Quantitative Ultrasound in Soft Tissues

Preface to the Second Edition
Contents
About the Editors
Part I Backscatter Coefficient Methods
1 Quantitative Ultrasound: An Emerging Technology for Detecting, Diagnosing, Imaging, Evaluating, and Monitoring Disease
	1.1 Introduction
	1.2 QUS Based on Spectrum Analysis and Envelope Statistics
		1.2.1 Spectrum-Analysis Techniques
			1.2.1.1 Spectral-Parameter Imaging
			1.2.1.2 Scatterer-Property Imaging
			1.2.1.3 Tissue-Type Imaging
		1.2.2 Envelope-Statistics Techniques
	1.3 Current and Potential Applications of QUS
	1.4 Future Technological Developments
		1.4.1 Advances Within Individual Emerging Ultrasound Technologies
		1.4.2 Advances Among Emerging Ultrasound Technologies
		1.4.3 Advances in Combinations of Ultrasonic and Other Technologies
	1.5 Conclusion
	References
2 Quantitative Ultrasound: Scattering Theory
	2.1 Introduction
	2.2 Continuum Scatterer Model
	2.3 Discrete Scatterer Model
	2.4 Concluding Remarks
	References
3 Quantitative Ultrasound: Experimental Implementation
	3.1 Introduction
	3.2 The Measurement Terms
	3.3 Attenuation Compensation
	3.4 Calibration Approaches
		3.4.1 Planar Reference
		3.4.2 Reference Phantom
		3.4.3 In Situ Calibration
		3.4.4 Reference Free
	3.5 Windowing Functions
	3.6 Conclusion
	References
4 Extracting Quantitative Ultrasonic Parameters from the Backscatter Coefficient
	4.1 Introduction
	4.2 Definitions
	4.3 Model-Based BSC Parameterization
		4.3.1 Assumptions and Notations
		4.3.2 Relating BSC to Scattered Acoustic Pressure Field
		4.3.3 Exact BSC Models from Acoustic Scattering Theory
		4.3.4 Approximate BSC Models Using Born Approximation
			4.3.4.1 Theoretical Framework
			4.3.4.2 Correlation Coefficient Models
			4.3.4.3 Rayleigh Scattering and Form Factor
			4.3.4.4 Strengths and Weaknesses of Correlation Models
		4.3.5 Scatterer Size Distribution
		4.3.6 Structure Function Models for Dense Media
	4.4 Model-Free BSC Parameterization
		4.4.1 Linear Regression
		4.4.2 Principal Component Analysis
	Appendices
		Appendix A: Matlab Code for the Anderson BSC Model
		Appendix B: Matlab Code for the Concentric Spheres BSC Model
		Appendix C: Matlab Code for the Monodisperse Hard Sphere SF Model
		Appendix D: Matlab Code for the Polydisperse Hard Sphere SF Model
	References
Part II Attenuation Estimation Methods
5 Attenuation Compensation and Estimation
	5.1 Introduction
	5.2 Impact of Attenuation on Backscattered Power Spectrum
	5.3 Local Attenuation Estimation Algorithms
		5.3.1 Spectral Shift Algorithm for Local Attenuation Estimation
		5.3.2 Spectral Difference Method for Local Attenuation Estimation
		5.3.3 Spectral Log Difference Method for Local Attenuation Estimation
		5.3.4 Hybrid Method for Local Attenuation Estimation
		5.3.5 Comparison of Spectral Difference, Spectral Log-Difference, and Hybrid Methods for Local Attenuation Estimation
	5.4 Total Attenuation Estimation Algorithms
		5.4.1 Multiple Filter Algorithm for Total Attenuation Estimation
		5.4.2 Spectral Fit Algorithm for Total Attenuation Estimation
		5.4.3 Comparison of Spectral Fit Algorithm and Multiple Filter Algorithm
	References
6 Recent Advances in Attenuation Estimation
	6.1 Introduction
	6.2 Bias Reduction
	6.3 Elimination of a Reference Phantom Normalization
	6.4 Variance Reduction
		6.4.1 Power-Spectrum Estimation
		6.4.2 Cramer-Raw Lower Bound
		6.4.3 Frequency Compounding
		6.4.4 Regularization Methods
	6.5 Summary and Conclusion
	References
Part III Envelope Statistics Methods
7 Review of Envelope Statistics Models for Quantitative Ultrasound Imaging and Tissue Characterization
	7.1 Introduction
	7.2 Chapter Content
	7.3 Statistical Models
		7.3.1 The Homodyned K-Distribution and Related Distributions
			7.3.1.1 The Rayleigh Distribution
			7.3.1.2 The Rice Distribution
			7.3.1.3 The K-Distribution
			7.3.1.4 The Homodyned K-Distribution
		7.3.2 Interpretation of the Distributions in the Context of Ultrasound Imaging
		7.3.3 The Nakagami Distribution as an Approximation
		7.3.4 Discussion
	7.4 Parameter Estimation Methods
		7.4.1 Overview of a Few Estimation Methods
			7.4.1.1 The MLE and the MAP
			7.4.1.2 Moments-Based Methods
			7.4.1.3 Log-Moments-Based Methods
		7.4.2 Parameter Estimation Method for the Rayleigh Distribution
		7.4.3 Parameter Estimation Methods for the Rice Distribution
			7.4.3.1 The MLE for the Rice Distribution
			7.4.3.2 Expression of Fractional Order Moments of the Amplitude
			7.4.3.3 Method Based on the Moments of the Amplitude
			7.4.3.4 Discussion
		7.4.4 Parameter Estimation Methods for the K-Distribution
			7.4.4.1 The MLE for the K-Distribution
			7.4.4.2 Expression of Fractional Order Moments of the Amplitude
			7.4.4.3 A Method Based on the Moments of the Intensity
			7.4.4.4 Two Methods Based on Fractional Order Moments of the Amplitude
			7.4.4.5 Two Log-Moments Methods
			7.4.4.6 Discussion
		7.4.5 Parameter Estimation Methods for the Homodyned K-Distribution
			7.4.5.1 Expression of Fractional Order Moments of the Amplitude
			7.4.5.2 A Method Based on the Moments of the Intensity
			7.4.5.3 A Method Based on the Moments of the Amplitude
			7.4.5.4 Methods Based on the SNR of Fractional Order Moments of the Amplitude
			7.4.5.5 A Method Based on the SNR and Skewness of the Amplitude
			7.4.5.6 A Method Based on the SNR, Skewness, and Kurtosis of Fractional Order Moments of the Amplitude
			7.4.5.7 Discussion
		7.4.6 Parameter Estimation Methods for the Nakagami Distribution
			7.4.6.1 The MLE for the Nakagami Distribution
			7.4.6.2 A Method Based on the First Two Moments of the Intensity
			7.4.6.3 Discussion
	7.5 Conclusion
	Appendix: Proofs of the New Results
	References
8 Information Entropy and Its Applications
	8.1 Introduction
	8.2 The Liver and Its Scattering Sources
	8.3 Statistical Analysis of Ultrasound Backscattering
	8.4 Fundamentals of Information Entropy
	8.5 A Basic Scheme for Ultrasound Entropy Imaging
	8.6 Clinical Examples of Ultrasound Entropy Imaging in Characterizing NAFLD
	8.7 Conclusions and Perspectives
	References
Part IV Ultrasound Computed Tomography
9 Ultrasound Tomography
	9.1 Introduction
		9.1.1 Advantages of USCT
		9.1.2 Challenges of USCT
		9.1.3 Definition of USCT and Differences to Sonography
	9.2 State of the Art of Ultrasound Tomography
		9.2.1 Current Systems
	9.3 Ultrasound Propagation in Tissue
		9.3.1 Acoustic Wave Equation and Assumptions
	9.4 Image Reconstruction
		9.4.1 Full-Waveform Tomography
		9.4.2 Diffraction Tomography
		9.4.3 Paraxial Tomography
		9.4.4 Ray Tomography
		9.4.5 Reflection Tomography
		9.4.6 Clinical Applicability of Reconstruction Methods
		9.4.7 Resources for USCT Data
	9.5 Technical Challenges and System Design
		9.5.1 Transducer Distribution
		9.5.2 Ultrasound Transducers for USCT
		9.5.3 Data Acquisition and Processing
		9.5.4 Calibration
		9.5.5 Medical Products and Standards
	9.6 Applications and Current Limitations of USCT
		9.6.1 USCT and the Breast
		9.6.2 Beyond the Breast: More Applications of USCT
		9.6.3 Joints
		9.6.4 Brain Imaging
		9.6.5 Ultrasound Therapy and USCT
		9.6.6 Modalities beyond Reflectivity, Speed of Sound and Attenuation
		9.6.7 Current Limitations and Possible Solutions
	9.7 Summary
	References
10 Full Wave Inversion and Inverse Scattering in Ultrasound Tomography/Volography
	10.1 Introduction
		10.1.1 Breast Cancer
		10.1.2 Historical Development in Last 40 Years
		10.1.3 Caveat
	10.2 Inverse Scattering
		10.2.1 Theory of Acoustic Wave Propagation
		10.2.2 Constant Density Assumption
		10.2.3 Attenuation
		10.2.4 1D, 2D, 3D
		10.2.5 Linearized Inverse Scattering
		10.2.6 Ray-Based Methods
		10.2.7 Full Wave Inversion
		10.2.8 NVIDIA Graphics Processing Units (GPUs) and a Mathematical Trick
		10.2.9 Interlude on Ray Tracing
	10.3 Introduction to Inverse Scattering
	10.4 Specially Designed Breast Scanner for Tomography/Volography
		10.4.1 Specially Designed Algorithms
		10.4.2 Physics of Ultrasound – Why 2D Ultrasound Tomography Is Not Enough
	10.5 Tomography (2D) Vs Volography (3D)
	10.6 Inverse Obstacle Problem
	10.7 Well-Posed and Ill-Posed Problems in the Sense of Hadamard
	10.8 Direct Scattering
	10.9 Inverse Medium Problem
	10.10 Integral Equation Formulation
		10.10.1 Lippmann-Schwinger Equation and Its Implications
	10.11 Born Approximation
		10.11.1 Weyl Decomposition
		10.11.2 Comments on Weyl Decomposition
	10.12 Summary: Utility of Integral Equation Approach
	10.13 The Gradient of the Functional Is the Product of Two “Total” Fields
	10.14 *-9pt
	10.15 Distorted Born Iterative and Related Methods (DBIM)
	10.16 Discussion of Propagation Formula
	10.17 Paraxial Approximation
	10.18 Inverse Scattering in the Paraxial Approximation
		10.18.1 Jacobian Action
		10.18.2 The Gradient of Functional
		10.18.3 Spatial Resolution
		10.18.4 NVIDIA GPUs
	10.19 The Reflection Algorithm
	10.20 Examples of Inverse Scattering Images
	10.21 Limited View
	10.22 Important Topics
		10.22.1 Timing, Stopping Criteria, L1 Norms, Frequency Hopping, Attenuation, and Regularization
		10.22.2 Stopping Criteria
		10.22.3 L1,L0 Norms
		10.22.4 Frequency Hopping
		10.22.5 Attenuation
		10.22.6 Regularization
		10.22.7 Artificial Intelligence
	10.23 Summary: Clinical Importance of 3D Volography
	References
11 Clinical Importance of 3D Volography in Breast Imaging
	11.1 Microanatomy
	11.2 Biomarkers
	11.3 Visual Grading Analysis (VGA)
	11.4 Breast Microcalcification Detection
	11.5 Breast Cyst Detection and Analysis
	11.6 Measurement of Dense Fibroglandular Tissue Volume In Vivo Using Transmitted Sound 3D Volography Imaging
	11.7 Use of AI to Differentiate Between Benign and Malignant Breast Masses
	11.8 Clinical Trial Results
	11.9 Conclusions
	References
Part V Acoustic Microscopy
12 Advanced Topics in Quantitative Acoustic Microscopy
	12.1 Introduction
	12.2 Current State-of-the-Art QAM Technology
		12.2.1 Industrial Systems
		12.2.2 Laboratory Systems
	12.3 Forward Model in QAM
	12.4 Inverse Models in QAM
		12.4.1 Hozumi Inverse Method
		12.4.2 Autoregressive Inverse Model
	12.5 Compressive Sensing in QAM
		12.5.1 Spatial Sampling Reduction via Wavelets and Approximate Message Passing
		12.5.2 Temporal Sampling Reduction via Finite Rate of Innovation
		12.5.3 Spatio-Temporal Data Reduction
	12.6 Super-resolution (SR) Methods in QAM
		12.6.1 Regularized Deconvolution
		12.6.2 Histology-Based Regularization
		12.6.3 Machine Learning Super-Resolution
		12.6.4 Discussion and Conclusions
	References
Part VI Phantoms for Quantitative Ultrasound
13 Phantoms for Quantitative Ultrasound
	13.1 Overview of Ultrasound Phantoms
		13.1.1 Acoustic Properties of TM Materials
		13.1.2 Development of TM Materials
		13.1.3 Commercially Available Materials
		13.1.4 Other Materials
	13.2 Measurements of Acoustic Properties
		13.2.1 Speed and Attenuation
		13.2.2 Backscatter Measurements
	13.3 Scattering Prediction
	13.4 Creating Phantoms with Specific Acoustic Properties
		13.4.1 Speed of Sound
		13.4.2 Attenuation Coefficient
		13.4.3 Scattering
	13.5 Review of Interlaboratory Comparisons
	13.6 Discussion and Conclusions
	References
Index