Front Cover -- Modelling Methodology for Physiology and Medicine -- Copyright Page -- Contents -- Preface -- Preface to the Second Edition -- List of Contributors -- 1 An Introduction to Modelling Methodology -- 1.1 Introduction -- 1.2 The Need for Models -- 1.2.1 Physiological Complexity -- 1.2.2 Models and Their Purposes -- 1.3 Approaches to Modelling -- 1.3.1 Modelling the Data -- 1.3.2 Modelling the System -- 1.4 Simulation -- 1.5 Model Identification -- 1.5.1 A Framework for Identification -- 1.5.2 Identification of Parametric Models -- 1.5.3 Identification of Nonparametric Models -- 1.6 Model Validation -- Reference -- 2 Control in Physiology and Medicine -- 2.1 Introduction -- 2.2 Modelling for Control System Design and Analysis -- 2.2.1 Sets of Ordinary Differential Equations -- 2.2.2 Linear State Space Models -- 2.2.3 Transfer Functions -- 2.2.3.1 Pole-Zero Cancellation -- 2.2.3.2 Right-Half-Plane Zeros and Time Delays -- 2.2.4 Discrete-Time State Space Models -- 2.2.5 Discrete Auto-Regressive Models -- 2.2.6 Step and Impulse Response Models -- 2.2.7 System Identification -- 2.3 Block Diagram Analysis -- 2.3.1 Continuous-Time Block Diagram Analysis -- 2.3.2 Discrete-Time Block Diagram Analysis -- 2.4 Proportional-Integral-Derivative Control -- 2.4.1 PID Tuning Techniques -- 2.4.1.1 Ziegler-Nichols Closed-Loop Oscillations -- 2.4.1.2 Frequency Response -- 2.4.1.3 Cohen-Coon -- 2.4.1.4 Internal Model Control-Based PID -- 2.4.1.5 Ad hoc -- 2.4.2 Discrete-Time PID -- 2.5 Model Predictive Control -- 2.6 Other Control Algorithms -- 2.6.1 Fuzzy Logic -- 2.6.2 Expert Systems -- 2.6.3 Artificial Neural Networks -- 2.6.4 On-Off -- 2.7 Application Examples -- 2.7.1 Type 1 Diabetes: Blood Glucose Control -- 2.7.1.1 Models for Simulation -- 2.7.1.2 Models for Control -- 2.7.1.3 Control -- 2.7.1.3.1 On-Off.

2.7.1.3.2 Proportional-Integral-Derivative (PID) -- 2.7.1.3.3 Model Predictive Control (MPC) -- 2.7.1.3.4 Fuzzy Logic -- 2.7.2 Intensive Care Unit Blood Glucose Control -- 2.7.2.1 Models -- 2.7.2.2 Control -- 2.7.3 Blood Pressure Control Using Continuous Drug Infusion -- 2.7.3.1 Models -- 2.7.3.2 Control -- 2.7.4 Control of Anesthesia and Sedation -- 2.7.4.1 Models -- 2.7.4.2 Open-Loop Control -- 2.7.4.3 Closed-Loop Control -- 2.8 Summary -- References -- 3 Deconvolution -- 3.1 Problem Statement -- 3.2 Difficulty of the Deconvolution Problem -- 3.2.1 Dealing with Physiological Systems -- 3.2.2 A Classification of the Deconvolution Approaches -- 3.3 The Regularization Method -- 3.3.1 Deterministic Viewpoint -- 3.3.1.1 The Choice of the Regularization Parameter -- 3.3.1.2 The Virtual Grid -- 3.3.1.3 Assessment of Confidence Limits -- 3.3.2 Stochastic Viewpoint -- 3.3.2.1 Confidence Limits -- 3.3.2.2 Statistically Based Choice of the Regularization Parameter -- 3.3.3 Numerical Aspects -- 3.3.4 Constrained Deconvolution -- 3.4 Other Deconvolution Methods -- 3.5 Conclusions -- References -- 4 Structural Identifiability of Biological and Physiological Systems -- 4.1 Introduction -- 4.2 Background and Definitions -- 4.2.1 The System -- 4.2.2 Structural Identifiability -- 4.3 Identifiability and Differential Algebra -- 4.3.1 The Problem -- 4.3.2 The Characteristic Set -- 4.3.3 A Benchmark Model -- 4.4 The Question of Initial Conditions -- 4.4.1 An Example -- 4.4.2 The Role of Accessibility -- 4.5 Identifiability of Some Nonpolynomial Models -- 4.6 A Case Study -- 4.7 Conclusion -- References -- 5 Parameter Estimation -- 5.1 Problem Statement -- 5.2 Fisherian Parameter Estimation Approaches -- 5.2.1 Least Squares -- 5.2.2 Maximum Likelihood -- 5.2.3 Analysis of the Residuals -- 5.2.4 Precision of the Estimates -- 5.2.5 Model Selection Among Candidates.

5.2.6 Case Study -- 5.3 Bayesian Parameter Estimation Approaches -- 5.3.1 Fundamentals -- 5.3.2 MAP Estimator in the Gaussian Case -- 5.3.2.1 Derivation of the MAP Estimator -- 5.3.2.2 Case Study -- 5.3.3 Prior Distribution in Bayesian Analysis -- 5.3.4 Use of Markov Chain Monte Carlo in Bayesian Estimation -- 5.3.4.1 The Algorithm -- 5.3.4.2 The Choice of the Proposal Distribution -- 5.3.4.3 Assessing the Convergence -- 5.3.5 Case Study -- 5.4 Conclusions -- References -- 6 New Trends in Nonparametric Linear System Identification -- 6.1 Introduction -- 6.2 System Identification Problem -- 6.2.1 Continuous-Time Formulation -- 6.2.2 Discrete-Time Formulation -- 6.3 The Classical Approach to System Identification -- 6.3.1 Model Structures Examples -- 6.3.2 Estimation of Model Dimension -- 6.4 Limitations of the Classical Approach to System Identification: Assessment of Cerebral Hemodynamics Using MRI -- 6.5 The Nonparametric Gaussian Regression Approach to System Identification -- 6.5.1 Estimate of the Impulse Response for Known Hyperparameters -- 6.5.2 Hyperparameter Estimation Via Marginal Likelihood Optimization -- 6.5.3 Covariances for System Identification: The Stable Spline Kernels -- 6.6 Assessment of Cerebral Hemodynamics Using the Stable Spline Estimator -- 6.7 Conclusions -- References -- 7 Population Modelling -- 7.1 Introduction -- 7.1.1 Problem Statement -- 7.2 Naïve Data Approaches: Naïve Average and Naïve Pooled Data -- 7.2.1 Naïve Average Data -- 7.2.2 Naïve Pooled Data -- 7.3 Two-Stage Approaches: Standard, Global, and Iterative Two-Stage -- 7.3.1 Standard Two-Stage -- 7.3.2 Global Two-Stage -- 7.3.3 Iterative Two-Stage -- 7.4 Nonlinear Mixed-Effects Modelling -- 7.4.1 Basic Definitions: Fixed Effects, Intersubject Variability, Residual Random Effects, Covariates -- 7.4.2 Formalization: First Stage and Second Stage.

7.4.2.1 First Stage (Observations) -- 7.4.2.2 Second Stage (Population) -- 7.4.3 An Example: A Population Model of C-Peptide Kinetics -- 7.4.3.1 First Stage (Observations) -- 7.4.3.2 Second Stage (Population) -- 7.4.4 Estimation Methods: First Order with Post Hoc, First-Order Conditional Estimation, Laplace, Stochastic Approximation ... -- 7.4.4.1 First Order -- 7.4.4.2 FOCE Approximation -- 7.4.4.3 Laplace Method -- 7.4.4.4 Stochastic Approximation of the Expectation-Maximization Algorithm -- 7.4.5 Bayesian Approach to Nonlinear Mixed-Effects Models -- 7.4.5.1 Stage 1-Model for the Data -- 7.4.5.2 Stage 2-Model for Heterogeneity Between Subjects -- 7.4.5.3 Stage 3-Model for the Priors -- 7.4.6 Evaluation of Modelling Results -- 7.4.6.1 Individual and Population Parameters-Standard Error of the Estimates -- 7.4.6.2 Individual and Population Prediction-Weighted Residuals -- 7.4.6.3 Population Estimates -- 7.4.6.4 Individual Estimates -- 7.4.6.5 Visual Predictive Check -- 7.4.6.6 Shrinkage -- 7.4.7 Model Selection for Nonlinear Mixed-Effects Models -- 7.5 Covariate Models in Nonlinear Mixed-Effects Models -- References -- 8 Systems Biology -- 8.1 Introduction -- 8.2 Modelling the System: ODE Models -- 8.2.1 Model Characterization -- 8.2.1.1 Mass Action Law -- 8.2.1.2 Michaelis-Menten Equation -- 8.2.1.3 Hill Equation -- 8.2.2 Simulation and Parameter Estimation of Oscillating Systems -- 8.2.2.1 Limit Cycle Models -- 8.2.2.2 Optimization Methods -- 8.2.3 Sensitivity Analysis for Oscillating Systems -- 8.2.3.1 Period Sensitivity -- 8.2.3.2 Phase Response Curve -- 8.3 Modelling the Data: Statistical Models -- 8.3.1 Inferential Statistics -- 8.3.2 Differentially Expressed Genes -- 8.3.2.1 Student's t-Test -- 8.3.2.2 LIMMA (Linear Models for Microarray Data) -- 8.3.2.3 Permutation Test -- 8.3.3 Pathway and Gene-Ontology Enrichment.

8.3.3.1 Over-Representation Analysis -- 8.3.3.2 Gene Set Enrichment -- 8.3.4 Pathway Inference -- 8.3.5 Supervised Classification -- 8.3.6 COMBINER (Core Module Biomarker Identification with Network Exploration) -- 8.4 Applications -- 8.4.1 Circadian Rhythms -- 8.4.1.1 Biological Motivation -- 8.4.1.2 Model Design -- 8.4.1.3 Parameter Estimation -- 8.4.1.4 Model Predictions and Validation -- 8.4.2 Posttraumatic Stress Disorder -- 8.4.2.1 Biomarkers for PTSD -- 8.4.2.2 Core Module Blood Biomarker Network -- 8.4.2.3 Core Module Brain Biomarker Network -- 8.5 Conclusions -- Acknowledgments -- References -- 9 Reverse Engineering of High-Throughput Genomic and Genetic Data -- 9.1 Introduction -- 9.2 Reverse Engineering Transcriptional Data -- 9.2.1 Pairwise Methods -- 9.2.2 Model-Based Methods -- 9.2.2.1 Boolean Models -- 9.2.2.2 Models Based on Differential Equations -- 9.2.3 Performance of Reverse Engineering Algorithms -- 9.3 Reverse Engineering Genetic Genomics Data -- 9.4 Conclusion -- References -- 10 Tracer Experiment Design for Metabolic Fluxes Estimation in Steady and Nonsteady State -- 10.1 Introduction -- 10.2 Fundamentals -- 10.3 Accessible Pool and System Fluxes -- 10.4 The Tracer Probe -- 10.5 Estimation of Tracee Fluxes in Steady State -- 10.5.1 Single Injection -- 10.5.2 Constant Infusion -- 10.5.3 Primed Continuous Infusion -- 10.6 Estimation of Nonsteady-State Fluxes -- 10.6.1 Assessment of Ra: The Tracer-to-Tracee Clamp -- 10.6.1.1 No Exogenous Source of Tracee -- 10.6.1.2 Known Exogenous Source of Tracee -- 10.6.1.3 Unknown Exogenous Source of Tracee -- 10.6.2 Assessment of Rd and U -- 10.7 Conclusion -- References -- 11 Stochastic Models of Physiology -- 11.1 Introduction -- 11.2 Randomness and Probability -- 11.3 Probability Distributions and Stochastic Processes -- 11.4 The Law of Large Numbers and Limit Theorems.

11.5 Analysis of Stochastic Associations: Correlation and Regression.