly extracting knowledge from large datasets and thus enable data-driven control policies to be developed. Although it is possible to treat the AP design problem as a pure ML problem (instead of a “classic” control problem), the key challenge is to ensure the reliability and complexity of the data-driven ML algorithms used in real time. In combination with machine learning techniques, however, model-based glucose controllers (e.g., MPC) can achieve enhanced performance by incorporating the additional knowledge and patterns learned through ML. In this section, we review a few machine learning aided approaches to the AP design in the literature. A detailed overview of machine learning and data mining methods in diabetes research can be found in [12].

1.7.1 Reinforcement-learning-based approach Reinforcement learning (RL) improves the performance at a given task through continuous interaction with its environment and optimizing decision policies [102]. It falls between supervised and unsupervised learning and is capable of performing optimization within an uncertain environment through learning from data. In [103], an RL-based approach was developed to obtain robust glucose regulation for T1DM given uncertainties from inter-/intrasubject variability. The approach relied on an actor-critic (AC) learning algorithm that performed personalized insulin infusion through model-free optimization of daily basal insulin rate and carbohydrate ratio, where the critic evaluated a control policy, and the actor was responsible to improve the control policy. Personalized tuning of the AC algorithm was obtained through estimating the transfer entropy from insulin to glucose that linked to patientdependent metrics related to TDI and insulin sensitivity (IS). The algorithm was evaluated on the UVA/Padova metabolic simulator under a multimeal protocol that considered meal uncertainty and diurnal IS circadian rhythm.

1.8 Summary

1.7.2 Gaussian process MPC Gaussian process (GP) is an efficient approach to regression and classification problems in supervised machine learning. It is particularly useful in learning an unknown function with the knowledge of the function at a finite number of data points [104]. This approach is often used together with other techniques to solve problems with a larger complexity (e.g., optimizing an unknown objective function based on sample measurements [105]). In [106], GP was utilized in conjunction with MPC and an unscented Kalman filter to explicitly take account of IS circadian rhythm in closed-loop glucose control. This approach was motivated from [107]. The goal of GP was to learn the effect of IS based on historical glucose data updated continuously in closed-loop control and system state information from an unscented Kalman filter. The overall algorithm was evaluated on Sorensen-model-based in silico studies for the scenarios of fasting, announced meals, and skipped meals.

1.7.3 Deep learning-assisted control Deep learning (DL) is relatively new area in ML that extracts complex relationships from data through learning multiple levels of representations, which correspond to a hierarchy of features and concepts [108]. In deep neural networks, higher-level representations are usually built on lower-level ones, and features on the same lower level can help define many higher-level features. In [109], a deep-learning-based assistive method capable of automatically estimating macronutrient content via real-time image recognition was proposed. Based on a meal image together with an estimated serving size, a deep convolutional neural network was utilized to predict food category, which was further used to query a nutritional database to obtain the macronutrient content. The proposed method could serve as a feedforward controller to eliminate the need of meal announcements in an AP and could be integrated with a conventional feedback controller. The strength of this hybrid control approach was illustrated through in silico results obtained using the UVA/Padova metabolic simulator controlled by a zone MPC.

1.8 Summary In this chapter, we have reviewed different controller design methods for AP systems in the literature and have discussed the features of the algorithms in detail. The methods covered include the simpler PID and FL controllers, the relatively more complicated MPC and LPV controllers, and the recently developed ML-based controllers. Many of the algorithms have been evaluated through large clinical studies, the results of which indicated their feasibility, safety, and robustness in glucose management. With the technological developments in CGM and continuous drug delivery, the availability of additional measurement signals, the need of embedded implemen-

21

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CHAPTER 1 Feedback control algorithms for glucose management

tation, and long-term home-use of the AP, the role and functionality of feedback control algorithms will continually evolve to address new challenges.

Acknowledgments This work was supported by the National Institutes of Health under Grants DP3DK104057 and UC4DK108483.

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[88] G.C. Goodwin, A.M. Medioli, H.V. Phan, B.R. King, A.D. Matthews, Application of MPC incorporating stochastic programming to type 1 diabetes treatment, in: Proc. Amer. Control Conf., 2016, pp. 907–912. [89] P.H. Colmegna, R.S. Sánchez-Peña, R. Gondhalekar, E. Dassau, F.J. Doyle III, Switched LPV glucose control in type 1 diabetes, IEEE Trans. Biomed. Eng. 63 (6) (2016) 1192–1200. [90] P.H. Colmegna, R.S. Sánchez-Peña, R. Gondhalekar, E. Dassau, F.J. Doyle III, Reducing glucose variability due to meals and postprandial exercise in T1DM using switched LPV control: in silico studies, J. Diabetes Sci. Technol. 10 (3) (2016) 744–753. [91] B.P. Kovatchev, M. Breton, C. Dalla Man, C. Cobelli, In silico preclinical trials: a proof of concept in closed-loop control of type 1 diabetes, J. Diabetes Sci. Technol. 3 (1) (2009) 44–55. [92] C. Dalla Man, F. Micheletto, D. Lv, M. Breton, B. Kovatchev, C. Cobelli, The UVA/PADOVA type 1 diabetes simulator: new features, J. Diabetes Sci. Technol. 8 (1) (2014) 26–34. [93] C.C. Palerm, H. Zisser, L. Jovanoviˇc, F.J. Doyle III, A run-to-run framework for prandial insulin dosing: handling real-life uncertainty, Int. J. Robust. Nonlin. 17 (13) (2007) 1194–1213. [94] Y. Wang, F. Gao, F.J. Doyle III, Survey on iterative learning control, repetitive control, and run-torun control, J. Process Control 19 (10) (2009) 1589–1600. [95] L. Magni, M. Forgione, C. Dalla Man, B. Kovatchev, G. De Nicolao, C. Cobelli, Run-to-run tuning of model predictive control for type 1 diabetes subjects: in silico trial, J. Diabetes Sci. Technol. 3 (5) (2009) 1091–1098. [96] C. Toffanin, R. Visentin, M. Messori, F.D. Palma, L. Magni, C. Cobelli, Toward a run-to-run adaptive artificial pancreas: in silico results, IEEE Trans. Biomed. Eng. 65 (3) (2018) 479–488. [97] Y. Wang, E. Dassau, F.J. Doyle III, Closed-loop control of artificial pancreatic β-cell in type 1 diabetes mellitus using model predictive iterative learning control, IEEE Trans. Biomed. Eng. 57 (2) (2010) 211–219. [98] Y. Wang, H. Zisser, E. Dassau, L. Jovanoviˇc, F.J. Doyle III, Model predictive control with learningtype set-point: application to artificial pancreatic β-cell, AIChE J. 56 (6) (2010). [99] Y. Wang, J. Zhang, F. Zeng, N. Wang, X. Chen, B. Zhang, D. Zhao, W. Yang, C. Cobelli, “Learning” can improve the blood glucose control performance for type 1 diabetes mellitus, Diabetes Technol. Ther. 19 (1) (2017) 41–48. [100] M.L. Fravolini, P.G. Fabietti, An iterative learning strategy for the auto-tuning of the feedforward and feedback controller in type-1 diabetes, Comput. Methods Biomech. Biomed. Engin. 17 (13) (2014) 1464–1482. [101] K. Turksoy, C. Monforti, M. Park, G. Griffith, L. Quinn, A. Cinar, Use of wearable sensors and biometric variables in an artificial pancreas system, Sensors 17 (3) (2017). [102] R.S. Sutton, A.G. Barto, Reinforcement Learning: An Introduction, vol. 1, MIT Press, Cambridge, 1998. [103] E. Daskalaki, P. Diem, S.G. Mougiakakou, Model-free machine learning in biomedicine: feasibility study in type 1 diabetes, PLOS ONE 11 (7) (2016) e0158722. [104] C.E. Rasmussen, C.K.I. Williams, Gaussian Processes for Machine Learning, vol. 1, MIT Press, Cambridge, 2006. [105] B. Shahriari, K. Swersky, Z. Wang, R.P. Adams, N. de Freitas, Taking the human out of the loop: a review of Bayesian optimization, Proc. IEEE 104 (1) (2016) 148–175. [106] L. Ortmann, D. Shi, E. Dassau, F.J. Doyle III, S. Leonhardt, B.J.E. Misgeld, Gaussian process-based model predictive control of blood glucose for patients with type 1 diabetes mellitus, in: Proc. Asian Control Conf., 2017, pp. 1092–1097. [107] E.D. Klenske, M.N. Zeilinger, B. Scholkopf, P. Hennig, Gaussian process-based predictive control for periodic error correction, IEEE Trans. Control Syst. Technol. 24 (1) (2016) 110–121. [108] L. Deng, D. Yu, Deep learning: methods and applications, Found. Trends Signal Process. 7 (3–4) (2014) 197–387. [109] A. Chakrabarty, F.J. Doyle III, E. Dassau, Deep learning assisted macronutrient estimation for feedforward-feedback control in artificial pancreas systems, in: Proc. Amer. Control Conf., 2018, pp. 3564–3570.

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Getting IoT-ready The face of next generation artificial pancreas systems

2

Ankush Chakrabarty, Stamatina Zavitsanou, Tara Sowrirajan, Francis J. Doyle III, Eyal Dassau Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

2.1 Introduction To understand the limitless potential of connected devices, let us review the following stories from the life of a person with type 1 diabetes mellitus (T1DM) in the age of smart and connected healthcare. Story 1: A sleep tracker infers the beginning of a new day. It pings a smart coffee machine to begin brewing. The coffee machine reads the label on the pod and sends relevant dietary information to a smartphone, which subsequently queries a continuous glucose monitor (CGM). The blood glucose (BG) reading along with the dietary value is sent to a decision-making app that decides whether or not to provide corrective insulin doses via an insulin pump (this combination of CGM, decision-making module, and the insulin pump is referred to as an artificial pancreas or AP). Story 2: At the gym, a smart activity tracker notes that a half-hour was spent running on the treadmill, followed by a few laps in the swimming pool. The smart device assesses whether exercise was aerobic or anaerobic and relays this along with the duration of exercise performed and relays this information to the AP. The AP uses this information to prime future insulin boluses, expecting that an exercise-induced hypoglycemia (blood glucose (BG) < 70 mg/dL) will likely occur based on the type of exercise. This information, coupled with corrective action from the AP, ensures minimization of hyperglycemia (BG > 180 mg/dL) and maximization of the time in the clinically accepted 70–180 mg/dL safe glucose range. Story 3: On a long drive in a smart car, the display unit of the car shows an alarm: severe hypoglycemia (BG < 54 mg/dL) is predicted. A list of nearby urgent care centers are displayed, and the autonomous vehicle navigates to the one selected by the user, while simultaneously, emergency services are briefed on the incoming patient. Story 4: At a restaurant, the smartphone accesses a photograph of an ordered meal (that was probably saved for an eventual social media upload) or reads an interactive menu and uses this image information to suggest an insulin bolus to compensate for the ingested meal (referred to as meal announcement if The Artificial Pancreas. https://doi.org/10.1016/B978-0-12-815655-1.00011-9 Copyright © 2019 Elsevier Inc. All rights reserved.

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done manually instead of automatically). These stories illustrate the criticality of smart and connected technologies as sources of actionable information for closedloop control in healthcare (specifically, in T1DM). For example, the coffee machine, the smartphone, the activity sensor, and the smart car all play vital roles in passing crucial information to assist decision-making. Although some of this technology (such as the smartphone and activity sensor) are widely available today, others, such as smart home appliances and connected cars, are far closer to science than sciencefiction. In fact, the last decade has borne witness to a prolific growth in research and development of areas that play key roles in smart and connected technology, for instance, big data analytics, sensor networks, and secure cyberphysical systems. Solutions developed in these areas have enabled vast, interoperable monitoring frameworks, aptly referred to as the “internet-of-things” (IoT) [1] or “smart-connected-products” [2]. More formally, the IoT is a network of connected technology capable of sensing/generating and securely exchanging data from which actionable information can be extracted and fed back to support decision-making and consequent actuation. Clearly, the sheer magnitude and universality of the IoT lends itself applicability to a wide range of scientific domains and engineering applications. In particular, the healthcare industry is rife with potential benefits that can be obtained by including emergent IoT technologies.1 It is hardly surprising, therefore, that with smart healthcare products exhibiting compounded annual growth rates at around 9%, the connected healthcare market valuation is poised to be above $50B by 2023 (see Transparency Market Research, 2016). Recent survey and perspective papers [3–7] list distributed computing, wearable devices, secure communication, cloud storage, and learning from big data as key players in smart healthcare. Effective use of these technologies are widely reported in the literature. Wearable sensors have been used successfully as part of body area networks in Parkinson’s disease [8] and cardiac fibrillation detection and inversion [9], whereas learning from healthcare data and medical sensors has proven effective in managing emergency medical services [10], Alzheimer’s disease [11], and activity recognition for successful aging [12]. By extrapolation the improvement of diabetes treatment by incorporating these technologies into classical feedback control schemes presents many exciting opportunities. This chapter discusses context/resource-aware ecosystems developed around an IoT-enabled AP that is hypothesized to improve the quality of care in T1DM. Customizations required to systematically leverage heterogeneous signals arising from the healthcare IoT are discussed, and simulation studies are presented to demonstrate the effectiveness of an AP leveraging additional signals from the IoT. Furthermore, current state and future challenges to be addressed in IoT-enabled AP research are presented. 1 This branch of the IoT is widely referred to as the “healthcare IoT”, “medical IoT”, or the “internet-

of-medical-things” and describes components of the IoT that contribute to decision support for in medical/healthcare applications.

2.2 IoT-enabled AP ecosystems

2.2 IoT-enabled AP ecosystems Current AP technology utilizes glucose estimates from CGM sensors to compute an appropriate insulin bolus to regulate glucose trends, and an insulin pump to bolus the insulin (or insulin/glucagon in a dual hormone AP). In this section, we offer an insight into AP ecosystems that can utilize the potential of the IoT. The most significant modifications required due to the inclusion of the IoT is expected to be in the following areas: (i) information extraction from sensors as additional IoT signals are employed for decision support; (ii) target hardware for deployment of control algorithms fueled by the advancement of wearable platforms; (iii) clinical and engineering objectives and constraints that will adapt with patient data to preempt wellness instead of reacting to health-critical events; and (iv) communication and data storage protocols to handle massive amounts of person-specific data generated by the ecosystem. A schematic diagram of such an IoT-enabled AP ecosystem is presented in Fig. 2.1.

FIGURE 2.1 IoT-enabled AP. Schematic diagram of an IoT-enabled artificial pancreas ecosystem. The feedback control loop consists of low-complexity decisions support systems that may be completely autonomous or hybrid (with user intervention for critical events via mobile devices). These decision-makers will be informed through secure communication channels by medical IoT sensors, including activity tracking, health records, crowdsourcing, to name a few. The ultimate end-goal of this patient-centric IoT-enabled AP will be to promote self-care and wellness in type 1 diabetics.

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2.2.1 The changing face of AP systems To investigate how these IoT-enabled ecosystems can assist people with T1DM, it is important to reflect upon the main challenges associated with the current standard of care. A widespread concern amongst type 1 diabetics is in glycemic dysregulation following meals or physical activity [13,14], especially in children and adolescents who are not always adept at carbohydrate counting [15,16], but exhibit active lifestyles [17,18]. Current AP technology requires meal announcement, where the user is required to manually provide insulin bolus to compensate for glycemic loads of ingested meals. Although sophisticated formulations of control algorithms [19] and alternative sites of delivery [20] have shown promising results in small cohorts with unannounced meals, use of IoT signals can also improve the quality of meal estimation, meal compensation, and postprandial regulation via querying of nutritional databases, analyzing dietary habits from past meals, and precision drug delivery by tailoring control actions to individuals based on prior insulin–glucose responses at meal times. Nocturnal hypoglycemia is also a critical concern that could be handled by effective use of sleep trackers and prior nighttime data to estimate and prevent pathological events; effective forms of nocturnal-hypoglycemia prevention algorithms already exist [21–23]. Long-term concerns such as the physical size and energy consumption of current AP technology can be tackled by using distributed and parallel computing to reduce computational burden, and IoT-ready embedded technology can greatly reduce area footprints without compromising quality of decision support [24]. A critical bottleneck in effectively leveraging the IoT for treating people with T1DM lies in tailoring IoT signals for incorporation into closed-loop formalisms. For example, the data discussed in our scenario at the start of the introduction is obtained from distributed sources and heterogeneous: the control algorithm receives not only glucose data from the CGM, but also image data, GPS data, and temporal data acquired at multiple time scales. Thus a shift of ideologies from centralized to distributed or decentralized computing becomes imperative to leverage such widespread networks. Distributed sensing and control is an area of active research, and some centralized control algorithms relevant to diabetes treatment have been reformulated as distributed controllers. For example, distributed proportional-integral-derivative (PID) control on heterogeneous networks [25] and event-triggered variants [26] to reduce controller actuation energy loss have been explored, and distributed model predictive control (MPC) formulations have been devised [27–29]. These sophisticated event-based resource saving approaches have only recently been evaluated in diabetes treatment [30–32]. Another, albeit simpler transformation, in controller design for the IoT-enabled AP will be from single-input–single-output controllers (SISO) to multiinput–multioutput (MIMO) controllers. Here, multiple sensor inputs and control actions will replace the classical insulin to glucose (single hormone) or insulin/glucagon to glucose (dual hormone) framework [33–35]. These MIMO controllers are expected to benefit from distributable, parallelizable, and scalable algorithms for optimization and storage induced by large state space dimensions [36, 37].

2.2 IoT-enabled AP ecosystems

2.2.2 AP research platforms: past and present Advances in embedded computing over the last decade have enabled AP researchers to seek solutions that promote portability while ensuring reliability and enhanced human–computer interaction. To this end, numerous research AP platforms have been developed [38] and clinically evaluated on laptops and miniaturized embedded platforms. Initial efforts within the research community primarily focused on the development of sophisticated control algorithms that maintain glucose control in a desired level. As discussed in previous sections, these efforts have generated very promising results. A critical challenge identified by the community toward the development of an IoT-enabled AP is in designing mobile AP platforms that adhere to clinical, technical, and product use requirements. The first research platforms were developed in the 1970s and were large in size: bedside AP systems intended for inpatient settings that involved intravenous glucose sensing and insulin infusion [39]. The invasive intravenous route of infusion and sensing and the inappropriate large size of the platforms signified the need for miniaturization of the AP system. This was accelerated by the simultaneous development of less invasive subcutaneous glucose sensing [40,41] and insulin infusion devices [42]. The feasibility of an integrated system consisting of an insulin pump (Medtronic 511 Paradigm), a CGM (Medtronic MiniMed, Northridge, CA), and a laptop hosting the control algorithm was clinically evaluated in [43]. The pump communicated with the laptop telemetrically while the sensor was connected to radio frequency (RF) transmitters (with a range of 10 m), which were communicating with the laptop. An AP prototype, the artificial pancreas system (APS), was developed at University of California at Santa Barbara by Dassau et al. [44] to facilitate the evaluation of AP algorithms in clinical trials; a mobile app version of the same was developed at Harvard University. A graphical user interface (GUI) was designed and displayed on a laptop computer that allowed users and caregivers to oversee relevant information of the closed-loop controller, the CGM, and the pump. The APS supported multiple sensor (Abbott FreeStyle Navigator, DexCom STS7) and insulin pump (Insulet OmniPod, Animas OneTouch Ping2 ) brands and different control algorithms (PID, MPC, fuzzy logic). The sensor signal was transferred to the laptop via a receiver using serial communication, whereas the pump used an RF signal to talk to the laptop. For the case of Omnipod and the available technology at the time of this development, RF was used to communicate with the interface device, and then an infrared data association (IrDA) link assisted the communication with the laptop. A safety layer of integrated interlocks, checklists, and alarms was incorporated to ensure patient safety. The APS system has been used in multiple clinical studies evaluating multiple AP control and supervisory algorithms [23,45–48]. The APS system was further advanced to enable the evaluation of AP algorithms in outpatient settings. The laptop computer was replaced by a tablet computer run2 Not commercially available anymore in US and Canada.

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ning on Windows operating system. The insulin pump communicates with the tablet via Bluetooth low-energy (BLE) communication protocol for the case of Omnipod, whereas for the case of OneTouch, the meter remote connects serially to the tablet. The sensor, on the other hand, transmits signals via RF to the receiver, which is connected to the tablet via USB cable. The users are able to move freely within 15 m of the device. This system, the portable APS (pAPS), was used in inpatient and outpatient clinical studies [49–51] and supported other studies involving automated drug delivery [52]. A cross-platform (Android and iOS), smartphone-based AP app, the APSApp, was developed by Dassau et al. at Harvard University. The APSapp supports Dexcom G5, G6 CGM. and Omnipod and Tandem t:slim insulin pumps. The CGM and insulin pump systems are integrated wirelessly with the app, adhering to industrystandard BLE communication specifications [53]. The APSapp can be used in a fully functional phone, and therefore the AP platform is no longer a dedicated device. Additionally, the system is supported by a web-based remote monitoring software that provides real-time updates of the subject’s glycemic status to the physician. An experimental, stripped smartphone AP platform, the Diabetes Assistant (DiAs), was developed by the research group of B. Kovatchev at the University of Virginia [54,55] to facilitate the evaluation of AP algorithms in outpatient clinical trials. Based on feedback from focus groups, a touch–based graphical user interface (UI) was designed to provide coherent information for the user and the AP system status, whereas interactive buttons enabled manual user intervention. The DiAs system was build on an Android mobile operating system equipped with BLE for communication with the insulin pump and the CGM. The Dexcom G4 CGM system and insulin pumps of multiple commercial brands (Roche Accu-Chek Spirit Combo, Tandem t:slim) are able to connect to the DiAs system. Communication with activity monitors is also supported (Zephyr HxM BT and BioHarness). Off-the-shelf smartphones (Google Nexus-5 and Verizon Moto-X) were used to host the DiAs system, and all mobile relevant functionalities such as calls, browsing, apps, etc. were disabled, constituting the smartphone a dedicated AP device. Visual and audio alarms were included in the design to inform the user of potential risk of imminent hypoglycemia or hyperglycemia. Additionally, DiAs can transmit real-time data via cellular or WiFi network to a central server and generate text and e-mail messages to notify the user when necessary. The system was evaluated in feasibility studies [56, 57] and was later used in a series of outpatient clinical studies [58–64]. The FlorenceD2A closed-loop system [65], developed by the research group of R. Hovorka at the University of Cambridge, consists of a smartphone operating on Android, a CGM (FreeStyle Navigator II, Abbott Diabetes Care), and an insulin pump (Dana R Diabecare, SOOIL). The insulin pump communicates directly with the smartphone via BLE, whereas the CGM is inserted into a purpose-made translator unit that translates a serial USB protocol into a BLE protocol. The translator communicates wirelessly with the smartphone. The smartphone that hosts the AP algorithm acts as a medical device, meaning that all other phone functionalities, such us calls/texts and use of other apps, are disabled. The system was evaluated in

2.2 IoT-enabled AP ecosystems

a 12-week, free-living home trial involving day and night closed-loop in adults [65]. Data transfer was enabled using a cloud server via 3G/GSM communication with the smartphone. The bioinspired artificial pancreas (BiAP) [66,67] has been developed by the research group of P. Georgiou at Imperial College London. The AP control algorithm differs from classical control approaches, and it is based on physiological regulation principles of the pancreatic alpha and beta cells. The control algorithm is implemented on a low-power CMOS microchip within a portable hand-held device that communicates with commercially available CGM (Medtronic Enlite) and insulin pump (Roche Accu-Chek Spirit Combo) systems. The sensor signal is transmitted to the hand-held unit via cable, whereas the insulin suggestions are transmitted to the insulin pump via BLE communication protocol. The hand-held unit is connected to a laptop computer via USB and a graphical user interface, implemented in MATLAB, is used to assist the clinical team to supervise the system performance in real time. The system has been evaluated in inpatient clinical settings [67,68]. A recently developed AP platform was designed [69] consisting of the custom printed circuit board (PCB) that hosts the control algorithm and handles the communication with Dexcom G5 CGM and a Tandem: t:slim insulin pump. An iPhone that runs an adaptive meal bolus calculator is integrated to the system architecture, and the system is supervised by telemonitoring. Clinical evaluation of the platform is currently ongoing. Table 2.1 Artificial Pancreas Research Platforms. RA = Remote Access. R ESEARCH P LATFORM

H ARDWARE

C ODING L ANGUAGE

Steil et al. [43] APS [44] pAPS [44] APSApp [53] DiAs System [54] FlorenceD2A [65] BiAP system [67] Bihormonal AP [70] Bihormonal AP [71] Bionic pancreas [72] #OpenAPSa

laptop laptop tablet smartphone smartphone smartphone microchip tablet smartphone smartphone mini-computer

n/a MATLAB C#.NET Java, C#.NET Java Java analog C#.NET C#.NET C++ Python

a

C OMMUNICATION CGM RF RF BLE BLE BLE BLE USB wireless BLE wireless USB/cloud

P UMP telemetric IrDA link BLE BLE BLE BLE BLE wireless BLE wireless RF

C TRL RA? A LGO PID All All MPC MPC MPC β-cell PID PID MPC All

✗ ✗ ✗ ✓ ✓ ✓ ✓ ✗ ✓ ✓ ✓

http://openaps.readthedocs.io/en/latest/index.html.

Research platforms supporting the clinical evaluation of bihormonal AP systems have also been developed. The Jacobs Lab (OHSU) developed and clinically evaluated a custom controller software running on a palm top tablet computer (Viliv, Yukyung) [70]. The software was developed in C#.NET and could communicate with two CGM (SEVEN PLUS and G4 PLATINUM, Dexcom, Inc.) and two pumps (Omnipod, Insulet Corporation) for insulin and glucagon automatic delivery. The sensors

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interfaced with their own receivers, and each pump was connected to its own personal diabetes manager (PDM, Insulet) through separate wireless channels. The sensor receivers and the PDMs were connected to the tablet with USB cables. The average of the two sensor values was used to determine the required insulin and glucagon delivery. This system was advanced to a modern portable AP system consisting of a smartphone app that is used as the host of the bihormonal AP system runs on Android operating system [71] (Google Nexus), a Dexcom G5 CGM, and two Tandem t:slim insulin pumps. Devices communicate via BLE protocol, whereas a cloud-based remote monitoring platform is supported for accessing subject data during and after clinical studies. The system was evaluated in an inpatient [35] and an outpatient [73] clinical trial. The Bionic Pancreas Team developed a bihormonal AP research platform, the bionic pancreas, which consists of a control algorithm written in C++ in an app running on an Apple iPhone 4S. The CGM levels are streamed online every five minutes using the integrated G4 Platinum CGM, and the controller commands insulin and glucagon deliveries using two t:slim infusion pumps for insulin and glucagon administration. This system has supported numerous outpatient clinical studies [34, 72,74]. The OpenAPS, do-it-yourself (DIY) initiative focuses on the development of an open-source, reference AP system, which can be widely adopted by self-motivated users. Developed by a patient-driven community, the OpenAPS project aims to accelerate AP technological progress beyond the established regulatory and financial framework. The OpenAPS platform consists of a minicomputer (such as the Intel Edison or Raspberry Pi) where the control algorithm resides, a compatible pump (several Medtronic models), and a glucose sensor (Dexcom G4 PLATINUM and G5, Abbott Libre, Medronic Enlite sensors).3 The sensor can be either connected serially to the chip, or the CGM data can be transmitted via the cloud using the Nightscout.4 The pump communicates with the chip using RF. Any control algorithm can be supported; however, according to the OpenAPS documentation, MPC is the most used algorithm. Details on the developed AP platforms are summarized in Table 2.1.

2.3 Interfacing with additional signals from the IoT This section discusses how interfacing with the IoT introduces context-awareness in the AP system. Examples are drawn from various IoT technologies that are expected to supplement CGM and fingerstick measurements to provide a holistic perspective of the current health of the person with T1DM. These additional IoT signals can serve to reduce user burden while enhancing automation in next-generation AP systems. 3 https://openaps.org/. 4 http://www.nightscout.info/.

2.3 Interfacing with additional signals from the IoT

2.3.1 Activity sensors Diabetes research has made tremendous progress in leveraging noninvasive activity sensors to improve glucose management, especially in individuals who lead active lifestyles [75–77]. This has been largely fueled by the widespread availability of activity sensing technology [78] and the development of sophisticated algorithms capable of converting activity time-series data into actionable information. For example, a 3-axis accelerometer and heart rate measurement device (Zephyr Bioharness, Annapolis, MD, USA) was used along with CGM measurements in order to augment a Kalman filter to predict hypoglycemia for automatic pump suspension [79]. Consequently, the method was tested on diabetics during a football game, with promising (albeit not statistically significant) results, with fewer people on the algorithm exhibiting hypoglycemia [80]. Heart rate variability was also demonstrated to be a key factor in effective glucose management. Heart rate signals from an RS800CX sports watch (Polar, Lake Success, NY, USA) informed an AP system that exhibited excellent regulatory performance during exercise; however, control performance under latent effects was not as clear [81]; similar results were shown in adolescent cohorts [82]. A limitation of these methods is that they require manual announcement of exercise. A recent method employing principal component analysis and confidence intervals has shown potential in automated exercise detection [83]. Additional biosignals such as galvanic skin response and energy expenditure also proved to be useful for activity detection [19]. Although not in a diabetes context, the use of handcrafted features for time-series data obtained from activity sensors and machine learning has been widely used for exercise detection and classification [84–86], and can be used as an event-trigger for postexercise glycemic control. Such an event could result in automated pump suspension or in alteration of clinical targets for optimization-based procedures like MPC.

2.3.2 Location sensors Location is an oft-unused measurement that can greatly improve glucose management. Recent work argues that consumer electronics containing geolocation information can be leveraged to switch control targets and pay less heed to long-term adaptation based on distance from home [87], along with meal recommendations and macronutrient information automatically downloaded from available restaurant menus, displaying proximity to clinical centers, and pinpointing user location for caregivers or emergency services [88]; this is especially relevant to vulnerable populations such as youth and the elderly.

2.3.3 Multimedia With advances in image and video processing, large datasets of diabetes-related data, and the prolific rise of deep learning, the use of multimedia in an IoT-enabled AP seems imminent. Image recognition with supervised learning has been shown as a path toward automated carbohydrate counting, which could help erode the bound-

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ary between announced and unannounced meals. This is expected to improve glucose self-management, as one of the leading causes of not reaching desired A1c targets is due to improper meal bolusing [15,89,90]. In the past, supervised learning methods such as support vector machines (SVMs) have demonstrated high classification accuracy [91,92] with standard food datasets, although most of these datasets contain fewer than 10 food categories. The inception of deep learning, especially deep convolutional neural networks (CNNs) [93,94], has remarkably improved image recognition performance, even with datasets with over 100 food categories. For instance, the authors in [95] reported excellent estimation results in automated CHO assessment using transfer learning with deep CNNs. Recent efforts have synthesized deep-learning-based meal estimates with automatic decision-making frameworks like predictive control [96] with good in silico performance; see Section 2.6 for a case study. Although image recognition research has shown great improvement with deep networks, a major challenge in automatic meal estimation is in using image processing to estimate meal sizes. Prior research has shown that volumes of mixed meals are extremely difficult to estimate, although [97] reports 10% error in volume estimation of mixed meals using advanced 3D model reconstruction and image segmentation methods, which is promising. The use of video remains an unexplored direction in automated meal bolus estimation, although this would require more sophisticated computational resources in the decision-making unit for streaming and processing.

2.3.4 Electronic health records An electronic health record (EHR) is a digital record of patient health information, which can be shared across a variety of healthcare scenarios. EHRs contain a wide range of data, including medical history and demographic information, and these systems securely store data in a systematic manner, allowing the analysis of several medically relevant trends and patient changes over time. The use of EHR infrastructure in healthcare has immense potential to improve the quality of care in several medical areas and has been used in diabetes care as well [98]. There have been several observational studies on the effects of using EHRs on large diabetic patient populations, which have shown improvements in care through reduced hospitalization and cost of care, and improved clinical biomarkers [99,100], which is thought to be from the use of EHRs encouraging the adoption of organizational guidelines for clinical diabetes care along with improved coordination between providers in the health care system [98]. There are two validated tools provided by the use of EHRs that have created the aforementioned benefits: diabetes registries and clinical decision support systems. Diabetes registries have been used to enhance patient-provider interactions, which can result in clinical benefits [101], and there were significant reductions in HbA1c, LDL cholesterol, and blood pressure using the data from the registry to send patients a customized health promotion letter. Moreover, only a small portion of clinicians utilized the clinical reminders [98], and although potentially useful, clinicians have the

2.4 Rewiring controllers for an IoT-enabled AP

relevant information to provide patients with the options for goals of better glycemic control. EHRs certainly offer very useful tools for stronger care, as healthcare systems are more integrated and there are more technologies that can utilize EHRs for further support. Traditional visit-based management of healthcare is now a model that can be reevaluated for more IT-supported health care models [98], offering convenience and accessibility among many other potential benefits.

2.3.5 Crowdsourcing Crowd-sourced apps have become popular in a variety of health-related domains, be it calorie-logging popular foods and exercise with MyFitnessPal or MyNetDiary, or the fitness blog-like interfaces of Fitbit. For diabetes in particular, crowdsourcing has potential to help other patients with diabetes in several ways. The experience of others with diabetes could possibly help inform younger patients or those with less experience, which is exploited in the app Health2Sync.5 HelpAround6 and Nightscout7 are medical apps that connect people with a chronic illness such as type 1 diabetes to others in close proximity. This approach to personalized medical care would enhance glucose management by bringing relevant knowledge and experience of others to aid less experienced AP users.

2.3.6 Calendar data Due to technological integration in daily life, a vast number of people use electronic calendars on their mobile devices, laptops, or email clients to schedule their lives. Mining such data is a relatively straightforward task and therefore can be used in conjunction with automatic control algorithms for diabetes management. For example, one can utilize calendar alerts to preempt closed-loop control algorithms to compute priming boluses or modify basal insulin magnitudes based on preplanned exercise periods and other relevant activities extracted from calendar data with very little additional effort from the AP user.

2.4 Rewiring controllers for an IoT-enabled AP Herein, we describe modifications that are required in order to implement various control algorithms widely used in diabetes research. We mainly focus on PID and MPC modifications, since fuzzy logic controllers are rule-based: therefore, the transition to multiple sensor inputs will involve the formulation and testing of more complex multiinput–multioutput rules [102].

5 www.health2sync.com. 6 helparound.co. 7 www.nightscout.info.

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2.4.1 PID Due to the interoperability and number of sensors feeding information to an IoTenabled AP, we do not expect complete decoupling of sensors. Therefore, a PID controller capable of leveraging this information may need to be designed via transfer matrices of the form ⎡ ⎤ G11 (s) G12 (s) . . . G1n (s) ⎢ .. .. ⎥ .. G(s) = ⎣ ... . . . ⎦ Gm1 (s) Gm2 (s) . . . Gmn (s) for m sensors and n control inputs that may arise hypothetically in a connected setting. As a consequence, tuning of multiloop SISO PID controllers or MIMO PID tuning rules becomes necessary for deriving the gains of these controllers. Although the sequential design procedure has shown good performance in the past [103,104], the sheer magnitude of the information and crosstalk associated with an IoT-ready AP may necessitate the use of more sophisticated direct MIMO tuning procedures [105, 106], capable of exploiting efficient convex solvers for optimizing performance. PID variants such as Smith predictors could also be used as prefilters [19] to other control algorithms to reduce the effect of sensor-actuator delays that are expected in connected settings such as the IoT.

2.4.2 MPC Major components of a model predictive controller that will require redesign to integrate with the IoT will be the state estimation framework, the inclusion of context into constraints, and the reformulation of optimization methods that can be deployed from low-complexity edge devices. Model predictive control employs dynamical models of the form xk+1 = f (xk , uk ), yk = h(xk ),

(2.1a) (2.1b)

in order to predict future physiological states xk ∈ Rn and outputs yk ∈ Rp of a patient based on the control actions uk ∈ Rm , where f and h are general nonlinear functions. The model (2.1) is used to predict Ny ∈ N steps into the future in order to compute opt a sequence of optimal control actions U1:Nu |k with control horizon Nu ∈ N. This involves solving a constrained optimization problem of the form opt

U1:Nu |k = arg min J U¯ 1:Nu |k

subject to: 0 ≥ G(x¯r , u¯ r ), 0 = H(x¯r , u¯ r ),

(2.2)

2.4 Rewiring controllers for an IoT-enabled AP

x¯r+1 = f (x¯r , u¯ r ), y¯r = h(x¯r ), x¯0 = xk , for r = 0, . . . , Ny − 1, with u¯ r = 0 for Nu ≤ r ≤ Ny − 1 when the control horizon is shorter than the prediction horizon. Here J is a cost function designed for glycemic regulation, and x¯ and u¯ are artificial variables used to denote open-loop states and control actions, respectively. The symbols G and H denote inequalities and equalities, respectively. One of the most useful features of MPC is its ability to explicitly handle constraints relevant to the regulation problem. Current MPC formulations, for example, constrain control inputs based on actuation constraints on the delivery system or the amount of insulin previously delivered [47,107]. Such insulin-on-board [108] constraints, generally written as the inequality u¯ r − uIOB max,k ≤ 0

∀ 0 ≤ r ≤ Nu − 1

(2.3)

within the optimization framework (2.2), are currently driven by CGM estimates and insulin history, but additional signals from the IoT can be used to supplement admissible insulin magnitudes based on the context. An analogous signal that protects against controller-induced hypoglycemia for PID control is insulin-feedback [109,110]. IoTrelated modifications to the insulin-on-board for MPC and insulin-feedback for PID can be designed similarly. Since MPC is typically used via state-feedback instead of output-feedback [14], it is necessary to obtain estimates of the states based on output measurements. This is typically done via linear observers [47,111], moving horizon estimators [112], or Kalman filters [113,114]. However, the large number of sensors associated with the IoT warrants modifications in the estimator design, a topic that remains largely unexplored. Recent efforts have been made to combine simple estimators capable of exploiting sensor fusion for glucose management [115] and incorporate event-driven communication into the AP to reduce the frequency (and hence, cost) of communication by sending CGM information only when deemed critical [30] or decision-making only when physiologically relevant events take place [31,32]. Challenges such as coherently gathering information from sensors operating at different sampling rates, heterogeneity of data in estimating glucose, and dimensionality of state and output vector fields in the IoT context need to be addressed. Another critical design factor is the optimization framework itself. For implementation on tablets or smartphones, we do not need to design around resource constraints since plenty of memory and power is available for extended operation. Recently, researchers have deployed the decision-making algorithm from a smartphone as an app instead of requiring the smartphone to be converted into a medical device solely for diabetes management. However, as a health-critical device, the development of an on-body AP necessitates small body area footprint, low weight, and meager power consumption. Therefore, resource constraints such as energy utilization and memory become crucial.

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Careful selection of model types and constraints can enable us to write the MPC problem (2.2) as a quadratic program (QP). Strongly convex problems of this type can be solved by many optimization algorithms that are implementable in spite of memory and size constraints [24]. While interior point methods and active set methods have been most commonly used to solve the problems in the past [116], recent advances in operator splitting methods such as alternating direction method of multipliers (ADMM), alternating minimization algorithms (AMA), and proximal gradient methods have proven useful in embedded implementation due to their lower computational cost per iteration, their ability to exploit sparsity in the problem structure, and their effectiveness in solve large-scale problems [117–120]. In the following sections, we present two case studies that illustrate the utility of control engineering and machine learning for glycemic regulation in a connected world.

2.5 Case study: efficient resource utilization in an MPC-based embedded AP Whereas most feedback systems operate in a time-triggered manner, that is, the control or communication step is periodic and determined by the sampling time of the process model, a shift toward event-triggering has recently been investigated in glucose management in T1DM [30–32]. The main idea in these algorithms is to identify when complex decision-making or communication can be avoided based either by performing simple computations on the sensor or checking whether solving optimization problems that occur in MPCbased AP systems will yield nontrivial solutions based on physiological insights. For example, simple extrapolation rules based on prior CGM values can be used in order to assess whether or not hypoglycemia is imminent: accordingly, we need not compute an optimal MPC action because the only option to raise BG levels in a single-hormone system is by suspending the pump. This gives rise to an eventtriggering rule uk = 0 if yˆk+r < ξ , where yˆk+r is a prediction of BG r ∈ N steps into the future, and ξ ∈ R is a positive scalar that serves as a user-defined threshold below which pump suspension occurs. Physiological insights into glucose management were used to propose eventbased conditions based on the insulin-on-board (IOB) constraint, presented in (2.3). Concretely, upon bolusing large magnitudes of insulin such as to counteract the effect of glycemic loads, the quantity uIOB max,k decreases, indicating that the maximal safe admissible insulin bolus is the basal insulin. Taking into account practical constraints such as pump quantization q, the AP is left with few admissible decisions: multiples of q up to the basal insulin, or pump suspension. As pump suspension is taken care of previously by predicting BG, we intuit that bolusing basal insulin instead of searching for optimal control actions will not significantly degrade control performance.

2.5 Case study I

FIGURE 2.2 Comparison of closed-loop control performance with and without event-based conditions. Adapted from [32]. (A) Glucose trajectories of event-triggered control (blue, continuous) and time-triggered control (orange, dashed) in the case of unannounced meals. (B) Glucose trajectories of event-triggered control (blue, continuous) and time-triggered control (orange, dashed) in the case of announced meals. (C) Comparison of processor runtimes using event-triggered (blue (dark gray in print version)) and time-triggered (orange (light gray in print version)) implementations on an embedded device for the case of unannounced meals.

With slight abuse of notation, we write the following event: uk = Basal if uIOB max,k = 0. The final event leverages a unique feature of MPC that is not available in fuzzy logic or PID control: the availability of a sequence of control actions based on model predictions. The basic idea is that the solution of the optimization problem (2.2) yields a sequence of control actions at each time instant k, namely Uk = {u¯ k , u¯ k+1 , . . . , u¯ k+Nu −1 }, where Nu is the control horizon of the MPC. Each element of Uk is computed via open-loop predictions based on the underlying insulin-glucose model. Thus, after computing an optimal control sequence at time k, we can use values from the tail of the control sequence without resolving the optimization problem. That is, we can use controls u¯ k+1 to u¯ k+Nu −1 as long as the error between real CGM values and open-loop model predicted BG values are within a specified tolerance. Reducing the

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tolerance results in frequent solving of the optimization problem and hence improved glycemic regulation, whereas increasing the tolerance reduces the need for frequent resource-intensive computations. The results of comparing this event-triggered formalism to the conventional zone MPC in a hardware in the loop simulation study is provided in Fig. 2.2A–C; for implementation details, we refer the reader to [32]. Specifically, Figs. 2.2A, B illustrate the median (calculated over 111 patients using the UVA/Padova simulator [76]) glucose variation under time-triggered and event-triggered zone MPC with nocturnal hypoglycemia and five large, unannounced and announced meals (inverted cyan triangles), respectively. While in the case of unannounced meals the two median trajectories can be discerned easily, the glucose trajectories with announced meals almost overlap throughout the simulation study. This is verified by calculating statistical significance among different glycemic metrics (using a Wilcoxon rank sum test) [32]. The mean ± one standard deviation percent time in the 70–180 mg/dL range is 66.0 ± 8.6 vs. 61.1 ± 8.9 for unannounced meals with and without eventtriggering, respectively, with p < 0.05, although the energy savings on an embedded device is cut by around 50%. With meal announcement, this time in range is clinically identical (86.7 ± 9.7 vs. 86.4 ± 10.4; p > 0.05) in spite of reducing the energy cost by about 75%. For both announced and unannounced meals, the time below 70 mg/dL in spite of exercise-induced nocturnal hypoglycemia is statistically insignificant.

2.6 Case study: IoT-enabled autonomous bolus assist via deep learning based zone MPC This example serves to illustrate the benefits of context-awareness in closed-loop AP systems leveraging heterogeneous signals from the IoT. The algorithm [96] operates as follows. When a user provides an image of a meal to be ingested, a deep convolutional neural network performs image recognition and identifies the food item. Subsequently, the algorithm queries a nutritional database and assesses the macronutrient content of the food item based on a user-provided serving size. Then, a meal bolus is computed and displayed to the user for affirmation. A feedback control algorithm acts as a safety layer to the meal bolus assistive system in order to provide robustness against meal size estimation inaccuracies of the user or prediction errors of the deep network. Since classical AP control algorithms use time-series data to calculate insulin boluses, the inclusion of a nonconventional IoT signal (i.e., an image) results in some unique implementation challenges. For example, controller development is generally done in MATLAB, but deep learning frameworks are much more tractable in Python, which requires additional coding gymnastics to set up transference of critical information between MATLAB and Python for testing this framework. Furthermore, design challenges arise from the coalescing of deep learning-based frameworks to deterministic control algorithms like MPC. To protect against noisy signals producing unusual deep network predictions [121], the algorithm employs a confidence metric

2.6 Case study II

on the food type prediction and acts as a recommendation system instead of autonomously bolusing for meals. A schematic diagram of the proposed algorithm is presented in Fig. 2.3.

FIGURE 2.3 Program flow. Automated meal bolus recommendation system using deep learning for context-awareness.

The Food-101 dataset [122] is currently the largest publicly available food dataset. It contains 101,000 images of C = 101 classes of most commonly uploaded food items available at foodspotting.com, a crowd-sourced website for sharing annotated food images. The dataset is divided into 750 × 101 = 75, 750 images used for training and 250 × 101 = 25, 250 images for testing an image recognition system. The dataset is quite challenging to develop classifiers for, due to the inherent diversity in image resolution, size, illumination, and noise, in conjunction with varied perspectives, obstruction of meals, and occasional mislabeling. The challenging nature of classifying this dataset is verified in [122], where the authors report top-1 accuracy of approximately 50% with hand-crafted features like color histograms, speeded-up robust features (SURF), or improved feature vectors, and a top-1 performance of only 56% with a direct implementation of the AlexNet CNN architecture [93]. Specific details of the training phase are provided in [96]. The trained neural network exhibits a top-1 accuracy of 81.65%, with initial preloading of the network requiring 96.94 s. The average and standard deviation of the prediction time for each image is 0.57 ± 0.02 s. For the purposes of illustration, we assume that the in silico patient perfectly estimates the weight of the food (in grams). Subsequently, we query a USDA food composition database for the macronutrient content of the predicted food item (assuming serving size is known). We perform in silico simulations by automatically estimating the CHO content of the meal in the image. To test the performance of the proposed algorithm, we randomly select 1000 images from among the test images of the Food-101 dataset. These are divided into 100 images per in silico patient of the 10-patient version of the UVA/Padova metabolic simulator. For each patient, we generate 10 scenarios with unique but random CGM noise seeds, each scenario comprised of 10 meals. Serving sizes are preselected to ensure that CHO content for any image was between 15 and 110 g. Out of 1000 images, 741 were identified with high confidence, of which 719 were predicted correctly, and only 1 image resulted in a CHO estimation error > 15 g. The feedback control algorithm used is identical to the periodic zone model predictive controller described in [111] except that zone boundaries are set at 80 mg/dL and 120 mg/dL during the day, and the lower bound is raised to 90 mg/dL at night. The model used for prediction is identical to that proposed in [123]. The results

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of comparing closed-loop control with deep learning, unannounced meals, and announced meals are presented in Fig. 2.4. As reported in [96], the performance of

FIGURE 2.4 Simulation results demonstrating the effect of context-awareness. (P=Proposed closed-loop system, U=Closed-loop system with fully unannounced meals, A=Closed-loop system with fully announced Meals) (A) Glucose trajectories induced by different control schemes with randomly chosen meal images and unannounced exercise inputs. (B) Percentage time in hypoglycemia. (C) Percentage time in euglycemia. (D) Percentage time in hyperglycemia. The  denotes statistical significance compared to the proposed algorithm with p < 0.05.

the deep learning assisted meal bolusing is between glycemic metrics obtained for meals with or without announcement, with the major advantage of the method being increased autonomy. As illustrated in Fig. 2.4A, the percent time spent in the clinically accepted safe glucose region of 70–180 mg/dL is 91.8 ± 7.2, which is closer to closed-loop control with announced meals 97.3 ± 2.9 (p < 0.05) than unannounced meals 78.8 ± 12.1 (p < 0.05). Interestingly, the proposed method significantly lowers percent time with BG> 250 mg/dL (0.2 ± 0.8) than control with unannounced meals (3.1 ± 4.9; p < 0.05), but this statistical significance is not exhibited comparing with meal announcement (0.0 ± 0.0). The time below 70 mg/dL is also clinically identical for all three paradigms.

2.7 High-level adaptation from big IoT data 2.7.1 The interplay of cloud, fog, and edge computing The options for big data storage are growing, and especially with the increasing number of IoT devices, exploring these avenues is relevant. Traditional IoT storage architecture utilizes the cloud for data storage and computation needs. Cloud computing is a paradigm that allows access to shared resources and services that can be

2.7 High-level adaptation from big IoT data

quickly provided, which provides a powerful tool for mass-scale computation [124]. Moreover, the need for storage or computing hardware is eliminated, which is a large advantage for IoT devices especially. There are many IoT devices in the healthcare domain, where using body sensors that generate large amounts of data that must be stored and analyzed is a common challenge in terms of physical storage and ubiquitous access among many other issues [125]. Thus the utility and necessity of cloud computing arises as an effective manner of managing sensor data. Cloud computing provides access to shared resources for storage and computation services, and with IoT devices, it serves as a natural infrastructure for medical sensor communication [125]. Fog and edge computing are used to make the process of data storage and analysis more efficient than traditional cloud architecture, which poses problems for latencysensitive applications such as the IoT, which necessitates mobility support and security. Fog computing uses near-user edge devices for storage, communication, control, and several other services to meet the IoT requirements of low latency, especially for healthcare applications, and efficacy for mobile applications, and it is complimentary to the cloud computation model [126], as data is moved to the local area network level of architecture. Fog networking is comprised of control and data planes, an example of the latter where computation is allowed to be at the edge of the network as opposed to servers [127], which reduces data storage required from the cloud and allows for short-term computation at the fog environment while the cloud environment has the capacity for more complex computation with larger resource requirements. Edge computing optimizes cloud computation by having data processing occur at the edge of the network close to the data source. This reduces the necessary communication bandwidth between sensors and data storage because processing occurs at the edge of the network. Computing power and data are pushed away from central points to network extremes [128] in devices such as programmable automation controllers (PACs). In comparison to fog computing, which involves several layers of communication to relay data, edge computing simplifies this process and reduces network architecture complexity and thus the potential points of failure, which is important for IoT devices. Moreover, edge computing decreases the volume of data that needs to be transmitted and also renders a core computational environment unnecessary, which adds efficacy to the system. There are additional security capacities offered with the use of both fog and edge computing over solely cloud computation models. Both fog and edge computing models used in conjunction with cloud computation for storage and processing hold the most promise for IoT devices, in particular, for the AP. An overview of fog and edge computing and their roles in the IoT are depicted in Fig. 2.5.

2.7.2 An AP that learns from big data Several limitations in healthcare stem from the lack of personalized medical solutions for patients, and this is also true in diabetes care. Advanced feedback control frameworks cannot reach their full potential without accounting for individual variability. Reinforcement learning (RL) offers a potential path to overcome these limitations by

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FIGURE 2.5 Computing architecture required for IoT-enabling. The interplay of cloud, fog, and edge computing in an IoT-ready architecture.

learning unmodeled dynamics and making decisions learned adaptively from incoming data [129]. Using RL and other similar tools hold promise to improve glycemic control and take into account patient variability. With the potential integration of IoT, additional sensor data with the AP, a larger volume of patient-specific data will be available, and through various mobile storage and processing options discussed previously, running reinforcement or machine leaning algorithms on patient data to supplement or replace a control algorithm is a possibility. The vast amount of data that will potentially be available from this future envisioning of the AP also holds promise for personalized healthcare applications among others. Big data positions us to be capable of discerning long-term trends in patient populations and perform a diverse array of analyses that may aid in understanding previously unknown relationships in diabetes within patient populations. This can better inform and supplement clinician-provided diabetes care and improve predictive analyses of treatment regimens. For example, access to big data would better inform the action space in an RL framework of the AP, leading to potentially better treatment actions selected. Big data from the IoT devices envisioned on the AP fits with the storage systems discussed previously with cloud, fog, and edge computing. From this basis we can expand to include reinforcement learning strategies to envision an AP that effectively adapts with more data, providing more personalized healthcare solutions to patients with diabetes.

2.8 Conclusions This chapter identified some major sensor signals that could be leveraged in an IoTenabled AP system to improve the quality of life and demonstrated how simple

References

modifications to decision-support systems using multisensor data can lead to improvement of glycemic regulation with heightened autonomy. The IoT is not a single market, but a conglomeration of multiple submarkets like communication technology, data science, hardware manufacturing, energy, to name a few. Thus a critical aspect for realizing the IoT will be interoperability: a tenet that requires key players to collaborate. The potential of this world interweaved with technology is immense: the onus is on us to channel this potential to improve the lives of people and families affected by diabetes.

Acknowledgments The authors gratefully acknowledge the support provided by the National Institutes of Health under Award Numbers DP3DK101068, DP3DK104057, and DP3DK113511 and access to the UVA/Padova metabolic simulator provided by Dr. Kovatchev (University of Virginia) and Dr. Cobelli (University of Padova) for research purposes. We also thank Sunil Deshpande and Dawei Shi at Harvard University for useful discussions during the preparation of this chapter.

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[108] Christian Ellingsen, Eyal Dassau, Howard Zisser, Benyamin Grosman, Matthew W. Percival, Lois Jovanoviˇc, Francis J. Doyle III, Safety constraints in an artificial pancreatic β cell: an implementation of model predictive control with insulin on board, J. Diabetes Sci. Technol. 3 (3) (2009) 536–544. [109] Cesar C. Palerm, Physiologic insulin delivery with insulin feedback: a control systems perspective, Comput. Methods Programs Biomed. 102 (2) (2011) 130–137. [110] Garry M. Steil, Cesar C. Palerm, Natalie Kurtz, Gayane Voskanyan, Anirban Roy, Sachiko Paz, Fouad R. Kandeel, The effect of insulin feedback on closed loop glucose control, J. Clin. Endocrinol. Metab. 96 (5) (2011) 1402–1408. [111] Ravi Gondhalekar, Eyal Dassau, Francis J. Doyle III, Periodic zone-MPC with asymmetric costs for outpatient-ready safety of an artificial pancreas to treat type 1 diabetes, Automatica 71 (2016) 237–246. [112] Ravi Gondhalekar, Eyal Dassau, Francis J. Doyle III, Moving-horizon-like state estimation via continuous glucose monitor feedback in MPC of an artificial pancreas for type 1 diabetes, in: Proc. Conf. Decis. Control, CDC, 2014, pp. 310–315. [113] Fraser Cameron, Darrell M. Wilson, Bruce A. Buckingham, Hasmik Arzumanyan, Paula Clinton, H. Peter Chase, John Lum, David M. Maahs, Peter M. Calhoun, B. Wayne Bequette, Inpatient studies of a Kalman-filter-based predictive pump shutoff algorithm, J. Diabetes Sci. Technol. 6 (5) (2012) 1142–1147. [114] Bruce Buckingham, Erin Cobry, Paula Clinton, Victoria Gage, Kimberly Caswell, Elizabeth Kunselman, Fraser Cameron, H. Peter Chase, Preventing hypoglycemia using predictive alarm algorithms and insulin pump suspension, Diabetes Technol. Ther. 11 (2) (2009) 93–97. [115] Xia Yu, Kamuran Turksoy, Mudassir Rashid, Jianyuan Feng, Nicole Hobbs, Iman Hajizadeh, Sediqeh Samadi, Mert Sevil, Caterina Lazaro, Zacharie Maloney, Elizabeth Littlejohn, Laurie Quinn, Ali Cinar, Model-fusion-based online glucose concentration predictions in people with type 1 diabetes, Control Eng. Pract. 71 (2018) 129–141. [116] Mark S.K. Lau, S.P. Yue, K.V. Ling, J.M. Maciejowski, A comparison of interior point and active set methods for FPGA implementation of model predictive control, in: Proc. Europ. Control Conf., ECC, 2009, pp. 156–161. [117] Yang Zheng, Giovanni Fantuzzi, Antonis Papachristodoulou, Paul Goulart, Andrew Wynn, Fast ADMM for semidefinite programs with chordal sparsity, in: Proc. Amer. Control Conf., ACC, 2017, pp. 3335–3340. [118] Brendan O’Donoghue, Giorgos Stathopoulos, Stephen Boyd, A splitting method for optimal control, IEEE Trans. Control Syst. Technol. 21 (6) (2013) 2432–2442. [119] Juan L. Jerez, Paul J. Goulart, Stefan Richter, George A. Constantinides, Eric C. Kerrigan, Manfred Morari, Embedded online optimization for model predictive control at megahertz rates, IEEE Trans. Automat. Contr. 59 (12) (2014) 3238–3251. [120] Pei Zhang, Joseph Zambreno, Phillip H. Jones, An embedded scalable linear model predictive hardware-based controller using ADMM, in: IEEE 28th International Conference on ApplicationSpecific Systems, Architectures and Processors, ASAP, 2017, pp. 176–183. [121] Anh Nguyen, Jason Yosinski, Jeff Clune, Deep neural networks are easily fooled: high confidence predictions for unrecognizable images, in: Proc. IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit., 2015, pp. 427–436. [122] Lukas Bossard, Matthieu Guillaumin, Luc Van Gool, Food-101—mining discriminative components with random forests, in: Comput. Vis. ECCV, Springer, 2014, pp. 446–461. [123] Klaske van Heusden, Eyal Dassau, Howard C. Zisser, Dale E. Seborg, Francis J. Doyle III, Controlrelevant models for glucose control using a priori patient characteristics, IEEE Trans. Biomed. Eng. 59 (7) (2012) 1839–1849. [124] Ibrahim Abaker Targio Hashem, Ibrar Yaqoob, Nor Badrul Anuar, Salimah Mokhtar, Abdullah Gani, Samee Ullah Khan, The rise of “big data” on cloud computing: review and open research issues, Inf. Syst. 47 (2015) 98–115. [125] Charalampos Doukas, Ilias Maglogiannis, Bringing IoT and cloud computing towards pervasive healthcare, in: Sixth International Conference on Innovative Mobile and Internet Services in Ubiquitous Computing, IMIS, 2012, 2012, pp. 922–926.

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[126] Flavio Bonomi, Rodolfo Milito, Preethi Natarajan, Jiang Zhu, Fog computing: a platform for Internet of things and analytics, in: Big Data and Internet of Things: a Roadmap for Smart Environments, Springer, 2014, pp. 169–186. [127] Jonathan Bar-Magen Numhauser, Jose Antonio Gutierrez de Mesa, XMPP distributed topology as a potential solution for fog computing, in: The Sixth International Conference on Advances in Mesh Networks, MESH, 2013. [128] Mohamed Medhat Gaber, João Bártolo Gomes, Frederic Stahl, Pocket Data Mining: Big Data on Small Devices, Series: Studies in Big Data, 2014. [129] Elena Daskalaki, Peter Diem, Stavroula G. Mougiakakou, Model-free machine learning in biomedicine: feasibility study in type 1 diabetes, PLOS One 11 (7) (2016) e0158722.

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3

Iman Hajizadeha , Mudassir Rashida , Sediqeh Samadia , Mert Sevilb , Nicole Hobbsb , Rachel Brandtb , Ali Cinara,b a Department

of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, IL, USA b Department of Biomedical Engineering, Illinois Institute of Technology, Chicago, IL, USA

3.1 Introduction The complexity of glucose–insulin dynamics in the body and the available technology challenge tight blood glucose concentration (BGC) regulation in people with type 1 diabetes (T1D). An artificial pancreas (AP) system capable of mimicking the glucose-regulating function of a healthy pancreas can automate BGC management, dramatically reduce diabetes-related risks, and improve lives of people with T1D. Most current AP systems are developed based only on CGM measurements, and some use meal and exercise announcements, whereas others do not require meal announcements. However, the effects of many factors such as meals, exercise, sleep, and stress (MESS) are seen in BGC with a time-varying delay [1]. An adaptive multivariable AP (M-AP) that uses physiological signals in addition to glucose measurements in estimation of future glucose concentrations and the AP control algorithms is a promising approach to design a fully automated AP where no manual entries are required to accommodate the major disturbances to the BGC, such as MESS [2–6]. The glucose–insulin dynamics model in people with T1D is the underlying system for the model-based AP control systems. The nonlinearities and time-varying changes in the parameters of blood glucose dynamics, the occurrence of nonstationary disturbances, time-varying delays on measurements and insulin infusion, and noisy data from sensors provide challenges for the AP systems. Furthermore, the glucose–insulin dynamics in the human body has high levels of intra- and intersubject variability. Many current model-based AP systems rely on fixed physiological models. These models are developed based on complex physiological phenomena, which require detailed knowledge about the human body. However, due to variability of glucose–insulin dynamics of different people with T1D and variations in glucose dynamics of the same person depending on various conditions, these models cannot be fitted to every person with T1D. They must be redefined/tuned for different people. Real-time modification may also be required due to different conditions such as MESS, which are known to have significant effects on glucose–insulin dynamics. The The Artificial Pancreas. https://doi.org/10.1016/B978-0-12-815655-1.00012-0 Copyright © 2019 Elsevier Inc. All rights reserved.

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computation cost of fixed physiological models is also high due to nonlinearities and large number of equations and parameters. Input–output models such as time series models and state-space models provide the ability to express how the inputs of a system affect the behavior of its outputs [1]. A more computationally viable alternative is subspace-based state-space system identification, where structured block Hankel matrices are constructed using measured input/output data and computationally efficient projection operations retrieve certain subspaces related to the system matrices. Recent developments in system identification with application to AP systems include a recursive predictor-based subspace identification (PBSID) method, which avoids the computationally burdensome procedure of computing or updating singular value decomposition (SVD) factorizations [7]. The PBSID approach is extended to provide a stable time-varying individualized state-space model for glycemic predictions using estimates of PIC and meal effects, and measured physiological signals [8,9]. The establishment of accurate predictive models allows for the optimal insulin infusion rates to be computed by formulating and solving dynamic optimization problems online that take advantage of the identified dynamic process models while accounting for system constraints. MPC is widely employed in AP systems because of its inherent ability to easily and effectively handle complex systems with control constraints and many input and output variables [10–17]. MPC algorithms exploit dynamic models of the system in the optimization problem to predict the future evolution of the glucose measurements over a finite-time horizon to determine the optimal insulin infusion rates with respect to a specified performance index. Furthermore, MPC can explicitly consider the system constraints and multivariable interactions in the optimization problem, and the MPC formulations are not inexorably restricted by the type of model, objective function, or constraints. Adaptive MPC control with frequently updated models provides an attractive solution for finding representative models for use in model-based controllers that respond better to the current state of the user when a patient’s metabolism, physical activities, or emotional state changes significantly. In this work, an MPC algorithm using the adaptive models is designed to effectively compute the optimal exogenous insulin delivery for AP systems [18,19]. Physical activity provides a major challenge to AP systems, especially when realtime information about the physical activity is not considered in the algorithms of the AP [2,20–25]. For example, it is known that aerobic physical activities usually induce hypoglycemia in T1D. An AP that is based only on CGM information cannot act fast enough to take action to minimize the possibility of exercise-induced hypoglycemia. By the time the effect is reported by CGM measurements, it might be too late for an AP system to manage the infused insulin. An AP system that is not aware of exercise may cause hypoglycemia due to lack of information about insulin sensitivity change. Additional data from wearable devices can be collected in real time to capture exercise information before BGC is affected and initiate actions to mitigate the effects of physical activity. The development of a fully automated AP that can function without any manual information about physical activities will necessitate developing multi-

3.2 Preliminaries

variable and adaptive AP systems that use information from wearable devices such as wristbands [2–6]. Another challenge that an AP system faces is meal consumption. The blood glucose rises drastically after carbohydrates are consumed, and it is necessary to counteract this significant disturbance with the required amount of insulin infusion rapidly. To detect meal consumption and give the insulin dose in a timely manner, several meal detection algorithms are developed [26–29]. In this work, we build upon these to handle the effects of meals and other disturbances that result in a rapid and persistent increase in the blood glucose. The proposed approach modifies the constraints if there is any rapid and significant increase in the glucose measurements to make the controller more aggressive to suggest an appropriate insulin bolus. The amount of previously administered insulin that is present in the blood or the subcutaneous space is referred to as the insulin on board (IOB). The IOB is typically determined in infusion pumps through static approximations of the insulin action curves [30,31]. The time-varying delays present in insulin diffusion, absorption, and utilization and the diurnal variations in the metabolic states of individuals have significant effects on the kinetics and dynamics of the metabolic system. Therefore, the insulin decay profiles and action curves used in calculating IOB are not accurate enough over the diverse conditions encountered throughout the day to be reliably used in an AP. In contrast, accurate estimates of the PIC can be obtained by using CGM measurements with adaptive observers designed for simultaneous state and parameter estimation. The estimated PIC can be subsequently used to design a predictive control algorithm that is dynamically constrained by the estimated PIC and thus explicitly considers the insulin concentration in the bloodstream as part of the optimal control solution [32,33]. Incorporating PIC constraints in the optimal control problems can prevent insulin stacking that may lead to hypoglycemia. In this chapter, a multimodule, multivariate, and adaptive AP system is described to deal with several realistic challenges faced by people with T1D. A personalized PIC estimator is proposed, and then integration of a plasma insulin compartment model with a recursive subspace-based system identification approach is introduced. The incorporation of algorithms to improve the response of the AP to meal and physical activities effects is presented. A predictive hypoglycemia alarm module is also proposed to reduce the probability of hypoglycemic events. The adaptive controller based on MPC using a multiinput–single-output recursive model of BGC dynamics is stated. The performance of the proposed adaptive M-AP is demonstrated using a multivariable simulator.

3.2 Preliminaries In this section, we provide a brief overview of the adaptive and personalized PIC estimator, followed by a review of the PBSID algorithm for the identification of linear, time-varying state-space models. Subsequently, we present the adaptive MPC formulation.

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3.2.1 Adaptive and personalized PIC estimator The PIC estimator is designed based on Hovorka’s model, a glucose-insulin dynamic model detailed in Eq. (3.1) [10]. The model has different compartments to characterize the blood glucose dynamics, the subcutaneous insulin infusion, and the glucose transport from plasma to interstitial tissues. The model equations are dS1 (t) dt dS2 (t) dt dI (t) dt dx1 (t) dt dx2 (t) dt dx3 (t) dt dQ1 (t) dt

S1 (t) , tmax,I (t) S1 (t) S2 (t) = − , tmax,I (t) tmax,I (t) S2 (t) − ke (t)I (t), = tmax,I (t)VI = U (t) −

= −ka,1 x1 (t) + kb,1 I (t), = −ka,2 x2 (t) + kb,2 I (t),

(3.1)

= −ka,3 x3 (t) + kb,3 I (t), c (t) − FR (t) − x1 (t)Q1 (t), = UG (t) − F01

+ k12 Q2 (t) + EGP0 (1 − x3 (t)) , dQ2 (t) = x1 (t)Q1 (t) − (k12 + x2 (t)) Q2 (t), dt   dGsub (t) 1 Q1 (t) − Gsub (t) , = dt τ VG where U(t) is the injected insulin (basal and bolus), the two state variables Q1 (t) and Q2 (t) denote the masses of glucose in the accessible and nonaccessible compartments, respectively, and the state variables S1 (t) and S2 (t) denote the absorption rate of subcutaneously administered insulin. The PIC I (t) is represented by a first-order differential equation. The insulin action is calculated by using three variables, the influence on transport and distribution (x1 (t)), the utilization and phosphorylation of glucose in adipose tissue (x2 (t)), and the endogenous glucose production in the liver (x3 (t)). The relationship between BGC and subcutaneous CGM measurement is considered a first-order dynamic equation. Incorporating uncertainty in the dynamics of the discretized system (referred to as process noise) and the noise in the discrete-time measurements, the model can be written in the form xk+1 = f (xk , Uk ) + ωk , ωk ∼N (0, Q), yk = g (xk ) + νk , νk ∼N (0, R),

(3.2)

3.2 Preliminaries

where ωk and νk denote the vectors for the process and observation noise, Q and R denote the covariance matrix and variance of the process and measurement noises, respectively, and xk = [S1,k

S2,k

Ik

x1,k

x2,k

x3,k

Q1,k

Q2,k

Gsub,k

tmax,I,k

ke,k

UG,k ]T

denotes the augmented state vector including the uncertain model parameters. The PIC is directly influenced by tmax,I and ke parameters that exist in the subcutaneous insulin absorption subsystem (dynamics of the state variables S1 , S2 , and I in Eq. (3.1)). Hence tmax,I and ke are considered as the uncertain time-varying parameters estimated as the extended states delineated in Eq. (3.2). Furthermore, as information about the time and quantity of meals is difficult to ascertain, the gut absorption rate UG (t) is also included as an extended state in the model (Eq. (3.2)). A nonlinear observer for the simultaneous estimation of the state variables and the time-varying parameters can be designed as     xˆk+1 = f xˆk , Uk + Kk yk − yˆk ,   yˆk = g xˆk ,

(3.3)

where xˆk denotes the estimated augmented state vector, and Kk is the observer gain chosen such that the observer error dynamics are asymptotically stable. The proposed PIC estimator is individualized as the initial value of the time-varying parameters in the model is computed by a partial least squares regression model where the readily attainable demographic information of the individuals, such as weight, body mass index, and duration with diabetes, are the inputs of model. After initialization, the time-varying parameters and the state variables are estimated online using a personalized observer. The proposed PIC estimator is able to capture the inter- and intrasubject variabilities to provide accurate information on the amount of insulin present in the body. In the proposed PIC estimation technique, the meal effect UG is simultaneously estimated along with the time-varying model parameters and state variables, thus avoiding the requirements for user-specified meal information [32,33].

3.2.2 Recursive subspace-based system identification A stable, reliable, and computationally tractable dynamic model is essential for the design of model-based predictive control algorithms in AP systems. To this end, the predictor-based subspace identification approach is implemented to track the system modeled as linear with time-varying parameters and is coupled with a constrained optimization solver to guarantee the stability of the model [7]. Consider a vector autoregressive model with exogenous variables (VARX) yˆk|k−1 =

p  i=0

u θk−i uk−i +

p  i=1

y

θk−i yk−i ,

(3.4)

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where yˆk|k−1 is the predicted output for the kth sampling instance using the inputs uk , . . . , uk−p and outputs yk−1 , . . . , yk−p . The VARX model parameter p is the length of the past window of data considered when predicting the future outputs. The coefficient matrices θ u and θ y are readily estimated though recursive least squares (RLS) techniques at each sampling time. Furthermore, the stacked vector yk−p,p is defined with respect to the past window of length p as yk−p,p = T  T T T yk−p yk−p+1 . . . yk−1 . The stacked vector uk−p,p is also similarly defined. Recognizing that the predicted state xˆk is given by xˆk = Ap xˆk−p + Luk−p,p + Kyk−p,p ,

(3.5) p−1

where L and K denote the extended controllability matrices L = A B . . . AB B

and K = Ap−1 K . . . AK K , and assuming that the state transition matrix is nilpotent with degree p, that is, the contribution of the initial state xˆk−p is negligible for sufficiently large p (Ap = 0), the predicted state can be expressed as xˆk = Luk−p,p + Kyk−p,p .

(3.6)

Premultiplying the predicted state by the observability matrix Γ gives Γ xˆk = Γ Luk−p,p + Γ Kyk−p,p with

(3.7)

⎡

⎤ C ⎢ CA ⎥ ⎢ ⎥ ⎥ Γ =⎢ ⎢ .. ⎥ . ⎣ . ⎦ CAp−1

The product of the matrices Γ L and Γ K can be constructed from the VARX model coefficient matrices as ⎡ u u u ⎤ θk−p θk−p+1 · · · θk−1 ⎢ ⎥ .. ⎢ 0 u u ⎥ θk−p . θk−2 ⎢ ⎥ ΓL=⎢ ⎥ ⎢ ⎥ . . . . ⎣ ··· . ··· . ⎦ u 0 0 · · · θk−f and

⎡ y θ ⎢ k−p ⎢ ⎢ 0 ΓK=⎢ ⎢ ⎢ ⎣ ··· 0

where f is the future window length.

y

θk−p+1 y

θk−p ··· 0

··· .. . .. . ···

y

θk−1

⎤

⎥ y ⎥ θk−2 ⎥ ⎥, .. ⎥ ⎥ . ⎦ y θk−f

3.3 Adaptive PIC cognizant MPC algorithm

Therefore, after estimating the VARX coefficient matrices, the estimated coefficient matrices θ u and θ y can be used to determine all quantities on the right-hand side of Eq. (3.7), and an SVD factorization can be used to readily obtain a low-rank approximation of the state sequence. For recursive identification, a selection matrix S of appropriate dimensions can be determined such that the basis of the state estimation is consistent at each sampling time as   (3.8) xˆk = Sk Wk Γ Luk−p,p + Γ Kyk−p,p , where Wk is a predefined weight matrix, and the selection matrix S can be recursively updated through the projection approximation subspace tracking (PAST) method. The estimated state sequence is then employed along with the inputs and measured outputs to estimate the system matrices by solution of RLS problems. Specifically, after computing an estimate of the state sequence xˆk , two RLS problems that ensure stability of the estimated system are used to determine the state-space matrices, thus yielding the identified model xˆk+1 = Ak xˆk + Bk uk + Kk ek , yk = Ck xˆk + Dk uk + ek ,

(3.9)

where A, B, C, and D are the system matrices, K is the Kalman gain matrix, and ek = yk − yˆk are used for feedback correcting the state variables. In this work, uk includes delayed estimates of PIC and meal effects, and measured physiological signals [18,19].

3.3 Adaptive PIC cognizant MPC algorithm In this section, the insulin compartment model of the glucose–insulin dynamic model is incorporated with the recursive PBSID approach to characterize the time-varying glycemic dynamics. Subsequently, the glycemic and plasma insulin risk indexes and the adaptive MPC formulation are presented.

3.3.1 Integrating insulin compartment models with subspace identification In this subsection, we integrate the data-driven model determined from the subspacebased system identification technique with a first-principles insulin compartment model derived from Hovorka’s model. To this end, consider the insulin absorption subsystem from Eq. (3.1) described by the compartment model   S1,k S1,k+1 = S1,k + Ts Uk − , (3.10) tmax,I,k   S2,k+1 S1,k+1 − , (3.11) S2,k+2 = S2,k+1 + Ts tmax,I,k tmax,I,k

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 Ik+3 = Ik+2 + Ts

 S2,k+2 − ke,k Ik+2 . tmax,I,k VI

(3.12)

The PIC value Ik+3 at the (k + 3)th sampling instance is affected by the infused basal/bolus insulin Uk at the kth sampling instance. The PIC variable computed by the compartment model (Eqs. (3.10) to (3.12)) handles the impulse variations in the injected basal and bolus insulin and also timedelays in the insulin absorption. So, the compartment model in Eqs. (3.10) to (3.12) is integrated with the recursively identified model Eq. (3.9) yielding xˆ˜k+1 = A˜ k xˆ˜k + B˜ k uk ,

(3.13)

y˜k = C˜ k xˆ˜k , where ⎡

Ak

⎢ ⎢[0...0]1×n ˜ Ak = ⎢ ⎢ ⎣[0...0]1×n

p1I · Bk1

p2I · Bk1

p3I · Bk1

p1S1

0

0

p1S2

p2S2

0

p1I

p2I ⎤

[0...0]1×n

⎡ pI · B 1 ⎢ 4 k ⎢ Ts B˜ k = ⎢ ⎢ S2 ⎣ p3

p5I

C˜ k = Ck

⎤ ⎥ ⎥ ⎥, ⎥ ⎦

p3I

Bk2,3 ⎥ [0 0]⎥ ⎥, ⎥ [0 0]⎦ [0 0]

0 0 0

(3.14)

(3.15)



(3.16)

with the new state vector of  T xˆ˜k = xˆk+3+d

T S1,k

S2,k+1

Ik+2

(3.17)

and the output y˜k = yˆk+3+d ,

(3.18)

where uk

includes delayed infused basal/bolus insulin information, estimates of meal effects, and measured physiological signals, and Bk = [Bk1 Bk2,3 ] (where Bk1 is for the PIC, and Bk2,3 for the estimates of meal effects and measured physiological signals) [34]. All other parameters of Eqs. (3.14) and (3.15) are detailed in the Appendix.

3.3.1.1 Set-point modification during exercise and recovery period To avoid hypoglycemia due to overdosing of insulin during aerobic exercise time and recovery period after exercise, the glucose set-point (reference trajectory) changes from the normal value of 110 mg/dL to 160 mg/dL during exercise. Furthermore,

3.3 Adaptive PIC cognizant MPC algorithm

a two-hours-long recovery period is considered after exercise, during which the setpoint is gradually brought back to 110 mg/dL.

3.3.1.2 Glycemic risk index The original glycemic risk index (GRI) presented in [35] is modified to be suitable for physical activity period. The GRI is used to determine the weighting matrix, denoted Q yˆk+d+3 , for penalizing the deviations of the outputs from their nominal set-point depending on the state of patient. To this end, the time-varying  positive semidefinite weighting matrix Qk is defined as Qk := Q yˆk+d+3 with   Q yˆk+d+3 := αyˆk+d+3 · Q, where Q denotes a nominal weight, and

αyˆk+d+3

⎧  1.3378 ⎪ 1.0567 × 10−2 Exc + 80 − yˆk+d+3 ⎪ ⎪ ⎪ ⎪ ⎪ if yˆk+d+3 ∈ Exc + [50, 80] , ⎪ ⎪ ⎪ ⎨ 0 if yˆ ∈ Exc + (80, 140] , k+d+3 :=  1.0601 ⎪ −2 ⎪ −(140 + Exc ) + yˆk+d+3 0.4607 × 10 ⎪ ⎪ ⎪ ⎪ ⎪ if yˆk+d+3 ∈ Exc + (140, 300] , ⎪ ⎪ ⎩ 1 otherwise,

(3.19)

where Exc is zero, unless during exercise times it changes to be 50 and then decreases slowly over 2 hours during the recovery period to be again zero.

3.3.1.3 Plasma insulin risk index A plasma insulin risk index (PIRI), denoted γk+d+3 , is defined to manipulate the weighting matrix for penalizing the amount of input actuation (aggressiveness of insulin dosing) depending on the estimated PIC, thus suppressing the infusion rate if sufficient insulin is present in the bloodstream. To this end, the time-varying positive definite weighting matrix Rk := R (γk+d+3 ) is developed from the PIRI as R (γk+d+3 ) := γk+d+3 · R, with R as a nominal weight and γk+d+3 defined as  γk+d+3 :=

PICk+d+3 PICbasal,k+d+3

2 ,

(3.20)

where PICbasal,k+d+3 :=

Idb,k+d+3 , VI · ke,k

(3.21)

and Idb is the patient-specific (possibly time-varying) basal insulin rate, which is known in practice, and VI and ke are the parameters of Hovorka’s model. Furthermore, the parameter ke is estimated online using the UKF and the CGM output measurements. A plot of the plasma insulin risk index (Fig. 3.1) indicates that as the penalty weight on the input action increases, the dosing becomes less aggressive if the estimated PIC is high.

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CHAPTER 3 Multivariable AP with adaptive control

FIGURE 3.1 Plot of the plasma insulin risk index.

3.3.1.4 Feature extraction for manipulating constraints Meal detection can be based on the qualitative description of segments of glucose time-series data. In this approach, features are extracted from the glucose measurement data using the first and second derivatives of a second-order polynomial fitted to the last few measurement data. If the first-order derivative is positive and greater than a threshold while taking into consideration the sign of second derivative, the constraints are modified to make the controller more aggressive to suggest a sufficient insulin dose. At every sampling time, the approach estimates the coefficients of the following polynomial function: Yk = pn1 × tk 2 + pn2 × tk 1 + pn3 ,

(3.22)

where pn1 , pn2 , and pn3 are the parameters of a second-order polynomial fitted to the last few glucose measurement, and tk is the sampling time. At each sampling instance, by updating Eq. (3.22), the parameter Pmeal is calculated by the first and second derivatives as follows:  Yk/T dm,1 if Y  ≥ T dm,11 , Y  ≥ 0, k k (3.23) Pmeal =  Yk/T dm,2 if Y  ≥ T dm,11 , Y  < 0, k k where the Yk and Yk are the first- and second-order derivatives at the last sampling time, and T dm,1 , T dm,2 , and T dm,11 are patient-specific threshold parameters.

3.3.1.5 Plasma insulin concentration bounds In the proposed MPC, the estimated future PIC is dynamically bounded depending on the value of the CGM measurements. For instance, if the CGM measurement values are elevated, then the bounds on the PIC are increased to ensure sufficient insulin is administered to regulate the glucose concentration. Furthermore, the PIC bounds also constrain the search space in the optimization problem, thus improving the computational tractability of the proposed MPC. The PIC are determined   bounds based on the CGM measurements as XPIC := (1 + Pmeal )X yˆk , where XPIC defines the lower and upper bounds and a desired target for the normalized PIC through the

3.3 Adaptive PIC cognizant MPC algorithm

FIGURE 3.2 Computing architecture required for IoT-enabling.  L,k : red (mid gray in print version) line, Plot of the plasma insulin concentration bounds, PIC  S,k : blue (dark gray in print version) line, and PIC  U,k : red (mid gray in print version) line. PIC

estimated CGM yˆk , and Pmeal is a parameter that modifies the bounds when there is a rapid increase in the CGM measurements. Fig. 3.2 depicts the bounds and the reference target for the normalized PIC as a function of the CGM measurement, and the MPC solution should satisfy the PIC constraints while maintaining the PIC close to the desired value. The nominal PIC bounds can be determined by multiplying the normalized PIC bounds with the basal PIC value. Therefore, appropriate PIC bounds can be determined based on each subject’s basal rate and the CGM measurement.

3.3.1.6 Hypoglycemia detection and carbohydrate suggestion To avoid any potential hypoglycemia, a predictive hypoglycemia alarm module is designed to suggest carbohydrates to be consumed by patient for the safety. Using 4-steps-ahead (20 minutes) prediction of CGM and considering the presence of physical activities and the amount of active insulin in the body (PIC), this module suggests 5–20 grams of fast-acting carbohydrates if the predicted CGM value is less than a safe threshold.

3.3.2 Adaptive MPC formulation In this subsection, we propose a novel adaptive MPC algorithm for computing the optimal insulin infusion rate. The proposed MPC formulation employs the glycemic and PIC risk indexes that manipulate the penalty weighting matrices in the cost function. It also uses the PIC bounds, the feature extraction method, and information from physiological signals to handle better unannounced disturbances. To this end, the MPC computes the optimal insulin infusion over a finite horizon using the identified subspace-based models with time-varying parameters by solving the following quadratic programming problem at each ith sampling instance:

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CHAPTER 3 Multivariable AP with adaptive control   ∗ nP −d−4  nP −d−4  uk k=0 := arg min JnP ,i yˆi+d+3 , γk+d+3 , uk k=0 u ∈U  ⎧ nP −1  ⎪ ˆ ˆ ⎪ , ⎨ x˜k+1 = Ak x˜k + Bk uk−d−3 ∀k ∈ Z0 n P s.t. y˜k = Ck x˜ˆk ∀k ∈ Z0 , ⎪ ⎪ ⎩ ˆ x˜0 = x˜ˆi , x ∈ X ,

(3.24)

with the objective function JnP ,i (·) :=

nP  k=0

ekT Qi ek +

nP −d−4

uk Ri uk , T

k=0

where xˆ˜ and y˜ denote the predicted states and outputs, respectively, for the prediction/control horizon nP , uk ∈ Rm denotes the vector of constrained input taking values in a nonempty convex set U  ⊆ Rm with U  :=   variables, m u ∈ R : umin ≤ uk ≤ umax , umin ∈ Rm and umax ∈ Rm denote the lower and upper bounds on the manipulated input, respectively, and ek := y˜k − ysp . The index Zn0 P represents all integers in a set as Zn0 P := {0, . . . , nP }, and X :=   x ∈ Rn˜ : xmin ≤ x ≤ xmax ⊆ Rn˜ is a nonempty convex set with xmin ∈ Rn˜ and xmax ∈ Rn˜ denoting the lower and upper bounds on the state variables, respectively, with one of the states as the estimated PIC constrained through the PIC bounds. Fur  thermore, xˆ˜i provides an initialization of the state vector, Q ≥ 0, Qk := Q yˆk+d+3 is a positive semidefinite symmetric matrix used to penalize the deviations of the outputs from their nominal set-point, R > 0, Rk := R (γk+d+3 ) is a strictly positive definite symmetric matrix to penalize the input variables.

3.4 Results The efficacy of the proposed M-AP is demonstrated using a multivariable simulator developed by our research group at Illinois Institute of Technology based on a modified Hovorka’s glucose–insulin dynamic model that can take into account the effects of different physical activities. For this purpose, aerobic exercises of treadmill and bicycle are considered for testing the M-AP system. Twenty virtual subjects are simulated for 3 days with varying times and quantities of meals consumed on each day and different types and times of physical activities as detailed in Table 3.1 and Table 3.2. The meal and physical activity information are not entered manually to the AP system as the AP controller is designed to regulate the BGC in the presence of significant disturbances such as unannounced meals and exercises. Using the physiological signals (Metabolic Equivalent (MET) Values) computed by the simulator, the start and end of exercise are detected using an exercise detection module and a recovery period after each exercise session is defined subsequently. To show the efficacy of

3.4 Results

Table 3.1 Computing architecture required for IoT-enabling. Meal scenario for three days closed-loop experiment using the multivariable metabolic simulator. Meal

First day Time Amount 50 g Breakfast 07:00 13:00 70 g Lunch 19:00 60 g Dinner Snack 21:30 30 g

Second day Time Amount 08:00 60 g 14:00 50 g 20:00 70 g 23:00 25 g

Third day Time Amount 07:30 55 g 13:30 60 g 19:30 50 g 22:00 20 g

Table 3.2 Computing architecture required for IoT-enabling. Exercise scenario for one hour duration for three days closed-loop experiment using the multivariable metabolic simulator. Exercise First day Second day Third day Bicycling at 09:00 Treadmill at 10:00 Bicycling at 09:30 Morning Afternoon Treadmill at 15:00 Bicycling at 16:00 Treadmill at 15:30

using physiological signals in the AP system, the S-AP does not use the physiological signals (MET Values) either as an input in the subspace-based system identification technique or in set-point modification during exercise and recovery period and in the glycemic risk index. In the MPC formulation, the umin is zero, and umax is defined as umax = Idb + IBolus,max × where

 IBolus,max := max

1000 , Ts

 yk − ysp Ik · VI − ,0 , CF 1000

(3.25)

(3.26)

where CF is the patient-specific correction factor, Ik is the PIC, VI is the insulin distribution volume, and therefore Ik · VI provides an estimate of the total insulin present in the body. The quantitative and qualitative evaluations of the closed-loop results based on the M-AP and S-AP are presented in Fig. 3.3 and Table 3.3. Table 3.3 gives the percentage of samples in defined glycemic ranges and selected statistics for the glucose measurements for the S-AP and M-AP. To better analyze the performance of each AP system, these glycemic ranges and selected statistics are calculated in different periods such as during exercise (EXC), exercise and recovery period (EXC & Rec), whole experiment (EXP), and whole experiment excluding the exercise and recovery periods (EXP ∼EXC & REC). It is readily observed that using the M-AP, no hypoglycemia occurs as the BGC is never below 70 mg/dL. For the S-AP, most hypoglycemia events occur during the EXC & Rec period where the CGM values drop

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FIGURE 3.3 Computing architecture required for IoT-enabling. Comparison of the S-AP (gray) and M-AP (white) during exercise (A), exercise and recovery period (B), whole experiment (C), and whole experiment excluding the exercise and recovery periods (D). The bottom and top of the boxes are the first and third quartiles and the line inside the box is the median. The whiskers ends represents minimum and maximum values, and + indicates mean values.

significantly due to the aerobic exercises. The percentage of time spent in the target range is significantly higher for the M-AP especially during the EXC and EXC & Rec periods. We can also observe that although the set-point changes to be higher during the EXC & Rec period in the M-AP, this modification does not have any adverse effect in the results of EXP ∼EXC & REC period. This shows that the M-AP controller is able to bring back the CGM to its normal set-point efficiently after the EXC session. Based on the average of maximum values of CGM and mean of CGM values in the EXP ∼EXC & REC period, the feature extraction method for manipulating constraints when meal period is detected performs very well in computing the required amount of insulin to avoid hyperglycemia. The relative changes in the CGM during 1-hour exercise and 2-hour recovery period have been plotted to show the efficacy of using physiological signals in an AP system in Fig. 3.4. We can see that using biosignals can benefit an AP system in regulating the BGC around a safer set-point and avoid any potential hypoglycemia.

3.5 Conclusions

FIGURE 3.4 Computing architecture required for IoT-enabling. Plot of the relative changes in the CGM during 1-hour exercise and 2-hour recovery period for the S-AP and M-AP.

3.5 Conclusions An adaptive MPC algorithm is proposed for a multivariable artificial pancreas (AP) system. Estimates of PIC and estimates of meal absorption rate and physiological variables are integrated with a recursive subspace-based system identification approach to characterize the transient dynamics of glycemic measurements. Subsequent to system identification, an MPC algorithm is designed using the adaptive models to effectively compute the optimal exogenous insulin delivery for AP systems without requiring any user-specified information on the time and amount of carbohydrate consumption and physical activity specifications. The performance of the proposed multivariable AP is demonstrated using simulation case studies.

Appendix 3.A In this section, we present the derivations for calculating the parameters in Eqs. (3.14) and (3.15):

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Table 3.3 Computing architecture required for IoT-enabling. Glycemic ranges and selected statistics for the glucose measurements for the S-AP and M-AP during exercise (EXC), exercise and recovery period (EXC & Rec), whole experiment (EXP), and whole experiment excluding the exercise and recovery periods (EXP ∼EXC & REC). Performance Index 80–140 mg/dL % 70–180 mg/dL % 180–250 mg/dL % 55–70 mg/dL % >250 % 0, w(t) = (4.10) 0 else, where σSM (t) is the sliding function defined simply as the difference between the actual IOB level and the imposed personalized limit: σSM (t)

= IOBj (t) − IOB(t).

(4.11)

The limit IOBj (t) is a priori considered piecewise constant, as it is explained later. Because IOB cannot be measured in real time, it must be estimated. To this effect, the model presented in [75] is considered: I˙sc1 (t) I˙sc2 (t)

= −KDIA Isc1 (t) + uw (t), =

KDIA [Isc1 (t) − Isc2 (t)] ,

IOB(t)

=

Isc1 (t) + Isc2 (t),

(4.12)

where Isc1 and Isc2 are, respectively, the amount of nonmonomeric and monomeric insulin in the subcutaneous space, uw is the exogenous insulin infusion rate in pmol/min/kg, and KDIA [min−1 ] is a constant rate. The advantage of this model is that it can be easily customized via KDIA so as to replicate each patient’s duration of insulin action (DIA) [47]. It should be noted that DIA is a clinical parameter adjusted in commercial insulin pumps. As a starting point, an average DIA of 5 hours was selected, leading to a KDIA fixed at 16.3 × 10−3 min−1 [37]. When the IOBj (t) limit is reached by the IOB estimation, a sliding regime is established over the surface σSM (t) = 0. During this mode, from (4.10), the signal w(t) switches at high frequency between 0 and 1 to fulfill the imposed restriction and forces system (4.12) to remain within the invariant set

= {x(t) | σSM (t) ≥ 0},

(4.13)

where x(t) ∈ R2 are the states of (4.12). The switching signal w(t) is then smoothed by a first-order filter (or averaged between infusion intervals), giving place to γ (t), which is the factor that finally modulates the signal commanding the pump.

4.3 ARG algorithm

Observation: It is easy to prove that the derivative of the switching function σSM (t) depends on the control action uw (t) and therefore on the discontinuous action w(t), which is a necessary condition for establishing the sliding mode, known as transversality condition. Like the main controller, the SAFE layer is implemented in a discrete way, obtained from (4.12) as follows:

1 − KDIA Tr x(k + 1) = KDIA Tr   IOB(k) = 1 1 x(k),



 1 0 x(k) + u (k), 1 − KDIA Tr 0 w (4.14)

where Tr = 0.1 min is the selected sample time. It should be noticed that Tr is smaller than Ts = 5 min since the SAFE algorithm is programmed entirely in software, and thus the switching frequency is only limited by the speed of the platform’s microprocessor. Although there may be different criteria to define the IOB limit, in this first approach, the following classification of the meal size was defined: • Small meal < 35 gCHO. IOBs,j (t) = IOBss,j (t) + 40 gCHO/CRj (t). • Medium meal [35, 65) gCHO. IOBm,j (t) = IOBss,j (t) + 55 gCHO/CRj (t). • Large meal ≥ 65 gCHO. IOBl,j (t) = IOBss,j (t) + 70 gCHO/CRj (t). Here IOBss,j (t) is the steady-state value of model (4.14) corresponding to the patient’s basal insulin rate ib,j (t), and X gCHO/CRj (t) is the insulin bolus related to X grams of carbohydrates (gCHO) using the patient’s Carbohydrate Ratio (CR) in [g/U]. When the system is not at a prandial period, the IOB limit is fixed to IOBs,j (t). In this manner, the controller has an extra degree of freedom to make adjustments to the basal infusion rate when necessary.

4.3.3 Auxiliary modules To minimize the risks of hypo- and hyperglycemia, two auxiliary modules, which are discussed below, have been added to the ARG algorithm to make it more robust against the time-varying nature and high uncertainty of the insulin–glucose dynamics.

Hypoglycemia-related module (Hypo-RM) Here an algorithm to lower the IOB limit when low glucose values are detected or predicted is defined as follows. 1: At every sampling time: 2: The glucose measured by the CGM sensor (g) in mg/dl is received, and a linear extrapolation strategy is used to estimate the glucose rate of change (gˆ˙ 30 ) in mg/dl/min. Besides, the future glucose concentration is predicted with a forecasting horizon of 15 min (gˆ 15 ), considering the last six glucose measurements, that is, the CGM samples received during the last 30 min.

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The IOB limit is set according to previous sections. if g < 60 then IOBj (t) = 0 else if g < 70 then IOBj (t) = 0.5IOBss,j (t) else if i = 1 and = 0 then if gˆ˙ 30 < −0.5 or [gˆ˙ 30 < 0.5 and IOB(t) ≥ IOBss,j (t)] then if gˆ 15 180 mg/dl PP O % time < 70 mg/dl PP O % time < 50 mg/dl PP LBGI HBGI Blood Glucose [mg/dl]

25 gCHO meal 50 gCHO meal 75 gCHO meal Mean Median IQR Mean Median IQR Mean Median IQR 127 126 [121, 131] 134 133 [128, 137] 143 142 [136, 148] 135 133 [126, 141] 160 159 [150, 167] 188 186 [175, 196] 99.7 100 [100, 100] 99.6 100 [100, 100] 96.7 100 [94.8, 100] 99.4 100 [100, 100] 99.0 100 [100, 100] 89.7 100 [83.3, 100] 98.7 100 [100, 100] 89.8 90.9 [88.1, 92.2] 83.0 83.8 [80.6, 86.8] 96.3 100 [100, 100] 67.7 71.0 [62.0, 75.0] 46.4 48.0 [38.0, 57.8] 0.0 0.0 [0.0, 0.0] 0.3 0.0 [0.0, 0.0] 3.2 0.0 [0.0, 5.2] 0.0 0.0 [0.0, 0.0] 0.9 0.0 [0.0, 0.0] 10.3 0.0 [0.0, 16.8] 1.0 0.0 [0.0, 0.0] 10.1 9.1 [7.8, 11.8] 16.9 16.3 [13.2, 19.4] 3.1 0.0 [0.0, 0.0] 32.2 29.0 [25.0, 38.0] 53.6 52.0 [42.3, 62.0] 0.3 0.0 [0.0, 0.0] 0.1 0.0 [0.0, 0.0] 0.1 0.0 [0.0, 0.0] 0.6 0.0 [0.0, 0.0] 0.1 0.0 [0.0, 0.0] 0.0 0.0 [0.0, 0.0] 0.0 0.0 [0.0, 0.0] 0.0 0.0 [0.0, 0.0] 0.0 0.0 [0.0, 0.0] 0.1 0.0 [0.0, 0.0] 0.0 0.0 [0.0, 0.0] 0.0 0.0 [0.0, 0.0] 0.1 0.0 [0.0, 0.1] 0.1 0.0 [0.0, 0.0] 0.0 0.0 [0.0, 0.1] 0.9 0.8 [0.6, 1.2] 2.0 1.8 [1.5, 2.3] 3.6 3.3 [2.7, 4.0]

IQR, interquartile range.

a larger density of points. However, this does not imply a greater risk to the patients’ health. In addition, the fact that a few subjects are in the C (2.7%), D (1.3%), and E (0.3%) zones could be analyzed as follows. On one hand, it must be considered that not every in silico patient has parameters that make sense physiologically, given that the database was generated for statistical ends. On the other hand, the proposed strategy allows tackling the singular cases where the controller action was either too conservative or too aggressive by slightly regulating the IOB constraint in terms of postprandial hypo- or hyperglycemia frequency. Numerical outcomes for all the considered cases are presented in Table 4.1. There the closed-loop results obtained in both the overall (O) and the 5-hour time interval following the start of the meal (postprandial period, PP) are analyzed separately. The Low Blood Glucose Index (LBGI) and the High Blood Glucose Index (HBGI) are also included. The scale for these indexes are defined according to [77]: • Risk of hypoglycemia: LBGI ≤ 2.5 (low); 2.5 < LBGI ≤ 5 (moderate); LBGI > 5 (high). • Risk of hyperglycemia: HBGI ≤ 4.5 (low); 4.5 < HBGI ≤ 9 (moderate); HBGI > 9 (high). We can observe that the ARG algorithm allowed achieving minimal risk of hypoand hyperglycemia. Even though the results are satisfactory, they can be further improved with the addition of the aforementioned meal size classifier to help establish a more adequate IOB constraint. For example, when the small-meal IOB limit IOBs,j is used in the simulations with the 25 gCHO meal, the mean time in hypoglycemia is reduced from 0.5% to 0.2%, maintaining a mean time of 96.5% in the range

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FIGURE 4.5 In silico closed-loop responses. Upper top: Closed-loop responses for all the in silico adults of the complete UVA/Padova simulator to 25, 50, and 75 gCHO meals. The solid lines indicate the mean glucose, and the shaded areas are ±1 standard deviations. Bottom top: Mean insulin infusions. Bottom: CVGA plot.

[70, 180] mg/dl in the postprandial period. On the other hand, when the large-meal IOB limit IOBl,j is used in the simulations with the 75 gCHO meal, the mean time in the range [70, 180] mg/dl increases from 46.3% to 52.5% during the postprandial period, with a minimal increase in the mean time in hypoglycemia from 0.0 to 0.1%. To further test the performance of the ARG algorithm, simulations considering different initial glucose values and errors in the adjustment of the basal insulin infusion rate were performed with the adult cohort of the distribution version of the

4.5 Clinical trials

UVA/Padova simulator. Two examples are illustrated in Fig. 4.6. In one case, a high initial glucose concentration of 210 mg/dl along with an insulin infusion rate that leads to a low steady-state glucose value of 70 mg/dl is considered (case 1). In the other case, the opposite scenario is tested, that is, a low initial glucose concentration of 70 mg/dl along with an insulin infusion rate that leads to a high steady-state glucose value of 210 mg/dl (case 2). As shown in the figure, the ARG algorithm was able to safely regulate the glucose level in both cases independently of the conditions. Indeed, the mean time in the range [70, 180] mg/dl was 91.1% for case 1 and 77.1% for case 2, whereas it is 90.0% when considering 120 mg/dl as initial and steady-state glucose value.

4.5 Clinical trials The first clinical trials with an AP in Latin America were carried out in two stages at the Hospital Italiano de Buenos Aires (HIBA). The first one was in November 2016 with the algorithm of the University of Virginia that had been tested internationally in several occasions. The second trial was in June 2017 with the ARG algorithm, fully developed in Argentina, in collaboration between researchers from the Instituto Tecnológico de Buenos Aires (ITBA), the Universidad Nacional de Quilmes (UNQ), and the Universidad Nacional de La Plata (UNLP). Both stages had the same numbers of patients (5) and hardware and followed the same clinical protocol. However, the

FIGURE 4.6 In silico closed-loop responses. Above: Closed-loop responses for all the in silico adults of the distribution version of UVA/Padova simulator to different glucose initial conditions and basal insulin rate adjustments. The solid lines indicate the mean glucose, and the shaded areas are ±1 standard deviations. Below: Mean insulin infusions.

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main difference between both trials is that in the latter, the patients had neither to count CHO nor to apply an insulin bolus. Here we focus on this second clinical trial. The selection of five patients with T1DM that participated in the trials was made according to the clinical protocol, particularly the inclusion and exclusion criteria as indicated in NCT02994277 (www.clinicaltrials.gov).

4.5.1 Hardware and software For the implementation of the AP, the following devices were used in each patient: • CGM Dexcom G4 Share; • Accu-Check Combo insulin pump from Roche; and • a NEXUS-5 smartphone based on Android containing the Diabetes Assistant (DiAs) from the University of Virginia (UVa) [78]. The Diabetes Assistant (DiAs) is a software that includes several mobile applications and allows every 5 minutes the communication between the control algorithm, the CGM sensor (through Android Bluetooth Low Energy), and the insulin pump (through standard Bluetooth). Due to FDA regulations, to be accepted as a Class III medical device, the phone, navigator, Android Market, games, and so on were removed. The system also includes the SQLite database for the asynchronous data management for requests from the user. The DiAs is a modular system where the control algorithm is contained. The ARG algorithm was programmed in the DiAs using object-oriented programming on the Eclipse IDE for Java Developers version: Kepler Service Release 2, with the plugin Android Development Tools (ADT).

4.5.2 Clinical procedures Patients were called to attend the HIBA nine days before the trial. That day, the protocol was explained in detail, the Informed Consent was signed, the inclusion/exclusion criteria were revised, and a blood extraction was made for laboratory screening. These results and a supervised glycaemia control were reviewed two days before the trial. That same day, the insulin pump and the CGM were connected to each patient, with a brief training in the use of both devices. The communication among these devices with the smartphone was verified, and the systems remained in open loop (without the algorithm active in the smartphone) in order for the patients to perform their usual controls. For comparison purposes, they also had to perform eight daily capillary glycaemia measurements until the day of the trial. The trial started at 1700 hs on day 0 and ended the morning of day 2. The loop was closed by activating the control algorithm in the smartphone, and all patients had five meals during the 36 hs tests: two dinners, one lunch, one breakfast, and one afternoon snack with a continuous monitoring of their glycaemia and injected insulin values from the medical and researcher staff room.

4.5 Clinical trials

The menu was coordinated by the nutritionist and had the following contents of CHO: breakfast or afternoon snack 28 g (wholegrain bread, water crackers, diet jam, spread cheese with tea, coffee or mate); dinner or lunch 55 g (wheat pasta with natural filetto sauce and lean meat with smashed potatoes, in both cases with fresh fruit).

4.5.3 Results Table 4.2 Clinical trial data. Comparison of the statistical data obtained from 36 hs in UC vs CL, considering a confidence interval of 95%. Mean % time [70, 250] mg/dl 82.9 % time [70, 180] mg/dl 59.1 % time < 70 mg/dl 7.6 % time < 50 mg/dl 1.7 LBGI 2.8 HBGI 7.2

UC CI 95% [67.3, 98.6] [41.9, 76.2] [2.9, 12.4] [0.3, 3.1] [1.8 3.7] [3.4, 11.0]

Mean 88.6 74.7 5.8 0.8 2.3 4.9

CL CI 95% [82.4, 94.7] [68.1, 81.4] [1.6, 10.0] [0.2, 3.5] [1.4, 3.1] [2.9, 6.9]

Next, a brief description of the results is presented. The Usual Care (UC) analysis was considered from 7 p.m. on the 21/09 up to 7 a.m. on the 23/09. In the case of the Closed Loop (CL) period, the time interval was considered from 7 p.m. on the 23/09 up to 7 a.m. on the 25/09. The insulin pump of one of the patients had an occlusion during the first night in CL, and therefore these hours were not considered in the analysis. The UC is used as a reference of their habitual glucose management, and it should be noted that the patients did not follow strictly the same diet during UC and CL. In Table 4.2 we can see the statistical data obtained from the 36 hours of CL trial and the comparison with those obtained in UC. We can observe that there is a significant improvement in the patient’s glucose regulation when using the ARG algorithm. The null hypothesis at a level of significance of 5% (ρ = 0.05), defined as the difference between the results obtained in UC and CL have zero mean, can be rejected in the percentage of time in euglycemic range [70, 180] mg/dl, being statistically significant (ρ = 0.0356). Since this is the first clinical trial of the ARG algorithm, three initial meals were used to make the necessary adjustments to the IOB maximum limit. For this reason, if the analysis of the results is concentrated in the last 15 hours of CL and it is compared with the 15 hours of UC that involve the same period of the day, then an even more significant control improvement is noticed, as it is shown in Table 4.3. The null hypothesis at a level of significance of 5% (ρ = 0.05), defined as the difference between the results obtained in UC and CL have zero mean, can be rejected in percentage time in euglycemic range [70, 180] mg/dl (ρ = 0.0142), in < 70 mg/dl (ρ = 0.049), LBGI index (p = 0.0383), and HBGI index (ρ = 0.0469), these being statistically significant.

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Table 4.3 Clinical trial data. Comparison of the statistical data obtained from first 15 hs in UC and the last 15 hs in CL with a confidence interval of 95%. Mean % time [70, 250] mg/dl 73.5 % time [70, 180] mg/dl 49.8 % time < 70 mg/dl 13.6 % time < 50 mg/dl 5.4 LBGI 4.2 HBGI 8.7

UC CI 95% [49.8, 97.2] [24.5, 75.1] [4.4, 22.7] [1.6, 16.4] [2.1 6.2] [2.9, 14.5]

Mean 94.7 82.6 4.1 0.2 1.8 2.8

CL CI 95% [83.8, 98.4] [69.9, 95.2] [0.8, 18.0] [0.0, 3.5] [0.3, 3.3] [0.1, 5.5]

It is important to remark that taking into account the night period (from 23 p.m. until 7 a.m.), the ARG algorithm presents a notorious improvement in comparison with the UC treatment. In Fig. 4.7, it is highlighted the comparison of the glucose excursion obtained during the second night in UC and in CL (time lapse without meals). In Table 4.4 the statistical data is presented regarding this period. Again, an improvement in percentage of time in euglycemia (ρ = 0.0351) and HBGI index (ρ = 0.0309) was obtained. Finally, in Fig. 4.8, the UC and CL percentage time in each glucose range and time-in-range cumulative plots are compared for both overall (36 h trial) and second night periods, showing again the effectiveness of the ARG algorithm. Table 4.4 Clinical trial data. Comparison of the statistical data obtained from the last nights in UC vs CL with a confidence interval of 95%. Mean % time [70, 250] mg/dl 78.1 % time [70, 180] mg/dl 50.3 % time < 70 mg/dl 3.6 % time < 50 mg/dl 0 LBGI 2.0 HBGI 9.8

UC CI 95% [29.1, 96.9] [23.2, 77.4] [0.3, 29.5] [0.0, 0.0] [0.6, 3.4] [2.8, 16.8]

Mean 95 87.7 5 0 1.5 1.9

CL CI 95% [66.9, 99.4] [76.5, 99.0] [0.6, 33.1] [0.0, 0.0] [0.4, 4.1] [0.4, 5.7]

4.6 Conclusions In this chapter, a brief review of the AP project in Argentina was presented alongside with a novel control strategy for glycemic regulation, the ARG algorithm. It consists of a two-degree-of-freedom control structure that includes a switched LQG inner controller together with an outer sliding-mode safety loop, the Safety Auxiliary Feedback Element (SAFE) mechanism, for IOB constraints. The switched LQG

4.6 Conclusions

FIGURE 4.7 Clinical test. Mean glycemic excursion of all five patients in UC (red (mid gray in print version)) and in CL (blue (dark gray in print version)) during night time. The solid line indicates mean, and the gray area ±1 standard deviation.

FIGURE 4.8 Clinical test. Glucose range percentage times and cumulative time-in-range for all patients in UC (red (mid gray in print version)) and in CL (blue (dark gray in print version)) during the whole trial (left half) and during the second night (right half). The dashed lines are the mean values, and the continuous lines are the envelopes.

control strategy is a simplified version of that in [33]. The switched nature of the inner controller enables different tunings for dealing with prandial and fasting periods and can be extended to other situations, for example, physical activity. New and more complex scenarios could be potentially addressed by redesigning the switching

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policy and/or the IOB constraints. The SAFE layer quickly adapts the controller gain to automatically obtain insulin spikes like the open-loop boluses. Promising results were obtained both in silico and later in vivo during the first clinical trials in Latin America.

Acknowledgments Access to the complete version of the University of Virginia/Padova metabolic simulator was provided by an agreement with Prof. C. Cobelli (University of Padova) and Prof. B. P. Kovatchev (University of Virginia) for research purposes. The authors would like to acknowledge Dr. Daniel Cherñavvsky for his very generous collaboration. We would also like to thank the physicians of the Hospital Italiano Ventura Simonovich, Paula Scibona, Cintia Rodriguez, Javier Giunta, and Valeria Beruto coordinated by Dr. Luis Grosembacher and Dr. Waldo Belloso, without whom the clinical trial could not have been possible. Additionally, we express our gratitude to the nutritionist Marianela Stasi, who worked with us in the elaboration of the menu used. The invaluable help during the tests of our students Emilia Fushimi, Marcela Moscoso-Vázquez, and Nicolás Rosales is deeply appreciated. Finally, we want to highlight the collaboration with Dexcom, the generous donation by Roche, and the funding of the Cellex (Spain) and Nuria (Argentina) Foundations.

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[67] G. Vinnicombe, Uncertainty and Feedback: H∞ Loop-Shaping and the ν-Gap Metric, Imperial College Press, London, 2001. [68] K.R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, Routledge, London, 1963. [69] F. Bianchi, M. Moscoso-Vázquez, P. Colmegna, R. Sánchez-Peña, Invalidation and low-order model set for artificial pancreas robust control design, J. Process Control (2019), https://doi.org/10.1016/j. jprocont.2019.02.004, in press. [70] Roy S.R. Smith, Model Validation for Uncertain Systems, Ph.D. thesis, California Institute of Technology, 1990. [71] Mario Sznaier, María C. Mazzaro, An LMI approach to control-oriented identification and model (in)validation of LPV systems, IEEE Trans. Autom. Control 48 (9) (2003) 1619–1624. [72] R. Smith, G. Dullerud, S. Rangan, K. Poolla, Model validation for dynamically uncertain systems, Math. Comput. Model. Dyn. Syst. 3 (1) (1997) 43–58. [73] J.P. Hespanha, A.S. Morse, Switching between stabilizing controllers, Automatica 38 (11) (2002) 1905–1917. [74] F. Garelli, R. Mantz, H. De Battista, Advanced Control for Constrained Processes and Systems, IET Institution of Engineering and Technology, London, United Kingdom, 2011. [75] M.E. Willinska, L.J. Chassin, H.C. Schaller, L. Schaupp, T.R. Pieber, R. Hovorka, Insulin kinetics in type 1 diabetes: continuous and bolus delivery of rapid acting insulin, IEEE Trans. Biomed. Eng. 52 (1) (2005) 3–12. [76] Fabián M.L. Vargas, Design and Implementation of a Closed-Loop Blood Glucose Control Systems in Patients with Type 1 Diabetes, Ph.D. thesis, Universitat de Girona, 2013. [77] B. Kovatchev, G. Umpierrez, A. DiGenio, R. Zhou, S.E. Inzucchi, Sensitivity of traditional and riskbased glycemic variability measures to the effect of glucose-lowering treatment in type 2 diabetes mellitus, J. Diabetes Sci. Technol. 9 (6) (2015) 1227–1235. [78] P. Keith-Hynes, B. Mize, A. Robert, J. Place, The diabetes assistant: a smartphone-based system for real-time control of blood glucose, Electronics 3 (4) (2014) 609–623.

CHAPTER

Use of intraperitoneal insulin delivery for artificial pancreas

5

Eric Renarda,b,c , Anne Farreta,c , Jerôme Placec a Department

of Endocrinology, Diabetes, Nutrition, University Hospital of Montpellier, Montpellier, France b Clinical Investigation Centre INSERM 1411, Montpellier, France c Institute of Functional Genomics, CNRS, INSERM, University of Montpellier, Montpellier, France

5.1 Bedside artificial pancreas: the birth of a concept Loss of insulin secretion in type 1 diabetes (T1D) implies the vital need of insulin administration, which became available shortly after the discovery of insulin in 1921. However, the variability of body insulin needs due to the many factors that influence blood glucose levels results in a difficult task for matching timely delivery of insulin according to T1D patient’s need. To allow fast tuning of insulin delivery, continuous infusion modulated according to blood glucose levels is needed. An automated glucose-controlled insulin delivery emerged forty years ago with the development of the bedside in-hospital artificial pancreas. Artificial (endocrine) pancreas models have been developed in the 1970s, almost simultaneously in Europe, Japan, and Northern America [1–4]. These systems, such as Biostator [5], included intravenous (IV) insulin infusion from a motor-driven syringe, continuous glucose measurement (CGM) by an extracorporeal enzymatic sensor from an access to IV blood, and a computing system that drove insulin delivery to keep glucose levels in a close to normal range based upon proportional-derivative (PD) algorithms. An IV glucose infusion line was also available in case of glucose lowering toward hypoglycaemia. These systems were shown to be able to keep blood glucose in a near-normal glucose range. The technologies were however unavailable by these times to allow ambulatory implementation.

5.2 Prioritization of subcutaneous insulin delivery in the development of a wearable artificial pancreas (AP) Portable insulin pumps were gradually developed from the 1980s, mostly using subcutaneous (SC) insulin infusion. Improvements in microelectronics have led to reliable pulsatile infusion systems, with no trauma to the insulin molecule, finely tuned and programmable insulin delivery, holding an autonomous durable power source The Artificial Pancreas. https://doi.org/10.1016/B978-0-12-815655-1.00014-4 Copyright © 2019 Elsevier Inc. All rights reserved.

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and reduced to the size of a cell phone. Continuous subcutaneous insulin infusion (CSII) is nowadays used by hundreds of thousands of patients with T1D all over the world. The availability of sufficiently safe and accurate SC enzymatic glucose sensors allowing continuous glucose measurement (CGM) in interstitial fluid from 1999 opened the door for a renewal of the AP concept for diabetes care [6]. Meanwhile, modeling of glucose metabolism and insulin action led to the development of simulation platforms that allowed the design and the assessment of closed-loop algorithms through in silico trials in which virtual patients with diabetes could be submitted to SC insulin infusion according to glucose evolution [7]. Whereas ADICOL experience [8] with simulated SC glucose sensing and newly designed model predictive control (MPC) algorithms, which took into account delays of SC sensing and SC insulin action, had shown the feasibility of a semiclosed-loop insulin delivery (i.e., closed-loop control between meals and prandial insulin bolus), the first full closed-loop 30-hour inpatient clinical experiment with actual SC sensing, SC insulin infusion, and a PID algorithm was reported by Steil et al. in a landmark paper in 2006 [9]. However, full closed-loop insulin delivery at mealtimes resulted in early blood glucose spikes followed by late post-meal hypoglycaemia due to the delayed action of SC infused insulin in response to the increase of blood glucose levels following meal intakes. This phenomenon could be prevented by manually ordered premeal bolus as shown by Weinzimer et al. [10]. Hence further developments of AP systems using SC glucose sensing and SC insulin infusion have followed this hybrid configuration of closedloop, also called semiclosed-loop, which includes meal announcement so that meal intakes are preceded by an insulin bolus computed according the carbohydrate component of the meal, the premeal blood glucose level, and the estimated “insulin on board” according to insulin infusion rate [11]. Funding by the Juvenile Diabetes Research Foundation (JDRF) from 2006, US National Institute of Health (NIH) from 2009 and European Union (EU) from 2010 have promoted the gradual development of closed-loop insulin delivery trials using CSII from hospital setting [12–16] to “home-like” conditions [17–25] and ambulatory free-life use for several months [26–31]. The last decade has shown dramatic advances with these closed-loop systems, which clearly document the feasibility of this mode of therapy for outpatients with T1D, its ability to improve time spent in close-to-normal glucose range with a reduction of risk for hypoglycemia, and its combined safety and efficacy for glucose control at night [32]. At the EASD meeting in September 2016, the results of a three-month prospective 24/7 closed-loop study involving 124 patients were presented [33]. While the patients used the Medtronic MiniMed 670G system, including an insulin pump with embedded control algorithm wirelessly connected to a CGM, with a median percent time of 87.2 in closed-loop mode, the sensor glucose moved from 66.7 at baseline to 72.2% for the 3 months in the 70–180 mg/dl target range, and the mean HbA1c level decreased from 7.4 to 6.9%. Over 12389 patient-days, no episodes of severe hypoglycaemia or ketoacidosis were observed. These robust safety data led to the FDA approval of this system for clinical use in the therapy of T1D, which represents a milestone in the development of

5.3 Rationale for using intraperitoneal insulin delivery

closed-loop insulin delivery. Besides, other AP systems are currently in development by industry [34], start-ups [35,36], and academic centers worldwide [37]. Systematic reviews of reported AP trials tell that outpatients using AP systems spend 60–70% of time in a glucose range of 70–180 mg/dl [32,38]. A remaining limitation of glucose control with closed-loop systems occurs at meal time. With currently available fast-acting analogues, meal announcement followed by a computed premeal bolus is still the only way to avoid postmeal hyperglycaemia [11]. Several options of faster insulin analogues now enter the clinical field such as the Fast Insulin Aspart (FIAsp) and the Biochaperone Insulin Lispro. These insulin formulations are characterized by a quicker availability for action during 30 minutes after delivery and a shorter duration of action. Closed-loop trials using these new insulin preparations will assess their effectiveness on glucose control after oral carbohydrate intakes, and whether the premeal bolus can be omitted. Besides, expected improvements in devices include better insulin infusion sets and more accurate and stable glucose sensing. Indeed, cannulas of insulin infusion sets remain prone to transitory occlusions and insulin under-delivery. Recent research also includes the development of algorithms that are able to identify a defect in insulin infusion from the increase of sensor glucose levels contrasting with ordered insulin delivery according to the control algorithm [39]. Glucose sensors have gradually improved during the last decade in terms of accuracy with a MARD, which is now below 10%. Interruptions of transmission of sensor signal may however corrupt control decisions and should be reduced by a simpler communication of sensor signal to the insulin pump in which the control algorithm is embedded. This “All-in-One” device concept should ease the communication process between the closed-loop components and make wearing AP less cumbersome. Progress in control can also be expected from adaptive algorithms that will adjust their own parameters automatically from the data collected during previous weeks [40]. Such “run-to-run” control modules were recently investigated in AP clinical trials [41,42]. Another option for full closed-loop control with no meal announcement includes the prediction of meal-associated sensor glucose increment according to patient habits of taking meals at predefined time periods [43,44]. Nevertheless, the size, visibility, and cumbersome wear of the currently developed AP systems have been identified as significant worries of parents whose children participated in closed-loop trials [45].

5.3 Rationale for using intraperitoneal insulin delivery Intraperitoneal insulin delivery has been used initially in patients with diabetes and renal failure treated by peritoneal dialysis and shown to be effective and convenient in these subjects [46]. Several studies have then been performed in animal models to assess the characteristics of peritoneal insulin absorption [47,48]. Insulin absorption from the peritoneal space was shown as volume-, concentration-, and time-dependent [47]. More interestingly, insulin was first distributed to the portal vein, before entering the systemic circulation [48]. A positive gradient between portal and systemic

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FIGURE 5.1 Pharmacokinetics of intraperitoneal insulin bolus delivered from implantable insulin pumps in patients with type 1 diabetes, personal data.

blood insulin was further demonstrated by IP insulin administration, which differed from intramuscular insulin injection but mimicked endogenous insulin secretion. In humans, IP insulin delivery was shown to allow quicker insulin peaks than SC route: 70 min vs. 120 min, and plasma insulin levels returned to baseline after 165 min as in normal subjects [49]. Whereas the rate of systemic appearance of IP infused insulin was lower than SC infused insulin at steady-state, the percent increase in the rate of systemic appearance after an increase of infusion rate was higher with IP route [50]. More recent investigations showed that the average time to peak of plasma insulin after an IP insulin bolus was close to 25 minutes (Fig. 5.1), that is, almost half the time measured after a SC insulin bolus [48]. These data showed a quicker absorption of insulin from peritoneum that prefigured a higher reactivity in clinical use and suggested the likely role of the liver in modulating peripheral insulin delivery. As a result, a lower peripheral insulinemia, close to physiological levels, was obtained in steady-state conditions with IP route than with SC insulin delivery. The answer to the question whether hepatic insulinization secondary to IP insulin delivery controls better hepatic glucose output than systemic insulin delivery is however still unclear. Since systemic insulin levels reduce the delivery of gluconeogenic substrates from peripheral tissues to the liver than portal insulin, they may in fact also lower fasting hepatic glucose output [51]. Studies in animals and in humans comparing the effects of IP and IV insulin infusions showed similar reductions of hepatic glucose output. Data from animal studies with IP and SC insulin demonstrate that the peripheral in-

5.4 Clinical experience with continuous intraperitoneal insulin infusion

sulin levels are 68% higher with the SC route, although the total insulin requirement is the same for both IP and SC routes. In addition, hepatic glucose output is 45% higher with SC insulin, whereas, for a similar level of glycaemic control, the IP route achieves peripheral insulin concentrations similar to those observed in nondiabetic animals [52]. Different responses have been observed in other metabolic pathways with IP compared with SC delivery. These are primarily related to higher portal insulin concentrations and lower peripheral concentrations. IP insulin in several studies has been observed to increase biologically active Insulin-like Growth Factor 1 (IGF-1) by both increasing IGF-1 itself and by reducing Insulin-like Growth Factor Binding Protein 1 (IGFBP-1) concentrations [53–56]. Growth hormone axis dysregulation has been described in type 1 diabetes and may have a role in macrovascular complications [57, 58]. This potential normalizing of the axis with IP insulin therefore may have a significant impact on quality of life by impacting on sleep and complication status and warrants further investigation. Compared to SC insulin, IP insulin also reduces hepatic sex hormone binding globulin (SHBG) production by around 20% (with a greater effect seen in women), leading to higher concentrations of free sex hormones [59], and has an effect on lipid metabolism by inhibiting hepatic very-low-density lipoprotein (VLDL) production and activating hepatic lipase [60]. Studies have suggested that IP insulin is associated with an increase in triglyceride concentration compared with SC insulin with a reduction or no change in high-density lipoprotein (HDL)-cholesterol but small numbers of subjects and short duration of follow-up limit the interpretation of these data [61,62]. The high HDL state seen with subcutaneous insulin administration presents a paradox as type 1 diabetes is associated with an excess cardiovascular risk despite apparently favorable concentrations of HDL. The effects on lipid profiles seen with intraperitoneal insulin may therefore have an impact on cardiovascular risk, and further studies are needed to elucidate this.

5.4 Clinical experience with continuous intraperitoneal insulin infusion First case-reports of IP insulin delivery from portable pumps and via a catheter that was indwelled into the peritoneal cavity through the abdominal wall indicated the effectiveness of this therapeutic mode in brittle diabetes after failures to achieve glucose control with SC, intramuscular, and sometimes IV insulin [63]. Selam et al. [64] reported a large experience with this technique, cumulating 472 patient-months in 40 type 1 diabetic patients. Metabolic control was significantly improved with reduced insulin doses. The technique was however associated with frequent local infectious complications around the implantation site of the catheter. No overdelivery of insulin occurred but underdeliveries related to pump failures or catheter obstructions were reported, so that one-year survival rate of pump and catheter were 46 and 70%, respectively. Fibrin nodes at the catheter tip or omental encapsulation of the catheter were

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FIGURE 5.2 Implantation procedure of an insulin pump for intraperitoneal delivery. Creation of the pump pocket and blind insertion of the peritoneal catheter, personal data.

shown to explain catheter obstructions. To overcome these problems, specific ports have been implanted in the abdominal wall through which the peritoneal catheter reached peritoneal space [65]. Using this technique, blocked catheters were expected to be more easily replaced. However, infections around the port frequently led to port removal, and catheter replacements in case of encapsulation remained sometimes hardly achievable. A new device (DiaPort, Roche Diagnostics, Mannheim, Germany) is currently under investigation in Europe, which might reduce the incidence of these complications. In spite of the drawbacks of these externally worn devices, IP insulin infusion has been shown as providing a tighter glucose control than SC infusion or injections during the operating time. A crucial benefit was the combination of a similar HbA1c or mean blood glucose and a very low incidence of severe hypoglycaemia, related to the pharmacokinetics of IP route [66]. To overcome infectious issues at implantation site, fully implantable insulin infusion systems have been developed (Fig. 5.2). Requirements for implantable insulin pumps include: physically and chemically stable insulin preparations, miniaturized and telemetry-controlled safe and reliable infusion systems, biocompatible materials for pump and catheter, and a sustained power source for long-term infusion from the implanted pump. An easy access to pump reservoir for insulin refills and to peritoneal catheter in case of underdelivery are also mandatory. The trend for insulin aggregation (i.e., physical instability) is a crucial phenomenon to overcome to allow safe and reliable artificial insulin delivery devices, as shown by the rapid failures of initial attempts to develop implantable pumps. Two main mechanisms involved in insulin aggregation are isoelectric precipitation and noncovalent polymerization (or fibrillation) [67]. Insulin precipitation is promoted by pH-fall and metal ions. This

5.4 Clinical experience with continuous intraperitoneal insulin infusion

process can be overcome by stabilizing solution pH by using buffer, preventing CO2 diffusion into the insulin solution by an appropriate choice of catheter components and avoiding metal ion liberation from the pump materials. The formation of insoluble insulin fibrils is promoted in artificial insulin delivery devices by a combination of heat, movement, and hydrophobic interactions. Interactions between insulin and hydrophobic surfaces have been pointed out as key-determinants of the aggregating process. Conformational changes of the tertiary structure of insulin at liquid-solid and liquid-air interfaces have been suspected to induce insulin noncovalent polymerization by promoting interactions between hydrophobic nonpolar side-chains of insulin molecules. Hence, the pump fluid system should be inert, airtight, and with a hydrophilic minimal inner surface. The elaboration of genapol (Hoechst AG, Frankfurt, Germany), a surface-active agent able to prevent hydrophobic interactions of insulin with surface materials of pump reservoirs and tubings by providing hydrophilicity, allowed considerable improvements in the physical stability of insulin preparation for implantable systems [68]. During these last years, a similar preparation of insulin for implantable pumps has been developed by Sanofi (Paris, France) by replacing semisynthetic human insulin by recombinant human insulin. U-400 solution of this insulin is currently investigated in MIP 2007 [69]. The largest experience with three available implantable programmable pump models at the beginning of the 1990s was reported by the EVADIAC study group, which collected in a central registry all data generated by seven French Centers [70]. The whole experience represented 224 type 1 diabetic patients to whom 260 pumps were implanted (205 MIP 2001, 48 Infusaid model 1000, and 7 Promedos ID3) followed up for 353 patient-years. EVADIAC experience first pointed out the metabolic benefits of implantable pumps using IP route. Whereas HbA1c fell from 7.4 ± 1.8 to 6.8 ± 1.0%, with a sustained improvement over 30 months, the incidence of severe hypoglycaemic events dramatically decreased from 15.2 to 2.5 per 100 patient-years (p < 0.001). Interestingly, severe hypoglycaemia was reported to recur in a subset of patients who went back to multiple daily injections or CSII after leaving implantable pump trial, whereas HbA1c also went back to higher levels [71]. Nathan et al. addressed the question of the mechanism of this reduction of severe hypoglycaemic events [72]. Attempts to induce hypoglycaemia were performed in eight patients using SC or IP/IV insulin administration at two different doses, the higher one being 1.75-fold normally used dose to cover a meal-intake. The explanation of the higher occurrence of hypoglycaemia with SC insulin came from the measurements of plasma insulin levels, which were significantly higher at 180 and 240 min after SC insulin administration for both doses. The area under the curve for insulin was also higher between 120 and 240 min for both doses after SC insulin. These data documented the reduced risk of hypoglycaemia with implantable pumps using IP or IV route by showing more physiological profiles of obtained postprandial insulin levels. Besides, Oskarsson et al. [73] demonstrated that the glucagon response to an induced hypoglycaemia by IV insulin was improved after a prolonged IP insulin infusion from implantable pumps when compared with that obtained while the same patients were treated by CSII. Glucagon response to exercise was similarly

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improved after prolonged IP insulin treatment using implantable pumps [74]. Both more physiological insulin kinetics and improved counter-regulatory capacity may thus be involved in the metabolic benefits obtained with implantable pumps. The Zwolle Group more specifically addressed the question of the benefits of CIPII vs. CSII in a randomized control trial [75]. In this cross-over study including 24 patients with Type 1 diabetes, CIPII from implanted insulin pumps improved HbA1c levels by 0.76% vs. CSII and significantly increased time spent in 4.6–17.3 mmol/l glucose range according to continuous glucose recordings whereas hypoglycaemic events were similar. The quality of life was also significantly improved with CIPII. Recently, the EVADIAC group reported sustained improvement of glucose control for up to 5 years with implantable pumps with HbA1c levels in 7.5–7.6% range with no simultaneous changes in body weight and diabetic complications [76]. Although the studies reported above supported the long-term feasibility of implantable pump therapy in T1D patients and pointed out specific benefits on blood glucose control, most of them also reported adverse events that raised questions about the risk/benefit ratio of this technique. The EVADIAC Study Group reported in the largest cumulated multicenter experience ever published (1180 patient-years) that 84 out of 352 patients (24%) were affected by complications at implantation site [77]. Sixty four per cent of these patients required pump explantations. Lesions included local inflammatory reactions, skin atrophy or erosion, and chronic seromas or infections. No risk factor could be identified, but complications seemed to occur more frequently in centers with a limited number of implants, suggesting the role of a lack of experience in the occurrence of these events. Two main causes of insulin underdeliveries are catheter occlusions and insulin precipitates in pumps. Reported incidences of IP catheter obstructions in early studies extended between 7.8 and 57.3 per 100 patient-years [78–82]. Two types of obstructions have been described: 1) tip obstructions by fibrin clots and 2) encapsulations forming a more or less extended sock around the peritoneal catheter. Although precipitation of insulin in pumps is solved in most cases by NaOH rinsing, their frequent occurrence tend to impair metabolic control and make heavier the management of the therapy. Following the availability of a redesigned catheter and changes in insulin preparation, a cumulated follow-up of 106 patient-years showed a lowered incidence of 4 catheter obstructions per 100 patient-years, but backflows related to insulin precipitation in pumps still occurred with an incidence of 33.7 per 100 patient-years [83]. The immunogenicity of peritoneal insulin delivery has been shown in animal studies and in humans treated by intraperitoneal insulin from external pumps [84]. It has been speculated that conformational modifications of the insulin molecule in implantable pumps might account for the production of specific antiinsulin antibodies, possibly in relationship with the formation of insulin aggregates [85]. Whether the affinity to insulin of these antibodies could be lower and consequently promote alterations of insulin pharmacokinetics responsible for clinical syndromes has not been explored. Since antiinsulin antibody response is more likely to occur in patients who

5.5 Closed-loop experience with IP insulin delivery

FIGURE 5.3 Picture of the connection of an external insulin pump to the DiaPort for intraperitoneal infusion, personal data.

present high antibody levels before moving to IP delivery [86], CIPII must be thoroughly debated, if not banned, in such cases due to the risk of inducing deleterious glucose disturbances related to antiinsulin antibody increase. Because of the initially reported high rate of adverse events with implantable pumps using IP insulin delivery and because of the cost of this therapy, less than 500 patients worldwide are using such devices for insulin administration at the present time. This population includes rare cases of subcutaneous insulin resistance, local skin reactions to insulin injections, for example, lipodystrophies, or to CSII catheters, or brittle diabetes of unknown origin, and the patients who cannot achieve glucose control with optimized SC insulin therapy due to high glucose variability including recurrent severe episodes of hyper- and/or hypoglycaemia [87,88]. The recently reinitiated development of the DiaPort, a port implanted in the abdominal wall allowing the insertion of an IP catheter, which can be connected to a portable insulin pump (Fig. 5.3), may represent an alternative to implanted insulin pumps to get the metabolic benefits of CIPII with reduced burdens and at a lower cost [89].

5.5 Closed-loop experience with IP insulin delivery 5.5.1 AP with IV glucose sensing and IP insulin delivery The first tested combination, whose results have been reported in 2001–2, included an implanted insulin pump using peritoneal route, connected to an implanted IV glucose sensor that provided inputs for control PD and then PID algorithms [90,91]. This fully

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FIGURE 5.4 Scheme of the Long-Term Sensor System, an investigational model of artificial pancreas combining central intravenous glucose sensing connected via a subcutaneous wire to an implanted insulin pump for intraperitoneal insulin infusion, personal data.

implanted artificial pancreas model has been developed by MiniMed Technologies, followed by Medtronic, under the denomination “Long term Sensor System (LTSS),” and investigated from 2000 to 2007 (Fig. 5.4). A dozen of 48-hour closed-loop experiments, during which three daily meals including predefined carbohydrate compositions were offered, have been performed with the LTSS. During these tests, 22–42% of total investigational time was spent in tight euglycaemia (80–120 mg/dl), 5–6% below 80 mg/dl, 50–60% between 120 and 240 mg/dl, and 2–10% above 240 mg/dl. Glucose control was close to normal at night time and during late postabsorption periods, whereas postmeal hyperglycaemic excursions were constantly observed for several hours. Hypoglycaemia occurred uncommonly in late postmeal (more than 2 hours after meal intakes) periods in most cases. A few trials have tested the addition of a manual premeal insulin bolus, resulting in a semiclosed-loop format. Major postmeal hyperglycaemic excursions were suppressed as well as hypoglycaemic episodes, so that 100% of the total investigational time was spent in the 80–240 mg/l range, including 35% between 80 and 120 mg/dl. The failure to achieve permanent glucose control in the target range was mainly explained by the delay in glucose sensing due to the internal structure of the glucose sensor. The limited operating time of the implanted sensors, close to 6 months on average, was related to the fragility of the implanted sensors, which were eroded by the shear forces of the central blood flow. The failure to improve the sensor life time without increasing dangerously the rigidity of the implanted sensor led to stop the development of this model.

5.6 Perspectives for IP insulin use in AP

5.5.2 AP with SC glucose sensing and IP insulin delivery 5.5.2.1 IP insulin delivery: closed-loop vs. open-loop The following investigations that combined a SC enzymatic glucose sensor, an implanted insulin pump using peritoneal delivery, and an improved PID algorithm, including a component for the modulation of insulin infusion according to estimated insulin level, in an hybrid system called HyPID, were performed in 2007–8 [92]. A pre-meal bolus was also manually ordered. The results show a better glucose control achieved when insulin delivery was driven by the sensor and the algorithm vs. adapted by the patient according to self-monitoring of blood glucose. Time spent in normoglycaemia (80–120 mg/dl) with the closed-loop system reached 39% vs. 28% in the open-loop system. Outside the immediate post-meal phases, which included the two hours following meals, mean blood glucose level was significantly lower, and the time spent in euglycaemia reached 46% in closed-loop conditions. Following these results, which showed the effectiveness of this specific model on glucose control, comparative trials vs. SC insulin delivery were needed to identify the specific benefits related to the IP route of insulin infusion on the performance of closed-loop control.

5.5.2.2 Closed-loop control with IP vs. SC insulin delivery A recently reported trial addressed this question [93]. Ten adults with T1D participated in a nonrandomized, nonblinded sequential AP study using the same SC glucose sensing and Zone Model Predictive Control (ZMPC) algorithm adjusted for insulin clearance. On first admission, subjects underwent the closed-loop control with SC delivery of a fast-acting insulin analogue for 24 hr. Following the implantation of a DiaPort IP insulin delivery system, the identical 24-hr trial was performed with IP regular insulin delivery. The clinical protocol included three unannounced meals with 70, 40, and 70 g carbohydrate. Percent time spent within 80–140 mg/dl range was significantly higher for IP delivery than SC delivery: 39.8 ± 7.6 vs. 25.6 ± 13.1 (p = 0.03). Mean BG (mg/dl) and percent time spent within broader 70–180 mg/dl range were also significantly better with IP insulin: 151.0 ± 11.0 vs. 190.0 ± 31.0 (p = 0.004) and 65.7 ± 9.2 vs. 43.9 ± 14.7 (p = 0.001), respectively. Superiority of glucose control with IP insulin came from reduced time spent in hyperglycaemia (>180 mg/dl: 32.4 ± 8.9 vs. 53.5 ± 17.4, p = 0.014; >250 mg/dl: 5.9 ± 5.6 vs. 23.0 ± 11.3, p = 0.0004). Higher daily doses of insulin (IU) were delivered with IP route (43.7 ± 0.1 vs. 32.3 ± 0.1, p < 0.001) with no increased percent time spent 50% in the 3 hours after the meal without causing hypoglycemia. These results confirmed what was found in silico.

6.5 Modeling subcutaneous glucose sensor delay Understanding interstitial fluid (I SF ) glucose kinetics is fundamental for continuous glucose monitoring (CGM), which is a key component of contemporary diabetes management. I SF is remote from blood and it is well known that I SF glucose is “delayed” with respect to blood glucose (BG). However, less appreciated is that I SF glucose is not simply a shifted-in-time version of BG, but a distorted version of BG [60]. Characterizing quantitatively this distortion is particularly important when using CGM in real-life, given that glucose is sensed in I SF using an sc sensing probe. To do that, a model of BG-I SF glucose kinetics is needed. Several studies have investigated the temporal relationship between BG and I SF glucose in subjects with and without T1D by using different experimental techniques (see [61] for a brief review), showing that a two-compartment model is adequate to describe BG-I SF glucose kinetics [62–65]. However, only recently an innovative multitracer and microdialysis experimental design was performed [66,67] allowing to simultaneously and frequently collect plasma and I SF glucose data in fasting conditions. Thanks to this unique data set, the model of BG-I SF glucose kinetics [61] was accurately identified in humans. The model allows us to quantify the equilibration time τ , a fundamental parameter describing the dynamics of BG-I SF glucose as a combination of model parameters: τ=

1 , k12 + k02

(6.8)

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where τ represents the time constant characterizing the response of the I SF compartment to a unit step glucose infusion in blood (Fig. 6.11). To gain insight into

FIGURE 6.11 The two-compartment model describing the blood-interstitium glucose kinetics [61]. The equilibration time τ is the time required by interstitium glucose to reach the value of 0.63 if a unit step glucose infusion is performed in blood at time 0. Figure modified from [60].

the meaning of the physiological “delay” between BG-I SF glucose, two in silico studies have been conducted by exploiting the BG-I SF glucose model. Two metrics have been introduced to characterize the complexity of the relationship between BG and the distorted (with respect to BG) I SF glucose: the time course of glucose differences (GL, glucose lag) between BG-I SF glucose at each time point and the time course of time differences (T L, time lag) when I SF glucose is equal to BG: GL(ti ) = BG(ti ) − I SF (ti ), T L(ti ) = ti − tk ,

(6.9) (6.10)

where tk (with k ≤ i) is the time where BG assumes the same value of I SF (ti ) glucose. The results show that the relationship between BG-I SF glucose profiles is inherently time-varying, with a complex pattern depending not only on the equilibration time τ but also on the time course of BG profile (Fig. 6.12) [60]. However, at present the only tracer-based quantification of the model kinetics is available in fasting conditions [61], but even in the case of nonsteady-state conditions, the argument still applies. This opens the door to incorporate predictive models or priors into contemporary sc glucose sensors in order to mitigate the delay for taking actions, for example, to predict ahead of time a hypoglycaemic event and take a rescue carb in advance. In a scenario of insulin dosing, for example, in an AP system, this delay calls again for the incorporation of this knowledge in the control algorithm to also compensate for the additional, and more important, delay of sc insulin absorption. Moreover, putting into the problem additional elements related to technological delays will simply make the picture more articulated but will not change the picture.

6.6 Nonadjunctive use of glucose sensors

FIGURE 6.12

Top panel : BG concentration data measured in a healthy subject after a meal and exercise session [68] (black line) and predicted ISF glucose time course (red (mid gray in print version) and blue (dark gray in print version) line for τ = 7.1 min and τ = 20.5 min, respectively). Middle panel : Time course of glucose differences (GL) between BG and ISF glucose at each time point for two equilibration times (red (mid gray in print version) and blue (dark gray in print version) line for τ = 7.1 min and τ = 20.5 min, respectively). Bottom panel : Time course of time differences (TL) for ISF glucose to equilibrate with BG for two equilibration times (red (mid gray in print version) and blue (dark gray in print version) line for τ = 7.1 min and τ = 20.5 min, respectively). Figure modified from [60].

6.6 The UVA/Padova T1D simulator for nonadjunctive use of glucose sensors In the past 10 years, the accuracy of sc glucose sensing has moved from MARD (mean absolute relative difference, a common metric used to compare CGM to reference blood glucose) of 19.7% of the Medtronic RT-Guardian to a 9% of the Dexcom G4 Platinum (with software 505). Does this improved accuracy make sc glucose sensors reliable for insulin treatment decisions in place of self-monitoring blood glucose (SMBG)? A clinical trial addressing this question would be almost impossible since the required number of patients to ensure exploration of the tails of the sensor MARD distribution would be prohibitive. Also, retrospective data are not useful because it is impossible to see what would have happened if insulin dosing was based on CGM rather than SMBG. Determining whether CGM is safe and effective enough to substitute SMBG in diabetes management has therefore become an important topic of investigation for the diabetes community and regulatory agencies. Computer simulation is of critical importance because it allows us to perform in silico clinical trials

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(see also the outcome of a recent FDA panel meeting [69] and commentary [70]. The simulator used in this case includes a patient decision-making model (Fig. 6.13) and defines in silico scenarios that recreate real-life conditions (e.g., 100 adults and 100 pediatric patients, three meals per day with variability in time and amount, and meal bolus behavior). Performance for both CGM and SMBG scenarios were evaluated using standard outcome metrics, like time in severe hypo, time in hypo, time in target, hypo- or hyperglycemic events. Our results (Fig. 6.14) support the nonin-

FIGURE 6.13 Block-scheme of the T1D patient decision-making simulator model. Arrows entering each block are inputs, whereas arrows exiting are causally related outputs. The input of the simulator is the sequence of meals, whereas the output is the BG concentration profile. The simulator includes parameters describing the patient’s physiology and therapy. The picture reports representative time courses for meals in input and BG in output for a simple scenario in which the patient takes 50 g for breakfast at 07:00 am. Figure modified from [71].

FIGURE 6.14 Modeling strategy to realize the 40,000 combinations of physiology, behavior, and hypoawareness on which the glucose sensor nonadjunctive use vs. SMBG has been tested.

6.7 Adaptive AP algorithms

feriority of CGM vs. SMBG [69,70]. Moreover, time below 50 and 70 mg/dL has significantly improved, time between 70 and 180 mg/dL and time above 180 mg/dL have slightly improved, and the number, extent, and duration of hypoglycaemic events have significantly reduced in the CGM vs. SMBG scenario [71].

6.7 Adaptive AP algorithms In the past decade the research has seen unprecedented advances in AP technology, which moved from short-term inpatient studies to short trials at home employing wireless portable wearable AP systems. Several studies were conducted in adults, for example, those using an AP system based on the Modular Model Predictive Control algorithm (MMPC) [72–74] in gradually less structured and less monitored settings: inpatient first [75], 2-day in hotel settings [76,77], and, recently, 2-month evening & night at home [21]. The formerly conducted studies had a limited duration and were restricted to evening and night, thus allowing us to neglect the impact of intraand interday glucose response variability of each subject, for example, to insulin and meals. The latter is a well-known phenomenon and became a major issue with the introduction of longer (week/month) home trials. This large subject-specific variability calls for an adaptive controller. In the following section, we describe in summary an adaptive AP MMPC algorithm based on the Run-to-Run (R2R) approach [78]. The R2R is a well-known learning-type control algorithm [79], which learns information about the control quality from the current run and changes the control variable to apply in the next run. The R2R strategy has already been used for glucose control in T1DM subjects on the basis of a few daily self-monitoring blood glucose (SMBG) measurements [80–84] or using CGM data [31,85,86] to adapt day-by-day basal insulin delivery or the insulin meal bolus. R2R in the AP context was introduced in [87], where the aggressiveness of the controller was adapted by using the maximum and minimum glucose values provided by CGM. Here a much more realistic R2R approach for tuning the MMPC algorithm is described, which adapts the basal insulin delivery during the night and the carbohydrate-to-insulin ratio (CR) during the day, and its in silico test using the new time-varying UVA/Padova T1D simulator.

6.7.1 Run-to-Run strategy for adaptive MPC tuning The MMPC algorithm considered here is the linear model predictive control described in [74]. The principal parameters used for control tuning and individualization are the basal insulin delivery, the carbohydrate-to-insulin ratio (CR), the correction factor (CF), and the body weight (BW). In particular, the MMPC computes an insulin variation with respect to the basal profile, uses CR and CF (taking into account also the insulin on board, that is, the amount of insulin, coming from previous bolus/infusions, that is still active in the body) to compute the insulin reference in the cost function, and BW and CR to tune the control aggressiveness. Thus the adaptive

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MMPC aims to (i) optimize the tuning of the controller parameters and (ii) adapt them to the interday variability. Specifically, the R2R strategy is applied to update both the basal insulin delivery and CR parameter (and thus the meal insulin bolus); the update is applied in the next day (run) on the basis of the performance measured during the previous day (run). The choice of the performance indices is a critical point for the success of the R2R. CGM sensors (usually employed in an AP context) allow including clinically relevant indices into the problem, for example, the percentage of time spent in hypo-, eu-, and hyperglycaemic range, and the average blood glucose (BG). In particular, since a major concern in T1DM therapy is to avoid hypoglycaemia, the updating law is primarily designed to lead to 0 the percentage of time spent in hypoglycaemia (i.e., BG < 70 mg/dL). Once this primary goal is achieved, a secondary updating law is designed to reduce the percentage of time spent above 180 mg/dL and to lead the average BG to the desired target. For each run, the variation of the basal insulin rate is proportional to the applied basal delivery and to the performance indices computed during the previous run. To give priority in avoiding hypoglycemia, a switching condition depending on the percentage of time spent below 70 mg/dL is introduced. A similar updating law is used to optimize the CR values, each of which is assumed to be constant along three daily intervals (postbreakfast/lunch/dinner). The stability of the proposed strategy can be demonstrated by applying the method described in [31], where an R2R approach for adapting a piecewise basal therapy in an open-loop context is proposed. A key assumption is that disjoint intervals are used to update basal insulin or CR: this is an important requirement; otherwise, the problem would move from several scalars to a multivariable framework with a significant increase of complexity both in terms of algorithm tuning and stability analysis.

6.7.2 In silico testing The R2R algorithm described before has been tested on 100 in silico adults of the simulator. A two-month scenario has been simulated, in which three meals per day are administered at 8:00 am, 1:00 pm, and 8:00 pm having 40 g, 80 g, and 60 g of CHO, respectively. Moreover, if the BG falls below 65 mg/dL, the protocol prescribes a rescue CHO dose of 16 g (hypotreatment). Two hypotreatments are separated by at least 30 minutes. The simulations are performed twice, either by using the MMPC strategy described in [74] (CL) or by employing the adaptive MMPC enhanced by the R2R strategy (CLR2R ), in which basal insulin and CR were updated during the night or daytime, respectively. Performance metrics include average BG (M) and standard deviation (SD), percentage of time spent in euglycaemic target range [70–180] mg/dL (Tr ), percentage of time spent above 180 mg/dL (Ta ), and percentage of time spent below 70 mg/dL (Tb ). The M ± SD of simulated BG after one week, four weeks, and eight weeks are shown in Fig. 6.15: the postprandial overshoots detected after lunch and dinner (Fig. 6.15A) are considerably reduced after one month of R2R (week 4, Fig. 6.15B). A further reduction is achieved after 2 months (week 8, Fig. 6.15C), also with a reduced BG variability.

6.8 Conclusions

Numerical comparison of CL vs. CLR2R on the whole experiment duration is reported in Table 6.1, where the improvement shown by CLR2R is evident. Performance indices show that the improvement of CLR2R vs. CL is modest after one week; after one month, the percent time in range, time in tight range, and time above 180 mg/dL are very much improved with respect to week 1. This performance is maintained until the end of the experiment (week 8). The encouraging results achieved in silico in a realistic one-month scenario have opened to an in vivo testing phase [88]. Specifically, 18 T1D patients underwent an outpatient 4-week study, aimed at comparing the performances achieved by CLR2R with respect to the nonadaptive CL (both used for 24/7). The details and results are reported in Chapter 7, Section 7.7.3.

FIGURE 6.15 Comparison of average ± SD glucose time courses in CL (blue (dark gray in print version)) vs. CLR2R (magenta (light gray in print version)) on week 1 (A), week 4 (B), and week 8 (C), respectively. Figure modified from [78].

6.8 Conclusions Modeling, in conjunction with tracers, has become an integral component of contemporary diabetes technology and has helped tremendously the development of the artificial pancreas. In this chapter, we have reviewed the key role of the UVA/Padova

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Table 6.1 Performance Metrics Improvements. Percent improvements obtained using the CLR2R algorithm with respect to the sole CL. M (mg/dL) Tt (%) Ttt (%) Ta (%)

Week 1 Week 4 Week 8 0.86% 4.81% 6.29% 1.69% 8.31% 11.39% 5.60% 28.37% 44.87% 7.94% 33.95% 48.74%

simulator by also giving a development perspective up to its most recent single-day version. In the beginning the simulator has allowed us to move to human studies on the only basis of in silico evidence with an important acceleration of artificial pancreas research. Crucial were also a number of ancillary models, for example, those describing intra- and interday patterns of insulin sensitivity and glucose absorption parameters, and those quantitating the blood glucose-interstitial fluid kinetics: all these models have been subsequently incorporated in the simulator allowing us to move into the new generation of adaptive closed-loop glucose control systems. In the most recent years the simulator has found new territories of application, which are briefly reviewed, notably the testing of new relevant molecules for better glucose control and the generation of in silico evidence of nonadjunctive use of glucose sensors.

Appendix 6.A 6.A.1 UVA/Padova T1D simulator model equation Glucose subsystem ⎧ ˙ p (t) = EGP (t) + Rameal (t) − Uii (t) ⎪ G ⎪ ⎪ ⎪ ⎨ − E(t) − k1 ·Gp (t) + k2 ·Gp t (t), ⎪ ˙ (t) = −U G ⎪ t id (t) + k1 ·Gp (t) − k2 ·Gp t (t), ⎪ ⎪ ⎩G(t) = G (t)/V , p

G

Gp (0) = Gpb , Gt (0) = Gtb , G(0) = Gb .

(A.1)

Insulin subsystem ⎧ ⎪ ⎨I˙p (t) = −(m2 + m4 )·Ip (t) + m1 ·Il (t) + RaI (t), I˙l (t) = −(m1 + m3 )·Il (t) + m2 ·Ip (t), ⎪ ⎩ I (t) = Ip (t)/VI ,

Ip (0) = Ipb , Il (0) = Ilb , I (0) = Ib .

(A.2)

6.A Appendix

Glucose rate of appearance ⎧ Qsto (t) = Qsto1 (t) + Qsto2 (t), ⎪ ⎪ ⎪ ⎪ ˙ ⎪ ⎪ ⎪Qsto1 (t) = −kgri ·Qsto1 (t) + D·δ(t), ⎨ ˙ sto2 (t) = −kempt (Qsto )·Qsto2 (t) + kgri ·Qsto1 (t), Q ⎪ ˙ gut (t) = −kabs ·Qgut (t) + kempt (Qsto )·Qsto2 (t), ⎪Q ⎪ ⎪ ⎪ ⎪ ⎪ f ·kabs ·Qgut (t) ⎩Ra , meal (t) = BW

Qsto (0) = 0, Qsto1 (0) = 0, Qsto2 (0) = 0, Qgut (0) = 0,

(A.3)

Rameal (0) = 0,

with kmax − kmin  · tanh[α(Qsto − β·D)] 2  − tanh[β(Qsto − c·D)] + 2 .

kempt (Qsto ) = kmin +

(A.4)

Endogenous glucose production EGP (t) = kp1 − kp2 ·Gp (t) − kp3 ·X L (t) + ξ ·X H (t), X˙ L (t) = −ki · [X L (t) − I  (t)], ˙



I (t) = −ki · [I (t) − I (t)], X˙ H (t) = −kH ·X H (t) + kH · max[(H (t) − Hb ), 0],

EGP = EGPb , (A.5) X L (0) = Ib , 

(A.6)

I (0) = Ib ,

(A.7)

X H (0) = 0.

(A.8)

Glucose utilization Uii (t) = Fcns , [Vm0 + Vmx ·X(t)·(1 + r1 ·risk)]·G(t) , Uid (t) = Km0 + Gt (t) ˙ X(t) = −p2U ·X(t) + p2U ·[I (t) − Ib ], X(0) = 0,

(A.10)

⎧ if G ≥ Gb , ⎪ ⎨0 risk = 10·[f (G)]2 if Gth ≤ G < Gb , ⎪ ⎩ 10·[f (Gth )]2 if G < Gth ,

r

r f (G) = log(G) 2 − log(Gb ) 2 .

(A.12)

(A.9)

(A.11)

with

(A.13)

Renal excretion  E(t) =

ke1 ·[Gp (t) − ke2 ] 0

if Gp (t) > ke2 , if Gp (t) ≤ ke2 .

(A.14)

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External insulin rate of appearance RaI (t) = RaI sc (t) + RaI id (t) + RaI ih (t).

(A.15)

Subcutaneous insulin kinetics 

RaI sc (t) = ka1 ·Isc1 (t) + ka2 ·Isc2 (t), I˙sc1 (t) = −(kd + ka1 )·Isc1 (t) + usc (t − τ ), I˙sc2 (t) = kd ·Isc1 (t) − ka2 ·Isc2 (t),

(A.16)

Isc1 (0) = Isc1ss , Isc2 (0) = Isc2ss .

(A.17)

Intradermal insulin kinetics 

RaI id (t) = idt1 (t) + ka ·Iid2 (t), I˙id1 (t) = −(0.04 + kd )·Iid1 (t) + uid (t), I˙id2 (t) = −ka ·Iid2 (t) + idt2 (t),

(A.18)

Iid1 (0) = Iid1 ss , Iid2 (0) = Iid2 ss ,

(A.19)

where idt1 (t) and idt2 (t) are defined by the transfer functions  T1 (s) =

b1 s + b1

2 =

L {idt1 (t)}   , T2 (s) = L 0.04·Idt1 (t)



b2 s + b2

a2

=

L {idt2 (t)}  . L kd ·Idt2 (t)

Inhaled insulin kinetics RaI ih (t) = kaI ih ·Iih (t),

(A.20)

I˙ih (t) = −kaI ih ·Iih (t) + FI ih ·uih (t),

Iih (0) = 0.

(A.21)

Gsc (0) = Gb .

(A.22)

H (0) = Hb ,

(A.23)

Subcutaneous glucose kinetics ˙ sc (t) = −1/Ts ·Gsc (t) + 1/Ts ·G(t), G

Glucagon kinetics and secretion H˙ (t) = −n·H (t) + SRH (t) + RaH (t), s d (t) + SRH (t), SRH (t) = SRH

⎧ s

b ⎪ (t) − SRH ⎨−ρ· SRH  

˙ sH (t) = SR σ [Gth − G(t)] s b ⎪ + SRH , 0 ⎩−ρ· SRH (t) − max I (t) + 1  dG(t) d ,0 . SRH (t) = δ· max − dt

(A.24) if G(t) ≥ Gb , if G(t) < Gb , (A.25) (A.26)

References

Subcutaneous glucagon kinetics 

H˙ sc1 (t) = −(kh1 + kh2 )·Hsc1 (t), H˙ sc2 (t) = kh1 ·Hsc1 (t) − kh3 ·Hsc2 (t),

Hsc1 (0) = Hsc1b , Hsc2 (0) = Hsc2b ,

RaH (t) = kh3 ·Hsc2 (t).

(A.27) (A.28)

Acknowledgments This work was supported by MIUR, Italian Ministry of Education, Universities and Research (grant FIRB RBFR08CHY6_002); University of Padova (grant CPDA145405/14); EU project ICT FP7-247138 “Bringing the Artificial Pancreas at Home (AP@home)” (Funding Agency: European Union’s Research and Innovation funding programme, FP7 initiative: FP7-ICT2007-2); Juvenile Diabetes Research Foundation (grant no. 17-2011-273); National Institutes of Health (grants DK-R01-085516, DK-DP3-094331, DK-R01-029953, DK-DP3-106785); Novo-Nordisk (research grant NN1218-3922).

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[79] Y. Wang, F. Gao, F.J. Doyle III, Survey on iterative learning control, repetitive control, and run-to-run control, J. Process Control 19 (10) (2009) 1589–1600. [80] C. Owens, H. Zisser, L. Jovanovic, B. Srinivasan, D. Bonvin, F.J. Doyle, Run-to-run control of blood glucose concentrations for people with type 1 diabetes mellitus, IEEE Trans. Biomed. Eng. 53 (6) (2006) 996–1005. [81] C.C. Palerm, H. Zisser, W.C. Bevier, L. Jovanovic, F.J. Doyle, Prandial insulin dosing using run-torun control: application of clinical data and medical expertise to define a suitable performance metric, Diabetes Care 30 (5) (2007) 1131–1136. [82] C.C. Palerm, H. Zisser, L. Jovanovic, F.J. Doyle III, A run-to-run framework for prandial insulin dosing: handling real-life uncertainty, Int. J. Robust Nonlinear Control 17 (13) (2007) 1194–1213. [83] C.C. Palerm, H. Zisser, L. Jovanovic, F.J. Doyle, A run-to-run control strategy to adjust basal insulin infusion rates in type 1 diabetes, J. Process Control 18 (3–4) (2008) 258–265. [84] H. Zisser, L. Jovanovic, F. Doyle, P. Ospina, C. Owens, Run-to-run control of meal-related insulin dosing, Diabetes Technol. Ther. 7 (1) (2005) 48–57. [85] P. Herrero, P. Pesl, M. Reddy, N. Oliver, P. Georgiou, C. Toumazou, Advanced insulin bolus advisor based on run-to-run control and case-based reasoning, IEEE J. Biomed. Health Inform. 19 (3) (2015) 1087–1096. [86] J. Tuo, H. Sun, D. Shen, H. Wang, Y. Wang, Optimization of insulin pump therapy based on high order run-to-run control scheme, Comput. Methods Programs Biomed. 120 (3) (2015) 123–134. [87] L. Magni, M. Forgione, C. Toffanin, C. Dalla Man, B. Kovatchev, G. De Nicolao, C. Cobelli, Runto-run tuning of model predictive control for type 1 diabetes subjects: in silico trial, J. Diabetes Sci. Technol. 3 (5) (2009) 1091–1098. [88] Mirko Messori, Jort Kropff, Simone Del Favero, Jerome Place, Roberto Visentin, Roberta Calore, Chiara Toffanin, Federico Di Palma, Giordano Lanzola, Anne Farret, Federico Boscari, Silvia Galasso, Angelo Avogaro, Patrick Keith-Hynes, Boris P. Kovatchev, Daniela Bruttomesso, Lalo Magni, J. Hans DeVries, Eric Renard, Claudio Cobelli, for the AP@home consortium, Individually adaptive artificial pancreas in subjects with type 1 diabetes: a one-month proof-of-concept trial in free-living conditions, Diabetes Technol. Ther. 19 (10) (2017) 560–571.

CHAPTER

Deployment of modular MPC for type 1 diabetes control: the Italian experience 2008–2016

7

Simone Del Faveroa , Chiara Toffaninb , Lalo Magnic , Claudio Cobellia b University

a University of Padova, Dep. of Information Engineering, Padova (PD), Italy of Pavia, Dep. of Electrical, Computer and Biomedical Engineering, Pavia (PV), Italy c University of Pavia, Dep. of Civil Engineering and Architecture, Pavia (PV), Italy

7.1 Introduction Automated devices for glycaemic control, the so-called Artificial Pancreas (AP), promise to revolutionize diabetes management by reducing patient burden and allowing more effective control. Enabled by advancement in pumps for Continuous Subcutaneous Insulin Infusion (CSII) and by the developments of minimally invasive sensors for Continuous Glucose Monitoring (CGM), the AP technology has its core in a control algorithm. A large spectrum of control techniques have been explored: PID, described in [1] and later equipped in [2] with a mechanism to mitigate insulin absorption delays (called “Insulin Feedback”); control law emulating pancreatic beta-cell secretion [3] or medical doctor reasoning [4]; and fuzzy logic [5]. MPC technique appears to be particularly suited for glucose control in view of its capability to handle constraints (insulin delivery is bounded to be positive) and to mitigate for insulin absorption delay employing predictive reasoning. For this reason, MPC was the technique of choice of a number of groups [6–10]. Moreover, alternative AP system architectures have been proposed: dual-hormone AP, infusing insulin and glucagon (the hormone antagonist to insulin), was investigated in [11,12]; multiinput MPC, exploiting ancillary measurements from accelerometers, gyroscopes, and so on was proposed in [13] to better estimate disturbances affecting the system; finally, AP exploiting other insulin infusion routes were proposed; see [14] for a discussion. In the last 10 years, an intense clinical research effort has been preformed to test AP prototypes, resulting in more than 50 clinical trials conducted on human subjects affected by T1D. The first clinical experiments were conducted on hospitalized subjects (in-patient); see [15–17] for a systematic review. Once the safety and efficacy of this technology has been proved in the controlled in-patient setup, experiments in semicontrolled out-patient setting were conducted with the aim to safely emulate the The Artificial Pancreas. https://doi.org/10.1016/B978-0-12-815655-1.00016-8 Copyright © 2019 Elsevier Inc. All rights reserved.

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unsupervised use of the AP by the patient in real-life; see, for instance, [18–21]. The development of wearable AP prototypes based on modified smartphones and (nearly) wirelessly connected to pump and sensor [22] were a key element that made this transition possible. Once validated in semisupervised setting, various AP prototypes entered the last, and most interesting, validation phase, the sustained independent use of the device in real life [23,24]. In this chapter, we illustrate the algorithmic, technical, and regulatory challenges we encountered in the process of designing and testing our control algorithm, the modular MPC (mMPC), and we describe the solution we adopted to overcome these challenges. In particular, we illustrate how modularity in control architecture allowed the progressive deployment of increasingly complex algorithms running on improved hardware.

7.2 AP hardware 7.2.1 APS: the in-patient hardware platform A first step toward the clinical validation of an AP was its testing in hospitalized patient to guarantee the higher level of patient safety. In this setting, medical and technical personnel were closely monitoring the patient throughout the study and operating on the AP prototype. Moreover, the collection of frequent blood samples was usually a mandatory requirement at this stage. The consequent need of an open intravenous access strongly limited patient’s freedom of movement. Given these constraints, the technological requirements for in-patient AP prototypes were limited. In some cases [25], a human operator was inserting manually on a laptop the sensor reading at each control step (usually 15 minutes); based on the reading, the control algorithm suggested an insulin infusion that, if deemed safe by the attending physician, was manually programmed on the pump. Other studies employed laptop-based platforms automating sensor-controller and controller-pump data transfer, so that manual data transfer between devices was no longer needed (Fig. 7.1, left panel). An important example is the APS© system [26], a Matlab-coded software that runs on a laptop and takes care of a low-level technical interface between component devices, allowing a “plug and play” use of a number of different sensors and pumps models. Moreover, the APS provides an Application Programming Interface (API), which allows for quick integration of Matlab-coded closed-loop control algorithms. Finally, the APS provided a Graphical User Interface (GUI), allowing the study team to interact with the control algorithm, and visual and audio alarms to point out malfunctioning or possibly dangerous events. The APS significantly eased the deployment and testing of a new controller also in a regulatory perspective, allowing stepwise validation of various system components, for example, a new API-compliant controller without the need to validate data-path continuity throughout the rest of the system.

7.2 AP hardware

FIGURE 7.1 Hardware of an AP system. The APS platform (left) used in [27] and two configurations of the DiAs System: with Omnipod and Dexcom Seven Plus used in [28,29] (center) and with Acchucheck Spirit Combo and Dexcom G4 Platinum used in [21] (right).

7.2.2 DiAs: the out-patient hardware platform Albeit enabling automated data transfer, the APS was not suited for out-patient reallife studies, since it limits patient mobility due to many wired connections among the components. An important step forward for the ambulatory use of an Artificial Pancreas was the introduction of the DiAs, University of Virginia [22]. The core component of the DiAs system is an off-the-shelf smartphone running the Android operating system (OS). To ensure the operation of the smartphone as a medical device, the OS was modified to disable processes not related to clinical operation and to include self-checks of system integrity. Patient-DiAs interaction takes place using a GUI [30]. This is a critical part of the system, since in out-patient AP studies the patient interacts with the system without supervision, at difference with in-patient studies. Designed in strict interaction with the patient through focus groups, the GUI allows the controller to receive information from the patient (e.g., meals and exercise session), triggering the appropriate feed-forward action, and the patient to receive information from the controller (e.g., imminent risk for hypoglycaemia requiring treatment). The communications between DiAs and the peripherals (pump and sensor) are wireless, giving the patient the freedom to be fully detached from the DiAs controller. The DiAs system can be used with different pumps and sensors, but in our out-patient studies, we used mostly three hardware configurations.

Config. A: Omnipod and Dexcom SEVEN PLUS The DiAs was first used with the Omnipod Insulin Pump (Insulet Corp, Bedford, MA) and with DexCom SEVEN PLUS (DexCom, Inc., San Diego, CA) sensor (Fig. 7.1, central panel). Since direct Bluetooth communication was not available in this pump

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and this sensor, the system components worn by the patient included a Bluetooth– USB hub connected to an iDex, an experimental device from Insulet Corp combining a DexCom Seven Plus receiver and OmniPod PDM. As we will discuss in the following (see Section 7.6), this configuration has been abandoned due to the multiple wired connections among the components, in favor of the integration of pumps offering direct bluetooth control.

Config. B: t:slim and G4 Platinum The t:slim pump (Tandem Diabetes Care, San Diego, CA), which provides LowPower Bluetooth access, has been integrated in the system. Furthermore, the next generation Dexcom sensor, G4 Platinum, has been employed. This sensor outperforms significantly its predecessor by providing much more accurate measurements and guaranteeing more stable wireless connection among transmitters placed on patient abdomen and Dexcom receiver [31]. Nevertheless, such a receiver has not accessible wireless link. Therefore this version of the system still requires either a direct wired connection between DiAs and Dexcom receiver or the use of a relay device bridging the information.

Config. C: Accu-Chek Combo and G4 Platinum Accu-Check Spirit Combo Pump (Roche, Mannheim, DE) has also been integrated, and thanks to the standard Bluetooth access it provides, no extra hardware was needed (Fig. 7.1, right panel). Dexcom G4 Platinum sensor was used in this configuration, which has been adopted in our most recent out-patient and real-life studies [21,24, 32] with increasingly small and reliable devices enabling bluetooth access to CGM data. Later on, we integrated in this configuration a new release of the same sensor, known as Dexcom G4AP, which offered direct bluetooth connection with the sensor receiver, removing the need of an extra relay device, and improved sensor accuracy thanks to better signal processing algorithms [33]. This DiAs configuration proved to be highly robust and well suited for sustained domestic use.

7.3 Telemedicine One of the critical issues in moving from inpatient to real-life trials is to guarantee the highest possible level of safety for the patient, a mandatory prerequisite to gain regulatory bodies approval. Obviously, the in-patient risk-mitigation solution, that is, having attending personnel directly watching the patient, is neither possible in real-life setting nor suited for the transitional out-patient setting, since the team would interfere with the study. To guarantee patient safety in out-patient and reallife settings, the DiAs streams in real-time patient data and information on system functioning to a telemonitoring website [34,35] exploiting the smartphone 3G connectivity. Accessing to the website via an ordinary PC, the study team is able to monitor from a remote location the status of the multiple patients and to check the

7.4 AP control algorithm

correct functioning of the system throughout the trial, without interfering/interacting with the experiment unless requested by protocol safety measures or for system troubleshooting. In the studies reported here, lasting less than 48 hours, the study team was constantly monitoring patients data and systems status. Moreover, the team was requested to remain in the vicinity of the patients to guarantee prompt intervention. In real-life month-lasting studies, where 24/7 monitoring was not be possible, a webbased remote alarm system, possibly sending e-mail messages to the study team if needed, has been introduced, and its effectiveness was validated. Unfortunately, the inclusion of these important safety measures is unavoidable because of the risk of inflating the estimated AP effect in a trial with respect to an unmonitored setup. In fact, it has been shown that tight telemonitoring alone in children camp has the potential to improve glucose control [36], at least when followed by prompt study team intervention.

7.4 AP control algorithm A layered architecture for AP has recently been presented in [37] and is depicted in Fig. 7.2. It decouples functionalities among modules, allowing independent development and solving integration hurdles. At the bottom of the architecture, there is the physical layer, containing the hardware components acting on the patient, and just above it the physical interface layer, containing the software for hardware management presented in the previous section. Above these layers, there is the so-called safety layer, a software module dedicated exclusively to maximize patient safety by detecting possible overinjections of insulin and reducing them. Further above this layer, there is the control layer, which contains the software computing a suitable insulin injection to keep patient blood-glucose (BG) in a nearly normal range. Safety and control layer employs different reasoning criteria and different patient models, guaranteeing a double check on any insulin injection proposed by the control layer. At the top of this architecture, there is the patient standard therapy provided by the diabetologist. This valuable information can be further improved by the adaptation layer, in charge of adjusting standard therapy parameters to follow patient changes over time; the optimized therapy is then provided to control layer for real-time feedback adjustments. In this chapter, we introduce one possible implementation for the safety layer, the Safety Supervision Module, SSM [37], and two possible implementations for the control layer of increasing complexity, the Mitigation Module (HMM) and a Model Predictive Control (MPC) algorithm. The modular controller employing SSM and HMM is called H2MS, Hypo- and Hyperglycaemia Mitigation System; the modular controller employing SSM and MPC is called the Modular Model Predictive Control (mMPC). In most of the clinical studies presented here, no adaptation module was present, but in our most recent clinical studies, presented in Section 7.7.3, we tested our mMPC equipped with an implementation of the adaptation layer based on a run-to-run algorithm (R2R mod-

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FIGURE 7.2 A schematic of our modular architecture.

ule). This controller will be further called Adaptive mMPC (A-mMPC). In short: H2MS = SSM + HMS, mMPC = SSM + MPC, A-mMPC = SSM + MPC + R2R.

7.4.1 Safety layer The Safety Supervision Module, SSM [37], computes a real-time estimate of the patient’s metabolic state based on CGM and insulin infusion data. Moreover, SSM can account for the insulin estimated to be still active in the body, the so-called Insulin

7.4 AP control algorithm

On Board, based on the method proposed in [38]. These estimates are used to predict hypo- and hyperglycaemia risks 30–45 min ahead. If a risk for hypoglycaemia is predicted, then SSM attenuates automatically any insulin requests in proportion to the predicted risk level. The proportionality factor is determined by readily available patient characteristics, for example, body weight, insulin-to-carbohydrate ratio, and basal insulin [39].

7.4.2 Control layer 7.4.2.1 Hyperglycaemia Mitigation System The Hyperglycaemia Mitigation System, HMS, is a heuristic controller whose primary target is to guarantee patient safety by preventing insulin overdelivery, rather than aiming to tight glycaemic control. HMS proposes the standard therapy and intervenes, at most once every hour, only if the hyperglycaemia risk is predicted. Intervention consists of a correction bolus targeting 150 mg/dl, whose amount is computed on the basis of predicted glucose value and patient’s standard therapy parameters. As an additional safety measure against possible prediction errors, only 50% of the computed bolus is actually delivered. Premeal boluses are calculated by the patients based on their usual routine and on the estimated carbohydrate content of the meal.

7.4.2.2 Model Predictive Control A less conservative implementation of the control layer, aiming to enforce tight glycaemic control, is based on an MPC regulator described further. The details can be found in [10,40,41]. The MPC approach prescribes to compute, at each control step Ts , the sequence of control actions {i(j )}j =(k+1)Ts ,k,... that is predicted to be the most effective, that is, optimal according to a predefined cost function. Moreover, the optimization problem can account for constraints on feasibility of a control action and on the acceptable states of the system. Predicted effects of a control sequence {i(j )}j =(k+1)Ts ,k,... relay on a process model. Then, in compliance with the receding horizon principle, only the first action i((k + 1)Ts ) of the sequence is applied. In this application, Ts = 15 [min], whereas the model, cost function, and constraints are discussed in the following.

Model Although the glucose–insulin system is nonlinear, the model used within our controller is a linear approximation. This model is obtained by starting from the nonlinear model of the UVA/Padova T1D simulator [42,43]. To describe in a realistic manner the variability among different subjects, the UVA/Padova simulator provides also a set of N = 100 samples of model parameter values (the so-called virtual subjects). These parameter samples are then averaged, and the average nonlinear model describing the adult virtual population of the UVA/Padova simulator is linearized around the equilibrium point (geq , ieq ) [10].

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Cost function In its most recent version [10], the MPC developed and tested in our group implements the cost k+P H −1 

J (i(·), k) =

q · |g(j )−g0 (j )|2 +|i(j )−i0 (j )|2 + TC,

(7.1)

j =k

where k is the current time, P H is the prediction horizon, g(j ) = g(j ) − geq is the difference of the predicted CGM measurement at time j with respect to the equilibrium glucose level geq , g0 (j ) = g0 − geq is the difference of glucose set-point with respect to the equilibrium glucose level, i(j ) = i(j ) − ieq is the difference of the insulin to be infused at each time j with respect to the equilibrium value ieq , i0 (j ) = i0 (j ) − ieq is the difference of the patient standard therapy insulin administration with respect to the equilibrium value, and TC is the so-called terminal cost introduced to improve stability property [10]. The parameter q allows us to trade-off the impact on the cost of the two terms |g(j ) − g0 (j )|2 and |i(j ) − i0 (j )|2 , accounting for tracking errors and discrepancy with respect to the nominal therapy, respectively. The larger the values of q, the more aggressive the control action. In its most recent version [10], the MPC aggressiveness parameter q is individualized to the specific diabetic patient based on readily available patient clinical characteristics, for example, the body weight, insulin-to-carbohydrate ratio, and basal insulin delivery. This is done as follows: 1. For each virtual subject of the UVA/Padova simulator, a large number of possible q values are tested, and the optimal q for that subject is determined. 2. A regression model that associates patient clinical parameters with the optimal q is learned on the virtual population. 3. The regressed law is then used to compute a suitable q for the patient [41].

Constraints The introduction of input constraints in the optimization problem improves controller safety in presence of model uncertainties, but it comes with the cost of an increased computational burden to solve the problem. Due to battery consumption constraints, real-time requirements to be enforced on a portable device with limited computational resource and to regulatory limitations, in [10], we chose not to include input constraints in the optimization process. Instead, we implemented the constraints as explicit saturation applied to the unconstrained solution. Although suboptimal, the resulting control law can be considered sufficiently close to that computed by explicitly accounting for the constraints [44].

Meal announcement and feed-forward action The meal represents a very large disturbance to glycaemic homeostasis, and its control is a major challenge. Standard therapy prescribes premeal insulin boluses, whose amount iBolus (t) is computed by the patient based on the estimated carbohydrate con-

7.4 AP control algorithm

tents of the meal m(t): iBolus (t) =

1 m(t) + icorr (t) = B(t)m(t) + icorr (t), CR(t)

where CR(t) is the carbohydrate-to-insulin ratio, a parameter provided to the patient 1 deby the attending physician and determined by trial-and-error, and B(t) := CR(t) notes its inverse. We point out that CR(t) and hence B(t) are not constant since CRs at breakfast, lunch, and dinner are different. In the formula, icorr represents a further correction bolus also delivered in occasion of a meal and aimed at compensating for premeal deviation of the blood glucose BG(t) from the target glucose (BGtarget ). Since the correction component is not relevant for the following discussion, here we only remind that it is computed as follows: icorr (t) = CF (t)(BG(t) − BGtarget ) − I OB(t), where CF (t) is the correction factor, another parameter provided to the patient by the attending physician and determined by trial-and-error, and I OB(t) accounts for residual insulin estimated to be still active from previous boluses or due to the controller action. Pure feedback compensation of meal disturbance proved to be less effective than the standard therapy premeal bolus for meal control [45] due to the large delays in subcutaneous insulin absorption. To circumvented the problem, the MPC presented here requires that the patient announces the meal and provides information on its carbohydrate content as for the standard therapy. This meal announcement is then used to formulate meal-aware predictions in the controller model and as a feed-forward action [41], which consists in: • delivering a fraction α of the bolus compensating for the meal, αiBolus (t); • including the remaining fraction 1 − α of the premeal bolus into i0 (t), the reference therapy for MPC. In this way the controller can modify i0 according to MPC predictive reasoning. More precisely, i0 (t) = b(t) + (1 − α)iBolus = b(t) + (1 − α)(B(t)m(t) + icorr (t)),

(7.2)

where b(t) is the time-varying basal profile provided by the diabetologist, and the second term is the above-mentioned fraction of the premeal bolus.

7.4.3 Adaptation layer As discussed before, MPC is designed to operates real-time corrections to the insulin infusion prescribed by the standard therapy i0 (t) in (7.2), which is used as a reference in the cost function (7.1). By doing so the important patient-specific knowledge contained in the basal insulin profile b(t) and in the meal boluses iBolus (t) is inherited by the controller from the attending physician. However, there is room for further improvement of these signals also because they may be inadequate due to patient

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changes over time (interday variability). To mitigate these problems, our algorithm is enriched with an additional module implementing a run-to-run (R2R) strategy devoted to daily updates of b(t) and B(t), as described before. Further details can be found in [46,47].

7.4.3.1 Adaption rules To keep independent the effects of these two variables, the basal delivery b(t) is adjusted during the night, that is, when no meal perturbations are present, whereas the update of B(t) is performed during the day by keeping the basal delivery b(t) not updated. At the end of each run k, lasting 24 hours, the average nocturnal basal b¯k is updated, and the variation of this quantity, which will used in the next day (subsequent run k + 1), is proportional to the current average basal and to the performance indexes computed during the completed run k. To give priority to avoiding hypoglycaemia, a switching condition depending on the percentage of time spent below 70 mg/dl is introduced. In particular, at run k, the updating law is defined as follows:

b¯k+1 =

⎧ ⎪ ¯ · k b · T hn ¯ ⎪ k 1 ⎨ bk − b 0  b n b ⎪ ¯ ¯ ⎪ ⎩ b k + b 0 k 2 · T H k + k3 ·

¯ n − Gb G k T GbT



if T hnk > 0, if T hnk = 0,

where the constants k1b , k2b , k3b are the R2R gains, GnT is the glycaemic target ¯ n are the R2R overnight, b¯0 is the initial average nocturnal basal, and T hnk , T Hkn , G k performance indices evaluated with the night interval of day k. In particular, T hn is time-in-hypo, that is, the percentage of time spent below 70 mg/dl, whereas T H n is ¯ n is the time-in-hyper, that is, the percentage of time spent above 180 mg/dl, and G average glucose concentration in the evaluation interval, which is equal to the night interval delayed by 3 hours. It is worth emphasizing that if a meal occurs within this interval, then its end is set equal to the meal time. A similar updating law is used to optimize the CR. This variable, and in turn its inverse B, is assumed to be constant B = t B . Let us denote by B along n daily intervals [tjB ; tjB+1 ], j = 1, ..., n, with tn+1 k,j 1 the value of B at day k during the j th portion of the day. The updating law for this quantity is defined as follows:

Bk+1,j

⎧ ⎪ · k1B · T hk,j if T hk,j > 0, ⎪ ⎨ Bk,j − B0,j   B ¯ = B k,j B Gk,j − GT ⎪ if T hk,j (k) = 0, ⎪ ⎩ Bk,j + B0,j k2 · T H + k3 · GB T

where the constants k1B , k2B , k3B are the R2R gains, GB T is the glycaemic target, constant for all the intervals, B0,j is the initial value of B during the interval j , and ¯ k,j are the R2R performance indices evaluated in the j interval of T hk,j , T H k,j , G day k. The maximum length of each j th evaluation interval is 7 h; it starts from the meal time in the j th interval and is truncated if another meal occurs.

7.4 AP control algorithm

The stability of the proposed strategy can be demonstrated by applying the method described in [46], where an R2R approach for adapting a piecewise basal therapy in an open-loop context is proposed. A key assumption is the use of disjoint intervals. Indeed, if the intervals of basal and bolus insulin delivery are not disjoint, then the problem moves from a several-scalar case to a multivariable framework, with a significant increase of complexity both in terms of algorithm tuning and stability analysis. The initial values b¯0 and B0 are usually set equal to the values adopted for the conventional basal-bolus therapy, whereas the gains k1b , k2b , k3b , k1B , k2B , k3B are equal for all the intervals and patients. In the tuning the gains must be considered in addition to stability issues, performance, and safety issues. In particular, there is a trade-off between R2R algorithms that learn quickly (the value of the parameters mainly depends from the last days) or slowly (the value of the parameters depends from a longer past period). The main drawback of a faster R2R is that it is more affected by occasional situations and prone to several safety problems related to important interday life style variability. The drawback of a slower R2R is that a longer time is required to improve the performance. In any case, daily changes of the patient’s life style (e.g., stress, exercise, different meals) must be compensated by the MPC controller and not by the R2R strategy that should only learn slow changes in patient behavior (i.e., weeks/month).

7.4.3.2 Real-life algorithm The algorithm has strong theoretical properties but needs some adjustments to cope with the uncertainties of a real-life scenario and possible malfunctioning of an AP system. In particular, the following aspects are considered: • Memory limitation: the AP system stores only a limited amount of data, not allowing covering the entire 24-hour period. • Malfunctioning: likely events are pump occlusions and connectivity losses. • User over rules: to ensure safety, the AP allows the user to change all settings, including the controller suggestions (boluses), the algorithm (from closed- to open-loop), or by setting a temporary basal rate. • Hypothesis violation: the algorithm assumes no overlapping between the intervals and nonoccurrence of simultaneous events, for example, only one meal per interval. Such a situation is likely not happening in a real-life scenario. To handle the memory limitation, the update for each parameter is computed as soon as the needed data become available, with the purpose to reduce the amount of data to store. The update is performed only if the user has not changed its clinical parameters and if no malfunctioning has occurred. Indeed, these events would introduce changes in the performance indices that are not directly caused by the control algorithm tuning. Moreover, the data for a specific interval can be limited by the occurrence of events like a previous meal that still influences the glucose concentration or a closedloop interruption due to system failure; in this case the update is computed only if the amount of available data is above a certain threshold. Multiconsecutive meals are

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Table 7.1 Summary of in-patient studies [27,45,48–52]. This research was funded by Juvenile Diabetes Research Foundation (JDRF), by the US National Institutes of Health (NIH), and by the EU FP7 Project “Bringing the Artificial Pancreas at home” (AP@home). CAM-MPC stands for the nonlinear MPC developed in Cambridge, UK. Pump & Sensor Omnipod Dexcom 7 plus or Free-Style Navigator (APS system)

Algorithm prototype mMPC

Protocol (Sponsor) Nonrandomized, night + breakfast. (JDRF)

Centers & # of patients Charlottesville (11 adults) Montpellier (3 adults) Padova (6 adults)

Reference [45,48,49]

Omnipod Dexcom 7 plus (APS system)

H2MS & mMPC

Randomized, 22-h duration. (JDRF)

Charlottesville

[27]

2011

Omnipod Dexcom 7 plus (APS system)

mMPC & CAM-MPC

Randomized, 23-h duration. (AP@home)

2012

Omnipod Dexcom 7 plus (APS system)

mMPC

Nonrandomized, 2 admissions, ∼28 hours each. (JDRF)

2008–2009

2010–2011

Montpellier Padova Amsterdam Cambridge Graz Montpellier Padova Profil, Neuss Barbara Davis Charlottesville Montpellier Padova Santa Barbara Standford Tel-Aviv

(9 adults) (11 adolesc.) (12 adults) (6 adults) (7 adults) (8 adults) (8 adults) (8 adults) (8 adults) (8 adults)

[50]

[51,52]

considered if they occur in the same interval; in this case the CR update is performed as usual by using the union of evaluation intervals as an evaluation interval.

7.5 In-patient studies Table 7.1 reports a summary of the studies conducted from 2008 to 2012 in hospitalized patients. In 2008–9, the first clinical test assessing a first prototype of the modular controller was performed in three centers: University of Padova (Italy), University of Montpellier (France), and University of Virginia (Charlottesville, Virginia, USA) [45, 48,49]. It consisted of a nonrandomized comparison of the mMPC vs. CSII managed by the attending clinician during overnight and breakfast. The study involved 20 adults. This first trial showed that the MPC-based modular controller can improve time-in-target and had less hypoglycaemic episodes overnight, although breakfast control was still unsatisfactory. After this first clinical experience, the mMPC was modified according to the insight gained. Later, in 2010 a multicenter randomized cross-over study tested both H2MS against patient-managed CSII and mMPC in-patient against patient-managed CSII [27]. More precisely, H2MS (called standard Control-To-Range, sCTR [27]) was tested on 11 adolescents enrolled at University of Virginia and on 15 adults (9 en-

7.5 In-patient studies

rolled in the same university and 6 in Montpellier), whereas mMPC (called enhanced Control-To-Range, e-CTR [27]) was tested on 12 subjects (6 enrolled at Montpellier and 6 in Padova). In this section, we focus in detail on this study, used as an example of in-patient studies. This study was chosen among those reported in Table 7.1 since it has the merit of allowing also a comparison between H2MS and mMPC inpatient. To prevent possible bias in such a comparison induced by the differences in the population studied, we will further focus on adults only.

7.5.1 Study design The two studies shared a 22-h protocol prescribing open- and closed-loop admissions in randomized order. In both admissions, glycaemic control was challenged by a moderate exercise at 16:00 and dinner at 19:00. Before bed time, at 22:30 a snack was served, and patients were encouraged to sleep. Breakfast was served at 8:00, and immediately after the patient was discharged. During the closed-loop admission, closed-loop started at 14:00. The pump, Insulet Omnipod (Insulet Corporation, Bedford, MA), was inserted at the beginning of the admission and filled with Humalog Insulin (Eli Lilly and Company, Indianapolis, IN). Two CGM sensors were inserted two days before the admission. Dexcom Seven Plus was used in Charlottesville and Padova, whereas Navigator (Abbot Diabetes Care Inc, Alameda, CA) was used in Montpellier. In both admissions, CGM and insulin data were automatically handled by APS. During both admissions, frequent blood samples were collected, at least one every 30 minutes and more frequently during exercise (every 5 min) and meals (every 10 min). Blood glucose was measured with YSI2300 STAT Plus analyzer (Yellow Spring Instrument, Lynchford House, Franborough, United Kingdom). To guarantee the highest level of safety and the correct functioning of the devices, a two-person team, composed by a physician and an engineer, was constantly attending the admission.

7.5.2 Data analysis Frequent YSI measurements allow us to reconstruct an accurate continuous blood glucose profile simply by linear interpolation. Interpolated profile was then used to compute percent time in target [70–180] mg/dl, percent time in tight target [80–140] mg/dl, percent time in hypoglycaemia (below 70 mg/dl), percent time in hyperglycaemia (above 180 mg/dl), and mean BG.

7.5.3 Results Results reported in [27] are summarized in Fig. 7.3, which compares glucose profiles obtained by open- and closed-loop controls. Population mean profile is depicted for both admissions, together with an interquartile population envelope, accounting for interpatient variability. As suggested by Fig. 7.3 (upper panel), H2MS improves time spent in near normoglycaemia significantly with respect to traditional therapy. As expected by design, H2MS time spent in tight glycaemic range did not differ between

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FIGURE 7.3 In-patient assessment of H2MS (upper panel) and mMPC (lower panel) vs open-loop [27]. Thick lines represent average results of open-loop (red (mid gray in print version)) and closed-loop (green (light gray in print version) and blue (dark gray in print version) for H2MS and mMPC), depicted together with their inter-quartile population envelope.

the two admissions overnight. Improved glycaemic control was achieved with simultaneous significant reduction of hypoglycaemic events. mMPC controller shows that overall percent time in near normoglycaemia increased significantly and that percent time in tight control increased significantly overnight, whereas improvements in tight control on the overall data were not statistically significant due to the effect of meal perturbation. Improved glucose control was achieved without significant increase in the risk of hypoglycaemia and with a significant decrease in the overall average plasma glucose.

7.5.4 H2MS and mMPC A comparison between the two controllers was performed in [27] by restricting the analysis to the adult population only and using univariate ANOVA with open-loop performance included as a covariate to compensate for the difference in the baseline standard therapy in the two populations, also apparent in Fig. 7.3. mMPC and H2MS both increased time spent in near normoglycaemia similarly, whereas mMPC increased overnight time spent in tight glycaemic control further, compared to H2MS. The comparison of the occurrence of hypoglycaemia in H2MS and mMPC was not conclusive.

7.6 Out-patient studies

7.5.5 Further inpatient studies testing the mMPC In 2011, mMPC controller was tested in a large multicenter study within the AP@home European Project and reported in [50]. The trial consisted in a threearm randomized cross-over trial comparing standard CSII therapy (manual therapy) with two AP control systems, one based on the mMPC and the other based on the nonlinear MPC controller developed at Cambridge University (CAM-MPC) [25]. 47 patients, recruited in six European centers completed the study. Each admission lasted about 22 h, including meal and exercise. Both algorithms were detuned in this trial to guarantee higher safety and avoid hypoglycaemia. An almost three-fold reduction of time in hypoglycaemia in both closed-loop algorithms with respect to open-loop was achieved at the expenses of an higher average glucose level. There were no significant differences in outcomes between algorithms. In 2012, mMPC was again tested in a large multicenter trial, which involved seven international centers [51,52]. The experiment consisted in a single-arm study prescribing two ∼2 h inpatient visits, and a total of 53 individuals were included (both adult and adolescents). Subjects received three mixed meals with meal announcement and automated insulin dosing by the controller (results reported in [51]). Furthermore, mMPC was also challenged to handle an overbolus of 30% delivered with meal and bolus purposely omitted. A bolus anticipation of 15 minutes was also tested in one meal (results reported in [52]). mMPC performed better overnight than during the day, but the system had difficulty preventing postmeal excursions above target range. The AP handled the abnormal bolus challenge safely, but at the expense of having elevated postprandial glucose levels in most subjects.

7.5.6 Concluding remarks The above findings provided solid evidences of superior safety and efficacy of AP in both tested configurations, with respect to manual control in the tightly controlled setting of these in-patient studies. The subsequent research step was to confirm that these benefits are present also in conditions not strictly regimented by tight protocols. The large bulk of data collected, besides allowing us to improve the modules, were crucial to obtain approval for out-patient testing described in the next section.

7.6 Out-patient studies Table 7.2 reports a summary of the out-patient studies conducted from 2011 to 2014. Here we will focus on three of these studies [21,28,29], which, except for minor modifications, share the same nonrandomized design summarized in the following section. In particular, [28] reports an out-patient study testing H2MS on 20 adults studied in two European and two US centers. With the same protocol and DiAs configuration (Section 7.2.2 A), [29] reports out-patient testing of mMPC on six adults in Padova. The study was then repeated, with an improved hardware configuration (Section 7.2.2 C) in 13 patients in three EU Centers [21].

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Table 7.2 Summary of out-patient studies [21,28,29,32,53,54]. This research was funded by Juvenile Diabetes Research Foundation (JDRF), by the US National Institutes of Health (NIH), and by the EU FP7 Project “Bringing the Artificial Pancreas at home” (AP@home). Oct 2011

Jan-Apr 2012

Oct 2012

May 2013

Sep-Nov 2013 Dec 2013Jan 2014

Pump & Sensor Omnipod Dexcom 7 plus (APS based Relay) Omnipod Dexcom 7 plus (Config. A)

Algorithm H2MS

Omnipod Dexcom 7 plus (Config. A) Tandem t:slim Dexcom G4 (Config. B)

mMPC

AccuChek SC Dexcom G4 (Config. C) AccuChek SC Dexcom G4 (Config. C)

H2MS

mMPC

mMPC

Heuristic

Protocol (Sponsor) Non Randomized, 42h duration. (JDRF) Non Randomized, 42h duration. (JDRF) Non Randomized, 42h duration. (AP@home) Randomized, 2 admissions, 40 hours each. (JDRF) Non Randomized, 42h duration (AP@home) Randomized, 5 days duration Overnight Only (NIH)

Centers & # of patients Montpellier (1 adult) Padova (1 adult)

Reference [53]

Montpellier Padova Charlottesville Santa Barbara Padova

(5 adults) (5 adults) (5 adults) (5 adults) (6 adults)

[28]

Montpellier Padova Charlottesville Santa Barbara Montpellier Padova Amsterdam Padova Charlottesville

(5 adults) (5 adults) (5 adults) (5 adults) (4 adults) (5 adults) (4 adults) (12 adults) (12 adults)

[54]

[29]

[21]

[32]

It should be noted that these studies were neither designed nor powered to compare open- and closed-loops, but rather to serve as preliminary tests of the wearable AP prototypes in different configurations and to collect preliminary data in outpatient settings, also for effective power calculations in larger real-life trials.

7.6.1 Study design The three studies shared a 42-h nonrandomized protocol prescribing the first 14 h in open-loop and the remaining 28 h in closed-loop. Study admission started at about 18:00, and therefore in both open- and closed-loop periods glycaemic control was challenged by a dinner, served between 19:30–20:30, and both periods included one night. Automated control was activated at about 07:45, and hence closed-loop was further challenged by two breakfasts at about 8:00 of study days 2 and 3 and by lunch at about 12:00 of study day 2. The sensor was inserted 2/3 days prior to admission, and the patient insulin pump was replaced by the study pump, filled with their usual insulin, at the beginning of the admission. Both open- and closed-loop insulin deliveries were performed through the DiAs. The large majority of the study was conducted in a hotel/guesthouse nearby the University Hospital, and the subjects were free to move in the facility and in its immediate vicinities. Dinner was consumed at the hotel restaurant, where patients were invited to choose a dinner menu in line with their daily habits, both in terms of meal amount and composition. After dinner the

7.6 Out-patient studies

patients spent the night in their hotel room. Throughout the night the study team was available in a nearby room. Two protocol differences among EU and US centers had to be included to fulfill local regulatory requirements: in US centers, during night time, only the SSM module was allowed to remain active, possibly reducing basal if hypoglycaemia was forecasted.

7.6.2 Data analysis In view of the US-EU design difference, possibly biasing the comparison, in the following analysis, we limit ourselves to EU centers data: 10 patients with H2MS, DiAs configuration A (7.2.2 A), 6 patients with mMPC, DiAs configuration A (7.2.2 A), and 13 patients with mMPC, DiAs configuration C (7.2.2 C). Furthermore, since the proposed analysis focuses on the control performance rather than on the overall system performance, we removed data portions where glycaemic control is affected by hardware malfunctioning (for a detailed analysis of system functioning, we refer to [21,28,29]).

7.6.3 Results The results are summarized in Fig. 7.4, where population mean profile is depicted together with the ± standard deviation envelope: open-loop is depicted in dashed red (mid gray in print version), H2MS is solid green (light gray in print version), and mMPC in solid blue (dark gray in print version). In this protocol, open- and closed-loop periods have not the same duration, and all comparisons reported in the following are restricted to common periods (Dinner & Overnight). Moreover, data in the following are reported as mean ± standard deviation if Gaussianity is not rejected by the Lilliefors test or as median [25th percentile, 75th percentile] otherwise. When appropriate, p-values are provided using paired t-test when Gaussianity is not rejected or Wilcoxon signed-rank test otherwise.

7.6.3.1 H2MS, DiAs configuration A [28] In this configuration, the system granted acceptable connectivity performance, allowing to reach ∼98% of percent time with the system active during the study, but requiring quite a number of study team interventions to fix/restart the system due to communication crashes. Specifically, 68 interventions where performed in 826.5 hours of trials. To further investigate this aspect, let us recall the system architecture in this configuration, described in Section 7.2.2: since direct Bluetooth communication with the pump and the sensor adopted was not available, AP included a data hub called iDex, an experimental device built by Insulet Corp combining a DexCom Seven Plus receiver and OmniPod PDM. Unfortunately, iDex offered only a USB access, so a further relay device with a bluetooth port and USB connected to iDex had to be added to forward wirelessly data from iDex to the DiAs phone. It should be added that, in the first part of the experiment (498.5 hours out of the 826.5) the relay device USB signal used to convert iDex signal into Bluetooth consisted of a Viliv S5 tablet and that 60

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FIGURE 7.4 Control achieved in out-patient setting by H2MS [28] and MMPC [21,29]. Thick lines represent average results, depicted together with their ± standard deviation envelope. Red (mid gray in print version) dashed line represent open-loop, green (light gray in print version) solid lines H2MS and Blue (dark gray in print version) solid lines MMP.

out of 68 study team interventions occurred with this relay device. The device was then replaced by a more reliable Samsung Galaxy Nexus smartphone with significantly better performance (8 interventions in 328 hours). For what concerns glucose control, also in the challenging out-patient settings, an improvement, although not statistically significant, was observed in overnight control using H2MS with respect to open-loop therapy, time-in-target from 73% ± 37% to 81% ± 25% (p = n.s.). As expected by design, time-in-tight-target is not improved, going from 47% ± 35% to 46% ± 29% (p = n.s.), whereas a nonsignificant reduction is observed is time-inhypo, going from 0% [0%, 3.7%] to 0% [0%, 0.5%] (p = n.s.). H2MS controller successfully prevented hypoglycaemia after dinner at difference with open-loop (time-in-hypo 0% [0%, 1.8%]) at the expenses of a decreased timein-target: from 81% ± 35% to 66% ± 40% (p = n.s.). Although the closed-loop was challenged with more meals than the open-loop, in terms of overall performance, percent time-in-target was on average above 75% with both treatments (75% ± 30% open-loop, 77% ± 23% closed-loop) with time-in-hypo below 2% (1.8% [0%, 3.3%] open-loop, 0.7% [0%, 1.6%] closed-loop). Mean ± standard deviation glucose profiles are illustrated in Fig. 7.4.

7.6 Out-patient studies

7.6.3.2 mMPC, DiAs configuration A [29] In this small exploratory study, the system granted acceptable connectivity performance, allowing to reach ∼90% of percent time with the system active during the study, but with a substantially smaller number of study team interventions to fix/restart the system due to communication crashes with respect to the previous study: 1 in 220 hours of trials. Nevertheless, this trial showed that the wired connection among the iDex and the relay device is prone to failure, a severe weakness for the system, as pointed out also by the previous study. Also, wireless communication among iDex and pump/sensor lacks the robustness requested for sustained use at home. Given that Insulet had to stop the development and maintenance program of iDex, it was decided to resort to other pumps, allowing direct wireless connection with the phone. For what concerns glucose control, overnight performance were very good with both treatments, time-in-target 94% [64%, 96%] open-loop vs. 100% [87%, 100%] closed-loop (comparison not significant, p = n.s.) and time-in-tight-target 49% ± 27% open-loop vs. 59% ± 46% closed-loop (p = n.s.), meaning that this small population was composed of very-well-controlled patients. Of note, in closed-loop, no patient experienced nocturnal hypoglycaemia, whereas in open-loop 1.8% [0%, 7.3%] time-in-hypo was observed. This study focused particularity in testing an anticipated meal-bolus strategy, which seemed promising as it resulted in nearly optimal dinner closed-loop control, time-in-target 95% ± 9%, and time-in-hypo was almost reduced to zero 0% [0%, 0%]), but the comparison with the open-loop (time-in-target 68% ± 27% and timein-hypo 5%, [0%, 24%] vs. 0% [0%, 0%]) was not statistically significant. Although the closed-loop was challenged with more meals than open-loop, in terms of overall performance, percent time-in-target was on average above 80% with both treatments (81% ± 15% open-loop vs. 85% ± 10% closed-loop), and a very low time-in-hypo was observed with closed-loop (4.1% [2.3%, 12.2%] open-loop vs. 0% [0%, 1.1%] closed-loop).

7.6.3.3 mMPC, DiAs configuration C [21] This configuration proved satisfactorily stable with the system correctly functioning for ∼99% of the time and no study team intervention to fix/restart the system, except for one case related to a bug in the interaction of the system with pumps settings in Dutch language. Despite the small sample size, in this trial, statistically sound evidences of superior performance of mMPC with respect to open-loop were found. Statistically significant improvement in time-in-target, 64% ± 33% open-loop vs. 92% ± 8% closed-loop (p = 0.01) were recorded combined with statistically significant reduction of time-in-hypo (0% [0%, 25.3%] open-loop vs. 0% [0%, 0%] closed-loop, p = 0.03). A nonsignificant increase in time-in-tight-target was observed, from 53% ± 39% open-loop to 76% ± 22% closed-loop (p = 0.11). We also observe that mMPC successfully prevented hypoglycaemia after dinner (0% [0%, 0%]) at variance with open-loop (time-in-hypo 0.4% [0%, 10.4%]), but at

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the expense of a decreased time-in-target: 63% ± 32% open-loop vs. 53% ± 32% closed-loop (p = n.s.). Joint evaluation of dinner and overnight shows a significant reduction of timein-hypo from 6.0% [1.6%, 19.5%] open-loop to 6.0% [1.6%, 19.5%] closed-loop (p < 0.01), together with a significantly improved time-in-target 62% ± 29 openloop vs. 84% ± 14% closed-loop (p = 0.04). Although the closed-loop was challenged with more meals than open-loop, in terms of overall performance, percent time-in-target did not reach 65% with openloop (64% ± 27%), while was around 75% with closed-loop (74% ± 13%) and a statistically significant reduction of time-in-hypo was observed: from 5.7% [1.5%, 18.1%] open-loop to 0% [0%, 3.1%] closed-loop.

7.6.4 Concluding remarks The above outpatient trials permitted the field test of multiple system configurations, allowing us to identify and fix critical hurdles and to abandon configurations that proved not suitable for long lasting real-life use. They also provided solid and statistically sound evidences of the superior efficacy and safety of AP with respect to manual control. These results paved the way to the long-lasting, randomized real-life testing of this technology, described in the following.

7.7 Real-life testing In 2014–15, an open-label study tested our AP system in real-life conditions for multiple weeks. No restriction was posed by protocol on patient activities during the study. The study was performed recruiting patients from medical centers at the Universities of Amsterdam (the Netherlands), Montpellier (France), and Padova (Italy). The used AP system consisted of our modular control algorithm, both without and with R2R adaptation, implemented on the DiAs platform configuration C (7.2.2 C), that is, with Accu-Check Spirit Combo Pump and the Dexcom G4 Platinum sensor, inserted in a small and reliable relay devices. The study consisted of three phases: • The first phase consisted of a randomized cross-over comparison of the glucose control achieved by our AP system based on mMPC (AP-period) versus patient managed Sensor Augmented Pump therapy (SAP, control-period). Each of the two periods lasted 8 weeks, and they were separated by a 4-week “wash-out” period. In this phase, AP was active only when the patient was at home (hence during the evening and nighttime). At the workplace and/or during leisure time outside home, the system was instead keep turned-off. This choice was done to ensure that the patient was using AP only in a context where she/he was able to focus on the device if needed. • The second phase was a 4-week extension period, conducted by a subpopulation of patients that participated to the first phase. In this (nonrandomized) extension

7.7 Real-life testing

phase the patients used AP day and night and hence also at work or during leisure time outside home. • The third phase consisted of a further 4-week extension period proposed to the patients that participated to the second phase. In this second (nonrandomized) extension, R2R adaptation was activated and tested for the fist time in real life.

7.7.1 Evening & night use of mMPC Thirty-five eligible patients were enrolled, but three dropped out before the completion of the study. Data from all the remaining 32 patients were analyzed. According to a statistical analysis plan, agreed by the investigators before the conduction of the study, the first two weeks of both intervention periods were excluded from data analysis as potentially affected by a learning curve. All glucose indices were computed from the CGM data. Considering the crossover design of the trial, carryover-effect was assessed. If a carryover-effect (p < 0.1) was found, then the second study period was excluded from the analysis. If no carryover-effect existed, a multiway analysis of variance (ANOVA) was performed including patient, treatment, and period as explanatory factors. Treatment and period effects were estimated by ANOVA when a period-effect was found (p < 0.05). If neither carryover- nor period-effect was found, normally distributed data were compared with a paired t-test and nonnormally distributed data with the Wilcoxon signed-rank test. The normality of residuals was verified with the Lilliefors test. As in the previous sections, we report variables as median [25th percentile, 75th percentile] for nonnormally distributed and as mean ± standard deviation otherwise. Furthermore, the estimated treatment effect , corrected for the period effect if need, is reported with its 95% confidence interval CI. Let us focus first on glucose control achieved from dinner until wake-up, that is, the portion of the day during which the AP system is active. Since there are no protocol prescribed constraints, it is difficult to know exactly this portion, which could vary significantly from patient to patient, and therefore we use as proxy the portion of time going from 20:00 to 08:00. Time-in-target (primary study endpoint), timein-hypo, and time-in-hyper were improved with AP. The mean time-in-target was higher during AP insulin delivery than during control (67% ± 10% vs. 58% ± 9%, p < 0.0001,  ∈ [5.8%, 11.4%]. The median time-in-hypo was reduced from 3.0% [1.6%, 4.9%] to 1.7%[0.8%, 2.5%] (p < 0.0001,  ∈ [−2.3%, −1.0%]. The evening and night only use of the AP resulted in a benefit over the 24 hours, where time-in-target, time-in-hypo, and time-in-hyper were improved with the AP compared to control period. Time-in-target was higher in the AP-period than in the control-period: 64% [60%, 70%] vs. 59% [57%, 64%], p < 0.0001,  ∈ [3%, 7%], whereas time-in-hypo was reduced from 3.6% ± 2.0% to 2.6% ± 1.4% (p = 0.00022,  ∈ [−1.5%, −0.5%]). Notably, decrease in HbA1c during AP-period was significantly larger than during control-period (−0.32% vs. −0.16%, p = 0.047,  ∈ [−0.36%, −0.00%]). A period effect was found for change in HbA1c (p = 0.003).

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The decreased time-in-hypo in the AP-period was confirmed by a significant reduction of moderately severe hypoglycaemic episodes < 50 mg/dL per patient per week (1.28 vs. 2.01 events, p = 0.00052,  ∈ [−1.18, −0.40]). No serious adverse events occurred, including no severe hypoglycaemic episodes and no hospitalization for ketoacidosis.

7.7.2 Day & night use of mMPC Out of the 32 patients that completed the first randomized phase, 20 patients completed the first extension and used the AP system for 24/7. On the subpopulation of these 20 patients, it is possible to compare the effect of three treatments: SAP vs. AP active only during evening and night (E&N-AP) vs. AP active all day (D&N-AP). The comparison was done via a multiway ANOVA including patient and treatment as explanatory factors. Since the order of the three treatments was not randomized, it is not possible to estimate the period effect to separate it from the treatment effect. If the residuals or the data were not normally distributed, then the nonparametric Friedman test was used. If the ANOVA or Friedman test detected a significant difference between treatments, then the determination of significant differences between treatments was performed by multiple comparisons. For what it concerns glucose control during day time, assessed in the proxy interval 8:00–20:00, no significant difference was found in time-in-target among three treatments during day-time, but a trend toward improvement of time-in-target range was recorded with D&N-AP vs. SAP: 65 ± 8 vs. 61 ± 10 (p = 0.09) and also when comparing D&N-AP vs. E&N-AP (61 ± 11) (p = 0.15). Simultaneously, time-inhypo with D&N-AP was significantly lower when compared to SAP: 2.3 ± 1.3 vs. 3.4 ± 2.2 (p = 0.01), whereas it was not significantly different between SAP and E&N-AP (2.9 ± 1.9) (p = 0.39). Of note, although time-in-hyper was similar during AP periods and SAP, with a difference in the percent time above 300 mg/dl significantly lower with D&N-AP vs. E&N-AP: 1.8% [0.4%, 3.1%] vs. 2.6% [0.7%, 5.6%] (p = 0.004). As expected, evening and night glucose control, assessed using the 20:00–08:00 interval as a proxy, was not found different between D&N-AP and E&N-AP. Time-intarget and time-in-hypo were significantly improved during both AP periods vs. SAP, whereas the percent time above the target range was only significantly reduced during E&N-AP vs. SAP, resulting also in a significantly increased time-in-tight-target E&N-AP vs. SAP. Over the 24 hours, time-in-target was improved with D&N-AP and E&N-AP with respect to SAP: 65 ± 8 and 64 ± 10 vs. 60 ± 10, significantly with D&N-AP (p = 0.01) and close to significance with E&N-AP (p = 0.06) on this reduced population of 20 subjects only. Time-in-hypo was improved both with D&N-AP and E&N-AP with respect to SAP: 1.9 ± 1.1 and 2.1 ± 1.3 vs. 3.2 ± 1.8 (both p < 0.001), and no difference was found between D&N-AP and E&N-AP (p = 0.74). Although direct comparison between the two AP options is not conclusive since D&N-AP use was a nonrandomized extension, and due to the reduced power of

7.7 Real-life testing

the comparison held only on 20 patient, it could be noticed that both D&N-AP and E&N-AP both achieved better glucose control than SAP under free-living, although the improvement during day time is not as large as hoped, supporting E&N-AP as a first commercial option for AP.

7.7.3 Adaptive mMPC Finally, 18 patients completed also the second 4-week extension phase, aimed at comparing the performances achieved by A-mMPC with respect to the nonadaptive mMPC (both used for 24 h). Comparison during the last week. Glucose control was evaluated during the last week of both one-month interventions (mMPC and A-mMPC) in order to see the impact of 3 weeks of adaptation. To evaluate the statistical significance of the difference of each index, a paired-sample t-test was used for normally distributed data. Otherwise, if at least one distribution was nonnormal, then the nonparametric Wilcoxon signed rank test was used. Since the order of the two extensions was not randomized, it is not possible to estimate the period effect to separate it from the treatment effect. Overall, a nonsignificant increase in time-in-target by A-mMPC vs. mMPC, 67% ± 13 vs. 62% ± 11, p = 0.09, and a nearly significant increase time-in-tighttarget 43% ± 12% 37 ± 10, p = 0.51, were observed. During nigh time, instead, time-in-target was significantly increased by 74% ± 15 vs. 64% ± 16, p = 0.034, whereas time-in-hyper was reduced by 24% ± 15 vs. 34.49% ± 16.25, p = 0.0266, and this reduction was also significant and not accompanied by an increased risk of hypoglycaemia. Finally, a difference in time-in-tight target, 50% ± 15 vs. 40 ± 18, was observed even though not statistically significant. Trends-in-Time. Glucose control metrics (time-in-target, time-in-tight-target, time-in-hyper, etc.) are expected to gradually improve over time, as the R2R adapt diurnal CRs and nocturnal basal insulin infusion based on the previous day performance. To verify this, we evaluated for each day d of the experiment, d = 1, . . . , D, with D = 28, and for each patient p, p = 1, . . . , P , with P = 18, these glucose control metrics. Let us denote by T TA-mMPC (d, p),

T tA-mMPC (d, p),

and

T HA-mMPC (d, p)

time-in-target, time-in-tight-target, and time-in-hypo recorded the dth day in the pth patient while using A-mMPC. Analogously, define the same quantities for the nonadaptive mMPC, T TmMPC (d, p), T tmMPC(d,p) , and T HmMPC (d, p). Now consider, for each metric, the paired differences in the two treatments: T T (d, p) = T TA-mMPC (d, p) − T TmMPC (d, p), where we focused only T T in our illustration, since the reasoning extends straightforwardly to the other metrics. We want to investigate the presence of a trend in time in these paired difference. For this purpose, for each metric and each patient p, we fit on the data a model for a linear trend-in-time as follows:

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FIGURE 7.5 Distribution of trend-in-times. Boxplot of trend-in-time for time-in-target, mT T (p), time-in-tight-target, mT t (p), and time-in-hyper, mT H (p).

T T (d, p) = qT T (p) + mT T (p) · d + e(d, p), where mT T (p) represents the trend-in-time for the patient under study, and a positive trend mT T (p) > 0 represents a tendency to increase over time for the improvement in time-in-target granted by A-mMPC with respect to nonadaptive mMPC in patient p. We then consider the distribution of mT T (p) over the patients. Fig. 7.5 shows the boxplot associated with the slopes distributions of each considered metric difference. Distributions of mean glucose and time-in-hyper (p = 0.041) are negatively biased, whereas distributions of time-in-target (p = 0.059) and time-in-tight-target (p < 0.001) are positively biased. To check if these biases are significantly different from zero, if the distribution was normal, then the mean trend was verified to be significantly different from zero by a paired-sample t-test. Conversely, in case of nonnormal trend distribution, the median trend was compared to zero with the Wilcoxon signed-rank test. Finally, Fig. 7.6 reports how time-in-target, time-in-tight-target, and time-in-hype distributions, respectively, changed over the 1-month period. Again focusing only on T T , for each study day d, a boxplot of the distribution T T (d, p) with respect to p is depicted. The 18 models of linear trends-in-time obtained for each patient were then averaged (mean or median) to identify a population trend-in-time model, which is represented by the black solid line.

7.8 Concluding remarks The presented real-life testing proves that this technology is more safe and effective than SAP also in real-life conditions. It also shows that day time and meal control

7.8 Concluding remarks

FIGURE 7.6 Distribution of trend-in-times. Illustration of how time-in-target, time-in-tight-target, and time-in-hyper distributions, respectively, changed over the 1-month period.

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remains challenging to improve. Finally, it shows the promising potential of R2R and its ability to create an improvement in glucose control over time, learning from glucose control achieved the previous days.

7.9 Conclusions In this contribution, we reviewed our experience in the modular deployment of an AP system, a venture that has involved a large international team and 127 T1D subjects participating to in-patient testing (recruited in 4 studies involving 11 centers of 7 different countries), 85 patients participating to the transitional studies held in a hotel (recruited in 5 studies involving 5 centers of 4 countries) and 32 patients participating to real-life AP testing (recruited in a study involving 3 centers of 3 countries). Overall, more than 300.000 hours of closed-loop data. We focused on devices, telemedicine, and algorithm issues. In particular, for what concerns control algorithms, we illustrated how modularity in control architecture allowed progressive deployment and testing of two control algorithms: H2MS, focusing on safety, and mMPC, aiming to enforce tight glycaemic control.

Acknowledgments This work was supported by the EU project ICT FP7-247138 “Bringing the Artificial Pancreas at Home (AP@home)” (Funding Agency: European Union’s Research and Innovation funding programme, FP7 initiative: FP7-ICT-2007-2); the Italian project “Artificial Pancreas: In Silico Development and In Vivo Validation of Algorithms for Blood Glucose Control” (Funding agency: MIUR, Italian Ministry of Education, Universities and Research; initiative: “Fondo per gli Investimenti della Ricerca di Base”); by the Italian SIR project RBSI14JYM2 “Learning Patient-Specific Models for an Adaptive, Fault-Tolerant Artificial Pancreas (Learn4AP)” (Funding agency: MIUR, Italian Ministry of Education, Universities and Research; initiative: SIR-Scientific Independence of young Researchers); by the Italian project 2015PJ28EP “Forgot Diabetes: Adaptive Physiological Artificial Pancreas” (Funding agency: MIUR, Italian Ministry of Education, Universities and Research; initiative: “PRIN- Progetti di ricerca di Rilevante Interesse Nazionale 2015”).

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[53] C. Cobelli, E. Renard, B. Kovatchev, P. Keith-Hynes, N. Ben Brahim, J. Place, S. Del Favero, M. Breton, A. Farret, D. Bruttomesso, E. Dassau, H. Zisser, F. Doyle III, S. Patek, A. Avogaro, Pilot studies of wearable outpatient artificial pancreas in type 1 diabetes, Diabetes Care 35 (9) (2012) e65–e67. [54] B.P. Kovatchev, E. Renard, C. Cobelli, H.C. Zisser, P. Keith-Hynes, S.M. Anderson, S.A. Brown, D.R. Chernavvsky, M.D. Breton, L.B. Mize, A. Farret, J. Place, D. Bruttomesso, S. Del Favero, F. Boscari, S. Galasso, A. Avogaro, L. Magni, F. Di Palma, C. Toffanin, M. Messori, E. Dassau, F.J. Doyle, Safety of outpatient closed-loop control: first randomized crossover trials of a wearable artificial pancreas, Diabetes Care 37 (7) (Jul 2014) 1789–1796.

CHAPTER

Integrating the clinical and engineering aspects of closed-loop control: the Virginia experience

8

Sue A. Browna,c , Stacey M. Andersona,c , Marc D. Bretona , Daniel R. Cherñavvskya , Mark DeBoera,b , Boris P. Kovatcheva a University

of Virginia Center for Diabetes Technology, Charlottesville, VA, USA of Virginia Department of Pediatrics, Charlottesville, VA, USA c University of Virginia Division of Endocrinology and Metabolism, Charlottesville, VA, USA b University

8.1 Introduction Over the past 50 years, the diabetes technology field progressed remarkably through continuous subcutaneous insulin infusion (CSII), mathematical models and computer simulation of the human metabolic system, real-time continuous glucose monitoring (CGM), and control algorithms driving closed-loop control (CLC) systems known as the “artificial pancreas” (AP). The transition of closed-loop control to everyday diabetes therapy is contingent upon the acceptance by patients and healthcare providers of an advanced CLC system ensuring concerted work of CGMs, insulin pumps, and control algorithms. In 2011, a new pathway toward the development of such a system was charted by the Diabetes Assistant (DiAs), a smartphone multiuse platform designed at UVA to operate in several treatment modes ranging from CGM or insulin pump support to overnight and 24/7 CLC [1–5]. Since its introduction in 2011, DiAs has earned regulatory approvals for use in studies in the U.S., France, Italy, Netherlands, Israel, and Argentina. Three different control algorithms have been implemented on the DiAs platform and used in 18 clinical trials, including long-term studies at home. The second generation of DiAs, inControl, was developed by TypeZero Technologies, Inc. InControl is a mobile AP system that was used and tested extensively in several clinical trials, including long-term large-scale studies of Mobile AP (e.g., NCT02679287, NCT02844517, and NCT02985866). The t:slim X2 insulin pump with Control-IQ Technology (Tandem Diabetes Care, San Diego, CA) is a 3rd generation descendant of inControl and the mobile DiAs system, which has completed pilot studies and was used in a multicenter winter-sport study of 48 adolescents and children ages 6 and up skiing in Virginia, California, and The Artificial Pancreas. https://doi.org/10.1016/B978-0-12-815655-1.00017-X Copyright © 2019 Elsevier Inc. All rights reserved.

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Colorado (NCT03369067). Control-IQ is now included in UVA’s Project Nightlight (NCT 02679287) and in Protocol 3 of the multicenter International Diabetes ClosedLoop (iDCL) Trial, a large-scale study funded by the NIH/NIDDK (NCT03563313). In this review, we follow the clinical trials and the engineering developments leading to the current large studies aiming regulatory approval and clinical acceptance of AP. With several ongoing studies, we can be optimistic that the AP will fulfill its promise to become the digital-age treatment of diabetes in the near future.

8.2 Overview of the technology As noted in the Introduction, several hardware configurations shared the same control algorithm, which was first introduced in DiAs. The distinguishing features of this algorithm include: (i) automated insulin correction boluses administered using CGMbased patient state estimation; (ii) a dedicated hypoglycaemia safety system, which attenuates smoothly or discontinuously insulin delivery using historical CGM and insulin information; and (iii) gradually intensified control overnight, sliding the algorithm target down to achieve blood glucose levels of approximately 100–120 mg/dl by the morning. The algorithm has a modular design [6,7] and includes: • Metabolic State Estimation, which takes CGM, insulin history, SMBG, and meal data as input and produces as output the following estimates: (i) a current estimate of blood glucose; (ii) 30-minute predictions of blood glucose; (iii) risks of hypo- and hyperglycaemia; and (iv) Insulin-on-board (IOB) estimate. These results are stored in the database for use by other algorithmic modules. • Hyperglycaemia Correction Module, which requests correction boluses hourly when the subject has high blood glucose levels and is intended to mitigate the effect of unbolused or underbolused meals. • Basal Increase Module, which increases smoothly the amount of basal insulin when the subject does not have sufficient estimated IOB. The target is variable, becoming more aggressive overnight with the intention of bringing the patient to approximately 100–120 mg/dl when they awaken. • Hypoglycaemia Safety Module, which has the task of attenuating the delivery of basal insulin whenever it predicts that there is a risk of imminent hypoglycaemia [8]. Over the past 8 years, the same control algorithm was used with four generations of continuous glucose monitoring sensors (Dexcom SEVEN, G4, G5, G6), two insulin pumps (Roche, Tandem), implemented in a Mobile AP based on a smartphone (DiAs and inControl AP), and is now embedded in an insulin pump (Tandem t:slim X2 with Control-IQ). Fig. 8.1 presents the evolution of these systems. This progress presented in this chapter is dependent on receiving regulatory approvals for the conduct of these trials. At least 19 IDEs to date have been obtained to support these studies described.

8.3 Early outpatient AP studies (2011–16)

FIGURE 8.1 Evolution of the AP Systems using the UVA Control algorithm.

FIGURE 8.2 Clinical Trials (2011–2016).

8.3 Early outpatient AP studies (2011–16) These studies included multisite and international trials done at several prominent clinical centers in the U.S. and overseas, ranging from early feasibility two-day studies in supervised outpatient environment to six-month trials at home. Our overall strategy has been to test, retest, and test again the performance of the AP in various conditions, clinical centers, and age groups. These studies accumulated a wealth of data (∼21 patient years of closed-loop control) and AP know-how, which then enabled the transition to the large-scale International Diabetes Closed-Loop (iDCL) Trial funded by NIH in 2016 (NIH/NIDDK grant UC4 DK 108483). The upper panel of Fig. 8.2 includes pediatric studies, whereas the lower panel presents studies in adults. Briefly, in 2012–13, we completed two international multisite trials, which confirmed the feasibility of DiAs and its efficacy to reduce hypoglycaemia in the outpa-

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tient setting; both were selected for the Diabetes Care symposiums at the 2013 and 2014 American Diabetes Association (ADA) Scientific Sessions [9,10]. Three summer camp trials of remote monitoring [11], overnight CLC [12], and 24/7 CLC [13] confirmed the efficacy of DiAs in children with T1D. In Europe, AP@home studies implemented an additional algorithm (University of Pavia) on the DiAs platform. AP@home ran two pilot trials to pave the way for the large-scale AP@Home-3, which included study phases of two-month overnight and two-month 24/7 CLC at home [14], which was the first study to report statistically significant reduction in HbA1c with CLC [15]. Two studies followed, testing the CLC system using the UVA algorithm only with adolescents missing or underestimating their premeal boluses [16] and with adults during overnight control [17]. In the first of these studies, CLC reduced the extent and duration of postprandial BG excursions: mean BG of 197 vs. 235 mg/dl (p < 0.05) on CLC vs. SAP and is further described in the pediatric section [16]. In the second study, CLC compared to SAP reduced mean BG level at 07:00 h (119.3 vs. 152.9 mg/dl; p < 0.001) and overnight (139.0 vs. 170.3 mg/dl; p < 0.001) [17]. Based on the success of this pilot study of overnight CLC, we extended these findings to include a larger number of adult subjects (N = 40, mean age 45.5, hemoglobin A1c 7.4%) at four clinical centers (UVA, Mayo, Mt. Sinai, and Padua) and included the first substudy of 5 nights of CLC at home [18]. This study showed that only CLC could extend the benefits of overnight over a 24-hour period as time in the target range (70 to 180 mg/dL) was significantly improved in CLC vs. SAP over 24 hours (78.3% vs. 71.4%; p = 0.003) in addition to the expected changes overnight (85.7% vs. 67.6%; p < 0.001). Similarly, the time spent in a hypoglycaemic range (1.1 at two clinical sites, UVA and Stanford University [21]. After 1 week of blinded baseline CGM, subjects were randomized to 4 weeks of home use of SAP or CLC. LBGI was assessed from the baseline 1-week use of CGM and the final week of CGM during CLC or SAP treatment. The percent sensor glucose (SG) time 250 mg/dL was calculated from CGM use in the baseline and last weeks of CLC and SAP. Compared to SAP therapy, CLC reduced the risk of hypoglycaemia as measured by the Low Blood Glucose Index (LBGI), % time 250 mg/dL.

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8.4 Pediatric studies An important consideration for diabetes technology research is assessment of these applications during childhood and adolescence. This is needed because the vast majority of individuals with T1D began their time with diabetes as children and adolescents, and in many cases, their experience with T1D during childhood and adolescence sets the stage for their later care. Because of this, the UVA Center for Diabetes Technology (CDT) has a strong history of advancing AP applications among pediatric populations. The first major forays into pediatric care started with application of AP technologies in diabetes camps, where large groups of children can be assessed concurrently in a challenging setting that involves greater risk of hypoglycaemia due to increased activity levels. Even though children typically have their insulin dosage decreased while at camp, episodes of hypoglycaemia continue to occur, including at night, when the children are usually not able to sense the symptoms that usually accompany hypoglycaemia. CDT investigators and their collaborators first addressed these risks by evaluating the effect of remote monitoring of glucose levels on overnight diabetes control. In 2012, when commercially available remote monitoring systems were not available, adolescents (mean age 13.9 years ± 3.8 years) wore CGM monitors that transmitted BG data through a smart phone to a centralized server that camp personnel could monitor and respond to imminent hypoglycaemia. Campers were randomized to be on this system or to receive the usual monitoring, which involved spot-checking campers at a specific time overnight. This demonstrated a reduction in hypoglycaemia overnight when using remote monitoring, completely eliminating hypoglycaemic events with a BG 2 hours [4,11]. Camp studies then progressed in 2013 to assessing overnight AP [12] as compared to SAP, with campers receiving their usual pump therapy during the daytime. Participants (mean age 15.3 ± 2.1 years) served as their own controls, crossing over between intervention groups on an every-other-night basis. In a perprotocol analysis, this resulted in a significant increase in time-in-range 70–150 mg/dL (73% for AP and 52% for SAP, p = 0.037) [12]. The overnight AP also resulted in significant decreases in time spent with hypoglycaemia compared to SAP. This study demonstrated the feasibility and efficacy of AP use in childhood summer camp situations. Camp studies in 2014–15 next evaluated use of round-the-clock AP compared to SAP, with participants (mean age 17.9 ± 5.5 years) randomized to 5 days of either treatment [22]. This demonstrated improved BG control, with a percent time in range (70–180 mg/dL) of 78.6% on AP vs. 65.4% on SAP (p < 0.01) and lower mean glucose (143 vs. 156 mg/dL, p < 0.01) despite less hypoglycaemia 50 subjects with HbA1c ≥7.5% and >50 subjects with HbA1c 0 is a discontinuous signal guaranteeing invariance of the set    := x(t) | I OB(t) ≤ I OB(t) (9.3) with x(t) being the system state. The signal w(t) is given by (see [36])  + w if σ (t) > 0, w(t) = 0 otherwise,

(9.4)

with w + > 0 large enough and σ (t) a sliding surface separating the space into feasible and unfeasible regions, which is defined as σ (t) := I OB(t) − I OB(t) +

l−1 

  τi I OB(t)(i) − I OB(t)(i) ,

(9.5)

i=1

where l is the relative degree between the output I OB(t) and the input ω(t), the superscript (i) denotes the ith derivative, and τi are constant gains to be tuned. Given the filter (9.2), the relative degree will be l = ν + 1, where ν is the relative degree of the pharmacokinetic model used to estimate insulin-on-board. In [36], the amount of insulin at the subcutaneous depot is used as an IOB measure, given rise to l = 2, since insulin infusion is an input flow to the subcutaneous compartment. However, other definitions are possible. Remark that the invariance condition (9.3) states that, given an initial state fulfilling the constraint I OB(t) ≤ I OB(t), it will be fulfilled for all t > 0. To achieve this, when the system reaches by its own dynamics the sliding surface σ (t), the sliding regime is established by conditioning the reference until the system returns, by itself again, to the feasible region. However, in front of feedforward actions such as meal insulin boluses, a bolus dose larger than I OB(t) will inevitably lead to a violation of the constraint. As a result, insulin pump will be shut off until the insulin-on-board I OB(t) enters the feasible region. Compared to IFB, SMRC will react earlier, often leading to pump shut-off after a meal. In [40], it is demonstrated in an in silico study that the combination of IFB and SMRC techniques in an extended structure (SMRC-IFB) can lead to better glucose control. Fig. 9.2 illustrates the resulting structure. In this case, SMRC acts as an ultimate safety layer, activated specially in large meals, where IFB shows poorer performance. While in the feasible region delimited by the sliding surface, the system consists in a standard IFB strategy. Fig. 9.3 illustrates the behavior of IFB versus

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FIGURE 9.2 IFB, SMRC and combined SMRC-IFB structures. In the IFB structure (dark-shadowed blocks), a subcutaneous insulin pharmacokinetic model is used to estimate plasma insulin and reduce insulin infusion (control action) proportionally to this estimation. In the SMRC structure (light-shadowed blocks), an IOB estimation is obtained from the pharmacokinetic model, modulating glucose target so that an upper limit for IOB is not violated. Both structures can be combined as in the figure, in which case, SMRC acts as a second safety layer.

SMRC-IFB for a meal, ingested at 14:00 h in a system with meal announcement. In case of SMRC-IFB, an upper limit for IOB of 6.5 U is defined. It is shown that IFB leads to a hypoglycaemia approximately at 16:15 h, despite the pump shut-off happening at 15:00 h when the estimation of plasma insulin is reaching its peak value. However, this is avoided in the SMRC-IFB structure due to the activation of the SMRC component (see the signal w at the bottom panel in Fig. 9.3) when the estimation of insulin-on-board is approaching fast the upper limit, as determined by the sliding surface (9.5). This provokes a decrease of insulin infusion around 14:30 h, which, together with the IFB action, avoids hypoglycaemia.

9.4 Feedforward actions in exercise-informed systems According to the American Diabetes Association, all individuals with type 1 diabetes should practice exercise or physical activity to improve their overall health, which includes glycaemic control [41]. However, the effect of exercise on glucose levels depends on the type, duration and intensity of the activity. Mild and moderate intensity exercise requires a reduction of insulin infusion, whereas more intense activities necessitate a rise in insulin, at least in early recovery [9]. In [42] the effect of an insulin infusion suspension is compared at the start of a 40-min continuous exercise (treadmill) versus circuit-based session. Despite the lower intensity of continuous exercise (average oxygen consumption: 47.5 vs. 54.5 mL Kg−1 min−1 ; average heart rate: 122 vs. 144 ppm, p = 0.003), it provokes a greater decrease in blood glucose (−68.4 vs. 9 mg/dL, p = 0.001). In addition, the subcutaneous insulin pharmacokinetics is also affected by exercise. In [10] an increase in circulating insulin is demonstrated after

9.4 Feedforward actions in exercise-informed systems

FIGURE 9.3 Comparison of postprandial response of IFB and SMRC-IFB structures. In red (mid gray in print version): IFB response; in blue (dark gray in print version): SMRC-IFB response. From top to bottom: glucose, insulin infusion rate (left axis), and meal insulin bolus (right axis), estimation of plasma insulin, estimation of insulin-on-board, discontinuous signal w modulating glucose target in the SMRC component. Hypoglycaemia (< 70 mg/dL) and hyperglycaemia (> 180 mg/dL) limits are shown in the first panel as dotted lines.

the reduction of basal insulin infusion before a moderate aerobic exercise, probably due to the increase in heart rate and the increase of subcutaneous blood flow during exercise, causing an acceleration of insulin absorption. The same effect is shown in [43]. Exercise may also compromise the accuracy of continuous glucose monitors with an overestimation of blood glucose [11]. Possible causes are changes in subcutaneous blood flow and increased body and skin temperature, which can affect the dynamics of glucose transport between the plasma and the interstitial space where the sensor is housed. All of these factors make the correct management of insulin

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delivery during and after exercise difficult, since the prediction of the actual effects of exercise on glucose control is not a trivial task. Several approaches have been proposed to inform the controller about exercise triggering feedforward actions to mitigate hypoglycaemia. For instance, in [44] the benefit of informing the controller with a heart rate (HR) signal in a controlled 26-hour study including 30 minutes of mild exercise (9–10 on the Borg scale) was evaluated. The heart rate signal was used to attenuate the basal insulin infusion after the detection of exercise. A reduction in glucose decrement during exercise was obtained, although glycaemic control was similar. In a later study with adolescents [45] a reduction of the time in hypoglycaemia during the exercise was demonstrated (0.5% vs. 7.4%; with HR vs. without HR) although this did not imply a decrease in the number of hypoglycaemic events or the time in hypoglycaemia during 24 h of the study. The time in the range (70–180 mg/dL) was not different either. Recently, a consensus statement has been published containing different strategies that can be used in conventional insulin therapy to properly manage glucose before, during, and after exercise [46]. Following the consensus recommendations, patients should anticipate actions to the beginning of the exercise if they are related with insulin dosage adjustment or with supplemental carbohydrate intake. This is in accordance with a simulation study [47], where individualized basal reductions as early as 90 min before the start of the exercise was needed. Thus, an exercise announcement by the patient might be necessary in the context of a single-hormone artificial pancreas system. In [48] a set of mitigation measures (feedforward actions), including an adaptation of the consensus recommendations in combination with controller retuning, is proposed and validated in silico to deal with announced aerobic exercise in a single-hormone artificial pancreas system based on the SMRC-IFB controller in Fig. 9.2. In this case, an upper IOB limit I OB := KIOB I OB basal

(9.6)

is defined, where KIOB = 1.3 in absence of exercise, and I OB basal is the estimated insulin-on-board for the patient’s open-loop basal insulin infusion. At the moment of an early announcement of exercise, two main different actions are feasible to reduce the risk of hypoglycaemia: to suggest carbohydrate intake and to adjust insulin delivery. The system in [48] suggests carbohydrate intake (CHO) based on two different rules that are evaluated at the moment of the exercise announcement, denoted here as k: i) based on CGM measurements, CGM(k); and ii) considering the estimation of insulin-on-board I OB(k) at the moment of announcement: ⎧ ⎪ ⎨20 g if CGM(k) ≤ 90 mg/dL, CH OCGM (k) = (9.7) 10 g if 90 < CGM(k) ≤ 124 mg/dL, ⎪ ⎩ 0 otherwise, CH OIOB (k) = CH O(k)

=

α(I OB(k) − 0.5I OB basal )

(9.8)

CH OCGM (k) + CH OIOB (k)

(9.9)

9.5 Carbohydrate intake suggestions

where α (g/U) is the inverse of the patient’s insulin-to-carbohydrate ratio. Besides, to adjust insulin delivery, other feedforward actions related to the parameters of the closed-loop controller are implemented, before (when the exercise is announced), during, and after exercise (see Fig. 9.4). Finally, bolus insulin for the next meal after exercise is reduced by 50%. These feedforward actions were evaluated in two scenarios: a) exercise sessions during postprandial period and b) exercise sessions during fasting period. An adult cohort of 10 patients from the meal simulation model [49] was used, which was extended with the exercise model C in [50]. The mitigation methods proposed were able to minimize the occurrence of hypoglycaemic events related with exercise in both scenarios. The time spent in hypoglycaemic range (≤ 70 mg/dL) in the 2-h period after exercise decreased from 33.3% to 0.0% (p < 0.01) and from 41.3% to 0.0% (p < 0.01) in both scenarios tested. Besides that, the occurrence of hypoglycaemic events after exercise sessions was also reduced. Fig. 9.5 shows the aggregate population GCM readings for all exercise sessions in both scenarios.

FIGURE 9.4 SMRC-IFB controller retuning for announced exercise. At the moment of announcement, t1 minutes before the start of exercise, more aggressive insulin limitation is set by decreasing KIOB , which defines the upper IOB limit, and increasing w, which defines aggressiveness of glucose reference increment when approaching the upper IOB limit. At the same time, open-loop basal is set to zero and derivative time of the PID controller, Td , is decreased. These values are kept until t2 minutes after the exercise session and then restored linearly toward nominal values during

t3 minutes.

9.5 Carbohydrate intake suggestions as counterregulatory control action Minimal intervention of the patient is desired in an artificial pancreas. In this context, feedforward actions as described in the previous section are not feasible since

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FIGURE 9.5 Population performance of SMRC-IFB with and without feedforward actions against announced exercise. Figure (A) corresponds to Scenario 1, and Figure (B) to Scenario 2. Shaded area represents the exercise period. Blue (dark gray in print version) lines are mean±SD for SMRC-IFB with feedforward actions (CLFF ) and pink (light gray in print version) lines are mean±SD for SMRC-IFB without feedforward actions (CL).

they require announcement of events from the patient. Especially challenging is the scenario of unannounced aerobic exercise, with a high risk of hypoglycaemia in the absence of anticipated actions. Besides, uninformed actions by the patient could lead to paradoxical situations in which the patient takes carbohydrates to anticipate to the effects of the exercise and the controller delivers more insulin to compensate for the momentary rise in glucose. In this case, it is desirable that all actions are originated by the controller, including the suggestion of carbohydrates intake when there is a risk of hypoglycaemia in single-hormone artificial pancreas systems. In this way, the controller will be aware of such actions avoiding undesired interactions with insulin infusion, considering of course patient’s adherence. Carbohydrates intake suggestion is addressed by safety monitoring systems as described in Section 9.2. For instance, in [51], 30-min ahead glucose predictions are obtained by using multivariable timeseries models where glucose concentration is expressed as a function of the past glucose concentration, physical activity signals readings, and infused insulin doses by using an ARMAX model structure [23]. According to the predicted glucose level and the speed of glucose decrease, different amounts of carbohydrates are suggested to patients for consumption, ranging from 4 to 24 grams, in steps of 4 grams, depending on the specific case. However, carbohydrate intake suggestion can also be casted as a multivariable control problem with a plant with two inputs (insulin and rescue carbohydrates) and

9.5 Carbohydrate intake suggestions

one output (glucose). This can bring the benefit of coordination among both control actions reducing undesired interactions between insulin delivery and carbohydrate intake. This is the approach introduced in [52], where an additional feedback loop acting as a carbohydrate recommender system is implemented in combination with an insulin controller. Due to practicalities and patient’s convenience, the suggestion of carbohydrates intake should be a quantified control action for predetermined amounts of carbohydrates. These can be easily customized according to the patient’s preferences and can be fixed to amounts that match commercially available products. Glucose gels of 15 grams of carbohydrate are considered in [52]. Fig. 9.6 shows the proposed control scheme applied to the SMRC-IFB insulin controller.

FIGURE 9.6 Carbohydrate controller loop in combination with SMRC-IFB insulin controller. A PID carbohydrate controller computes a real-valued carbohydrate intake control action. A quantization logics defines when carbohydrate intake will be suggested to the patient, which is done in fixed amounts of 15 grams. Insulin infusion inhibits carbohydrate intake control action, whereas an estimation of carbohydrates-on-board inhibits insulin infusion, to avoid undesired interactions.

The carbohydrate loop features: (1) a PID controller computing a real-valued amount of carbohydrates, uPID,CHO , based on the glucose deviation with respect to a specific glucose target, Gr,CHO ; (2) a quantifier of the carbohydrate control action, which determines whether to recommend or not fixed amounts of 15 grams of carbohydrates, uCHO . Decisions are based on past and future carbohydrate control actions in a time window (± 15 min), with the use of an online recursive estimator with a patient individualized glucose prediction model; (3) inhibition signals between both insulin and carbohydrate loops, in both directions, to avoid oscillatory behaviors. The output computed by the insulin controller, multiplied by a conversion factor γ , inhibits carbohydrates control action, whereas insulin delivery is inhibited by a mea-

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sure of “carbohydrates-on-board” (COB). COB is a similar concept as IOB, that is, the COB are the carbohydrates that have been ingested but still have not appeared in plasma. Here, the COB is used to estimate how many of the recommended carbohydrates will still increase glucose concentration in the future. The linear second-order meal absorption model in [53] is adapted for fast-absorption carbohydrate intake to estimate COB: dG1 (t) dt dG2 (t) dt

=

Ug (t)

=

=

−G1 (t) + D(t)B, τmax G1 (t) − G2 (t) , τmax G2 (t) , τmax

(9.10) (9.11) (9.12)

where D(t) is the amount of recommended carbohydrate intake, B is the carbohydrate bioavailability, Ug is the carbohydrate rate of appearance, and τmax is the time of maximum appearance rate of glucose. Simple models like this can sufficiently represent the absorption of simple nutritional food such as glucose gels or sugary drinks. Then, when the patient responds to a carbohydrate recommendation at t = t0 , an impulse input D(t) = Dδ(t − t0 ), D = 15 g, is considered. The parameter values tmax = 20 min and B = 0.9 are considered. Then, the COB estimation is defined as t  =1− COB(t)

−

t

DBte τmax 2 t0 tmax

DB

dt .

(9.13)

In the following, we compare the SMRC-IFB controller presented in Section 9.3 to the new controller with carbohydrate recommendations. A challenging scenario including unannounced aerobic exercise has been used to benchmark the controllers. The scenario duration is 15 days, and the cohort and simulator used is the same as in the previous section. Meals were scheduled at 8:30, 13:00, and 19:00 (30, 60, and 50 g, respectively). The controller is challenged by continuous aerobic exercise sessions of 50 min at 60% VO2max. Eight exercise sessions were scheduled for each patient during the simulation period. Every other day, exercise sessions occurred at 07:00, 10:00, 15:00, and 21:00 and followed this time schedule twice. The results of this comparison are shown in Table 9.1. During the night period, both treatments are almost identical. We only obtained statistical significance in the mean CGM (110.5 mg/dL vs. 112.5 mg/dL, p < 0.01) and in the time below 70 mg/dL (2.1% vs. 0.9%, p < 0.01). This difference may be caused by the days where exercise was performed at 21:00. During daytime, statistical significant differences were found for most of the performance indicators. It is remarkable that the times in all hypoglycaemia ranges decrease. This means that the correct use of the carbohydrate recommender was able to reduce in median, for the whole cohort, more than 10 hours of time spent below 70 mg/dL. This decrease of time in hypoglycaemia did not translated into much increase of the time in hyperglycaemia, above

9.5 Carbohydrate intake suggestions

Table 9.1 Performance under unannounced exercise. Performance indicator Night-time (24:00–06:00) Mean CGM (mg/dL) Median CGM (mg/dL) % of time CGM 70–140 mg/dL 70–180 mg/dL >300 mg/dL >250 mg/dL >180 mg/dL 180 mg/dL