Modelling of Complex Signals in Nerves

Preface
Acknowledgements
Contents
Chapter 1 Introduction
	References
Part I Complexity and Waves
Chapter 2 Complexity
	2.1 Complexity of Physical Systems
	2.2 Complexity in Biology
	2.3 Mathematical Modelling
	References
Chapter 3 Waves
	3.1 Preliminaries
	3.2 Mathematical Physics
	3.3 Wave Equations
	3.4 Reaction-Diffusion Equations
	3.5 Physical Effects
	3.6 TheWave Equation with Forcing
	3.7 Solitary Waves and solitons
	References
Part II Dynamical Processes in Nerve Axons
Chapter 4 Nervous Signals
	References
Chapter 5 Dynamical Effects in Nerves
	References
Part III Modelling of Dynamical Physiological Processes
Chapter 6 Mathematics of Single Effects
	6.1 The Action Potential
		6.1.1 The Classical Hodgkin-Huxley Model
		6.1.2 The FitzHugh-Nagumo Model
		6.1.3 The Evolution Equation
	6.2 The LongitudinalWave in a Biomembrane
		6.2.1 Model Derivation
		6.2.2 Steady Solutions
		6.2.3 Solution Types
		6.2.4 Solutions Emerging from Arbitrary Initial Conditions
		6.2.5 Interaction of Solitons
		6.2.6 Discussion
	6.3 TheWave Equations with Coupling
	References
Chapter 7 Physical Mechanisms
	7.1 Basic Elements of an Ensemble of Waves
	7.2 Qualitative Observations from Experiments
	7.3 Modelling of Coupled Signals and Coupling Forces
	7.4 Possible Interactions
	7.5 The Concept of Internal Variables
	References
Chapter 8 An Ensemble ofWaves
	8.1 The Model
		8.1.1 Notations, Variables and Parameters in the Model
		8.1.2 Coupling Forces
	8.2 Energetical Balance
	8.3 Simplifications
		8.3.1 Action Potential
		8.3.2 Pressure Wave in Axoplasm
		8.3.3 LongitudinalWave in Biomembrane
		8.3.4 Temperature
		8.3.5 Neglecting Effects
	8.4 Modifications
		8.4.1 Properties of the Environment
		8.4.2 Properties of Structures
		8.4.3 Mechanisms
		8.4.4 Systems
	8.5 Dimensions
		8.5.1 Governing Equations in Physical Units
		8.5.2 Coupling Forces in Physical Units
		8.5.3 Summary
	References
Chapter 9 In Silico Experiments
	9.1 Numerical Method
	9.2 AP Coupled to Single Mechanical Effects
	9.3 The AP Coupled to All Mechanical Effects
	9.4 Temperature Changes Accompanying the AP
	9.5 Full Coupled Model
	9.6 Dimensionalised Example
	References
Chapter 10 Final Remarks
	References
Appendices
	Appendix A The Numerical Scheme
		A.1 Initial and Boundary Conditions
		A.2 The Derivatives and Integration
		A.3 Handling of Mixed Derivatives
		A.4 The Time Derivatives VZ•[Z and PZ
		A.5 Technical Details and Numerical Accuracy
		References
	Appendix B The example scripts
		B.1 Example: the script for an example
		B.2 Example: the script for visualisation
Index