Introduction to Modeling in Physiology and Medicine

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Introduction to Modeling in Physiology and Medicine
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Preface to the second edition
Preface to the first edition
1 Introduction
	1.1 Introduction
	1.2 The book in context
	1.3 The major ingredients
	1.4 Readership and prerequisites
	1.5 Organization of the book
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
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
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 Gastrointestinal 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
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
			5.4.1.1 The single-capillary model
			5.4.1.2 The capillary–interstitial fluid model
			5.4.1.3 The capillary–interstitial fluid-cell model
			5.4.1.4 The whole-organ model
		5.4.2 Hepatic removal of materials
		5.4.3 Renal medulla
			5.4.3.1 Model assumptions
			5.4.3.2 Principles of the mathematical formulation for the tubular structures
			5.4.3.3 Interstitial compartment
			5.4.3.4 Transmural flux
	5.5 Nonlinear modeling
		5.5.1 The action potential model
			5.5.1.1 An electrical model of the cell membrane
			5.5.1.2 The Hodgkin–Huxley model
			5.5.1.3 Potassium conductance
			5.5.1.4 Sodium conductance
		5.5.2 Enzyme dynamics
		5.5.3 Baroreceptors
		5.5.4 Central nervous control of heart rate
		5.5.5 Compartmental modeling
			5.5.5.1 The model
		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
			5.5.9.1 The controlled system
			Inspiration
			Expiration
			5.5.9.2 The controller
			Inspiratory flow controller
			Inspiratory time controller
			Expiratory time controller
	5.6 Time-varying modeling
		5.6.1 An example in cardiac modeling
	5.7 Stochastic modeling
		5.7.1 Cellular modeling
			5.7.1.1 The conceptual model
			5.7.1.2 The mathematical model
		5.7.2 Insulin secretion
		5.7.3 Markov model
	5.8 Summary
	5.9 Exercises and assignment questions
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
7 Parametric modeling—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
			Stage A
			Stage B
				Stage B is not necessary
				Dual input/four output experiment
				Two input/three output experiment
	7.7 Summary
	7.8 Exercises and assignment questions
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
9 Nonparametric 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
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
			Empirical
			Theoretical
			Pragmatic
			Heuristic
	10.3 Validation strategies
		10.3.1 Validation of a single model—basic approach
			Overall patterns of response
			Features of response
		10.3.2 Validation of a single model—additional quantitative tools for numerically identified models
			Parameter precision
			Residuals of the mismatch between model and data
			Parameter plausibility
		10.3.3 Validation of competing models
			Goodness of fit
			Features of response
			Model plausibility
	10.4 Good practice in good modeling
	10.5 Summary
	10.6 Exercises and assignment questions
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
			11.5.1.1 First-phase secretion
			11.5.1.2 Second-phase secretion
		11.5.2 The whole-body model
	11.6 Case study 6: a model of insulin control
		WARNING!!! DUMMY ENTRY
			Glucose effectiveness
			Insulin sensitivity
	11.7 Case study 7: a simulation model of the glucose-insulin system
		11.7.1 Model formulation
			11.7.1.1 Glucose subsystem
			11.7.1.2 Insulin subsystem
			11.7.1.3 Unit process models and identification
				Endogenous glucose production
				Glucose rate of appearance
				Glucose utilization
				Insulin secretion
				Glucose renal excretion
		11.7.2 Results
			Meal in normal subject
			Meal in type 2 diabetic subject
			Daily life for a normal subject
			Daily life for a subject with impaired glucose tolerance
	11.8 Case study 8: the University of Virginia (UVA)/Padova type 1 simulator – in silico artificial pancreas, glucose sensor...
		11.8.1 In silico artificial pancreas trials
		11.8.2 In silico glucose sensors trials
		11.8.3 In silico inhaled insulin trials
	11.9 Case study 9: illustrations of Bayesian estimation
		11.9.1 Database
		11.9.2 The two-exponential model: ML versus MAP
		11.9.3 The three-exponential model: ML versus MAP
		11.9.4 Two versus three-exponential model order choice
		11.9.5 Data-poor situation: ML versus MAP
	11.10 Postscript
References
Index
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