Modelling Optimization and Control of Biomedical Systems

Efstratios N. Pistikopoulos, PhD, is the Interim Co-Director and Deputy Director of the Texas A&M Energy Institute, as well as a TEES Distinguished Research Professor in the Artie McFerrin Department of Chemical Engineering at Texas A&M University. Professor Pistikopoulos received the Computing in Chemical Engineering Award from the American Institute of Chemical Engineers (AIChE) in 2012 and was elected Fellow of the Royal Academy of Engineering in the UK in 2013. Ioana Na&#537cu, PhD, MEng, is a Postdoctoral Research Associate at Artie McFerrin Department of Chemical Engineering, Texas A&M University. Her research focuses on developing advanced multi-parametric optimization and control strategies for biomedical processes. Eirini G. Velliou, PhD, MEng, FHEA, is Principal Investigator and founder of the Bioprocess and Biochemical Engineering Group (BioProChem) at the Department of Chemical and Process Engineering of the University of Surrey. Her research focus includes cancer tissue engineering and environmental (cancer cell) stress response.

• List of Contributors xiiiPreface xvPart I 11 Framework and Tools: A Framework for Modelling, Optimization and Control of Biomedical Systems 3Eirini G. Velliou, Ioana Naşcu, Stamatina Zavitsanou, Eleni Pefani, Alexandra Krieger, Michael C. Georgiadis, and Efstratios N. Pistikopoulos1.1 Mathematical Modelling of Drug Delivery Systems 31.1.1 Pharmacokinetic Modelling 31.1.1.1 Compartmental Models 31.1.1.2 Physiologically Based Pharmacokinetic Models 51.1.2 Pharmacodynamic Modelling 51.2 Model analysis, Parameter Estimation and Approximation 71.2.1 Global Sensitivity Analysis 81.2.2 Variability Analysis 81.2.3 Parameter Estimation and Correlation 91.3 Optimization and Control 9References 112 Draft Computational Tools and Methods 13Ioana Naşcu, Richard Oberdieck, Romain Lambert, Pedro Rivotti, and Efstratios N. Pistikopoulos2.1 Introduction 132.2 Sensitivity Analysis and Model Reduction 142.2.1 Sensitivity Analysis 142.2.1.1 Sobol’s Sensitivity Analysis 162.2.1.2 High‐Dimensional Model Representation 172.2.1.3 Group Method of Data Handling 182.2.1.4 Gmdh–hdmr 192.2.2 Model Reduction 202.2.2.1 Linear Model Order Reduction 212.2.2.2 Nonlinear Model Reduction 222.3 Multiparametric Programming and Model Predictive Control 242.3.1 Dynamic Programming and Robust Control 282.4 Estimation Techniques 332.4.1 Kalman Filter 342.4.1.1 Time Update (Prediction Step) 342.4.1.2 Measurement Update (Correction Step) 342.4.2 Moving Horizon Estimation 342.5 Explicit Hybrid Control 392.5.1 Multiparametric Mixed‐Integer Programming 402.5.1.1 Problem and Solution Characterization 402.5.1.2 Literature Review 422.5.1.3 A General Framework for the Solution of mp‐MIQP Problems 482.5.1.4 Detailed Analysis of the General Framework 502.5.1.5 Description of an Exact Comparison Procedure 54References 573 Volatile Anaesthesia 67Alexandra Krieger, Ioana Naşcu, Nicki Panoskaltsis, Athanasios Mantalaris, Michael C. Georgiadis, and Efstratios N. Pistikopoulos3.1 Introduction 673.2 Physiologically Based Patient Model 693.2.1 Pharmacokinetics 693.2.1.1 Body Compartments 723.2.1.2 Blood Volume 733.2.1.3 Cardiac Output 733.2.1.4 Lung Volume 743.2.2 Pharmacodynamics 743.2.3 Individualized Patient Variables and Parameters 743.3 Model Analysis 753.3.1 Uncertainty Identification via Patient Variability Analysis 753.3.2 Global Sensitivity Analysis 773.3.3 Correlation Analysis and Parameter Estimation 813.3.4 Simulation Results 833.4 Control Design for Volatile Anaesthesia 863.4.1 State Estimation 873.4.1.1 Model Linearization 883.4.2 On‐Line Parameter Estimation 903.4.2.1 Control and Algorithm Design 913.4.2.2 Testing of the On‐Line Estimation Algorithm 933.4.3 Case Study: Controller Testing for Isourane‐Based Anaesthesia 96Conclusions 98Appendix 99References 1004 Intravenous Anaesthesia 103Ioana Naşcu, Alexandra Krieger, Romain Lambert, and Efstratios N. Pistikopoulos4.1 A Multiparametric Model‐based Approach to Intravenous Anaesthesia 1034.1.1 Introduction 1034.1.2 Patient Model 1044.1.3 Sensitivity Analysis 1084.1.4 Advanced Model‐based Control Strategies 1104.1.4.1 Extended Predictive Self‐adaptive Control (EPSAC) Strategy 1114.1.4.2 Multiparametric Strategy 1114.1.5 Control Design 1124.1.5.1 Case 1: EPSAC 1154.1.5.2 Case 2: mp‐MPC Without Nonlinearity Compensation 1164.1.5.3 Case 3: mp‐MPC With Nonlinear Compensation 1174.1.5.4 Case 4: mp‐MPC With Nonlinearity Compensation and Estimation 1184.1.6 Results 1184.1.6.1 Induction Phase 1194.1.6.2 Maintenance Phase 1234.1.6.3 Discussion 1254.2 Simultaneous Estimation and Advanced Control 1304.2.1 Introduction 1304.2.2 Multiparametric Moving Horizon Estimation (mp‐MHE) 1304.2.3 Simultaneous Estimation and mp‐MPC Strategy 1324.2.4 Results 1344.2.4.1 Induction Phase 1354.2.4.2 Maintenance Phase 1384.3 Hybrid Model Predictive Control Strategies 1424.3.1 Introduction 1424.3.2 Hybrid Patient Model Formulation 1434.3.3 Control Design 1444.3.3.1 Hybrid Formulation of the Control Problem: Intravenous Anaesthesia 1444.3.3.2 Robust Hybrid mp‐MPC Control Strategy: Offset Free 1464.3.3.3 Control Scheme 1474.3.4 Results 1474.3.4.1 No Offset Correction 1474.3.4.2 Offset Free 1504.3.5 Discussion 1504.4 Conclusions 153References 153Part II 1575 Part A: Type 1 Diabetes Mellitus: Modelling, Model Analysis and Optimization 159Stamatina Zavitsanou, Athanasios Mantalaris, Michael C. Georgiadis, and Efstratios N. Pistikopoulos5.a Type 1 Diabetes Mellitus: Modelling, Model Analysis and Optimization 1595.a.1 Introduction: Type 1 Diabetes Mellitus 1595.a.1.1 The Concept of the Artificial Pancreas 1605.a.2 Modelling the Glucoregulatory System 1625.a.3 Physiologically Based Compartmental Model 1625.a.3.1 Endogenous Glucose Production (EGP) 1675.a.3.2 Rate of Glucose Appearance (Ra) 1685.a.3.3 Glucose Renal Excretion (Excretion) 1685.a.3.4 Glucose Diffusion in the Periphery 1685.a.3.5 Adaptation to the Individual Patient 1695.a.3.5.1 Total Blood Volume 1695.a.3.5.2 Cardiac Output 1705.a.3.5.3 Compartmental Volume 1705.a.3.5.4 Peripheral Interstitial Volume 1715.a.3.6 Insulin Kinetics 1715.a.4 Model Analysis 1725.a.4.1 Insulin Kinetics Model Selection 1725.a.4.2 Endogenous Glucose Production: Parameter Estimation 1765.a.4.3 Global Sensitivity Analysis 1775.a.4.3.1 Individual Model Parameters 1785.a.4.4 Parameter Estimation 1825.a.5 Simulation Results 1835.a.6 Dynamic Optimization 1855.a.6.1 Time Delays in the System 1855.a.6.2 Dynamic Optimization of Insulin Delivery 1885.a.6.3 Alternative Insulin Infusion 1895.a.6.4 Concluding Remarks 192Part B: Type 1 Diabetes Mellitus: Glucose Regulation 192Stamatina Zavitsanou, Athanasios Mantalaris, Michael C. Georgiadis, and Efstratios N. Pistikopoulos5.b Type 1 Diabetes Mellitus: Glucose Regulation 1925.b.1 Glucose–Insulin System: Typical Control Problem 1925.b.2 Model Predictive Control Framework 1945.b.2.1 “High‐Fidelity” Model 1945.b.2.2 The Approximate Model 1955.b.2.2.1 Linearization 1955.b.2.2.2 Physiologically Based Model Reduction 1965.b.3 Control Design 1995.b.3.1 Model Predictive Control 1995.b.3.2 Proposed Control Design 2005.b.3.3 Prediction Horizon 2005.b.3.4 Control Design 1: Predefined Meal Disturbance 2025.b.3.5 Control Design 2: Announced Meal Disturbance 2025.b.3.6 Control Design 3: Unknown Meal Disturbance 2025.b.3.7 Control Design 4: Unknown Meal Disturbance 2045.b.4 Simulation Results 2045.b.4.1 Predefined and Announced Disturbances 2045.b.4.2 Unknown Disturbance Rejection 2045.b.4.3 Variable Meal Time 2075.b.4.4 Concluding Remarks 2075.b.5 Explicit MPC 2085.b.5.1 Model Identification 2095.b.5.2 Concluding Remarks 211Appendix 5.1 212Appendix 5.2 215Appendix 5.3 215References 217Part III 2256 An Integrated Platform for the Study of Leukaemia 227Eirini G. Velliou, Maria Fuentes‐Gari, Ruth Misener, Eleni Pefani, Nicki Panoskaltsis, Athanasios Mantalaris, Michael C. Georgiadis, and Efstratios N. Pistikopoulos6.1 Towards a Personalised Treatment for Leukaemia: From in vivo to in vitro and in silico 2276.2 In vitro Block of the Integrated Platform for the Study of Leukaemia 2286.3 In silico Block of the Integrated Platform for the Study of Leukaemia 2296.4 Bridging the Gap Between in vitro and in silico 231References 2317 In vitro Studies: Acute Myeloid Leukaemia 233Eirini G. Velliou, Eleni Pefani, Susana Brito dos Santos, Maria Fuentes‐Gari, Ruth Misener, Nicki Panoskaltsis, Athanasios Mantalaris, Michael C. Georgiadis, and Efstratios N. Pistikopoulos7.1 Description of Biomedical System 2337.1.1 The Human Haematopoietic System 2337.1.2 General Structure of the Bone Marrow Microenvironment 2357.1.3 The Cell Cycle 2367.1.4 Leukaemia: The Disease 2387.1.5 Current Medical Treatment 2397.2 Experimental Part 2407.2.1 Experimental Platforms 2407.2.2 Crucial Environmental Factors in an in vitro System 2417.2.2.1 Environmental Stress Factors and Haematopoiesis 2417.2.3 Growth and Metabolism of an AML Model System as Influenced by Oxidative and Starvation Stress: A Comparison Between 2D and 3D Cultures 2447.2.3.1 Materials and Methods 2447.2.3.2 Results and Discussion 2477.2.3.3 Conclusions 2547.3 Cellular Biomarkers for Monitoring Leukaemia in vitro 2557.3.1 (Macro‐)autophagy: The Cellular Response to Metabolic Stress and Hypoxia 2557.3.2 Biomarker Candidates 2567.3.2.1 (Autophagic) Biomarker Candidates 2567.3.2.2 (Non‐autophagic) Stress Biomarker Candidates 2577.4 From in vitro to in silico 257References 2588 In silico Acute Myeloid Leukaemia 265Eleni Pefani, Eirini G. Velliou, Nicki Panoskaltsis, Athanasios Mantalaris, Michael C. Georgiadis, and Efstratios N. Pistikopoulos8.1 Introduction 2658.1.1 Mathematical Modelling of the Cell Cycle 2668.1.2 Pharmacokinetic and Pharmacodynamic Mathematical Models in Cancer Chemotherapy 2688.1.2.1 PK Mathematical Models 2698.1.2.2 PD Mathematical Models 2738.2 Chemotherapy Treatment as a Process Systems Application 2738.2.1 Physiologically Based Patient Model for the Treatment of AML With DNR and Ara‐C 2758.2.2 Design of an Optimal Treatment Protocol for Chemotherapy Treatment 2778.2.3 Mathematical Model Analysis Using Patient Data 2788.2.3.1 Model Sensitivity Analysis 2788.2.3.2 Patient Data 2798.2.3.3 Estimation of Patient‐specific Cell Cycle Parameters 2808.3 Analysis of a Patient Case Study 2828.3.1 First Chemotherapy Cycle 2828.3.2 Second Chemotherapy Cycle 2828.4 Conclusions 285Appendix 8A Mathematical Model 286Appendix 8B Patient Data 290References 296Index 301