Modelling Methodology for Physiology and Medicine

Transcription

1 Modelling Methodology for Physiology and Medicine Ewart Carson, Editor Centre for Measurement and Information in Medicine City University London, England Claudio Cobelli, Editor Dipartimento di Elettronica Universita di Padova Padova, Italy ACADEMIC PRESS An Imprint of Elsevier San Diego San Francisco New York Boston London Sydney Tokyo

2 List of Contributors Preface xv xiii Chapter 1 An Introduction to Modelling Methodology Claudio Cobelli and Ewart Carson 1.1 Introduction The Need for Models Approaches to Modelling Simulation Model Identification Model Validation Reference 13 Chapter 2 Control in Physiology And Medicine Ewart Carson, Tom Hennessy, and Abdul Roudsari 2.1 Introduction A Systems and Control Approach Control Mechanisms in Physiology Control System Representations of the Clinical Process Control System Approaches to Drug Therapy Planning and Administration 35 V

3 2.6 Conclusions References 43 Chapter 3 Deconvolution Giovanni Sparacino, Giuseppe De Nicolao, and Claudio Cobelli 3.1 Introduction Problem Statement Difficulty of the Deconvolution Problem The Regularization Method Other Deconvolution Methods Conclusions Acknowledgements References 72 Chapter 4 A priori Identifiability of Physiological Parametric Models Maria Pia Saccomani, Leontina D'Angio', Stefania Audoly, and Claudio Cobelli 4.1 Introduction The System-Experiment Model A Priori Identifiability Available Methods An Identifiability Algorithm for Nonlinear Models An Identifiability Algorithm for Linear Compartmental Models Conclusions References 101 Appendix A: The Characteristic Set 103 Appendix B: THE Gröbner Basis 104 Chapter 5 Parameter Estimation Roman Hovorka and Paolo Vicini 5.1 Introduction Least Squares and Maximum Likelihood Estimators 108

4 vu 5.3 Bayesian Estimator Population Kinetic Analysis Acknowledgement References 148 Chapter 6 Tracer Experiment Design for Metabolic Fluxes Estimation in Steady and Nonsteady State Andrea Caumo and Claudio Cobelli 6.1 Introduction Fundamentals Accessible-Pool and System Fluxes The Tracer Probe Estimation of Tracee Fluxes in Steady State Estimation of Nonsteady-State Fluxes Conclusions References 177 Chapter 7 Physiological Modelling of Positron Emission Tomography Images Alessandra Bertoldo and Claudio Cobelli 7.1 Introduction Modeling Strategies Positron Emission Tomography Measurement Error Models of Regional Glucose Metabolism Models of [ 15 0]H 2 0 Kinetics to Assess Blood Flow Models of the Ligand-Receptor System Conclusions References 208 Chapter 8 Identification and Physiological Interpretation of Aortic Impedance in Modelling Roberto Burattini

5 viii Contents 8.1 Introduction The Modelling Process and Related Problems of Identifiability and Determinacy Vascular Impedance Data-Driven Models of Vascular Impedance (Frequency Response Technique) Historical Development of Windkessel Models Where Windkessel Models' Identification Meets Physiological Interpretation Contradictions in Clinically Oriented Compliance Estimation Methods (How the Viscoelastic Windkessel Resolves them) Distributed Description of Linear Arterial Systems to Infer Aortic Wave Reflection Identifiability: A Key Issue in the Assessment of Physiological Relevance of Г-Tübe Model Conclusions References 248 Chapter 9 Mathematical Modelling of Pulmonary Gas Exchange Stephen E. Rees, Soren Kjxrgaard, and Steen Andreassen 9.1 Standard Equations Used to Describe Gas Transport in the Lungs Models of Diffusion Limitation Models of Ventilation Perfusion Mismatch Application of Mathematical Models of Ventilation, Perfusion, and Diffusion References 273 Appendix A: GLossary 276 Appendix B: Calculations Necessary to Convert Inspired Gas at ATPD to BTPS 277 Chapter 10 Mathematical Models of Respiratory Mechanics Gianluca Nucci and Claudio Cobelli 10.1 Introduction Breathing Mechanics: Basic Concepts 280

6 ix 10.3 First-Order Models Second-Order Models Respiratory Oscillation Mechanics Simulation Models of Breathing Mechanics Conclusions References 301 Chapter 11 Insulin Modelling Gianna Maria Toffolo 11.1 Introduction Models of Whole-body Insulin Kinetics An Organ Model of Insulin Secretion Estimation of Insulin Secretion by Deconvolution A Structural Model to Estimate Insulin Secretion and Secretory Indices Estimation of Hepatic Insulin Extraction Conclusions References 333 Chapter 12 Glucose Modeling Andrea Caumo, Monica Simeoni, Claudio Cobelli 12.1 Introduction Models of Whole-body Kinetics in Steady State Models of Regional Kinetics in Steady State Models of Whole-body Kinetics in Nonsteady State Models of Glucose and Insulin Control on Glucose Metabolism Simulation Models Conclusions References 370 Chapter 13 Blood-Tissue Exchange Modelling Paolo Vicini

7 X Contents 13.1 Introduction Experimental Approaches Models of Blood-Tissue Exchange Conclusions References 397 Index 403