Improved Endocardial Border Definition with Short-lag Spatial

Improved Endocardial Border Definition with

Short-lag Spatial Coherence (SLSC) Imaging

by

Muyinatu Adebisi Lediju Bell

Department of Biomedical EnginerringDuke University

Date: April 26, 2012

Approved:

Gregg E. Trahey, Supervisor

Jeremy J. Dahl

Stephen W. Smith

Caterina M. Gallippi

Joseph A. Kisslo

Dissertation submitted in partial fulfillment of the requirements for the degree ofDoctor of Philosophy in the Department of Biomedical Enginerring

in the Graduate School of Duke University2012

Abstract

Improved Endocardial Border Definition with Short-lag

Spatial Coherence (SLSC) Imaging

by

Muyinatu Adebisi Lediju Bell

Department of Biomedical EnginerringDuke University

Date: April 26, 2012

Approved:

Gregg E. Trahey, Supervisor

Jeremy J. Dahl

Stephen W. Smith

Caterina M. Gallippi

Joseph A. Kisslo

An abstract of a dissertation submitted in partial fulfillment of the requirements forthe degree of Doctor of Philosophy in the Department of Biomedical Enginerring

in the Graduate School of Duke University2012

Copyright c© 2012 by Muyinatu Adebisi Lediju BellAll rights reserved except the rights granted by the

Creative Commons Attribution-Noncommercial License

http://creativecommons.org/licenses/by-nc/3.0/us/

Abstract

Clutter is a problematic noise artifact in a variety of ultrasound applications.

Clinical tasks complicated by the presence of clutter include detecting cancerous

lesions in abdominal organs (e.g. livers, bladders) and visualizing endocardial borders

to assess cardiovascular health. In this dissertation, an analytical expression for

contrast loss due to clutter is derived, clutter is quantified in abdominal images, and

sources of abdominal clutter are identified. Novel clutter reduction methods are also

presented and tested in abdominal and cardiac images.

One of the novel clutter reduction methods is Short-Lag Spatial Coherence (SLSC)

imaging. Instead of applying a conventional delay-and-sum beamformer to measure

the amplitude of received echoes and form B-mode images, the spatial coherence of

received echoes are measured to form SLSC images. The world’s first SLSC images

of simulated, phantom, and in vivo data are presented herein. They demonstrate

reduced clutter and improved contrast, contrast-to-noise, and signal-to-noise ratios

compared to conventional B-mode images. In addition, the resolution characteristics

of SLSC images are quantified and compared to resolution in B-mode images.

A clinical study with 14 volunteers was conducted to demonstrate that SLSC

imaging offers 19-33% improvement in the visualization of endocardial borders when

the quality of B-mode images formed from the same echo data was poor. There were

no statistically significant improvements in endocardial border visualization with

SLSC imaging when the quality of matched B-mode images was medium to good.

iv

In honor of my late mother, for her steadfast commitment to my success, despite the

many hardships that could have easily deterred her

v

Contents

Abstract iv

List of Tables xii

List of Figures xiii

List of Abbreviations and Symbols xvii

Acknowledgements xx

1 Introduction 1

1.1 Clinical Motivation and Significance . . . . . . . . . . . . . . . . . . . 1

1.2 Dissertation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Background 6

2.1 van Cittert-Zernike Theorem . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Beamforming: B-mode vs. SLSC Imaging . . . . . . . . . . . . . . . . 9

3 Quantitative Assessment of Clutter Magnitudes in Simulated, Phan-tom, and In Vivo Ultrasound Data 12

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2.1 Analytical Expression for Contrast Loss Due to Clutter . . . . 14

3.2.2 Field II Simulations . . . . . . . . . . . . . . . . . . . . . . . 16

3.2.3 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . 17

3.2.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

vi

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3.1 Contrast Loss Due to Clutter . . . . . . . . . . . . . . . . . . 19

3.3.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3.3 Phantom Results . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3.4 In Vivo Results . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.3.5 Clutter Variation with Distance . . . . . . . . . . . . . . . . . 25

3.3.6 Clutter Reduction with Harmonic Imaging . . . . . . . . . . . 29

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4.1 Impact and Magnitude of Clutter . . . . . . . . . . . . . . . . 30

3.4.2 Comparison of Predicted and Measured Contrast Losses Dueto Clutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4.3 Importance of Clutter Reduction in Abdominal Images . . . . 33

3.4.4 Clutter Reduction with Harmonic Imaging . . . . . . . . . . . 34

3.4.5 Relationship Between Clutter and Body Mass Indices (BMIs) 35

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Motion-based Clutter Reduction Techniques 37

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.2.1 Field II simulations . . . . . . . . . . . . . . . . . . . . . . . 38

4.2.2 Phantom and In Vivo Studies . . . . . . . . . . . . . . . . . . 39

4.2.3 Clutter Reduction with Motion Filters . . . . . . . . . . . . . 42

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.3.1 Field II simulations . . . . . . . . . . . . . . . . . . . . . . . 44

4.3.2 Phantom Experiments . . . . . . . . . . . . . . . . . . . . . . 47

4.3.3 In Vivo Experiment: Bladder Images . . . . . . . . . . . . . . 50

vii

4.3.4 In Vivo Experiment: Liver Images . . . . . . . . . . . . . . . 54

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.4.1 Implications for Clutter Reduction in Abdominal Images . . . 57

4.4.2 Motion Filter Advantages and Limitations . . . . . . . . . . . 58

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62


5 Clutter Reduction with SLSC Imaging 63

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2 Short-Lag Spatial Coherence . . . . . . . . . . . . . . . . . . . . . . . 66

5.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.3.1 Theoretical Prediction of Short-Lag Spatial Coherence . . . . 69

5.3.2 Field II Simulations . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3.3 Tissue-Mimicking Phantoms and In Vivo Experiments . . . . 72

5.3.4 Coherence Image Processing . . . . . . . . . . . . . . . . . . . 73

5.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

5.4.1 Field II simulations . . . . . . . . . . . . . . . . . . . . . . . . 74

5.4.2 Experiments in Tissue-Mimicking Phantom . . . . . . . . . . . 79

5.4.3 SLSC of Expanded Targets . . . . . . . . . . . . . . . . . . . . 80

5.4.4 In Vivo Human Thyroid Images . . . . . . . . . . . . . . . . . 83

5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88


6 Resolution Characteristics of SLSC Imaging 90

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.2 Short-lag Spatial Coherence Imaging . . . . . . . . . . . . . . . . . . 96

viii

6.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.3.1 Field II Simulations . . . . . . . . . . . . . . . . . . . . . . . . 98

6.3.2 Point Target Measurements . . . . . . . . . . . . . . . . . . . 98

6.3.3 Autocorrelation Measurements . . . . . . . . . . . . . . . . . . 101

6.3.4 Brightness and RMS Amplitude Measurements . . . . . . . . 102

6.3.5 Experimental Demonstration . . . . . . . . . . . . . . . . . . . 102

6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

6.4.1 Resolution in the Presence of Channel Noise and Clutter . . . 102

6.4.2 Resolution and Texture Size vs. SLSC Imaging Parameters . . 104

6.4.3 Depth of Field Effects . . . . . . . . . . . . . . . . . . . . . . 106

6.4.4 Experimental Images . . . . . . . . . . . . . . . . . . . . . . . 109

6.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6.5.1 SLSC Resolution in the Presence of Noise and Clutter . . . . . 111

6.5.2 Resolution Characteristics with Varied Receive Aperture Sizesand SLSC Image Parameters . . . . . . . . . . . . . . . . . . . 112

6.5.3 Similarities Between Texture Size and Resolution . . . . . . . 113

6.5.4 Depth-Dependent Resolution Effects . . . . . . . . . . . . . . 114

6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116


7 SLSC Applied to In Vivo Cardiac Images 117

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.2 Short-Lag Spatial Coherence Imaging . . . . . . . . . . . . . . . . . . 119

7.2.1 Image Formation . . . . . . . . . . . . . . . . . . . . . . . . . 119

7.2.2 Motion Tracking with SLSC Images . . . . . . . . . . . . . . . 120

7.3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.3.1 Study Population . . . . . . . . . . . . . . . . . . . . . . . . . 121

ix

7.3.2 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.3.3 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . 122

7.3.4 Endocardial Visibility and Scoring System . . . . . . . . . . . 123

7.3.5 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . 123

7.3.6 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.4.1 Short Axis Views . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.4.2 Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . 127

7.4.3 Independent Observer Reviews . . . . . . . . . . . . . . . . . 129

7.4.4 Apical Four Chamber Views . . . . . . . . . . . . . . . . . . . 130

7.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.5.1 Improvements with SLSC Imaging . . . . . . . . . . . . . . . . 133

7.5.2 Study Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 136

7.5.3 Clinical Implications . . . . . . . . . . . . . . . . . . . . . . . 137

7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137


8 Conclusions and Future Directions 139

8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

8.2 The Future of SLSC . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

8.2.1 Harmonic SLSC . . . . . . . . . . . . . . . . . . . . . . . . . . 141

8.2.2 Motion Tracking with SLSC Images . . . . . . . . . . . . . . . 142

8.2.3 3D SLSC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

8.2.4 Real-Time SLSC Imaging . . . . . . . . . . . . . . . . . . . . 143

8.2.5 Application of SLSC Principles to Related Areas . . . . . . . . 144

Bibliography 145

x

Biography 155

xi

List of Tables

3.1 Ages and BMIs of the five volunteers whose bladders were imaged tomeasure abdominal clutter magnitudes . . . . . . . . . . . . . . . . . 24

4.1 Transducer Parameters for Field II Simulations . . . . . . . . . . . . 40

4.2 Contrast and contrast-to-noise ratios (CNRs) in reference and filteredimages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.1 Simulated Transducer Parameters . . . . . . . . . . . . . . . . . . . . 71

5.2 Contrast, CNR, and SNR at focus of experimental phantom, simu-lated, and in vivo thyroid data. . . . . . . . . . . . . . . . . . . . . . 85

6.1 Simulated Transducer Parameters . . . . . . . . . . . . . . . . . . . . 98

xii

List of Figures

2.1 Sample transmit pressure field and scattering functions . . . . . . . . 7

2.2 Expected coherence functions . . . . . . . . . . . . . . . . . . . . . . 8

2.3 Average measured spatial coherence functions for a point target, ane-choic region, and speckle background . . . . . . . . . . . . . . . . . . 9

2.4 Cluttered B-mode image of an ovine heart, acquired shortly after eu-thanasia and a matched SLSC image created from the same data . . . 11

3.1 Schematic of a lesion in the absence and presence of a uniform cluttersignal that overlays the entire image . . . . . . . . . . . . . . . . . . . 14

3.2 Contrast loss as a function of clutter relative to the background signalfor eight values of “uncluttered” lesion contrast. . . . . . . . . . . . . 19

3.3 Simulated B-mode images of a block and a spherical void and corre-sponding contour plots of clutter magnitude . . . . . . . . . . . . . . 20

3.4 B-mode images of a bladder phantom and corresponding contour plotsof clutter magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.5 B-mode images of a fetal phantom in the absence and presence ofa clutter-generating layer and corresponding contour plots of cluttermagnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.6 In vivo bladder images from a volunteer whose BMI indicates that heis overweight and corresponding contour plots of clutter magnitude . 25

3.7 In vivo bladder images from a volunteer whose BMI is indicative ofobesity and corresponding contour plots of clutter magnitude . . . . . 26

3.8 Clutter magnitudes in fundamental images as a function of distancefrom the bladder walls . . . . . . . . . . . . . . . . . . . . . . . . . . 27

xiii

3.9 Clutter magnitudes in harmonic images as a function of distance fromthe bladder walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.10 Map of regional signal differences between fundamental and harmonicB-mode images of the in vivo bladder . . . . . . . . . . . . . . . . . . 29

4.1 FIR and BSS filters applied to simulated data. . . . . . . . . . . . . . 45

4.2 Time and depth projections of the simulated data. . . . . . . . . . . . 46

4.3 Measured displacements of a bladder phantom imaged during con-trolled motion of the ultrasound probe. . . . . . . . . . . . . . . . . . 48

4.4 FIR- and BSS-filtered phantom images. . . . . . . . . . . . . . . . . . 49

4.5 FIR- and BSS-filtered bladder images. . . . . . . . . . . . . . . . . . 52

4.6 Measured displacements of the abdominal wall and underlying clutter,relative to the stationary bladder wall. . . . . . . . . . . . . . . . . . 53

4.7 FIR- and BSS-filtered liver images. . . . . . . . . . . . . . . . . . . . 55

5.1 Examples of expected coherence functions in a point target and specklebackground and an experimentally-measured coherence function fromin vivo thyroid tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.2 Simulated B-mode and SLSC images of 3-mm lesions with varyingcontrasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.3 Mean contrast and CNR observed in the lesions of the simulated B-mode and SLSC images, as a function of the intrinsic lesion contrast . 76

5.4 Point target conspicuity as a function of target brightness in B-modeand SLSC images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.5 Theoretical calculations of the SLSC image compared to simulatedB-mode and SLSC images . . . . . . . . . . . . . . . . . . . . . . . . 77

5.6 Contrast, CNR, SNR, and lateral resolution as a function of Q . . . . 78

5.7 B-mode and SLSC images of 4mm anechoic lesions in a tissue-mimickingphantom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.8 B-mode and SLSC images of 1-cm lesions formed from simulated andexperimental phantom data . . . . . . . . . . . . . . . . . . . . . . . 81

xiv

5.9 Theoretical SLSC image calculations of lesions of varying sizes andcontrasts, compared to simulated and experimental data from the 1-cm lesion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.10 B-mode and SlSC images of a cyst in a human thyroid . . . . . . . . 83

6.1 Coherence functions for a sinusoidal target . . . . . . . . . . . . . . . 95

6.2 Target and SLSC profiles and their corresponding frequency spectrums 96

6.3 B-mode and SLSC images of point targets and associated point spreadfunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

6.4 B-mode and SLSC resolution vs. channel NSR . . . . . . . . . . . . . 103

6.5 B-mode and SLSC resolution vs. clutter magnitude . . . . . . . . . . 104

6.6 SLSC resolution vs. correlation kernel size . . . . . . . . . . . . . . . 105

6.7 Resolution vs. the M used to from SLSC images and the number ofreceive elements used to form B-mode images . . . . . . . . . . . . . 106

6.8 B-mode and SLSC resolution vs. depth . . . . . . . . . . . . . . . . . 107

6.9 RMS amplitude of channel signals vs. depth . . . . . . . . . . . . . . 108

6.10 B-mode and SLSC image brightness vs. depth . . . . . . . . . . . . . 109

6.11 Experimental demonstration of resolution characteristics in B-modeand SLSC images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

7.1 Measured vs. actual axial displacement tracking of SLSC, RF, anddetected data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

7.2 Short axis view of a difficult-to-image patient . . . . . . . . . . . . . 125

7.3 Short axis view of good quality B-mode and SLSC images . . . . . . 126

7.4 Short axis view of a poor quality B-mode image and an improvedquality SLSC image . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7.5 Performance metrics in cardiac images: B-mode vs. SLSC . . . . . . 128

7.6 Performance metrics in SLSC cardiac images as a function of M . . . 128

7.7 Visibility of the LV endocardial segments in good, medium, and poorquality images of the short axis views of the LV . . . . . . . . . . . . 129

xv

7.8 Apical four chamber view of the LV with more clearly-defined bordersin the SLSC image compared to the B-mode image . . . . . . . . . . 131

7.9 Apical four chamber view of the LV with reduced clutter in the SLSCimage compared to the B-mode image . . . . . . . . . . . . . . . . . . 132

7.10 Visibility of endocardial segments in the apical four chamber views ofthe LV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

7.11 Mean visibility score of each segment in B-mode and SLSC images ofthe apical four chamber view . . . . . . . . . . . . . . . . . . . . . . . 134

8.1 Fundamental and harmonic B-mode and SLSC images of a left ventricle142

xvi

List of Abbreviations and Symbols

Symbols

c Speed of sound, typically 1540 m/s in tissue

C Theoretical spatial covariance

C Experimental spatial covariance

C Contrast

C Clutter

D Aperture width

F Fourier transform

H Incident transmit pressure field

k Kernel size used to calculate spatial correlations

λ The ultrasound wavelength

Λ Triangle function

m Spacing between two transducer elements

M The short-lag value used to create the SLSC image

n Depth in sample number

N The number of elements in the transmit aperture

Q The short-lag value used to create the SLSC image, expressed asa a percentage of the transmit aperture (Q = M/N%)

R The normalized spatial coherence across the receive aperture (i.e.the experimentally-determined spatial coherence function)

Rsl Short-lag spatial coherence

xvii

S Mean of signal amplitudes

σ Standard deviation of signal amplitudes

T Tissue

u Lateral spatial frequency

v Elevational spatial frequency

ν Eigenvector of basis function in BSS filtering

χ Scattering function

x Data matrix of unfiltered image

x Lateral dimension of the aperture plane

x′ Spatial difference between two points in the lateral dimension ofthe aperture plane

x0 Lateral location of the mainlobe of the transmit beam relativeto the scattering function

y Data matrix of BSS-filtered image

y Elevation dimension of the aperture plane

y′ Spatial difference between two points in the elevation dimensionof the aperture plane

z Axial focus

Abbreviations

2D Two dimensional

3D Three dimensional

AC Apical cap

AL Apical lateral

A-line Amplitude line, i.e. one line in a B-mode image

AS Apical septum

BL Basal anterolateral

xviii

BMI Body Mass Index

B-mode Brightness mode

BS Basal inferoseptum

BSS Blind Source Separation

CNR Contrast-to-noise ratio

FIR Finite Impulse Response

FWHM Full width at half maximum

GCF Generalized coherence factor

GPU Graphics processing unit

LV Left ventricle of the heart

ML Mid anterolateral

MS Mid inferoseptum

NSR Noise-to-signal ratio

PCF Phase coherence factor

PSF Point spread function

RF Radio frequency

RMS Root mean squared

ROI Region of interest

SLSC Short-lag Spatial Coherence

SNR Signal-to-noise ratio

TEE Transesophogeal echocardiography

TCR Tissue-to-clutter ratio

VCZ van Cittert-Zernike

xix

Acknowledgements

It is a pleasure for me to thank those who have made this dissertation possible.

To my advisor, Dr. Gregg Trahey, you have offered exemplary support, guidance,

creative vision, and technical foresight every step of the way. Thanks also for working

with me even though I was sort of a night owl and my work schedule differed from

the mainstream. To Dr. Jeremy Dahl, I appreciate that you were never too busy

to discuss technical details with me and to help me understand some of the more

challenging ultrasound principles. To the remainder of my committee members, Dr.

Caterina Gallippi, Dr. Stephen Smith, and Dr. Joseph Kisslo, and to Dr. Kathy

Nightingale and Dr. Mark Palmeri, thanks for helping to shape the direction of my

research and for offering necessary critiques and reviews.

Thanks to all members of the Trahey and Nightingale labs, past and present, who

helped me to navigate graduate school when I was a novice and who helped me to

hone my research skills by asking probing questions when I became more seasoned.

Thanks also for the non-work-related conversations, the BC runs, and other unofficial

weekend and weekday lab outings. Thanks to members of the Bouchet Society, past

and present, who provided a social outlet and served as an academic resource for

me on many occasions. Special thanks to one of my best friends, Letitia Hubbard,

who sat a few doors down from me and always brightened my day with advice,

encouragement, and casual conversation. Altogether, these experiences helped me

to thoroughly enjoy the time I spent in graduate school.

xx

I am grateful for BME staff like Kathy Barbour, Joyce Franklin, Susan Story-Hill,

Ellen Ray, and Erica Clayton, who readily assisted me with administrative details

that ranged from obtaining signatures for my grant applications, to processing my

travel reimbursements and filing the paper work to facilitate my surname change. I

am also appreciative of the cheerful greeting I received whenever I entered the BME

front office. Thanks also to Ned Danieley for managing the compute nodes and file

back-ups needed to sustain my computationally-intensive simulations and the large

volume of data that I accrued over the years.

Thanks to the various funding agencies who provided financial support and

funded my research-related travels around the world: the UNCF/Merck Gradu-

ate Science Research Dissertation Fellowship; the Whitaker International Fellowship

that allowed me to collaborate with the Institute of Cancer Research in the United

Kingdom under the tutelage of Dr. Jeffrey Bamber, a great mentor whose ideas

and insightful comments have helped me to think critically about my research and

broaden my skill set; the NIH Research Supplement to Promote Diversity and the

NIH Medical Imaging Training Grant; Student Travel Awards from the IEEE to

attend symposias in China and Spain; and the Duke Endowment Fellowship.

To my family, thanks for your love and support. My amazing husband, Renaldo

Bell, has exhibited an admirable amount of patience and understanding throughout

this journey. Thank you for being my number one fan since the day we met. To

my brother, Abdul-Rahman Lediju, Esq., you have always been a role model and

inspiration for me for as long as I can remember, and I thank you for your constant

support and encouragement. I am also grateful for the love and support I received

each week from my church family at Immanuel Temple. Thanks also to my extended

circle of spiritual mentors for your prayers and encouragement. Finally, I believe that

“I can do all things through Christ who strengthens me” (Phil. 4:13), and I know

that this accomplishment would not have been possible without my faith in God.

xxi

1

Introduction

1.1 Clinical Motivation and Significance

Ultrasound has been used in the medical field to visualize internal tissue struc-

tures since the 1950s [1]. It is a competitive alternative to magnetic resonance imag-

ing and other imaging modalities because it is less expensive and more portable.

Additionally, it does not introduce harmful ionizing radiation into the body, unlike

x-ray imaging or computed tomography.

Some of the more recent advancements in ultrasound imaging include smaller

hand-held systems [2], the imaging of mechanical properties with compression-based

[3] and acoustic radiation force-based [4] techniques, and real-time 4D imaging with

matrix array probes [5, 6]. Despite these remarkable contributions to ultrasound

imaging and instrumentation, none improve the fundamental processing of ultra-

sound data. A conventional delay-and-sum beamformer, or variations thereof, has

always been applied to the echo signals received by individual transducer elements

to process ultrasound data and form an image. Ultrasound images formed by this

method are typically challenged by artifacts like clutter.

1

Clutter is a problematic noise artifact in a variety of diagnostic ultrasound appli-

cations. It is most noticeable in the anechoic regions of images and appears as diffuse

acoustic echoes when, by definition, no echoes should be present. Clutter may also be

found in hypoechoic or isoechoic regions of an image, making a similar appearance as

a diffuse, haze-like noise artifact. As its name suggests, this noise artifact “clutters”

ultrasound images and obfuscates signals of diagnostic importance. Clutter arises

from a variety of acoustic properties, including the reverberation of sound in multi-

ple tissue layers, acoustic scattering from off-axis structures, and random electrical

or thermal noise [7, 8, 9]. Clinical tasks that are complicated by the presence of

clutter include the detection of microcalcifications that indicate early-stage breast

cancer [7], measuring the intima-media thickness of a carotid artery to determine

cardiovascular health [10], and identifying cancerous lesions in the liver or kidneys.

In echocardiography, clutter is problematic because it obscures endocardial bor-

ders. Visualization of these borders is necessary to measure several predictive factors

of heart disease, including mass, volume, ejection fraction, and myocardial strain [11].

Clutter also inhibits visualization of tumors, vegetations, and other cardiac abnor-

malities [12, 13, 14]. Approximately 10-20% of patients have suboptimal echocardio-

grams due to clutter [14, 15]. Vancon et al. [16] reported myocardium-to-cavity echo

magnitude ratios as low as 0.7, which indicates that clutter noise can be stronger

than the myocardium itself. Giglio et al. [17] noted that signals measured in my-

ocardial cavities can be dominated by clutter, rather than by scattering from blood

cells.

Harmonic imaging is one of the most widely used clutter reduction methods.

Instead of forming images from echoes that have the same frequency spectrum as

transmitted pulses, harmonic images are created from echoes that have an integer

multiple of the frequency spectrum of the transmitted pulses. These harmonic fre-

quencies are generated as a pulse travels through non-linear tissue. One reason for

2

the reduced clutter content in harmonic images is that harmonic frequencies are not

fully developed near the transducer surface, where sound reverberations typically

occur [18, 19, 20, 21]. In several studies, harmonic imaging lowered the percentage

of patients with suboptimal images due to clutter from 45-51% to 11-24% [22, 23],

indicating that harmonic imaging does not always sufficiently reduce clutter.

Another approach to clutter reduction is to separate tissue signals from clutter

noise using motion filters or principal component analysis-based filters [8, 24, 25,

26]. These filters are effective at reducing stationary or slowly-moving clutter. In

echocardiography, this type of clutter is often due to acoustic reverberations within

the chest wall or reflections from stationary extracardiac off-axis structures such

as the ribcage and lungs. The challenge with these filters is their limited ability

to remove the higher-velocity clutter that is due to reflections from intracardiac

structures like the chordae tendineae, valves, and myocardial walls [8, 27, 28].

In transesophageal echogcardiography (TEE), images are acquired by inserting an

ultrasound transducer in the esophagus, rather than utilizing the standard transtho-

racic window [13, 29]. Despite the improvements in image quality, TEE poses a

discomfort to patients and is not recommended for routine clinical use [13, 30].

Another alternative is contrast echocardiography, which utilizes contrast agents

to enhance endocardial border visualization [31]. However, the injection of contrast

agents presents an additional expense to patients and necessitates a sterile environ-

ment for intravenous access [32, 33, 34].

Short-Lag Spatial Coherence (SLSC) imaging [35] is a novel beamforming tech-

nique that overcomes many of the challenges and limitations associated with existing

clutter reduction methods and border enhancement approaches. It utilizes the spa-

tial coherence of backscattered ultrasound echoes to form images. SLSC images

demonstrate superior signal-to-noise and contrast-to-noise ratios when compared to

conventional B-mode images. The work herein demonstrates SLSC imaging’s po-

3

tential to reduce cardiac clutter, clarify endocardial borders, and thereby improve

border-dependent cardiac measurements.

1.2 Dissertation Overview

The foundation of this dissertation relies on the content of individual, peer-

reviewed publications. Multiple sections contain portions of these manuscripts in

their original, unaltered forms. As a result, there are redundancies regarding the ex-

planation of recurring principles in separate chapters. However, these redundancies

are essential to the flow and content of the individual chapters.

Additionally, there are variations in the calculation of the following performance

metrics: contrast, contrast-to-noise ratio (CNR), and resolution. Although variations

exist throughout the dissertation, the methods are consistent within each chapter,

and each metric is consistent with its general definition. For example, contrast is

generally defined as the ratio of the brightness of one region relative to another. CNR

is generally defined as a measure of the difference in brightness between two regions

relative to signal variance. Resolution is generally defined as the width of a point

spread function. Therefore, in each chapter, an improvement in contrast, CNR, or

resolution has the same general meaning, regardless of any inter-chapter variations

in calculation methods.

This dissertation is organized as follows. Chapter 2 offers a brief introduction to

fundamental topics that form the basis of SLSC imaging. In Chapter 3, clutter mag-

nitudes are quantified and an analytical expression for the loss of image contrast due

to clutter is derived and compared to measured results in simulated and experimental

images. Although the primary focus is clutter in abdominal images, the measure-

ments are applicable to other imaging scenarios. In Chapter 4, a novel motion-based

clutter reduction method is proposed and tested with simulated, phantom, and in

vivo data. The method demonstrates the reduction of stationary abdominal clutter.

4

In Chapter 5, the development of SLSC imaging is discussed in detail. SLSC is an

attractive clutter reduction approach for both stationary and non-stationary clut-

ter in ultrasound images. In Chapter 6, axial and lateral resolution characteristics

of SLSC images are investigated and compared to conventional B-mode resolution

metrics. In Chapter 7, SLSC imaging is applied to clinical in vivo cardiac data, and

it is presented as a viable clutter reduction method in echocardiography. Finally,

Chapter 8 summarizes overall conclusions from all of the work contained herein and

offers a brief discussion on the potential future directions of SLSC imaging.

5

2

Background

2.1 van Cittert-Zernike Theorem

SLSC imaging is based on the van Cittert-Zernike (VCZ) theorem applied to

ultrasound, which predicts the spatial coherence of backscattered waves [36, 37].

The prediction states that a spatial coherence function may be calculated with the

following equation:

C(m) =

∫ ∞

−∞|χ(x) ·H(x)|2 e−j2π m

λzxdx, (2.1)

where C is spatial covariance (a measure of spatial coherence), m is the lateral spacing

between two observation points on a receive aperture, χ is the scattering function,

H is the transmit pressure field, x is the lateral spatial coordinate at the ultrasound

focal depth, z is the focal depth, and λ is the ultrasound wavelength. Thus, the VCZ

theorem predicts that the spatial covariance of wavefronts across an aperture is the

Fourier transform of the square of the product of the lateral transmit beam pressure

and the lateral backscatter, or source function, evaluated at spatial frequencies equal

to m/λz.

6

H(x)

(a)

χ(x) = Diffuse Scatterers

(b)

χ(x) = Point Target

(c)

χ(x) = Lesion

(d)

Figure 2.1: (a) Estimated transmit pressure field and sample scattering functionsfor (b) diffuse scatterers, (c) a point target, and (d) a lesion.

The transmit pressure field, H(x), is estimated from the geometry of the aper-

ture, using the Fraunhofer approximation applied to ultrasound. This approximation

states that the ultrasound beam’s pressure amplitude pattern in the far field of the

aperture is the Fourier transform of the transducer aperture [38]. Representing a

rectangular aperture function as a rect and applying the Fraunhofer approximation

yields an ultrasound pressure amplitude pattern that is a sinc function. Hence, H(x),

may be modeled as a sinc, as demonstrated in Fig. 2.1(a).

Notice the target dependency characterized by the scattering function, χ(x), in

Eq. 2.1. When imaging diffuse scatterers, the source function may be modeled as a

constant, as demonstrated in Fig. 2.1(b), and the expected spatial coherence across

the receive aperture is a triangle. The triangle decreases from 1 at zero lag to 0

at lag N -1, where N refers to the number of elements in the transmit aperture, as

demonstrated in Fig. 2.2. The spatial coherence of tissue is expected to be similar

to that of diffuse scatterers.

When imaging a point target, the scattering function can be modeled as a delta

function with infinite amplitude in one lateral location, as shown in Fig. 2.1(c), and

the expected spatial coherence is simply a constant. For an anechoic or hypoechoic

7

0 N−10

1

Lag (Spacing Between Recieve Elements)

Cor

rela

tion

Diffuse ScatterersPoint TargetInside Lesion

Figure 2.2: The expected coherence functions for diffuse scatterers, a point target,and inside a lesion. The abscissa represents the lag, or spacing between receiveelements. The ordinate represents inter-element RF echo correlation.

lesion, the scattering function looks more like one period of a pulse wave, with its

high level outside of the lesion and its low level inside the lesion, as depicted in

Fig. 2.1(d). The product of this pulse wave multiplied by a sinc is weighted more in

regions where the pulse is high and less in regions where the pulse is low. The Fourier

transform of the square of this product, when the mainlobe of the sinc is aligned with

the low level of the pulse wave (i.e. the spatial coherence function inside the lesion)

is demonstrated in Fig. 2.2. It has a marked decrease from 1 to 0 in the short lag

region.

To compare expected spatial coherence functions with those measured in ultra-

sound data, the three source functions were created and imaged using Field II sim-

ulations [39]. The average measured spatial coherence of a point target surrounded

by scatterers, an anechoic cyst surrounded by scatterers, and the surrounding diffuse

scatterers are shown in Fig. 2.3. The error bars indicate plus or minus one standard

deviation within the region of interest. Notice the many similarities between Fig. 2.2

and Fig. 2.3. On average, the point target has fairly constant coherence across the

receive aperture, the average coherence of the diffuse tissue-like region looks much

like the expected triangle, and that of the region inside the anechoic lesion shows a

8

0 20 40 60 80−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Lag (Receive Element Spacing)

Cor

rela

tion

inside cystoutside cystpt target

Figure 2.3: Measured average spatial coherence across a 96-element receive aper-ture for the following simulated scattering functions: point targets (pt target), ananechoic region (inside cyst), and a speckle background (outside cyst).

steep decrease from 1 to 0. This steep decrease is observed in anechoic and hypoe-

choic lesions, and it indicates that the region inside such lesions has very low spatial

coherence relative to the surrounding tissue. This type of decrease is observed in sim-

ilar lesions that are corrupted by clutter. Note that the largest differences between

the different spatial coherence functions occur in the short-lag region.

2.2 Beamforming: B-mode vs. SLSC Imaging

Beamforming is a term used to describe the processing of signals received by

individual transducer elements to form an ultrasound image. For a receive aperture

with N elements of equal spacing, the signal received by the ith element is defined

as si(n), where n is a depth or time sample number, and si is a zero-mean signal.

The signals are received in order of the time that they arrived at the surface of the

transducer aperture. However, they must be time-delayed to ensure that all of the

signals at sample n correspond to the same depth location, instead of the same arrival

time.

After time delay of the element signals, the beamforming methods for B-mode

9

and SLSC imaging diverge. To create one beam of ultrasound data (i.e. one A-line

in a B-mode image), the delayed echoes are summed, envelope detected, and log

compressed. To create one pixel in a SLSC image, the estimated spatial correlation

across the receive aperture is calculated using the following equation [40]:

R(m) =1

N −m

N−m∑i=1

∑n2

n=n1si(n)si+m(n)√∑n2

n=n1s2

i (n)∑n2

n=n1s2

i+m(n). (2.2)

where m is the distance, or lag, in number of elements.

Since the largest differences between the spatial coherence of different target types

occur in regions of low lags, the short-lag spatial coherence is computed from the

integral of a spatial coherence function over the first M lags:

Rsl =M∑

m=1

R(m). (2.3)

where M is typically a value that corresponds with 1-30% of the transmit aperture.

To create SLSC images, the short-lag spatial coherence at selected depths, n, of the

channel signals that form one A-line is computed with Eqs. 2.2 and 2.3, using a

correlation kernel size (i.e. n2 − n1) of approximately one wavelength.

Figure 2.4 demonstrates the SLSC beamforming technique with transthoracic

imaging of the left ventricle of an ovine heart, shortly after euthanasia. The channel

signals received by a cardiac transducer were acquired from the center of the image.

The channel signals were used to generate conventional B-mode and SLSC images.

In the B-mode image, the left ventricular wall is indistinguishable from the chamber

because of the high magnitude of clutter. The contrast and CNR of the surrounding

tissue with the ventricular chamber is 3.6 dB and 0.51, respectively. In the SLSC

image, the ventricular wall is remarkably clearer and has significantly greater contrast

and CNR, specifically 7.4 dB and 3.63, respectively.

10

Figure 2.4: Transthoracic B-mode and SLSC images of the left ventricle in a sheep,shortly after euthanasia. The ventricular wall is indistinguishable from clutter in the nearfield of the B-mode image. The wall is highly visible in the SLSC image and has improvedcontrast and CNR with the ventricular chamber.

11

3

Quantitative Assessment of Clutter Magnitudes inSimulated, Phantom, and In Vivo Ultrasound Data

The work presented in this chapter was published in the following manuscript:

Lediju MA, Pihl MJ, Hsu SJ, Dahl JJ, Trahey GE. Quantitative assessment of

the magnitude, impact, and spatial extent of ultrasonic clutter. Ultrasonic Imag-

ing 30(3):151-168. 2008.

3.1 Introduction

Clutter is a ubiquitous phenomenon in ultrasonic imaging. It appears as a dif-

fuse haze and is most easily visualized in anechoic or hypoechoic regions. Clutter

typically overlays structures or signals of interest and often degrades image contrast.

In Doppler blood flow imaging of the heart chambers and blood vessels, clutter from

the surrounding tissue and vessel walls is typically 40-100 dB stronger than echoes

from blood [10] and wall filtering is necessary to observe and measure blood flow.

12

Similarly, in cardiac B-mode imaging, clutter obstructs important diagnostic infor-

mation and is one of the most problematic noise artifacts [8]. In breast imaging,

clutter reduces image contrast, limits the depth at which diagnostic information can

be obtained, and diminishes the ability to visualize cystic contents, calcifications, and

other subtle diagnostic details [7, 41]. The important anatomical features of a fetus

can also be obscured in the presence of strong clutter noise [42]. The appearance of

clutter varies from patient to patient, however it is observed to be more prevalent

in overweight or obese individuals [43, 18]. Sources of acoustic clutter include sound

reverberation in tissue layers, scattering from off-axis structures, ultrasound beam

distortion, returning echoes from previously transmitted pulses, and random acoustic

or electronic noise [8, 7, 18, 44, 9, 45].

One method reported to reduce clutter is harmonic imaging [18, 19]. In this tech-

nique, the higher harmonics generated by nonlinear wave propagation through tissue

are imaged, as opposed to the first, or fundamental, harmonic of the transmitted

pulse [18, 20, 21]. These nonlinear waves are not fully developed near the transducer

surface, which is one postulated reason why the near-field clutter seen in fundamental

images is not as prevalent in harmonic images [46]. Other explanations for clutter

reduction with harmonic imaging include reduced sensitivity of harmonic beams to

phase aberration and suppressed side and grating lobes [46, 47, 29]. However, har-

monic imaging does not reduce clutter in all patients; in some cases, fundamental

images exhibit less clutter, while in other cases there is no difference [44, 48].

There is a need for greater insight into clutter phenomena in order to design

more robust methods for clutter reduction. The goals of this paper are to determine

the effect of clutter on lesion detectability and to quantify clutter magnitudes in

simulated, phantom, and in vivo data. An analytical expression for contrast loss due

to clutter is derived and compared to phantom data. Simulations and phantoms are

utilized to quantify the magnitude of clutter resulting from known sources. Images of

13

urine-filled bladders of five volunteers are examined to determine clutter magnitude

as a function of distance from the bladder walls. The effectiveness of harmonic

imaging with respect to clutter reduction is analyzed with contour maps displaying

pixel-wise brightness differences between fundamental and harmonic images.

3.2 Methods

3.2.1 Analytical Expression for Contrast Loss Due to Clutter

(a) (b)Figure 3.1: Schematic of a lesion in the (a) absence and (b) presence of a uniformclutter signal that overlays the entire image.

Consider an ultrasound image of a hypoechoic lesion surrounded by a uniform

background, as shown in the schematic of Fig. 3.1 (a). The definition of lesion

contrast is taken to be

C = SB/SL, (3.1)

where SB and SL are the mean envelope-detected radio-frequency (RF) signals in

the background and lesion, respectively. The contrast can also be defined as

CdB = 20log(SB/SL)

= xB − xL, (3.2)

where xB and xL are the background and lesion signals, respectively, in units of dB

relative to the background signal. Eq. (3.2) is the expression for image contrast in

the absence of clutter.

14

When clutter noise is present, as shown in the schematic of Fig. 3.1 (b), the

definition of contrast becomes

C ′dB = x′B − x′L

= 20log(S ′B/S ′

L), (3.3)

where S ′B and S ′

L represent the mean value of the cluttered envelope-detected RF

signals in the background and lesion, respectively, and x′B and x′L represent the

cluttered background and lesion signals, respectively, in units of dB relative to the

cluttered background signal.

In the RF domain, clutter noise is assumed to be a zero-mean Gaussian random

variable that is uncorrelated with and independent of the speckle in the “unclut-

tered” ultrasound image. The RF echoes used to form an uncluttered image of a

diffuse speckle-generating structure can also be described by a zero-mean Gaussian

random variable [49]. Assuming that the cluttered image can be modeled as the

sum of these two zero-mean Gaussian random variables, the result is a new zero-

mean Gaussian random variable that characterizes the RF echoes of the cluttered

image. After envelope detection, a zero-mean Gaussian random variable is trans-

formed into a Rayleigh random variable [49, 36, 50]. Because the clutter and the

speckle in the uncluttered image are uncorrelated and independent, the mean of the

combined envelope-detected echoes (i.e., the Rayleigh random variable characteriz-

ing the cluttered image) can be expressed in terms of the means of the individual

Rayleigh random variables [50], as shown in Eq. (3.4).

S ′B =

√S2

B + S2C and S ′

L =√

S2L + S2

C , (3.4)

where SC is the mean of the signal due solely to clutter.

Using Eq. (3.4), Eq. (3.3) can be further refined to give an expression for C ′dB

in terms of the mean signals of the background, lesion, and clutter, as shown in Eq.

15

(3.5).

C ′dB = 20log

√S2

B + S2C

S2L + S2

C

. (3.5)

The difference between Eqs. (3.2) and (3.5) is the contrast loss due to clutter:

Closs = CdB − C ′dB

= 20log

(SB

SL

√S2

L + S2C

S2B + S2

C

)

= 20log

√1 + (SC/SL)2

1 + (SC/SB)2. (3.6)

By definition of the decibel, Eq. (3.6) can be rewritten as Eq. (3.7),

Closs = 20log

√1 + 10(xC−xL)/10

1 + 10(xC−xB)/10, (3.7)

where xC is the signal due solely to clutter in units of dB relative to the background

signal, xB.

3.2.2 Field II Simulations

Simulations of acoustic clutter in ideal imaging situations were performed using

Field II [39, 51]. A 2.5 MHz, 70% bandwidth, 128-element linear array having

elements with 0.48 mm lateral pitch and 1.4 mm height was simulated. The lateral

transmit focus of the array was set to 6 cm, and a lens provided elevation focusing

at 6 cm. Dynamic focusing was applied during receive beamforming, and Hanning

window apodization was applied to the transmit and receive apertures. The effects

of aberration, reverberation, and electronic or acoustic noise were not included in

the simulations.

Two targets were imaged with the simulated array. The scatterer density of

each target was 10 scatterers per resolution volume. The first target was a 1.2

16

cm (lateral) x 2 cm (axial) x 1 cm (elevation) block of scatterers positioned to the

right of the array’s center, such that 0.6 cm of the block and 1.2 cm of anechoic

space were imaged. This target was used to measure the clutter generated when

scatterers were placed in one lateral tail of the beamformer’s point spread function

(PSF). The second target was a 5 cm spherical void within a 13 cm (lateral) x 7 cm

(axial) x 6 cm (elevation) block of scatterers. This target was used to simulate the

bladder geometry and to measure the clutter generated from both lateral tails of the

beamformer’s PSF.

3.2.3 Experimental Methods

A Siemens Antarestm ultrasound scanner and CH6-2 curvilinear transducer (Siemens

Medical Solutions USA, Inc., Issaquah, WA) were used to obtain images of phan-

toms and in vivo bladders. The scanner was operated in the tissue harmonic imaging

mode with a transmit frequency of 2.5 MHz. The Axius Direct Ultrasound Research

Interface (Siemens Medical Solutions USA, Inc., Issaquah, WA) was used to acquire

raw radio frequency (RF) data without significant time-gain compensation and be-

fore the application of nonlinear processing steps. In the harmonic imaging mode,

the scanner implements the pulse inversion technique [52, 53], and therefore, the raw

RF data consists of both normal and inverted pulse-echo signals. Fundamental im-

ages were constructed from the normal pulses, and harmonic RF data was obtained

by summing the normal and inverted pulse echoes. To form B-mode images, the

RF data was envelope detected, normalized to the brightest point, log compressed,

limited to a dynamic range of 45 dB, and then scan converted.

A commercially available CIRS (Norfolk, VA) Biometric Fetal Ultrasound Train-

ing Phantom (Model 068) and a custom bladder phantom were used to illustrate the

imaging system’s capability to display anechoic regions and to provide baseline mea-

surements for the clutter analysis methods. The bladder phantom was created by

17

submerging a water-filled balloon in a graphite, propanol, and water solution (RMI

(now Gammex, Inc., Middleton, WI) SuperSpheres Model TM-C, discontinued by

manufacturer). Clutter was introduced into several phantom images by placing a 1

cm-thick copper wire mesh at the transducer surface.

In vivo human bladder images were acquired from five male volunteers. The lat-

eral span of the transducer was roughly aligned with the transverse plane and angled

approximately perpendicular to the abdominal wall. The same data acquisition and

image formation methods described for the phantom studies were used in the in

vivo study. All image processing and analysis was implemented with Matlab (The

Mathworks Inc., Natick, MA), and all echo magnitude values were measured from

the envelope detected RF data. Outlines of the fetal phantom, bladder phantom, and

in vivo bladder wall were subjectively estimated from B-mode images and displayed

as a visual aid during image analysis.

3.2.4 Data Analysis

Contour plots and graphs of clutter magnitude as a function of distance from

echogenic structures were used to assess clutter magnitudes in the simulated, phan-

tom, and in vivo images. The contour plots were created from low-pass filtered,

envelope-detected data. Low-pass filtering was achieved by convolving the envelope-

detected RF data with a rectangular kernel of 201 pixels x 15 pixels, which corre-

sponds to 0.96 mm x 4.2 mm in the simulated block image, 0.96 mm x 7 mm in

simulated bladder image, and 3.9 mm x 4.5◦ in the scan-converted phantom and

in vivo images. The contour lines were then overlaid on an image of the echogenic

border outlines. Each contour line on the plot represents the echo magnitude in

units dB relative to the mean brightness of the contour data contained within each

respective outline.

Regional variations in fundamental and harmonic images were assessed with con-

18

tour maps. Pre-scan-converted, envelope-detected images were low-pass filtered with

a rectangular kernel of 151 x 15 pixels (which corresponds to 2.9 mm x 4.5◦ in the

scan converted image). The pixel-wise ratio between the filtered fundamental and

harmonic images was then calculated and discretized into 3 dB intervals ranging from

27 dB to -6 dB.

3.3 Results

3.3.1 Contrast Loss Due to Clutter

The degree to which clutter degrades lesion contrast, as predicted by equation

(7), is shown in Fig. 3.2. The contrast loss due to clutter is plotted as a function of

clutter magnitude relative to the background signal for eight values of “uncluttered”

lesion contrast. The loss in contrast increases with increasing clutter levels. Each

curve asymptotes to the contrast of the uncluttered lesion.

−30 −20 −10 0 10 200

5

10

15

20

25

30

35

40

45

50

Clutter relative to background (dB)

Con

tras

t los

s (d

B)

48 dB42 dB36 dB30 dB24 dB18 dB12 dB 6 dB

Figure 3.2: Contrast loss as a function of clutter relative to the background signalfor eight values of “uncluttered” lesion contrast.

3.3.2 Simulation Results

The simulated block image is shown in Fig. 3.3 (a). The corresponding contour

plot (Fig. 3.3 (b)) shows a rapid transition from echogenic to anechoic, and the

spacing between the contour lines gradually increases at greater distances from the

19

Lateral Position (cm)

Axi

al P

ositi

on (

cm)

−1 −0.5 0 0.5

5

5.5

6

6.5

Axi

al P

ositi

on (

cm)


−70

−70

−65−60

−55

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

−5

0

0

0

00

0

0

0−1 −0.5 0 0.5

5

5.2

5.4

5.6

5.8

6

6.2

6.4

6.6

6.8

Con

tour

line

s (d

B)

−75−70−65−60−55−50−45−40−35−30−25−20−15−10 −5 0

−1 −0.5 0 0.5−80

−70

−60

−50

−40

−30

−20

−10

0


Mag

nitu

de (

dB)

(a) (b) (c)


Axi

al P

ositi

on (

cm)

−2 0 2

3

4

5

6

7

8

9

Axi

al P

ositi

on (

cm)


0

−35

−35 −35

−35−35 −40

−40

−40−40

−40

−40

−45

0

0

00

0 0 00

0

0

0−5−5 −5 −5

0 0 0 0

−40

−3 −2 −1 0 1 2 3

3

4

5

6

7

8

9

Con

tour

line

s (d

B)

−75−70−65−60−55−50−45−40−35−30−25−20−15−10 −5 0

−2 −1 0 1 2−60

−50

−40

−30

−20

−10

0


Mag

nitu

de (

dB)

(d) (e) (f)Figure 3.3: Field II simulated images of (a) a block and (d) a spherical void.The corresponding contour plots (b and e) are referenced to the mean signal of therespective echogenic borders. The graphs of average signal magnitudes as a functionof lateral position (c and f) are referenced to their respective maxima, and the verticallines delineate echogenic borders. The values in (c) were obtained from averagingaxial positions 5-7 cm, and (f) shows the average of axial positions 5.5-6.5 cm.

echogenic border. The average magnitude of axial positions 5 cm through 7 cm in

the simulated block image is shown in Fig. 3.3 (c) as a function of lateral position.

The minimum signal is -72 dB relative to the maximum of the averaged values and

occurs at a distance of 1.2 cm from the block boundary.

The simulated bladder image is shown in Fig. 3.3 (d). Unlike the simulated

block image, the anechoic space of the simulated bladder image is surrounded by

scatterers in the elevation dimension. The contour plot of the simulated bladder

image is shown in Fig. 3.3 (e). There are rapid signal transitions from 0 dB to -35

dB near the echogenic border, and the minimum signal is -45 dB further away from

the borders. These measurements are relative to the mean signal of the contour data

contained within the outlined border. The average magnitude of axial positions 5.5

cm to 6.5 cm is plotted as a function of lateral position in Fig. 3.3 (f). The minimum

20

Axi

al P

ositi

on (

cm)

Lateral Position (cm)−5 0 5

0

2

4

6

8

Axi

al P

ositi

on (

cm)


0

2

4

6

8

(a) (b)

Axi

al P

ositi

on (

cm)


−33−33

−30−27

−30

−30

−24 −27−27

−24

−27−30

−27

−27−18

−24

−30−21−18

−27

−27

3 03 3

3

0

00

03

333

0

−3

0

3

3

0

−3

−3

−6

−9

−30−24

−9

−6−3

−6−9

−12

−3 −30

0

0

0

−30

−3

−3

−6

0−3

−6

−9

−12

−3

3

−3

−30

−5 0 5

0

2

4

6

8

Con

tour

line

s (d

B)

−42−39−36−33−30−27−24−21−18−15−12 −9 −6 −3 0 3

Axi

al P

ositi

on (

cm)


−12−21

−24−24−27

−30

−30−33

−33−30

−33

−30

−27

−30

−27

−24

−24

−15

−30

−27

30 −3 −3

0−63

3

3

033

0

3

3

0−3−30

−24

−24

−3−3

0

3

3

0−3−6−9−12−15 −18

−21 −15−9−6

−12

−24 −24

00

−5 0 5

0

2

4

6

8

Con

tour

line

s (d

B)

−42−39−36−33−30−27−24−21−18−15−12 −9 −6 −3 0 3

(c) (d)Figure 3.4: Simultaneously acquired (a) fundamental and (b) harmonic images ofthe bladder phantom and corresponding contour plots.

signal is -53 dB relative to the maximum of the averaged values.

3.3.3 Phantom Results

Simultaneously acquired fundamental and harmonic images of the bladder phan-

tom are shown in Fig. 3.4 (a) and (b), respectively. Contrast in the fundamental

bladder phantom images with and without the clutter layer were calculated using two

equally sized regions (2.6 cm x 0.2 cm) in the bladder and background, at a depth

of 1 cm from the proximal bladder boundary. (The image of the bladder phantom

with the clutter layer is not shown.) Without the clutter layer, the contrast at the

specified location is 29 dB. This contrast is reduced to 9 dB in the presence of the

clutter-producing layer, resulting in a contrast loss of 20 dB.

Contour plots of the fundamental and harmonic bladder phantom images without

the clutter-producing layer are shown in Fig. 3.4 (c) and (d), respectively. Rever-

berations from the bottom of the water tank that housed the phantom are apparent

21

Axi

al P

ositi

on (

cm)


0

2

4

6

8

10

Axi

al P

ositi

on (

cm)


0

2

4

6

8

10

Axi

al P

ositi

on (

cm)


0

2

4

6

8

10

(a) (b) (c)

Axi

al P

ositi

on (

cm)


−40−44 −40 −40

−44−40

−40−280

−48−44−36

−20 −20

−40−44 −32

−40−40

0−32

−28

−24−28

−2840

−16−8

40

0

4−32

−28

−24

−20

−16 −16−20−20

−16−20

−4

4 −4 04−4

−40

−16−8

−44

−16−16−20

−4

−36

−44

0

4

−5 0 5

0

2

4

6

8

10C

onto

ur li

nes

(dB

)−56−52−48−44−40−36−32−28−24−20−16−12 −8 −4 0 4

Axi

al P

ositi

on (

cm)


−15

−6−9

33

3

−18 −18−21

−15

−15

−18

−18

−21−9 −9 −9

−9

−18

−15

−12−9

−6−33

−9−15−18

−24−27

−30

−15

−12

−9−6−3

03

−15−120

−3−6−93−3

−6

−3

−3 −6

−3

−3

−18−18−18

3−60

−5 0 5

0

2

4

6

8

10

Con

tour

line

s (d

B)

−42−39−36−33−30−27−24−21−18−15−12 −9 −6 −3 0 3

Axi

al P

ositi

on (

cm)


−12−6−30

3

−21

−21−24−24−33−27

−18−27−24−30

−27

−9−24

−21−18

−24

−21

−18

−15

−12−9

−21−18

−15−12

−9−6

−30

3

00

−3−6

−6−12

−18 0

−3

−6

−6−6

−30

30

−27 −33

−18−18

−5 0 5

0

2

4

6

8

10

Con

tour

line

s (d

B)

−42−39−36−33−30−27−24−21−18−15−12 −9 −6 −3 0 3

(d) (e) (f)Figure 3.5: Images and contour plots of the fetal phantom in the absence andpresence of a clutter-producing layer. (a) Fundamental B-mode image of the fetalphantom. Simultaneously acquired (b) fundamental and (c) harmonic images withclutter-producing layer placed between the transducer and phantom. The ROIs in-side and to the right of the ventricles were used for the contrast calculations describedin the text. Accompanying contour plots: (d) fundamental image in the absence ofclutter, (e) fundamental image in the presence of clutter-producing layer, and (f)harmonic image in the presence of clutter-producing layer. Note the differences incolor scales.

in both images. The contour plots show rapid signal transitions near the echogenic

borders, ranging from 0 dB to -18 dB in the fundamental image and 0 dB to -24 dB

in the harmonic image. The minimum signal inside the bladder phantom is -33 dB

in both the fundamental and harmonic images.

A fundamental image (Fig. 3.5 (a)) of the fetal phantom, simultaneously acquired

fundamental (Fig. 3.5 (b)) and harmonic (Fig. 3.5 (c)) images of the fetal phantom

with the clutter-producing layer placed at the transducer surface, and associated

contour plots are shown in Fig. 3.5. The contour plot corresponding to Fig. 3.5 (a)

shows a steep transition from 0 dB to -36 dB near the fetal face and the dorsal side

of the fetal hand. The near-field anechoic region is at most 48 dB down relative to

the echogenic border. Clutter magnitudes are greater in the hypoechoic regions to

22

the left of the fetal head, in the ventricles of the fetal head, and underneath the fetal

hand. Similar results are seen in the contour plot of the harmonic image without

the clutter layer (not shown), where the near-field anechoic region is at most 44 dB

down relative to the echogenic border.

When the clutter-producing layer is placed between the phantom and transducer,

the fundamental image shown in Fig. 3.5 (b) exhibits a clutter signal that overlays the

entire image and is most easily observed in the hypoechoic regions of the phantom.

The accompanying contour plot in Fig. 3.5 (e) reveals that the clutter magnitude in

the near-field region is on average 18 dB down relative to the fetal boundary. Clutter

magnitudes are greater in the hypoechoic regions to the left of of the fetal head and

in the ventricles. The clutter-producing layer is visible at 0-1 cm in the fundamental

B-mode image and is 9 dB down relative to the fetal boundary. In the corresponding

harmonic image (Fig. 3.5 (c)), much of the visible clutter is eliminated and the

clutter-producing layer is no longer visualized. The accompanying contour plot in

Fig. 3.5 (f) reveals that the near-field signal is on average 24 dB down relative to

the fetal boundary. Clutter magnitudes are greater in the hypoechoic regions to the

left of the fetal head, in the ventricles, and underneath the fetal hand.

The contrast between two regions of interest (ROIs) at the same depth, inside

and to the right of the ventricles, was measured in the simultaneously acquired

fundamental and harmonic images with the clutter-producing layer. The ROIs were

placed in identical locations in the fundamental and harmonic images (see Fig. 3.5).

The measured contrasts (as defined by equation (3), with the ventricles representing

the “lesion”) in the fundamental and harmonic images were 11.8 dB and 11.5 dB,

respectively.

23

3.3.4 In Vivo Results

The in vivo study consisted of five volunteers whose ages and body mass indices

(BMIs) are recorded in Table 3.1. Volunteer 2 has a BMI of 25.8, which is considered

overweight [54]. The magnitude and spatial extent of clutter in a bladder image

from this volunteer are shown in Fig. 3.6. The contour plot of the fundamental

image (Fig. 3.6 (b)) shows a gradual decrease in clutter as a function of distance

from the proximal bladder wall. Near the lateral and distal bladder walls, the signal

transitions are more rapid. Similarly, in the contour plot of the harmonic image (Fig.

3.6 (d)), the rate of signal transitions near the proximal bladder wall is more gradual

than the rate of signal transitions near the lateral and distal walls. The minimum

clutter magnitudes inside the fundamental and harmonic bladder images are -27 dB

and -30 dB, respectively.

Table 3.1: Age and Body Mass Index (BMI) of each volunteer

Volunteer No. Age BMI1 53 30.42 31 25.83 29 22.64 51 23.75 41 20.7

Bladder images and associated contour plots for Volunteer 1, whose BMI (30.4)

is indicative of obesity [54], are shown in Fig. 3.7. There is more clutter in these

bladder images than in those from Volunteer 2 (Fig. 3.6). As a result, the rate of

signal transitions in the contour plots are more gradual near the bladder walls of

this volunteer. Signal transitions near the proximal and lateral bladder walls are

more gradual in the contour plot of the fundamental image (Fig. 3.7 (b)) than they

are in the contour plot of the harmonic image (Fig. 3.7 (d)). Signal transitions

near the distal bladder wall are similar in both images. The harmonic image has

lower clutter magnitudes than the fundamental image. The minimum magnitude in

24

Axi

al P

ositi

on (

cm)


0

2

4

6

8

10

Axi

al P

ositi

on (

cm)


−27−24

−24

−21

−21−24

−21

−24 −21

−21

−24−15

−9 −6−15 −9

0

−15

0 0 06

−3

0

30

6

612126

912

9

−9

6

−3

3

−12 −18−9

−9−12−18

−18−15

−6

−3−12

−12

9 6 3 3 123

−3

−15

−15

0

−15

−12

−18

−15

−21

−6

−9

0

−5 0 5

0

2

4

6

8

10

Con

tour

line

s (d

B)

−30−27−24−21−18−15−12 −9 −6 −3 0 3 6 9 12 15

(a) (b)

Axi

al P

ositi

on (

cm)


0

2

4

6

8

10

Axi

al P

ositi

on (

cm)


−27−24

−27−24

−30−30−24

−27−24 −21

−18 −15−21

−21−24−21

0−6−3−30

−3−3

3

−3

3612

129

1515

6

−9

−3

3

−27−24 −18−24−24

−6

−15−18

−6

−3

−15

−15

−3 6 63

30 6 9

0 −6

−9

−15

0

−21

−6

−21

−21−24

−15

−18

0

−5 0 5

0

2

4

6

8

10

Con

tour

line

s (d

B)

−30−27−24−21−18−15−12 −9 −6 −3 0 3 6 9 12 15

(c) (d)Figure 3.6: Simultaneously acquired in vivo bladder images ((a) fundamental and(c) harmonic) from Volunteer 2 (age 31, BMI 25.8) and corresponding contour plots.

the fundamental image is -15 dB, whereas the minimum magnitude in the harmonic

image is -24 dB.

3.3.5 Clutter Variation with Distance

Graphs of clutter magnitude in the fundamental and harmonic images of all vol-

unteers (and of the bladder phantom displayed in Fig. 3.4) are shown in Figs. 3.8

and 3.9, respectively. These graphs are shown as a function of distance from four

locations along the estimated bladder outlines: proximal, distal, left, and right. In-

formation for the graphs was extracted from contour plot data by manually selecting

a point (using the computer mouse) on the bladder outline and obtaining contour

data along the axial or lateral line emanating from that point. This process was

25

Axi

al P

ositi

on (

cm)


0

2

4

6

8

10

Axi

al P

ositi

on (

cm)


−12−12

−15 −15

−9

−9−9

−9

−6−3

00

−12−12

9 9 96

−30

−3

−3

−303000

0−3

−6−6−3

36

66

6

0−3

−3−6

−9

−12

−3

−6−60

−3

0−3

−6

−3−9

6

−6−6−9

−12−18

−12

−3

−3

−3

−3

−36

36

−3−5 0 5

0

2

4

6

8

10

Con

tour

line

s (d

B)

−30−27−24−21−18−15−12 −9 −6 −3 0 3 6 9 12 15

(a) (b)

Axi

al P

ositi

on (

cm)


0

2

4

6

8

10A

xial

Pos

ition

(cm

)


−24−21

−18

−15−12−9−6 −3

0

−18

−15

−15

−12 −6−12

−18

−12

−6

3 33

03

6

99 6 9

9

3

0

−3

−6−9

0 0−3

−15 −15−21−6

−3

0

−3

−3

−12

−3

−3

0

0−3

−3

−9

9

−3−15

−18

−5 0 5

0

2

4

6

8

10

Con

tour

line

s (d

B)

−30−27−24−21−18−15−12 −9 −6 −3 0 3 6 9 12 15

(c) (d)Figure 3.7: Simultaneously acquired in vivo bladder images ((a) fundamental and(c) harmonic) from Volunteer 1 (age 53, BMI 30.4) and corresponding contour plots.

repeated for a minimum of 10 points at each of the four outline locations. To display

the extracted results, contour line data for each location were averaged, normalized

to the mean contour value of the selected outline points at the specified location, and

graphed as a function of distance from the corresponding location. For each location,

the mean clutter magnitude of the five volunteers was calculated and displayed on

the graph.

Clutter magnitudes as a function of distance from the proximal bladder wall are

shown in Fig. 3.8 (a). This clutter persists well into the bladder, and the mean

clutter magnitude is 16.5 dB down from the proximal wall at 3 cm. Fig. 3.8 (b)

shows clutter magnitudes as a function of distance from the distal bladder wall. At

comparable distances, the mean magnitude is lower near the distal wall than it is

26

0 0.5 1 1.5 2 2.5 3−35

−30

−25

−20

−15

−10

−5

0

Distance from proximal boundary outline (cm)M

agni

tude

rel

ativ

e to

bou

ndar

y ou

tline

(dB

)

Volunteer 1Volunteer 2Volunteer 3Volunteer 4Volunteer 5MeanPhantom

0 0.2 0.4 0.6 0.8 1 1.2−35

−30

−25

−20

−15

−10

−5

0

Distance from distal boundary outline (cm)

Mag

nitu

de r

elat

ive

to b

ound

ary

outli

ne (

dB)


(a) (b)

0 0.2 0.4 0.6 0.8 1 1.2−35

−30

−25

−20

−15

−10

−5

0

Distance from left boundary outline (cm)

Mag

nitu

de r

elat

ive

to b

ound

ary

outli

ne (

dB)


0 0.2 0.4 0.6 0.8 1 1.2−35

−30

−25

−20

−15

−10

−5

0

Distance from right boundary outline (cm)

Mag

nitu

de r

elat

ive

to b

ound

ary

outli

ne (

dB)


(c) (d)Figure 3.8: Clutter magnitude in fundamental images of the in vivo bladders andthe bladder phantom as a function of distance from the (a) proximal, (b) distal, (c)left, and (d) right outline boundaries. The mean of the five volunteers is shown inbold. The phantom data was extracted from the contour plot data of Fig. 3.4 (c).

near the proximal wall. For example, the mean magnitude at 1.2 cm from the distal

wall is -18.5 dB, which is 7.2 dB less than the mean magnitude at 1.2 cm from the

proximal wall. Clutter magnitudes as a function of distance from the lateral bladder

walls are shown in Fig. 3.8 (c) and (d). The means for the five volunteers are within

0.2 dB at a distance of 1.2 cm from the left and right bladder walls.

The clutter magnitudes of the obese volunteer (Volunteer 1, BMI 30.4) are con-

sistently greater than the mean of the five volunteers. The overweight volunteer

(Volunteer 2, BMI 25.8) has greater clutter magnitudes than the normal-weight vol-

unteers as a function of distance from the proximal bladder wall, up to about 1.6

cm.

Analogous plots for the simultaneously acquired harmonic images are shown in

Fig. 3.9. Similar to the plots for the fundamental images, the mean signal is greater

27

0 0.5 1 1.5 2 2.5 3−35

−30

−25

−20

−15

−10

−5

0

Distance from proximal boundary outline (cm)M

agni

tude

rel

ativ

e to

bou

ndar

y ou

tline

(dB

)


0 0.2 0.4 0.6 0.8 1 1.2−35

−30

−25

−20

−15

−10

−5

0

Distance from distal boundary outline (cm)

Mag

nitu

de r

elat

ive

to b

ound

ary

outli

ne (

dB)


(a) (b)

0 0.2 0.4 0.6 0.8 1 1.2−35

−30

−25

−20

−15

−10

−5

0

Distance from left boundary outline (cm)

Mag

nitu

de r

elat

ive

to b

ound

ary

outli

ne (

dB)


0 0.2 0.4 0.6 0.8 1 1.2−35

−30

−25

−20

−15

−10

−5

0

Distance from right boundary outline (cm)

Mag

nitu

de r

elat

ive

to b

ound

ary

outli

ne (

dB)


(c) (d)Figure 3.9: Clutter magnitude in harmonic images of the in vivo bladders and thebladder phantom as a function of distance from the (a) proximal, (b) distal, (c) left,and (d) right outline boundaries. The mean of the five volunteers is shown in bold.The phantom data was extracted from the contour plot data of Fig. 3.4 (d).

at comparable distances from the proximal bladder wall (Fig. 3.9 (a)) when compared

to the distal bladder wall (Fig. 3.9 (b)). Additionally, the mean clutter magnitudes

as a function of distance from the lateral bladder walls (Figs. 3.9 (c) and (d)) are

within 0.6 dB at a distance of 1.2 cm.

Figs. 3.8 and 3.9 can be used to compare relative clutter magnitudes in funda-

mental and harmonic images. For each of the four bladder wall locations, the mean

clutter magnitude is lower in the harmonic images. For example, at a distance of 3

cm from the proximal bladder wall, the mean clutter magnitude is approximately 3

dB lower in the harmonic image (Fig. 3.9 (a)) than in the fundamental image (Fig.

3.8 (a)). At a distance of 1.2 cm from the distal bladder wall, the mean signal is 3.9

dB lower in the harmonic image (Fig. 3.9 (b)) than in the fundamental image (Fig.

3.8 (b)). However, when the results are compared on an individual basis, clutter

28

Axi

al (

cm)

Lateral (cm)

−5 0 5

0

2

4

6

8

10

Sig

nal R

educ

tion

(dB

)

24

21

18

15

12

9

6

3

0

Figure 3.10: Map of regional signal reductions in the harmonic image of Volunteer1. These measurements are based on the simultaneously acquired fundamental andharmonic images shown in Fig. 3.7 (a) and (c), respectively.

reduction is greater than the mean in some volunteers and close to zero in others.

For example, the fundamental image of Volunteer 1 has a clutter magnitude of -12.3

dB at a distance of 3 cm from the proximal bladder wall whereas the harmonic im-

age has a magnitude of -21.3 dB at this same distance, a 9 dB reduction in clutter.

Conversely, the clutter reduction for Volunteer 5 is less than 1 dB at 3 cm from the

proximal bladder wall.

3.3.6 Clutter Reduction with Harmonic Imaging

Clutter in fundamental and harmonic images were compared on a pixel-wise basis

with contour maps illustrating the measured signal reductions in harmonic images.

A representative contour map for Volunteer 1 is shown in Fig. 3.10. The clutter

adjacent to the distal and proximal bladder walls experiences similar reductions to

the surrounding tissue, in the range of 9-15 dB. The mean signal reduction in the

tissue surrounding the bladders of the five volunteers ranges from 8-11 dB, and the

average of the means is 10 ± 1.

The clutter in the interior bladder region experiences greater reductions than the

surrounding tissue. This clutter is lower by 18 to 21 dB in the harmonic image of

Volunteer 1 (Fig. 3.10), similar to signal reductions at the top of the image where

higher-order harmonics are not fully developed. The mean clutter reduction in the

29

bladder interior of the five volunteers ranges from 11-18 dB, and the average of the

means is 15 ± 3 dB.

3.4 Discussion

3.4.1 Impact and Magnitude of Clutter

The presence of clutter degrades ultrasound image quality. Often, diagnoses are

made using subtle brightness differences in B-mode images, where lesion contrast is

on the order of 1-10 dB [55]. The presence of clutter is therefore a serious problem,

particularly when imaging small, low-contrast lesions. Clutter noise contributes to

these low contrast values, and the extent to which it reduces contrast is characterized

by Eq. (3.7).

The measured signals in the simulated data show clutter resulting from the

isochronous volume of the beamformer’s point spread function (PSF) and represent

clutter magnitudes in anechoic regions under ideal imaging conditions. When the

block of diffuse scatterers was imaged, the magnitude of the anechoic region to the

left of the block was -72 dB at 1.2 cm from the echogenic boundary. This is the lowest

signal observed in our study and represents the clutter resulting from the presence of

scatterers in only one lateral tail of the beamfomer’s PSF. The minimum magnitude

in the simulated bladder image was -45 dB, and this represents the clutter associ-

ated with both lateral tails and the elevation response of the beamformer’s PSF.

Hence, when beamforming under ideal imaging conditions (i.e. no aberration, no

reverberation), the resulting PSF does not introduce a significant amount of clutter.

In addition to the clutter associated with beamforming discussed above, the

phantom images include clutter originating from random acoustic and electric noise,

acoustic reverberation within the transducer lens and between the transducer lens

and phantom structures, echoes from previously-transmitted pulses, and non-idealities

in the system beamformer. The simulated bladder and the bladder phantom have

30

comparable geometries, yet the minimum clutter magnitude in the contour plot of

the simulated bladder image is 12 dB less than the minimum clutter magnitude in

fundamental and harmonic bladder phantom images. The difference between mini-

mum clutter magnitudes in the simulated and phantom images is likely due to the

additional mechanisms for clutter generation.

The measured clutter magnitudes would be expected to vary with different real-

izations of transmit and receive apodization. An investigation of the optimal transmit

and receive weighting functions is beyond the scope of this paper. However, the same

imaging parameters, and hence the same weighting functions, were used for phantom

and in vivo images, such that comparisons among them are independent of apodiza-

tion. Similarly, comparisons between the two simulated images are independent of

apodization.

The minimum clutter magnitudes in the in vivo bladder images are greater than

those in the phantom images. The in vivo clutter magnitudes are also different

among the five volunteers, likely due to differences in bladder shapes and sizes. These

differences likely contribute to differences in acoustic interaction with the surrounding

tissue. For example, in Fig. 3.3, the magnitude at 1.2 cm to the left of the simulated

block is approximately 30 dB less than magnitudes at the same distance from the

lateral borders of the simulated bladder, evidence that shape and size differences

contribute to differences in clutter magnitudes. Differences in volunteer BMIs and

in abdominal wall fat-to-muscle ratios may also be a source of the clutter magnitude

differences [46, 56].

There were large differences in clutter magnitudes between some of the simulta-

neously acquired fundamental and harmonic in vivo images, which is not true for

the simultaneously acquired fundamental and harmonic phantom images without

the clutter-producing layer. The inclusion of the wire mesh yielded similar clutter

magnitudes, similar clutter magnitude differences between simultaneously acquired

31

fundamental and harmonic images, and similar clutter reductions with harmonic

imaging, when compared to some of the in vivo bladder images. These similarities

suggest that near-field layers are a significant source of clutter.

3.4.2 Comparison of Predicted and Measured Contrast Losses Due to Clutter

The analytical result depicted in Fig. 3.2 can be compared to empirical mea-

surements by using the relevant “uncluttered” contrast curve to predict the contrast

loss due to clutter. The analytical result contains an expression for clutter magni-

tudes relative to the background of an uncluttered image, xC − xB. However, this

information is unavailable when clutter noise overlays the entire image, and two as-

sumptions must be made in order to predict the contrast loss in such cases. The

first assumption is that the cluttered image contains an anechoic region corrupted

by clutter noise, which can be used to measure the signal due solely to clutter (i.e.

xC ≈ x′L). Secondly, one must assume that the uncluttered background signal is

much larger than the signal due solely to clutter, such that the background signals in

the cluttered and uncluttered images are approximately the same (i.e. if SB >> SC ,

then S ′B ≈ SB, as follows from Eq. (3.4)). If these assumptions are true, the clutter

magnitude in an anechoic region can be compared to the background signal in the

cluttered image (i.e. xC − xB ≈ x′L − x′B; notice xC − xB ≈ −C ′dB).

The above-stated assumptions are valid when the bladder phantom images with

and without the wire mesh are taken to be the “cluttered” and “uncluttered” im-

ages, respectively. The bladder phantom is filled with water, which is known to

be anechoic, and the measured envelope-detected background signals in the bladder

phantom images with and without the clutter-producing layer are comparable. The

measurements for CdB, C ′dB, and contrast loss at 1 cm from the proximal boundary

were 29 dB, 9 dB, and 20 dB, respectively. According to the analytical result, on a 29

dB “uncluttered” contrast curve, the contrast loss for a clutter magnitude of -9 dB is

32

predicted to be 20 dB. The analytical prediction is therefore in good agreement with

the empirical result. The analytical result in Fig. 3.2 can also be used to predict the

contrast loss due to clutter in in vivo images (see following section).

3.4.3 Importance of Clutter Reduction in Abdominal Images

The in vivo bladder likely represents a “best case” scenario for clutter magnitudes

in abdominal images. The nearby tissues that cause clutter are farther apart in the

center of the filled bladder than they are in other abdominal organs, such as the

liver or kidney. By similar reasoning, clutter magnitudes in lesions and other small

structures in abdominal organs are likely greater than clutter magnitudes in bladder

images. The high clutter magnitudes measured in in vivo bladder images can be

problematic in numerous abdominal imaging environments, such as in fetal imaging

or in viewing subtle hepatic or renal masses.

Even though the urine-filled bladder is much larger than cysts, blood vessels,

and other similarly-sized hypoechoic structures, Figs. 3.8 and 3.9 show high clutter

magnitudes at distances comparable to typical lesion sizes. Clutter magnitudes at

these distances serve as rough estimates of the minimum clutter magnitude within

small structures (e.g., cysts, tumors, blood vessels) in abdominal images.

Clutter magnitudes in in vivo bladder images range from -30 dB to nearly 0 dB

relative to the mean signal in the bladder wall, and as described above, this range

is taken to be the minimum amount of clutter overlaying other abdominal organs.

Fig. 3.2 shows that there is a loss of 0–45 dB in contrast for the range of clutter

magnitudes observed in in vivo bladder images, where the exact value depends on

the contrast that would exist if clutter were not present. Removing this clutter would

improve image contrast.

33

3.4.4 Clutter Reduction with Harmonic Imaging

The fetal phantom images with the clutter-producing layer show the extent to

which harmonic imaging removes clutter generated by near-field sources. The har-

monic image with the wire mesh placed at the transducer surface (Fig. 3.5 (c))

appears similar to the fundamental image without the wire mesh (Fig. 3.5 (a)), es-

pecially in the near field. Additionally, the wire mesh is barely visible in the harmonic

image. Results reported by van Wijk and Thijssen [48] show that harmonic imag-

ing improves the near-field tissue-to-clutter ratio (TCR), as defined by equation (3).

Existing literature [46, 57] postulates that harmonic waves are not fully developed

near the transducer surface, and hence, they are not as sensitive to clutter-producing

structures in this region. These theories are consistent with the reduced near-field

clutter magnitudes and the diminished visibility of the clutter-producing layer. Fur-

ther away from the transducer surface, there is less clutter reduction with harmonic

imaging. Comparison of the contour plots in Fig. 3.5 reveals that harmonic imaging

does not restore the near-field hypoechoic regions to magnitudes that were present

before the clutter layer was introduced.

In the phantom and in vivo data, there were instances where harmonic imaging

did not reduce clutter, consistent with previous studies [44, 48]. The measured

contrast, or TCR, in the ventricles of the fetal head is similar in the fundamental

and harmonic fetal phantom images with the clutter layer, indicating that harmonic

imaging did not reduce clutter in this hypoechoic region. The apparent clutter

suppression in the corresponding B-mode image (Fig. 3.5 (c)) is possibly due to

image display settings. The dynamic range of the displayed images is limited to 45

dB. The clutter magnitude in the ventricles of the fundamental image is within the

45 dB limit, while the clutter magnitude in the ventricles of the harmonic image is

not. When the dynamic range is limited to 55 dB in the fundamental and harmonic

34

images, the clutter in the ventricles no longer appears suppressed in the harmonic

image, while the clutter in the near-field is still suppressed.

In the fetal phantom image without the clutter layer, the minimum magnitude

in the fundamental image (-48 dB) is lower than the minimum magnitude in the

simultaneously acquired harmonic image (-44 dB). In the bladder phantom without

the clutter layer (Fig. 3.4), harmonic imaging reduced clutter magnitudes near the

echogenic border, but it did not lower the minimum clutter magnitude in the anechoic

region. The in vivo results also show that there are some instances where clutter

reduction with harmonic imaging is minimal.

Typical findings in literature report that harmonic images have 10-20 dB less

RF signal strength than fundamental images [46, 57]. The results represented by

Fig. 3.10 support these measurements, and the average signal reduction in the tissue

surrounding the in vivo bladders is 10 ± 1 dB for the five volunteers. Although

the high average (15 ± 3 dB) for clutter reduction in the bladder interiors suggests

that images from all volunteers experience clutter reduction with harmonic imaging,

several images show minimal clutter reduction when the signal reduction in the

surrounding tissue is considered.

3.4.5 Relationship Between Clutter and Body Mass Indices (BMIs)

Clinicians have observed that clutter is more apparent in overweight or obese

individuals. According to standards set by the NIH National Heart, Lung, and Blood

Institute [54], our experimental study contains one obese volunteer (Volunteer 1, BMI

30.4), one overweight volunteer (Volunteer 2, BMI 25.8), and three normal-weight

volunteers. The clutter magnitudes in Figs. 3.8 and 3.9 are somewhat consistent with

the clinical observations, especially near the proximal bladder wall. More volunteers

in each BMI category are needed to determine the relationship between BMIs and

the appearance of clutter in ultrasound images.

35

3.5 Conclusion

Clutter is an inherent property of many ultrasound images. It degrades contrast

and corrupts diagnostic information. In this paper, we derived an analytical expres-

sion for contrast degradation due to clutter and compared analytical results to the

measured contrast in a bladder phantom with and without a clutter-producing layer.

Contour plots and graphs derived from contour plot data were used to quantitatively

assess clutter magnitudes in simulated, phantom, and in vivo data. The simulations

were performed to determine clutter magnitudes under ideal imaging conditions.

Clutter magnitudes were less than ideal in fundamental and harmonic phantom and

in vivo images.

The low clutter magnitudes measured in the simulated data indicate that the

beamformer’s PSF, under ideal imaging conditions, is not a significant source of

clutter when there is no aberration. The similarities between in vivo images and

phantom images with the clutter-producing layer suggest that near-field layers are a

more significant source of clutter.

Clinicians have observed that clutter is more apparent in overweight or obese

individuals. Due to the limited sample size of overweight and obese individuals, we

are not able to draw conclusive remarks about the correlation between BMIs and

clutter magnitudes in obese, overweight, and normal-weight volunteers.

3.6 Acknowledgements

Funding for this research was provided by the NIH Medical Imaging Training Grant

(T32-EB001040), the NIH Supplement to Promote Diversity in Biomedical Research

(R01-CA114093-04S1), and the Duke Endowment Fellowship. Special thanks to

Siemens Medical Solutions, Inc. USA, Ultrasound Division for supplying the imaging

equipment.

36

4

Motion-based Clutter Reduction Techniques


Lediju MA, Pihl MJ, Hsu SJ, Dahl JJ, Gallippi CM, Trahey GE. A motion-based

approach to abdominal clutter reduction. IEEE Transactions on Ultrasonics, Fer-

roelectrics, and Frequency Control,56(11):2437-49, 2009, with Fig. 4.7 selected for

publication as the front cover image.

4.1 Introduction

In diagnostic ultrasound, clutter is a noise artifact that appears as diffuse echoes

overlying structures or signals of interest. It is most easily observed in anechoic or

hypoechoic regions of images, such as in the gall bladder or urinary bladder. Clutter

obscures diagnostic measurements and degrades image contrast [58].

Previous work identifies two primary mechanisms of clutter generation: off-axis

scatter and reverberation [25, 59, 60]. Harmonic imaging, in which higher harmonics

generated by nonlinear sound propagation through tissue are imaged, has been shown

to reduce clutter due to both mechanisms [43, 18, 46, 47, 57]. A wide range of

37

apodization [61, 62] and adaptive beamforming [45, 63, 64] techniques are aimed at

reducing clutter due to off-axis scatterers. In this paper, we present a technique for

reducing clutter due to abdominal wall reverberations.

Abdominal images can be modeled as containing two components, the abdominal

wall and an underlying organ of interest, each contributing to image clutter via one

of the primary clutter generation mechanisms. Clutter due to off-axis scattering is

proposed to arise from axial and elevational structures in and surrounding the organ

of interest, while structures in the abdominal wall are proposed to cause clutter

due to reverberation. Random (thermal) noise is also a potential source of clutter,

however clutter appears stationary in most applications, indicating that this clutter

contribution is minimal and can be neglected.

The proposed clutter reduction method is well-suited for abdominal images, where

tissue-to-clutter ratios can range from 0-35 dB [58]. The method requires axial

displacement of the abdominal wall during real-time imaging. Given the proposed

model, clutter that arises from acoustic interaction (i.e. reverberation) in abdominal

wall structures would experience similar displacements to the abdominal wall. This

clutter is reduced by applying motion filters to the acquired images. The proposed

method was tested in simulated, phantom, and in vivo images.

4.2 Methods

4.2.1 Field II simulations

Field II [39, 51] was used to simulate clutter moving in the same direction and

with the same velocity as the transducer, in the presence of stationary tissue, a nec-

essary condition for the proposed clutter reduction method. When the motion is

considered in a reference frame attached to the transducer, clutter moving with the

transducer appears stationary, and stationary tissue appears to be moving. Thus,

motion was simulated by incrementally displacing one speckle pattern representa-

38

tive of homogeneous tissue relative to a stationary speckle pattern representative of

clutter.

The speckle patterns were created by insonifying a 6 cm (axial) x 5 cm (lat-

eral) x 1 cm (elevation) phantom, containing at least 10 scatterers per resolution

volume. Half of the scatterers in the phantom were given random amplitudes at

random locations, representative of homogeneous tissue. The other scatterers were

given random amplitudes weighted by a factor of 10(1− zp/6), where zp is the axial

distance (cm) from the proximal phantom surface. (Note: zp is defined for 0 < zp < 6

and zp = z−3, where z is the axial distance (cm) from the transducer surface.) This

weighting function resulted in random scatterer amplitudes that linearly decreased

with depth, similar to clutter noise in phantom and in vivo images [58]. The scat-

terers representing tissue were shifted ten times in 0.1 mm increments toward the

transducer to create motion relative to the simulated clutter. In addition to imaging

tissue moving in the presence of stationary clutter, the tissue and clutter were im-

aged separately (i.e. all phantom scatterers represented either stationary clutter or

moving tissue), and the resulting images were placed side by side.

The transducer parameters used in the simulations are listed in Table 6.1. The

axial transmit focus was 6 cm. Dynamic focusing was applied during receive beam-

forming, and Hanning window apodization was applied to the transmit and receive

apertures.

4.2.2 Phantom and In Vivo Studies

A Siemens Antarestm ultrasound scanner and Siemens CH6-2 curvilinear trans-

ducer (Siemens Medical Solutions USA, Inc., Issaquah, WA) were used to obtain

phantom images and in vivo bladder and liver images from two male volunteers

(ages 53 and 33). The scanner was operated in fundamental and harmonic imaging

modes with transmit frequencies of 4.4 MHz and 2.5 MHz, respectively. The Ax-

39

Table 4.1: Transducer Parameters for Field II Simulations

Parameter Value

Number of Elements (total) 192Number of Elements in Subaperture 64Element Height 12 mmElement Width 0.314 mmKerf 0.014 mmCenter Frequency 2.5 MHzSampling Frequency 100 MHzFractional Bandwidth 60%

ius Direct Ultrasound Research Interface (Siemens Medical Solutions USA, Inc., Is-

saquah, WA) was used to acquire raw radio frequency (RF) data without significant

time-gain compensation and before the application of nonlinear processing steps.

In harmonic imaging mode, the scanner implements the pulse inversion technique

[52, 53], and harmonic RF data was obtained by summing the normal and inverted

pulse-echo signals. To form B-mode images, the RF data obtained in fundamental or

harmonic imaging mode were envelope detected, normalized to the brightest point,

log-compressed, limited to a dynamic range of 45 dB, and then scan-converted. The

axial sampling frequency was 40 MHz. The line densities were 0.25, 0.28, and 0.30

degrees per line, respectively, in phantom and in vivo liver images, in vivo funda-

mental bladder images, and in vivo harmonic bladder images. The pulse repetition

frequencies were 7.2, 4.0, and 5.3 kHz, respectively. The frame rates were 25, 15,

and 11 Hz, respectively. All image processing and analysis was implemented with

Matlab (The Mathworks Inc., Natick, MA) software.

A custom bladder phantom was created by submerging a water-filled balloon in a

slurry solution of graphite, propanol, and water (RMI, now Gammex, Inc., Middle-

ton, WI, SuperSpheres Model TM-C, discontinued by manufacturer). The ultrasonic

transducer was placed in the slurry solution, with its imaging surface approximately

2 cm above the submerged balloon. A linear translation stage (Newport Motion

40

Controller Model MM3000, Newport Corporation, Irvine, CA) was used to axially

translate the transducer at a controlled velocity of 0.5 mm/s during real-time imag-

ing. The distance the transducer traveled between successive images was 0.02 mm.

To generate clutter that moved with the transducer, a wiry copper household scour-

ing pad (ScrubIT R© Copper Scourers, Supply Plus, Inc. Newark, NJ) cut to 1 cm in

thickness was placed at the transducer surface, the transducer and wire mesh were

confined in a transducer bag containing enough water to provide acoustic coupling,

and the motion experiment was repeated. In a previous study [58], the copper wire

mesh was shown to generate clutter with similar characteristics to that of in vivo

data (i.e. similar in magnitude, clutter magnitude greatest in near field, magni-

tude decreases with depth). This clutter is likely a reverberation artifact due to the

highly-reflective metallic material.

As a corollary to the phantom study, the abdominal wall was translated during

successive-frame in vivo imaging of the bladder and liver. Abdominal wall motion

was achieved by asking the volunteers to slowly translate their abdominal muscles

while the hand-held transducer, resting and lightly supported on the abdominal

skin, followed the motion. We anticipate that this motion allows the transducer,

abdominal wall, and underlying clutter to move approximately in unison, while distal

tissues remain stationary.

Displacement estimates for phantom and in vivo data were obtained by applying

a normalized 2D cross-correlation search method (i.e. speckle tracking) to successive

frames of envelope-detected RF data [65]. Thus, while displacements are assumed

to be axial along the probe axis, they were calculated along the beam axis. Given

that a curvilinear probe was used for imaging, these two axes are similar for center

beams (to the extent that the small angle approximation is valid) but not for outer

beams.

The speckle tracking kernel size was selected by minimizing false peaks in the

41

cross correlation function, while maintaining acceptable resolution in displacement

results. The optimal kernel size in fundamental bladder images was 25 x 5 pixels,

and this kernel size was kept constant for all data. In scan converted images, the

kernel sizes correspond to 0.48 mm x 1.3◦ in phantom and in vivo liver data, 0.48

mm x 1.4◦ in in vivo fundamental bladder images, and 0.48 mm x 1.5◦ in harmonic

images. Kernels in one frame were compared to search regions of 100 x 10 pixels in

the consecutive frame. In scan converted images, the search region sizes correspond

to 1.9 mm x 2.5◦ in phantom and in vivo liver data, 1.9 mm x 2.8◦ in in vivo

fundamental bladder images, and 1.9 mm x 3.0◦ in harmonic images. The search

regions were centered about the kernel location. The speckle tracking algorithm was

not applied to kernels near the edges of the B-mode image where the search region

extended beyond the image border.

4.2.3 Clutter Reduction with Motion Filters

Motion filters were applied to simulated, phantom, and in vivo images to remove

clutter moving in the same direction and with the same velocity as the transducer (i.e.

clutter that appears stationary to the transducer). The first filter was a conventional

1,-1 FIR motion filter, also known as a stationary echo canceler, wherein the RF

echoes in one frame was subtracted from those in a consecutive frame to reject

stationary RF echoes [66]. The second filter was a BSS filter, where basis functions

were selected and/or rejected to reconstruct a filtered image [24, 67, 68].

BSS filtering was implemented by performing robust principal component analysis

with the robpca function in the Matlab Library for Robust Analysis [69, 70]. This

function requires an input data matrix with observations in its rows and variables in

its columns. The input data matrix consisted of envelope-detected RF echoes taken

from the same lateral position (observations) in consecutive images (variables). Basis

function selection was based on the time and depth projections associated with the

42

principal components of the input data [67, 68].

As described by Gallippi et al. [67, 68], a time projection yields the motion

profile associated with a particular principal component, while the corresponding

depth projection indicates the relative strength of that principal component at each

axial position. For example, a time projection with zero slope represents a basis

function associated with a stationary signal component, while a time projection with

nonzero slope represents a basis function associated with a moving signal component.

A depth projection with uniform amplitude represents a basis function associated

with a signal component that is equally weighted at all axial positions. A depth

projection with dominant magnitudes at specific axial positions indicates that the

associated basis function is dominant at those positions. The relative amplitudes

in a depth projection also depends on relative amplitudes in the associated signal

component.

While known to be true in simulated images and expected to be true in phantom

images, axial motion was assumed to be uniform across the lateral dimension of in

vivo images. Uniform motion implies similar basis functions for all lateral positions,

thus the selected basis function generated by one lateral position was used to filter

all axial lines in an image. To reconstruct a BSS-filtered image, the data matrix of

each axial line was projected onto the selected basis function, as described by:

yi = xiννT , (4.1)

where yi is ith lateral position (or ith axial line) of the filtered image, xi is the

data matrix of the ith lateral position in the original image, ν is the eigenvector of

the selected basis function, and νT is the eigenvector transposed. The filtered RF

lines were then normalized to the brightest point, log-compressed, and limited to a

dynamic range of 45 dB. Scan conversion was the final step in filtered phantom and

in vivo images.

43

Filter efficacy was demonstrated with contour maps illustrating magnitude dif-

ferences between filtered and reference images. The contour maps were formed from

envelope-detected RF echo data. The reference and motion-filtered data were low-

pass filtered with a rectangular kernel of 151 x 15 pixels (2.9 mm x 4.1◦ and 2.9 mm

x 4.5◦ in scan-converted fundamental and harmonic images, respectively), and the

pixel-wise ratio between resulting images was calculated.

The contrast in reference and filtered phantom and in vivo data was calculated

using,

C = 20log10

(So

Si

), (4.2)

where So and Si are the mean envelope-detected radio-frequency (RF) data outside

and inside a hypoechoic region, respectively. The contrast-to-noise ratio (CNR) in

phantom and in vivo data was calculated using,

CNR =C

20log10(σo),(4.3)

where σo is the standard deviation of the envelope-detected RF data outside the

hypoechoic region [71, 72].

4.3 Results


Fig. 4.1 (a) shows the simulated images representing linearly decreasing clutter

noise (left panel), homogeneous tissue in the presence of the clutter noise (middle

panel), and tissue (right panel). A stationary echo canceler FIR filter was applied

to the RF data in two consecutive frames, and the resulting image is shown in Fig.

4.1 (b). The corresponding map of magnitude reductions in the filtered image is

shown in Fig. 4.1 (c). The left panel of this image shows the reduction of the clutter

44

Lateral (cm)

Axi

al (

cm)

C

−1 0 1

4

5

6

7

8

9

Lateral (cm)

C+T

−1 0 1Lateral (cm)

T

−1 0 1

(a)

Axi

al (

cm)

Lateral (cm)

C

−1 0 1

4

5

6

7

8

9

Lateral (cm)

C+T


T

−1 0 1

Axi

al (

cm)

Lateral (cm)

C

−1 0 1

4

5

6

7

8

9

Lateral (cm)

C+T


T

−1 0 1

Sig

nal R

educ

tion

(dB

)

3330272421181512 9 6 3 0−3−6

(b) (c)

Axi

al (

cm)

Lateral (cm)

C

−1 0 1

4

5

6

7

8

9

Lateral (cm)

C+T


T

−1 0 1

Axi

al (

cm)

Lateral (cm)

C

−1 0 1

4

5

6

7

8

9

Lateral (cm)

C+T


T

−1 0 1

Sig

nal R

educ

tion

(dB

)

3330272421181512 9 6 3 0−3−6

(d) (e)Figure 4.1: (a) Simulated phantom images showing clutter noise (C), clutter noisemixed with homogeneous tissue (C + T), and homogeneous tissue (T). (b) FIR-filtered images and (c) corresponding maps of magnitude reductions. (d) BSS-filteredimages and (e) corresponding maps of magnitude reductions.

noise. Although the contour map was limited to 33 dB, the clutter in this region was

reduced to zero, and the magnitude reduction in this region is infinity. In the second

panel, the maximum reduction in the proximal region (3-3.5 cm) ranges from 21-24

dB. The distal region (8.5-9 cm) experiences 0-3 dB magnitude reduction. There

are also regions with a 3-6 dB signal increase. In the third panel, the average signal

increase is 4 dB. Notice that the magnitude increase at the bottom of the second

panel is similar to the increase in the third panel.

Robust principal component analysis was applied to the central lateral position of

45

2 4 6 8 10−1

−0.5

0

0.5

1

Mag

nitu

deFrame No.

4 6 80

0.2

0.4

0.6

0.8

1

Mag

nitu

de

Depth (cm)

2 4 6 8 10−1

−0.5

0

0.5

1

4 6 80

0.2

0.4

0.6

0.8

1

2 4 6 8 10−1

−0.5

0

0.5

1

4 6 80

0.2

0.4

0.6

0.8

1

2 4 6 8 10−1

−0.5

0

0.5

1

4 6 80

0.2

0.4

0.6

0.8

1

4 5 6 7 8 90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Depth (cm)

Nor

mal

ized

Ave

rage

Mag

nitu

de

0 2 4 6 8 10 12−5

0

5

Ave

rage

Mag

nitu

de

0 2 4 6 8 10 12

−20

−10

0

Frame No.

Ave

rage

Mag

nitu

de

(a) (b) (c)Figure 4.2: BSS time and depth projections of the simulated data. (a) The firstfour time (top) and depth (bottom) projections for the central lateral position. (b)Average of the first depth projection of all lateral positions. (c) Average of thefirst (top) and second (bottom) time projections of all lateral positions. Error barsindicate one standard deviation.

Fig. 4.1 (a) (0 cm in the C + T image), and Fig. 4.2 (a) shows the first four time and

depth projections, corresponding to the four most energetically significant principal

components. The first depth projection has a slope that decreases with depth, much

like the slope of the weighting function applied to the simulated clutter amplitudes.

Similar results were achieved for the first depth projection of all lateral positions, as

shown in Fig. 4.2 (b). The first time projection has zero slope, indicating that this

component of the signal is stationary (relative to the transducer). Similar results

were achieved for the first time projections of all lateral positions, as shown in the

top panel of Fig. 4.2 (c). The described characteristics of the first depth and time

projections provide strong evidence that the first basis function is associated with

the simulated clutter.

The slope of the second time projection in Fig. 4.2 (a) is constant and nonzero

throughout, indicating that it is associated with uniform displacement, much like

the incremental displacement applied to the simulated tissue. Similar results were

achieved for the second time projections of all lateral positions, as shown in the

bottom panel of Fig. 4.2 (c). The described characteristics of the second time

projection provide compelling evidence that the second basis function is associated

46

with the simulated tissue motion. Given the characteristics of the third and fourth

time and depth projections, their basis functions are likely associated with a mixture

of stationary noise and tissue motion.

The second basis function generated by the central lateral position was deter-

mined to represent the most energetic non-stationary principal component. It was

selected to filter all axial lines and reconstruct the BSS-filtered image shown in Fig.

4.1 (d). A filter performance map of magnitude reductions in the filtered image is

shown in Fig. 4.1 (e). In the left panel of this image, the average reduction is 38

dB. In the middle panel, the map shows a maximum clutter reduction of 33 dB near

the proximal phantom surface and a minimum reduction of 0-3 dB near the distal

surface. In the right panel, the average reduction is 7 dB. Notice that the reductions

at the top and bottom of the center panel are similar to the reductions of the left

and right panels, respectively.

4.3.2 Phantom Experiments

Fig. 4.3 (a) shows a B-mode image of the bladder phantom. The map of peak

correlation coefficients between two successive frames acquired during transducer

displacement is shown in Fig. 4.3 (b). The frames were highly correlated in the

regions surrounding the bladder, as well as inside the bladder, near the borders.

There is less correlation inside the bladder, farther away from the borders, though

the correlation coefficients are still high. Fig. 4.3 (c) displays the corresponding axial

displacement map, with displacement estimates shown relative to the transducer

surface. In the reference frame of the transducer, the entire phantom is shown to

have consistent motion toward the transducer.

Fig. 4.3 (d) shows a B-mode image acquired when the clutter-generating wire

mesh was placed between the transducer and the bladder, during simultaneous trans-

lation and successive-frame imaging. A map of the peak correlation coefficients be-

47

Axi

al P

ositi

on (

cm)

Lateral Position (cm)−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7


Axi

al P

ositi

on (

cm)

−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Cor

rela

tion

Coe

ffici

ent

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Aix

ial P

ositi

on (

cm)


−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Axi

al D

ispl

acem

ent (

mm

)

−0.06

0

0.06

(a) (b) (c)

Axi

al (

cm)

Lateral (cm)−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Lateral Position (cm)A

xial

Pos

ition

(cm

)

−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Cor

rela

tion

Coe

ffici

ent

0.9

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

Aix

ial P

ositi

on (

cm)


−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Axi

al D

ispl

acem

ent (

mm

)

−0.06

0

0.06

(d) (e) (f)Figure 4.3: (a) B-mode image of the bladder phantom. Corresponding maps of (b)correlation coefficients and (c) axial displacements between two consecutive framesin the data set. (d) B-mode image of bladder phantom with clutter-generating layerplaced at the transducer surface. (The boxes show ROIs used to calculate contrastand CNR in reference and filtered data.) Corresponding maps of (e) correlation co-efficients and (f) axial displacements between two consecutive frames in the data set.Displacements are relative to the transducer surface, where negative indicates motiontoward the transducer and positive indicates motion away from the transducer.

tween two successive frames is shown in Fig. 4.3 (e). Similar to Fig. 4.3 (b),

the correlation coefficients are highest in the regions surrounding the bladder. The

coefficients are also high inside the bladder, in a region extending well below the

proximal wall. This highly correlated region inside the bladder corresponds to the

clutter generated by the wire mesh, as seen in the B-mode image of Fig. 4.3 (d).

In the corresponding axial displacement map of Fig. 4.3 (f), the region containing

the wire mesh and the clutter region extending below the wire mesh have similar

displacement estimates, displacements that are approximately 0 mm relative to the

transducer. The surrounding regions have consistent upward motion relative to the

transducer, similar to the displacements observed in Fig. 4.3 (c).

The regions with lower correlation coefficients (approximately 0.95) in Fig. 4.3 (e)

have discontinuous displacement estimates in the corresponding axial displacement

48

Axi

al (

cm)

Lateral (cm)−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Axi

al (

cm)

Lateral (cm)

−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Sig

nal R

educ

tion

(dB

)

272421181512 9 6 3 0−3−6

(a) (b)

Axi

al (

cm)

Lateral (cm)−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Axi

al (

cm)

Lateral (cm)

−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

Sig

nal R

educ

tion

(dB

)

272421181512 9 6 3 0−3−6

(c) (d)Figure 4.4: Single frame results of the motion filters applied to the phantom data.(a) FIR-filtered image and (b) corresponding map of regional magnitude reductionsin the filtered image (when compared to the reference image in Fig. 4.3 (d)). (c)BSS-filtered image and (d) corresponding map of regional magnitude reductions inthe filtered image (when compared to the reference image in Fig. 4.3 (d))

map of Fig. 4.3 (f) (e.g. the region surrounding axial position 1 cm, lateral position

-3 cm). This type of displacement is not consistent with the transducer’s uniform

motion toward the bladder. Therefore, regions showing such random motion are

interpreted as regions of indeterminate displacements.

Results of the FIR filter applied to two consecutive frames of the phantom image

with the wire mesh are shown in Fig. 4.4 (a) and (b). Reductions of 6-18 dB are

seen in the clutter region inside the bladder cavity. Reductions of 18-27 dB are

seen in the proximal regions occupied by the wire mesh (0-1 cm) and distal to the

wire mesh (1-3 cm). The regions with reduced magnitudes were shown to have

approximately zero displacement (relative to the transducer) in Fig. 4.3 (f). The

regions of interest (ROIs) shown in Fig. 4.3 (d) were used to calculate contrast and

CNR in the reference and filtered phantom images. There is a 7 dB contrast increase

49

and 42% CNR increase in the FIR-filtered image (see Table 4.2).

The BSS filter results shown in Fig. 4.4 (c) and (d) are similar to the FIR filter

results. The central lateral position (0 cm) was used to generate basis functions for

image reconstruction. Depth projections with large amplitudes in the distal bladder

wall region and time projections with decreasing slopes represented the principal

components associated with motion (relative to the transducer). The first basis

function had the steepest time projection slope (i.e. it represented the most energetic

component associated with motion), and it was therefore selected to reconstruct the

filtered image. Reductions of 3-18 dB are seen in the clutter region inside the bladder

cavity. Reductions of 18-21 dB are seen in the proximal regions occupied by the wire

mesh (0-1 cm) and distal to the wire mesh (1-3 cm). Similar to FIR-filtered images,

the regions with reduced magnitudes in the BSS-filtered images were shown to have

approximately zero displacement (relative to the transducer) in Fig. 4.3 (f). There

is a 9 dB contrast increase and 44% CNR increase in the BSS-filtered image (see

Table 4.2).

The proximal bladder wall is not visualized in the filtered B-mode images of Fig.

4.4 (a) and (c), because the gain in this region of the original B-mode image was

minimized to achieve uniform image brightness (see Fig. 4.3 (d)). However, when the

dynamic range (currently 45 dB) was increased above 60 dB in the filtered images,

the proximal bladder wall was more apparent, but so was the clutter inside the blad-

der. The filter performance maps of Fig. 4.4 (b) and (d) reinforce this observation,

because the region representing the proximal bladder wall has a reduction that is 3-6

dB greater than the region representing the bladder interior.

4.3.3 In Vivo Experiment: Bladder Images

Fig. 4.5 (a) shows a fundamental bladder image from Volunteer 1, with a man-

ually estimated outline of the bladder wall superimposed on the image. Fig. 4.5

50

(d) shows displacement estimates between two consecutive bladder images acquired

during axial displacement of the abdominal wall. The displacement of the abdominal

wall is approximately 0 mm relative to the transducer, confirming the anticipated

outcome that the abdominal wall and the transducer moved approximately in unison.

Similar to the phantom experiment with the wire mesh, the displacement map shows

that clutter in the proximal bladder cavity was also moving with the abdominal wall

(displacement estimates of approximately 0 mm relative to the transducer). The lat-

eral and distal bladder walls and adjacent tissue have displacements of approximately

0.1 mm relative to the transducer. These results support the hypotheses about the

applied motion, that the transducer, abdominal wall, and underlying clutter move

approximately in unison while distal tissues remain stationary.

Fig. 4.5 (g) shows a harmonic bladder image from Volunteer 1, with a manually

estimated outline of the bladder wall superimposed on the image. A corresponding

map of axial displacements between two consecutive harmonic images is shown in

Fig. 4.5 (j). Although the 2D displacement maps in Fig. 4.5 (d) and (j) show

displacements between two consecutive frames, similar results were achieved in all

consecutive frames of each data set, as shown in Fig. 4.6. Similar results were

achieved in fundamental and harmonic bladder images from Volunteer 2 (images not

shown).

It is important to note that the displacement results of Figs. 4.5 and 4.6 were

obtained while the abdominal muscles were relaxed (i.e. the muscles were not

tensed/tightened while being translated). With the abdominal muscles tightened

during translation (results not shown), instead of having 0 mm displacement in the

proximal bladder cavity region, displacement estimates in this region were more spa-

tially random, much like those at 6-9 cm in the hypoechoic bladder region of Fig.

4.5 (d). The distal and lateral bladder wall regions contained displacement esti-

mates near 0.1 mm, and the proximal bladder wall was shown to have similar axial

51

Axi

al (

cm)

Lateral (cm)−5 0 5

0

2

4

6

8

10

Axi

al (

cm)


0

2

4

6

8

10

Axi

al (

cm)


0

2

4

6

8

10

(a) (b) (c)

Aix

ial (

cm)

Lateral (cm)

−5 0 5

0

2

4

6

8

10

Axi

al D

ispl

acem

ent (

mm

)

−0.1

0

0.1

Axi

al (

cm)

Lateral (cm)

−5 0 5

0

2

4

6

8

10

Sig

nal R

educ

tion

(dB

)

272421181512 9 6 3 0−3−6

Axi

al (

cm)

Lateral (cm)

−5 0 5

0

2

4

6

8

10

Sig

nal R

educ

tion

(dB

)

272421181512 9 6 3 0−3−6

(d) (e) (f)

Axi

al (

cm)


0

2

4

6

8

10

Axi

al (

cm)


0

2

4

6

8

10

Axi

al (

cm)


0

2

4

6

8

10

(g) (h) (i)

Aix

ial (

cm)

Lateral (cm)

−5 0 5

0

2

4

6

8

10

Axi

al D

ispl

acem

ent (

mm

)

−0.1

0

0.1

Axi

al (

cm)

Lateral (cm)

−5 0 5

0

2

4

6

8

10

Sig

nal R

educ

tion

(dB

)

272421181512 9 6 3 0−3−6

Axi

al (

cm)

Lateral (cm)

−5 0 5

0

2

4

6

8

10

Sig

nal R

educ

tion

(dB

)

272421181512 9 6 3 0−3−6

(j) (k) (l)Figure 4.5: (a) Fundamental and (g) harmonic B-mode bladder images from Vol-unteer 1, with estimated bladder outlines superimposed. (The images were acquiredat different times, hence the different appearances.) The boxes show ROIs used tocalculate contrast and CNR in reference and filtered data. (b) FIR- and (c) BSS-filtered fundamental images. Corresponding maps of (d) axial displacements betweentwo consecutive frames, (e) FIR filter performance and (f) BSS filter performance.(h) FIR- and (i) BSS-filtered harmonic images. Corresponding maps of (j) axialdisplacements, (k) FIR filter performance and (l) BSS filter performance. Axial dis-placements are relative to the transducer surface, where negative indicates motiontoward the transducer and positive indicates motion away from the transducer. Axialdisplacement maps show ROIs in the abdominal wall, clutter distal to the abdom-inal wall, and the distal bladder wall. These ROIs were used to calculate averagedisplacements in all consecutive frames of the data set (see Fig. 4.6).

52

0 2 4 6 8−0.1

−0.05

0

0.05

0.1

Frame Number

Aix

ial D

ispl

acem

ent (

mm

)

Abdominal WallClutterDistal Bladder Wall

0 1 2 3 4 5 6 7−0.1

−0.05

0

0.05

0.1

Aix

ial D

ispl

acem

ent (

mm

)

Frame Number

Abdominal WallClutterDistal Bladder Wall

(a) (b)Figure 4.6: Average axial displacements of select regions in displacement maps ofconsecutive (a) fundamental and (b) harmonic images. The ROIs used to calculateaverage displacements are shown in Fig. 4.5 (d) and (j), respectively. Displacementsare relative to the transducer surface, where negative indicates motion toward thetransducer and positive indicates motion away from the transducer.

displacements to the lateral and distal bladder walls.

Results of the FIR filter applied to two consecutive fundamental images from Vol-

unteer 1 are shown in Fig. 4.5 (b) and (e). Clutter reductions of 3-9 dB are seen in

the proximal bladder cavity (2-6 cm). Results of the FIR applied to two consecutive

harmonic images are shown in Fig. 4.5 (h) and (k), where clutter reductions of 0-12

dB are seen in the proximal bladder cavity (3-6 cm). The clutter regions with reduced

magnitudes in FIR-filtered fundamental and harmonic images were shown to have

approximately zero displacement in Fig. 4.5 (d) and (j), respectively. In correspond-

ing filter performance maps (Fig. 4.5 (e) and (k)), the abdominal wall experiences

a magnitude reduction ranging from 3-18 dB (with negligible regions showing 21-24

dB reduction), while the distal and lateral walls experience a signal increase of 3-6

dB. The contrasts are improved by 5 dB in the FIR-filtered fundamental image and

4 dB in the FIR-filtered harmonic image, while the CNRs are improved by 31% and

21%, respectively (see Table 4.2).

Results of the BSS filter applied to fundamental and harmonic images are shown

in Fig. 4.5 (c) and (i), respectively. A central lateral position (0 cm and -0.7 cm,

53

respectively) was used to generate basis functions for image reconstruction. Depth

projections with large-amplitude near-field signals and time projections with slopes

close to zero represented principal components associated with stationary clutter

(relative to the transducer). Depth projections with large amplitudes in the distal

bladder wall region and time projections with decreasing slopes represented the prin-

cipal components associated with motion (relative to the transducer). The second

basis function had the steepest time projection slope and was selected for image

reconstruction.

As shown in Fig. 4.5 (f) and (l), respectively, clutter in the proximal bladder

cavity was reduced by 18-24 dB in the filtered fundamental image and 12-14 dB

in the filtered harmonic image. The clutter regions that experienced magnitude

reductions were shown to be approximately stationary relative to the transducer, as

demonstrated in Fig. 4.5 (d) and (j). In the fundamental BSS-filtered image, the

abdominal wall experienced similar reductions to the proximal clutter region inside

the bladder. In the harmonic BSS-filtered image, the abdominal wall was reduced by

15-21 dB. The tissue surrounding the lateral and distal bladder walls in fundamental

and harmonic BSS-filtered images experienced reductions of 6-15 dB and 3-9 dB,

respectively, similar to the distal clutter region inside the bladder. The contrast

improvements in the BSS-filtered fundamental and harmonic images were 8 dB and

6 dB, respectively, while the CNRs were increased by 108% and 45%, respectively

(see Table 4.2).

4.3.4 In Vivo Experiment: Liver Images

A fundamental B-mode image of the gall bladder and surrounding liver tissue of

Volunteer 1 is shown in Fig. 4.7 (a). Successive-frame liver images were acquired

during axial translation of the abdominal wall. Displacement estimates between two

consecutive images are shown in Fig. 4.7 (b). The abdominal wall and a region distal

54

Axi

al (

cm)

Lateral (cm)−6 −4 −2 0 2 4 6

0

2

4

6

8

Aix

ial P

ositi

on (

cm)


−6 −4 −2 0 2 4 6

0

1

2

3

4

5

6

7

8

Axi

al D

ispl

acem

ent (

mm

)

−0.1

0

0.1

(a) (b)

Axi

al (

cm)

Lateral (cm)−6 −4 −2 0 2 4 6

0

2

4

6

8

Axi

al (

cm)

Lateral (cm)

−6 −4 −2 0 2 4 6

0

2

4

6

8

Sig

nal R

educ

tion

(dB

)

272421181512 9 6 3 0−3−6

(c) (d)

Axi

al (

cm)

Lateral (cm)−6 −4 −2 0 2 4 6

0

2

4

6

8

Axi

al (

cm)

Lateral (cm)

−6 −4 −2 0 2 4 6

0

2

4

6

8

Sig

nal R

educ

tion

(dB

)

272421181512 9 6 3 0−3−6

(e) (f)Figure 4.7: Results of the motion-based clutter reduction method applied to anin vivo liver. (a) Fundamental liver image from Volunteer 1. (The boxes showROIs used to calculate contrast and CNR in reference and filtered data.) (b) Mapof axial displacements between two consecutive frames in the image sequence. (c)FIR-filtered image and (d) corresponding map of regional magnitude reductions inthe filtered image. (e) BSS-filtered image and (f) corresponding map of regionalmagnitude reductions in the filtered image.

to the abdominal wall are shown to be stationary relative to the transducer, while

the distal tissues are shown to move toward the transducer. The stationary region is

similar to that of in vivo bladder images from the same volunteer. Furthermore, the

stationary region is juxtaposed to the moving region in the liver image, whereas the

two regions are separated by a region of random displacements in bladder images.

55

Table 4.2: Contrast and contrast-to-noise ratios (CNRs) in reference and filteredimages

Contrast (dB) CNRBladder Phantom ImagesReference 23.2 0.50FIR-Filtered 30.5 0.71BSS-Filtered 32.1 0.72In Vivo Bladder ImagesReference (fundamental) 12.1 0.26FIR-Filtered 17.4 0.34BSS-Filtered 19.7 0.54Reference (harmonic) 15.8 0.38FIR-Filtered 19.5 0.46BSS-Filtered 22.0 0.59In Vivo Gall Bladder ImagesReference 16.9 0.31FIR-Filtered 29.4 0.52BSS-Filtered 26.0 0.52

An FIR filter was applied to two consecutive frames in the data set. The filtered

image is shown in Fig. 4.7 (c) and the corresponding filter performance map is shown

in Fig. 4.7 (d). Regions that were shown to move with the transducer were reduced

by 3-24 dB in the filtered image. Most of the distal tissues experienced a 0-3 dB

signal increase. There is a 12 dB contrast increase and 68% CNR increase in the

FIR-filtered image (see Table 4.2).

The BSS-filtered image is shown in Fig. 4.7 (e). The lateral position of the

brightest point inside the gall bladder image (-0.2 cm) was used to generate the basis

functions for image reconstruction. The second basis function had the steepest time

projection slope, and it was selected for image reconstruction. As shown in Fig.

4.7 (f), the clutter in the gall bladder is reduced by 19-21 dB. The region that was

shown to move with the abdominal wall (see Fig. 4.7 (b)) is reduced by 12-21 dB

(disregarding the small 3-9 dB regions to the right of the image). There is a 9 dB

contrast increase and 68% CNR increase in the BSS-filtered image (see Table 4.2).

56

4.4 Discussion

4.4.1 Implications for Clutter Reduction in Abdominal Images

Clutter noise is apparent in the hypoechoic regions of the bladder and gall blad-

der (previous literature states that these regions should be hypoechoic or anechoic

in the absence of clutter [73, 74]). Such hypoechoic regions are not always present

in abdominal images of diagnostic interest. The tissue may be completely echogenic

throughout the field of view, allowing clutter noise to be less noticeable. The simula-

tion results of Fig. 4.2 demonstrate that the FIR and BSS filters are able to reduce

stationary clutter in the midst of moving tissue signals that are completely echogenic.

These results imply that the proposed motion-based clutter reduction method can

be implemented in several types of abdominal images, with or without hypoechoic

regions for easy visualization of clutter reductions.

The inclusion of the wire mesh in phantom images produced clutter distal to the

mesh, which moved with the transducer during axial translation (Fig. 4.3 (f)). When

the mesh was absent, the clutter seen in the anechoic region of the phantom image

did not move with the transducer (Fig. 4.3 (c)). The clutter that moved with the

transducer is suspected to arise from sound reverberation in the wire mesh. It was

reduced, as shown in Fig. 4.4, via the proposed clutter reduction methods.

Similarly, in the hypoechoic regions of in vivo bladder and liver images, the

displacement maps of Figs. 4.5 and 4.7 show that there is a persistent region of

clutter distal to the abdominal wall that moved at the same rate as the transducer

and the displaced abdominal wall. This clutter is suspected to arise from acoustic

interactions within the abdominal wall, such as sound reverberation. This clutter

region was not as prevalent in displacement maps when the experiment was performed

with tightened abdominal muscles, further supporting the hypothesis that a major

source of this clutter is reverberation in abdominal tissue. A region of similar shape

57

and size appears in the hypoechoic region of bladder images from the same volunteer

(e.g. compare Figs. 4.5 (d) and 4.7 (b)), as well as in the anechoic region of the

phantom image with the wire mesh (Fig. 4.3 (f)). This region of clutter is believed

to overlay a large portion of the in vivo liver image (not just the hypoechoic region)

and is most likely present in other abdominal images.

Additional confirmation that clutter overlays abdominal images is found in the

displacement data of in vivo images. While random displacements were primarily

seen at the boundary separating stationary and moving signals in hypoechoic regions

of bladder images (see Fig. 4.5 (d) and (j)), such random displacements did not

separate the two motions in the liver image (see Fig. 4.7 (b)). Instead, the regions

containing the two motions were juxtaposed, and the boundary separating them

occurred in the echogenic tissue region distal to the gall bladder. Thus, the echogenic

regions distal to the gall bladder (as well as the echogenic regions surrounding the

gall bladder) are either due to tissue (moving regions) or clutter overlying the tissue

(stationary regions). This is most likely true for echogenic regions in other abdominal

images. As demonstrated with simulated and in vivo liver data, the proposed clutter

reduction method is feasible in such echogenic environments.

4.4.2 Motion Filter Advantages and Limitations

The expected performance of the FIR and BSS motion filters is confirmed by

simulation results. In the left panel of Fig. 4.1 (the panel containing only clutter

noise), the FIR filter successfully cancels stationary echoes, reducing the magnitude

to zero, while the BSS filter reduces clutter magnitude by 38 dB. In the right panel

of Fig. 4.1 (the panel containing only tissue), the filters have similar responses to

the distal region (8.5-9 cm) of respective center panels, confirming the similarity of

these regions and demonstrating repeatable filter performance. In the FIR-filtered

image, the distal region of the center panel experiences a magnitude reduction of 0-3

58

dB, which is expected given that the clutter in this region has approximately zero

amplitude. Furthermore, the proximal region (3-3.5 cm) of this FIR-filtered image

experiences a magnitude reduction ranging from 18-24 dB, which is close to expected,

given that the average magnitude of the clutter noise in this region is approximately

10 times (20 dB) greater than the average magnitude of the simulated tissue. The

BSS-filtered image has greater reductions than the FIR-filtered image, as discussed

in greater detail later in this section. The center panels of both FIR- and BSS-filtered

images have the greatest reductions in the near-field and decreasing reductions with

depth.

Similar to the center panel of filtered simulation images, the near-field regions in

phantom and in vivo images experience the greatest clutter reduction. The near-field

reduction is most dramatic in the filtered phantom images (Fig. 4.4 (a) and (c)),

where both clutter and tissue signal are removed. Reduction of the tissue signal in

the phantom data indicates that the proposed BSS and FIR filters reduce slowly

moving tissue as well as stationary echoes (relative to the transducer). However,

when applied to the in vivo data, the filters yield a more realistic representation of

near-field structures.

Considering that the primary goal of these filters is to reduce echoes which are

stationary relative to the transducer, it is expected that the wire mesh (phantom

images) and the abdominal wall (in vivo images) would be reduced in the filtered

images, because these structures were moving with the transducer. While this goal

is beneficial when considering clutter that moves with the wire mesh and abdominal

wall, it results in the reduction of these structures. To circumvent this issue, one

might consider cropping near-field structures out of the image before motion filtering,

then adjoining the cropped portion to the filtered image afterwards. Nevertheless,

when imaging structures at depth, near-field abdominal layers are often unimportant.

The simulated and in vivo FIR-filtered images show increased signal magnitudes

59

in regions that are moving relative to the transducer. Signal increases are not ob-

served in the phantom FIR-filtered images. The increase is likely due to the sub-

traction of RF lines with large axial shifts (shifts in simulated and in vivo data are

an order of magnitude larger than shifts in phantom data). For example, if iden-

tical regions in the shifted RF lines have the same magnitude but opposite signs,

subtraction would yield a signal that is twice the magnitude of the original signal.

This situation may be encountered when RF lines are shifted by half the transmit

pulse wavelength, λ, which occurs when there is a displacement of λ/4 relative to

the transducer. Axial displacements are comparable to λ/4 in simulated and in vivo

images and smaller than λ/4 in phantom images (λ/4 = 0.15 mm in simulation and

harmonic images, λ/4 = 0.088 mm in fundamental images). Thus, large (∼ λ/4)

axial displacements are likely the reason for the 3-6 dB signal increases observed in

FIR filter performance maps of simulated and in vivo data.

While the performance of FIR- and BSS-filters is similar in phantom images, the

reductions in simulated and in vivo BSS-filtered images are greater than those in re-

spective FIR-filtered images. The greater reductions in BSS-filtered simulation and

in vivo images are likely due to the fact that the second principal components were

used to reconstruct simulated and in vivo data, while the first principal component

was used to reconstruct the phantom image. Since higher-order principal components

contain less of the original image energy [24, 68], it is expected that images recon-

structed with the second principal component would contain less energy than images

reconstructed with the first principal component. Thus, images reconstructed with

higher order principle components experience signal attenuation and are expected to

contain decreased signal-to-noise ratios when significant levels of random (thermal)

noise are present.

Despite the greater reductions seen in BSS filter performance maps of simulated

and in vivo images, the relative clutter reductions in BSS filter performance maps

60

are comparable to relative clutter reductions in corresponding FIR filter performance

maps. This explains why some BSS filter performance maps show greater reductions

than corresponding FIR filter performance maps, yet the clutter seen in correspond-

ing FIR- and BSS-filtered B-mode images is similar (e.g. compare Fig. 4.5 (b) with

Fig. 4.5 (c)).

Previous studies have shown that harmonic imaging reduces clutter in bladder

images by 15 ± 3 dB (average of five volunteers) [58]. Clutter reductions achieved

with the BSS filter applied to in vivo fundamental images is comparable to clutter

reductions achieved with harmonic imaging, while the FIR filter yields less clutter

reductions. The FIR and BSS filters applied to harmonic images were shown to re-

duce clutter in the harmonic images, suggesting that higher levels of clutter reduction

may be achieved when this motion-based approach is applied to harmonic images.

Note that motion artifacts in the harmonic data are negligible, given the high pulse

repetition frequency (5.3 kHz) compared to the smaller frame rate (11 Hz).

The contrast in filtered phantom and in vivo images was increased by 4-12 dB.

The CNR was improved by 21-68% in FIR-filtered images and 44-108% in BSS-

filtered images. Given the limited number of volunteers, performance assessment

in a broad range of individuals is unavailable and beyond the scope of this paper.

However, similar contrast and CNR improvements are likely if the proposed clutter

reduction method were applied to other abdominal images.

Real-time implementation of the proposed method is more feasible for the 1,-1

FIR filter since it only requires a lag of one frame and a subtraction operation. On the

other hand, the BSS filter must be implemented over several frames, and appropriate

basis functions must be identified before filter implementation. The speed of the

processor and the size of data sets are also important factors in determining the

real-time feasibility of BSS filtering.

61

4.5 Conclusion

The proposed clutter reduction method requires axial displacement of the ab-

dominal wall during real-time imaging. The method assumes uniform displacement

of the abdominal wall and associated clutter, both of which appear stationary to

the imaging transducer. FIR and BSS motion filters were applied to reduce the sta-

tionary clutter. The method was tested in simulated, phantom, and in vivo images.

The results demonstrate that the FIR and BSS filters are able to isolate and reduce

clutter noise in hypoechoic and echogenic regions moving relative to the transducer.

Clutter reductions ranged from 12-24 dB and contrast improvements ranged from

4-12 dB. The CNR was improved by 21-68% in FIR-filtered images and 44-108%

in BSS-filtered images. The successes achieved in simulated, phantom, and in vivo

images are promising evidence of this method’s potential for reducing clutter in a

vast array of abdominal images.


Funding for this research was provided by the NIH Medical Imaging Training Grant

(T32-EB001040), the NIH Supplement to Promote Diversity in Biomedical Research

(R01-CA114093-04S1), and the Duke Endowment Fellowship. Special thanks to

Siemens Medical Solutions, Inc. USA, Ultrasound Division for supplying the imaging

equipment.

62

5

Clutter Reduction with SLSC Imaging


Lediju MA, Trahey GE, Byram BC, Dahl JJ. Spatial coherence of backscattered

echoes: Imaging characteristics, IEEE Transactions on Ultrasonics, Ferroelectrics,

and Frequency Control, 58(7):1377-88. 2011.

5.1 Introduction

In ultrasound, spatial coherence is a measure of the similarity of backscattered

echoes received by individual transducer elements at a given time, as a function of

element separation. The spatial coherence of backscattered ultrsound waves is de-

scribed by the van Cittert Zernike (VCZ) theorem, a fundamental tenet of modern

optics. The VCZ theorem predicts the mutual intensity (also termed spatial covari-

ance or mutual coherence evaluated at zero delay) of a wave field produced by an

incoherent source [36]. According to this theorem, the spatial covariance in an ob-

servation region is the scaled Fourier transform of the intensity distribution of an

incoherent source.

63

Mallart and Fink [37] and Liu and Waag [75] discuss the VCZ theorem’s appli-

cability to pulse-echo ultrasonic imaging, where diffuse scatterers in the isochronous

volume insonified by a transmit beam represent an incoherent source. At the trans-

mit focus, the spatial covariance of uniformly backscattered echoes can be modeled as

the autocorrelation of the transmit aperture. For a 1-D linear array with no apodiza-

tion, spatial covariance is equal to a triangle function with a base that is twice the

transmit aperture width. This theoretical model of spatial covariance has been com-

pared to simulation and experimental results with notable agreement [37, 76, 77, 78].

Walker and Trahey [79] utilized a k-space representation to predict spatial covariance

and arrived at a similar result.

Although the spatial coherence of backscattered echoes is independent of fre-

quency and focal depth (for a focused transmit aperture and a uniform target), it is

affected by other parameters, such as transmit beam shape, scatterer characteristics,

receiver directivity, aberrations, gross velocity errors, and element nonuniformities.

These factors scale, alter, or invalidate theoretical predictions of spatial coherence.

For example, broad transmit beams, focal errors, aberrations, and element nonuni-

formities shorten coherence lengths [37, 80, 77, 76]. When the transmit aperture is

Gaussian apodized, coherence is increased between closely spaced elements and de-

graded at large element spacings [76]. Diffuse or coherent targets laterally displaced

from the transmit beam will decrease coherence lengths.

Geiman et al. [81] used the inverse Fourier transform of measured spatial co-

herence functions to reconstruct in vivo fundamental and harmonic transmit beam

patterns and to experimentally demonstrate the effect of phase aberration on these

beam patterns. Spatial coherence has also been used to derive analytical predictions

of the performance of adaptive imaging methods. Methods that improve spatial

coherence were shown to decrease aberration across an aperture, resulting in more

accurate echo time-delay estimation [76].

64

Mallart and Fink [80] describe a coherence-based metric to analyze signals from

scattering media. This metric, named the coherence factor by Hollman et al. [82], is a

ratio of the coherent sum of signals across an aperture to the incoherent sum of these

signals. The coherence factor describes focusing quality in the targeted medium. Li

and Li [83] proposed an adaptive imaging technique based on a generalized version

of the coherence factor. In this method, data containing high spatial frequencies

across the receive array are excluded from the coherent sum. The exclusion of high

spatial frequencies suppresses signals from off-axis targets or signals corrupted by

phase aberration. The generalized coherence factor (GCF) is then calculated as the

ratio of the modified coherent sum to the incoherent sum and is used to weight

the beamsum prior to image formation. Variations of this method are described by

Ustuner et al. [84]. Liu and Waag [85] describe a measure of waveform similarity

that is similar to the coherence factor used by Li and Li [83]. Camacho et al. [86]

utilized a phase coherence factor (PCF), which is based on the standard deviation of

the phase of backscattered signals across the aperture, to weight the beamsum prior

to image formation.

Bamber et al. [77] show a direct relationship between spatial coherence and receive

beamformer gain. Gain is defined as the ratio between beamformer output power

and the total power of echoes at each element. It may also be represented as the

weighted area under Mallart and Fink’s normalized spatial coherence function [77].

In this paper, a new approach to extracting useful information from spatial coher-

ence functions is demonstrated, yielding images that have the potential to compete

with conventional ultrasound B-mode images, particularly in cases where there is

corruption due to noise artifacts like clutter. Clutter originates from acoustic inter-

actions with surrounding tissue (e.g. reverberation, off-axis scattering, phase aberra-

tion) [58, 87, 88], and it is a significant problem in numerous imaging environments,

including vascular [10], cardiac [8], abdominal [42], and breast imaging [41, 7]. The

65

0 N−1−0.5

0

1

Cor

rela

tion

Lag (Receive Element Spacing)

Point targetSpeckleIn vivo tissue

Figure 5.1: Examples of coherence functions in a point target and speckle back-ground, as well as an experimental coherence function from in vivo thyroid tissue.The abscissa represents the lag, or spacing between receive elements. The ordinaterepresents inter-element RF echo correlation.

proposed image processing method, described in Section II, is based on local mea-

surements of the spatial coherence of backscattered echoes and is likely to have wide

clinical utility in high-noise environments. Theory and simulation results obtained

utilizing this method under various imaging conditions are explored. Experimental

phantom and in vivo images based on this method are presented and compared to

matched B-mode images (i.e. B-mode images created with the same data as that

used to form coherence-based images).

5.2 Short-Lag Spatial Coherence

For a receive aperture with N elements of equal spacing, the time-delayed signal

received by the ith element is defined as si(n), where n is the depth or time, in sam-

ples, and si(n) is a zero-mean signal. The signals arriving across the receive aperture

are time-delayed to ensure that the signals at sample n correspond to the same loca-

tion. After time delay of the element signals, the estimated spatial covariance across

the receive aperture is calculated as

66

C(m) =1

N −m

N−m∑i=1

n2∑n=n1

si(n)si+m(n), (5.1)

where m is the distance, or lag, in number of elements between two points in the

aperture. Normalizing the covariance by the variance of the signals si(n) and si+m(n),

the spatial correlation can be computed by

R(m) =1

N −m

N−m∑i=1

∑n2


n=n1s2

i (n)∑n2

n=n1s2

i+m(n). (5.2)

The choice of the normalizing term differs from that used by Mallart and Fink [37]

who normalized Eq. 5.1 by the estimated spatial covariance at zero lag. However,

both normalization terms serve the same purpose in that the relative strength of the

echo signals are removed from the spatial covariance terms. Eq. 5.2 is identical to

the spatial coherence calculation used by Fedewa et al. [40]. While spatial covariance

(Eq. 5.1) and spatial correlation (Eq. 5.2) have different definitions, the term “spatial

coherence” refers to both (i.e. both are a measure of the similarity of backscattered

echoes as a function of element separation). The term spatial coherence will be used

hereafter in reference to Eq. 5.2, and spatial covariance is used in reference to Eq.

5.1.

Fig. 5.1 illustrates the normalized theoretical spatial covariance across the receive

aperture for a point target positioned at the transmit focus and uniformly-distributed

diffuse scatterers, compared to the spatial coherence of in vivo echoes from a human

thyroid. For a point target, the source function is modeled as an impulse, so the

spatial coherence is constant across the aperture. For diffuse scatterers, the source

function is modeled as a constant, and the source intensity distribution (i.e. the

square of the lateral transmit beam shape) is modeled as a squared sinc function.

The corresponding expected spatial coherence function is a triangle, or a line de-

67

creasing from 1 at zero lag to 0 at lag N -1, where N refers to the number of elements

in the transmit aperture, which is assumed to be identical to the receive aperture for

simplicity. The spatial coherence of in vivo tissue from a human thyroid is expected

to be similar to that of diffuse scatterers. However, the coherence demonstrated in

Fig. 5.1 indicates that there is underlying corruption of the signals, such as rever-

beration clutter, strong off-axis targets, phase aberration, or electronic noise, that

decreases spatial coherence across the aperture.

For a given transmit beam shape, the spatial coherence will vary depending on

the lateral backscatter distribution and the amount of signal corruption. While it is

difficult to increase spatial coherence above the predicted coherence for diffuse scat-

terers without a strongly-reflecting and/or a laterally-compact target at the transmit

focus, a decrease in spatial coherence below the expected value for diffuse targets is

relatively easy to obtain via increased noise or decreased on-axis source strength. In

this case, the largest losses in spatial coherence will occur in the regions of low lags,

or in the coherence between closely-separated elements, as has been observed in the

spatial coherence of backscattered signals with phase aberration [76]. We therefore

describe a metric, called the short-lag spatial coherence (SLSC), as the integral of

the spatial coherence function over the first M lags:

Rsl =

M∫1

R(m) dm ≈M∑

m=1

R(m). (5.3)

Given that coherence functions scale with the size of the transmit aperture, a param-

eter Q is introduced to report values of M as a percentage of the transmit aperture

width, where

Q =M

N× 100%. (5.4)

Q ranges from 1-30% for our proposed realizations of SLSC imaging.

68

5.3 Methods

To evaluate the characteristics of images created using the short-lag spatial co-

herence, simulated images using Field II [51] were created. A numerical computation

of the SLSC image at the focal depth, based on the theoretical spatial coherence, was

compared to the simulated images. SLSC images of tissue-mimicking phantoms and

in vivo human thyroid were also generated to demonstrate the potential application

to clinical imaging.

5.3.1 Theoretical Prediction of Short-Lag Spatial Coherence

The spatial covariance of wavefronts across an aperture can be predicted by the

Fourier Transform of the square of the product of the lateral transmit beam pressure

and the lateral backscatter, or source, function [37]. In mathematical notation,

spatial covariance is given by

C(u, v) =

∫ ∞

−∞

∫ ∞

−∞|χ(x, y)H(x, y)|2 e−j2π(xu+yv)dxdy, (5.5)

where x and y are the spatial dimensions in the source plane, χ(x, y) is the source

(or scattering) function, H(x, y) is the transmit beam amplitude, and u and v are

spatial frequencies evaluated at u = x′/λz and v = y′/λz. The variable x′ is the

spatial difference between two points in the x dimension of the aperture plane, y′ is

the spatial difference between two points in the y dimension of the aperture plane, z

is the distance between the source and the aperture planes, and λ is the ultrasonic

wavelength.

To predict the lateral profiles of SLSC images at the focal depth, the lateral trans-

mit beam amplitude, H(x), was modeled as a sinc function based on the parameters

in Table 6.1. For a lesion, the source function χ(x) was modeled as a constant minus

a rectangular pulse, where the ratio of the pulse amplitude to the constant was equal

69

to the contrast of the lesion and the width of the pulse was equal to the diameter

of the lesion. Note that χ or H may be modified to arbitrary geometries, enabling

theoretical predictions for other target types or transmit beam shapes.

The spatial covariance in the lateral dimension was numerically computed using

the Fast Fourier Transform of |H(x)χ(x)|2. The spatial covariance was then normal-

ized at zero lag and resampled at the spacing of the array elements to create a spatial

coherence function. The theoretical short-lag spatial coherence was then calculated

by integrating the resulting spatial coherence function over the first M lags, as de-

cribed by Eq. 5.3. Noise was not considered in this numerical computation. Note

that this description of short-lag spatial coherence is valid only at the focal depth

of the transmit beam. Computation at other depths requires incorporation of the

lateral intensity of the defocused transmit beam. There is no variance in predicted

values because the theoretical model of the spatial coherence does not account for

the randomness of diffuse scatterers.


Field II was used to simulate the received, individual-channel, echo signals from a

variety of imaging targets. Three-dimensional phantoms containing a 3-mm spherical

lesion and three point targets were utilized, where the contrast of the lesion was varied

from anechoic to 6 dB. The point target brightness in each phantom was varied from 6

to 24 dB relative to the root-mean-square (rms) value of the diffuse scatterer strength.

Each phantom measured 6mm axially by 10mm laterally by 10mm in elevation

and contained 20 scatterers per resolution volume. The simulated transducer was a

linear array with a 5.7MHz center frequency and 60% fractional bandwidth. The

array had a lens focused at 3.75 cm in elevation, and the lateral focus was positioned

at the same depth. An F/2 transmit aperture was employed and dynamic-receive

beamformer delays were applied to the channel signals. No apodization was applied

70

Table 5.1: Simulated Transducer Parameters

Parameter Value

Number of Elements 96Element Height 7.5mmElement Width 0.176mmKerf 0.025mmCenter Frequency 5.71MHzSampling Frequency 160MHzFractional Bandwidth 60%

to the transmit aperture. The full list of parameters of the simulated transducer are

shown in Table 6.1.

In Field II, regions that do not contain scatterers have low amplitude echoes

in the received channel signals. These echoes are a few orders of magnitude be-

low backscattered and off-axis echoes and often reside below the noise floor seen

in experimentally-obtained ultrasonic data. Because coherence calculations do not

depend on signal magnitude, these low-amplitude echoes yield coherence estimates

unlikely to be observed in experimental measurements. Therefore, uniform white

noise was bandpass filtered and added to the channel signals to suppress coherence

from low-amplitude echoes created by Field II, and the resulting SNR of the channel

signals was 10 dB, comparable to that measured in in vivo data [89]. The cutoff

frequencies used in the bandpass filter were equal to the -6 dB bandlimits of the

transducer in order to simulate acoustic noise received by the transducer. Introduc-

ing incoherent noise with amplitudes greater than the spurious echoes suppresses

artifacts in the simulated images and adds a degree of realism to the echo signals.

To analyze the lateral resolution of SLSC images, a numerical differentiation

technique described in Ref. [90] is employed because conventional techniques, such

as the autocorrelation of speckle or the width of a point target, are not practical

due to the spurious echoes described previously. In this method, two phantoms, each

containing two adjacent vertical regions of differing contrast, were used to compute a

71

spatial step function. For B-mode resolution calculations, one of the vertical regions

was anechoic. For SLSC resolution calculations, the backscatter difference between

the two regions was 12 dB. To determine lateral resolution, an estimated lateral point

spread function (PSF) was created by numerical differentiation of the step function,

and the width of the resulting PSFs was measured at -6 and -10 dB.

To study SLSC imaging characteristics of expanded targets, six independent

speckle realizations of a 1-cm spherical lesion phantom were simulated, using the

transducer parameters listed in Table 6.1. The contrast of the lesion was -9.8 dB,

which was chosen to match the phantom experiment described in Section 5.3.3. Each

phantom measured 15mm axially by 30mm laterally by 1mm in elevation and con-

tained 20 scatterers per resolution volume. The simulated transducer array had a

lens focused at 3.75 cm in elevation, and the lateral focus was positioned at the same

depth. An F/2 transmit aperture was employed and dynamic-receive beamformer

delays were applied to the channel signals. No apodization was applied to the trans-

mit aperture. Simulations were performed with and without noise that was 10 dB

down from the channel signals.

5.3.3 Tissue-Mimicking Phantoms and In Vivo Experiments

An RMI 408 Spherical Lesion Phantom (Gammex, RMI, Middleton, WI) con-

taining 4-mm anechoic lesions spaced 1 cm apart was used as an imaging target to

compare B-mode and SLSC imaging. Individual channel signals were acquired on

a VF10-5 linear array transducer (Siemens Medical Solutions USA, Inc., Issaquah,

WA) attached to a Siemens Antarestm ultrasound scanner (Siemens Medical Solu-

tions USA, Inc.). The transmit frequency was 8.0 MHz, and the number of transmit

elements was adjusted to maintain a constant F/2 transmit. Individual channel sig-

nals were acquired using the Axius Direct Diagnostic User Interface (Siemens Medical

Solutions USA, Inc., Issaquah, WA) [91] in conjunction with a synthetic receive aper-

72

ture technique [89]. Signals were acquired with a transmit focus of 2.0 cm. The total

number of receive elements in the array was 192, however only echoes from the 64

elements centered about the transmit aperture for that beam were acquired. Indi-

vidual channel signals were acquired for 54 A-lines. Dynamic-receive beamforming

delays were applied to the channel signals.

A contrast-detail phantom (ATS Laboratories, Bridgeport, CT), described by

Smith and Lopez [92], was utilized to image a 1-cm cross-section of a conical lesion.

An identical setup to the RMI phantom experiments was employed, except that a

VF7-3 linear array transducer was used with a center frequency of 5.7 MHz and a

transmit focus of 3.75 cm. Echoes from 64 elements were acquired for 108 A-lines.

In vivo individual channel data from the thyroid of a 34-year-old male volunteer

were acquired in addition to phantom data. An identical setup to the RMI phan-

tom experiments was employed, except that 48 receive elements centered about the

transmit aperture were used to acquire three sets of individual channel signals, each

with a unique transmit focus of 0.5, 1.5, or 2.5 cm.

5.3.4 Coherence Image Processing

The short-lag spatial coherence was computed for simulated, phantom, and in

vivo data using Eqs. 5.2 and 5.3. SLSC images were formed by computing the

short-lag spatial coherence at each depth n of each A-line, using a correlation kernel

size (i.e. n2 − n1 in Eq. 5.2) of one wavelength. The size of the correlation ker-

nel impacts the quality of the correlation calculation as well as the axial resolution

of SLSC images. A kernel size of one wavelength was chosen to maintain an ax-

ial resolution that is comparable to B-mode images, yet produce stable coherence

functions. B-mode images were constructed with the same individual channel data

using conventional delay-and-sum methods. The contrast (C), contrast-to-noise ra-

tio (CNR), and speckle signal-to-noise ratio (SNR) in the B-mode and SLSC images

73

were calculated using the following equations:

C = 20log10

(Si

So

), (5.6)

where So and Si are the mean signals at the same depth outside and inside a lesion,

respectively.

CNR =|Si − So|√σi

2 + σo2, (5.7)

where σo and σi are the standard deviations of signals at the same depth outside and

inside a lesion, respectively.

SNR =So

σo

. (5.8)

Point target conspicuity in simulated images was calculated using

Conspicuity =Smax − So

σo

, (5.9)

where Smax is the peak brightness of the point target and So and σo are the mean

brightness and standard deviation, respectively, of a background region at the same

depth as the point target. All image processing and data analysis was performed

with Matlab (The Mathworks Inc., Natick, MA) software.

5.4 Results


Matched B-mode and SLSC images are displayed in Fig. 5.2. The first row shows

B-mode images with anechoic, -24 dB-contrast, and -18 dB-contrast lesions, from left

to right, respectively. The second row shows B-mode images with lesion contrasts of

-12 dB, -6 dB, and 6 dB, from left to right, respectively. Corresponding SLSC images

74

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40A

xial

(m

m)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Axi

al (

mm

)

Lateral (mm)−3 −2 −1 0 1 2 3

35

36

37

38

39

40

Figure 5.2: Simulated B-mode images of 3-mm lesions with contrasts of anechoic,-24 dB, -18 dB from left to right in the first row, and -12, -6, and 6 dB from left toright in the second row. The corresponding SLSC images created with Q=20.8%are shown in rows 3 and 4. B-mode and SLSC images are shown with 40 dB ofdynamic range. The boxes in the upper-left image indicate ROIs used to calculatethe contrast, CNR, SNR, and point target conspicuity.

created with Q equal to 20.8% are shown in rows three and four. The B-mode

and SLSC images show 40 dB of dynamic range. Identical regions from all images

(indicated by the white boxes in the upper-left image) were used to calculate contrast,

CNR, SNR, and point target conspicuity. Visual inspection of the SLSC images

75

reveal similarity to corresponding B-mode images, however there is a significant loss

in visualization of the point targets. The variance in the background region appears

to be reduced as well.

AN −24 −18 −12 −6 6−60

−50

−40

−30

−20

−10

0

10

Lesion Contrast (dB)

Mea

sure

d C

ontr

ast (

dB)

B−modeSLSC, Q=5.2%SLSC, Q=20.8%Ideal

(a)

AN −24 −18 −12 −6 60

1

2

3

4

5

6

7

CN

R

Lesion Contrast (dB)

B−modeSLSC, Q=5.2%SLSC, Q=20.8%

(b)

Figure 5.3: Mean (a) contrast and (b) CNR observed in the lesions of the simulatedB-mode and SLSC images, as a function of the intrinsic lesion contrast. Contrastof the B-mode images are a close match to ideal values. SLSC imaging suffers asignificant decrease in contrast when Q=5.2%, but is more similar to B-mode imagingwhen Q=20.8%. SLSC imaging with Q=5.2% and 20.8% shows considerably higherCNR for hypoechoic lesions than B-mode imaging. Error bars indicate one standarddeviation.

6 12 18 240

5

10

15

20

25

30

Point Target Brightness (dB)

Con

spic

uity

B−modeSLSC

Figure 5.4: Point target conspicuity increases as a function of target brightness forB-mode imaging, but remains flat for SLSC imaging regardless of brightness or Q.Error bars indicate one standard deviation.

Measured contrast and CNR of the simulated lesions, as a function of lesion

contrast, are displayed in Fig. 5.3. Contrast of the lesions in the B-mode images have

76

−4 −3 −2 −1 0 1 2 3 4−5

0

5

10

15

20

25

30

Lateral (mm)

Imag

e M

agni

tude

SLSC, TheorySLSC, SimulationB−mode (Normalized)

(a)

Figure 5.5: Theoretical calculations of the short-lag spatial coherence image com-pared to the simulated B-mode and SLSC images for a lateral slice through the centerof a spherical 3mm anechoic lesion with -24 dB contrast.

excellent agreement with ideal values (i.e. the intrinsic contrast of the lesions). At

Q=5.2%, contrast is reduced in SLSC images compared to B-mode images. However

when Q was increased to 20.8%, the contrast in the SLSC and B-mode images are

similar. CNR increased significantly in the SLSC images compared to B-mode images

as a result of a large increase in SNR. The average SNR at the focal depth in the

B-mode images is 2.1±0.3 and in the SLSC images formed with Q equal to 5.2% and

20.8% is 11.3±2.2 and 5.7±0.9, respectively. Point target conspicuity as a function

of point target brightness is displayed in Fig. 5.4. Conspicuity increases with target

brightness in B-mode images, but remains flat and significantly lower in SLSC images.

SLSC results are shown for Q=20.8%, but are nearly identical for Q=5.2%.

In Fig. 5.5, simulated B-mode and SLSC images without added noise are com-

pared to a numerical computation of the theoretical SLSC image. Six independent

realizations of simulated B-mode and SLSC images were averaged to reduce back-

ground variance for a better comparison with theory. The averaged B-mode image

was normalized to the same scale as the theoretical SLSC image. There is good

agreement between simulated and theoretical SLSC images.

Fig. 5.6 (a) and (b) respectively shows the contrast and CNR of the -24 dB lesion

77

0 10 20 30 40 50−45

−40

−35

−30

−25

−20

−15

−10

Q

Con

tras

t (dB

)

SLSCB−mode

(a)

0 10 20 30 40 501

2

3

4

5

6

7

Q

CN

R

SLSCB−mode

(b)

0 10 20 30 40 500

5

10

15

Q

SN

R

SLSCB−mode

(c)

0 10 20 30 40 500.4

0.5

0.6

0.7

0.8

0.9

Q

Late

ral R

esol

utio

n (m

m)

SLSC, −6 dBSLSC, −10 dBB−mode, −6 dBB−mode, −10 dB

(d)

Figure 5.6: (a) Contrast and (b) CNR for the -24 dB lesion, (c) SNR, and (d)lateral resolution as a function of Q. Q indicates the size of the receive apertureexpressed as a percentage of the transmit aperture used to create the SLSC andB-mode images. Error bars indicate one standard deviation for six simulations.

in SLSC and B-mode images as a function of Q, where Q refers to the percent of the

transmit aperture for SLSC and B-mode images. Contrast in SLSC images is optimal

for Q greater than 20%. Contrast in B-mode images improves with an increasing

number of receive elements. The CNR of SLSC images peaks at Q = 10.4%, however

CNR is relatively flat for B-mode images. Fig. 5.6(c) shows SNR as a function of Q.

Predictably, the SNR in B-mode images is unchanged as a function aperture size,

but SNR in the SLSC images decreases with increasing Q and is up to an order of

magnitude higher than that of B-mode images.

Fig. 5.6(d) shows lateral resolution at -6 and -10 dB as a function of Q, as mea-

78

sured with the numerical differentiation technique. Compared to resolution values

measured using the lateral width of a simulated point target (not shown), the re-

ported B-mode image resolution values reflect better resolution by an average of 0.13

and 0.18mm at -6 and -10 dB, respectively. Although similar biases are suspected

in SLSC resolution calculations, the trends observed using this method are expected

to be valid. These trends include a general improvement in lateral resolution with

increasing Q and slightly better resolution in SLSC images compared to B-mode

images of equivalent-sized apertures, particularly at -6 dB.

The lateral resolution of SLSC images at Q=20.8% (i.e. same Q used to make

the SLSC images in Fig. 5.2) is 0.47 and 0.63mm at -6 and -10 dB, respectively, as

reported in Fig. 5.6(d). The lateral resolution of the B-mode images in Fig. 5.2,

which were created with the entire transmit aperture, measured 0.43 and 0.55mm

at -6 and -10 dB, respectively, using the numerical differentiation technique. Using

the lateral width of a simulated point target, lateral resolution measured 0.50 and

0.65mm at -6 and -10 dB, respectively.

The axial resolution of the coherence images is approximately equal to the cor-

relation kernel length convolved with half the pulse length, as in correlation-based

imaging techniques such as ARFI [93, 94] and elastography [95, 96]. In all SLSC

images, the correlation kernel length was equal to λ.

5.4.2 Experiments in Tissue-Mimicking Phantom

Matched B-mode and SLSC images (Q equal to 7.8%, 15.6%, and 23.4%) of

the RMI spherical lesion phantom are shown in Fig. 5.7 and demonstrate changes

in image characteristics with increasing Q. SLSC images have increased focal gain

with increasing Q, but lesions are still easily visualized, with the exception of the

shallower lesions. In addition, lesion boundaries appear sharper with increasing Q,

an indication of increased resolution.

79

Axi

al (

mm

)

Lateral (mm)−5 0 5

5

10

15

20

25

30

35

(a)

Axi

al (

mm

)


0

5

10

15

20

25

30

35

40

(b)A

xial

(m

m)


0

5

10

15

20

25

30

35

40

(c)

Axi

al (

mm

)


0

5

10

15

20

25

30

35

40

(d)

Figure 5.7: Matched B-mode (a) and SLSC (b-d) images of 4mm spherical ane-choic lesions in a tissue-mimicking phantom. The SLSC images were created withQ equal to 7.8, 15.6, and 23.4%, from left to right, respectively. The SLSC imagesshow improved CNR and SNR and increased depth-of-field effects for smaller Q.Resolution differences are observable with increasing Q.

Contrast and CNR of the focal lesion and SNR at the focus of B-mode and SLSC

images in Fig. 5.7 are reported in Table 5.2. The differences in contrast are marginal

for the three SLSC images, but CNR and SNR decrease with increasing Q.

5.4.3 SLSC of Expanded Targets

Matched B-mode and SLSC images of the simulated and experimental 1-cm lesion

are shown in Fig. 5.8. In the simulated SLSC image (Fig. 5.8 (b)), the lesion is

well visualized but has lower contrast compared to the corresponding B-mode image

(Fig. 5.8 (a)). While the lesion borders are well defined, the center of the lesion

shows more coherence than the borders, resulting in lower contrast and CNR when

compared to the matched B-mode image. This image characteristic will be referred

80

Axi

al (

mm

)


32

34

36

38

40

42

44

(a)

Axi

al (

mm

)


32

34

36

38

40

42

44

(b)

Axi

al (

mm

)


25

30

35

40

45

50

(c)

Axi

al (

mm

)


25

30

35

40

45

50

(d)

Figure 5.8: Matched B-mode (left) and SLSC (right) images of 1-cm lesions, formedfrom simulated data without noise (top) and experimental data (bottom). Q is equalto 20.8% and 20.3% in simulated and experimental data, respectively. The boxesindicate ROIs used to calculate the contrast, CNR, and SNR. B-mode and SLSCimages are shown with 50 dB dynamic range.

to as “recorrelation”. The experimental SLSC image (Fig. 5.8 (d)) does not appear

to have the recorrelation characteristic. The contrast, CNR, and SNR of lesions in

Fig. 5.8 were calculated using the ROIs shown, and the values are listed in Table 5.2.

Averaged lateral profiles about the focus of the simulated B-mode and SLSC

images from Fig. 5.8 are compared to the theoretical computation of the SLSC

profile in Fig. 5.9 (a). Six independent realizations of simulated B-mode and SLSC

81

−10 −5 0 5 100

0.5

1

1.5

2

Azimuth (mm)

Nor

mal

ized

Mag

nitu

de

SLSC TheorySLSC SimulationB−mode

(a)

−5 0 50

0.5

1

1.5

2

Azimuth (mm)

Nor

mal

ized

Mag

nitu

de

SLSC TheorySLSC Simulation with NoiseB−mode Simulation with NoiseSLSC ExperimentB−mode Experiment

(b)

−10 −5 0 5 100.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Lateral Position (mm)

Nor

mal

ized

Mag

nitu

de

1 mm3 mm9 mm15 mm

(c)

−10 −5 0 5 100

0.2

0.4

0.6

0.8

1

Lateral Position (mm)

Nor

mal

ized

Mag

nitu

de

−24 dB−18 dB−12 dB−6 dB

(d)

Figure 5.9: Theoretical calculations of the short-lag spatial coherence image. Alateral slice through the center of a spherical 1cm lesion with -12 dB contrast iscompared to simulated data with no noise (a), simulated data with noise, and ex-perimental data (b). (c) Theoretical -12 dB contrast lesions of varying sizes. (d)Theoretical 12mm lesions of varying contrasts, with the vertical lines denoting lesionboundaries. Q is equal to 20.8% in theory and simulations and 20.3% in experimentaldata.

images were averaged to reduce background variance for a better comparison with

theory. The simulated SLSC and B-mode profiles were normalized by the mean of

the background. There is good agreement between simulated and theoretical SLSC

images, as the lesion center in both images has more coherence than its borders (i.e.

they both have the recorrelation effect).

Fig. 5.9(b) shows lateral profiles about the focus for the experimental 1-cm

lesion displayed in Fig. 5.8 (c) and (d). The experimental SLSC profiles do not show

recorrelation at the lesion center and are more similar to the SLSC simulation results

82

Axi

al (

mm

)

Lateral (mm)−4 −2 0 2 4

0

5

10

15

20

25

30

(a)Lateral (mm)

Axi

al (

mm

)

−4 −2 0 2 4

0

5

10

15

20

25

30

(b)Lateral (mm)

Axi

al (

mm

)

−4 −2 0 2 4

0

5

10

15

20

25

30

(c)Lateral (mm)

Axi

al (

mm

)

−4 −2 0 2 4

0

5

10

15

20

25

30

(d)

Axi

al (

mm

)

Lateral (mm)−4 −2 0 2 4

0

5

10

15

20

25

30

(e)

Figure 5.10: (a) In vivo B-mode image of a cyst at 1.5 cm depth in a humanthyroid. SLSC images of the thyroid formed with (b) Q=10.4% (c) Q=20.8%, and(d) Q=31.2%. (e) A spatial-compounded image of the thyroid. The SLSC imagesshow improved CNR of the cyst and improved SNR of the thyroid tissue compared tothe B-mode and spatial-compounded images. The SLSC images also show improvedresolution compared to the spatial-compounded image.

with added noise. Notice that the addition of noise to the simulation eliminates the

recorrelation effect and increases the contrast and CNR of the lesion. Contrast, CNR,

and SNR at the focus of the simulated images with noise are reported in Table 5.2.

Fig. 5.9(c) illustrates theoretical predictions for various lesion sizes with the same

-12 dB contrast, normalized by maximum values. Recorrelation is not apparent in

small lesions. In larger lesions, the recorrelation effect increases with lesion size.

Fig. 5.9(d) demonstrates theoretical predictions for 12-mm lesions with differing

contrasts. The amount of recorrelation changes as a function of the intrinsic lesion

contrast.

5.4.4 In Vivo Human Thyroid Images

In vivo B-mode, SLSC (Q equal to 10.4%, 20.8%, and 31.2%), and spatial-

compounded images of a human thyroid are shown in Fig. 5.10. Each image was

83

created from data acquired at three transmit foci and blended to form a single

image. The spatial-compounded image was created from 43 B-mode images with

coherent receive apertures equal to 10.4% of the transmit aperture and spaced 2.1%

of the transmit aperture apart. A cyst is visible in the thyroid at 1.5 cm depth. The

B-mode, SLSC, and spatial-compounded images are shown with 50 dB of dynamic

range.

Contrast and CNR of the cyst and SNR of the thyroid tissue at 1.5 cm are

reported in Table 5.2. Contrast is improved by 17, 36, and 25 dB in the SLSC images

formed with Q=10.4, 20.8, and 31.2%, respectively, when compared to the B-mode

image. Contrast in the spatial-compounded image is reduced by 6 dB compared to

the B-mode image. CNR and SNR are greatest in SLSC images, particularly when

Q=10.4%, and decrease with increasing Q.

5.5 Discussion

The short lags of the spatial coherence function allow discrimination of imaging

targets without direct utilization of echo brightness. Generally, bright diffuse scatter-

ers have higher spatial coherence at short lags, when compared to adjacent anechoic

regions. The source of contrast in SLSC images when two adjacent regions of diffuse

scatterers only differ in magnitude is counterintuitive because the spatial coherence

calculated by Eq. 5.2 has no dependence on echo brightness. Intuition might predict

that the two backscattered echoes should have the same spatial coherence and there-

fore produce a uniform SLSC image. However, we hypothesize that off-axis echoes

from nearby higher-amplitude regions are added out of phase to echoes received from

hypoechoic regions, thereby decreasing spatial coherence in hypoechoic regions, thus

generating contrast in SLSC images. As the distance between the main lobe of the

transmit beam and the interface of the two regions increases, the contribution from

interfering echoes diminishes and the coherence of on-axis signals in the hypoechoic

84

Table 5.2: Contrast, CNR, and SNR at focus of experimental phantom, simulated,and in vivo thyroid data.

Contrast (dB) CNR SNRExperimental phantom images, 3-mm lesionsB-mode -17.3 1.6 1.7SLSC, Q= 7.8% -13.6 6.4 15.8SLSC, Q=15.6% -14.3 6.9 9.0SLSC, Q=23.4% -14.3 6.0 6.2Simulation images with no noise, 1-cm lesions (mean ± s.d.)B-mode -10.0±0.6 1.2±0.1 1.9±0.0SLSC, Q=6.3% -0.5±0.1 1.2±0.1 128.9±8.7SLSC, Q= 10.4% -1.1±0.1 1.2±0.1 45.6±2.6SLSC, Q=20.8% -1.2±0.2 0.9±0.1 16.0±0.8Simulation images with noise, 1-cm lesions (mean ± s.d.)B-mode -9.9±0.7 1.2±0.1 1.9±0.0SLSC, Q=6.3% -5.0±0.5 2.2±0.2 11.7±1.0SLSC, Q= 10.4% -5.0±0.5 2.2±0.2 11.6±1.0SLSC, Q=20.8% -4.9±0.5 2.1±0.2 10.5±0.8Experimental phantom images, 1-cm lesionB-mode -9.8 1.1 1.9SLSC, Q= 12.5% -8.4 2.1 9.9SLSC, Q=21.9% -7.5 2.1 10.8SLSC, Q=31.3% -6.7 2.1 10.2In vivo thyroid imagesB-mode -20.3 1.9 2.1SLSC, Q=10.4% -37.7 5.3 5.8SLSC, Q=20.8% -56.7 4.0 4.2SLSC, Q=31.2% -44.8 3.1 3.2Spatial-compounded -14.4 2.8 3.5

region is increased. This recovery of the coherence is responsible for the recorrela-

tion demonstrated in Figs. 5.8(b) and 5.9(a). Figs. 5.5 and 5.9 demonstrate that

theoretical predictions and simulation results without noise are consistent with these

hypotheses. Simulations with added noise and experimental results with intrinsic

noise show mitigation of the recorrelation effect observed in noise-free environments.

Moreover, the appearance of the recorrelation effect is dependent on the amount of

noise added to simulated data. For this simulation, noise in the range of 6dB down

85

from the channel signals will show minimal recorrelation reduction, while noise as

great as 20 dB eliminates the recorrelation effect.

There are four notable features of SLSC imaging. First, the SNR for regions of

diffuse scatterers is markedly higher in SLSC images compared to B-mode images.

This is due to the low variance at short lags of the spatial coherence function for

diffuse scattering regions. The variance in the spatial coherence function is not easily

modeled, however empirical determination of the variance shows that it typically

increases with decreasing correlation for a diffuse scattering region. In addition, the

variance is not evenly distributed about the mean and is skewed toward unity for

the higher correlation coefficients.

Second, resolution is improved by increasing Q, as shown in Fig. 5.6(d) and

evident in Figs. 5.7 and 5.10. The improved resolution is due to the addition of

higher spatial frequency content from the larger lags of the receive beamformer.

Furthermore, SLSC images appear to have better lateral resolution than B-mode

images formed with equivalent aperture sizes, as shown in Fig. 5.6(d) for simulated

data and illustrated in Fig. 5.10 (b) and (e) for experimental data.

Third, while the contrast of SLSC images generally improves with an increase in

the number of lags summed, SNR improves with decreasing Q. There appears to be a

trade-off among contrast, CNR, and SNR when selecting a value for Q. Nevertheless,

the SNR of SLSC images is larger than that of B-mode images, and the large gain

in CNR is due to the increased SNR of the background.

Fourth, there is an apparent decrease in focal gain with increasing Q, as depicted

in Fig. 5.7. This decrease is attributed to a relatively broad transmit beam proximal

and distal to the focal zone. The challenges associated with the short coherence

lengths produced by a broad transmit beam outside of the focal region may be

overcome by using a larger number of emission focal points, as demonstrated in

Fig. 5.10, or by applying depth-dependent gain to the SLSC image.

86

Spatial compounding is a favored method for reducing speckle variance in ultra-

sound images, often performed at the expense of lateral resolution. Fig. 5.10 (b) and

(e) may be used to compare equivalent-sized receive apertures in SLSC and spatial-

compounded images, respectively, and demonstrates a distinct difference between the

two imaging modalities. The SNR of a homogeneous region in the thyroid improved

by a factor of 2 in the spatial-compounded image compared to the B-mode image,

whereas a factor of 3 increase was achieved in the SLSC image. In addition, the

apparent detail of the cyst is worse in the spatial-compounded image than in the

comparable SLSC image, even though resolution is expected to differ by less than

0.2 mm, as estimated with Fig. 5.6(d).

The SLSC metric differs from other coherence metrics in its calculation and in

its direct application to image formation. However, it can be utilized like other

coherence metrics. The primary proposed use of the GCF and PCF coherence metrics

developed by Li and Li [83] and Camacho et al. [86] was to weight B-mode data.

Like these metrics, the SLSC value can be used to weight the B-mode image rather

than form a direct image of SLSC values. In this case, speckle will be present in the

weighted image and the anticipated benefits in CNR and SNR would be lost in favor

of improved contrast.

One notable limitation of SLSC imaging is its inability to detect point-like tar-

gets in speckle-based background. The point targets in SLSC images of Fig. 5.2 are

not present because the coherence of speckle is similar to that of the point target

for short lags. Clinical tasks that depend on point target conspicuity, such as mi-

crocalcification detection, will be difficult with SLSC imaging. Such tasks are best

achieved in the presence of acoustic noise, as demonstrated in Chapter 6.

A potential application of SLSC imaging is to reduce clutter, particularly in

cardiovascular or fetal imaging. Figs. 5.10 demonstrates that SLSC imaging is the

preferred technique in the presence of clutter or other noise sources that corrupt

87

diagnostic information. The SLSC images of Fig. 5.10 have 20-30 dB more contrast

than corresponding B-mode images due to reduced clutter inside the anechoic cyst.

Such large contrast improvements are not observed in simulated data when the sim-

ulated noise level is lower than the magnitude of noise present in the thyroid images.

While the simulation analysis does not include the influence of clutter on B-mode

and SLSC images, the experimental thyroid data reveal that SLSC imaging yields

greater clutter suppression than B-mode imaging.

As mentioned in Section I, the shape of a transmit beam influences the spatial

coherence of backscattered echoes. For example, a change in the transmit aperture

apodization alters the transmit beam shape and thus alters the expected spatial

coherence function (as predicted by Eq. 5.5) and the resulting SLSC image. It is

likely that optimal apodization for SLSC imaging differs from the typical apodization

used in B-mode imaging.

The challenges for real-time implementation of SLSC imaging are similar to

the challenges associated with phase aberration correction and adaptive (or data-

dependent) beamforming methods. For example, access to the channel signals is

required in these approaches and is influenced by the ultrasound system’s ability

to provide such signals. In addition, the computational complexity of SLSC imag-

ing is far greater than delay-and-sum beamforming. SLSC imaging uses many more

cross correlations than phase aberration correction techniques, but is on par with the

amount used in more advanced adaptive beamforming methods [97]. SLSC would

likely be easily realized on software-biased beamformers.

5.6 Conclusion

We have developed an imaging technique based on the spatial coherence of ultra-

sound signals, with potential applications to clutter reduction. The spatial coherence

between closely-spaced elements may be used to create images having the potential

88

to compete with conventional B-mode images. SLSC images demonstrate inferior

point target conspicuity compared to B-mode imaging, but show superior SNR and

CNR as demonstrated in simulation, tissue-mimicking phantom, and in vivo hu-

man thyroid experiments. In expanded targets, a recorrelation effect is observed

in theoretical and simulated results without noise. However, when noise is present,

this recorrelation effect is mitigated, as demonstrated in experimental results and

simulations with added noise.

SLSC images demonstrate a trade-off among contrast, CNR, and SNR with in-

creasing short-lag values. SLSC imaging shows improved resolution with increas-

ing lag and demonstrates better resolution than B-mode imaging for comparatively

same-sized transmit apertures. The in vivo application of SLSC imaging to human

thyroid tissue shows images that are substantially better than conventional speckle-

reduction techniques, in addition to having better contrast, CNR, and SNR than

B-mode images.


This work was supported by NIH Grants R01-CA114093-04S1 from the National

Cancer Institute, R21-EB008481 and T32-EB001040 from the National Institute of

Biomedical Imaging and Bioengineering, and the Duke Endowment Fellowship. Spe-

cial thanks to Siemens Medical Solutions, Inc. USA, Ultrasound Division for in-kind

and technical support.

89

6

Resolution Characteristics of SLSC Imaging

6.1 Introduction

Short-lag spatial coherence (SLSC) imaging is a novel approach to ultrasound im-

age formation that utilizes local measurements of the spatial coherence of backscat-

tered echoes [35]. Its utility as a clutter reduction technique has been demonstrated

in several ultrasound applications, including cardiac, liver, vascular, and thyroid

imaging [35, 98]. The technique is based on the van Cittert Zernike (VCZ) theorem

[36] applied to pulse-echo ultrasound [37], which states that the spatial coherence of

a wavefront is equal to: ∣∣F {[H(x) · χ(x)]2}∣∣ , (6.1)

where F denotes the Fourier transform, H(x) is the lateral transmit beam pressure,

and χ(x) is the lateral reflectivity profile of the target being imaged. Spatial coher-

ence is measured experimentally as the spatial correlation of backscattered echoes

received by individual transducer elements (after focusing delays have been applied),

as a function of transducer element spacing, or lag. To create one pixel in a SLSC

image, the sum of spatial correlation values in the short-lag region of a coherence

90

function is calculated. Matched B-mode images may be constructed with the same

individual channel data used to create SLSC images by applying a conventional

delay-and-sum beamformer. These principles are described in more detail in Section

6.2.

Knowledge of resolution limits is essential to the development of SLSC imaging.

It is particularly important with regard to clinical tasks that potentially favor SLSC

imaging due to its clutter reduction capabilities. Such clinical tasks include measur-

ing the intima-media thickness in carotid images, estimating left ventricular volume

in cardiac images, and identifying cancerous microcalcifications in breast images. To

frame the resolution limits for clinical tasks like these, this chapter quantifies the

resolution characteristics of SLSC images under various imaging conditions. Com-

parative results in B-mode images are also presented.

Resolution is commonly quantified by measuring the mainlobe width of a point

target at various levels of magnitude, such as the full width at half maximum

(FWHM) [99]. Another closely-related resolution metric is defined as the ability

to resolve two closely-spaced point targets. Alternatively, Wagner et al. [49] have

shown that the autocorrelation of texture (i.e. speckle) in the focal zone of B-mode

images is equivalent to the convolution of the imaging system’s point spread func-

tion (PSF) with itself. The FWHM of this autocorrelation function was shown to be

approximately equal to λz/D, where λ is the ultrasonic wavelength, z is the axial

focus, and D is the transducer aperture width. Thus, B-mode image resolution at the

focus can be determined from the autocorrelation of speckle. Another approach to

measuring B-mode resolution is to characterize the input-output frequency response

of sinusoidally-varying targets and create a transfer function.

Quantification of SLSC resolution is challenging for several reasons. First, lateral

resolution in SLSC images depends on the profile of the target being imaged, as

indicated by the VCZ theorem applied to ultrasound. Thus, there are different

91

resolution characteristics for a point target surrounded by speckle, a point target

surrounded by noise, and the boundary of a lesion. Resolution does not have this

type of target-dependency in B-mode images. The second challenge is that differences

in spatial coherence are required to achieve contrast in SLSC images, unlike B-mode

images where contrast is based on differences in signal amplitudes. Finally, the

challenges with transfer function analyses are considered.

Consider using a transmit beam pressure, H(x), that is modeled as a sinc function

to image a target, χ(x), that can be modeled as a pure cosine wave with only one

spatial frequency, uo. To achieve a spatial coherence function for these geometries,

the VCZ theorem predicts that the spatial covariance, C, as a function of spatial

frequency, u, is as follows:

C(u) = F{[H(x) · χ(x)]2

}= F

{[H(x)]2

}∗ F

{[χ(x)]2

}= F

[D

λzsinc2

(D

λzx

)]∗ F [cos2(2πuox)]

= Λ

(λz

Du

)∗ 1

2F [1 + cos(4πuox)]

= Λ

(λz

Du

)∗ 1

2

[δ(u) +

1

2δ(u + 2u0) +

1

2δ(u− 2u0)

]

=1

2Λ

(λz

Du

)+

1

4Λ

(λz

D(u + 2u0)

)+

1

4Λ

(λz

D(u− 2u0)

)(6.2)

where Λ denotes the triangle function and ∗ denotes the convolution operation. Eq.

6.2 represents a coherence function when the mainlobe of the transmit beam is aligned

with a peak in the cosine wave.

As the transmit beam is laterally translated by a value, x0, to create the coherence

92

function for another lateral location, the shift property of Fourier transforms dictates:

C(u) = F[

D

λzsinc2

(D

λz(x− x0)

)]∗ F [cos2(2πuox)]

= e−2πix0uΛ

(λz

Du

)∗ 1

2

[δ(u) +

1

2δ(u + 2u0) +

1

2δ(u− 2u0)

]. (6.3)

Note that shifting the target relative to the transmit beam yields the same spatial

coherence functions as shifting the transmit beam relative to the target. Thus, to

simplify this analysis, the target is shifted instead of the transmit beam, as follows:

C(u) = F[

D

λzsinc2

(D

λzx

)]∗ F [cos2(2πuo(x− x0)]

= F[

D

λzsinc2

(D

λzx

)]∗ 1

2F [1 + cos(2πuo(x− x0)]

= Λ

(λz

Du

)∗ 1

2

[δ(u) +

[1

2δ(u + 2u0) +

1

2δ(u− 2u0)

]e−2πix0u

]

= Λ

(λz

Du

)∗[1

2δ(u) +

1

4δ(u + 2u0) · e−2πix0u +

1

4δ(u− 2u0) · e−2πix0u

]

=1

2Λ

(λz

Du

)+

[1

4Λ

(λz

D(u + 2u0)

)+

1

4Λ

(λz

D(u− 2u0)

)]e−2πix0u

=1

2Λ

(λz

Du

)+

1

4e−2πix0u

[Λ

(λz

D(u + 2u0)

)+ Λ

(λz

D(u− 2u0)

)]

=1

2Λ

(λz

Du

)+

1

4[cos(2πx0u) + i sin(2πx0u)] ·

[Λ

(λz

D(u + 2u0)

)+ Λ

(λz

D(u− 2u0)

)](6.4)

The magnitude of Eq. 6.4 is given by the square root of the square of the real

93

component plus the square of the imaginary component:

|C(u)| =

√Re (C)2 + Im (C)2

=

√1

4Λ2

(λz

Du

)+

1

16

[cos2(2πx0u) + sin2(2πx0u)

]·[Λ

(λz

D(u + 2u0)

)+ Λ

(λz

D(u− 2u0)

)]2

+

1

4cos(2πx0u) · Λ

(λz

Du

)·[Λ

(λz

D(u + 2u0)

)+ Λ

(λz

D(u− 2u0)

)].

=

√1

4Λ2

(λz

Du

)+

1

16

[Λ

(λz

D(u + 2u0)

)+ Λ

(λz

D(u− 2u0)

)]2

+

1

4cos(2πx0u) · Λ

(λz

Du

)·[Λ

(λz

D(u + 2u0)

)+ Λ

(λz

D(u− 2u0)

)]. (6.5)

Eq. 6.5 demonstrates that as the transmit beam is laterally translated by x0 to form

a SLSC image, a target with only one spatial frequency (u0) results in coherence

functions that are the sum of multiple triangle functions with varied slopes and

varied spatial frequencies. A subset of the individual triangle functions are weighted

by a cosine term that varies as a function of x0.

Mathematica software (Wolfram Research, Champaign, IL) was used to plot Eq.

6.5 as a function of u and x0. The lag between echo correlations, m, is related to

spatial frequency, u, through the expression: u = mλ/z. Fig. 6.1 shows the theoret-

ical spatial coherence as a function of m and x0. Notice the different combinations

of triangle functions with varied heights and slopes as x0 is varied.

The integral of Fig. 6.1 in the “Lag” dimension, evaluated from 0 to a short-

lag value, M , for each value of x0, yields the lateral profile of one slice in a SLSC

image. Mathematica was used to integrate Eq. 6.5 as described and create one

lateral slice through an SLSC image. This slice is compared with the original cosine

94

-N0

NLag

-2 Π

-Π0

Π2 Πx0

0.0

0.5

1.0

1.5

Figure 6.1: Theoretical coherence functions for a sinusoidally-varying target withone unique frequency. As the transmit beam is laterally translated by x0 to form aSLSC image, the coherence functions at each value of x0 is a sum of multiple trianglefunctions. N is the number of transducer elements in the transmit aperture. Lagrefers to the spacing between transducer elements.

target in Fig. 6.2 (a). Notice that the SLSC image has its lowest values at the

zero-crossings of the target. The frequency spectrums of these two lateral profiles

were obtained by applying a Fourier transform to the individual profiles. Fig. 6.2 (b)

demonstrates that the frequency spectrum of the target profile contains the expected

single frequencies at ± 12π

. The frequency spectrum of the SLSC profile contains

dominant peaks at 0 and ± 1π, with less influential peaks at integer multiples of 1

π.

The ratio between the peaks at ± 1π

and ± 2π

is 18.6dB. The ordinate scale of the

frequency spectrum was adjusted and displayed in Fig. 6.2 (c) to show more of

the less influential peaks. The apparent non-linearity between input and output

frequencies complicates transfer function analyses.

To overcome these challenges and obtain resolution measurements for SLSC im-

ages, the width of point targets in the presence of incoherent noise are considered.

The rationale for including incoherent noise is explained in Section 6.3.2. In addi-

tion to point target measurements, the texture size of SLSC images is considered

95

2 Π 6 Π 10 Π

x0

-1

1

2

3

4

5

6

Target and SLSC Image Lateral Profiles

(a)

-5 - ��1

Π��1

Π

5@HzD

Frequency Spectrum

(b)0-5 - ��

4

Π- ��

8

Π- ��

12

Π��12

Π��8

Π��4

Π5

@HzD

Scale-Adjusted Frequency Spectrum

(c)

Figure 6.2: (a) Lateral slices through a theoretical sinusoidally varying target(bottom) and a theoretical SLSC image (top), which was calculated by integratingEq. 6.5. (b) The corresponding frequency spectrums of these lateral profiles. (c)The same frequency spectrums with the ordinate scales adjusted to show the lessinfluential frequencies in the SLSC profile.

and compared with speckle size in matched B-mode images.

6.2 Short-lag Spatial Coherence Imaging

SLSC imaging is described in detail in Ref. [35]. To summarize briefly, time-

delayed echoes received by individual transducer elements are cross-correlated and

displayed as a function of element separation, m. Due to signal non-idealities like

aberration, thermal noise, or clutter, experimental coherence functions do not always

appear as predicted. In addition, the geometry of the image target (i.e. differences

in χ(x)), contributes to differences in spatial coherence functions. In both cases,

the largest differences in spatial coherence occur in regions of low lags (i.e. where

96

there is a small separation between elements). The short-lag spatial coherence is

defined as the integral of the spatial coherence function over the first M lags, where

M is typically a value that corresponds with 1-30% of the transmit aperture. The

relationship between M and resolution is evaluated in more detail in Section 6.4.2.

The short-lag spatial coherence is measured from experimental data using the

following equations:

R(m) =1

N −m

N−m∑i=1

∑n2


n=n1s2

i (n)∑n2

n=n1s2

i+m(n), (6.6)

Rsl =M∑

m=1

R(m). (6.7)

where R(m) is the normalized spatial coherence across the receive aperture [40], N

is the number of receive elements, si(n) is the time-delayed signal received by the

ith element at depth, or time, n, expressed in number of samples, and Rsl is the

short-lag spatial coherence.

One pixel in a SLSC image is formed by computing Eqs. 7.1 and 7.2 at one depth,

n, of the channel signals, using a correlation kernel size of k = n2−n1, centered about

n. This process is repeated for a range of axial and lateral positions to create a SLSC

image. Matched B-mode images are constructed by applying a conventional delay-

and-sum beamformer to the same channel signals used to make SLSC images. The

size of the correlation kernel impacts the quality of the correlation calculation as well

as the axial resolution of SLSC images. Unless otherwise stated, SLSC images were

created with k approximately equal to one wavelength. The relationship between

correlation kernel size and resolution is evaluated in more detail in Section 6.4.2.

97

Table 6.1: Simulated Transducer Parameters

Parameter Value

Number of Elements 96Element Height 7.5mmElement Width 0.176mmKerf 0.025mmCenter Frequency 5.71MHzSampling Frequency 160MHzFractional Bandwidth 60%

6.3 Methods


Field II was used to simulate the received, individual-channel, RF echo signals

from point targets and from diffuse scatterers. The simulated transducer was a 96-

element linear array with a 5.71MHz center frequency and 60% fractional bandwidth.

The array had a lens focused at 3.75 cm in elevation, and the lateral focus was

positioned at the same depth. Dynamic-receive beamformer delays were applied to

the channel signals. No apodization was applied to the transmit aperture. Unless

otherwise stated, an F/2 transmit aperture was employed, which corresponds to 93

transmit elements for the 37.5-cm focus. The parameters of the simulated transducer

are listed in Table 6.1. B-mode and SLSC image processing and the following data

analyses were performed with Matlab (The Mathworks Inc., Natick, MA) software.

6.3.2 Point Target Measurements

One challenge with using conventional point target width measurements to esti-

mate SLSC resolution is the larger appearance of a point target in a simulated SLSC

image, compared to a matched B-mode image created from the same channel data,

as demonstrated in Fig. 6.3 (a) and (b). This significant loss in resolution is not

observed in experimental phantom or clinical SLSC images, but occurs in simulations

because of low-magnitude, spatially-coherent echoes from the region surrounding the

98

point target. The amplitudes of these echoes are a few orders of magnitude below

backscattered and off-axis echoes and reside below the noise floor typically measured

in experimentally-obtained ultrasound data. Thus, coherence estimates from these

low-amplitude echoes are unlikely to be present in experimental measurements. Uni-

form white noise was bandpass filtered with cutoff frequencies equal to the -6 dB

bandlimits of the transducer to simulate acoustic noise received by the transducer.

This noise was added to the channel signals to mitigate coherence from the low-

amplitude echoes. In Fig. 6.3 (c), noise was added such that the SNR of the channel

signals was 10 dB, which corresponds with the channel SNR measured in vivo [89].

To evaluate the relationship between channel noise and resolution, axial and lateral

point target widths were measured as the channel SNR was varied from 40 dB to -20

dB (i.e. the channel noise-to-signal ratio, or NSR, was varied from -40 dB to 20 dB).

The lateral beamplots created from the point targets in Fig. 6.3 (a)-(c) are shown

in Fig. 6.3 (d), where axial and lateral resolution were measured at the -6dB, -10dB,

and -20dB beamwidths. In some cases, the amplitude of the noise floor was greater

than -6, -10, and/or -20dB and therefore, the width of the point target at these levels

could not be measured. Resolution measurements were excluded if they included the

side lobes of the point target, as is the case with the B-mode beamplot at -20dB in

Fig. 6.3 (d). Unless otherwise stated, this approach was used to measure axial and

lateral resolution in SLSC images.

Noise from off-axis scatterers, a common source of clutter in ultrasound images,

was simulated by placing one 2mm (axial) x 2mm (lateral) x 1mm (elevation) block of

diffuse scatterers on each side of the point target. The blocks were separated by 4mm

in the lateral dimension. Their presence created scattering within the isochronous

volume of the transmit beam. Clutter in the B-mode image was measured within

a square region centered around the point target, with inner dimensions 0.6 mm x

0.6 mm (axial x lateral) and outer dimensions 1 mm x 1mm (axial x lateral). This

99

Lateral (mm)

Axi

al (

mm

)

−3 −2 −1 0 1 2 3

3737.5

38

(a)

Lateral (mm)

Axi

al (

mm

)

−4 −2 0 2 4

3737.5

38

(b)

Lateral (mm)

Axi

al (

mm

)

−4 −2 0 2 4

3737.5

38

(c)

−4 −2 0 2 4−30

−25

−20

−15

−10

−5

0

Lateral (mm)

Mag

nitu

de (

dB)

B−modeSLSCSLSC with noise

(d)

Figure 6.3: (a) B-mode image of a point target with no noise added to the channeldata. (b,c) SLSC (M = 20) images of a point target in the absence and presence of-10 dB channel noise, respectively. (d) Lateral point spread functions derived fromthe point target images.

clutter was measured relative to the average signal in a 0.2mm x 0.2mm (axial x

lateral) square region centered on the point target. The amplitude of the blocks was

varied such that the measured clutter surrounding the point target in the B-mode

image ranged from -83 to -21 dB, relative to the point target. Axial and lateral point

target widths in B-mode and SLSC images created from the same channel data were

calculated as a function of the measured clutter magnitudes in the B-mode images.

Measurements were repeated for six independent speckle realizations. No noise was

100

added to simulated data for this experiment.

Resolution was investigated as a function of the short-lag value, M , and corre-

lation kernel length, k, in SLSC images. Point target images were created with M

ranging from 4 to 94, and the resolution at the focus was measured for each value of

M . These measurements were compared to B-mode images of point targets created

with receive apertures that contained 4 to 94 elements. Resolution at the focus of

the B-mode images was measured for each receive aperture size. Similarly, the cor-

relation kernel length used to create the SLSC point target image was varied from

12λ to 6λ, and point target width was measured for each correlation kernel length.

To make these measurements, noise was added such that the channel NSR was -10

dB.

To evaluate depth-of-field effects in SLSC images, a phantom containing 9 point

targets spaced by 2.5 mm axially was imaged with F/2 and F/3 transmit beams.

Noise was added to the simulated data for SLSC images, resulting in an average

channel NSR of -10dB. SLSC images with added channel noise were compared to

matched B-mode images without added channel noise to measure axial and lateral

resolution as a function of depth.

6.3.3 Autocorrelation Measurements

Simulated SLSC and B-mode images of diffuse scatterers were utilized to measure

the autocorrelation of image texture at the focal depth. The simulated phantom

measured 25mm axially by 10mm laterally by 10mm in elevation and contained 40

scatterers per resolution volume. To calculate lateral texture size, a 1.7 mm x 4.1 mm

(axial x lateral) kernel in the focal zone was correlated with a 8.0 mm lateral search

region from the same image, centered about the kernel. To calculate axial texture

size, a 1.7 mm x 8 mm (axial x lateral) kernel in the focal zone was correlated with a

2.4 mm axial search region from the same image, centered about the kernel. The -6

101

dB widths of the resulting autocorrelation functions were recorded as a function of

M and as a function of the number of receive elements used to make B-mode images.

This measurement was repeated for six independent speckle realizations.

6.3.4 Brightness and RMS Amplitude Measurements

Simulated B-mode and SLSC images of the diffuse scatterer phantom described

in Section 6.3.3 were utilized to measure the signal mean (i.e. signal brightness) as

a function of depth. In addition, the RMS amplitude of the channel signals that

created these data was measured as a function of depth.

6.3.5 Experimental Demonstration

A VerasonicsTM ultrasound scanner (Redmond, WA) and ATL P4-2 probe was

used to acquire experimental data from individual channel elements. The probe

contained 64 elements, the transmit frequency was 2.5 MHz, and the focus was 4

cm. This configuration was used to image a CIRS ultrasound phantom (Model 54,

Norfolk, VA) containing point targets and hypoechoic lesions embedded in a speckle-

generating background. Matched B-mode and SLSC images with and without added

noise were created from these data to demonstrate some of the characteristic trends

of resolution in SLSC images.

6.4 Results

6.4.1 Resolution in the Presence of Channel Noise and Clutter

Axial and lateral point target widths measured in the presence of various noise

levels are displayed in Fig. 6.4 (a) and (b), respectively, for matched B-mode and

SLSC images. The plots indicate that the resolution of SLSC images improves with

increasing noise, while the resolution of B-mode images is relatively constant at

the lower noise values. Axial B-mode resolution is degraded as the channel NSR

102

−40 −20 −12 −6 0 6 120.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Channel NSR (dB)

Axi

al R

esol

utio

n (m

m)

−6 dB SLSC−6 dB B−mode−10 dB SLSC−10 dB B−mode−20 dB SLSC−20 dB B−mode

(a)

−40 −20 −12 −6 0 6 120

0.5

1

1.5

2

2.5

Channel NSR (dB)

Late

ral R

esol

utio

n (m

m)


(b)

Lateral (mm)

Axi

al (

mm

)

−2 −1 0 1 2

37

37.5

38

(c)Lateral (mm)

Axi

al (

mm

)

−2 −1 0 1 2

37

37.5

38

(d)

Figure 6.4: (a) Axial and (b) lateral resolution as a function channel noise-to-signalratios (NSR), measured at the -6, -10, and -20 dB PSF widths. Matched (c) B-modeand (d) SLSC images with 6 dB channel NSR.

approaches -12 dB, while lateral B-mode resolution has a higher threshold at -6dB

NSR.

The loss in B-mode resolution at higher noise levels is illustrated in Fig. 6.4 (c)

for +6dB channel NSR. The noise floor of Fig. 6.4 (c) is too large to measure the

FWHM of the PSF in the axial dimension, hence there are no measurements for +6

dB noise in Fig. 6.4 (a). However, as demonstrated in the matched SLSC image in

Fig. 6.4 (d), SLSC resolution continues to improve at these higher noise levels. For

noise values greater than +12 dB, the point target was no longer visualized in the

SLSC image and thus, resolution could not be measured beyond this value.

Fig. 6.5 displays B-mode and SLSC images of a point target in the center of two

diffuse-scattering regions separated by 4mm. In the B-mode image (Fig. 6.5 (a)), the

measured clutter surrounding the point target is -37 dB relative to the point target.

The amplitude of the diffuse scatterer region was varied to vary the resulting clutter

103

magnitude surrounding the point target. Axial and lateral resolutions as a function

of the clutter magnitude measured in B-mode images are shown in Fig. 6.5(c) and

(d), respectively. These plots indicate that the resolution of SLSC images improves

as clutter magnitude increases. In B-mode images, resolution is relatively constant

for most clutter magnitudes and starts to degrade for clutter magnitudes of -29 dB

and greater.

6.4.2 Resolution and Texture Size vs. SLSC Imaging Parameters

Axial and lateral point target width as a function of the correlation kernel length

used to create SLSC images is shown in Fig. 6.6. The axial resolution worsens as

the kernel length increases, while the lateral resolution is relatively constant.

Lateral point target width as a function of the short-lag value (M) used to create

SLSC images and as a function of the number of receive elements (N) used to create

Lateral (mm)

Axi

al (

mm

)

−3 −2 −1 0 1 2 3

36.5

37

37.5

38

38.5

(a)Lateral (mm)

Axi

al (

mm

)

−3 −2 −1 0 1 2 3

36.5

37

37.5

38

38.5

(b)

−90 −80 −70 −60 −50 −40 −30 −200

0.2

0.4

0.6

0.8

1

Clutter Magnitude (dB)

Axi

al R

esol

utio

n (m

m)

6 dB SLSC6 dB B−mode10 dB SLSC10 dB B−mode

(c)

−90 −80 −70 −60 −50 −40 −30 −200

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Clutter Magnitude (dB)

Late

ral R

esol

utio

n (m

m)

6 dB SLSC6 dB B−mode10 dB SLSC10 dB B−mode

(d)

Figure 6.5: (a) B-mode and (b) SLSC images of a point target in the presence ofoff-axis scatterers with -27dB clutter magnitude relative to the point target in the B-mode image. (c) Axial and (d) lateral resolution as a function of clutter magnitude,measured at the -6 and -10 dB PSF beam widths.

104

1/2 1 2 3 4 5 60.2

0.4

0.6

0.8

1

1.2

Correlation Kernel Length (λ)

SLS

C R

esol

utio

n (m

m)

−6 dB Axial−6 dB Lateral−10 dB Axial−10 dB Lateral−20 dB Axial−20 dB Lateral

Figure 6.6: Axial and lateral resolution as a function of the correlation kernellength used to create SLSC images, measured at the -6, -10, and -20 dB PSF beamwidths, in the presence of -10dB noise.

B-mode images is shown in Fig. 6.7 (a). This plot indicates that lateral resolution

improves as M or N increases. Lateral point target width at the short lags (M ≤ 30)

of SLSC images is 0.3-0.5 mm worse than lateral resolution in B-mode images created

with the full receive aperture.

The same measurements were employed in the axial dimension, as shown in Fig.

6.7 (b). The results indicate that the choice of N has no effect on axial resolution in

B-mode images, while the -10dB axial resolution measurements increase with M in

SLSC images. Axial point target width is approximately 0.15 mm smaller in B-mode

images compared to SLSC images.

The autocorrelation of image texture measured in the lateral dimension as a

function of M and N is shown in Fig. 6.7 (c). This plot demonstrates smaller SLSC

texture size with increasing M , for values of M ≥ 16, and smaller B-mode speckle

size (i.e. improved resolution) with increasing N , for values of N ≥ 40. The mean

lateral texture size of SLSC images is at least 0.05 mm smaller than that of B-mode

images created with the full receive aperture.

Axial texture size has insignificant changes as a function of N in B-mode images,

as shown in Fig. 6.7 (d). In SLSC images, the axial texture size increases with M .

105

0 20 40 60 80 100

0.4

0.5

0.6

0.7

0.8

0.9

1

M or N

Late

ral R

esol

utio

n (m

m)

−6 dB SLSC−6 dB B−mode−10 dB SLSC−10 dB B−mode

(a)

0 20 40 60 80 1000.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

M or N

Axi

al R

esol

utio

n (m

m)

−6 dB SLSC−6 dB B−mode−10 dB SLSC−10 dB B−mode

(b)

0 20 40 60 80 1000.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

M or N

Late

ral T

extu

re S

ize

(mm

)

B−modeSLSC

(c)

0 20 40 60 80 1000.2

0.22

0.24

0.26

0.28

0.3

0.32

M or N

Axi

al T

extu

re S

ize

(mm

)

B−modeSLSC

(d)

Figure 6.7: (a) Lateral and (b) axial resolution as a function of M for SLSC imagesand N for B-mode images, measured at the -6 and -10 dB PSF beam widths. (c)Lateral and (d) axial texture size as a function of M and N, measured from the -6dBwidth of the autocorrelation function. M is the short-lag value used to make SLSCimages. N is the number of receive elements used to make B-mode images.

A similar trend is observed for the -10 dB axial point target width measurements in

Fig. 6.7 (b).

6.4.3 Depth of Field Effects

Matched B-mode and SLSC images of point targets at various depths, acquired

with an F/2 transmit are shown in Fig. 6.8 (a) and (b), respectively. The same

targets acquired with an F/3 transmit are shown in Fig. 6.8 (c) and (d), respectively.

Noise was added to the channel data prior to creating the SLSC images. No noise

was added to the B-mode images.

106

Lateral (mm)

Axi

al (

mm

)

B−mode, F/2

−4 −2 0 2 4

30

35

40

45

(a)Lateral (mm)

Axi

al (

mm

)

SLSC, F/2

−4 −2 0 2 4

30

35

40

45

(b)Lateral (mm)

Axi

al (

mm

)

B−mode, F/3

−4 −2 0 2 4

30

35

40

45

(c)Lateral (mm)

Axi

al (

mm

)

SLSC, F/3

−4 −2 0 2 4

30

35

40

45

(d)

25 30 35 40 45 500

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Depth (mm)

F/2

Lat

eral

Res

olut

ion

(mm

)


(e)

25 30 35 40 45 500.5

1

1.5

2

Depth (mm)

F/3

Lat

eral

Res

olut

ion

(mm

)

(f)

25 30 35 40 45 500.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Depth (mm)

F/2

Axi

al R

esol

utio

n (m

m)

(g)

25 30 35 40 45 500.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Depth (mm)

F/3

Axi

al R

esol

utio

n (m

m)

(h)

Figure 6.8: (a,c) B-mode and (b,d) SLSC images of a point targets at variousdepths, created with F/2 (a,b) and F/3 (c,d) transmit beams. The SLSC imagescontain -10dB channel noise, and the B-mode images have no added noise. SLSCimages were formed with M=20. Lateral and axial resolution was measured at the-6, -10, and -20 dB PSF beam widths, as a function of depth for the F/2 (e andg, respectively) and F/3 (f and h, respecitvely) transmit beams. Error bars shownfor the -20 dB axial and lateral beamwidths represent one standard deviation fromthe mean. Error bars for other axial and lateral beamwidths are similar and wereomitted for ease of plot readability.

107

25 30 35 40 45 500.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Depth (mm)

RM

S o

f Nor

mal

ized

Cha

nnel

Dat

a

F/2F/3

Figure 6.9: The average root-mean-square (RMS) amplitude of individual channelsignals from six independent realizations of diffuse scatterers, created with F/2 andF/3 transmit beams.

Lateral point target width as a function of depth is shown for the F/2 and F/3

transmit beams in Fig. 6.8 (e) and (f), respectively. The lateral resolution of the

SLSC images is best at the focus and is degraded away from the focus, particularly

evident with the F/2 transmit. The lateral resolution of B-mode images degrades as

depth increases, most noticeable for the F/3 transmit. Lateral resolution in B-mode

images is better than that of SLSC images outside of the depth of field.

Axial point target width as a function of depth is shown for the F/2 and F/3

transmit beams in Fig. 6.8 (g) and (h), respectively. The axial resolution of B-mode

images shows little variation with depth, while that of SLSC images seems to improve

with depth, as observed in Fig. 6.8 (a)-(d).

To demonstrate the depth-dependency of channel SNR, the average root-mean-

square (RMS) amplitude of normalized individual channel signals from six indepen-

dent realizations of diffuse scatterers is shown in Fig. 6.9, as a function of depth

for F/2 and F/3 transmit beams. No noise was added prior to obtaining these

measurements. Note that the RMS amplitude decreases as depth increases. The

decrease with respect to depth indicates that the channel SNR is depth dependent

given constant noise and/or clutter.

108

25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

1.2

1.4

Depth (mm)

Mea

n B

right

ness

Nor

mal

ized

5 lags10 lags 20 lagsB−mode

(a)

25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

1.2

1.4

Depth (mm)

Mea

n B

right

ness

Nor

mal

ized

5 lags10 lags 20 lagsB−mode

(b)

Figure 6.10: Brightness as a function of depth for B-mode and SLSC images createdwith (a) F/2 and (b) F/3 transmit beams.

Mean brightness as a function of depth was measured in B-mode and SLSC images

of diffuse scatterers created with F/2 and F/3 transmit beams, as shown in Fig. 6.10

(a) and (b), respectively. B-mode images have maximum brightness at the focus, and

as distance from the focus increases, B-mode and SLSC image brightness decreases.

The brightness decreases by similar amounts at equal distances from the focus in

B-mode images. In SLSC images, however, notice the unequal brightness values at

equal distances from the focus. Note also that as distance from the focus increases,

the brightness in SLSC images decreases as M increases. In addition, B-mode and

SLSC images created with the F/3 transmit beam are brighter at greater distances

from the focus, when compared with images created from the F/2 transmit beam.

6.4.4 Experimental Images

An experimental B-mode image of a phantom containing point targets and hy-

poechoic lesions is shown in Fig. 6.11 (a). The -6dB axial and lateral widths of the

point target at the focus (4 cm) are 0.21 mm and 0.20 mm, respectively. An SLSC

image created with the same channel data is displayed in Fig. 6.11 (c). It demon-

strates the difficulty associated with using SLSC images to image point targets in

the presence of diffuse scatterers. Without added noise, the coherence of the speckle

109

Axi

al (

cm)

Lateral (cm)−4 −2 0 2 4

0

1

2

3

4

5

(a)

Axi

al (

cm)

Lateral (cm)−4 −2 0 2 4

0

1

2

3

4

5

(b)

Axi

al (

cm)

Lateral (cm)−4 −2 0 2 4

0

1

2

3

4

5

(c)

Axi

al (

cm)

Lateral (cm)−4 −2 0 2 4

0

1

2

3

4

5

(d)

Figure 6.11: (a) B-mode and (c) SLSC images of an experimental phantom in theabsence of added channel noise. (b) B-mode and (d) SLSC images with 6dB addedchannel noise.

background and the point target are similar, and there is no differentiation between

the two target types at the FWHM of the point target. Thus, resolution could not

be measured using this metric.

When noise was added to the experimentally-obtained channel data, point target

visibility was enhanced in the SLSC image (Fig. 6.11 (d)) and unaffected in the

B-mode image (Fig. 6.11 (b)). Note that in addition to better visualization of

the point target at the focus, the point targets at 3-cm depth are also more easily

visualized in the SLSC image with added noise. The -6dB axial and lateral widths

of the point target at the focus of the SLSC image with noise are 0.12mm and 0.16

mm, respectively. Thus, there is a 0.9 mm improvement in lateral resolution and a

110

0.04 mm improvement in axial resolution in the SLSC image with noise, compared

to the B-mode image without noise.

6.5 Discussion

6.5.1 SLSC Resolution in the Presence of Noise and Clutter

The measured resolution of B-mode images was consistent with conventional res-

olution metrics, such as point target width and speckle size. To obtain comparative

values for SLSC imaging, it was necessary to add channel noise to simulated point

target data, as demonstrated in Fig. 6.4. SLSC point target width decreased as the

channel NSR increased.

The addition of channel noise to SLSC point target data is supported by the

results in Fig. 6.5. The clutter generated by two off-axis blocks of diffuse scatterers

caused a decrease in SLSC point target size, and the SLSC point target size decreased

with increasing clutter magnitudes. Previous measurements of clutter magnitudes

indicate that clutter can range from -35 to 0 dB relative to surrounding tissue [58].

For this range of clutter magnitudes, Fig. 6.5 indicates poor B-mode resolution and

good SLSC resolution. At the -21 dB clutter magnitude in Fig. 6.5 (b) and (c),

the point target was barely visualized, which gives the false impression of improved

resolution at this location. Results are not shown for clutter magnitudes greater

than -21dB because the point target was not visualized.

While adding noise and introducing off-axis scatterers to simulate clutter both

have the same effect on resolution, the addition of channel noise simulates a larger

variety of clutter sources (e.g. reverberation, thermal noise, and clutter due to off-axis

scattering). Thus, the addition of noise is the preferred clutter simulation method

to obtain SLSC resolution measurements.

The addition of at most -6dB channel noise improves the resolution of SLSC

images, without significant changes to the B-mode image resolution. Noise levels

111

greater than -6dB cause diminished resolution in B-mode images, yet improved res-

olution in SLSC images. Generally, improved resolution is observed in the SLSC

images with increasing channel NSR, until noise levels are too large for the point

target to be distinguished.

In the experimental demonstration of Fig. 6.11, SLSC point target conspicuity

and resolution improved with the addition of noise. This has greatest implications

for the visualization of microcalcifications and similar point-like structures in breast

imaging and other ultrasound applications. The simulation and experimental results

demonstrate that point-like structures are more easily visualized in SLSC images in

the presence of clutter or acoustic noise.

6.5.2 Resolution Characteristics with Varied Receive Aperture Sizes and SLSC Im-age Parameters

B-mode and SLSC images have similar lateral resolution characteristics when the

number of receive transducer elements is considered, as demonstrated in Fig. 6.7

(a). Lateral resolution improves with increased number of elements in the receive

aperture used to form B-mode images (N) and with increased number of receive

element lags integrated to form SLSC images (M). Although M and N are not

direct comparisons, the results indicate that the inclusion of more elements improves

lateral resolution in B-mode and SLSC images.

Improved lateral resolution with increasing M should be considered in tandem

with other performance metrics for SLSC imaging, such as contrast, contrast-to-

noise, and signal-to-noise ratios when selecting the optimal value for M . There is a

trade-off among these performance metrics. For example, using the highest M value

possible to achieve the best lateral resolution, will likely yield an SLSC image with

the lowest signal-to-noise ratio [35].

Axial resolution is constant as a function of N in B-mode images, as demonstrated

112

in Fig. 6.7 (b). In the SLSC images, axial resolution is constant as a function of M

at the -6dB level of the PSF, while the point target width at the -10 dB level slightly

increases as a function of M . The reason for this increase is not fully understood, but

one hypothesis is that the fewer correlations at larger values of M cause increased

variance in the coherence estimates. Another hypothesis is that the increased phase

difference between signals separated by larger lags causes the increased variance

at higher values of M . Either way, this increased variance results in larger mean

correlation estimates at higher values of M . This increase is not observed near the

center of the point target where the -6dB level of the PSF is located because the

spatial coherence function is closer to unity for all values of M in this location, and

it is not possible for the correlation estimate to be increased above unity.

The axial resolution in B-mode images is equal to 12

the transmit pulse length.

This is the expected resolution limit for SLSC images. For simulated data, the pulse

length is 0.51mm, resulting in an axial resolution limit of 0.26mm, which is consistent

with measurements in Fig. 6.7 (b). The axial resolution of SLSC is also dictated

by the correlation kernel length, as demonstrated in Fig. 6.6, where axial resolution

is degraded as the kernel length increases. To achieve the best axial resolution

in SLSC images, it is best to use the smallest kernel length above the resolution

limit of B-mode that accurately describes the correlation between RF echoes. This

accuracy corresponds with a minimum kernel length of approximately one ultrasound

wavelength (λ= 0.27mm in the simulated data).

6.5.3 Similarities Between Texture Size and Resolution

The trends for texture size as a function of M and N are similar to those for

point target width, as illustrated in Fig. 6.7 (c) and (d). In B-mode imaging, point

target width and texture size are both metrics of resolution, so the similarity between

these measurements is expected. At low values of N in B-mode images, the lateral

113

texture size is constant. This is likely due to the smaller receive beam relative to

the transmit beam, and hence, the width of the transmit beam dominates the lateral

texture size measurements in this region.

For SLSC imaging, the theoretical link between texture size and resolution has

not yet been proven, however in the focal zone, the texture size of diffuse scatterers

is remarkably similar in B-mode and SLSC images (i.e. compare the diffuse scatterer

regions in Fig. 6.11). In addition, texture size is often used to approximate the

resolution of an imaging system [100]. The autocorrelation measurements indicate

that the texture size in SLSC images created with low values of M is similar to that

in matched B-mode images created with the full receive aperture.

Note that the increased axial texture size as a function of M in SLSC images

is likely due to the broadened axial PSF as a function of M , as demonstrated in

Fig. 6.7 (b) at the -10 dB level. This broadening of the PSF causes closely-spaced

scatterers to appear as if they are fused together in the axial dimension. Nonetheless,

in the short lag region (M ≤ 30), the axial texture size of B-mode and SLSC images

are similar.

6.5.4 Depth-Dependent Resolution Effects

Depth-of-field trends in B-mode and SLSC images are similar, particularly for

lateral point target measurements with an F/2 transmit (Fig. 6.8 (c)). In both

image types, the best lateral resolution is observed near the focus (i.e. within the

depth-of-field). Outside of the depth of field, the lateral resolution of the B-mode

image outperforms that of the SLSC image.

For an F/3 transmit (Fig. 6.8 (f)), the -6, -10, and -20 dB lateral point target

widths in the B-mode image are smaller than the respective point target widths

within and outside of the depth of field in the SLSC image, indicating better resolu-

tion with B-mode imaging.

114

The B-mode lateral resolution measurements in Fig. 6.8 (e) and (f) increase

with depth because of the implementation of dynamic receive beamforming. With

dynamic receive beamforming, the receive beam is wider in the far-field, hence the

increased B-mode lateral resolution at larger depths. The SLSC lateral resolution is

not affected by dynamic receive beamforming because SLSC theory does not rely on

the shape of the receive beam, as suggested by Eq. 6.1.

The axial resolution of B-mode images was fairly constant as a function of depth,

while that of SLSC images improved with depth in Fig. 6.8 (g) and (h). This

improvement is attributed to increased channel NSR as a function of depth. The

addition of uniform channel noise does not account for depth-dependent changes in

the RMS amplitude of the channel signals (Fig. 6.9). While the added noise results

in an average NSR of -10 dB, the actual channel noise at the depth of each point

target is less than -10 dB for shallow targets and greater than -10 dB for deeper

targets. As shown in Fig. 6.4 (a), the axial resolution of SLSC images improves

as channel noise increases, and hence, improved axial resolution is observed for the

more distal point targets. This is not a concern in B-mode images because noise was

not added to them to make the point target width measurements.

Fig. 6.10 indicates that SLSC and B-mode images have similar brightness at the

focus, and hence, similar ability to detect scatterers in this region of images. The

different brightness values at equal distances from the focus in SLSC images is likely

due to different transmit beam shapes shallow and distal to the focus, as spatial

coherence is partially determined by the shape of the transmit beam. In addition,

compared to an F/2 transmit beam, an F/3 transmit beam is narrower over larger

depths. In the SLSC images, this narrower beam contributes to increased spatial

coherence, and hence increased brightness, at greater distances from the focus

The brightness of diffuse scatterers, point targets, and other structures are ex-

pected to follow these depth-dependent trends in experimental SLSC images. Most

115

of these trends are demonstrated in Fig. 6.11. These trends are particularly impor-

tant when considering resolution outside of the depth-of-field, as the brightness of

SLSC images, and hence the ability to measure resolution, varies with distance from

the focus.

6.6 Conclusion

Resolution characteristics of SLSC images were investigated and compared to

conventional ultrasound B-mode images. Resolution was obtained by measuring

point target widths in B-mode and SLSC images. The autocorrelation of image

texture (i.e. speckle in B-mode images) was also considered. Axial and lateral

resolution in SLSC images improved with increasing channel noise ranging from

−40 to 12 dB and increasing clutter magnitude ranging from -37 to -21 dB. Lateral

resolution increased with short-lag value and was best at the focus and within the

depth-of-field. Axial resolution was most degraded with increasing correlation kernel

length. Outside of the depth-of-field, B-mode images demonstrated significantly

better lateral resolution than SLSC images. Axial resolution was constant with

depth in B-mode images and decreased with depth in SLSC images, due to depth-

dependent changes in SNR. Finally, experimental data were used to demonstrate

that point-like structures in the midst of diffuse scatterers are more easily visualized

in SLSC images when noise is present.


This work was supported by the UNCF-Merck Graduate Science Research Disserta-

tion Fellowship, NIH Grants (R01-CA114093-04S, R21-EB008481, T32-EB001040),

and the Duke Endowment Fellowship.

116

7

SLSC Applied to In Vivo Cardiac Images

7.1 Introduction

Clutter is one of the most problematic noise artifacts in echocardiography, ob-

scuring visualization of endocardial borders, tumors, vegetations, and other cardiac

abnormalities [12, 14]. It presents a major challenge in strain imaging and automated

or manual border detection [11, 101, 102, 103]. Approximately 10-20% of patients

have suboptimal echocardiograms due to clutter [14, 15]. Sources of cardiac clutter

include reverberations and reflections from extracardiac off-axis structures such as

the ribcage and lungs, as well as from intracardiac structures such as the chordae

tendineae, valves, and myocardial walls.

Harmonic imaging is a common approach to clutter reduction in cardiac images.

In this technique, the higher harmonics generated by non-linear wave propagation

through tissue are imaged, rather than the first, or fundamental, harmonic of the

transmitted pulse. Factors that contribute to clutter reduction with harmonic imag-

ing include underdeveloped non-linear waves near the transducer surface, minimal

harmonic content in reverberant echoes, low amplitude harmonic signals from mul-

117

tiple scattering, and suppressed side and grating lobes [18, 29, 47, 104]. In several

studies, the application of harmonic imaging lowered the percentage of patients with

suboptimal images due to clutter from 45-51% to 11-24% [22, 23]. However, the

existence of this subset of patients with suboptimal harmonic images indicates that

the technique is not always sufficiently effective at reducing clutter.

Other clutter reduction approaches include transesophogeal echocardiography

(TEE) [29] and various filtering methods, such as stationary clutter rejection [8]

and principal component analysis [26, 105]. Despite these advances, filters have lim-

ited ability to remove high-velocity clutter, and TEE is not recommended for routine

clinical use. TEE poses a discomfort to patients and is only recommended in cases

where transthoracic images are diagnostically inconclusive or difficult to acquire [30].

An alternative to reducing clutter is to enhance endocardial borders via contrast

echocardiography [31]. However, this approach requires the injection of contrast

agents, presents an additional expense to patients, and necessitates a sterile environ-

ment for intravenous access [32, 33, 34].

Short-lag spatial coherence (SLSC) imaging [35], a novel approach that utilizes

the spatial coherence of backscattered ultrasound echoes, overcomes many of the

challenges with existing clutter-reduction and border-enhancement approaches. The

spatial coherence of echoes from myocardium exhibits different characteristics from

that of clutter and blood [77]. Since this difference is most noticeable over small

spatial differences, SLSC imaging is implemented by computing the spatial coherence

of echoes for short distances of element separation. This method is described in

more detail in Section 7.2.1. When compared to conventional B-mode images, SLSC

images demonstrate superior contrast, contrast-to-noise, and signal-to-noise ratios in

in vivo applications [35], particularly in the presence of acoustic noise (i.e. clutter)

[98].

118

7.2 Short-Lag Spatial Coherence Imaging

7.2.1 Image Formation

To measure spatial coherence experimentally, the time-delayed echoes received

by individual transducer elements are cross-correlated and plotted as a function of

element separation. Due to signal non-idealities like clutter, aberration and thermal

noise, experimental coherence functions do not always appear as predicted. The

largest differences in spatial coherence occur in regions of low lags (i.e. where there is

a small separation between elements). The short-lag spatial coherence is the integral

of the spatial coherence function over the first M lags, where M is a value that

typically corresponds to 1-30% of the transmit aperture.

This is described mathematically with the following equations:

R(m) =1

N −m

N−m∑i=1

∑n2


n=n1s2

i (n)∑n2

n=n1s2

i+m(n), (7.1)

Rsl =M∑

m=1

R(m). (7.2)

where R(m) is the normalized spatial coherence measured across a receive aperture

[40], m is the element separation distance, N is the number of receive elements, si(n)

is the time-delayed signal received by the ith element at depth, or time, n, expressed

in number of samples, and Rsl is the short-lag spatial coherence.

One pixel in a SLSC image is formed by computing the short-lag spatial coherence

at one depth, n, of the channel signals, using a correlation kernel size (n2 − n1) of

one wavelength. This process is repeated at numerous axial and lateral positions

to create a SLSC image. Matched B-mode images are constructed by applying a

conventional delay-and-sum beamformer to the same channel signals used to make

SLSC images.

119

As noted in [35], there is a trade-off among imaging performance metrics as a

function of M . Generally, lateral resolution is improved, the signal-to-noise ratio

(SNR) is degraded, and the contrast and contrast-to-noise ratio (CNR) increases

then decreases as the value of M increases.

7.2.2 Motion Tracking with SLSC Images

The ability to track motion with SLSC images has benefits with regard to visual

assessment of endocardial borders and myocardial strain imaging [11]. To demon-

strate the feasibility of motion tracking with SLSC imagaes, diffuse scatterers were

axially shifted by 1, 10, and 100µm increments and imaged using the Field II simula-

tion package. The simulated transducer was a 50-element linear array with a 8MHz

center frequency and 60% fractional bandwidth.

Radio-frequency (RF), detected, and SLSC data were tracked using normalized

cross correlation with a kernel size of 0.14mm x 0.50 mm and a search region of

2.4mm x 1.0mm. Displacements were averaged over 8,000 tracking kernels. Fig. 7.1

shows average displacement results ranging from (a) 0-10µm, (b) 0.01-0.1mm, and

(c) 0.1-1 mm. The mean displacement values for RF, envelope-detected, and SLSC

data are in agreement, except for SLSC displacements greater than 0.4 mm. At

the micron displacement level, the jitter in SLSC and detected data is too large to

accomplish tasks that require tenths of a micron jitter (i.e. acoustic radiation force

impulse imaging and Doppler imaging). However, the larger displacement results

(0.01-0.3 mm) show that SLSC images are suitable for tasks such as cardiac motion

tracking.

120

0 2 4 6 8 10x 10

−3

0

2

4

6

8

10x 10

−3

Actual Displacement (mm)

Mea

sure

d (m

m)

DetectedSLSCRF

(a)

0.02 0.04 0.06 0.08 0.1

0.02

0.04

0.06

0.08


Mea

sure

d (m

m)

DetectedSLSCRF

(b)

0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

1.2


Mea

sure

d (m

m)

DetectedSLSCRF

(c)

Figure 7.1: Measured vs. actual displacement tracking of SLSC, RF, and detecteddata.

7.3 Methods

7.3.1 Study Population

The study population consisted of 14 volunteers (age mean ± s.d. = 55 ± 17

years, age range = 33-85, 9 men, 5 women). Six of the volunteers were employees

of Duke University and eight were patients scheduled for an echocardiogram at the

Duke University Medical Center. Two of the patients required the use of contrast

agents for endocardial visualization during a standard exam, one patient suffered

from pulmonary hypertension, and two patients had scar tissue in the chest wall, one

from a heart transplant and one from breast surgery. This study was approved by

the Duke University Institutional Review Board and informed consent was obtained

from all volunteers.

7.3.2 Data Acquisition

Each volunteer was placed in the left lateral decubitus position to acquire mid-

level short axis views and apical four chamber views of the left ventricle (LV).

A VerasonicsTM ultrasound scanner (Redmond, WA) and a 64-element ATL P4-2

phased array transducer were utilized to acquire thirty-five frames of data at a rate

of approximately 7 frames per second. The sector width of each frame was 45o. The

minimum depth required to display the entire LV in each volunteer was selected from

121

preset values of 8, 10, 12, 14, 16 or 18 cm. In the short axis views, the focus was

consistent with the location of the LV, and in the apical views, it was consistent

with at least two of the seven endocardial segments. The axial sampling frequency

was 30 MHz, and the transducer transmit frequency was 2 MHz. Gain settings were

standardized for all volunteers.

The ultrasound echo data received by the 64 individual transducer elements was

processed offline to create matched B-mode and SLSC images. The size of the single

channel data set required to make one cine loop was approximately 6-7 gigabytes.

B-mode images were created with logarithmic compression settings determined to

be optimal by the cardiologist who performed the acquisitions. SLSC images were

created with M = 6, for reasons discussed in Section 7.5.1.

7.3.3 Performance Metrics

For each volunteer, the B-mode image with the most clearly-defined endocardial

border was selected from the short axis view of the LV. The selected B-mode image

and its matched SLSC image were used to characterize performance. Performance

was evaluated by measuring contrast (C), CNR, and SNR in the same locations in

the matched B-mode and SLSC images, using the following equations:

C = 20log10

(Se

Sv

), (7.3)

where Sv and Se are the mean signals in the ventricle and endocardium, respectively.

CNR =|Sv − Se|√σv

2 + σe2, (7.4)

where σv and σe are the standard deviations of signals in the ventricle and endo-

cardium, respectively.

SNR =Se

σe

. (7.5)

122

The SLSC images were also used to characterize these performance metrics as a

function of M for each volunteer.

7.3.4 Endocardial Visibility and Scoring System

Cine loops of the short axis views were grouped separately from those of the

apical 4 chamber views. Each group was randomized and reviewed independently by

three cardiology fellows. One reviewer was the cardiologist who acquired the images

(Reviewer 1), and the other two reviewers were blinded to the study (Reviewers 2 and

3). Cine loops were observed in the cardiology reading room at the Duke University

Hospital, with the same equipment and lighting conditions used to diagnose clinical

conditions.

The observers were given segment models that complied with the American Soci-

ety of Echocardiography standards for short axis and apical four chamber views [106].

The six segments in the short axis view are: anterior, antero-septum, infero-septum,

inferior, infero-lateral, and antero-lateral. The seven segments in the apical four

chamber view are: apical cap, apical septum, apical lateral, mid inferoseptum, mid

anterolateral, basal inferoseptum, and basal anterolateral. Qualitative assessment of

endocardial visualization of each segment of the LV during systole and diastole was

performed with a visual scoring system ranging from 1 to 3 as follows: 1 = endocar-

dial border clearly visible; 2 = endocardial border visible, but not clearly; and 3 =

no endocardial border visible.

7.3.5 Statistical Analysis

In the short axis and apical four chamber views, results were separated according

to B-mode image quality, where good was defined as 80% or more of the endocardial

segments were visualized by the three reviewers in systole and diastole (3 volunteers),

poor was defined as 80% or more of the endocardial segments could not be visualized

123

by the three reviewers in systole or diastole (3 volunteers). The remaining volunteers

were grouped as having medium-quality B-mode images (8 volunteers). The number

of segments in each “score” category for each “image-quality” category was recorded

by each reviewer. Data are reported as the median and interquartile range of the per-

centage of total segments evaluated by each reviewer in each category. The number

of segments not visible in B-mode and SLSC images (score=3) for each image-quality

category was compared by a Wilcoxon signed rank test for paired data. Differences

were considered statistically significant for p values < 0.1.

Due to the small sample size and the few number of segments at the focus in the

apical four chamber view, the data from this view were also summarized as the mean

visibility score of each segment in B-mode and SLSC images. Differences between the

means were compared with a paired t test, and statistical significance was maintained

at p < 0.1.

7.3.6 Software

All image processing and data analyses were performed with Matlab (The Math-

works Inc., Natick, MA) software. With Matlab Executable (MEX) files that en-

abled the interface of C++ subroutines and a 3.5 GHz processor, the time to calculate

one SLSC image was approximately 2s.

7.4 Results

7.4.1 Short Axis Views

Matched B-mode and SLSC images of the LV of one volunteer are shown in Fig.

7.2 (a) and (b), respectively. The left ventricular and adjacent right ventricular and

atrial cavities in Fig. 7.2 (b) contain less clutter than the respective locations in the

matched B-mode image. Observation of the cine loop revealed a reduction of both

stationary and nonstationary clutter, for all frames of acquired data, particularly in

124

B−mode

Axi

al (

cm)


0

2

4

6

8

10

12

14

16

(a)

Axi

al (

cm)

Lateral (cm)

SLSC

−5 0 5

0

2

4

6

8

10

12

14

16

(b)

Axi

al (

cm)

M−mode

0.2 0.4 0.6 0.8 1

0

5

10

15

Axi

al (

cm)

Time (s)

SLSC

0.2 0.4 0.6 0.8 1

0

5

10

15

(c)

Figure 7.2: Matched (a) B-mode and (b) SLSC images of the left ventricle ofVolunteer 2. The endocardial border was manually outlined using visual inspectionof a cine loop and the outlined ROIs were used to calculate contrast, CNR, and SNR.(c) Corresponding M-mode and SLSC images as a function of time.

the near-field region.

SLSC and traditional M-mode images were created from channel data by forming

an image of the same lateral position as a function of time. The comparative M-

125

B−mode

Axi

al (

cm)


0

2

4

6

8

10

12

(a)

Axi

al (

cm)

Lateral (cm)

SLSC

−5 0 5

0

2

4

6

8

10

12

(b)

Figure 7.3: Matched (a) B-mode and (b) SLSC images of the left ventricle ofvolunteer 5. The B-mode image is an example of a good quality image, where morethan 80% of the endocardial border is visualized. The corresponding SLSC imageshows reduced clutter and more well-defined borders.

modes in Fig. 7.2 (c) reveal that the SLSC image clarifies the inferior endocardial

border, while the pericardium and anterior endocardial border are well visualized.

The SLSC image was used to manually trace the endocardial border in the LV

shown in Fig. 7.2 (b). Contrast, CNR, and SNR, calculated from signals in the

regions of interest (ROIs) indicated in Fig. 7.2 (b), measured 6.6 dB, 1.1, and 2.3,

respectively, in the B-mode image and 9.1 dB, 1.1, and 2.0, respectively, in the SLSC

image. Thus, there is approximately a 3 dB improvement in contrast in the SLSC

image, while the CNR and SNR are similar in the B-mode and SLSC images. ROIs in

similar locations were used to calculate performance metrics for all of the volunteers.

Matched B-mode and SLSC images of the LV and mitral valves in another vol-

unteer are shown in Fig. 7.3 (a) and (b), respectively. The B-mode image is an

example of a good quality image, where more than 80% of the endocardial border

is visualized. Clutter is reduced and contrast is improved by approximately 4 dB in

126

B−mode

Axi

al (

cm)


0

2

4

6

8

10

12

14

(a)

Axi

al (

cm)

Lateral (cm)

SLSC

−5 0 5

0

2

4

6

8

10

12

14

(b)

Figure 7.4: Matched (a) B-mode and (b) SLSC images of the left ventricle ofvolunteer 7. The B-mode image is is an example of a poor quality image, where lessthan 80% of the endocardial border is clearly visualized. The endocardial border ismore well defined in the SLSC image.

the SLSC image. CNR is improved by 0.5 and SNR is increased by 0.4 in the SLSC

image. The SLSC image also shows reduced clutter and more well-defined borders.

An example of a poor-quality B-mode image is shown in Fig. 7.4 (a), where less

than 80% of the endocardial border is clearly visualized. The borders are clearer in

the matched SLSC image in Fig. 7.4 (b). The contrast between the ventricle and the

endocardium is improved by 11 dB in the SLSC image. CNR and SNR are improved

by 1.5 and 1.6, respectively, in the SLSC image.

7.4.2 Performance Metrics

The comparative performance of B-mode and SLSC images from all volunteers

was measured using contrast, CNR, and SNR metrics. These performance metrics

were measured in matched B-mode and SLSC images from each volunteer. Matched

values are compared in the scatter plots of Fig. 7.5, where B-mode performance is

127

0 20 400

10

20

30

40

50

B−mode Contrast

SLS

C C

ontr

ast

(a)

0 1 2 30

1

2

3

B−mode CNR

SLS

C C

NR

(b)

1 2 31

1.5

2

2.5

3

3.5

B−mode SNR

SLS

C S

NR

(c)

Figure 7.5: Scatter plots of (a) contrast, (b) CNR, and (c) SNR measured in B-mode and SLSC images from the 14 volunteers. Data points above the solid lineindicate better contrast, CNR, or SNR in the SLSC image compared to the matchedB-mode image. The SLSC values were calculated with M = 6.

displayed on the abscissa and SLSC performance is displayed on the ordinate axis.

Values above the solid line indicate improvement with SLSC imaging. The contrast,

CNR, and SNR is improved in most SLSC images.

The performance metrics were measured as a function of the short-lag value M

in SLSC images from the fourteen volunteers. Fig. 7.6 illustrates that as M is

increased, the mean contrast increases then remains constant for M ≥ 6, the mean

SNR decreases, and the mean CNR increases then decreases.

0 5 10 15 20 250

5

10

15

20

25

30

35

M

Con

tras

t (dB

)

(a)0 5 10 15 20 25

0.5

1

1.5

2

2.5

3

3.5

M

CN

R

(b)0 5 10 15 20 25

1

2

3

4

5

6

7

8

9

10

M

SN

R

(c)

Figure 7.6: Mean (a) contrast, (b) CNR, and (c) SNR measured in SLSC imagesfrom the 14 volunteers, as a function of the short-lag value M . Error bars indicate± one standard deviation from the mean.

128

B−mode SLSC0

50

100%

% o

f Seg

men

ts w

ith V

isib

ility

Sco

re o

f 1, 2

, or

3

in

Sys

tole

Good Quality

123

B−mode SLSC0

50

100%

in

Dia

stol

e

(a)

B−mode SLSC0

50

100%

% o

f Seg

men

ts w

ith V

isib

ility

Sco

re o

f 1, 2

, or

3

in

Sys

tole

Medium Quality

B−mode SLSC0

50

100%

in

Dia

stol

e

(b)

B−mode SLSC0

50

100%

% o

f Seg

men

ts w

ith V

isib

ility

Sco

re o

f 1, 2

, or

3

in

Sys

tole

Poor Quality

B−mode SLSC0

50

100%

in

Dia

stol

e

(c)

Figure 7.7: Visibility of the segments in the short axis view of the LV. The imageswere separated by B-mode image quality (good, medium, poor). The number ofsegments with each visibility score (1=clearly seen, 2=poorly seen, 3=not visible)is expressed as a percentage of the total number of segments in each image qualitycategory. The height of the bars represent the median of the three independentobservers and the error bars show the interquartile range for each score categoryin each image quality category in sytole and diastole. The p-values were (a) 1 insystole and diastole in good quality images, (b) 0.45 and 0.64 in systole and diastole,respectively, in medium quality images, and (c) 0.047 and 0.0078 in systole anddiastole, respectively, in poor quality images.

7.4.3 Independent Observer Reviews

A summary of the scores assigned to each segment in the short axis view is

displayed in Fig. 7.7. Improvement in segment visibility between B-mode and SLSC

results is indicated by an increase in the height of the bars labeled with scores of

129

1 (clearly visible) and 2 (poorly visible), for each image quality category in systole

or diastole. Improvement is also indicated by a decrease in the height of the bars

labeled with a score of 3 (segments not visible). The greatest improvement with

SLSC imaging was observed in poor-quality B-mode images, where the percentage of

segments not visualized with B-mode imaging decreased by 33% and 22% in systole

and diastole, respectively (p < 0.1). In good- and medium-quality images, there are

no statistically significant differences between endocardial border visualization with

B-mode and SLSC images.

7.4.4 Apical Four Chamber Views

Matched B-mode and SLSC images of the apical four chamber view from one

volunteer are shown in Fig. 7.8 (a) and (b), respectively. The images display a

portion of chordae tendineae in the LV. Note how the clutter in the near field obscures

definition of the apical endocardium segments. The three reviewers rated the apical

cap as not visible (score=3) in the B-mode image. Reviewers 1 and 2 observed

better visualization of this segment (score = 2) in the SLSC image, while Reviewer

3 recorded no difference.

The three reviewers also noted that the three lateral segments (apical lateral,

mid anterolateral, and basal anterolateral) were not visualized in the B-mode image.

In the SLSC images, these three segments maintained poor visibility by Reviewer 1

(score =3) and were better visualized by Reviewer 2 (score = 2). Reviewer 3 recorded

better visibility (score =2) of the apical lateral segment in the SLSC image during

systole. The other two lateral segments were rated as not visible by this reviewer.

Matched B-mode and SLSC images of an apical four chamber view from another

volunteer are shown in Fig. 7.9 (a) and (b), respectively. These images include a

portion of chordae tendineae in the LV. Visibility of the apical segments is obscured

by the presence of clutter in the near-field. Reviewers 1 and 3 rated the apical cap,

130

B−mode

Axi

al (

cm)


0

2

4

6

8

10

12

14

(a)

Axi

al (

cm)

Lateral (cm)

SLSC

−5 0 5

0

2

4

6

8

10

12

14

(b)

Figure 7.8: Apical four chamber view of the left ventricle of volunteer 3 in matched(a) B-mode and (b) SLSC images. The endocardial borders are more clearly defined,particularly in the near field. The transmit focus was 8.3 cm.

apical septum, and mid inferoseptum as not visible with B-mode imaging during

diastole (score = 3). With SLSC imaging, these segments maintained poor visibility

by Reviewer 3 (score = 3) and were better visualized by Reviewer 1 (score = 2).

However, Reviewer 2 rated these three segments with the same visibility in B-mode

and SLSC images (2, 2, and 1, respectively). These and the previous examples

demonstrate the variability in reviewer scores for the apical four chamber views.

It is interesting to note that the three reviewers visualized (score = 1 or 2) the

basal lateral segment in the B-mode and SLSC cine loops represented in Fig. 7.9.

Two of the reviewers rated this segment with equal visibility in the B-mode and

SLSC images, while one reviewer recorded that this segment was better visualized

in the SLSC image.

Of all the reviewed cine loops from the apical four chamber views, those repre-

sented by the B-mode and SLSC images in Figs. 7.8 and 7.9 were the only ones that

contained intracardiac structures in the imaging plane.

131

B−mode

Axi

al (

cm)


0

2

4

6

8

10

12

14

(a)

Axi

al (

cm)

Lateral (cm)

SLSC

−5 0 5

0

2

4

6

8

10

12

14

(b)

Figure 7.9: Apical four chamber view of the left ventricle of volunteer 2 in matched(a) B-mode and (b) SLSC images. There is reduced clutter in the near field of theSLSC image. The focus was 8.3 cm.

A summary of the scores assigned to each segment in the apical four chamber

view is displayed in Fig. 7.10. The greatest improvement with SLSC imaging was

observed in poor-quality B-mode images during systole, where the percentage of

segments not visualized with B-mode imaging decreased by 19% (p < 0.1). In good-

and medium-quality images, there are no statistically significant differences between

endocardial border visualization with B-mode and SLSC images.

The mean of the visibility scores (1=clearly seen, 2=poorly seen, 3=not visible)

for the apical four chamber views are reported in Fig. 7.11. The means ranged

from 2.1 to 2.6, indicating that a majority of these apical views contained segments

that were not visible or poorly visible. Differences between B-mode and SLSC mean

visibility scores are not statistically significant.

132

B−mode SLSC0

50

100%

% o

f Seg

men

ts w

ith V

isib

ility

Sco

re o

f 1, 2

, or

3

in

Sys

tole

Good Quality

123

B−mode SLSC0

50

100%

in

Dia

stol

e

(a)

B−mode SLSC0

50

100%

% o

f Seg

men

ts w

ith V

isib

ility

Sco

re o

f 1, 2

, or

3

in

Sys

tole

Medium Quality

B−mode SLSC0

50

100%

in

Dia

stol

e

(b)

B−mode SLSC0

50

100%

% o

f Seg

men

ts w

ith V

isib

ility

Sco

re o

f 1, 2

, or

3

in

Sys

tole

Poor Quality

B−mode SLSC0

50

100%

in

Dia

stol

e

(c)

Figure 7.10: Visibility of the segments in the apical four chamber view of theLV. The images were separated by B-mode image quality (good, medium, poor).The number of segments with each visibility score (1=clearly seen, 2=poorly seen,3=not visible) is expressed as a percentage of the total number of segments in eachimage quality category. The height of the bars represent the median of the threeindependent observers and the error bars show the interquartile range for each scorecategory in each image quality category in sytole and diastole. The p-values were(a) 0.50 and 1 in systole and diastole, respectively, in good quality images, (b) 0.55and 0.35 in systole and diastole, respectively, in medium quality images, and (c) 0.06and 0.25 in systole and diastole, respectively, in poor quality images.

7.5 Discussion

7.5.1 Improvements with SLSC Imaging

Examples of a difficult-to-image patient with conventional B-mode imaging (Figs.

7.2 and 7.4) are contrasted with examples from a less challenging patient (Fig. 7.3).

133

AC AS MS BS AL ML BL0

0.5

1

1.5

2

2.5

3

3.5

Systole

Mea

n V

isib

ility

Sco

re

(a)AC AS MS BS AL ML BL

0

0.5

1

1.5

2

2.5

3

3.5

Diastole

Mea

n V

isib

ility

Sco

re

B−mode SLSC

(b)

Figure 7.11: The mean of the visibility scores (1=clearly seen, 2=poorly seen,3=not visible) of each segment in B-mode and SLSC images of the apical four cham-ber view in (a) systole and (b) diastole. AC=apical cap, AS=apical septum, MS=midinferoseptum, BS=basal inferoseptum, AL=apical lateral, ML=mid anterolateral,and BL=basal anterolateral. The p values exceed 0.1 for all segments in systole anddiastole, indicating no statistically significant differences.

The clutter is noticeably reduced in these SLSC images, when compared to matched

B-mode images. The observed clutter reduction is best characterized by the improved

contrast in most of the SLSC images (see Fig. 7.5 (a)). This improvement implies

that SLSC imaging has the potential to reduce clutter in a range of patient types.

Statistically significant improvements in segment visibility was observed in pa-

tients with poor-quality B-mode images, as illustrated in Figs. 7.7(c) and 7.10(c),

where SLSC imaging offers a 19-33% decrease in the percentage of myocardial seg-

ments not visualized with B-mode imaging. No statistically significant differences

were observed in good- and medium-quality images, indicating that SLSC imaging

improves poor-quality B-mode images without significantly degrading medium and

good quality images.

As discussed in Ref. [35], when low-amplitude signals are surrounded by struc-

tures with higher amplitudes and high spatial coherence, the coherence of the lower

amplitude signal is decreased relative to that of the higher amplitude signal, thus

134

providing a source of contrast in SLSC images. This decrease benefits endocardial

border definition in the presence of intracardiac structures such as the mitral valve

and chordae tendineae, which have greater coherence in the presence of the surround-

ing clutter and blood, as demonstrated in Figs. 7.3 and 7.8, respectively.

Note that at the focus of Fig. 7.9, the high spatial coherence of the pericardium re-

duces the coherence of the lower amplitude endocardium, and as a result endocardial

border definition of the basal anterolateral segment at the focus suffers. The three

reviewers did not notice the loss in visibility of this segment because the matched

B-mode and SLSC cine loops were not compared side-by-side. This subtle obser-

vation and the previously-discussed results indicate that the location of intra- and

extra-cardiac structures should be considered when making SLSC images. The ideal

SLSC image for reducing cardiac clutter would likely contain internal structures such

as mitral valves, papillary muscles, or chordae tendineae in the imaging plane. In ad-

dition, placing the focus at the location of the bright pericardium should be avoided

to reduce the loss of endocardium in the SLSC image.

Although one frame of data was acquired and processed in approximately 2s,

real-time SLSC imaging requires faster processing times, which could potentially be

achieved with optimized correlation algorithms, advanced processors, and graphics

processing unit (GPU)-based computing. Once real-time SLSC imaging is achieved,

the sonographer or cardiologist performing the real-time scan would have the ability

to adjust the short-lag value (M) to optimize SLSC images. When adjusted, this

value produces varied contrast, CNR and SNR, as demonstrated in Fig. 7.6, which is

consistent with previous observations in simulated SLSC images [35]. M = 6 was the

value chosen to display images throughout this chapter and to make the cine loops

that were reviewed, because it is the lowest short-lag value with the best average

contrast. Higher values of M have poorer CNR and SNR. It is interesting to note

that endocardial border definition in difficult-to-image patients is improved when

135

viewing a cine loop of SLSC images acquired at the same time, but created with

increasing values of M (ranging from 1 to 20).

7.5.2 Study Limitations

B-mode and SLSC endocardial segment scores were based on visual semi-quantitative

estimates, introducing a degree of reviewer subjectivity. Yet, the improvements with

SLSC imaging of poor-quality B-mode images were statistically significant. In ad-

dition, objective measurements of contrast, CNR, and SNR were performed on the

raw data. Note that harmonic imaging was not applied, which might have led to fur-

ther contrast enhancement and improvements in endocardial border definition with

B-mode [107, 108] and SLSC imaging.

Prospective studies with larger numbers of patients are required to fully assess

the clinical role of SLSC imaging. Particularly, the high mean visibility scores in

Fig. 7.11 indicate that there were few images with visible segments in the apical four

chamber views. This is likely due to the presence of clutter in B-mode images. In

SLSC images, the poor visibility is due to a complicated combination of the presence

of bright extracardiac scatterers, the absence of intracardiac structures in the image

plane, and the location of the focus. Nonetheless, the examples presented in Figs.

7.8 and 7.9 suggest improved endocardial visualization in the apical segments when

nearby intracardiac structures are present in the image plane. It can, therefore, be

expected that a study of this region with a larger sample size of images that contain

intracardiac structures would produce statistically significant results.

A significance level of 10% (p< 0.1) was chosen because of the small sample size

of 3 volunteers in the poor-quality image category. While a significance level of 5%

(p < 0.05) would not change the statistical significance of the results in Fig 7.7 (c),

at this significance level, the results in Fig. 7.10 (c) are not statistically significant.

However, it is quite remarkable that a significance level of 10% yields statistically

136

significant results with this small sample size. If data from more poor-quality images

were available, statistical significance at the 5% or 1% significance level would likely

be achieved.

Improvements in the apical four chamber views relied largely on the cardiologist

who reviewed the scans. The analysis would have been more consistent if the three

reviewers were asked to reach a consensus.

7.5.3 Clinical Implications

SLSC imaging significantly improves endocardial visualization of the LV in pa-

tients with poor-quality B-mode images. Thus, there is potential for SLSC imaging

to improve clinical measurements that rely on endocardial border definition, such

as volume, mass, and ejection fraction. In addition, the reduced clutter in the near

field region of the apical four chamber views suggests that SLSC might be a preferred

method for imaging apical cardiac masses like tumors or thrombi.

7.6 Conclusion

Short-lag spatial coherence imaging improves endocardial border definition when

B-mode images contain a majority of poorly-visualized endocardial segments due to

clutter. Quantitative metrics revealed better contrast, CNR, and SNR with SLSC

imaging in most patients. This work provides evidence of SLSC imaging’s potential to

reduce cardiac clutter, clarify endocardial borders, and thereby improve visualization

of cardiac abnormalities and border-dependent cardiac measurements.


This work was supported by the UNCF-Merck Graduate Science Research Disser-

tation Fellowship and NIH Grant R37-HL096023. Special thanks to Dongwoon

Hyun for assistance with MEX-File programming, Vaibhav Kakkad for assistance

137

with intensity measurements, Mark Palmeri for assistance with binary data, Joseph

A. Kisslo for granting access to patients in the Duke University Medical Center,

and cardiologists Robi Goswami (Reviewer 1), Prateeti Khazanie (Reveiwer 2), and

Sreekanth Vemulapalli (Reviewer 3).

138

8

Conclusions and Future Directions

8.1 Conclusions

This dissertation presents the first quantitative assessment of clutter in abdominal

ultrasound images and the first study of clutter sources in in vivo abdominal images.

Novel clutter reduction approaches that utilize the motion of abdominal muscles and

the spatial coherence of ultrasound echoes are also presented.

The presented quantitative assessment underscores the severity of the clutter

problem. In vivo clutter magnitudes measured 0 to -30 dB relative to surrounding

tissue, indicating that clutter can be as strong as the signal of interest. For this

range of clutter magnitudes, analytical expressions predict a maximum contrast loss

of 94% due to the presence of clutter. This quantitative assessment is not limited

to abdominal images. Similar levels of clutter magnitude and contrast loss due to

clutter are expected in other organ sites of the body, such as the heart.

The motion-based clutter reduction methods presented herein relies on external

movement of the abdominal muscles relative to the organ of interest. The method,

however, is not suitable for cardiac imaging, because it is has limited ability to re-

139

move non-stationary clutter. An alternative clutter reduction approach, which was

invented during the course of these studies, considers the spatial coherence of ultra-

sound echoes. It is founded on the classic VCZ theorem. The VCZ theorem applied

to pulse-echo ultrasound was used to describe differences between the spatial coher-

ence of tissue and the spatial coherence of other image targets (i.e. the anechoic

or hypoechoic regions of a cyst or cardiac chamber). These differences are promi-

nent in the presence of clutter and are most appreciable in the short-lag region of

coherence functions. The integral of the short-lag region of coherence functions was

used to characterize these differences and form the foundation of Short-Lag Spatial

Coherence imaging. This novel beamforming technique was tested in simulated and

experimental data and compared to conventional B-mode imaging with favorable

results, namely reduced clutter and improved contrast, CNR, and SNR.

The capstone project of this dissertation was to investigate the performance of

SLSC imaging in echocardiography. Visual and quantitative assessments of cardiac

images revealed a reduction in clutter with SLSC imaging. Similar to simulated and

experimental phantom results, the contrast, CNR and SNR was also improved in

most SLSC images. In the short axis views of the left ventricle, the endocardial

border was better visualized with SLSC images in cases where 80% or more of the

endocardial border could not be visualized in matched B-mode images. Thus, the

results from this capstone project support the hypothesis that SLSC imaging is a

useful tool for reducing clutter and identifying endocardial borders in poor-quality

ultrasound B-mode images.

8.2 The Future of SLSC

There are many fundamental questions about SLSC imaging that remain unan-

swered due to the novelty of the technique. SLSC imaging has the potential to

improve the standard of care in virtually any clinical task that is susceptible to ul-

140

trasonic clutter, including measuring the intima media thickness in vascular imaging,

identifying cancerous microcalcifcations in breast imaging, diagnosing abnormalities

in fetal imaging, and detecting lesions in abdominal images. The following is a short

discourse on five of the many potential future directions of SLSC imaging.

8.2.1 Harmonic SLSC

SLSC may be combined with harmonic imaging to further reduce clutter in ul-

trasound images. Similar experimental methods to those described in Chapter 7

were used to acquire an apical four chamber view of the LV in one volunteer with

pulse-inversion harmonic imaging. A custom-built connector was used to interface

a Siemens PH4-1 transducer with the VerasonicsTM ultrasound scanner. This setup

modification was better suited for harmonic imaging due to the wider bandwidth

of the PH4-1 probe. The only other differences between this set up and the one

described in Chapter 7 were that 35 sector lines were acquired instead of 50, and two

pulses (one normal, the other inverted) were transmitted for each sector line.

Echoes received from the normal pulses were utilized to make fundamental B-

mode and SLSC images, using the same methods described in various portions of

this dissertation (e.g. Chapter 2). Harmonic RF data was obtained by summing the

normal and inverted pulse-echo signals. The same methods applied to the fundamen-

tal data were applied to the resulting harmonic data to make harmonic B-mode and

harmonic SLSC images. Example images are shown in Fig. 8.1. Notice the slightly

reduced clutter and improved endocardial border definition in the harmonic B-mode

image, when compared with the fundamental B-mode image. The fundamental and

harmonic SLSC images offer increased clutter reduction benefits, and the harmonic

SLSC image shows better definition of the endocardial border.

141

Fundamental B−mode

−4 −2 0 2 4

0

2

4

6

8

Harmonic B−mode

−4 −2 0 2 4

0

2

4

6

8

Fundamental SLSC

−4 −2 0 2 4

0

2

4

6

8

Harmonic SLSC

−4 −2 0 2 4

0

2

4

6

8

Figure 8.1: Fundamental and Harmonic B-mode and SLSC images of a left ventri-cle. The units of the axial and lateral scales are centimeters.

8.2.2 Motion Tracking with SLSC Images

The ability to track motion with SLSC images demands further investigation if

SLSC imaging is expected to compete with a broad range of clinical imaging tasks.

Such tasks include myocardial strain imaging [11] and automatic motion compensa-

tion for radiotherapy procedures [109]. The preliminary results presented in Chapter

7 demonstrate that motion tracking with SLSC images is feasible, particularly for

cardiac and liver tracking, where displacements ranging from 0.01-0.3 mm are typi-

cally encountered.

142

8.2.3 3D SLSC

Three dimensional (3D) ultrasound images are becoming increasingly popular

among patients and physicians alike. Physicians use 3D ultrasound to estimate

volumes with increasing accuracy in cardiac and bladder images. Pregnant mothers-

to-be are interested in viewing their unborn fetus in three dimensions, because 3D

rendering makes facial features and body parts appear more “human-like”, thus

enhancing the mother-to-baby emotional connection. Given the growing market

niche for 3D ultrasound, manufacturers have increasing incentive to develop real-

time three dimensional ultrasound systems with two dimensional (2D) matrix array

probes. If SLSC imaging is expected to compete with B-mode imaging in this regard,

investigations into 3D SLSC are necessary.

Spatial coherence can be computed as a 2D function of lag in the lateral and

elevation dimensions. When implemented with data from a 2D array, there are

numerous options for 3D rendering of SLSC images. For example, coherence may be

calculated as a function of lag in all possible directions, and the resulting coherence

functions could be integrated to make SLSC images. Another approach relies on the

fact that conventional delay-and-sum beamforming can be separated into lateral and

elevation components. Thus, a delay-and-sum beamformer can be applied to groups

of elements first. Multi-dimensional coherence functions may then be computed as

if the data came from a smaller 2D array. There are numerous possibilities for

combining conventional beamforming with SLSC imaging in this regard.

8.2.4 Real-Time SLSC Imaging

Real-time SLSC imaging is challenging due to the time required to calculate

many correlations. However, the algorithms used throughout this dissertation were

not completely optimized for speed. There are a few options that could be imple-

mented to achieve real-time SLSC imaging. One option is to research the minimum

143

correlations actually needed to calculate a SLSC image with little to no loss in overall

image quality. Another option is to program SLSC algorithms on GPUs to decrease

the time required to calculate the many correlations. Further, decreasing both the

number of calculations required and the calculation time would markedly improve

the likelihood of real-time implementation.

8.2.5 Application of SLSC Principles to Related Areas

The basic principles of SLSC imaging may also be applied to other imaging modal-

ities such as photoacoustic imaging or optical coherence tomography. There is also

potential to apply SLSC principles to non-destructive evaluation (NDE) of materials

with ultrasound. For example, NDE is useful with regard to evaluating tiny cracks

and predicting the failure of an airplane wing. Clutter is reported as a problem in

this type of NDE ultrasound application [110]. SLSC is one potential method that

could be used to image the airplane wing with less clutter from off-axis echoes. SLSC

also has a potential niche in other radar and sonar applications, as well as in seismol-

ogy and wireless communications. These disciplines all require beamforming of some

type. Similar to ultrasound imaging, the conventional delay-and-sum beamformer in

these applications is challenged by clutter noise [111, 112, 113].

144

Bibliography

[1] J. Wild and J. Reid, “Diagnostic use of ultrasound.” The British journal ofphysical medicine, including its application to industry, vol. 19, no. 11, p. 248,1956.

[2] W. Richard, D. Zar, and R. Solek, “A low-cost b-mode usb ultrasound probe,”Ultrasonic Imaging, vol. 30, no. 1, pp. 21–28, 2008.

[3] L. Gao, K. Parker, R. Lerner, and S. Levinson, “Imaging of the elastic proper-ties of tissuea review,” Ultrasound in Medicine and Biology, vol. 22, no. 8, pp.959–977, 1996.

[4] K. Nightingale, “Acoustic radiation force impulse (arfi) imaging: a review,”Current Medical Imaging Reviews, vol. 7, no. 4, pp. 328–339, 2011.

[5] J. Kisslo, B. Firek, T. Ota, D. Kang, C. Fleishman, G. Stetten, J. Li,C. Ohazama, D. Adams, C. Landolfo et al., “Real-time volumetric echocar-diography,” Echocardiography, vol. 17, no. 8, pp. 773–779, 2000.

[6] O. Von Ramm and S. Smith, “Real time volumetric ultrasound imaging sys-tem,” Journal of Digital Imaging, vol. 3, no. 4, pp. 261–266, 1990.

[7] S. Huber, M. Wagner, M. Medl, and H. Czembirek, “Real-time spatial com-pound imaging in breast ultrasound,” Ultrasound in Medicine and Biology,vol. 28, no. 2, pp. 155–63, 2002.

[8] G. Zwirn and S. Akselrod, “Stationary clutter rejection in echocardiography,”Ultrasound in Medicine and Biology, vol. 32, no. 1, pp. 43–52, 2006.

[9] N. Bylund, M. Ressner, and H. Knutsson, “3d wiener filtering to reduce rever-berations in ultrasound image sequences,” Image Analysis, pp. 342–342, 2003.

[10] S. Bjaerum, H. Torp, and K. Kristoffersen, “Clutter filter design for ultra-sound color flow imaging,” IEEE Transactions on Ultrasonics, Ferroelectricsand Frequency Control, vol. 49, no. 2, pp. 204–216, February 2002.

[11] A. Teske, B. De Boeck, P. Melman, G. Sieswerda, P. Doevendans, andM. Cramer, “Echocardiographic quantification of myocardial function using

145

tissue deformation imaging, a guide to image acquisition and analysis usingtissue Doppler and speckle tracking,” Cardiovascular Ultrasound, vol. 5, no. 1,p. 27, 2007.

[12] A. Patel, A. Moorthy, V. Yap, and J. Thomsen, “Cardiac metastasis from tran-sitional cell carcinoma: a subtle echocardiographic entity,” Journal of ClinicalUltrasound, vol. 8, no. 1, 1980.

[13] M. Ragland and T. Tak, “The role of echocardiography in diagnosing space-occupying lesions of the heart,” Clinical Medicine & Research, vol. 4, no. 1,pp. 22–32, 2006.

[14] D. Mele, O. Soukhomovskaia, E. Pacchioni, E. Merli, N. Avigni, L. Federici,R. Levine, and R. Ferrari, “Improved detection of left ventricular thrombiand spontaneous echocontrast by tissue harmonic imaging in patients withmyocardial infarction,” Journal of the American Society of Echocardiography,vol. 19, no. 11, pp. 1373–1381, 2006.

[15] S. Mulvagh, A. DeMaria, S. Feinstein, P. Burns, S. Kaul, J. Miller, M. Mon-aghan, T. Porter, L. Shaw, and F. Villanueva, “Contrast echocardiography:current and future applications,” Journal of the American Society of Echocar-diography, vol. 13, no. 4, pp. 331–342, 2000.

[16] A. Vancon, E. Fox, C. Chow, J. Hill, A. Weyman, M. Picard, and M. Scherrer-Crosbie, “Pulse inversion harmonic imaging improves endocardial border vi-sualization in two-dimensional images: comparison with harmonic imaging,”Journal of the American Society of Echocardiography, vol. 15, no. 4, pp. 302–308, 2002.

[17] V. Giglio, V. Pasceri, L. Messano, F. Mangiola, L. Pasquini, A. Dello Russo,A. Damiani, M. Mirabella, G. Galluzzi, P. Tonali et al., “Ultrasound tissuecharacterization detectspreclinical myocardial structural changes inchildren af-fected by Duchenne muscular dystrophy,” Journal of the American College ofCardiology, vol. 42, no. 2, pp. 309–316, 2003.

[18] F. Tranquart, N. Grenier, V. Eder, and L. Pourcelot, “Clinical use of ultrasoundtissue harmonic imaging.” Ultrasound in Medicine and Biology, vol. 25, no. 6,pp. 889–94, 1999.

[19] R. Shapiro, J. Wagreich, R. Parsons, A. Stancato-Pasik, H. Yeh, and R. Lao,“Tissue harmonic imaging sonography: evaluation of image quality comparedwith conventional sonography,” American Journal of Roentgenology, vol. 171,no. 5, pp. 1203–1206, 1998.

[20] T. Muir and E. Carstensen, “Prediction of nonlinear acoustic effects at biomed-ical frequencies and intensities.” Ultrasound in Medicine and Biology, vol. 6,no. 4, pp. 345–57, 1980.

146

[21] H. Starritt, F. Duck, A. Hawkins, and V. Humphrey, “The development of har-monic distortion in pulsed finite-amplitude ultrasound passing through liver,”Physics in Medicine and Biology, vol. 31, no. 12, pp. 1401–1409, 1986.

[22] F. Chirillo, A. Pedrocco, A. De Leo, A. Bruni, O. Totis, P. Meneghetti, andP. Stritoni, “Impact of harmonic imaging on transthoracic echocardiographicidentification of infective endocarditis and its complications,” British MedicalJournal, vol. 91, no. 3, pp. 329–333, 2005.

[23] C. Caiati, N. Zedda, C. Montaldo, R. Montisci, and S. Iliceto, “Contrast-enhanced transthoracic second harmonic echo doppler with adenosine A non-invasive, rapid and effective method for coronary flow reserve assessment,”Journal of the American College of Cardiology, vol. 34, no. 1, pp. 122–130,1999.

[24] C. Gallippi and G. Trahey, “Adaptive clutter filtering via blind source sepa-ration for two-dimensional ultrasonic blood velocity measurement.” UltrasonicImaging, vol. 24, no. 4, pp. 193–214, 2002.

[25] M. A. Lediju, M. J. Pihl, S. J. Hsu, J. J. Dahl, C. M. Gallippi, and G. E.Trahey, “Magnitude, origins, and reduction of abdominal ultrasonic clutter,”in Proceedings of the IEEE International Ultrasonics Symposium, 2008, pp.50–53.

[26] F. Mauldin, D. Lin, and J. Hossack, “The singular value filter: A general filterdesign strategy for pca-based signal separation in medical ultrasound imaging,”IEEE Transactions on Medical Imaging, no. 99, pp. 1–1, 2011.

[27] E. Yeh, “Reverberations in echocardiograms,” Journal of Clinical Ultrasound,vol. 5, no. 2, 1977.

[28] G. Cloutier, D. Chen, and L. Durand, “A new clutter rejection algorithm forDoppler ultrasound,” IEEE Transactions on Medical Imaging, vol. 22, no. 4,pp. 530–538, 2003.

[29] R. Ward, K. Collins, B. Balasia, K. Spencer, J. DeCara, V. Mor-Avi, L. Sugeng,and R. Lang, “Harmonic imaging for endocardial visualization and myocardialcontrast echocardiography during transesophageal echocardiography,” Journalof the American Society of Echocardiography, vol. 17, no. 1, pp. 10–14, 2004.

[30] P. Hanrath, “Transoesophageal echo-Doppler in cardiology,” British MedicalJournal, vol. 86, no. 5, pp. 586–592, 2001.

[31] G. Zwirn, R. Beeri, D. Gilon, Z. Friedman, and S. Akselrod, “Quantitativeevaluation of local myocardial blood volume in contrast echocardiography,”Medical Image Analysis, vol. 13, no. 1, pp. 62–79, 2009.

147

[32] H. Al-Mansour, S. Mulvagh, G. Pumper, K. Klarich, and D. Foley, “Usefulnessof harmonic imaging for left ventricular opacification and endocardial borderdelineation by optison,” The American Journal of Cardiology, vol. 85, no. 6,pp. 795–799, 2000.

[33] S. Moir and T. Marwick, “Combination of contrast with stress echocardiogra-phy: A practical guide to methods and interpretation,” Cardiovascular Ultra-sound, vol. 2, no. 1, 2004.

[34] J. Ophir and K. Parker, “Contrast agents in diagnostic ultrasound,” Ultrasoundin Medicine and Biology, vol. 15, no. 4, pp. 319–333, 1989.

[35] M. A. Lediju, G. E. Trahey, B. C. Byram, and J. J. Dahl, “Short-Lag SpatialCoherence of Backscattered Echoes: Imaging Characteristics,” IEEE Transac-tions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 58, no. 7, p.1337, 2011.

[36] J. Goodman, Statistical Optics. John Wiley and Sons, Inc., 1985.

[37] R. Mallart and M. Fink, “The van Cittert–Zernike theorem in pulse echo mea-surements,” The Journal of the Acoustical Society of America, vol. 90, p. 2718,1991.

[38] J. Goodman, Introduction to Fourier Optics. Ncw York: McGrew Hill, 1986.

[39] J. A. Jensen and N. B. Svendsen, “Calculation of pressure fields from arbitrarilyshaped, apodized, and excited ultrasound transducers,” IEEE Transactionson Ultrasonics, Ferroelectrics, and Frequency Control, vol. 39, pp. 262–267,1992. [Online]. Available: http://server.oersted.dtu.dk/personal/jaj/field/

[40] R. J. Fedewa, K. D. Wallace, M. R. Holland, J. R. Jago, G. C. Ng, M. R.Rielly, B. S. Robinson, and J. G. Miller, “Spatial coherence of the nonlinearlygenerated second harmonic portion of backscatter for a clinical imaging sys-tem,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control,vol. 50, no. 8, pp. 1010–1022, 2003.

[41] R. Entrekin, P. Jackson, J. Jago, and B. Porter, “Real time spatial com-pound imaging in breast ultrasound: technology and early clinical experience,”MedicaMundi, vol. 43, no. 3, pp. 35–43, September 1999.

[42] S. Miyashita, “Efficacy of dynamic flow ultrasonography in fetal vascular imag-ing,” Med. Rev, vol. 27, p. 1, 2003.

[43] R. Lencioni, D. Cioni, and C. Bartolozzi, “Tissue harmonic and contrast-specific imaging: back to gray scale in ultrasound,” European Radiology, vol. 12,no. 1, pp. 151–165, 2002.

148

http://server.oersted.dtu.dk/personal/jaj/field/

[44] K. Spencer, J. Bednarz, P. Rafter, C. Korcarz, and R. Lang, “Use of harmonicimaging without echocardiographic contrast to improve two-dimensional imagequality,” The American Journal of Cardiology, vol. 82, no. 6, pp. 794–799, 1998.

[45] F. Viola, M. Ellis, and W. Walker, “Time-Domain Optimized Near-Field Esti-mator for Ultrasound Imaging: Initial Development and Results,” IEEE Trans-actions on Medical Imaging, vol. 27, no. 1, pp. 99–110, 2008.

[46] M. Averkiou, “Tissue harmonic imaging,” in Proceedings of the IEEE Interna-tional Ultrasonics Symposium, vol. 2. IEEE, 2000, pp. 1563–1572.

[47] F. A. Duck, “Nonlinear acoustics in diagnostic ultrasound.” Ultrasound inMedicine and Biology, vol. 28, no. 1, pp. 1–18, 2002.

[48] M. van Wijk and J. Thijssen, “Performance testing of medical ultrasoundequipment: fundamental vs. harmonic mode,” Ultrasonics, vol. 40, no. 1-8,pp. 585–591, 2002.

[49] R. Wagner, S. Smith, J. Sandrik, and H. Lopez, “Statistics of speckle in ultra-sound B-scans,” IEEE Transactions on Sonics and Ultrasonics, vol. 30, no. 3,pp. 156–163, 1983.

[50] A. Papoulis, Probability, Random Variables, and Stochastic Processes.(McGraw-Hill, 1965).

[51] J. A. Jensen, “Field: A program for simulating ultrasound systems,” Medicaland Biological Engineering and Computing, vol. 10th No, pp. 351–353, 1996.[Online]. Available: http://server.oersted.dtu.dk/personal/jaj/field/

[52] Q. Ma, Y. Ma, X. Gong, and D. Zhang, “Improvement of tissue harmonic imag-ing using the pulse-inversion technique.” Ultrasound in Medicine and Biology,vol. 31, no. 7, pp. 889–94, 2005.

[53] D. Simpson, C. Chin, and P. Burns, “Pulse inversion Doppler: a new methodfor detecting nonlinearechoes from microbubble contrast agents,” IEEE Trans-actions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 46, no. 2, pp.372–382, 1999.

[54] M. Settings, “Executive summary of the clinical guidelines on the identification,evaluation, and treatment of overweight and obesity in adults,” Journal of theAmerican Dietetic Association, vol. 98, no. 10, pp. 1178–1191, 1998.

[55] B. Fahey, R. Nelson, D. Bradway, S. Hsu, D. Dumont, and G. Trahey, “In vivovisualization of abdominal malignancies with acoustic radiation force elastog-raphy,” Physics in Medicine and Biology, vol. 53, no. 1, pp. 279–293, 2008.

149

http://server.oersted.dtu.dk/personal/jaj/field/

[56] L. Hinkelman, T. Mast, L. Metlay, and R. Waag, “The effect of abdominalwall morphology on ultrasonic pulse distortion. Part I. Measurements,” TheJournal of the Acoustical Society of America, vol. 104, p. 3635, 1998.

[57] J. Thomas and D. Rubin, “Tissue harmonic imaging: why does it work?” JAm Soc Echocardiogr, vol. 11, no. 8, pp. 803–8, 1998.

[58] M. A. Lediju, M. J. Pihl, J. J. Dahl, and G. E. Trahey, “Quantitative as-sessment of the magnitude, impact, and spatial extent of ultrasonic clutter,”Ultrasonic Imaging, vol. 30, no. 3, pp. 151–68, 2008.

[59] J. Dahl, G. Pinton, M. Lediju, and G. Trahey, “Simulation and ExperimentalAnalysis of Ultrasonic Clutter in Fundamental and Harmonic Imaging,” SPIEMedical Imaging, 2009.

[60] P. Carson and T. Oughton, “A modeled study for diagnosis of small anechoicmasses with ultrasound,” Radiology, vol. 122, pp. 765–771, 1977.

[61] H. Stankwitz, R. Dallaire, and J. Fienup, “Nonlinear apodization for sidelobecontrol in SAR imagery,” IEEE Transactions on Aerospace and Electronic Sys-tems, vol. 31, no. 1, pp. 267–279, 1995.

[62] C. Seo and J. Yen, “Sidelobe suppression in ultrasound imaging using dualapodization with cross-correlation,” IEEE Transactions on Ultrasonics, Ferro-electrics and Frequency Control, vol. 55, no. 10, pp. 2198–2210, 2008.

[63] J. Mann and W. Walker, “A constrained adaptive beamformer for medical ul-trasound: initial results,” in Proceedings of the IEEE International UltrasonicsSymposium, vol. 2, 2002.

[64] F. Vignon and M. Burcher, “Capon beamforming in medical ultrasound imag-ing with focused beams,” IEEE Transactions on Ultrasonics, Ferroelectrics andFrequency Control, vol. 55, no. 3, pp. 619–628, 2008.

[65] G. Pinton, J. Dahl, S. Rosenzweig, and G. Trahey, “A heterogeneous nonlinearattenuating full-wave model of ultrasound.” IEEE Transactions on Ultrasonics,Ferroelectrics and Frequency Control, vol. 56, no. 3, p. 474, 2009.

[66] J. A. Jensen, “Stationary echo canceling in velocity estimation by time-domaincross-correlation,” IEEE Transactions on Medical Imaging, vol. 12, no. 3, pp.471–477, 1993.

[67] C. Gallippi, K. Nightingale, and G. Trahey, “BSS-based filtering of physiolog-ical and ARFI-induced tissue and blood motion,” Ultrasound in Medicine andBiology, vol. 29, no. 11, pp. 1583–1592, 2003.

150

[68] C. Gallippi, “Blind source separation for selective tissue motion measurementin ultrasonic imaging,” Ph.D. dissertation, 2003.

[69] S. Verboven and M. Hubert, “LIBRA: a MATLAB library for robust analysis,”Chemometrics and Intelligent Laboratory Systems, vol. 75, no. 2, pp. 127–136,2005.

[70] M. Hubert, P. Rousseeuw, and K. Vanden Branden, “ROBPCA: a new ap-proach to robust principal component analysis,” Technometrics, vol. 47, no. 1,pp. 64–79, 2005.

[71] M. Karaman, P. Li, and M. O’Donnell, “Synthetic aperture imaging for smallscale systems,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Fre-quency Control, vol. 42, no. 3, pp. 429–442, 1995.

[72] P. Li, G. Yu, P. Xin, and Z. Bian, “A clutter removal method for the Dopplerultrasound signal based on a nonlinear diffusion equation,” Measurement Sci-ence and Technology, vol. 19, no. 5, p. 55101, 2008.

[73] D. Ortega, P. Burns, D. Hope Simpson, and S. Wilson, “Tissue HarmonicImaging Is It a Benefit for Bile Duct Sonography?” American Journal ofRoentgenology, vol. 176, no. 3, pp. 653–659, 2001.

[74] S. Yarmenitis, “Ultrasound of the gallbladder and the biliary tree,” EuropeanRadiology, vol. 12, no. 2, pp. 270–282, 2002.

[75] D. Liu and R. Waag, “About the application of the van Cittert-Zernike theoremin ultrasonic imaging,” IEEE Transactions on Ultrasonics, Ferroelectrics andFrequency Control, vol. 42, no. 4, pp. 590–601, 1995.

[76] W. Walker and G. Trahey, “Speckle coherence and implications for adaptiveimaging,” Journal of the Acoustical Society of America, vol. 101, no. 4, pp.1847–1858, 1997.

[77] J. Bamber, R. Mucci, and D. Orofino, “Spatial Coherence and BeamformerGain,” Acoustical Imaging, vol. 24, pp. 43–48, 2000.

[78] J. Bamber, R. Mucci, D. Orofino, and K. Thiele, “B-mode speckle texture: theeffect of spatial coherence,” Acoustical Imaging, vol. 24, pp. 141–146, 2000.

[79] W. Walker and G. Trahey, “The application of k-space in pulse echo ultra-sound,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Con-trol, vol. 45, no. 3, pp. 541–558, 1998.

[80] R. Mallart and M. Fink, “Adaptive focusing in scattering media through sound-speed inhomogeneities: The van Cittert Zernike approach and focusing crite-rion,” The Journal of the Acoustical Society of America, vol. 96, no. 6, pp.3721–3732, 1994.

151

[81] B. Geiman, L. Bohs, M. Anderson, S. Breit, and G. Trahey, “A novel interpo-lation strategy for estimating subsample speckle motion,” Physics in Medicineand Biology, vol. 45, no. 6, pp. 1541–1552, 2000.

[82] K. W. Hollman, K. W. Rigby, and M. O’Donnell, “Coherence factor of specklefrom a multi-row probe,” in Proceedings of the IEEE International UltrasonicsSymposium, vol. 2, 1999, pp. 1257–1260.

[83] P. Li and M. Li, “Adaptive imaging using the generalized coherence fac-tor,” IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control,vol. 50, no. 2, pp. 128–141, 2003.

[84] K. F. Ustuner, P.-C. Li, M.-L. Li, L. J. Thomas, and A. Gee, “Coherencefactor adaptive ultrasound imaging methods and systems,” Oct. 2005, uS2005/0228279 A1.

[85] D. Liu and R. Waag, “Correction of ultrasonic wavefront distortion using back-propagation and a reference waveform method for time-shift compensation,”The Journal of the Acoustical Society of America, vol. 96, p. 649, 1994.

[86] J. Camacho, M. Parrilla, and C. Fritsch, “Phase coherence imaging,” IEEETransactions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 56,no. 5, pp. 958–974, 2009.

[87] M. A. Lediju, M. J. Pihl, S. J. Hsu, J. J. Dahl, C. M. Gallippi, and G. E. Tra-hey, “A motion-based approach to abdominal clutter reduction,” IEEE Trans-actions on Ultrasonics, Ferroelectrics and Frequency Control, vol. 56, no. 11,p. 2437, 2009.

[88] M. O’Donnell and S. Flax, “Phase aberration measurements in medical ultra-sound: human studies,” Ultrasonic Imaging, vol. 10, no. 1, pp. 1–11, 1988.

[89] J. J. Dahl, M. S. Soo, and G. E. Trahey, “Spatial and temporal aberratorstability for real-time adaptive imaging,” IEEE Transactions on Ultrasonics,Ferroelectrics and Frequency Control, vol. 52, no. 9, pp. 1504–1517, 2005.

[90] J. J. Dahl, D. A. Guenther, and G. E. Trahey, “Adaptive imaging and spatialcompounding in the presence of aberration,” IEEE Transactions on Ultrason-ics, Ferroelectrics and Frequency Control, vol. 52, no. 7, pp. 1131–1144, 2005.

[91] S. S. Brunke, M. F. Insana, J. J. Dahl, C. Hansen, M. Ashfaq, and H. Ermert,“An ultrasound research interface for a clinical system,” IEEE Transactions onUltrasonics, Ferroelectrics and Frequency Control, vol. 54, no. 1, pp. 198–210,2007.

[92] S. Smith and H. Lopez, “A contrast-detail analysis of diagnostic ultrasoundimaging,” Medical Physics, vol. 9, p. 4, 1982.

152

[93] K. R. Nightingale, M. S. Soo, R. W. Nightingale, and G. E. Trahey, “AcousticRadiation Force Impulse imaging: In vivo demonstration of clinical feasibility,”Ultrasound in Medicine and Biology, vol. 28, no. 2, pp. 227–235, 2002.

[94] J. J. Dahl, D. M. Dumont, E. M. Miller, J. D. Allen, and G. E. Trahey, “Acous-tic radiation force impulse imaging for noninvasive characterization of carotidartery atherosclerotic plaques: A feasibility study,” Ultrasound in Medicineand Biology, vol. 35, no. 5, pp. 707–716, 2009.

[95] R. Righetti, J. Ophir, and P. Ktonas, “Axial resolution in elastography,” Ul-trasound in Medicine and Biology, vol. 28, no. 1, pp. 101–113, 2002.

[96] S. Srinivasan, R. Righetti, and J. Ophir, “Trade-offs between the axial reso-lution and the signal-to-noise ratio in elastography,” Ultrasound in Medicineand Biology, vol. 29, no. 6, pp. 847–866, 2003.

[97] Z. Wang, J. Li, and R. Wu, “Time-delay-and time-reversal-based robust caponbeamformers for ultrasound imaging,” IEEE Transactions on Medical Imaging,vol. 24, no. 10, pp. 1308–1322, 2005.

[98] J. J. Dahl, D. Hyun, M. A. Lediju, and G. E. Trahey, “Lesion detectabilityin diagnostic ultrasound with short-lag spatial coherence imaging.” UltrasonicImagaing, vol. 33, no. 2, p. 119, 2011.

[99] B. Steinberg, “Principles of aperture and array system design: Including ran-dom and adaptive arrays,” New York, Wiley-Interscience, 1976. 374 p., vol. 1,1976.

[100] C. Burckhardt, “Speckle in ultrasound B-mode scans,” IEEE Transactions onSonics and Ultrasonics, vol. 25, no. 1, pp. 1–6, 1978.

[101] B. Vandenberg, L. Rath, P. Stuhlmuller, H. Melton, and D. Skorton, “Esti-mation of left ventricular cavity area with an on-line, semiautomated echocar-diographic edge detection system,” Circulation, vol. 86, no. 1, pp. 159–166,1992.

[102] G. Bezante, G. Rosa, R. Bruni, X. Chen, G. Villa, A. Scopinaro, M. Balbi,A. Barsotti, and K. Schwarz, “Improved assessment of left ventricular volumesand ejection fraction by contrast enhanced harmonic color Doppler echocar-diography,” The International Journal of Cardiovascular Imaging (formerlyCardiac Imaging), vol. 21, no. 6, pp. 609–616, 2005.

[103] D. Skolnick, S. Sawada, H. Feigenbaum, and D. Segar, “Enhanced endocardialvisualization with noncontrast harmonic imaging during stress echocardiogra-phy,” Journal of the American Society of Echocardiography, vol. 12, no. 7, pp.559–563, 1999.

153

[104] M. Averkiou, D. Roundhill, and J. Powers, “A new imaging technique basedon the nonlinear properties of tissues,” vol. 2, October 1997, pp. 1561–1566.

[105] M. A. Lediju, B. C. Byram, and G. E. Trahey, “Sources and characterizationof clutter in cardiac b-mode images,” in Proceedings of the IEEE UltrasonicsSymposium, 2009, pp. 1419–1422.

[106] R. Lang, M. Bierig, R. Devereux, F. Flachskampf, E. Foster, P. Pellikka, M. Pi-card, M. Roman, J. Seward, J. Shanewise et al., “Recommendations for cham-ber quantification: a report from the american society of echocardiography’sguidelines and standards committee and the chamber quantification writinggroup, developed in conjunction with the european association of echocardio-graphy, a branch of the european society of cardiology.” Journal of the Amer-ican Society of Echocardiography: official publication of the American Societyof Echocardiography, vol. 18, no. 12, p. 1440, 2005.

[107] H. Becher, K. Tiemann, T. Schlosser, C. Pohl, N. Nanda, M. Averkiou, J. Pow-ers, and B. Luderitz, “Improvement in endocardial border delineation usingtissue harmonic imaging,” Echocardiography, vol. 15, no. 5, pp. 511–517, 1998.

[108] J. Kasprzak, B. Paelinck, F. Ten Cate, W. Vletter, N. de Jong, D. Polder-mans, A. Elhendy, A. Bouakaz, and J. Roelandt, “Comparison of native andcontrast-enhanced harmonic echocardiography for visualization of left ventric-ular endocardial border,” The American Journal of Cardiology, vol. 83, no. 2,pp. 211–217, 1999.

[109] M. Lediju Bell, B. Byram, E. Harris, P. Evans, and J. Bamber, “In vivo livertracking with a high volume rate 4d ultrasound scanner and a 2d matrix arrayprobe,” Physics in Medicine and Biology, vol. 57, p. 1359, 2012.

[110] M. Li and G. Hayward, “Ultrasound nondestructive evaluation (nde) imagingwith transducer arrays and adaptive processing,” Sensors, vol. 12, no. 1, pp.42–54, 2011.

[111] K. McLaughlin, H. Israelsson, and B. Kohl, “Evaluation of a time-domainadaptive beamformer for regional phase detection,” Bulletin of the Seismolog-ical Society of America, vol. 97, no. 6, pp. 1880–1889, 2007.

[112] T. Counts, G. Larson, A. Gurbuz, J. McClellan, and W. Scott Jr, “Investigationof the detection of shallow tunnels using electromagnetic and seismic waves,”in Proceedings of SPIE, vol. 6553, 2007, pp. 65 531G1–65 531G11.

[113] D. Jenn, Y. Loke, T. Matthew, Y. Choon, O. Siang, and Y. Yam, “Distributedphased arrays and wireless beamforming networks,” International Journal ofDistributed Sensor Networks, vol. 5, no. 4, pp. 283–302, 2009.

154

Biography

MUYINATU ADEBISI LEDIJU BELL

Date of Birth: August 3, 1984

Place of Birth: Brooklyn, NY USA

Education

Duke University, Durham, NC, USAPh.D., Biomedical Engineering, 2012

Institute of Cancer Research and Royal Marsden Hospital, Sutton, Surrey, UKVisiting Scholar, Joint Department of Physics, 2009-2010

Massachusetts Institute of Technology, Cambridge, MA, USAB.S., Mechanical Engineering with minor in Biomedical Engineering, 2006GPA: 4.7 / 5.0

Grants and Fellowships

2011 UNCF-Merck Graduate Science Research Dissertation Fellowship2009 Whitaker International Fellowship2008 NIH Research Supplement to Promote Diversity in Biomedical Research2008 NSF Graduate Research Fellowship Honorable Mention2006 NIH Medical Imaging Training Grant2006 Duke Endowment Fellowship

155

Refereed Publications

1. Lediju Bell MA, Trahey GE, Dahl JJ. Resolution characteristics of short-lagspatial coherence (SLSC) imaging, IEEE Transactions on Ultrasonics, Ferro-electrics, and Frequency Control, in preparation.

2. Lediju Bell MA, Byram BC, Harris EJ, Evans PM, Bamber JC. In vivo livertracking with a high volume rate 4D ultrasound scanner and a 2D matrix arrayprobe, Physics in Medicine and Biology, 57(3):1359-1374, 2012.

3. Dahl JJ, Hyun D, Lediju MA, Trahey GE. Lesion detectability in diagnos-tic ultrasound with short-lag spatial coherence imaging. Ultrasonic Imaging33(2):119-133, 2011.

4. Lediju MA, Trahey GE, Byram BC, Dahl JJ. Spatial coherence of backscat-tered echoes: Imaging characteristics, IEEE Transactions on Ultrasonics, Fer-roelectrics, and Frequency Control, 58(7):1377-88, 2011.

5. Lediju MA, Pihl MJ, Hsu SJ, Dahl JJ, Gallippi CM, Trahey GE. A motion-based approach to abdominal clutter reduction. IEEE Transactions on Ul-trasonics, Ferroelectrics, and Frequency Control, 56(11):2437-49, 2009 (key re-search results were selected for publication as the front cover image).

6. Lediju MA, Pihl MJ, Hsu SJ, Dahl JJ, Trahey GE. Quantitative assessmentof the magnitude, impact, and spatial extent of ultrasonic clutter. UltrasonicImaging, 30(3):151-168, 2008.

Conference Proceedings

1. Lediju Bell MA, Goswami R, Trahey GE. Clutter reduction in echocardiogra-phy with short-lag spatial coherence (SLSC) imaging, published in Proceedingsof the 2012 IEEE International Symposium on Biomedical Imaging, Barcelona,Spain, May 2-5, 2012.

2. Lediju Bell MA, Dahl JJ, Trahey GE. Comparative Resolution and Track-ing Performance in B-mode and Short-Lag Spatial Coherence (SLSC) Imaging,published in Proceedings of the 2011 IEEE International Ultrasonics Sympo-sium, Orlando, FL, October 18-21, 2011.

3. Dahl JJ , Pinton GF, Lediju MA, Trahey GE. A Novel Imaging TechniqueBased on the Spatial Coherence of Backscattered Waves: Demonstration inthe Presence of Acoustical Clutter, published in Proceedings of SPIE MedicalImaging 2011, Orlando, FL, February 12-17, 2011.

156

4. Lediju MA, Trahey GE, Jakovlijevic M, Byram BC, Dahl JJ. Short-Lag Spa-tial Coherence Imaging, published in Proceedings of the 2010 IEEE Interna-tional Ultrasonics Symposium, San Diego, CA, October 11-14, 2010.

5. Lediju MA, Byram BC, Harris EJ, Evans PM, Bamber JC. 3D Liver TrackingUsing a Matrix Array: Implications for Ultrasonic Guidance of IMRT, pub-lished in Proceedings of the 2010 IEEE International Ultrasonics Symposium,San Diego, CA, October 11-14, 2010.

6. Lediju MA, Byram BC, Trahey GE. Sources and Characterization of Clutterin Cardiac B-mode Images, published in Proceedings of the 2009 IEEE Inter-national Ultrasonics Symposium, Rome, Italy, September 20-23, 2009.

7. Dahl JJ, Pinton GF, Lediju MA, Trahey GE. Simulation and ExperimentalAnalysis of Ultrasonic Clutter in Fundamental and Harmonic Imaging, pub-lished in Proceedings of SPIE Medical Imaging 2009, Orlando, FL, February7-12, 2009.

8. Lediju MA, Pihl MJ, Hsu SJ, Dahl JJ, Gallippi CM, Trahey GE. Magnitude,origins, and reduction of abdominal ultrasonic clutter, published in Proceed-ings of the 2008 IEEE International Ultrasonics Symposium, Beijing, China,November 2-5, 2008.

9. Dahl JJ, Lediju MA, Pihl MJ, Hsu SJ, Gallippi CM, Trahey GE. Clutterreduction methods from compression of tissue, Sixth International Conferenceon the Ultrasonic Measurement and Imaging of Tissue Elasticity, Santa Fe,New Mexico, November 2-5, 2007.

Intellectual Property

1. Dahl JJ, Lediju MA, Trahey GE, Method and Apparatus for Van-CittertZernike Imaging, Duke University (USPTO application filed 2011)

157

Documents

Improved Endocardial Border Definition with Short-lag Spatial