Fundamentals of Chaos and Fractals for Cardiology

Preface
Acknowledgments
Contents
1: Introduction
	1.1	 Nonlinear Cardiovascular System Examples
		1.1.1	 Blood Vessel Mechanics
		1.1.2	 Cardiac Valve
		1.1.3	 Chaotic Signals
	1.2	 Fractals
		1.2.1	 Branching Structures
	1.3	 Book Organization
	References
Part I: Fundamentals of Nonlinear Dynamics and Chaos in Cardiology
	2: Topics in Nonlinear Dynamics
		2.1	 The Cardiovascular System
		2.2	 Respiratory Physiology
		2.3	 Population Dynamics
		2.4	 Population Model Solution
		2.5	 Bio-oscillation
		2.6	 Basic Nonlinear Oscillator
		2.7	 Nonlinear Dynamic Properties
		References
	3: Bifurcation Mapping and Chaos
		3.1	 The Bifurcation Diagram Procedure
		References
	4: Identifying Chaos
		4.1	 Chaos Versus Noise and Chaos in Experimental Data
		4.2	 Frequency Spectrum
		4.3	 The Bifurcation Diagram
		4.4	 The Poincare and Phase Plots
		References
	5: Controlling Chaos
		5.1	 Introduction
		5.2	 Method of Controlling Chaos
		5.3	 Control of Chaos Applied to Cardiac Arrhythmia Treatment
		References
	6: Nonlinear Cardiology
		6.1	 Introduction: The Cardiac Arrhythmia
		6.2	 Nonlinear Oscillators
		References
Part II: Fractals
	7: Fractal Geometry
		7.1	 Introduction to Fractals
		7.2	 Biological Branching Structure Examples
		7.3	 Fractal Time and the Mathematical Fractal
		7.4	 Fractals Defined
		7.5	 Defining the Fractal Dimension
		7.6	 Measuring the Fractal Dimension
		7.7	 Statistical Fractals
		References
	8: Fractal Time and Noise
		8.1	 Three-Dimensional Fractals
		8.2	 Fractal Time
		8.3	 Fractal Time Generation
		8.4	 Fractal Time in the Frequency Domain
		8.5	 The Hurst Dimension
		References
	9: Biomedical Signal Analysis and Fractal Time
		9.1	 Fractals and Time Signals
		9.2	 Finding Fractal D of Time Signals
		9.3	 Procedure to Test for Random Signals Using the Fractal D
		9.4	 Fractals in Cardiology or “Nonlinear Cardiology”
		9.5	 Measuring Heart Rate Variability
		9.6	 Chronobiology
		References
	10: Deterministic Fractals
		10.1	 Introduction
		10.2	 The Julia Set
		References
	11: Fractals and the Cardiovascular System
		11.1	 Myocardial Blood Flow
		11.2	 Microcirculation Branching Structures
		11.3	 Vascular Design Principles
		References
	12: Recurrence and the Embedding Dimension
		12.1	 Introduction
		12.2	 Recurrence Analysis Procedure
		Reference
Part III: Cardiovascular Dynamics Applications
	13: Nonlinear Flow Dynamics and Chaos in a Flexible Vessel Model
		13.1	 Introduction
		13.2	 The Model Geometry
		13.3	 Arterial Segment Dynamic Flow Model
		13.4	 Computational Flow Evaluation
		13.5	 Nonlinear Vessel Segment Analysis
		13.6	 Summary
		References
	14: The Origin of Heart Rate Variation Using a Nonlinear Modeling Approach
		14.1	 Introduction
		14.2	 Physiological Modeling Approach to HRV
		14.3	 Heart Rate Regulation Physiology: The Baroreceptor Reflex System
		14.4	 The SA Node Oscillator
		14.5	 The Ventricular Pressure
		14.6	 The Arterial Circulation and Blood Pressure
		14.7	 The Baroreceptor Function
		14.8	 CNS Function
		14.9	 Modeling Heart Rate and Variability
		14.10	 Summary and Conclusion
		References
	15: Nonlinear Oscillator Circuit Model Lab Exercise (Properties of Self-Excitable Cells)
		15.1	 Introduction: Self-Excitable Oscillations in Excitable Cells
		References
Correction to: Nonlinear Flow Dynamics and Chaos in a Flexible Vessel Model
Index