The Physics of Cerebrovascular Diseases

, by Hademenos, George J.; Massoud, Tarik F.

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ISBN: 9781563965586 | 1563965585
Cover: Hardcover
Copyright: 1/1/1998

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Disease of the blood vessels of the brain currently ranks among the leading causes of death in western countries and leads to significan problems in health care. The neurological effects of non-fatal strokes can be devastating. Modern treatment methods, however, can significantly alleviate these. The improvements have been developed from an understanding of the biophysical basis of blod flow in the brain. This textbook provides a review of our current understanding of the physical phenomena associated with the flow of blood through the brain and applies these concepts to the physiological and medical aspects of cerebrovascular disease in a way that will be useful to both the scientist and the clinician. Specifically it discusses: - the physical bases for the development of cerebrovascular disease and for its clinical consequences - specific current and possible future therapies - experimental, clinical, and computational techniques used to investigate cerebrovascualr disease - blood dynamics and its role - imaging methods used in the diagnosis and management of cerebrovascualr disease. Intended for a one- or two-semester course in biophysics, biomedical engineering or medical physics, the book will also be of interest to medical students and interns in neurology and cardiology and will provide a useful overview of current practice for researchers and clinicians. A volume in the AIP International Series in Basic and Applied

Foreword

vii

(2)

Series Preface

(2)

Preface

(4)

Acknowledgments

Chapter 1. Mathematical Fundamentals

(38)

1.1 Introduction

(1)

1.2 Functional Analysis

(8)

1.2.1 Polynomial Functions

(1)

1.2.2 Trigonometric Functions

(3)

1.2.3 Exponential Functions

(1)

1.2.4 Logarithmic Functions

(1)

1.2.5 Special Functions

(1)

1.3 Differential Calculus

(2)

1.4 Integral Calculus

(3)

1.5 Ordinary Differential Equations

(4)

1.5.1 Radioactive Decay

(1)

1.5.2 Electrical Circuits

(2)

1.5.3 Harmonic Oscillator

(1)

1.6 Vector Analysis

(6)

1.6.1 Resolution of Vectors

(1)

1.6.2 Addition and Subtraction of Vectors

(1)

1.6.3 Multiplication of Vectors

(2)

1.7 Partial Differential Equations

(3)

1.7.1 The Del Operator

(1)

1.7.2 The Laplacian Operator

(1)

1.8 Matrices

(3)

1.8.1 Vector Multiplication

(1)

1.8.2 Image Processing

(1)

1.9 Fourier Analysis

(2)

1.10 Complex Variables

(2)

1.11 Summary

(1)

1.12 References

(1)

1.13 Problems

(2)

Chapter 2. The Physics of Elasticity

(29)

2.1 Introduction

(2)

2.2 Stress

(3)

2.3 Strain

(2)

2.4 Hooke's Law

(2)

2.5 Elastic Modulus

(1)

2.6 Elastic Limit

(2)

2.7 Laplace's Law

(4)

2.7.1 Laplace's Law for an Elastic Cylinder

(2)

2.7.2 Laplace's Law for an Elastic Sphere

(2)

2.8 Equations of Motion of Elastic Objects

(7)

2.8.1 Equation of Motion of an Elastic Sphere

(6)

2.8.2 Equation of Motion of an Elastic Cylinder

(1)

2.9 Viscoelasticity

(2)

2.10 Summary

(1)

2.11 References

(3)

2.12 Problems

(1)

Chapter 3. Circulation: Structure and Physiology

(33)

3.1 Introduction

(2)

3.2 Physics of the Heart

(3)

3.3 Circulatory Network: General Considerations

(3)

3.3.1 Blood Vessel Types and Structure

(1)

3.3.2 Mechanical Properties of Vessels

(1)

3.3.3 Physiological Properties of Vessels

(1)

3.4 Circulatory Network: Specific Considerations

(6)

3.4.1 Blood Pressure

(1)

3.4.2 Arterial Pulse

(1)

3.4.3 Resistance and Capacitance Vessels

(1)

3.4.4 Arterial Blood Flow and Pressure

(2)

3.4.5 Methods for Measuring Blood Pressure

(2)

3.5 Bioenergetics of the Circulation

(1)

3.6 Analog Models of the Circulation

(5)

3.6.1 Windkessel Model

(1)

3.6.2 Electrical Analogs

(3)

3.7 Circulatory Network: Cerebral Circulation

(9)

3.7.1 Vascular Supply of the Brain

(2)

3.7.2 Cerebral Blood Flow

(1)

3.7.3 Experimental Models of the Cerebral Circulation

(1)

3.7.4 Measurement of Cerebral Blood Flow

(5)

3.7.4.1 Nitrous Oxide Inhalation

(1)

3.7.4.2 Computed Tomography

(2)

3.7.4.3 Single-Photon Emission Computed Tomography

(1)

3.7.4.4 Positron Emission Tomography

(1)

3.7.4.5 Magnetic Resonance Imaging

(1)

3.8 Summary

(1)

3.9 References

(3)

3.10 Problems

100

(1)

Chapter 4. Hemodynamics: The Physics of Blood Flow

101

(31)

4.1 Introduction

101

(1)

4.2 Fluid Mechanics and Dynamics

102

(10)

4.2.1 Dynamic Characteristics of a Fluid

102

(4)

4.2.1.1 Viscosity

103

(1)

4.2.1.2 Laminar versus Turbulent Flow

104

(1)

4.2.1.3 Steady versus Pulsatile Flow

105

(1)

4.2.1.4 Compressible versus Incompressible Flow

105

(1)

4.2.1.5 Newtonian versus Non-Newtonian Fluid Flow

105

(1)

4.2.1.6 Vessel Structure

106

(1)

4.2.2 Equation of Continuity

106

(5)

4.2.3 Streamlines

111

(1)

4.3 Properties of Blood

112

(1)

4.4 Hemodynamics

113

(9)

4.4.1 Steady Flow through a Rigid Tube

113

(3)

4.4.2 Pulsatile Flow through a Rigid Tube

116

(6)

4.4.2.1 Navier-Stokes Equation

116

(6)

4.5 Experimental Measurement Techniques of Vascular Blood Flow

122

(4)

4.5.1 Electromagnetic Flowmeter

122

(2)

4.5.2 Ultrasonic Doppler Probe Flowmeter

124

(1)

4.5.3 Videodensitometric Methods

125

(1)

4.6 Hemodynamics of a Catheter

126

(1)

4.7 Summary

127

(1)

4.8 References

127

(3)

4.9 Problems

130

(2)

Chapter 5. The Physics of Stroke

132

(34)

5.1 Introduction

132

(2)

5.2 Biophysical and Hemodynamic Mechanisms of Stroke

134

(3)

5.2.1 Atherosclerosis

134

(2)

5.2.2 Embolus

136

(1)

5.2.3 Thrombus

136

(1)

5.2.4 Hemorrhage

136

(1)

5.2.5 Vasospasm

137

(1)

5.3 Hemodynamics of the Carotid Artery Bifurcation

137

(4)

5.3.1 Hemodynamics at the Vessel Curvature

138

(2)

5.3.2 Hemodynamics at an Arterial Bifurcation Apex

140

(1)

5.4 Hemodynamics of a Stenosis

141

(7)

5.4.1 Reduced Volumetric Blood Flow Rate

145

(1)

5.4.2 Increased Blood Flow Velocity

146

(1)

5.4.3 Compliance Mismatch

147

(1)

5.5 Theoretical and Experimental Models of Stroke

148

(1)

5.6 Diagnostic Techniques for Stroke

149

(6)

5.6.1 The Physics of Ultrasound Imaging

151

(4)

5.7 Assessment of Risk for Stroke

155

(1)

5.8 Therapeutic Treatments for Stroke

156

(2)

5.8.1 Carotid Endarterectomy

157

(1)

5.8.2 Carotid Artery Angioplasty

158

(1)

5.8.3 Pharmacological Treatment

158

(1)

5.9 Summary

158

(1)

5.10 References

159

(5)

5.11 Problems

164

(2)

Chapter 6. The Physics of Intracranial Aneurysms

166

(72)

6.1 Introduction

166

(2)

6.2 Natural History of Intracranial Aneurysms

168

(6)

6.3 Experimental Models of Intracranial Aneurysms

174

(9)

6.3.1 Biomathematical Models

174

(2)

6.3.2 Computational Simulations

176

(4)

6.3.3 In Vitro Vascular Phantoms

180

(1)

6.3.4 Animal Models

181

(2)

6.4 Saccular Aneurysms

183

(23)

6.4.1 Initiation of Saccular Aneurysms

183

(7)

6.4.1.1 Static Equilibrium of an Arterial Bifurcation

185

(1)

6.4.1.2 Hemodynamics at an Arterial Bifurcation

186

(4)

6.4.2 Development of Saccular Aneurysms

190

(8)

6.4.2.1 An Equation of Motion for a Saccular Aneurysm

194

(3)

6.4.2.2 Intra-Aneurysmal Hemodynamics

197

(1)

6.4.3 Rupture of Saccular Aneurysms

198

(8)

6.4.3.1 A Critical Radius for Saccular Aneurysms

201

(3)

6.4.3.2 The Influence of Resonance in Aneurysm Rupture

204

(2)

6.5 Fusiform Aneurysms

206

(6)

6.5.1 Initiation and Development of Fusiform Aneurysms

208

(3)

6.5.2 Rupture of Fusiform Aneurysms

211

(1)

6.6 Clinical Assessment of Aneurysm Stability and Risk of Aneurysm Rupture

212

(2)

6.7 Diagnostic Techniques for Intracranial Aneurysms

214

(1)

6.8 Therapeutic Techniques for Intracranial Aneurysms

215

(8)

6.9 Summary

223

(1)

6.10 References

224

(12)

6.11 Problems

236

(2)

Chapter 7. The Physics of Intracranial Arteriovenous Malformations

238

(53)

7.1 Introduction

238

(1)

7.2 Natural History of Intracranial Arteriovenous Malformations

239

(1)

7.3 Anatomy and Physiology of Intracranial Arteriovenous Malformations

240

(7)

7.3.1 Anatomy of Intracranial AVMs

240

(4)

7.3.2 Hemodynamics of Intracranial AVMs

244

(3)

7.3.2.1 Cerebrovascular Steal

245

(1)

7.3.2.2 Autoregulatory Capacity

246

(1)

7.4 Experimental Models of Intracranial AVMs

247

(32)

7.4.1 Biomathematical Models

247

(32)

7.4.1.1 An Electrical Network Model of Intracranial AVMs

248

(31)

7.5 Management of Intracranial AVMs

279

(4)

7.6 Summary

283

(1)

7.7 References

283

(7)

7.8 Problems

290

(1)

Glossary

291

(9)

Answers to Odd-Numbered Problems

300

(9)

Subject Index

309

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The Physics of Cerebrovascular Diseases

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