Part I Applied Methodology
1 Introduction to Quantitative Physiology 3
1.1 Understanding Physiology 3
1.2 Towards Quantitative Science 4
1.3 FromGenome to Physiome 5
1.4 Dealing with Complexity 6
1.5 Why It Is Timely to Study Quantitative Physiology 6
1.5.1 Multi-Omic Revolution in Biology 6
1.5.2 Big Data and PersonalisedMedicine 7
1.5.3 Genetic Editing and Synthetic Biology 8
1.6 Questions 8
References 8
2 Systems and Modelling 11
2.1 Modelling Process 11
2.2 Physiological Organ Systems 13
2.3 EquationModels 14
2.4 Using ODEs in Modelling Physiology 16
2.4.1 Modelling Oscillations 16
2.4.2 Linear Stability Analysis 16
2.4.3 Solving ODEs with the δ-Function 17
2.5 Conservation Laws in Physiology 18
2.5.1 Conservation ofMomentumand Energy 18
2.5.2 Boxing With and Without Gloves 19
2.5.3 RotationalMovement 20
2.6 Questions 20
References 21
3 Introduction to Basic Modelling 23
3.1 Building a SimpleMathematicalModel 23
3.1.1 Model of Falling Flea 23
3.1.2 Scaling Arguments. 25
3.1.3 Example:How High Can an Animal Jump? 25
3.1.4 Example:How Fast Can we Walk before Breaking into a Run? 25
3.2 Models that InvolveMetabolic Rate 26
3.2.1 Modelling Metabolic Rate 26
3.2.2 Example:Why do Large Birds find it Harder to Fly? 27
3.2.3 Ludwig von Bertalanffy's GrowthModel 28
3.3 Questions 29
Reference 29
4 Modelling Resources 31
4.1 Open Courses 31
4.2 Modelling Software 31
4.3 Model Repositories 34
4.4 Questions 35
References 35
Part II Basic Case Studies
5 Modelling Gene Expression 39
5.1 Modelling Transcriptional Regulation and Simple Networks 39
5.1.1 Basic Notions and Equations 39
5.1.2 Equations for Transcriptional Regulation 39
5.1.3 Examples of Some Common Genetic Networks 41
5.2 Simultaneous Regulation by Inhibition and Activation 42
5.3 Autorepressor with Delay 43
5.4 Bistable Genetic Switch 44
5.5 Questions 44
References 45
6 Metabolic Network 47
6.1 Metabolismand Network 47
6.2 ConstructingMetabolic Network 49
6.3 Flux Balance Analysis 50
6.4 MyocardialMetabolic Network 51
6.5 Questions 51
References 52
7 Calcium Signalling 53
7.1 Functions of Calcium 53
7.2 Calcium Oscillations 54
7.3 CalciumWaves 59
7.4 Questions 59
References 60
8 Modelling Neural Activity 61
8.1 Introduction to Brain Research 61
8.2 The Hodgkin-Huxley Model of Neuron Firing 62
8.3 The FitzHugh-Nagumo Model:A Model of the HH Model 63
8.3.1 Analysis of Phase Plane with Case Ia=0 63
8.3.2 Case Ia>0 and Conditions to Observe a Limit Cycle 64
8.4 Questions 65
References 66
9 Blood Dynamics 67
9.1 Blood Hydrodynamics 67
9.1.1 Basic Equations 67
9.1.2 Poiseuille's Law 67
9.2 Properties of Blood and ESR 68
9.3 Elasticity of Blood Vessels 69
9.4 The PulseWave 69
9.5 Bernoulli's Equation and What Happened to Arturo Toscanini in 1954 70
9.6 The Korotkoff Sounds 71
9.7 Questions 71
Reference 72
Contents xvii
10 Bone and Body Mechanics 73
10.1 Elastic Deformations and the Hooke's Law 73
10.2 Why Long Bones are Hollow or Bending of Bones 74
10.3 Viscoelasticity of Bones 77
10.4 Questions 83
Reference 83
Part III Complex Applications
11 Constructive Effects of Noise 87
12 Complex and Surprising Dynamics in Gene Regulatory Networks 147
13 Modelling Complex Phenomena in Physiology 189
13.1 Cortical Spreading Depression (CSD) 189
13.1.1 What is CSD 189
13.1.2 Models of CSD 189
13.1.3 Applications of CSD Models 192
13.1.4 Questions 196
13.2 Heart Physiome 197
13.2.1 Cardiovascular System 197
13.2.2 Heart Physiome 198
13.2.3 Multi-Level Modelling 199
13.2.4 Questions 201
13.3 Modelling of Kidney Autoregulation 202
13.3.1 Renal Physiology 202
13.3.2 Experimental Observations 204
13.3.3 Model of Nephron Autoregulation 205
13.3.4 Questions.209
13.4 Brain Project 209
13.4.1 Mystery of Brain 209
13.4.2 Brain Projects 210
13.4.3 Brain Simulation 212
13.4.4 Mammalian Brain as a Network of Networks 215
13.4.5 Calculation of Integrated Information 223
13.4.6 Astrocytes and Integrated Information Theory of Consciousness 224
13.4.7 Questions 233
References 233
