Chapter 1 – Introduction
- Introduction
- The book in context
- The major ingredients
- Readership
- Organization of the book
Chapter 2 – Physiological Complexity and the Need for Models
2.1 Introduction
2.2 Complexity
2.3 System dynamics
2.3.1 First-order linear time-invariant systems
2.3.2 The dynamic behavior of first-order linear time-invariant systems – solution by
integration
2.3.3 The classical solution for a first-order system
2.3.4 General case of a first-order linear system
2.4 Feedback
2.4.1 Negative feedback
2.4.2 Positive feedback
2.4.3 Inherent feedback
2.4.4 Combining negative and positive feedback
2.4.5 Derivative and integral feedback
2.4.6 Effects of feedback on the complexity of system dynamics
2.5 Control in physiological systems
2.5.1 General features
2.5.2 Enzymes
2.5.3 Hormones
2.6 Hierarchy
2.7 Redundancy
2.8 Function and behavior and their measurement
2.9 Challenges to understanding
2.10 Exercises and assignment questions
Chapter 3 – Models and the Modeling Process
3.1 Introduction
3.2 What is a model?
3.3 Why model? – the purpose of modeling
3.4 How do we model? – the modeling process
3.5 Model formulation
3.6 Model identification
3.7 Model validation
3.8 Model simulation
3.9 Summary
3.10 Exercises and assignment questions
Chapter 4 – Modeling the Data
4.1 Introduction
4.2 The basis of data modeling
4.3 The why and when of data models
4.4 Approaches to data modeling
4.5 Modeling a single variable occurring spontaneously
4.5.1 Temperature
4.5.2 Urine potassium
4.5.3 Gastro-intestinal rhythms
4.5.4 Hormonal time series
4.6 Modeling a single variable in response to a perturbation
4.6.1 Glucose home monitoring data
4.6.2 Response to drug therapy – prediction of bronchodilator response
4.7 Two variables causally related
4.7.1 Hormone/hormone and substrate/hormone series
4.7.2 Urine sodium response to water loading
4.8 Input/output modeling for control
4.8.1 Pupil control
4.8.2 Control of blood glucose by insulin
4.8.3 Control of blood pressure by sodium nitroprusside
4.9 Input/output modeling: impulse response and deconvolution
4.9.1 Impulse response estimation
4.9.2 The convolution integral
4.9.3 Reconstructing the input
4.10 Summary
4.11 Exercises and assignment questions
Chapter 5 – Modeling the System
5.1 Introduction
5.2 Static models
5.3 Linear modeling
5.3.1 The windkessel circulatory model
5.3.2 Elimination from a single compartment
5.3.3 Gas exchange
5.3.4 The dynamics of a swinging limb
5.3.5 A model of glucose regulation
5.4 Distributed modeling
5.4.1 Blood-tissue exchange
5.4.2 Hepatic removal of materials
5.4.3 Renal medulla
5.5 Nonlinear modeling
5.5.1 The action potential model
5.5.2 Enzyme dynamics
5.5.3 Baroreceptors
5.5.4 Central nervous control of heart rate
5.5.5 Compartmental modeling
5.5.6 Insulin receptor regulation
5.5.7 Insulin action modeling
5.5.8 Thyroid hormone regulation
5.5.9 Modeling the chemical control of breathing
5.6 Time-varying modeling
5.6.1 An example in cardiac modeling
5.7 Stochastic modeling
5.7.1 Cellular modeling
5.7.2 Insulin secretion
5.7.3 Markov model
5.8 Summary
5.9 Exercises and assignment questions
Chapter 6 – Model Identification
6.1 Introduction
6.2 Data for identification
6.2.1 Selection of test signals
6.2.2 Transient test signals
6.2.3 Harmonic test signals
6.2.4 Random signal testing
6.3 Errors
6.4 The way forward
6.4.1 Parameter estimation
6.4.2 Signal estimation
6.5 Summary
6.6 Exercises and assignment questions
Chapter 7 – Parametric Models – The Identifiability Problem
7.1 Introduction
7.2 Some examples
7.3 Definitions
7.4 Linear models – the transfer function method
7.5 Nonlinear models – the Taylor series expansion method
7.6 Qualitative experimental design
7.6.1 Fundamentals
7.6.2 An amino acid model
7.7 Summary
7.8 Exercises and assignment questions
Chapter 8 – Parametric Models – The Estimation Problem
8.1 Introduction
8.2 Linear and nonlinear parameters
8.3 Regression – basic concepts
8.3.1 The residual
8.3.2 The residual sum of squares
8.3.3 The weighted residual sum of squares
8.3.4 Weights and error in the data
8.4 Linear regression
8.4.1 The problem
8.4.2 Test on residuals
8.4.3 An example
8.4.4 Extension to the vector case
8.5 Nonlinear regression
8.5.1 The scalar case
8.5.2 Extension to the vector case
8.5.3 Algorithms
8.5.4 An example
8.6 Tests for model order
8.7 Maximum likelihood estimation
8.8 Bayesian estimation
8.9 Optimal experimental design
8.10 Summary
8.11 Exercises and assignment questions
- Chapter 9 – Non-parametric Models - Signal Estimation
9.1 Introduction
9.2 Why is deconvolution important?
9.3 The problem
9.4 Difficulty of the deconvolution problem
9.5 The regularization method
9.5.1 Fundamentals
9.5.2 Choice of the regularization parameter
9.5.3 The virtual grid
9.6 Summary
9.7 Exercises and assignment questions
Chapter 10 - Model Validation
10.1 Introduction
10.2 Model validation and the domain of validity
10.2.1 Validation during model formulation
10.2.2 Validation of the completed model
10.3 Validation strategies
10.3.1 Validation of a single model – basic approach
10.3.2 Validation of a single model – additional quantitative tools for numerically identified
models
10.3.3 Validation of competing models
10.4 Good practice in good modeling
10.5 Summary
10.6 Exercises and assignment questions
Chapter 11 - Case Studies
11.1 Case study 1: A sum of exponentials tracer disappearance model
11.2 Case study 2: Blood flow modeling
11.3 Case study 3: Cerebral glucose modeling
11.4 Case study 4: Models of the ligand-receptor system
11.5 Case study 5: A model of insulin secretion: from a stochastic cellular model to a whole-body model
11.5.1 The stochastic cellular model
11.5.2 The whole-body model
11.6 Case study 6: A model of insulin control during an intravenous and oral glucose tolerance test
11.7 Case study 7: A simulation model of the glucose-insulin system
11.7.1 Model formulations
11.7.2 Results
11.8 Case study 8: The UVA/Padova type 1 diabetes simulator: in silico clinical and drug trials
11.9 Case study 9: Illustrations of Bayesian estimation
11.10 Postscript
References
Index
