Chapter
Chapter 2 Draft Computational Tools and Methods
2.2 Sensitivity Analysis and Model Reduction
2.2.1 Sensitivity Analysis
2.2.1.1 Sobol’s Sensitivity Analysis
2.2.1.2 High-
Dimensional Model Representation
2.2.1.3 Group Method of Data Handling
2.2.2.1 Linear Model Order Reduction
2.2.2.2 Nonlinear Model Reduction
2.3 Multiparametric Programming and Model Predictive Control
2.3.1 Dynamic Programming and Robust Control
2.4 Estimation Techniques
2.4.1.1 Time Update (Prediction Step)
2.4.1.2 Measurement Update (Correction Step)
2.4.2 Moving Horizon Estimation
2.5 Explicit Hybrid Control
2.5.1 Multiparametric Mixed-Integer Programming
2.5.1.1 Problem and Solution Characterization
2.5.1.2 Literature Review
2.5.1.3 A General Framework for the Solution of mp‐MIQP Problems
2.5.1.4 Detailed Analysis of the General Framework
2.5.1.5 Description of an Exact Comparison Procedure
Chapter 3 Volatile Anaesthesia
3.2 Physiologically Based Patient Model
3.2.1.1 Body Compartments
3.2.3 Individualized Patient Variables and Parameters
3.3.1 Uncertainty Identification via Patient Variability Analysis
3.3.2 Global Sensitivity Analysis
3.3.3 Correlation Analysis and Parameter Estimation
3.4 Control Design for Volatile Anaesthesia
3.4.1.1 Model Linearization
3.4.2 On-Line Parameter Estimation
3.4.2.1 Control and Algorithm Design
3.4.2.2 Testing of the On‐Line Estimation Algorithm
3.4.3 Case Study: Controller Testing for Isourane‐Based Anaesthesia
Chapter 4 Intravenous Anaesthesia
4.1 A Multiparametric Model-based Approach to Intravenous Anaesthesia
4.1.3 Sensitivity Analysis
4.1.4 Advanced Model-based Control Strategies
4.1.4.1 Extended Predictive Self-adaptive Control (EPSAC) Strategy
4.1.4.2 Multiparametric Strategy
4.1.5.2 Case 2: mp-MPC Without Nonlinearity Compensation
4.1.5.3 Case 3: mp-MPC With Nonlinear Compensation
4.1.5.4 Case 4: mp-MPC With Nonlinearity Compensation and Estimation
4.1.6.2 Maintenance Phase
4.2 Simultaneous Estimation and Advanced Control
4.2.2 Multiparametric Moving Horizon Estimation (mp-MHE)
4.2.3 Simultaneous Estimation and mp-MPC Strategy
4.2.4.2 Maintenance Phase
4.3 Hybrid Model Predictive Control Strategies
4.3.2 Hybrid Patient Model Formulation
4.3.3.1 Hybrid Formulation of the Control Problem: Intravenous Anaesthesia
4.3.3.2 Robust Hybrid mp-MPC Control Strategy: Offset Free
4.3.4.1 No Offset Correction
Chapter 5 Part A: Type 1 Diabetes Mellitus: Modelling, Model Analysis and Optimization
5.a Type 1 Diabetes Mellitus: Modelling, Model Analysis and Optimization
5.a.1 Introduction: Type 1 Diabetes Mellitus
5.a.1.1 The Concept of the Artificial Pancreas
5.a.2 Modelling the Glucoregulatory System
5.a.3 Physiologically Based Compartmental Model
5.a.3.1 Endogenous Glucose Production (EGP)
5.a.3.2 Rate of Glucose Appearance (Ra)
5.a.3.3 Glucose Renal Excretion (Excretion)
5.a.3.4 Glucose Diffusion in the Periphery
5.a.3.5 Adaptation to the Individual Patient
5.a.3.5.1 Total Blood Volume
5.a.3.5.3 Compartmental Volume
5.a.3.5.4 Peripheral Interstitial Volume
5.a.4.1 Insulin Kinetics Model Selection
5.a.4.2 Endogenous Glucose Production: Parameter Estimation
5.a.4.3 Global Sensitivity Analysis
5.a.4.3.1 Individual Model Parameters
5.a.4.4 Parameter Estimation
5.a.6 Dynamic Optimization
5.a.6.1 Time Delays in the System
5.a.6.2 Dynamic Optimization of Insulin Delivery
5.a.6.3 Alternative Insulin Infusion
5.a.6.4 Concluding Remarks
Part B: Type 1 Diabetes Mellitus: Glucose Regulation
5.b Type 1 Diabetes Mellitus: Glucose Regulation
5.b.1 Glucose–Insulin System: Typical Control Problem
5.b.2 Model Predictive Control Framework
5.b.2.1 “High-Fidelity” Model
5.b.2.2 The Approximate Model
5.b.2.2.2 Physiologically Based Model Reduction
5.b.3.1 Model Predictive Control
5.b.3.2 Proposed Control Design
5.b.3.3 Prediction Horizon
5.b.3.4 Control Design 1: Predefined Meal Disturbance
5.b.3.5 Control Design 2: Announced Meal Disturbance
5.b.3.6 Control Design 3: Unknown Meal Disturbance
5.b.3.7 Control Design 4: Unknown Meal Disturbance
5.b.4.1 Predefined and Announced Disturbances
5.b.4.2 Unknown Disturbance Rejection
5.b.4.3 Variable Meal Time
5.b.4.4 Concluding Remarks
5.b.5.1 Model Identification
5.b.5.2 Concluding Remarks
A5.1 Model of UVa/Padova Simulator
Chapter 6 An Integrated Platform for the Study of Leukaemia
6.1 Towards a Personalised Treatment for Leukaemia: From in vivo to in vitro and in silico
6.2 In vitro Block of the Integrated Platform for the Study of Leukaemia
6.3 In silico Block of the Integrated Platform for the Study of Leukaemia
6.4 Bridging the Gap Between in vitro and in silico
Chapter 7 In vitro Studies: Acute Myeloid Leukaemia
7.1 Description of Biomedical System
7.1.1 The Human Haematopoietic System
7.1.2 General Structure of the Bone Marrow Microenvironment
7.1.4 Leukaemia: The Disease
7.1.5 Current Medical Treatment
7.2.1 Experimental Platforms
7.2.2 Crucial Environmental Factors in an in vitro System
7.2.2.1 Environmental Stress Factors and Haematopoiesis
7.2.3 Growth and Metabolism of an AML Model System as Influenced by Oxidative and Starvation Stress: A Comparison Between 2D and 3D Cultures
7.2.3.1 Materials and Methods
7.2.3.2 Results and Discussion
7.3 Cellular Biomarkers for Monitoring Leukaemia in vitro
7.3.1 (Macro-)autophagy: The Cellular Response to Metabolic Stress and Hypoxia
7.3.2 Biomarker Candidates
7.3.2.1 (Autophagic) Biomarker Candidates
7.3.2.2 (Non-autophagic) Stress Biomarker Candidates
7.4 From in vitro to in silico
Chapter 8 In silico Acute Myeloid Leukaemia
8.1.1 Mathematical Modelling of the Cell Cycle
8.1.2 Pharmacokinetic and Pharmacodynamic Mathematical Models in Cancer Chemotherapy
8.1.2.1 PK Mathematical Models
8.1.2.2 PD Mathematical Models
8.2 Chemotherapy Treatment as a Process Systems Application
8.2.1 Physiologically Based Patient Model for the Treatment of AML With DNR and Ara‐C
8.2.2 Design of an Optimal Treatment Protocol for Chemotherapy Treatment
8.2.3 Mathematical Model Analysis Using Patient Data
8.2.3.1 Model Sensitivity Analysis
8.2.3.3 Estimation of Patient‐Specific Cell Cycle Parameters
8.3 Analysis of a Patient Case Study
8.3.1 First Chemotherapy Cycle
8.3.2 Second Chemotherapy Cycle
Appendix 8A Mathematical Model
8A.2 Pharmacokinetic Model
8A.3 Pharmacodynamic Model
8A.4 Cancer Cell Cycle Model
8A.5 Normal Cell Cycle Model
8A.6 Drug Subcutaneous Route
Modelling Optimization and Control of Biomedical Systems
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