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9780195168310

Foundations of Biomedical Ultrasound

by
  • ISBN13:

    9780195168310

  • ISBN10:

    0195168313

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2006-09-07
  • Publisher: Oxford University Press

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Summary

"Drawn from many years of classroom notes, student reactions, and personal experience, Foundations of Biomedical Ultrasound covers the fundamental physics and engineering behind ultrasound systems, properties of acoustic wave motion, the behavior of waves in various media, nonlinear wave propagation, and the formation of ultrasound images. It provides a comprehensive coverage of the field and is an indispensable reference for medical and industrical professionals working with and designing ultrasound systems. The text also provides a valuable introduction to the subject for students."--BOOK JACKET.

Table of Contents

1 Introduction
3(93)
1.1 Physical Nature of Acoustic Wave Motion
4(4)
1.1.1 Wave Propagation in a Semi-Infinite Medium
4(2)
1.1.2 Longitudinal and Transverse Waves
6(2)
1.1.3 Rayleigh and Lamb Waves
8(1)
1.2 Properties of Isotropic Media
8(7)
1.2.1 Compressibility and Bulk Modulus: Liquids and Gases
8(5)
1.2.2 Solids: Young's Modulus, Poisson's Ratio, and Shear Modulus
13(1)
1.2.3 Temperature Effects
14(1)
1.3 Equations Governing Wave Propagation in Fluids
15(9)
1.3.1 Euler's Equation of Motion
16(2)
1.3.2 Continuity Equation
18(1)
1.3.3 Equation of State
19(1)
1.3.4 Navier-Stokes Equation
20(1)
1.3.5 Small-Signal Approximations
21(3)
1.4 Propagation in Liquid and Solid Media
24(17)
1.4.1 Phase and Group Speed
24(5)
1.4.2 Longitudinal Wave Speed in Fluids and Gases
29(7)
1.4.3 Compressional and Shear Wave Propagation in Solids
36(5)
1.5 Impedance, Energy Density, Intensity, and Radiation Pressure
41(8)
1.5.1 Specific Acoustic Impedance, Characteristic Impedance, and Acoustic Impedance
41(1)
1.5.2 Energy and Energy Density
42(2)
1.5.3 Energy Flux and Intensity
44(1)
1.5.4 Radiation Pressure
45(4)
1.6 Reflection and Refraction
49(13)
1.6.1 Compressional Waves in Fluid Media
51(8)
1.6.2 Wave-Mode Conversion
59(3)
1.7 Elements of Diffraction
62(7)
1.7.1 Historical Background: Huygens' Principle
62(2)
1.7.2 Approximate Analysis of Diffraction by a Half-Plane
64(2)
1.7.3 Sommerfeld's Exact Analysis of Diffraction by a Half-Plane
66(2)
1.7.4 Babinet's Principle
68(1)
1.8 Attenuation, Absorption, Scattering, and Dispersion
69(18)
1.8.1 Absorption and Scattering Attenuation Coefficients
72(9)
1.8.2 Heat Generation
81(3)
1.8.3 Absorption and the Bulk (Volume) Viscosity of Fluids
84(2)
1.8.4 Shear Wave Absorption in Fluids and Tissue
86(1)
Problems
87(3)
References
90(6)
2 Theoretical Basis for Field Calculations
96(39)
2.1 The Rayleigh-Sommerfeld Diffraction Equations
97(13)
2.1.1 Volume Source in an Unbounded Medium
100(2)
2.1.2 Source Distribution Enclosed by a Surface in an Infinite Medium
102(1)
2.1.3 Bounded Region with no Internal Sources
103(4)
2.1.4 Diffraction Equations
107(3)
2.2 The Rayleigh Integral
110(11)
2.2.1 Impulse Response
110(2)
2.2.2 The Piston Transducer On-Axis
112(9)
2.3 Angular Spectrum Method
121(8)
2.3.1 Basic Principles
122(1)
2.3.2 Angular Spectrum of the Velocity Potential and its Relation to the Velocity
123(2)
2.3.3 Transfer and Point Spread Function Representations
125(3)
2.3.4 Relation to the Rayleigh Integral
128(1)
Problems
129(2)
References
131(4)
3 Field Profile Analysis
135(92)
3.1 Angular Spectrum Method
135(8)
3.1.1 Spatial Spectrum of a Piston
136(2)
3.1.2 Angular Spectrum in Spherical Coordinates
138(1)
3.1.3 Field Profile
138(1)
3.1.4 Fourier Transform Method
139(4)
3.2 Integral Methods
143(5)
3.2.1 Rigid Baffle Boundary Condition
143(4)
3.2.2 Three Sets of Boundary Conditions
147(1)
3.2.3 Pressure Distribution On- and Off-Axis
148(1)
3.3 Impulse Response Method
148(7)
3.3.1 Piston Transducer
151(1)
3.3.2 Experimental and Theoretical Results
152(3)
3.4 Approximate Methods
155(8)
3.4.1 Fresnel and Fraunhofer Approximations
155(2)
3.4.2 Fraunhofer Approximation
157(1)
3.4.3 Fraunhofer Approximation for a Piston Transducer: Directivity Function
157(6)
3.4.4 Fresnel Approximation for a Piston Transducer
163(1)
3.5 Concave and Convex Transducers
163(13)
3.5.1 Fundamental Approximations
164(1)
3.5.2 Impulse Response Using the Ring Function Method
164(2)
3.5.3 Sinusoidal Response
166(4)
3.5.4 Velocity and Intensity
170(2)
3.5.5 Approximate Axial and Lateral Fields near the Focus
172(1)
3.5.6 Lateral Resolution and Depth of Field
173(1)
3.5.7 Comparison with Experimental Results
174(2)
3.6 Annular Ring, Annulus, and Conical Transducers
176(6)
3.6.1 Annular Ring
176(2)
3.6.2 Annulus
178(2)
3.6.3 Conical (Axicon) Geometry
180(2)
3.7 Line, Strip, Triangular, and Rectangular Elements
182(7)
3.7.1 Line Element
183(1)
3.7.2 Infinite Strip
184(1)
3.7.3 Rectangular Transducer
185(4)
3.8 Transducer Apodization
189(6)
3.8.1 Gaussian Apodization
189(6)
3.9 Diffractionless and Limited Diffraction Beams
195(10)
3.9.1 Plane Wave Solution
197(1)
3.9.2 Bessel Function Beam
198(3)
3.9.3 Superluminal Pulse
201(1)
3.9.4 X-Waves
202(3)
3.10 Effects of Attenuation
205(12)
3.10.1 Kramers-Kronig Relationships
206(1)
3.10.2 Transfer Function and Impulse Response
207(3)
3.10.3 Some Simplified Models
210(2)
3.10.4 Accounting for Attenuation and Dispersion
212(1)
3.10.5 Classical Viscous Loss
213(2)
3.10.6 Formulations for an Attenuation Power Law
215(2)
Problems
217(4)
References
221(6)
4 Nonlinear Ultrasonics
227(41)
4.1 Introduction
227(1)
4.2 Lagrange and Eulerain Coordinate Systems
228(2)
4.2.1 Density in Terms of Displacement
230(1)
4.3 Exact 1-D Waves for an Inviscid Medium
230(3)
4.3.1 Exact Equation for an Adiabatic Gas
231(1)
4.3.2 First Integral of Exact Wave Equation
232(1)
4.4 Wave Propagation Speed in a Gas
233(5)
4.4.1 Why Does the Speed Vary?
235(1)
4.4.2 Coefficient of Nonlinearity and Parameter of Nonlinearity for Liquids and Gases
236(2)
4.5 Reduced Equations
238(2)
4.5.1 Exact Form
238(1)
4.5.2 Approximate Form: Quadratic Nonlinearity
239(1)
4.6 Sinusoidal Excitation
240(2)
4.6.1 Particle Velocity
240(1)
4.6.2 Pressure Distribution
241(1)
4.7 Harmonic Content
242(2)
4.7.1 Inviscid Medium
242(1)
4.7.2 Effect of Attenuation
243(1)
4.8 Shock Wave Formation
244(3)
4.8.1 Plane Shock Waves
245(1)
4.8.2 Shock Parameter
246(1)
4.9 Effects of Nonlinearity, Diffraction, and Attenuation
247(6)
4.9.1 Burgers' Equations
248(2)
4.9.2 Khokhlov-Zabolotskaya-Kuznetsov (KZK) Equation
250(2)
4.9.3 Attenuation
252(1)
4.10 Numerical Methods and Results
253(11)
4.10.1 Using the KZK Equation
253(4)
4.10.2 Other Frequency- and Time-Domain Methods
257(7)
References
264(4)
5 Scattering of Ultrasound
268(61)
5.1 Spherical and Cylindrical Representations of a Plane Wave
269(1)
5.2 Scattering Cross-Sections
270(1)
5.3 Exact Analysis: Boundary Value Method
271(12)
5.3.1 Rigid Spherical Scatterer
272(5)
5.3.2 Compressible Spherical Scatterer
277(4)
5.3.3 Compressible Cylindrical Scatterer
281(2)
5.4 Integral Equation Methods
283(7)
5.4.1 Wave Equation for an Inhomogeneous Region
283(2)
5.4.2 Integral Scattering Equation
285(2)
5.4.3 Scattering Approximations
287(3)
5.5 Matrix Methods
290(5)
5.5.1 The T-Matrix of Waterman
290(3)
5.5.2 Scattering by a Red Blood Cell
293(2)
5.6 Time-Domain Scattering Equations
295(2)
5.7 Pulse-Echo Response
297(6)
5.7.1 Continuum Model
298(3)
5.7.2 Single Particle Model
301(2)
5.8 One-Dimensional Scattering
303(3)
5.9 Scattering by Distributions
306(18)
5.9.1 Random Distributions of Point Scatterers
307(1)
5.9.2 Backscattering Coefficient
308(1)
5.9.3 A Random Distribution of Scatterers
309(3)
5.9.4 Backscattering by Blood
312(12)
References
324(1)
Problems
324(5)
6 Ultrasound Transducers
329(84)
6.1 The Direct and Inverse Piezoelectric Effect
330(6)
6.1.1 Piezoelectric Material Development
332(3)
6.1.2 High-Frequency Materials
335(1)
6.2 Characteristic Piezoelectric Equations
336(8)
6.2.1 Constitutive Relations
339(3)
6.2.2 Piezoelectric Coupling Factor
342(2)
6.3 Ceramic and Polymer Materials
344(5)
6.3.1 Piezoceramics
344(3)
6.3.2 Piezoelectric Polymer Materials
347(2)
6.4 Methods for Enhancing the Performance
349(12)
6.4.1 Composite Materials
349(7)
6.4.2 Multilayer Transducers
356(5)
6.5 One-Dimensional Transducer Models
361(16)
6.5.1 Analysis
361(4)
6.5.2 Four Transducer Models
365(6)
6.5.3 Matrix Computation Methods
371(6)
6.6 Application of the KLM Model
377(13)
6.6.1 Quarter-Wave Matched and Air-Backed
379(1)
6.6.2 Unloaded Input Impedance
380(1)
6.6.3 Loaded Input Impedance
381(1)
6.3.4 Power Transfer Efficiency
381(7)
6.6.5 Effect of Backing
388(2)
6.7 Transient Response
390(3)
6.7.1 Impulse Response
390(2)
6.7.2 Differential Phase Delay
392(1)
6.8 Protection Circuits
393(4)
6.8.1 Low Frequency Protection Circuits
394(2)
6.8.2 High-Frequency Protection Circuits
396(1)
6.9 Noise Considerations
397(4)
6.10 Capacitive Transducers
401(4)
References
405(8)
7 Ultrasound Imaging Arrays
413(79)
7.1 Historical Background
414(13)
7.1.1 A- and B-Mode Systems
414(8)
7.1.2 Dynamic Range Issues
422(1)
7.1.3 C-Mode Imaging
422(1)
7.1.4 M-mode Recording
423(2)
7.1.5 Imaging Arrays
425(2)
7.2 Properties of Imaging Arrays
427(33)
7.2.1 Steering and Focusing: A Geometric Approach
429(8)
7.2.2 Grating and Side Lobes
437(1)
7.2.3 Linear Point Source Arrays
438(4)
7.2.4 Planar Point Source Arrays
442(1)
7.2.5 Linear Array of Rectangular Elements
442(5)
7.2.6 Obliquity Factor
447(1)
7.2.7 Sparse Arrays
448(2)
7.2.8 Inter-Element Cross-Coupling
450(1)
7.2.9 Amplitude Weighting (Apodization)
451(3)
7.2.10 Separate Transmit and Receive Apertures
454(2)
7.2.11 Wave Distortion Due to Dynamic Focusing
456(4)
7.3 Arrays for Two- and Three-Dimensional Imaging
460(17)
7.3.1 One-Dimensional Arrays
460(4)
7.3.2 Three-Dimensional Imaging
464(6)
7.3.3 Two Dimensional Arrays for Two-Dimensional and Three-Dimensional Real-Time Imaging
470(7)
7.4 Summary of Design Factors
477(1)
7.5 Array Field Synthesis
477(4)
7.5.1 Field Conjugation Method
479(2)
7.5.2 A Pseudoinverse Method
481(1)
References
481(11)
8 Ultrasound Imaging Systems: Design, Properties, and Applications
492(116)
8.1 B-Mode Imaging Systems
492(5)
8.1.1 Array System Design
492(2)
8.1.2 Envelope Estimation
494(1)
8.1.3 Imaging Theory
494(3)
8.2 Image Speckle
497(13)
8.2.1 Speckle Analysis
500(6)
8.2.2 Speckle Reduction Techniques
506(4)
8.3 Resolution, Contrast, and Signal-to-Noise Ratio
510(7)
8.3.1 Axial Resolution
511(1)
8.3.2 Contrast and Resolution
512(3)
8.3.3 Signal-to-Noise Ratio
515(2)
8.4 Coded Transmission Systems
517(13)
8.4.1 Principles
517(2)
8.4.2 FM Chirp
519(6)
8.4.3 Golay Code
525(2)
8.4.4 Imaging Blood Flow
527(3)
8.5 Synthetic Aperture Systems
530(5)
8.6 Linear and Nonlinear Imaging
535(15)
8.6.1 Contrast Media Imaging
536(12)
8.6.2 Tissue Harmonic Imaging
548(2)
8.7 Ultrasound Computed Tomography
550(7)
8.7.1 Transmission Tomography
553(3)
8.7.2 Pulse-Echo Tomography
556(1)
8.8 Ultrasound Elastography
557(14)
8.8.1 Correlation Methods
562(3)
8.8.2 Pulsed Velocity Estimation Methods
565(3)
8.8.3 Shear Wave Propagation in Tissue
568(3)
8.9 Ultrasound Microscopy and Biomicroscopy
571(9)
8.9.1 Background
571(2)
8.9.2 Scanning Acoustic Microscope
573(1)
8.9.3 Scanning Biomicroscopy
574(2)
8.9.4 Biomicroscopy of the Eye
576(2)
8.9.5 Biomicroscopy of Skin
578(2)
8.10 Endoluminal and Intravascular Imaging
580(13)
8.10.1 Side-Viewing Transducers
581(2)
8.10.2 Three-Dimensional Imaging
583(3)
8.10.3 Forward-Viewing Transducers
586(5)
8.10.4 Flow Measurement
591(2)
References
593(15)
9 Principles of Doppler Ultrasound
608(44)
9.1 Historical Background
608(3)
9.2 Ultrasonic Transit-Time and Phase-Delay Method
611(3)
9.3 Doppler Equation for Moving Scatterers
614(4)
9.3.1 Refractive Effects
618(1)
9.4 Continuous-Wave Doppler Systems
618(5)
9.4.1 Probe Design
620(1)
9.4.2 Extracting the Doppler Signal
620(3)
9.5 Continuous-Wave Doppler Spectrum Related to Velocity Profile
623(10)
9.5.1 Steady Flow Spectra
624(3)
9.5.2 Characteristics of Pulsatile Blood Flow in Arteries
627(2)
9.5.3 Characteristics of the Doppler Signal and its Power Spectrum
629(4)
9.6 Properties of the Doppler Signal
633(4)
9.6.1 Statistical Properties
633(3)
9.6.2 Doppler Simulation Models
636(1)
9.7 Doppler Spectral Broadening
637(9)
9.7.1 Intrinsic Broadening
639(6)
9.7.2 Extrinsic Broadening
645(1)
9.7.3 Maximum Velocity Estimation Errors
645(1)
References
646(6)
10 Pulsed Methods for Flow Velocity Estimation and Imaging 652(91)
10.1 Introduction
653(5)
10.1.1 Historical Background
656(2)
10.2 Physical Principles of Pulsed Systems
658(6)
10.2.1 Velocity Estimation Methods
661(1)
10.2.2 Critical Velocities
662(2)
10.3 Simplified Theory
664(18)
10.3.1 Demodulation by Direct RF Signal Sampling
669(1)
10.3.2 Phase-Quadrature Demodulation
670(4)
10.3.3 Axial Resolution, SNR, and Range-Gate Duration
674(2)
10.3.4 Shape of the Sample Volume
676(1)
10.3.5 Ensemble of Scatterers
677(2)
10.3.6 Coded Excitation
679(3)
10.4 Velocity Estimation using Time-Shift Cross-Correlation
682(6)
10.4.1 Time-Delay Estimation
682(2)
10.4.2 Effects of De correlation
684(3)
10.4.3 Approximate Method for Cross-Correlation Calculation
687(1)
10.5 Velocity Estimation Based on Phase Shift and Frequency
688(3)
10.6 Multigate Pulsed Wave Methods
691(3)
10.6.1 System Design
691(1)
10.6.2 Deconvolution Correction
692(2)
10.7 Principles of CW and Pulsed Wave Flow imaging
694(6)
10.7.1 Historical Background
694(5)
10.7.2 Pulsed Wave Color Flow Imaging
699(1)
10.7.3 Principles
699(1)
10.8 One-Dimensional Autocorrelation Methods
700(10)
10.8.1 Effects of Frequency-Dependent Attenuation and Scattering
706(2)
10.8.2 Clutter Rejection Techniques
708(2)
10.9 Two-Dimensional Methods
710(9)
10.9.1 Discrete Fourier Transform Methods
712(3)
10.9.2 Two-Dimensional Autocorelation Method
715(2)
10.9.3 Target Tracking Techniques
717(2)
10.10 Enhanced Flow Imaging Methods
719(8)
10.10.1 Color Flow Imaging: Frame Rate Considerations
720(1)
10.10.2 Power Flow Imaging
720(2)
10.10.3 Tissue Imaging
722(1)
10.10.4 Contrast Flow Imaging
723(4)
10.11 Volume Flow Estimation Techniques
727(9)
10.11.1 Local Mean Velocity Methods
729(2)
10.11.2 Power Spectrum Methods
731(2)
10.11.3 Compensation Methods
733(3)
10.12 Velocity Vector Estimation Methods
736(7)
10.12.1 Velocity Reconstruction Techniques
737(2)
10.12.2 Reconstruction Algebra
739(4)
References 743(11)
Appendix A Properties of Time- and Space-Invariant Linear Systems 754(2)
Appendix B Function Definitions and Transform Pairs 756(4)
Appendix C Some Integral and Function Relations 760(3)
Appendix D Some Vector Relations 763(3)
List of Principal Symbols and Abbreviations 766(7)
Index 773

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