Front Cover

Modelling Methodology for Physiology and Medicine

Copyright Page

Contents

List of Contributors

Preface

Chapter 1. An Introduction to Modelling Methodology

1.1 Introduction

1.2 The Need for Models

1.3 Approaches to Modelling

1.4 Simulation

1.5 Model Identification

1.6 Model Validation

1.7 Reference

Chapter 2. Control in Physiology And Medicine

2.1 Introduction

2.2 A Systems and Control Approach

2.3 Control Mechanisms in Physiology

2.4 Control System Representations of the Clinical Process

2.5 Control System Approaches to Drug Therapy Planning and Administration

2.6 Conclusions

2.7 References

Chapter 3. Deconvolution

3.1 Introduction

3.2 Problem Statement

3.3 Difficulty of the Deconvolution Problem

3.4 The Regularization Method

3.5 Other Deconvolution Methods

3.6 Conclusions

3.7 Acknowledgements

3.8 References

Chapter 4. A priori Identifiability of Physiological Parametric Models

4.1 Introduction

4.2 The System-Experiment Model

4.3 A Priori Identifiability

4.4 Available Methods

4.5 An Identifiability Algorithm for Nonlinear Models

4.6 An Identifiability Algorithm for Linear Compartmental Models

4.7 Conclusions

4.8 References

Appendix A: The Characteristic Set

Appendix B: THE Gröbner Basis

Chapter 5. Parameter Estimation

5.1 Introduction

5.2 Least Squares and Maximum Likelihood Estimators

5.3 Bayesian Estimator

5.4 Population Kinetic Analysis

5.5 Acknowledgement

5.6 References

Chapter 6. Tracer Experiment Design for Metabolic Fluxes Estimation in Steady and Nonsteady State

6.1 Introduction

6.2 Fundamentals

6.3 Accessible-Pool and System Fluxes

6.4 The Tracer Probe

6.5 Estimation of Tracee Fluxes in Steady State

6.6 Estimation of Nonsteady-State Fluxes

6.7 Conclusions

6.8 References

Chapter 7. Physiological Modelling of Positron Emission Tomography Images

7.1 Introduction

7.2 Modeling Strategies

7.3 Positron Emission Tomography Measurement Error

7.4 Models of Regional Glucose Metabolism

7.5 Models of [15O]H2O Kinetics to Assess Blood Flow

7.6 Models of the Ligand-Receptor System

7.7 Conclusions

7.8 References

Chapter 8. Identification and Physiological Interpretation of Aortic Impedance in Modelling

8.1 Introduction

8.2 The Modelling Process and Related Problems of Identifiability and Determinacy

8.3 Vascular Impedance

8.4 Data-Driven Models of Vascular Impedance (Frequency Response Technique)

8.5 Historical Development of Windkessel Models

8.6 Where Windkessel Models' Identification Meets Physiological Interpretation

8.7 Contradictions in Clinically Oriented Compliance Estimation Methods (How the Viscoelastic Windkessel Resolves Them)

8.8 Distributed Description of Linear Arterial Systems to Infer Aortic Wave Reflection

8.9 Identifiability: A Key Issue in the Assessment of Physiological Relevance of T-Tube Model

8.10 Conclusions

8.11 References

Chapter 9. Mathematical Modelling of Pulmonary Gas Exchange

9.1 Standard Equations Used to Describe Gas Transport in the Lungs

9.2 Models of Diffusion Limitation

9.3 Models of Ventilation Perfusion Mismatch

9.4 Application of Mathematical Models of Ventilation, Perfusion, and Diffusion

9.5 References

Appendix A. GLossary

Appendix B. Calculations Necessary to Convert Inspired Gas at ATPD to BTPS

Chapter 10. Mathematical Models of Respiratory Mechanics

10.1 Introduction

10.2 Breathing Mechanics: Basic Concepts

10.3 First-Order Models

10.4 Second-Order Models

10.5 Respiratory Oscillation Mechanics

10.6 Simulation Models of Breathing Mechanics

10.7 Conclusions

10.8 References

Chapter 11. Insulin Modelling

11.1 Introduction

11.2 Models of Whole-body Insulin Kinetics

11.3 An Organ Model of Insulin Secretion

11.4 Estimation of Insulin Secretion by Deconvolution

11.5 A Structural Model to Estimate Insulin Secretion and Secretory Indices

11.6 Estimation of Hepatic Insulin Extraction

11.7 Conclusions

11.8 References

Chapter 12. Glucose Modeling

12.1 Introduction

12.2 Models of Whole-body Kinetics in Steady State

12.3 Models of Regional Kinetics in Steady State

12.4 Models of Whole-body Kinetics in Nonsteady State

12.5 Models of Glucose and Insulin Control on Glucose Metabolism

12.6 Simulation Models

12.7 Conclusions

12.8 References

Chapter 13. Blood-Tissue Exchange Modelling

13.1 Introduction

13.2 Experimental Approaches

13.3 Models of Blood-Tissue Exchange

13.4 Conclusions

13.5 References

Index