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High frequency ultrasound elastography and its biomedical applications

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High frequency ultrasound elastography and its biomedical applications

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High Frequency Ultrasound Elastography
and its Biomedical Applications

By

Xuejun Qian

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(BIOMEDICAL ENGINEERING)

May 2019
II

Dedication

To my beloved
Parents
Jiheng Qian & Chunfang Lu

Portion of chapter 2 ©2017 NPG, chapter 3 and chapter 4 ©2018 IEEE
All other materials © 2019 Xuejun Qian

Xuejun Qian

All Rights Reserved

III

Acknowledgements
The thesis would not have been possible without the help of so many people in so many
ways. This four years journey through graduate school has brought me in contact with
many wonderful people who have contributed immensely to my personal development as
a scientist and engineer, and to the development of high frequency ultrasonic imaging on
medical applications.
First, I am sincerely grateful to Dr. Qifa Zhou and Dr. K. Kirk Shung for their
supervision, mentoring and support throughout my doctoral research. From the first time
that I entered our NIH Ultrasonic Transducer Resource Center (UTRC), I know little
knowledge about ultrasound, to the present day that I’m able to fabricate ultrasonic
transducer, build my own ultrasound imaging system as well as many imaging processing
skills. Your patient, your profound knowledge, your trust encourage me to become better
and better. I have to say that you are truly great mentors who pass to me not only their
knowledge but also their life philosophy. Thank you so much, Dr. Zhou and Dr. Shung.
I also like to express my sincere gratitude to other committee members of my
dissertation, Dr. Keith Jenkins, Dr. Michael Khoo and Dr. Megan Laura McCain for their
insightful suggestions and valuable time.
I would like to acknowledge our collaborators, Dr. Mark S. Humayun, Dr. Martin Heur,
Dr. Edward Grant and Dr. Ronald H. Silverman for sharing their expertise and clinical
perspectives for this research.
I am greatly thankful to all my colleagues and friends of UTRC lab at the University of
Southern California, Dr. Ruimin Chen, Dr. Harry Chiu, Dr. Teng Ma, Dr. Yang Li, Dr.
Zeyu Chen, Dr. Mingyue Yu, Dr. Nestor Cabrera, Mr. Runze Li, Mr. Haocheng Kang and
IV

Mr. Gengxi Lu, our visiting scholar Dr. Xiaoyang Chen, Dr. Jun Zhang, Dr. Ming Qian,
Dr. Di Li, Dr. Zhiqiang Zhang, Dr. Hanmin Peng and our budget analyst Peter Lee, Tanisha
Hughes, Sydney Burke. We have been working together for many years and shared a lot
pains and happiness. They supported me throughout my study and made my stay at the
center an enjoyable experience. I will miss all of you.
Lastly, I would like to thank my parents and family for their unconditional love,
guidance, and encouragement throughout my dissertation work. Mother and Father, this
dissertation is dedicated to you.

V

Table of Contents

Dedication ....................................................................................................................................... II
Acknowledgements ....................................................................................................................... III
Table of Contents ............................................................................................................................ V
List of Tables ................................................................................................................................ VII
List of Figures ............................................................................................................................. VIII
Abstract ........................................................................................................................................... X
Chapter 1 Introduction ..................................................................................................................... 1
1.1 Soft Tissue Biomechanics ..................................................................................................... 1
1.2 Ultrasonic Elasticity Imaging ................................................................................................ 3
1.2.1 Pushing Methods ............................................................................................................ 4
1.2.2 Detection Methods .......................................................................................................... 5
1.3 Motivations and Objectives ................................................................................................... 7
1.4 Outline ................................................................................................................................... 8
Chapter 2 The Development of High Resolution Ultrasonic Elastography Imaging System ....... 11
2.1 Background and Literature Review ..................................................................................... 11
2.2 Methods and Materials ........................................................................................................ 14
2.2.1 System Configuration and Data Acquisition ................................................................ 14
2.2.2 Imaging Subjects Preparation ....................................................................................... 17
2.2.3 ARF based Elastography Imaging ................................................................................ 18
2.3 Results ................................................................................................................................. 21
2.3.1 Acoustic Parameters of Ultrasonic Transducers ........................................................... 21
2.3.2 Gelatin Tissue Mimicking Phantom Imaging ............................................................... 22
2.3.3 Spatial Resolution and Image Contrast ........................................................................ 27
2.3.4 Ex vivo Chicken Liver .................................................................................................. 29
2.4 Discussion and Conclusion.................................................................................................. 30
Chapter 3 Ultrasonic Micro-elastography System on Assessing Corneal Biomechanics ............. 35
3.1 Introduction ......................................................................................................................... 35
3.2 Materials and Methods ........................................................................................................ 38
3.2.1 Experimental Setup ...................................................................................................... 38
3.2.2 Viscoelastic model ........................................................................................................ 40
VI

3.2.2 Post-processing and data analysis................................................................................. 41
3.2.3 Porcine Cornea Preparation .......................................................................................... 44
3.3 Results ................................................................................................................................. 46
3.3.1 Cross-linked Corneal Biomechanics ............................................................................ 46
3.3.2 Corneal Biomechanics with respect to IOPs ................................................................ 49
3.4 Discussion and Conclusion.................................................................................................. 52
Chapter 4 Quantitative Assessment of Thin Layer Tissue Viscoelastic Properties Using Lamb
Wave Model .................................................................................................................................. 60
4.1 Introduction ......................................................................................................................... 60
4.2 Materials and Methods ........................................................................................................ 63
4.2.1 Lamb Wave Model ....................................................................................................... 63
4.2.2 Data Collection and Processing .................................................................................... 65
4.2.3 Phantom and Biological Tissue Preparation ................................................................. 68
4.3 Results ................................................................................................................................. 71
4.4 Discussion and Conclusion.................................................................................................. 79
Chapter 5 Array based Elastography Imaging System .................................................................. 84
5.1 Introduction ......................................................................................................................... 84
5.2 Methods ............................................................................................................................... 86
5.2.1 Ultrafast plane wave imaging ....................................................................................... 86
5.2.2 Array based elastography system ................................................................................. 87
5.2.3 Imaging Subject ............................................................................................................ 89
5.3 Results and Discussion ........................................................................................................ 89
Chapter 6 Summary and Future Work ........................................................................................... 92
6.1 Summary ............................................................................................................................. 92
6.2 Future Work ........................................................................................................................ 93
BIBLIOGRAPHY ......................................................................................................................... 94

VII

List of Tables
Table 4-1. Shear elasticity and shear viscosity of 7%, 12% gelatin and 1.5% agar phantoms with
thickness of 2, 3, 4 mm obtained by fitting the Lamb wave model to the experimental data from the
impulse and harmonic methods against the results of mechanical tests and shear wave model in the
bulk phantoms. .............................................................................................................................. 69
Table 5-1. The FWHM spatial resolution of the linear array transducer. ...................................... 89

VIII

List of Figures
Figure 1-1. Ultrasound elastography among breast, liver, carotid artery and prostate tissue. (Source
data is from Google Images) ........................................................................................................... 3
Figure 2-1. Schematic diagram of designed multi-functional ultrasonic micro-elastography
imaging system. (a) The experimental setup and transducer parameters calibration, (b) The
synchronized timing sequence controlled by multi-functional ultrasonic micro-elastography
imaging system. ............................................................................................................................. 16
Figure 2-2. The principle comparison and analysis of ARFI and SWEI. ..................................... 19
Figure 2-3. Imaging system validation on homogenous gelatin phantom. (a-c) Dynamic
displacement curve under different excitation voltage/ excitation duration and phantom stiffness.
B-mode/ ARFI/ SWEI images of homogenous phantom (d-f) 2% gelatin concentration, (g-i) 5%
gelatin concentration. .................................................................................................................... 22
Figure 2-4. Bi-layer phantom imaging results and its corresponding FWHM resolution. 2D cross-
sectional B-mode image, ARFI image and SWEI image (a-c) Left-right phantom with a vertical
boundary at a width of 1.6 mm, (g-i) Up-down phantom with a horizontal boundary at a depth of
0.8 mm; (d,j) schematic diagram of uniformly selected curve profiles, N = 20 for both Left-right
phantom and Up-down phantom; Lateral FWHM resolution model of (e) ARFI image and (f) SWEI
image; Axial FWHM resolution model of (k) ARFI image and (l) SWEI image. ........................ 23
Figure 2-5. Inclusion phantom imaging results and transitional curve profiles. (a-c) 2D cross-
sectional B-mode image, ARFI image and SWEI image. The raw data profiles (d) at a depth of 1.1
mm and (g) at a width of 1.8 mm were selected. The raw data and fitted curve of ARFI and SWEI
at (e,f) lateral direction, (h,i) axial direction. The phantom has a 1.2mm diameter cylinder inclusion
with a background-interior-background structure. ........................................................................ 25
Figure 2-6. 3D visualization of a side by side gelatin tissue-mimicking phantom. (a) B-mode image,
(b) ARFI image and (c) SWEI image. Volume dimensions (xyz) are 1.8mm× 3.6mm× 2mm....... 26
Figure 2-7. Ex vivo 3D visualizations of chicken liver. (a-c) Normal liver and (d-f) Liver with
artificially induced “fibrosis” using formalin solution. Volume dimensions (xyz) are
1.2mm× 2mm× 1.8mm. The red arrows in (d-f) indicate the position of formalin injection. ......... 29
Figure 3-1. Schematic diagram of the ultrasonic micro-elastography system and the synchronized
timing sequence for the excitation and detection transducers. Two transducer are first confocally
aligned before the experiment. A commercial artificial anterior chamber was used here to hold the
cornea tissue. ................................................................................................................................. 40
Figure 3-2. The post-processing procedures to emphasis how to get the phase velocity curve from
the experimental collected axial displacement maps. (a) axial displacement map, (b) k-space, (c)
phase velocity curve, and (d) fitting curve with selected frequency range from 200 Hz to 800 Hz
with a 50 Hz interval. .................................................................................................................... 43
Figure 3-3. A time series of B-mode and ARFI images for one cornea sample. The blue arrow
indicates the small spot of formalin drop between each time-point. (a,e) control group with no
formalin drop; experimental groups with (b,f) 2 minutes, (c,g) 5 minutes and (d,h) 10 minutes
formalin drop. In the cross-linking experiments, the intraocular pressure was set at 5 mmHg so as
to maintain normal corneal curvature. ........................................................................................... 46
Figure 3-4. The reconstructed 3D B-mode and ARFI maps of the cornea (a,c) at control condition,
(b,d) at experimental condition – 20 minutes after formalin-induced sclerosis. (e,f) show shear wave
propagation and current (after 1.5 ms ARF excitation) wave fronts position marked by gray dash
lines. The red arrow indicates the ARF excitation position which is 2mm away from the central
IX

cornea. The blue arrow indicates the site of formalin drop. Volume dimensions (xyz) are 4.8 mm
× 1.5 mm × 1 mm for (a-d) and 6 mm × 1.5 mm × 1 mm for (e-f), respectively. ............................. 47
Figure 3-5. B-mode and ARFI images of the cornea under various intraocular pressure. (a,g) – 5
mmHg, (b,h) – 10 mmHg, (c,i) – 15 mmHg, (d,j) – 20 mmHg, (e,k) – 25 mmHg and (f,l) – 30
mmHg. The ROI is +/- 0.5 mm of the central cornea which was relative uniformly distributed
demonstrated by high resolution ARFI images. ............................................................................ 49
Figure 3-6. Shear wave propagation after (a) 0.1 ms, (b) 0.3 ms and (c) 0.5 ms ARF excitation. It
was observed that the shear wave propagates faster at higher IOP. Based on high resolution ARFI
images, the Young’s modulus of the cornea under different IOP were reconstructed within +/- 0.5
mm uniform region. ....................................................................................................................... 50
Figure 3-7. The averaged Young’s modulus of the cornea at elevated IOPs. And it expressed as a
linear relationship within the normal physiological IOP range (12-22 mmHg). ........................... 52
Figure 4-1. Scanning scheme of high frequency ultrasonic micro-elastography imaging system (a)
and representative timing diagram for the impulse method and the harmonic method (b). .......... 65
Figure 4-2. Flow chart for the post processing ............................................................................ 66
Figure 4-3. Results of each post-processing step by performing the impulse method (a)-(d) and the
harmonic method (e)-(f) in the 7% gelatin phantom with a thickness of 4 mm. Axial displacement
map (a) and (e), k-space (b) and (f), phase velocity curve (c) and (g) as well as fitting curve (d) and
(h), are presented. .......................................................................................................................... 71
Figure 4-4. Group velocity and the phase velocity in 7% gelatin (a), 12% gelatin (b) and 1.5% agar
phantoms (c). ................................................................................................................................. 73
Figure 4-5. Experimental phase velocity (symbols) of gelatin and agar phantoms with different
thicknesses of 4 mm (a) and (d), 3 mm (b) and (e), and 2 mm (c) and (f), as well as their
corresponding fitting curve (lines) from the impulse method (a)-(f) and the harmonic method (g)-
(i). .................................................................................................................................................. 74
Figure 4-6. Shear elasticity of 7% gelatin (a), 12% gelatin (b) and 1.5% agar phantoms (c) with
thicknesses of 2, 3 and 4 mm against the results of the mechanical tests and the shear wave
rheological model in the bulk phantoms. ...................................................................................... 76
Figure 4-7. Shear viscosity of 7% gelatin (a) and 12% gelatin (b) with thicknesses of 2, 3 and 4
mm against the results of the shear wave rheological model in the bulk phantoms. ..................... 77
Figure 4-8. Phase velocity of porcine cornea and its corresponding fitting curve by using the
impulse and harmonic method....................................................................................................... 78
Figure 4-9. Phase velocity of rabbit carotid artery and its corresponding fitting curve by using the
impulse and harmonic method....................................................................................................... 78
Figure 5-1. Verasonics system and its array transducers. (Source data from Verasonics website)
....................................................................................................................................................... 85
Figure 5-2. The photography of the array elastography system setup. The pushing and array
transducer were aligned using a wire phantom where the focal point of the pushing transducer is
located in the middle of the array transducer. ............................................................................... 88
Figure 5-3. The B-mode image and shear wave propagation at three time-series of (a) the 6%
gelatin concentration tissue-mimicking phantom, and (b) one ex vivo posterior segment of porcine
eyeball. The shear wavefronts were clearly observed along all directions of phantom and the
curvature of posterior sclera. According to the shear wavefront location and propagation time, the
Young’s modulus of phantom/posterior sclera was reconstructed from the estimated shear wave
speed. The arrow in the figures showed that the region of the applied ARF force and the dash line
described the boundary of the sclera tissue observed from B-mode image. ................................. 91

X

Abstract
Based on the fact that a pathological process alters the elastic properties of the involved
tissue, the biomechanical properties of the soft tissue therefore provide an additional
contrast and clinically relevant information for disease diagnosis and tissue
characterization. To measure the tissue biomechanics, a medical imaging modality called
elastography, has been the focus of intense research activity since the mid-1990s.
Acoustic radiation force (ARF) based ultrasonic elastography methods, such as
acoustic radiation force impulse (ARFI) imaging, shear wave elasticity imaging (SWEI),
and supersonic shear imaging (SSI), capitalizing on the advantage of synchronization of
ARF excitation and ultrasonic detection, have been used to characterize the tissue
biomechanical properties in a more effective and accurate manner. However, most of the
current ultrasonic elastography studies, utilizing the standard clinical frequency range (1-
20 MHz), could only provide spatial resolution up to sub-millimeter level and significantly
narrows some clinical applications that needs micron-scale level visualization. For
example, thin layer tissues such as the artery and ocular tissues.
The work presented in this dissertation investigates an ultrasonic micro-elastography
imaging technique utilizing the dual frequency configuration to fill the gaps between
conventional ultrasound elastography and optical coherence elastography (OCE) on
imaging resolution and penetration depth. The low frequency transducer which can sustain
high voltage and long duration has the ability to generate enough “pushing force”, and high
frequency transducer with good spatial resolution is used to map elasticity distribution. The
developed system was first calibrated through gelatin mimicking phantoms, and then
implemented on a thin layer tissue - the cornea. In addition, an advanced model - Lamb
XI

wave model is proposed to increase the accuracy of the reconstructed Young’s modulus by
considering the shear wave dispersion issue. All these results demonstrate the capability of
the developed ultrasonic micro-elastography imaging system on potential clinical
application – thin layer tissue. Lastly, due to the low frame rate of single-element based
micro-elastography system, we have improved this technique using high frequency array
transducer which has both high resolution and high frame rate. The preliminary studies has
been shown on posterior sclera tissue.
1

Chapter 1 Introduction
1.1 Soft Tissue Biomechanics
Many diseases cause changes in the mechanical properties of tissues which can barely
be detected by its structural information. To be specific, the propagation of mechanical
waves allows the construction of morphological images of organs or tissues (Sarvazyan et
al., 2013), but lacks a fundamental and quantitative information on tissue elastic properties.
Manual palpation has been served as a standard in routine physical examinations to assist
physicians in decision making. Typically, the growth of malignant tumors replacing the
healthy tissues will have an increased stiffness of the local tissues. Thus, given the fact that
the biomechanical properties of soft tissues are highly correlated to pathological and
functional change such as the growth of tumor, inflammation infection (Fung, 2013), the
study of soft tissue biomechanics is of particular significance and attracts an increasing
interest in recent decades (Doyley and Parker, 2014; Parker et al., 2010). It has been shown
that the change in tissue elastic properties would provide additional diagnosis information
in many medical applications, such as breast tumors (Krouskop et al., 1998), liver disease
(Liedtke et al., 2013; Rouviere et al., 2006), calcific aortic tissues (Blacher et al., 2001),
and so forth.
Soft tissues are viscoelastic, inhomogeneous, and anisotropic material, which means it
contains the properties of both elastic solids and viscous fluids (Famaey and Sloten, 2008;
Achenbach, 2012). Under the assumption of relatively small strains, soft tissues are often
described as linear, elastic solids. In general, the tissue stiffness can be quantified by
several mechanical parameters such as Young’s modulus (𝐸 , a material’s resistance to
2

deformation in uniaxial compression or tension), shear modulus (𝜇 , the resistance to shear,
angular deformation) or bulk modulus (𝜅 , the molecular structure of soft tissue properties).
The Young’s modulus is determined by the ratio of the stress (𝜎 ) and the corresponding
strain (𝘀 ), as shown in equation (1-1). Stress represents the force per unit area that
counteracts the applied force, and the strain relates the deformed configuration of a material
to its initial reference configuration (Doherty et al., 2013).
𝐸 =
𝜎 𝜀 =
𝐹 𝐴 ⁄
∆𝐿 𝐿 ⁄
(1-1)
where 𝐸 is the Young’s modulus, 𝐹 is the applied force, 𝐴 is the surface area, ∆𝐿 is the
tissue displacement, 𝐿 is the original thickness. By further assuming homogeneous and
isotropic, an equation (1-2) derived from Hooke’s Law describing the relationship between
stress and strain can be represented as
𝜎 𝑖𝑗
= 𝜆 𝛿 𝑖𝑗
𝘀 𝑘𝑘
+ 2𝜇 𝘀 𝑖𝑗
(1-2)
where (𝜆 ) and (𝜇 ) are two material coefficients known as the Lamé constants, 𝘀 𝑖𝑗
is the
strain, 𝜎 𝑖𝑗
is the stress and 𝛿 𝑖𝑗
is the Kronecker delta.
In the case of simple uniaxial stress, the following equations (1-3, 1-4) related with
Young’s modulus and Poisson’s ratio (𝜈 ) are achieved:
𝘀 𝑖𝑗
=
1+𝜈 𝐸 𝜎 𝑖𝑗
−
𝜈 𝐸 𝛿 𝑖𝑗
𝜎 𝑘𝑘
(1-3)
𝜆 =
𝐸𝜈
( 1+𝜈 ) ( 1−2𝜈 )
, and 𝜇 =
𝐸 2( 1+𝜈 )
(1-4)
For incompressible materials, the Poisson’s ratio is 0.4999, thus the shear modulus can
be linked with the Young’s modulus using equation (1-5):
𝜇 =
𝐸 3
(1-5)
3

1.2 Ultrasonic Elasticity Imaging

Figure 1-1. Ultrasound elastography among breast, liver, carotid artery and prostate tissue. (Source data is
from Google Images)

Palpation, a simple method to quantify the tissue stiffness, has been successfully
validated in breast tumor characterization and liver fibrosis stages. However, palpation has
some limitations – need a direct contact and can only be applied to superficial organs.
Elastography, an imaging based technology to estimate tissue biomechanical properties
through tissue displacement, stiffness or viscoelastic parameters that could help
differentiate benign from malignant (Sarvazyan et al., 2011; Doherty et al., 2013) has been
4

proposed since 1990s. Different from palpation, elastography has the ability to
quantitatively image the stiffness distribution of the soft tissues deep inside organs. It opens
new diagnostic possibility in healthcare. Compared with other diagnostic imaging
modalities such as Computed Tomography, Magnetic Resonance Imaging and Optical
Imaging, ultrasound imaging is widely used in clinical practice for more than 40 years
because of its ease of use, real time capability and low cost. Therefore, in this research,
ultrasound based elastography technique will be discussed. Figure 1-1 lists some potential
ultrasound elastography applications, including breast lesion, liver fibrosis, carotid artery
and prostate tissue.
To assess the biomechanical properties of soft tissues, the elastography technique
requires an external pushing force to induce the tissue deformation and a tracking method
to capture the resulting movements.

1.2.1 Pushing Methods
In general, there are two excitation modes. One is quasi-static to achieve a steady-state
response. Another one is the dynamic method utilizing either external force or internal
force.
In the case of quasi-static excitation, a slow constant compressive stress is applied on
the tissues. Its deformation and the generated strain can be estimated using cross-
correlation techniques on radio-frequency (RF) signals. To avoid decorrelation and retain
the good singal to noise ratio (SNR), the strain level is on the order of 1%.
In dynamic excitation, the force is time-dependent parameter which can be either using
external force or internal force in the form of transient or periodic stresses. The induced
5

tissue deformation could be estimated from on-axis tissue displacement at the region of
excitation, or through the shear wave propagation.
Compared with external force, internal force attracts an increasing interest in recent
years because of its ability to have a controllable force deep inside the tissue. A typical
approach to generate an interval vibration is the use of the acoustic radiation force (ARF).
The phenomenon of ARF generation results from the propagation of acoustic waves
through a dissipative medium. It is caused by a transfer of momentum from the wave to
the medium, arising either from absorption or scattering. In general, the contribution to the
ARF by scattering in soft tissues can be neglected. Thus, in an absorbing medium, and
under plane wave assumptions, the ARF can be defined as (1-6):
𝐹 =
2𝛼𝐼
𝑐 (1-6)
where 𝐹 is acoustic radiation force, 𝛼 is the absorption coefficient of the medium, 𝑐 is the
speed of sound in the medium, 𝐼 is the temporal average intensity at a given point in space
(Palmeri et al., 2005; Torr, 1984). For a focused acoustic beam, the radiation force is
applied throughout the focal region of the acoustic beam. The region of excitation (ROE)
defines the focal zone of the ARF. The generated wave at the edges of ROE which
propagates orthogonally to the direction of the ARF is shear waves. The speed of shear
wave propagation is typically linked with shear modulus for quantitative estimation.

1.2.2 Detection Methods
Based on requirements of qualitative or quantitative estimation, the detection mode can
be categorized to on-axis methods (via acoustic radiation force impulse, ARFI) to provide
6

relative measurement or off-axis methods (via the speed of shear wave propagation which
is directly linked to shear modulus).
In this research, we are focusing on the most popular two approaches – ARFI and SWEI
imaging.

1) Acoustic radiation force impulse (ARFI) imaging:
It was proposed by Nightingale et al (Nightingale et al., 2001; Nightingale et al., 2002).
Three different pulse types are involved in ARFI. First, reference pulses are acquired to
record the initial position of target region. Then, excitation pulses (typically few hundred
micron seconds) are fired to induce tissue deformation. Finally, detection pulses are applied
to monitor the recovery process of the soft tissue. Using either phase-shift or normalized
cross correlation algorithm, the axial displacement versus time curve is established. The
relative stiffness of the soft tissue can be expressed as the maximum tissue displacement,
the time to reach the maximum displacement or the time to recovery back to original tissue
position. In this research, maximum displacement is selected as the expression form
(equation 1-7) of ARFI.
𝐸 1
𝐸 2
= 𝑘 ∆𝐿 2
∆𝐿 1
(1-7)
where 𝐸 is the Young’s modulus, ∆𝐿 is the tissue displacement, 𝑘 is determined by the
ratio of acoustic attenuation in two different samples.

2) Shear wave elasticity imaging (SWEI):
7

In 1998, Sarvazyan et al. came up with SWEI method by combining ultrasound
excitation and MRI detection to quantify tissue stiffness (Sarvazyan et al., 1998). Later,
Nightingale et al. implemented this concept using conventional pulse-echo ultrasound to
monitor shear wave propagation outside the ROE (Nightingale et al., 2003). The positions
of detection pulses are the only difference between ARFI and SWEI. The shear wave speed
is typically determined using time-of-flight (TOF) methods. The reconstructed shear wave
speed, so called group velocity, can be calculated by the ratio of total propagation distance
of shear wave front and travel time or estimated using linear regression between lateral
positive and the wave arrival time. The Young’s modulus of the soft tissue is then
reconstructed using the well-known equation (1-8)
𝐸 = 3𝜌 𝐶 𝑠 2
(1-8)
where E is the Young’s modulus, ρ is the tissue density, C
s
is the shear wave speed.

1.3 Motivations and Objectives
Most of the commercial and research ultrasonic elastography studies, carried out in
the standard clinical frequency range, could only provide spatial resolution ranging from
sub-millimeter to several millimeters and significantly narrows clinical applications that
require microscale level visualization, for example, early stage cancer diagnosis, tumor
margin detection, ophthalmologic tissue characterization, and atherosclerotic plaque
composition analysis. Optical coherence elastography (OCE), the so-called optical
analog of ultrasonic elastography, is a newly developed high resolution elastography
technique based on the optical coherence tomography (OCT) (Kennedy et al., 2015;
Nguyen et al., 2014; Kennedy et al., 2011). Within the classification of OCE, acoustic
8

radiation force optical coherence elastography (ARF-OCE) (Qi et al., 2014) and
ultrasonically-induced shear wave optical coherence elastography (Zhu et al., 2015;
Ambroziński et al., 2016; Nguyen et al., 2015) are the prominent techniques that
combine the dynamic ultrasonic excitation and high resolution optical detection for
characterizing the biomechanical properties of soft tissue at the microscale level.
However, similar to other optical techniques, the shallow penetration depth significantly
limits its translational potential in the clinical study. To fill the gap between
conventional ultrasonic elastography and OCE on spatial resolution and penetration
depth, developing a high resolution ultrasonic elastography attracts an increasing
interest in both research and clinical studies.

1.4 Outline
The thesis proposal is outlined as follows:
Chapter 1 introduces the concept of soft tissue biomechanics and its clinical requirement
for elasticity imaging. Then, a more controllable and accurate excitation method called
acoustic radiation force (ARF) was introduced. The ARF based ultrasonic elastography
including ARFI and SWEI are proposed to quantify tissue biomechanics in both qualitative
and quantitative ways. Finally, the motivation and potential clinical needs for developing
high frequency ultrasound based elastography technique are addressed.
Chapter 2 proposes the newly developed multi-functional ultrasonic micro-elastography
imaging system. The proposed system has the ability to provide both qualitative (via ARFI)
and quantitative (via SWEI) measurements of tissue biomechanical properties. System
parameters such as image contrast, imaging field of view, spatial resolution are measured
9

from bi-layer gelatin based tissue mimicking phantom. The performance of our proposed
micro-elastography imaging system were further validated on inclusion phantom and ex
vivo chicken liver tissue.
Chapter 3 applies the ultrasonic micro-elastography imaging system into a micron size
structure tissue – porcine cornea (typically, corneal thickness is around 0.8 mm). To further
evaluate the capability of our imaging system, the small changing biomechanical properties
of the cornea were observed on either cross-linked cornea (cross-linking is a clinical
surgery to halt the progress of ectasia) or cornea with various intraocular pressure levels
(IOP is major determination factor for glaucoma).
Chapter 4 investigates the effect of thin-layer structure on shear modulus reconstruction.
The cornea or artery is a plate-like tissue whose thickness is relative to shear wave
wavelength. The group velocity extracted from previous chapter is not accurate and may
lead to some bias because of boundary conditions. The mode type of generated mechanical
waves in thin-layer tissue is a guided Lamb wave with significant frequency dispersion
(phase velocity) instead of conventional group velocity. Thus, this chapter describes the
integrating of a lamb wave model with our developed micro-elastography system to
quantify the viscoelastic properties of either cornea or artery.
Chapter 5 shows the preliminary studies on array based elastography system which
utilizing a low frequency pushing transducer and a high frequency linear array transducer.
The array based elastography system enables to tracking the shear wave propagation at a
high frame rate. The performance of the array based elastography was first validated on a
homogenous phantom and then applied on ex vivo posterior sclera tissue.
10

Chapter 6 summaries the current work on ultrasonic micro-elastography imaging system,
including system calibration, imaging subjects of cornea and artery tissues. The
preliminary study on posterior sclera using array based elastography system was proposed
as well. The future work will focus on two aspects. One is to optimize the array system
using advanced beamforming technique and modeling. Another is to design and implement
2D array to fully reconstruct the 3D spatial information.

11

Chapter 2 The Development of High Resolution Ultrasonic
Elastography Imaging System
2.1 Background and Literature Review
It was documented that the tissue biomechanics are highly correlated to pathological
and functional change such as the growth of tumor, inflammation and infection (Fung,
2013). Elastography, a medical imaging modality, is able to provide an additional
contrast mechanism and clinically relevant information for disease diagnosis and tissue
characterization (Doyley and Parker, 2014; Parker et al., 2010). To build an elastography
imaging system typically needs a pushing source and a tracking source. The pushing
source is responsible for inducing a small deformation inside the tissue (strain less than
1%) via static compression or dynamic vibration, and the tracking part utilizes the
traditional imaging techniques, such as ultrasound (Shung, 2015), magnetic resonance
imaging (MRI) (Muthupillai et al., 1995) and optical coherence tomography (OCT)
(Huang et al., 1991), to track the on-axis tissue displacement or off-axis generated shear
wave propagation.
In early 1990s, quasistatic ultrasonic elastography has been developed to diagnose
the liver fibrosis and breast cancer by measuring the deformation of soft tissue under a
manual compression force (Ophir et al., 1991). However, the diagnostic procedure of
quasistatic elastography is highly dependent on the physician’s experience, and its
accuracy is distorted by any intervening tissue and an increase in penetration depth. In
the recent decade, acoustic radiation force (ARF) has been developed to serve as the
remote pushing source to precisely induce a controllable deformation deep inside the
12

region of interest (ROI) (Doherty et al., 2013; Palmeri and Nightingale, 2011). Based
on various combinations of pushing and tracking approaches, many ARF-based
ultrasonic elastography methods has been proposed. They are but not limited to acoustic
radiation force impulse (ARFI) imaging (Nightingale et al., 2001; Nightingale et al.,
2002), shear wave elasticity imaging (SWEI) (Sarvazyan et al., 1998; Nightingale et al.,
2003), harmonic motion imaging (HMI) (Konofagou and Hynynen, 2003; Ma et al.,
2015) and supersonic shear imaging (SSI) (Bercoff et al., 2004). Owing to the
synchronization of ARF pushing force and ultrasonic tracking beams, ARF-based
ultrasonic elastography has been proven to quantify the mechanical properties of soft
tissues in a more effective and accurate manner. However, the spatial resolution of most
of current ultrasonic elastography studies is up to sub-millimeter level, which is mainly
restricted by the implementation of relative low frequency transducers (1 – 20 MHz).
As a result, it significantly narrows clinical applications that require microscale level
visualization, for example, early stage cancer diagnosis, tumor margin detection,
ophthalmologic tissue characterization, and atherosclerotic plaque composition analysis.
Optical coherence elastography (OCE), the so-called optical analog of ultrasonic
elastography, is a newly developed high resolution elastography technique based on the
OCT (Kennedy et al., 2015; Nguyen et al., 2014; Kennedy et al., 2011). Within the
classification of OCE, acoustic radiation force optical coherence elastography (ARF-
OCE) (Qi et al., 2014) and ultrasonically-induced shear wave optical coherence
elastography (Zhu et al., 2015; Ambroziński et al., 2016; Nguyen et al., 2015) are the
prominent techniques that combine the dynamic ultrasonic excitation and high
resolution optical detection for characterizing the biomechanical properties of soft tissue
13

at the microscale level. However, similar to other optical techniques, the shallow
penetration depth significantly limits its translational potential in the clinical study.
To fill the gap between conventional ultrasonic elastography and OCE on spatial
resolution and penetration depth, developing a high resolution ultrasonic elastography
attracts an increasing interest in both research and clinical studies. To achieve this goal,
the novel methodology of combining low-frequency transducer as ARF pushing source
and high-frequency transducer to precisely track ARF induced tissue motion has been
raised. Specifically, Shih et al. accomplished ARFI imaging to assess the porcine
corneal sclerosis by using a dual-frequency confocal transducer (Shih et al., 2013),
however, the fixed confocal transducer impairs its capability to track the off-axis
generated shear wave propagation whose speed is directly linked with the absolute
Young’s modulus of the tissue. In addition, the focused tracking element has a small
ROI, resulting in additional axial depth scanning to increase its field of view (FOV) at
the expense of time. Later, Yeh et al. implemented SWEI to monitor the process of
mouse liver fibrosis using two side by side single-element transducers (Yeh et al., 2015).
The absolute Young’s modulus at different liver fibrous stages were measured by the
moving tracking transducer and reconstructed using time of flight shear wave speed
reconstruction algorithm. One limitation of this study is that no 2D/3D elasticity image
or spatial resolution were reported.
To the best of knowledge, there is no study to show that ARF-based ultrasound-only
elastography achieved a micron-level imaging resolution together with a large FOV. To
achieve this goal, we have developed a multi-functional ultrasonic micro-elastography
imaging system to provide both qualitative (via ARFI) and quantitative (via SWEI)
14

measurements of tissue biomechanical properties on the microscale with Young’s
modulus in the range of 0.1–100 kPa. Since the open platform of high frequency
ultrasound array transducer (>35 MHz) and its corresponding imaging system are not
released, herein, dual frequency single-element transducers, including a 4.5 MHz
focused ring shape transducer to generate effective ARF pushing force and a 40 MHz
unfocused needle transducer to precisely detect tissue deformation, were designed and
implemented to demonstrate the concept of ultrasonic micro-elastography. The
performance of our high-resolution imaging system was verified on 2D/3D gelatin
tissue-mimicking phantoms and an ex vivo chicken liver, in which ARFI provides a
higher spatial resolution and a faster data acquisition speed, whereas SWEI affords the
absolute Young’s modulus and a better image contrast. These results demonstrate that
this ultrasonic micro-elastography imaging system is able to provide comparable full-
width at half maximum (FWHM) spatial resolution and preferable FOV in comparison
with OCE imaging techniques, which indicate its promising future for improving the
diagnosis for multiple clinical applications.

2.2 Methods and Materials
2.2.1 System Configuration and Data Acquisition
In this study, we have designed and fabricated a 4.5 MHz ring shape and a 40 MHz
needle tracking transducer. The 4.5 MHz pushing frequency was determined by the
balance between acoustic intensity and potential bio-effects while 40 MHz needle
transducer was selected as the balanced between spatial resolution and penetration depth.
The schematic diagram of the multi-functional ultrasonic micro-elastography imaging
15

system is shown in Fig. 2-1(a). As shown in the Fig. 2-1(a), the 40 MHz needle
transducer was first inserted into the center hole of the 4.5 MHz transducer and then two
transducers were carefully aligned axially under the guidance of a hydrophone. To
induce tissue motion, the 4.5 MHz excitation transducer was driven by an arbitrary
function generator (AFG 3252 C, Tektronix, Beaverton, OR, USA) using 4.5 MHz
sinusoid tone bursts with a duration from 100 µs to 300 µs and then amplified between
100 V and 140 V by an RF power amplifier (100A250A, Amplifier Research, Souderton,
PA, USA). The 40 MHz needle transducer was driven by a pulser/receiver (JSR500,
Ultrasonics, NY, USA) and triggered by the arbitrary function generator with a pulse
repetition frequency (PRF) of 20 kHz. Before acquired using a 12-bit digitizer card
(ATS9360, Alazartech, Montreal, QC, Canada) at a sampling rate of 1.8 GS/s, the
ultrasonic signals were filtered by an analog band-pass filter to remove signal
contamination of the pushing beam. In order to reduce system jitter, the same clock was
used to synchronize the digitizer, pulser/receiver, and arbitrary function generator.

16

Figure 2-1. Schematic diagram of designed multi-functional ultrasonic micro-elastography imaging system.
(a) The experimental setup and transducer parameters calibration, (b) The synchronized timing sequence
controlled by multi-functional ultrasonic micro-elastography imaging system.

Fig. 2-1(b) shows the synchronized timing sequence used for data acquisition. To be
specific, at each scanning position, the radio-frequency (RF) signal was acquired for
10 ms to ensure that the tissue returned to its original position and the pushing transducer
was excited 50 µs after the acquisition. All raw RF data were saved to disk for offline
processing. The first tracking A-line at each scanning position served as the reference
for the initial tissue position. Then tissue displacements were calculated using 1-D
normalized cross-correlation technique with a symmetric search region and 1.5 λ
window size (Lubinski et al., 1999; Pinton et al., 2006). The dynamic displacement data
were displayed as the peak displacement in ARFI and time to peak (TTP) displacement
in SWEI (Rouze et al., 2012). To obtain a 2D/3D image, both of the pushing and tracking
transducer were mounted on a 3-D motorized linear stage (SGSP33-200, OptoSigma
Corporation, Santa Ana, CA, USA) for mechanical scanning. Since the data acquisition
time at each scanning position is very short (millisecond level), the image reconstruction
rate is mainly determined by motor speed and selected scanning distance. Herein, 36 μm
was chosen as the step size, and the time to finish 1-D scanning is only few seconds
which is acceptable in the preclinical study. To reconstruct the shear wave propagation
at different lateral locations, the distance between pushing and tracking transducer was
controlled by another 1-D motorized linear stage. The final 2D/3D images were obtained
after a median filter in order to increase the signal to noise ratio (SNR). Data collection
17

and analysis process were performed using MATLAB 2014b (The MathWorks, Natick,
MA, USA).

2.2.2 Imaging Subjects Preparation
The gelatin (Gelatin G8-500, Fisher Scientific, USA) based tissue-mimicking
phantoms with the same concentration of silicon carbide powder (S5631, Sigma-Aldrich,
St.Louis, MO, USA) as the sound scatters were fabricated. Phantoms comprising gelatin
at concentrations of 2% and 5% were used in this study to represent materials of different
stiffness (Hall et al., 1997). All phantoms have a cylindrical shape with a 50 mm
diameter and 12 mm height. The homogeneous phantoms with 2% gelatin concentration
and 5% gelatin concentration were used to build the calibration data. Bi-layer Phantom
consisting of 2% gelatin concentration on the left and 5% on the right were used to
calibrate lateral resolution. Bi-layer phantom consisting of 2% gelatin concentration on
the top and 5% at the bottom were used to calibrate axial resolution. The phantom with
a 1.2 mm diameter 5% gelatin concentration cylindrical inclusion surrounded by 2%
gelatin concentration background was used to test the feasibility of our high resolution
imaging system on a more complex structure.
Liver tissue was selected as an imaging subject because of the following reasons.
First, the effectiveness of some newly developed drugs or therapeutic procedures has to
be verified on the small animal model in preclinical studies. Various studies about the
progression of liver fibrosis and the evaluation of anti-fibrosis medication have been
carried out by performing quantitative imaging of experimental animal (Liedtke et al.,
2013). Second, several high resolution elastography imaging techniques (Kennedy et al.,
18

2012) have been reported to be integrated with Fine Needle Aspiration Cytology (FNAC)
needle, which enables the future in vivo guiding percutaneous biopsy and therapeutic
methodologies of the thyroid gland, breast and liver cancer. Ultrasonic micro-
elastography can potentially be modified into a handheld device so as to facilitate the
tissue differentiation and boundary detection for various deep organ biopsy guidance
application including liver.
Our liver samples were bought from a local slaughterhouses (Sierra Medical Science,
Inc., Whittier, CA, USA). Because the increased liver stiffness is linked with the
development of fibrosis stage (Wang et al., 2009), formalin solution (F79-1
Formaldehyde, Fisher Scientific, Waltham, MA, USA) was used to artificially induce
liver cirrhosis to represent the “fibrosis” stage. To demonstrate the sensitivity of our
system, normal livers were considered as the control group while formalin-fixed livers
were treated as experimental group. To couple with transducers, livers were immersed
with HBSS (Life Technologies Co, CA, USA) solution at room temperature during the
experiment.

2.2.3 ARF based Elastography Imaging
2.2.3.1 Acoustic Radiation Force Impulse Imaging (ARFI)
ARFI is used to monitor the tissue deformation underneath the same position of the
pushing force. The axial displacement curve can be recovered from a single reference
pulse and all other detection pulses. The maximum displacement can be used to depict
the relative stiffness of soft tissues using equation (2-1)
𝐸 1
𝐸 2
= 𝑘 ∆𝐿 2
∆𝐿 1
(2-1)
19

where 𝐸 is the Young’s modulus, ∆𝐿 is the tissue displacement, 𝑘 is determined by the
ratio of acoustic attenuation in two different samples (Cook et al., 2011; Zhai et al., 2010).
In general, softer regions will displace farther than stiff regions.

2.2.3.2 Shear Wave Elasticity Imaging (SWEI)
Under the assumption of a purely elastic, incompressible, homogeneous medium,
SWEI is used to quantify tissue stiffness by a well-known equation (2-2)
𝐸 = 3𝜌 𝐶 𝑠 2
(2-2)
where E is the Young’s modulus, ρ is the tissue density, C s is the shear wave speed. By
further assuming a fixed direction of propagation (perpendicular to excitation beam axis)
and negligible dispersion issue, the SWS can be calculated from the time of flight (TOF)
based approach (McLaughlin and Renzi, 2006; Palmeri et al., 2008).

Figure 2-2. The principle comparison and analysis of ARFI and SWEI.
20

In TOF SWS reconstruction algorithm, the shear wave propagation timing at each
lateral off-axis position outside the ROE is indicated by the time to reach its peak
displacement. Giving a lateral propagation distance (Δx), TOF SWS can be calculated
by overall propagation time (two detection positions) approach using 𝐶 𝑠 =
∆𝑥 ∆𝑡 or
multiple arrival time (multiple detection positions) approach using linear regression
algorithm. Compared with only one detection position of ARFI, the data acquisition time
of SWEI is significant longer. Multiple arrival time approach is typically implemented
in an array system to image a large region. To get a fine spatial resolution and speed up
the data acquisition speed, overall propagation time approach was implemented in this
study for SWEI.
As indicated in the introduction section, the purpose of our imaging system is to
characterize small scale soft tissues with expected Young’s modulus in the range 0.1–
100 kPa. By assuming a constant density of soft tissue, typically 1000 kg/m
3
, the
detectable SWS should be less than 5.8 m/s in SWEI. According to the designed
minimum time interval (50 µs determined by 20 kHz PRF), the minimum distance
between pushing and tracking transducer is 290 µm. In order to satisfy the condition that
the region in which the shear wave propagates is homogeneous and to sustain a high
resolution, a small propagation distance is preferred. However, the propagation distance
is better to be larger than the beamwidth of the pushing transducer (Palmeri et al., 2010).
Thus, a 350 µm laterally off-axis distance (Δx) was used to quantify the SWS with a
good balance between precision and resolution. The detail principle and comparison
between ARFI and SWEI are displayed in Fig. 2-2.
21

2.3 Results
2.3.1 Acoustic Parameters of Ultrasonic Transducers
To measure acoustic fields of ultrasonic transducers, a customer built hydrophone
(HGL-0085, ONDA Co, Sunnyvale, CA, USA) system was used. During the testing, the
pushing transducer is working on selected excitation parameters in the actual experiment,
Isppa of the excitation transducer at the focal point was 49.01W/cm
2
in water condition.
Taking into account the derating factor of acoustic attenuation in liver tissue (0.9 dB/cm-
MHz), the calibrated Isppa was 36.9W/cm
2
and its corresponding Ispta was 369 mW/cm
2
.
The propagation distance of the excitation transducer (f-number=1) is 30mm in axial
direction. The measured beam profile has a −6dB beamwidth and −3dB depth of focus
(DOF) of 350µ m and 2.6mm, respectively. With respect to the detection transducer, there
is a 2mm axial depth region maintaining 280 µm beamwidth at −3dB level.
Figure 2-3(a–c) shows the induced dynamic displacement curves under different
excitation voltage, excitation duration and phantom stiffness. Based on our previous
experience, the peak displacement should maintain at least 1 µ m but less than 10 µ m so as
to sustain a good SNR while avoiding any potential ultrasound bio-effects, such as thermal
effect. It was demonstrated that 120V and 200 µ s were the reasonable excitation parameters
in this study.

22

2.3.2 Gelatin Tissue Mimicking Phantom Imaging
The FOV of the imaging system was first determined using homogeneous gelatin tissue-
mimicking phantoms. The results indicated that the effective FOV of ARFI is 1.5 mm in
depth (indicated by maximum displacement region within 5% discrepancy) and SWEI has
a 2mm in depth (specified by TOF-based linear regression algorithm with a 0.95 threshold
of R
2
to meet goodness-of-fit metrics), which means that SWEI provides a slightly larger
effective FOV than ARFI for the same imaging subject.

Figure 2-3. Imaging system validation on homogenous gelatin phantom. (a-c) Dynamic displacement curve
under different excitation voltage/ excitation duration and phantom stiffness. B-mode/ ARFI/ SWEI images
of homogenous phantom (d-f) 2% gelatin concentration, (g-i) 5% gelatin concentration.

Next, we verified the stability and the accuracy of the reconstructed Young’s modulus
of our imaging system. The same testing was repeated 10 times in total. The results showed
that ARFI tended to have 8.5 ± 0.5 µ m (2% gelatin) and 3.05± 0.15 µ m (5% gelatin)
maximum displacement and SWEI reconstructed 1.13± 0.07 kPa (2% gelatin) and
23

12.18±0.42 kPa (5% gelatin) Young’s modulus, respectively. Figure 2-3(d–i) displays the
corresponding imaging results. The same homogeneity was observed in B-mode, ARFI and
SWEI images. It was observed that the stiffer phantom had a smaller displacement and a
larger Young’s modulus. As expected, it reflects that the displacement in ARFI has the
inverse relation with Young’s modulus in SWEI. In color-coded elasticity map, the softer
region was mapped to the red color in ARFI and the blue color in SWEI while the stiffer
region was mapped to the blue color in ARFI and the red color in SWEI. To check the
accuracy of the reconstructed Young’s modulus in SWEI, uniaxial mechanical testing
(Model 5942, Instron Corp., MA, USA) was performed on the same phantoms immediately
after the experiment. The mechanical testing results show that values in SWEI are slightly
different from the values got in the mechanical test (1.26± 0.1 kPa and 12± 0.5 kPa,
respectively).

Figure 2-4. Bi-layer phantom imaging results and its corresponding FWHM resolution. 2D cross-sectional
B-mode image, ARFI image and SWEI image (a-c) Left-right phantom with a vertical boundary at a width
24

of 1.6 mm, (g-i) Up-down phantom with a horizontal boundary at a depth of 0.8 mm; (d,j) schematic diagram
of uniformly selected curve profiles, N = 20 for both Left-right phantom and Up-down phantom; Lateral
FWHM resolution model of (e) ARFI image and (f) SWEI image; Axial FWHM resolution model of (k)
ARFI image and (l) SWEI image.

Figure 2-4(a–c,g–i) displays pairs of B-mode/ARFI/SWEI images of bi-layer phantoms.
It was observed that the regions with different stiffness exhibited a homogeneous
echogenicity in the B-mode image and less contrast information (except for some bright
speckle signals caused by the precipitation of silicon dioxide powder in up-down phantom).
However, in ARFI image, the relative stiffness distribution could be easily distinguished
and its border was clearly visualized from the sharp transition. In SWEI image, the
mapping of the absolute Young’s modulus exhibited a relative broad transition edge,
especially for lateral direction. Outside transition region, it was observed that the Young’s
modulus in each layer were well matched with the measured Young’s modulus in
corresponding homogeneous phantom indicated by the similar color under the same color
bar.
25

Figure 2-5. Inclusion phantom imaging results and transitional curve profiles. (a-c) 2D cross-sectional B-
mode image, ARFI image and SWEI image. The raw data profiles (d) at a depth of 1.1 mm and (g) at a width
of 1.8 mm were selected. The raw data and fitted curve of ARFI and SWEI at (e,f) lateral direction, (h,i) axial
direction. The phantom has a 1.2mm diameter cylinder inclusion with a background-interior-background
structure.

The results of the cylindrical inclusion phantom are shown in Fig. 2-5(a–c). Both B-
mode and ARFI image have a clear circular-shape boundary in good agreement with
designed morphological feature. SWEI image shows an irregular circular-shape with a
bulge in deformation due to the poor elastography resolution. Besides structure information,
the relative/absolute stiffness distribution was clearly delineated in ARFI/SWEI. However,
it was observed that the deeper image region of ARFI had a significantly reduced peak
displacement while SWEI image maintained a uniform stiffness distribution beyond
1.5mm. This phenomenon was caused by the different effective FOV of ARFI and SWEI.
It was indicated that time-to-peak (TTP) displacement may be expected to be independent
26

of acoustic attenuation within the FOV while maximum displacement still suffers from
acoustic attenuation within the FOV, especially for deeper region (Palmeri et al., 2006).

Figure 2-6. 3D visualization of a side by side gelatin tissue-mimicking phantom. (a) B-mode image, (b)
ARFI image and (c) SWEI image. Volume dimensions (xyz) are 1.8mm× 3.6mm× 2mm.

Fig. 2-6 portrays a 3D B-mode image to observe a stereo morphological structure of
phantom side by side and the corresponding ARFI/SWEI images to view the biomechanical
property distribution. In Fig. 2-6(a), B-mode image provides 3D structure information and
shows little contrast for left-right transition. Benefiting from high spatial resolution of
elastography, ARFI image shows a highly correlated morphological structure with B-mode
image, especially for irregular shape of surface in Fig. 2-6(b). In addition, 3D stiffness
distribution supplies a good contrast for left-right transition layer. In SWEI image, although
it does not maintain the same structure compared with ARFI, a better image contrast
together with the absolute Young’s modulus is a great advantage over ARFI. For example,
a 2D transition surface is observed in Fig. 2-6(c).

27

2.3.3 Spatial Resolution and Image Contrast
To verify the high resolution capability of our imaging system, bi-layer phantoms with
vertical/horizontal transition edge were used to quantify the spatial resolution. Specifically,
the edge spread function (ESF) can be obtained by fitting the experimentally measured
curve profile into a sigmoid function model using the following equation (2-3)
𝑝 ( 𝑥 )= ( 𝑝 1
− 𝑝 2
)[
1
𝑒 −( 𝑥 −𝑏 ) /𝜆 +1
] + 𝑝 2
(2-3)
where 𝑥 is the lateral position, 𝑝 1
and 𝑝 2
represent displacement in ARFI and Young’s
moduli in SWEI, respectively. 𝑏 is the location of the layer boundary, 𝜆 represents the
width of the ESF - transition from one layer to another. Giving a curve profile, all
parameters in the sigmoid function model were estimated using standard non-linear least
squares fitting algorithm (Rouze et al., 2012). The first derivative of ESF results in a point
spread function (PSF). Then the FWHM of the PSF is used to estimate elastography
resolution (Smith, 1997; Mezerji et al., 2011). The mathematical formula of FWHM
resolution is given in equation (2-4).
FWHM = 2 ln( 3 + 2√ 2)𝜆 (2-4)
Figure 2-4(e,f,k,l) shows the FWHM resolution calculated from the sigmoid fitting
model in the lateral and axial direction of ARFI and SWEI. For statistical analysis, 20
horizontal/vertical experimental curve profiles selected uniformly from bi-layer phantoms
shown in Fig. 2-4(d,j) were used to calculate FWHM resolution distribution. Finally, the
averaged FWHM value was treated as the lateral/axial resolution of actual elastography
image. The measured lateral and axial resolutions are 223.7± 20.1 µ m and 109.8± 6.9 µ m
for ARFI, 543.6± 39.3 µ m and 117.6± 8.7 µ m for SWEI, respectively.
28

Inclusion phantom with background-interior-background profiles in all direction
represents a complex multi-layer structure. Because there are two transition edges in each
direction, equation (1) was rewritten as the product of two sigmoid functions. To observe
the lateral/axial resolution of inclusion phantom, raw curve profiles were selected across
through the center of inclusion at a depth of 1.1 mm and at a width of 1.8mm, respectively.
Figure 2-5(d,g) shows the diagram of selected curves. Figure 2-5(e,f,h,i) displays the raw
data profiles and fitting results of inclusion phantom along the lateral and axial direction.
These symmetrical curves are well matched with the symmetric property of circular
inclusion, except the one in Fig. 2-5(h) which was caused by attenuated displacement
beyond 1.5mm in ARFI. It was indicated that there is a wider transition width in inclusion
phantom than that in bi-layer phantom due to the non-prefect flat surface.
In addition to spatial resolution, image quality is also assessed by contrast. The previous
study shows that image contrast is affected by tissue stiffness difference and the relation
between region of excitation (ROE) size and the volume of the lesion (Nightingale et al.,
2006). The equation (2-5) is used to evaluate the contrast of ARFI and SWEI on the
inclusion phantom
𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 =
|𝑃 𝑖𝑛
−𝑃 𝑜𝑢𝑡 |
𝑃 𝑜𝑢𝑡 (2-5)
where 𝑃 𝑖𝑛
and 𝑃 𝑜𝑢𝑡 are the mean pixel values of the target and background, respectively.
The calculated contrast is 0.59 for ARFI and 7.66 for SWEI.

29

2.3.4 Ex vivo Chicken Liver

Figure 2-7. Ex vivo 3D visualizations of chicken liver. (a-c) Normal liver and (d-f) Liver with artificially
induced “fibrosis” using formalin solution. Volume dimensions (xyz) are 1.2mm×2mm×1.8mm. The red
arrows in (d-f) indicate the position of formalin injection.

Fig. 2-7(a,d) show the B-mode images of normal and formalin-fixed chicken liver,
respectively. The small anatomical structures of chicken liver were clearly revealed in the
B-mode image where the morphological difference between normal and formalin fixed
liver was caused by injection operation. The corresponding ARFI images in Fig. 2-7(b,e)
point out that the normal liver tends to have a homogeneous stiffness distribution indicated
by the same color and the formalin-fixed region located at the left bottom area of liver has
a smaller displacement with a gradually changing color. The high resolution of ARFI image
provides a well-matched morphological structure with the B-mode image, especially for
uneven surface of formalin-fixed liver. Moreover, an accurate stiffness distribution and the
30

diffusion process of “fibrosis” were observed in ARFI image. SWEI image results are
shown in Fig. 2-7(c, f). The average reconstructed Young’s moduli for normal liver is
5.69± 0.8 kPa which is smaller than 5.8± 0.35 kPa performed by the same uniaxial
mechanical testing. In formalin-fixed region, it was observed that there is a significant
increasing stiffness with the average measured Young’s moduli – 19.22± 2.2 kPa in SWEI
image. Clearly, the spatial resolution of ARFI is better than SWEI, particularly for the
serious distorted formalin-fixed liver. However, SWEI has a better contrast indicated by a
larger dynamic range color bar.

2.4 Discussion and Conclusion
The calculated Isppa and Ispta were within the limitation of United States Food and Drug
Administration (FDA). For single short exposure time (less than 1 ms), the output power
was much lower than the threshold of occurring ultrasound bio-effects. In addition, the
beamwidth of excitation transducer was larger than motor step size in this study. Thus, the
temporal average intensity still not exceed the limitation of FDA and has a small risk to
increase the temperature level.
The measured DOF of excitation transducer is 2.6mm, and the detection transducer has
a 2mm DOF with a nearly uniform beamwidth. The elastography imaging resolution was
guaranteed by imaging our target within the maximum overlap of the two DOFs which is
the definition of elastography FOV. It was well-documented that the spatial resolution of
elastography is determined by both excitation and detection transducers as well as signal
processing parameters. Specifically, axial resolution is on the order of ultrasonic
wavelength and lateral resolution is proportional to the beamwidth of ultrasonic system (an
31

empirical expression of elastographic lateral resolution is given by 𝑅 𝑙 = 𝑘 ∙ 𝑑 , where 𝑑 is
the beamwidth of ultrasonic system, the value of 𝑘 would not exceed 1). Righetti et al.
performed a simulation study to estimate the spatial resolution of elastography based on
the distance between the FWHM of the strain profiles of two equally stiff lesions embedded
in a softer homogeneous background (Righetti et al., 2002; Righetti et al., 2003). However,
fabricating a phantom with a very thin transition layer separated by two equal lesions is
very challenging, especially for the high resolution imaging such as optical imaging and
high frequency ultrasonic imaging. In addition, mechanical parameters such as the contrast-
transfer efficiency and complex boundary conditions will affect the practically achievable
resolution (Srinivasan et al., 2003). Therefore, a simplified bi-layer phantom with
distinguished stiffness transition in horizontal/vertical direction has been used to
experimentally quantify imaging resolution of high frequency ultrasound and OCT
(Kennedy et al., 2015; Shih et al., 2013). In 2012, Rouze et al. developed a sigmoid
function fitting model method and define 20–80% transition width as elastography
resolution. However, “20–80% transition” resolution, as a relative parameter to evaluate
resolution performance, cannot exactly represent the resolution of actual elastography
images. PSF, the first derivative of ESF, describing the impulse response of an imaging
system seems to be a more standard approach. Therefore, the spatial resolution of
elastography was defined as the “FWHM of the PSF” in this study.
Compared with ARFI, the lateral resolution of SWEI is additionally restricted by off-
axis distance (∆𝑥 ) due to boundary conditions. In Fig. 2-4(b,c), it is noticed that the width
of transition boundary of ARFI is sharper than SWEI because a propagation distance is
needed for time-of-flight (TOF) shear wave speed (SWS) reconstruction algorithm and
32

SWS is likely misleading by reflection or refraction at the boundary. In Fig. 2-7(f), the
distorted morphological structure and some estimation artifacts were observed in the ex
vivo formalin-fixed chicken liver. Due to the reconstruction inaccuracy, the boundary
exhibits a wide transition region, failing to resolve the exact edge position in SWEI.
Therefore, the lateral resolution of SWEI will be greatly influenced by its propagation
distance (∆𝑥 = 350 µ𝑚 ) and the excitation beam width, which is much worse than that of
ARFI. The axial resolution of SWEI is comparable with that of ARFI. The possible reason
is that the horizontal edge is paralleling to the shear wave propagation direction in Fig. 2-
4(i) where less shear wave distortion phenomenon occurs.
Apparently, attenuation of ARF varies from tissue to tissue. Cook et al. indicated that
acoustic attenuation of gelatin tissue-mimicking phantom depends on both gelatin and
scatter concentration. Based on equation (4) where 𝑘 is larger than 1 by assuming 𝐸 1
is
greater than 𝐸 2
, the contrast of SWEI should be better than that of the ARFI theoretically,
which was verified by our experimental results. All results demonstrated that ARFI
mapping with maximum displacement has a better spatial resolution while SWEI mapping
with Young’s modulus obtains a better image contrast.
The results show that the estimated Young’s modulus in SWEI has a small variance
compared to that in mechanical testing. The underestimation/overestimation issue was
caused by the error of TOF SWS reconstruction. When the shear wave propagation time is
less than 50 µ s, the TTP displacement timing will be set to either forward timing or
backward timing limited by 20 kHz PRF. Although the PRF was increased to 60 kHz with
spline interpolation to track the sub-timing position to reduce the error in this study, the
measured propagation time is still slightly different from the true propagation time. Besides,
33

the SNR of induced peak displacement in SWEI is lower than that in ARFI because all
detection positions are out of ROE, which leads to some artifacts in TOF SWS
reconstruction results. Moreover, the liver tissue is not a pure elastic and isotropic medium,
especially for the formalin-fixed liver. Shear wave dispersion and irregular structure may
also reduce the accuracy of TOF SWS reconstruction result. Thus, a higher PRF and a
better SNR are required to further increase the accuracy.
It was well-established that the conventional ultrasound possesses a deep penetration
depth while OCT has superior resolution for accessing the anatomy of tissue. The most
recent developed ultrahigh resolution OCE achieved spatial resolution less than 2 µ m
which is highest report to date in optical elastography (Curatolo et al., 2016). Besides the
spatial resolution, OCE provides a better sensitivity than ultrasound. The non-contact 4D
OCE imaging system has the ability to detect tissue deformation in nanometer scale while
ultrasound is only sensitive to sub-micron or micrometer level deformation. Although
swept-source OCT has achieved extended imaging depth in ocular tissue owing to its low
sensitivity roll-off with depth (Potsaid et al., 2010), optical imaging is somewhat organ
dependent and is still feeble to most highly-scattered tissues other than the eye. Instead,
high frequency ultrasound is able to provide a more effective and uniform FOV at deeper
tissue while maintaining high spatial resolution, which serves as the desirable imaging
technique for various clinical applications. Therefore, our newly developed high resolution
ultrasonic micro-elastograhy system was proved to bridge the gap in between the
conventional ultrasonic elastography and OCE on spatial resolution and penetration depth.
In summary, both high resolution ARFI and SWEI are essentially useful to characterize
tissue biomechanical properties. The experimental results suggest that the multi-functional
34

ultrasonic micro-elastography imaging system provides a non-invasive way to differentiate
tissue biomechanical properties with a very fine resolution (~100 µ m) and deep penetration
depth, indicating the capability to quantify the relative and absolute Young’s modulus
using single system setup. Combined 3D morphological and biomechanical information of
soft tissue will improve the visualization of the anatomical structure of soft tissues and
offer potential diagnostic advantages in clinical application.
35

Chapter 3 Ultrasonic Micro-elastography System on Assessing
Corneal Biomechanics
3.1 Introduction
The cornea is the transparent, anterior tissue of the eye that provides approximately two-
thirds of the total refractive power (Ruberti et al., 2011). Its unique structure exhibits both
transparency to allow light to pass through and high tensile strength to maintain shape
whilst subject to the forces of intraocular pressure (IOP) during cardiac cycle. Many factors
such as ageing, disease, and trauma or as a result of surgery affect the physiological
function of the cornea (Wilson et al., 2016). Current quantitative assessments of the cornea
based on corneal morphologic features include thickness and curvature measurements are
all secondary signs of diagnosis purpose for corneal disease such as keratoconus and post-
refractive surgery ectasia (Andreassen et al., 1980; Binder, 2007). It was proposed that the
primary abnormality is the biomechanical properties as knowledge of its significant
implications on current ocular treatments and diagnosis, which is garnering increasing
interest in many potential clinical applications (Roberts and Dupps, 2014).
Many interventions such as photorefractive keratectomy (PRK) (Munnerlyn et al., 1988)
and laser-assisted in situ Keratomileusis (LASIK) (Pallikaris et al., 1990) are effective on
modifying corneal structural properties and have become popular for the treatment of
ametropia. It is widely accepted that the postoperative residual corneal thickness should be
at least 250 µ m to reduce the risk of post-refractive keratectasia. However, corneal stiffness
may vary among different individuals, and there have been reported cases of post-refractive
keratectasia occurring in individuals with residual bed thickness greater than 250 µ m (Ou
36

et al., 2002). The incidence of keratoconus has been reported to be as high as 1 in 2000,
and there is a need for early identification of these patients because there now is a treatment
that can halt the progression of the disease. UV-induced collagen cross-linking (CXL),
which was recently approved by the Food and Drug Administration (FDA) for the
treatment of keratoconus, strengthens the cornea by introducing covalent links between
collagen lamellar and halts the progression of ectasia (Wollensak et al., 2003). Given the
fact that the standard CXL treatment is not customized for individual case, the additional
information provided by preexisting biomechanical properties as well as the changes in
elasticity during the CXL treatment itself would attribute to an optimal CXL treatment.
Therefore, to precisely track the stiffness distribution or changes of the cornea is needed
among various purpose such as diagnosis, tracking and treatment.
The progress in relating biomechanical properties to clinical diagnosis or treatment is
currently limited by the lack of tools that has the ability to precisely determine corneal
biomechanical properties. Goldmann applanation tonometry (GAT) is the gold standard
for measuring IOP in clinical. It makes assumptions regarding corneal stiffness and its
measurement is significantly associated with central corneal thickness (CCT). It was shown
that corneal biomechanics across individuals may have a greater impact on tonometry IOP
readings than CCT or curvature (Liu and Roberts, 2005). Because corneal biomechanical
properties can influence the IOP reading with standard GAT, Ocular Response Analyzer
(ORA) was first developed to measure corneal biomechanics in vivo and provides IOP
measurements taking its biomechanical properties into consideration (Luce, 2005). To be
specific, the system uses a transient air-pulse to calculate cornea hysteresis based on the
difference in air pressures between force-in and force-out applanation at the surface of the
37

cornea. Later, a similar clinical available device called Corvis ST with implementation of
a high speed Scheimpflug-camera to record the air pulse induced reaction of the cornea
was released to measure biomechanical corrected IOP (Hong et al., 2013). However, the
sensitivity of both ORA and Corvis ST remains questionable. Moreover, either ORA or
Corvis ST only provides an average stiffness of the entire cornea instead of the point-to-
point stiffness mapping, which increases the possibility of missing focal abnormalities.
It is notable that the Ultrasound Biomicroscopy (UBM) has become an indispensable
technique for ophthalmic imaging owing to its natural advantage of visualizing some ocular
structures such as ciliary body and zonules through the use high frequency ultrasound with
high resolution (Ishikawa and Schuman, 2004; Silverman, 2009). Several UBM-based
elastography methods have been developed toward the goal of characterizing the
biomechanical properties of the corneal tissue (Hollman et al., 2013; Urs et al., 2014).
However, these UBM-based methods suffer from limited field of view (FOV) as well as
the insufficient sensitivity to capture subtle structural details of the cornea.
In this chapter, we implemented the multi-functional ultrasonic micro-elastography
technique (Qian et al., 2017) that has the capability to provide a qualitative corneal stiffness
distribution at micrometer resolution via acoustic radiation force impulse imaging (ARFI).
Owing to the low imaging resolution of shear wave elasticity imaging (SWEI), in this study,
we only capture the Young’s modulus at some region of interest (ROI) instead of imaging
mapping. Our dual frequency ultrasonic imaging system consists of a 4.5 MHz focused
ring shape transducer for inducing tissue deformation and a 40 MHz unfocused needle
transducer for precise detection of tissue deformation. Using the high resolution stiffness
map labelled with some reconstructed Young’s modulus at ROI, we can evaluate direct
38

delineation of the local deformations of the cornea in response to either cross-linking
intervention or IOP elevations which is important in clinic.

3.2 Materials and Methods
3.2.1 Experimental Setup
A schematic diagram of the experimental setup consisting of dual-frequency transducers
and synchronized timing sequence is shown in Figure 3-1. The 40 MHz needle detection
transducer was first inserted to the hole of the 4.5 MHz ring shape excitation transducer,
and both of them were mounted on a 3-axis translation motorized linear stages (SGSP33-
200, OptoSigma Corporation, Santa Ana, CA, USA) for mechanical scanning. In order to
track the shear wave propagation, the pushing transducer was fixed at the target position
while the tracking transducer was controlled by a linear stage which was moved based on
the designed distance between the central positions of the pushing and tracking transducers.
In detail, the step size and scanning distance are 39 µ m and 3.9 mm, respectively. In
addition, to avoid any issues with vibration of the needle during movement, the time delay
between successive positions was set to 200 ms, including the data acquisition time and
extra wait time. Before the experiment, two transducers were carefully aligned along both
axial and lateral direction under the guidance of hydrophone to eliminate any offset.
The arbitrary function generator (AFG 3252C, Tektronix, Beaverton, OR, USA)
generating 4.5 MHz sinusoid tone bursts signal was first connected to the radio-frequency
(RF) power amplifier (100A250A, Amplifier Research, Souderton, PA, USA) and then
transmitted to the 4.5 MHz excitation transducer for inducing tissue deformation. The 40
MHz needle transducer was set in conventional pulse-echo mode and was driven by a
39

pulser/receiver (JSR500, Ultrasonics, NY, USA) with a pulse repetition frequency (PRF)
of 10 kHz. After 20-80 MHz analog band-pass filtering (Mini-Circuits, Brooklyn, NY,
USA) to remove signal contamination from the excitation beam, the RF ultrasonic data was
captured using a 12-bit digitizer (ATS9360, Alazartech, Montreal, QC, Canada) at a
sampling rate of 1.8 GHz and stored for off-line analysis. To reduce system jitter, the same
clock was used to synchronize the digitizer, pulser/receiver, and arbitrary function
generator.
To record the initial tissue position at each scanning position, the first tracking A-line
acquired by the tracking transducer served as the reference point and the pushing transducer
was excited 100 µ s after the tracking transducer started to acquire data. Based on our
previous calibration studies and potential issues caused by obvious increased stiffness at
high IOP, the voltage applied on the pushing transducer was set to 140V peak to peak in
amplitude corresponding to 2 MPa acoustic pressure, and the excitation duration of the
pushing transducer was fixed at 200 µ s. All parameter settings were kept constant for all
measurements.
40

Figure 3-1. Schematic diagram of the ultrasonic micro-elastography system and the synchronized timing
sequence for the excitation and detection transducers. Two transducer are first confocally aligned before the
experiment. A commercial artificial anterior chamber was used here to hold the cornea tissue.

3.2.2 Viscoelastic model
Available literature clearly suggests that the cornea is a viscoelastic material. The shear
wave speed (SWS) for viscoelastic material increases monotonically with frequency
instead of maintaining a constant value in a pure elastic medium (Chen et al., 2004). It has
been well established that the Kelvin-Voigt and Maxwell models are linear descriptions of
a viscoelastic medium. They consist of an elastic spring and a viscous dashpot, either in
parallel (Kelvin-Voigt) or in series (Maxwell). In the elasticity imaging community, the
Kelvin-Voigt model is preferred to quantify both tissue elasticity and viscosity by
evaluating dispersion of shear wave propagation speed versus its frequency (W Urban et
41

al., 2012). For a homogeneous medium, the shear wave propagation speed 𝑐 𝑠 is related to
its angular frequency 𝜔 𝑠 by the equation (3-1).
𝑐 𝑠 =
√
2( 𝜇 1
2
+𝜔 𝑠 𝜇 2
2
)
𝜌 ( 𝜇 1
+√𝜇 1
2
+𝜔 𝑠 𝜇 2
2
)
(3-1)
where 𝜌 is the corneal density – around 1062 kg/m
3
(Kampmeier et al., 2000). 𝜇 1
and
𝜇 2
are shear elasticity, and shear viscosity of the cornea, respectively. Once the
experimental dispersion curves are obtained, 𝜇 1
and 𝜇 2
can be determined by fitting this
Kelvin-Voigt equation to the phase velocity curve (described in the next Section) using the
linear least square algorithm. The fitting relation is 𝑐 𝑠 = 𝑐 𝑝 ( 𝜔 ) where the frequency
selected in the model ranges from 200 Hz to 800 Hz with a step size of 50 Hz.
Under the assumption of a homogenous, isotropic medium, the Young’s modulus (𝐸 )
can be further derived from the Poisson’s ration (𝜐 ) and the shear elasticity (𝜇 1
) using
equation (3-2).
𝐸 = 2 ∙ ( 1 + 𝜐 )∙ 𝜇 1
(3-2)
Where Poisson’s ratio is assumed to be 0.49 due to the near incompressibility of the
corneal tissue (Cartwright et al., 2011).

3.2.2 Post-processing and data analysis
Data analysis was performed using MATLAB 2017a software (The MathWorks, Natick,
MA, USA). The dynamic tissue displacements were calculated using 1-D normalized
cross-correlation tracking algorithm with a symmetric search region and 1.5λ window size
(λ is the wavelength of the detection transducer). The peak deformation of each dynamic
displacement curve at each lateral position was used to construct the axial displacement
42

map. The final reconstructed 2D/3D images were generated after applying a median filter
so as to increase the SNR.
The equation (3-3) reveals the relationship between Young’s modulus and peak
displacement.
𝐸 =
𝐹 𝐴 ⁄
∆𝐿 𝐿 ⁄
(3-3)
where 𝐸 is Young’s modulus, 𝐹 is force, 𝐴 is sample surface area, 𝐿 is sample thickness,
∆𝐿 is the peak tissue displacement. To reconstruct shear wave speed, the axial displacement
map was first obtained by averaging axial displacements over the depth direction so as to
improve the SNR of the displacement map (the averaging depths were determined by the
region that has relative uniform distributed displacements in the ARFI image). For example,
the center position of the cornea ± 0.5 mm was selected in the IOP experiment. Then the
propagation distance versus time shifts curve was obtained from the axial displacement
map where the wave propagation distance was measured by the moving step size of the
tracking transducer and the time shift was defined as the time to reach the peak
displacement at each dynamic displacement.
As opposed to group velocity (cg), which is estimated by applying a linear regression
to the time shifts versus the distance between each lateral position of the axial displacement
map (Palmeri et al., 2008), phase velocity (cp) as a function of frequency can be obtained
using the Fourier transform. Figure 3-2 shows the post-processing steps used to obtain the
phase velocity curve for one of the control corneas at 5 mmHg IOP. The axial displacement
map was first transformed from the spatial-temporal domain into the wavenumber-
frequency domain (also denoted as k-space) by using the 2D discrete Fast Fourier
Transform to obtain an initial k-space map. To avoid low frequency noise, the initial k-
43

space map with frequency below 5 Hz was masked. The masked k-space map was then
interpolated to obtain the final k-space map. The wave number (𝑘 𝐿 ) for each frequency (𝑓 )
in the first quadrant of k-space was found by identifying the intensity maximum at that
frequency. The phase velocity curve (𝑐 𝑝 ) was calculated by the ratio of 𝑓 and 𝑘 𝐿 through
equation (3-4):
𝑐 𝑝 =
𝑓 𝑘 𝐿 (3-4)
With 𝑓 being the frequency at each specific position in the phase velocity –frequency
map.

Figure 3-2. The post-processing procedures to emphasis how to get the phase velocity curve from the
experimental collected axial displacement maps. (a) axial displacement map, (b) k-space, (c) phase velocity
curve, and (d) fitting curve with selected frequency range from 200 Hz to 800 Hz with a 50 Hz interval.

44

3.2.3 Porcine Cornea Preparation
In some slaughterhouses, porcine eyes are scalded with hot water before harvest. Thus,
fourteen fresh, unscalded porcine eyes were obtained from a local service-oriented
company (Sierra Medical Science, Inc., Whittier, CA, USA) within 24 hours of death in
this study. The corneas were carefully removed and stored in 10% dextran solution
(Dextran 40, Sigma-Aldrich Inc, MO, USA) for approximately one hour at 5 ° C prior to
imaging (Hamaoui et al., 2001). Before the experiments, each cornea was mounted on an
artificial anterior chamber (K20-2125, Katena Products Inc, Denville, NJ, USA) with two
ports of silicone tubing to control and read the true IOP inside. During the experiment, the
sample was submerged in a tank with balanced salt solution (Life Technologies Co, CA,
USA) to minimize cornea edema.
The first task was to observe small elasticity changes with respect to different
crosslinking time. The second task was to monitor the effect of elevated IOP on corneal
elasticity, and in the meantime to investigate the relationship between the corneal elasticity
and different IOP levels. The detailed operating procedures for each task are described
below.
To artificially induce local corneal cross-linking, 0.05 cc of formalin solution (F79-1
Formaldehyde, Fisher Scientific, Waltham, MA, USA) was applied to a small spot of the
corneal surface via a 1-cc disposable syringe with a 30-gauge needle. The 30-gauge needle
was bundled at a fixed position of the top surface of a home-made mold that is well fitted
with the artificial anterior chamber to ensure the formalin drop location at each time. At
the end of each formalin drop time, the cornea was washed and then submerged for
scanning. After each scanning, the cornea was removed from the water tank and a new
45

formalin drop was applied at the same spot between each time-point. In this task, one fresh
cornea was used to observe the time-dependent crosslinking effect though cross-sectional
view. To be specific, the control group had no formalin drops while experimental groups
had formalin drops administered at 2, 5, and 10 minutes, respectively (All times in this
study are cumulative exposure times. For example, ‘5 minutes’ here means that there is an
addition 3 minutes added to the ‘2 minutes’ from the first exposure). To obtain a 3D view
of the cornea with or without crosslinking, another fresh cornea was first scanned as a
control group (no formalin drop), then was dropped with a single formalin at 20 minutes
only, and finally imaged as an experimental group. IOP was controlled at 5 mmHg for all
crosslinking experiments.
For the second task, all corneas were not formalin-treated and the only variable was the
IOP. As mentioned above, the artificial anterior chamber has two ports. One port was
connected to the balanced saline solution bag set at various heights to manipulate IOP. The
other port was connected to a pressure sensor (Model SPR-524, Millar Inc, TX, USA) to
read the true IOP inside the chamber. Because the normal physiological IOP range is 12-
22 mmHg, thus, six IOP levels - 5, 10, 15, 20, 25 and 30 mmHg were investigated in this
study.

46

3.3 Results
3.3.1 Cross-linked Corneal Biomechanics

Figure 3-3. A time series of B-mode and ARFI images for one cornea sample. The blue arrow indicates the
small spot of formalin drop between each time-point. (a,e) control group with no formalin drop; experimental
groups with (b,f) 2 minutes, (c,g) 5 minutes and (d,h) 10 minutes formalin drop. In the cross-linking
experiments, the intraocular pressure was set at 5 mmHg so as to maintain normal corneal curvature.

Figure 3-3 (a, e) show the 2D cross-sectional B-mode image and its corresponding ARFI
image of an ex vivo porcine cornea in control group. The morphology of cornea is clearly
discernable by different echogenicity in the B-mode image. The CCT is around 1 mm
which is reasonable compared with literature study. The color-coded ARFI image shows a
regional stiffness map with softer areas in red and stiffer areas in blue. From ARFI image
result, the cornea is a relative homogeneous tissue at health condition.
47

Figure 3-3 (b-d) show the B-mode images obtained at three experimental conditions - 2,
5, 10 minutes after artificially induced cross-linking where the blue arrow indicates the site
of cross-linking. At each experimental condition, B-mode images show the almost identical
structures except that the cornea thickness has a slightly increasing from 1 mm (control
condition) to 1.2 mm (10 minutes experimental condition). At the cross-linking site, the
high resolution ARFI images in Fig. 3-3 (f-h) show an increasing stiffness relative to post-
drop time with a corresponding color change from red to yellow to green. In addition, the
volume of the stiffening became greater because of the random diffusion effects of formalin
solution.
The reconstructed Young’s modulus values at the small cross-linked spot are 4.39 kPa
for the control group, 4.56 kPa in the experimental group with 2 minutes formalin drop,
4.81 kPa in the experimental group with 5 minutes formalin drop, and 5.03 kPa in the
experimental group with 10 minutes formalin drop. The apparent increasing trend of the
Young’s modulus is consistent with ARFI observations.

Figure 3-4. The reconstructed 3D B-mode and ARFI maps of the cornea (a,c) at control condition, (b,d) at
experimental condition – 20 minutes after formalin-induced sclerosis. (e,f) show shear wave propagation and

Fig. 1. Magnetization as a function of applied field. Note that “Fig.” is
abbreviated. There is a period after the figure number, followed by two spaces.
It is good practice to explain the significance of the figure in the caption.

48

current (after 1.5 ms ARF excitation) wave fronts position marked by gray dash lines. The red arrow indicates
the ARF excitation position which is 2mm away from the central cornea. The blue arrow indicates the site of
formalin drop. Volume dimensions (xyz) are 4.8 mm × 1.5 mm × 1 mm for (a-d) and 6 mm × 1.5 mm × 1 mm
for (e-f), respectively.

Figure 3-4 (a-d) shows 3D maps of morphological structure and relative stiffness
distribution of the cornea in the control group, and the experimental group (20 minutes).
The volume dimensions (xyz) of the reconstructed 3D images are 4.8× 1.5× 1 mm. With the
high resolution capability of the B-mode and ARFI images, it is straight-forward to locate
the ROI which is the site of formalin drop in this study. By moving the pushing transducer
2mm away from the central cornea (opposite direction of the site of formalin drop), shear
wave propagation at the ROI can be observed. The Young’s modulus at the ROI before
and after the formalin drop were then reconstructed which is 4.4 kPa and 6.55 kPa,
respectively. Figure 3-4 (e,f) show the shear wave fronts after 1.5 ms ARF pushing. From
the gray dash line, it can clearly be seen that the shear wave front propagated faster in the
experimental group than that in the control group.

49

3.3.2 Corneal Biomechanics with respect to IOPs

Figure 3-5. B-mode and ARFI images of the cornea under various intraocular pressure. (a,g) – 5 mmHg,
(b,h) – 10 mmHg, (c,i) – 15 mmHg, (d,j) – 20 mmHg, (e,k) – 25 mmHg and (f,l) – 30 mmHg. The ROI is +/-
0.5 mm of the central cornea which was relative uniformly distributed demonstrated by high resolution ARFI
images.

The biomechanical response to IOP elevations were also investigated in this study. In
Figure 3-5(a-f), it was observed that it’s difficult to find out the changes from B-mode
images caused by IOP elevations. Although there might be subtle changes of the thickness
or curvature, it’s not easy to provide any quantitative measurements only rely on B-mode
50

images. From the view of figure 3-5(g-l), it was obvious that ARFI imaging is a better
indicator because of a larger dynamic change of stiffness. To be specific, the cornea has a
tendency to become stiffer with the increasing IOP. This change in elasticity was noted to
be more prominent in the central cornea than in the peripheral cornea. From high resolution
ARFI images, the ROI defined by +/- 0.5 mm of the central cornea is relative uniform
under different IOPs, which satisfied the prerequisite tracking conditions of the shear wave.

Figure 3-6. Shear wave propagation after (a) 0.1 ms, (b) 0.3 ms and (c) 0.5 ms ARF excitation. It was
observed that the shear wave propagates faster at higher IOP. Based on high resolution ARFI images, the
Young’s modulus of the cornea under different IOP were reconstructed within +/- 0.5 mm uniform region.

51

Figure 3-6 shows three timing (0.1 ms, 0.3 ms, 0.5 ms) of shear wave propagation under
six IOPs. shows three timing intervals (0.1 ms, 0.3 ms, 0.5 ms) of shear wave propagation
under elevated IOP. The color bar in Fig.6 was normalized based on the maximum and
minimum displacement at t=0 which can help us to directly visualize the shear wave speed
at different IOPs.
In this experiment, to determine the relationship between Young’s modulus of the
cornea and elevated IOP, twelve porcine corneas were used. The reconstructed Young’s
modulus are all expressed as mean ± standard deviation. In detail, the reconstructed values
were 3.6 ± 0.71 kPa at 5 mmHg, 7.94 ± 1.86 kPa at 10 mmHg, 15.03 ± 3.78 kPa at 15
mmHg, 22.11 ± 5.69 kPa at 20 mmHg, 32.29 ± 6.84 kPa at 25 mmHg, and 43.05 ± 5.01
kPa at 30 mmHg, respectively. The differences between the various IOP values were
evaluated by one-way ANOVA. The statistical analysis showed that changes in Young’s
modulus were statistically significant at different IOP values where P < 0.01 was
considered to be significant. In Figure 3-7, by plotting Young’s modulus versus IOPs, we
found that it can be well fitted by a linear equation (3-5) using standard nonlinear least
squares fitting algorithm. 𝑅 2
, a parameter to reflect the goodness of fit, is greater than 0.95
in this study.
𝐸 = 𝐴 · 𝐼𝑂𝑃 + 𝐵 (3-5)
where 𝐸 is Young’s modulus, 𝐼𝑂𝑃 is the intraocular pressure, 𝐴 is the slope of linear trend.
52

Figure 3-7. The averaged Young’s modulus of the cornea at elevated IOPs. And it expressed as a linear
relationship within the normal physiological IOP range (12-22 mmHg).

3.4 Discussion and Conclusion
High frequency transducers provide excellent resolution for both B-mode and elasticity
imaging. However, previously, it has been difficult to induce significant deformation of
tissue using high frequency transducers due to their low power output. In this study, a dual
frequency configuration was implemented to push/track tissue utilizing the high power
capability of the 4.5 MHz transducer and high resolution of the 40 MHz transducer. Also,
a hollow shaped pushing transducer coaxially aligned with a needle tracking transducer
eliminate dual-frequency transducer offset and ensure that the pushing force is applied
orthogonally to the imaging subject in order to provide shear wave propagation only.
According to the previous study by Palmeri et. al., the frequency bandwidth of phase
velocity depends on the excitation duration and spatial beamwidth used to generate the
shear wave (Palmeri et al., 2014). Widman further used different excitation durations from
100 to 700 µ s to induce shear wave propagation in porcine arteries. The results
53

demonstrated that shorter excitation duration can obtain wider bandwidth and more
accurate estimation of elasticity (Widman et al., 2016b). However, shorter excitation
duration leads to a smaller intensity to push the tissue. Usage of excitation duration below
200 µ s would not induce enough detectable displacement in our system, especially when
the shear wave propagates far away from the region of excitation of the pushing transducer.
Therefore, the pushing duration of ARF was set to 200 µ s as a balance in this study. Since
both formalin cross-linking and various IOP levels were tested here, the tissue deformation
under these conditions has a large dynamic range. To better highlight disparities and help
with comparison, a log10 scale was used in all axial displacement maps.
Corneal biomechanical behavior is primarily a function of the stroma consisting
primarily of water and collagen fibrils that confer its strength and form. Specifically, the
orientation and spacing of the collagen fibrils provide the cohesive forces to confer most
of the structural stability. Corneal cross-linking intervention induces covalent bonds
between collagen lamellae to halt the progression of corneal ectasia and was recently
approved by the US FDA for the treatment of keratoconus. Figure 3-3 shows a time-series
of the corneal cross-linking effect where the blue arrow indicates a small spot where a
formalin drop was applied. A slight increase in CCT caused by swelling of the tissue after
inducement was observed in the B-mode images. This is because two confounding
variables are unavoidable under ex vivo conditions: the lack of aqueous humor production/
outflow, and corneal desiccation. Previous findings on porcine corneas indicate that cross-
linking might enhance corneal swelling which can explain these phenomena (Wollensak et
al., 2007). Moreover, there was an increase in stiffness with a longer formalin drop time,
and the increased stiffness extended both horizontally and vertically as shown by ARFI
54

images in Figs. 3-3 (e-h). This likely represented the diffusion of formalin within the
corneal stroma. Through high resolution stiffness distribution, the Young’s modulus was
reconstructed by tracking the shear wave propagation within the ROI. Figure 3-4 (e,f)
showed that the shear wave front in the experimental group is further away from the
pushing point than that in the control group. The increasing stiffness from 4.4 kPa in the
control group to 6.55 kPa in the experimental group is consistent with our ARFI
observations. Our imaging system demonstrated the capability to precisely track small
changes in local stiffness and provide the quantified Young’s modulus of the cross-linked
region which is potentially useful in cornea-like microstructure tissue characterization.
Moreover, 3D volume imaging capability achieves some valuable information such as the
exact formalin drop position, volume of the target of interest and stereo tissue anisotropy
which may be useful for physicians performing refractive surgery or observing changes
after CXL treatment.
Any imbalance between aqueous humor production and outflow leads to abnormal IOPs
associated with eye diseases such as glaucoma. Therefore, the relationship between central
cornea stiffness and IOPs is important. Figure 3-5 (a-f) show the B-mode images under six
different IOP conditions. The thickness and curvature changes in B-mode at elevated IOP
are not obvious while ARFI images in Fig. 3-5 (g-l) show a better contrast than B-mode
images. In addition, the ARFI images, clearly show that corneal elasticity is IOP dependent,
and corneal structure appears to provide the central cornea with a greater stiffness than that
in the peripheral cornea (associated with greater tolerance to elevation in IOP). This finding
is consistent with previous studies (Elsheikh et al., 2015). Another possible influence factor
here is the boundary effect. In this study, the corneal tissue was mounted on a tissue
55

pedestal and its peripheral region was locked using a tissue retainer and locking ring which
were part of the artificial anterior chamber. This structure created additional boundary
conditions to affect the estimation accuracy of the peripheral cornea. In the present study,
we focused mainly on the central region of the cornea which appeared to be uniformly
distributed. The increasing stiffness of the central cornea at elevated IOP is based on the
fact that collagen fibers become taut at high IOP (Kling et al., 2010). Figure. 3-6 depicts a
visualization of shear wave propagation for different IOP levels, it’s obvious that shear
wave propagates further at higher IOPs under the same traveling time through tracking the
shear wavefront. Twelve cornea tissues were used to statistically investigate the
relationship between Young’s modulus and IOP as shown in Fig. 7. It has been previously
reported that under increasing IOP, collagen fibrils give rise to a non-linear mechanical
behavior of the cornea with a stiffening effect at IOP greater than 60 mmHg (Zhou et al.,
2017). It has also been shown both by finite element modeling as well as experimental data
analysis, that it is reasonable to model the cornea as a linear viscoelastic material around
the normal IOP range (12-22 mmHg) (Elsheikh et al., 2007; Elsheikh et al., 2010). In this
study, the stiffness of the cornea increased linearly as a function of IOP which is consistent
with previous literature studies.
The elasticity range of the cornea in the literature is very large, spanning a few orders
of magnitude from 1 kPa to greater than 1 MPa depending on many parameters such as test
conditions, species, and most importantly, measurement technique (Dias et al., 2015;
Elsheikh et al., 2008; Mikula et al., 2014; Wollensak et al., 2003). Some studies also
indicated that the thickness, curvature and fluid structure interface between the corneal
posterior surface and aqueous humor all must be considered for accurate biomechanical
56

assessment of the cornea (Han et al., 2017). In this study, the corneal tissue was mounted
at the artificial anterior chamber instead of using a whole eye globe. As a result, the
boundary conditions may also affect the measured corneal elasticity. According to the
previous literature, the Young’s modulus of the porcine cornea at 20 mmHg was reported
to be 1-10 kPa using ultrasound (Zhou et al., 2017) and around 60 kPa using OCE (Han et
al., 2015a; Han et al., 2017). Since there is no gold standard to follow and compared with
results above, our results are in a reasonable range. The cross-linked corneal elasticity is
influenced by many factors such as the amount and concentration of the formalin solution,
and the treatment time. It is therefore difficult to obtain quantitative comparison of our
observed cross-linked corneal elasticity measurements with those in the literature.
Nevertheless, the achievement of observing the small cross-linked region helps us to
demonstrate the high resolution capability of our system. Viscosity is another parameter
that is crucial for biomechanical characterization of tissues but is not easily measured in
cornea-like solids. To the best of our knowledge, viscosity of the cornea has not been well
measured experimentally.
Herein, we successfully demonstrate the capability of our imaging system to
characterize the biomechanical properties of the cornea through a high resolution ARFI
imaging and a quantitative Young’s modulus estimation at the ROI. However, there are
still some limiting factors that hinder the technology’s translational potential for clinical
diagnosis. First of all, the measured Ispta.3 (44.5 mW/cm
2
) of our imaging system is above
the FDA approved value (17 mW/cm
2
for ocular tissue). Given the fact that the minimum
displacement in the normal physiological IOP range (12-22 mmHg) in the current
experiments is ten times higher than our system’s minimum detectable ultrasonically
57

induced displacement (± 0.1 µ m), the acoustic output power can be expected to decrease
by at least a factor of 10 to meet the FDA standard without sacrificing too much image
contrast.
Second, the imaging frame rate is limited by the moving speed of the translation
motorized linear stage used in this study. In our current setup, the time to reconstruct one
group of images including the B-mode image, ARFI image, and the reconstructed Young’s
modulus map is on the order of tens of seconds which is still relatively slow. Integrating a
high-speed sector scanning motor would potentially achieve a much higher frame rate
without compromising the current image quality. Moreover, the future implementation of
advanced plane wave image processing algorithms using high frequency array-based
ultrasonic systems will further drive the practice of ultrasonic micro-elastography imaging
into in vivo study (Huang et al., 2017).
Third, formalin solution was used in this proof-of-concept study for artificially induced
corneal cross-linking because it is easier to use and more readily available than a
commercial FDA approved ultraviolet-activated riboflavin (UV-A) crosslinking machine.
Formalin crosslinking has been previously used by groups performing both ultrasound
(Shih et al., 2013) and OCT (Qu et al., 2016b) studies. In addition, therapeutic corneal
cross-linking using formaldehyde releasing agents is an open research topic (Babar et al.,
2015). However, it is recognized that in clinical practice and in vivo studies formalin is not
a current acceptable solution for general practice. In the future, UV-A crosslinking
procedures such as the UV-A dose time, intensity and spot size of the commercial UV-A
CXL system, would be comprehensively evaluated for human cornea or clinical translation
study.
58

Finally, the simple Kelvin-Voigt model for corneal elasticity assessment in this study is
known to be inaccurate and may lead to some bias because of boundary conditions and the
ratio of corneal thickness to shear wavelength. Derived from the Kelvin-Voigt model,
guided Lamb wave models have been proposed to further enhance estimation accuracy by
considering the confined structure of the cornea. For example, Nenadic et al. inferred the
Lamb wave model by considering corneal tissue bounded on both two fluids sides (Nenadic
et al., 2011b; Nenadic et al., 2011e); Han et al. calculated a modified Lamb wave model
which has no stress on the anterior surface and fluid on the posterior surface (Han et al.,
2017). In other words, Lamb wave model based results are highly influenced by the
structural definition and coupling medium conditions. In addition, Couade et al. suggested
that the experimental Lamb wave velocities are different from the measured values
(Couade et al., 2010a). The possible reason is the ratio between A1 and A0 modes in water.
These results indicate that the guided Lamb wave model is still under investigation and a
detailed analysis of mechanical mode propagation in a bounded medium is complicated,
requiring a careful theoretical analysis to account for the spherical geometry of the eye.
In summary, investigating the link between corneal microstructure and biomechanics of
the cornea may provide additional information that could be valuable in corneal disease
diagnosis and refractive surgery planning. We show proof of principle of using ultrasonic
micro-elastography to characterize biomechanical properties of the cornea qualitatively
and quantitatively. Achieving micro-level resolution, this technique can also be employed
to image the entire anterior segment of the eye where the UBM is currently used. Therefore,
the proposed ultrasonic micro-elastography method can provide clinicians with a powerful
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tool to assess both morphological and biomechanical properties of ocular tissue, potentially
leading to a new, routinely performed imaging modality in the field of ophthalmology.
Integrating a lamb wave model with our current ultrasonic micro-elastography imaging
system for quantitatively obtaining accurate viscoelastic properties of the cornea will be
introduced in next chapter.
60

Chapter 4 Quantitative Assessment of Thin Layer Tissue
Viscoelastic Properties Using Lamb Wave Model
4.1 Introduction
The mechanical properties of soft tissue are considered effective biomarkers for
diagnosis of various diseases. For example, several ophthalmic diseases affect corneal
viscoelastic properties, such as keratoconus and glaucoma (Kirwan and O’Keefe, 2008;
Deol et al., 2015). Arterial viscoelasticity has been associated with multiple comorbidities
such as type-1 and type-2 diabetes (Tryfonopoulos et al., 2005; Stehouwer et al., 2008),
hypertension(Laurent et al., 2003), coronary artery disease (Duprez and Cohn, 2007) and
most important hyperlipidemia (Simons et al., 1999). Even smoking and alcohol intake
would vary the stiffness of the arteries and lead to arterial diseases (Vlachopoulos et al.,
2010). However, characterization of the viscoelastic properties of the tissues at micro-level
thickness, such as the artery and the cornea, has been a challenge for many years. To date,
the mechanical properties of the cornea are commonly measured by Ocular Response
Analyzer (ORA) via corneal hysteresis curves. However, ORA cannot provide the
quantitative measurement of the corneal viscoelasticity. On the other hand, the stiffness of
artery is extensively detected by pulse wave velocity (PWV) technique, but only the global
average stiffness of artery can be obtained (Chiu et al., 1991). Despite the proposal of the
local PWV, it is still difficult to stream the dynamic physiological phenomena due to the
low frequency of the pulse wave (typically 1-2Hz) (Vappou et al., 2010). In addition, the
quantified viscosity is absent in both ORA and PWV methods for their objects. Therefore,
a suitable technique capable of high spatial resolution for accurately assessing the
quantitative viscoelasticity in the micro-level tissues is still necessary.
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In the past two decades, shear wave elastography (SWE) techniques (Chen et al., 2004;
Bercoff et al., 2004; Nightingale et al., 2003; Chen et al., 2009) have been proposed to
measure the mechanical properties of local tissue non-invasively. In SWE, an acoustic
radiation force was applied to induce the elastic wave propagation in the tissue, and the
measured speed of the shear wave is related to the elastic properties. The SWE technique
developed so far can be divided into two types, group velocity and phase velocity. Group
velocity is the speed of the envelope of the propagating elastic wave which is assumed to
travel in a purely elastic medium. Based on this assumption, SWE has been applied in
several tissues (breast (Tanter et al., 2008), liver (Palmeri et al., 2008), kidney (Syversveen
et al., 2011), cornea (Tanter et al., 2009), and artery (Ramnarine et al., 2014; Garrard et
al., 2015)). However, most of these studies cannot reflect the viscosity behavior of the
medium due to the physical limitation of group velocity, which might lead to the biased
estimation of elasticity in the confined geometry (Bernal et al., 2011).
On the contrary, the phase velocity (the velocity varies with the frequency) can reflect
both elastic and viscous information of the medium. To obtain the phase velocity, shear
wave dispersion ultrasound vibrometry (SDUV) has been proposed for estimating the
viscoelastic tissues. In this method, the dispersive shear wave was produced using an
acoustic radiation force or an external force with different vibrating frequencies. The
viscoelastic properties can be calculated by fitting the phase velocity curve using the
rheological model (Huang et al., 2013). A drawback of this method is that several
measurements have to be performed to obtain the whole dispersion curve. Recently, an
impulse method has been proposed to obtain phase velocity of tissue. In this method, the
elastic wave was produced by an acoustic radiation impulse force, and the phase velocity
62

was obtained from the k-space which was transformed by a spatial-temporal displacement
map from one measurement (Couade et al., 2010b). The impulse method has been recently
applied on the high-frequency ultrasound with a 40 MHz single transducer to measure the
viscoelasticity of the extracellular matrix of lung cancer cells for comparing the rheological
modulus of cells before and after drug treatment (Kuo et al., 2017). Although this was the
first phase-velocity-based SWE study using high-frequency ultrasound (> 30 MHz), the
study didn’t consider the geometry of medium, which might lead to an inaccurate result.
In a confined geometry, elastic wave propagation is strongly affected by the internal
reflections at the medium’s boundaries, resulting in guided wave propagation. The guided
wave is dispersive and complex, even when the material is only associated with elastic
properties. Recently, an anti-symmetric Lamb wave equation that reduces the complexity
has been proposed to mathematically model the guided wave propagation in a plate or a
cylinder with two free space in the fluid (Nenadic et al., 2011d). Several groups have
devoted to studying the Lamb wave effects or phenomena related to ultrasonic elastography
(Maksuti et al., 2016; Widman et al., 2016a). Moreover, the arterial stiffness has been
widely studied by using the Lamb wave model with the impulse method. In addition, Lamb
wave dispersion ultrasound vibrometry (LDUV) modified from SDUV has also been
proposed to measure the shear elasticity and the shear viscosity of gelatin, porcine spleen
and left ventricular myocardium (Nenadic et al., 2011a). In that method, the guided wave
was induced by using a shaker and was tracked by using a 7.5 MHz single transducer.
Similarly, most of these studies have been carried out by using the low-frequency
ultrasound to image the samples with a thickness of half-centimeter order. However, it
63

lacks the spatial resolution required to accurately detect the viscoelasticity of tissues like
the coronary artery or the cornea.
To improve the resolution for adapting the micro-level (dozen to hundred microns)
tissues in ultrasound, higher frequency transducers must be applied. However, high-
frequency ultrasound directly leads to higher acoustic attenuation which would not only
reduces the penetration but also drastically decrease the acoustic radiation force in the
tissue. In other words, the reduced acoustic radiation force might not induce enough
amplitude of elastic wave for detecting. This has led to the development of an ultrasonic
micro-elastography imaging system that utilized the dual-frequency set-up for effective
excitation in tissues by the low-frequency ultrasound and accurate detection of induced
displacements by the high-frequency ultrasound (Qian et al., 2017). Therefore, the aim of
the study is to integrate the Lamb wave model with our previously developed ultrasonic
micro-elastography imaging system for obtaining accurate viscoelastic properties in thin-
layer tissues.

4.2 Materials and Methods
4.2.1 Lamb Wave Model
Assuming elastic wave propagates in a homogeneous, isotropic, linear, infinitely large
and purely elastic medium, the speed of the elastic wave is considered as a constant and
unique velocity, which is defined as a group velocity (cg). With this assumption, the shear
elastic modulus ( μ) can be derived from the medium density ( ρ) and cg by equation (4-1)
µ = 𝜌 𝑐 𝑔 2
(4-1)
64

However, most tissues naturally exhibit both elastic and viscous behavior. A
viscoelastic description of the mechanical behavior of tissue is more accurate and
physically correct than a linear elastic one. The speed of elastic waves propagating in the
viscoelastic medium is dispersive (i.e., waves at different frequencies travel at different
speeds) rather than a constant, which is also defined as phase velocity (cp). The mechanical
properties can be estimated through the rheological models. Kelvin-Voigt elastic model
was applied in the study, which is widely used in gelatin phantom and most tissues. The
equation (4-2) is related to the phase velocity and the frequency
𝑐 𝑠 = √
2( 𝜇 2
+𝜔 2
𝜂 2
)
𝜌 ( 𝜇 +√𝜇 2
+𝜔 2
𝜂 2
)
(4-2)
where ω = 2πf is the angular frequency of vibration, µ and ɳ is the shear elasticity and shear
viscosity, respectively. µ and ɳ can be determined by fitting this elastic wave model
equation to the phase velocity curve cs= cp ( ω ).
The Lamb wave here is assumed that the guided wave travels in a thin layer when
satisfied the following two conditions: the compressional wave number for the thin layer
and the surrounding fluid are relatively small compared to the Lamb wave number; the thin
layer and fluid have a similar density. There are several modes of Lamb wave, which can
be mainly categorized into two groups: antisymmetric (An, n=0, 1, 2, …N) and symmetric
(Sn, n=0, 1, 2, …N). In the study, antisymmetric mode of Lamb wave was mainly induced
because the acoustic radiation force pushes in the same direction through the thickness of
the thin layer. Moreover, the zero-order modes can propagate at any frequency. Therefore,
antisymmetric with 0-order (A0) of Lamb wave can be detected (Couade et al., 2010b;
Nenadic et al., 2011d). The anti-symmetric Lamb wave dispersion equation (4-3) for a
viscoelastic thin layer submerged in an incompressible water-like fluid is as follows:
65

4𝑘 𝐿 3
𝛽 𝐿 cosh( 𝑘 𝐿 ℎ) sinh( 𝛽 𝐿 ℎ)− ( 𝑘 𝑠 2
− 2𝑘 𝐿 2
)
2
sinh( 𝑘 𝐿 ℎ) cosh( 𝛽 𝐿 ℎ) =
𝑘 𝑠 4
cosh ( 𝑘 𝐿 ℎ) cosh ( 𝛽 𝐿 ℎ) (4-3)
where 𝛽 𝐿 = √𝑘 𝐿 2
− 𝑘 𝑠 2
, 𝑘 𝐿 = 𝜔 /𝑐 𝐿 is the Lamb wave number, ω = 2πf is the angular
frequency, 𝑐 𝐿 = 𝑐 𝑝 is the frequency dependent Lamb wave velocity, 𝑘 𝑠 = 𝜔 √𝜌 𝑚 /𝑈 is the
shear wave number, 𝜌 𝑚 is the density of the sample, h is the half-thickness of the sample,
and U is the shear modulus. The shear modulus U can be expressed in terms of the
viscoelastic rheological models. To compare this Lamb wave mode with the shear wave
mode mentioned above, Kelvin-Voigt model was used for this equation, which is
represented to 𝑈 = 𝜇 + 𝑖𝜔 ɳ. µ and ɳ are the shear elasticity and shear viscosity.

4.2.2 Data Collection and Processing
The schematic of the experimental setup is shown in Figure 4-1(a). The detail
description can be found in Chapter 3.

Figure 4-1. Scanning scheme of high frequency ultrasonic micro-elastography imaging system (a) and
representative timing diagram for the impulse method and the harmonic method (b).
66

Figure 4-2. Flow chart for the post processing

The obtained RF raw data exported from the system were processed using Matlab
R2016b software (The MathWorks, Natick, MA, USA). Figure 4-2 illustrates the post-
processing steps for obtaining the shear viscoelasticity of tissues from RF raw data
generated by impulse and harmonic methods, respectively. Axial displacements over time
along each lateral position and depth was estimated using the gold standard normalized
cross-correlation algorithm with 1.5λ window size. The axial displacement map along
lateral position and time was obtained by averaging the axial displacements over the depths
of 1 mm (center of the medium ± 0.5mm) in all phantoms and the cornea, and 0.4 mm
(center of the medium ± 0.2mm) in the artery. All these regions were within the field of
view of our imaging system determined by the full width at half maximum (FWHM) of
axial intensity. Group velocities (cg) was estimated by applying a linear regression to the
67

time shifts versus the distance between each lateral position of the axial displacement map
generated from the impulse method. The time shift was defined as the time to get the
maximum derivative of displacement with respect to time at every lateral position. Shear
elastic modulus (µ ) can be derived from the density (𝜌 ) of the tissue and the cg following
by Equation (4-1). Phase velocity (cp) as a function of frequency (dispersion curve) can be
obtained by using both the impulse and harmonic methods. To be specific, the axial
displacement map was transformed from the spatial-temporal domain into the wavenumber
domain (k-space) by using 2D fast Fourier transfer to obtain an initial k-space map. To
avoid the low frequency/spatial frequency noise, the initial k-space map with frequency
below 5 Hz and spatial frequency below 125 cyc/m was masked. The masked k-space map
was then interpolated to obtain the final k-space map. The main spatial frequency (𝑘 𝐿 /2𝜋 )
for each frequency (f) in the first quadrant of k-space was found by identifying the intensity
maximum at that frequency. The phase velocity curve was calculated by the ratio of 2𝜋 f
and 𝑘 𝐿 (equation 4-4):
𝑐 𝑝 = 2𝜋𝑓 /𝑘 𝐿 (4-4)
The curve fitting was performed on the phase velocity at the certain frequencies. In the
harmonic method, the fundamental harmonic frequency is 50 Hz, so the phase velocities
were chosen at its harmonics from 200 Hz to 1000Hz. In general, an entire spectrum of the
phase velocity curve would be generated using the impulse method, however, in order to
compare with the harmonic method, the velocities at the frequencies of each 50 Hz from
200 to 1000 Hz were chosen in the impulse method as well. The final phase velocity curve
was then fit by linear least squares to Equation (4-2) and Equation (4-3), respectively, to
obtain the shear viscoelasticity of the tissues. The shear elasticity and shear viscosity were
68

varied in the model y(µ , ɳ)I with a step size of 0.1 kPa and 0.1Pa∙s until the error (R
2
)
between the model and the phase velocity data (cp(fi)) was minimized (equation 4-5):
𝑚𝑖𝑛 𝑅 2
= ∑[𝑦 ( µ, ɳ)
𝑖 − 𝑐 𝑝 ( 𝑓 1
, 𝑓 2
, 𝑓 3
, … , 𝑓 𝑛 ) ]
2
(4-5)
In the study, error ratio (ER) was calculated to present the differences between the
obtained fitting curve (Cfitting(fi)) and the data (equation 4-6):
𝐸𝑅 = 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 (
√
( 𝑐 𝑓𝑖𝑡𝑡𝑖𝑛𝑔 ( 𝑓𝑖 ) −𝑐 𝑝 ( 𝑓𝑖 ) )
2
𝑐 𝑝 ( 𝑓𝑖 )
) ∗ 100% (4-6)

4.2.3 Phantom and Biological Tissue Preparation
In the study, gelatin-(Gelatin G8-500, Fisher Scientific, USA) and agar-(Agar A360-
500, Fisher Scientific, USA) based tissue-mimicking phantoms with the same
concentration of silicon carbide powder (S5631, Sigma-Aldrich, St. Louis, MO, USA) as
the sound scatters were fabricated. Phantoms comprising gelatin at concentrations of 7%
and 12% and agar at concentrations of 1.5% were used in this study to represent materials
of different elasticity and viscosity. The gelatin and the agar were poured into the container
with a cylindrical cap with a diameter of 10 mm at the bottom when they were liquid. After
the gelatin and the agar coagulated, the cap was removed, so that the phantoms could be
considered to have a thin layer structure containing two free circular boundaries with a
diameter of 10 mm, as shown in Figure 4-1(a). Each phantom with differently designed
stiffness has three thicknesses of 2, 3, and 4 mm, respectively. Because the stiffness of the
gelatin phantoms could be affected by the temperature, all of the experiments were
performed at a constant room temperature of 25 C (Karpiouk et al., 2009). The repeating
69

measurements were performed using different speckle realizations in the phantoms by rotating
the sample with each angle around 120° .
To check the accuracy of the estimated viscoelasticity in the study, two viscoelastic
techniques were used: 1.) uniaxial mechanical testing (Model 5942, Instron Corp., MA,
USA) was performed on the same concentration of phantoms with a diameter of 25.4 mm
and a height of 10 mm to measure the shear elasticity. The tested shear elasticity is 2.9 ±
0.2 kPa, 10.9 ± 0.4 kPa and 26.0 ± 1.3 kPa for the 7%-gelatin, 12%-gelatin and 1.5%-agar
phantom, respectively, as listed in Table 4-1. 2.) shear wave rheological model (Equation
4-2) was applied on the bulk phantoms (200 mm (L) x 100 mm (W) x 50 mm (D)) of 7%
gelatin, 12% gelatin and 1.5% agar. The shear elasticity of the 7%-gelatin, 12%-gelatin and
1.5%-agar phantom was measured to be 3.0± 0.2, 10.4± 0.7 and 26.2± 1.3 kPa, respectively.
The shear viscosity was measured to be 0.6± 0.09 and 1.7± 0.16 for 7%- and 12%-gelatin
phantoms, respectively.

Table 4-1. Shear elasticity and shear viscosity of 7%, 12% gelatin and 1.5% agar phantoms with thickness of
2, 3, 4 mm obtained by fitting the Lamb wave model to the experimental data from the impulse and harmonic
methods against the results of mechanical tests and shear wave model in the bulk phantoms.

70

The biological tissue experiments were performed on a porcine cornea and a rabbit
carotid artery ex vivo. Fresh unscalded porcine eyeballs and rabbit carotid artery were
collected from a local slaughter house (Sierra Medical Science, Inc., Whittier, CA, USA),
with all experiments being performed within 12 h of their collection. To guarantee the
objects were with two free boundaries in the fluid, the posterior segment of the eyeball and
one side of the arterial wall along the axial direction were embedded in the coagulated 8%
gelatin in the container. The prepared samples were immersed into the saline solution in a
water tank when performing the experiments. All the experiments were performed at a
room temperature of 25 C. The intra-ocular pressure (IOP) of the ex vivo eyes was
maintained at 5-mm Hg without applying additional pressure during the experiment. The
thickness of the porcine cornea and the rabbit artery was measured 1.5 mm and 0.8 mm,
respectively, by the B-mode images using the 40 MHz needle transducer.

71

4.3 Results

Figure 4-3. Results of each post-processing step by performing the impulse method (a)-(d) and the harmonic
method (e)-(f) in the 7% gelatin phantom with a thickness of 4 mm. Axial displacement map (a) and (e), k-
space (b) and (f), phase velocity curve (c) and (g) as well as fitting curve (d) and (h), are presented.

Figure 4-3 illustrated the representative results of each post-processing step by
performing the impulse method (Figure 4-3(a)-(d)) and the harmonic method (Figure 4-
3(e)-(f)), respectively, on the 7% gelatin phantom with a thickness of 4 mm. The axial
72

displacement map along the lateral positions versus the time is shown in Figure 4-3(a) and
(e). The guided wave traveled in the two reverse directions from the lateral position of 0
mm at which the pushing beam of ring transducer focused. The traveling wave crest
exhibits a linear trend, so that the group velocity could be approximated by using a linear
regression of the slope of the wave crest, as indicated by the black line in Figure 4-3(a).
The k-space maps along the wavenumber and the frequency were transformed from the
half of the spatiotemporal map (region within the orange line in Figure 4-3(a) and (e)).
Since the combined effect of the viscoelastic properties and the confined geometry of the
phantom, the dispersive phenomenon was obviously apparent in the k-space, as shown in
Figure 4-3(b) and (f). The phase velocity curve was estimated by Equation (4-4) related to
the frequency and the main wavenumbers found by identifying the maximum intensity at
each frequency. The phase velocity curve of the impulse method could fully cover the
frequency range up to 1000 Hz, as shown in Figure 4-3(c). However, the phase velocities
of the harmonic method were scattered until the phase velocities were selected at the
fundamental frequency of 50 Hz and its harmonic frequencies from 200 Hz to 1000 Hz, as
shown in Figure 4-3(g). To compare with the harmonic method, the same frequencies and
their corresponding velocities were selected for the impulse method. The final shear
viscoelasticity and its corresponding phase velocity curve can be obtained by fitting the
phase velocity data to the Lamb wave model (Equation (4-3)).

73

Figure 4-4. Group velocity and the phase velocity in 7% gelatin (a), 12% gelatin (b) and 1.5% agar phantoms
(c).

Figure 4-4 demonstrates the phase velocities at 1000 Hz and the group velocities from
all the phantoms, including 7%-gelatin, 12%-gelatin and 1.5%-agar phantoms with
different thicknesses (2, 3 and 4 mm), by using the impulse and harmonic methods. In all
the cases, the velocity increased with the thickness of phantom, which is consistent with
the previous literature that uses the finite element method to simulate elastic plates with
varied thicknesses (Maksuti et al., 2017; Han et al., 2015b). The phase velocities generated
by the impulse method and the harmonic method are almost identical at 1000 Hz. In
addition, the group velocities and the phase velocity are in good agreement for all of the
phantom, except the 12%-gelatin and 1.5%-agar phantom with 2 mm thickness. Given the
fact that the group velocity cannot reflect the real situation for the thin layer structure,
which is reconfirmed by using the high-frequency ultrasound.
74

Figure 4-5. Experimental phase velocity (symbols) of gelatin and agar phantoms with different thicknesses
of 4 mm (a) and (d), 3 mm (b) and (e), and 2 mm (c) and (f), as well as their corresponding fitting curve
(lines) from the impulse method (a)-(f) and the harmonic method (g)-(i).

Figure 4-5 illustrates the phase velocities and their corresponding fitting curves from all
the thin-layer phantoms. All fitting results of shear elasticity and shear viscosity are listed
in Table 4-1. The fitting curves in Figure 4-5 were estimated by taking the mean shear
viscoelasticity in Table 4-1 into Equation (4-3) with frequency. With the same thickness,
the wave velocities in the 1.5%-agar phantoms are higher than those in the 12%- and 7%-
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gelatin phantoms, and the lowest wave velocities were associated with the 7%-gelatin
phantom. All the fitting curves by using Lamb wave model were well matched. For the
gelatin phantoms, the average ERs were ranged from 1.2 to 3.2 % by using the Lamb wave
model. In the study, the agar phantoms were assumed to be homogeneous and isotropic
with a negligible viscosity (Han et al., 2015c; Ahmad et al., 2014). The fitting curves of
Lamb wave model in the agar phantoms are still dispersive with average ERs ranged from
7.3 to 10.5 %. The results demonstrate that the guided wave propagation in a confined
geometry is still dispersive, even the medium itself is purely elastic, such as seen in
viscoelastic media.
Figure 4-6 presents all of the measured shear elasticity in Table 4-1 as vertical bars.
First of all, the elasticity measured from the bulk phantoms are in good agreement with the
results of the mechanical test. For the thin-layer phantoms, the shear elasticity estimated
by the group velocity were all obviously underestimated, especial for the phantoms with 2
mm thickness. However, by using the impulse method and the harmonic method with the
Lamb wave model, the shear elasticity of 7%-, 12%-gelatin and 1.5%-agar phantoms with
three thicknesses are in good agreement with the elasticity of the bulk phantoms measured
from the mechanical test and the shear wave rheological model. These results confirmed
that the Lamb wave model is superior to the group velocity equation on quantitatively
assessing the elastic properties of thin-layer structure by using the high-frequency
ultrasound.
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Figure 4-6. Shear elasticity of 7% gelatin (a), 12% gelatin (b) and 1.5% agar phantoms (c) with thicknesses
of 2, 3 and 4 mm against the results of the mechanical tests and the shear wave rheological model in the bulk
phantoms.

The viscosities of 7%- and 12%-gelatin phantoms with different thicknesses were
measured 0.20 to 0.42 Pa∙s and 0.85 to 1.26 Pa∙s, respectively, by using the Lamb wave
model (including two excitation methods), as listed in Table 4-1. Compared to the results
measured from the bulk phantoms with the same concentration gelatin by using the shear
wave rheological model, the viscosity from the thin-layer phantoms were slightly
underestimated, as shown in figure 4-7 (a) and (b). However, the viscosity of the polymer,
such as these gelatin phantoms, still has no golden standard to follow. According to the
previous literature (Huang et al., 2011), the viscosity was reported 0.3 Pa∙s in a 7% gelatin
phantom by measuring the displacements of a solid sphere embedded in the gelatin induced
by the acoustic radiation force. The viscosity of 12% gelatin has never been reported, the
nearest measurement was performed on a 15% gelatin phantom by measuring the Lamb
wave dispersion induced by applying a sinusoidal force from a shaker. In their results, the
viscosity of 15% gelatin was measured with a wide variation from 0.3 to 1.1 Pa∙s. Therefore,
the results of the viscosity of the gelatin phantoms in our study were considered within a
reasonable range.
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Figure 4-7. Shear viscosity of 7% gelatin (a) and 12% gelatin (b) with thicknesses of 2, 3 and 4 mm against
the results of the shear wave rheological model in the bulk phantoms.

Figure 4-8 demonstrates the results of the porcine cornea. The phase velocities data were
obtained from both the impulse method and the harmonic method. The curves were fitted
by the Lamb wave model with ERs from 1.5 to 2.1 %. The shear elasticity and the shear
viscosity was measured 9.6 kPa and 0.8 Pa∙s by using the impulse method, 8.2 kPa and 0.9
Pa∙s by using the harmonic method. Several studies have investigated the elastic properties
of cornea thorough shear wave measurement by using ultrasonic or optical method, but few
of them took the confined geometry and viscosity into consideration (Wang and Larin,
2014; Hollman et al., 2002; Han et al., 2017; Qu et al., 2016a). A study by Han et al.
reported that the shear viscoelasticity of porcine cornea was estimated to be 13.9 kPa with
0.7 Pa∙s at the applied IOP of 15 mm-Hg by using an optical coherence elastography (OCE)
system with a modified Rayleigh-Lamb wave model (Han et al., 2017). Given the fact that
the shear elasticity increase with the applying IOP and the viscosity decrease with the IOP,
our measured elasticity and viscosity, obtained at an IOP of 5 mm-Hg, are within a
reasonable range.
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Figure 4-9 demonstrates the fitting results of the intact rabbit carotid artery by using the
impulse method and the harmonic method with the Lamb wave model. The shear elasticity
and the shear viscosity was measured 27.9 kPa and 0.1 Pa∙s by using the impulse method

Figure 4-8. Phase velocity of porcine cornea and its corresponding fitting curve by using the impulse and
harmonic method

Figure 4-9. Phase velocity of rabbit carotid artery and its corresponding fitting curve by using the impulse
and harmonic method.

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(ER=4.5 %), 26.5 kPa and 0.1Pa∙s by using the harmonic method (ER=3.4 %), respectively.
According to the previous literature (Matthews et al., 2010; Garcia and Kassab, 2009;
Gundiah et al., 2008), the elasticity range of the artery is very large, spanning a few orders
of magnitude from tens to hundreds of kPa depending on many parameters such as testing
conditions, species, and most importantly, measurement technique. However, our results
of the arterial elasticity are within the same order as the study using the Lamb wave model,
which reported that the shear elasticity of porcine carotid artery was measured from 24.22
to 44.71 kPa at transmural pressure from 10 to 100 mm-Hg, respectively.

4.4 Discussion and Conclusion
Since it is difficult to use a high frequency transducer to induce enough amplitude of
the shear wave because of the attenuation of the acoustic radiation force, the high frequency
shear wave/Lamb wave imaging systems have been carried out by using two separate
transducers for push and track individually. To the best of our knowledge, the study from
Kuo et al. has been the only one high frequency shear wave imaging technique related to
the phase velocity. Due to the size of the transducers, the pushing transducer was tilted
with the vertical axis, and the imaging transducer was perpendicular to the length of the
objects. Similar system setups were also found in OCE with a modified Rayleigh–Lamb
wave model for assessing the cornea using a tiled air-port (Han et al., 2014), and acoustic
micro-tapping technique using a tiled air-coupled ultrasound transducer (Ambroziński et
al., 2016). However, guided waves propagating along a free plate can be separated in two
uncoupled kinds of waves: Love waves (the displacements have a zero projection on the
normal to the plate) or Lamb waves (the projection of the displacements on the normal to
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the plate is nonzero). All of these setups might lead to the inaccurate estimation because of
the component of love wave in the Lamb wave. For comparison, the acoustic radiation
force is applied orthogonally to the thin layer structure, meaning only the Lamb waves are
generated in our experimental setup.
The harmonic method proposed in the study improved the efficiency of SDUV/LDUV
technique. In SDUV/LDUV, several measurements should be performed by changing the
different modulated frequencies to obtain a whole dispersive curve. However, the
dispersion curve can be obtained in a single measurement by extracting velocities at the
fundamental frequency and its harmonics. The estimated values of the shear elasticity and
viscosity for the gelatin, agar, cornea and carotid artery samples using the harmonic method
are in good agreement with the results using the impulse method which has been so far a
standard method, as shown in Figure 4-5, 4-8 and 4-9. The advantage of applying the
acoustic force with mono-frequency for elastography has been discussed in the previous
literature using optical coherence elastography. Since the materials respond primarily at
their mechanical resonant frequencies, the contrast of the elastography has been found
significantly improved by applied the ARF at the resonate frequency of the targeting
samples (Adie et al., 2010; Qi et al., 2013). Therefore, although the harmonic method
consumed more time than the impulse method during scan (200 ms vs 10 ms for one
representative timing step), we believed it still has potential for implemented on a specific
frequency to suit the medium’s natural resonant frequency to obtain a higher contrast
elastography, especially for atherosclerosis which has the varying resonant frequencies in
different fibrous caps.
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In the study, the frequency response of the gelatin phantoms, agar phantoms, cornea and
artery was assumed to obey the Kelvin-Voigt model which consists of an elastic term and
a frequency dependent viscous term. The Kelvin-Voigt model has been widely used to
estimate the viscoelastic properties of gelatin phantoms and agar phantoms (Catheline et
al., 2004), as well as several soft tissues including artery and cornea (Sunagawa and Kanai,
2005; Zhang et al., 2005). However, the comparisons among each linear viscoelastic model
for the appropriateness of cornea and artery has not been extensively studied. On the other
hand, a large number of the linear viscoelastic models with various characteristic
frequencies can be used to approximate the continuous spectrum functions in principle
(Zhang et al., 2007). Since the guided wave in the viscoelastic medium of the thin layer is
highly frequency dependent and have different modes, a more complex model with
multiple elastic and viscous terms (which cover a range of characteristic frequency), such
as generalized Maxwell model, might be necessary to describe the whole dispersive
phenomenon. However, the complex model with multi parameters would lead to the
incredible complexity and difficulties for the Lamb wave model fitting. To overcome this
problem, a model-free method has been developed by Nenadic’s group. In their method,
the viscoelastic properties can be estimated through a simple calculation by measuring the
wave velocity and attenuation.
Generally, an antisymmetric mode with zero order (A0) of Lamb wave was mainly
induced by using acoustic radiation force technique. This is because the acoustic radiation
force pushes in the same direction through the thickness of the thin layer and induced the
bandwidth of the guided wave is usually below 2000 Hz. However, the other modes,
especially A1, can be still produced and might also merge into the measured phase velocity
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to cause large biased estimation at low frequency (Nenadic et al., 2011c). The phase
velocity at low frequencies is not reliable. Moreover, the bandwidth of the phase velocity
depends on the excitation duration and the harmonic frequency used to generate the guided
wave propagation. In our settings, the intensity of the impulse and harmonic signals above
the frequency of 1000 Hz were too low to detect. Several studies have set the cut-off
frequency for fitting the biological data to the Lamb wave model. Maksuti et al. estimated
the elastic properties of plate- and hollow cylinder-PVA phantoms by fitting the phase
velocity within the frequency range from 200 Hz to 1000 Hz to the Lamb wave model. Han
et al. estimated the viscoelastic properties of porcine corneas by fitting the phase velocity
within the frequency range from 200 Hz to 800 Hz to a modified Rayleigh-Lamb wave
model. Therefore, following the previous literature, the fit between the plate model and the
experimental dispersion curve was performed for the reliable frequency range from 200 to
1000 Hz.
This study successfully combined the Lamb wave model with our previously developed
ultrasonic micro-elastography imaging system for obtaining the viscoelastic properties in
the thin-layer tissues. The phase velocity in the tissue was induced by the impulse method
and the harmonic method. Based on the Lamb wave model, the measured shear elasticity
of the thin layer tissue-mimicking phantoms with different thicknesses are consistent with
the results of the mechanical test and the shear wave rheological model in the bulk
phantoms, and the trend of the measured shear viscosities of these phantoms were in a good
agreement with the results of the shear wave rheological model. On the contrary, the shear
viscoelasticity of the thin-layer phantoms estimated from the group velocity were not
matched with the results of the mechanical tests. The shear elasticity and the shear viscosity
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of the porcine cornea and the rabbit are also reported by using both of the impulse and
harmonic methods. All of the results demonstrate that this ultrasonic micro-elastography
imaging system combining with the Lamb wave model can provide accurate shear
viscoelasticity of the thin layer tissues, which indicates its promising future for improving
the diagnosis for multiple clinical applications.

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Chapter 5 Array based Elastography Imaging System
5.1 Introduction
Compared with other imaging modalities such as MRI, CT, the beauty of ultrasound
imaging is the high frame rate capability (up to 50 fps in conventional ultrasound imaging).
However, our previous studies with the implementation of high frequency single-element
needle transducer have a relative low frame rate restricted by mechanical scanning
(typically need 1-2 minutes to finish 1D scanning), which limits its ability to translate into
in vivo or clinical study. In addition, for needle transducer based micro-elastography
system, it can only monitor the tissue response at one lateral location for each induced
deformation. It means that we need to ‘push’ the same tissue multiple times to get the time-
dependent displacement curves at all lateral propagation locations. Due to the limitations
of low frame rate and potential thermal bio-effect, a high frequency array transducer
(Huang et al., 2017) that allows for the electronic steering of detection beams is a favorable
solution for improving elastography resolution, FOV and frame rate.
Glaucoma is a leading cause of vision loss and blindness worldwide and yet the
pathophysiology of the glaucomatous process is still not fully understood. Loss of vision
in glaucoma is due to damage to the retinal ganglion cell axons that carry visual information
to the brain. This damage is believed to initiate at the level of the ONH from higher pressure,
within the ONH which may be caused from sclera. In the vast majority of instances, vision
lost to glaucoma cannot be recovered, and therefore early detection and prevention are key
areas of ongoing research. Elevated IOP is one of the top risk factors for the disease and
the only known risk factor that can be modified. However, the effects of elevated IOP on
the eye can vary substantially from one eye to another. Eyes with similar clinical features
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can progress very differently under the same level of IOP. Some eyes can withstand high
levels of IOP with no glaucomatous vision loss (ocular hypertension) whereas others
exhibit glaucomatous damage at statistically normal levels of IOP (normal tension
glaucoma). There, exploring the biomechanical properties of the sclera in conjunction with
glaucoma is an important research goal. The previous proposed needle transducer based
elsatography system is not suitable to image the posterior sclera of the eye globe because
the needle transducer is not able to insert and locate inside the eye globe. Therefore, we
developed an array based elastography system to characterize the biomechanics of the
posterior sclera.

Figure 5-1. Verasonics system and its array transducers. (Source data from Verasonics website)

86

5.2 Methods
5.2.1 Ultrafast plane wave imaging
Figure. 5-1 shows the Verasonics high frequency imaging system used to drive the high
frequency array transducer. To develop array based elastography system, the excitation
source can be either single-element transducer for fixed pushing beam or low frequency
array to create dynamic focusing beams. Regarding of the detection part, the conventional
line by line electronic scanning mode with up to 50 fps rate is not enough to enable the
visualization of transient events such as shear wave propagation for elasticity imaging. To
overcome this issue. Fink and co-authors successfully demonstrate the concept of plane
wave illuminations leading to ultrafast frame rate (Tanter and Fink, 2014). Instead of firing
the elements line by line in conventional ultrasound, plane wave imaging fires all the
elements simultaneously. As a results, the maximum frame rate is only determined by the
time to transmit a beam and receive the backscattered echoes (round trip of penetration
depth).
Owing to the lack of the transmit focusing in plane wave imaging, there is a reduced
image contrast and resolution. To overcome this limitation, Montaldo et al. (Montaldo et
al., 2009) proposed to implement several tilted plane waves and coherently added to
produce a full image. This technique presents strong conceptual analogies with the
synthetic aperture method. The quality of the reconstructed image is determined by the
number of angles. The more angles used will increase the image qualify but decrease the
frame rate of the data acquisition system. Therefore, there is a trade-off between the image
quality and the maximum frame rate. It was demonstrated that the coherent summation of
compounding plane wave is a very promising mode for transient elastography imaging
87

because it maintains the high image quality while increasing the temporal resolution
(around a factor of 10 comparing with conventional imaging mode).

5.2.2 Array based elastography system
Similar with previous reported studies, the array based elastography system needs the
dual-frequency configuration as well. Herein, we used the linear array transducer with the
center frequency of 18 MHz as the receiver transducer. Five different transmission angles
(-6° to 6° with a step size of 3° ) were implemented and then coherently added to produce
one higher-contrast ultrasound image at 3 kHz effective pulse repetition frequency (PRF).
The effective PRF is chosen based on the distance between imaging probe and imaging
subject and the maximum possible shear wave speed. All time gain compensation (TGC)
options were kept the same for all acquisitions. Delay-and-sum (DAS) based software
beamforming was applied to raw RF data and the beamformed IQ data were saved for post-
processing using MATLAB 2018a software (The MathWorks, Natick, MA, USA).
In order to induce the deformation in stiff tissue – posterior sclera, a piston low
frequency transducer was designed and fabricated. The pushing transducer has 8 mm
aperture size with a center frequency of 5.4 MHz. Figure 6-2 shows the alignment of the
array elastography system. The pushing transducer was put in the middle of the array
transducer and both of the transducers are aligned using a wire phantom at the focal
distance of the pushing transducer – 8 mm.
The spatial resolution of the array based elastography system is mainly determined by
the detection array transducer. In order to evaluate the spatial resolution of array transducer
under current compounding plane wave setup, a wire phantom consisting of one piece 10
88

µ m of tungsten wire (California fine wire company, Grover beach, CA, USA) was used.
The wire was first positioned normal to the ultrasound image plane so that the cross-section
of the wire was estimated to be significantly smaller than the diffraction limited resolution
of the scanner and was used to mimic a point scatter. The perpendicular alignment of the
transducer with the wire was performed with an estimated error of less than 5° . Then the
transducer was positioned at the center of the field of view and was moving axially to adjust
the distance between the array and the wire phantom. The full width half maximum
(FWHM) through the pixel that contained the centroid was calculated for every individual
frame and the imaging resolution of the array system was measured as the average FWHM
of all frames. Table 5-1 lists the experimentally test FWHM spatial resolution at different
depth.

Figure 5-2. The photography of the array elastography system setup. The pushing and array transducer were
aligned using a wire phantom where the focal point of the pushing transducer is located in the middle of the
array transducer.

89

5.2.3 Imaging Subject
To first demonstrate the capability of the array based elastography system on tracking
shear wave propagation, we designed and fabricated a homogenous gelatin phantom with
an estimated Young’s modulus of 17 kPa. To image the posterior sclera, we removed the
anterior chamber of the porcine eyeball and used the gelatin phantom as the base to hold
the posterior segment of the eye. During the experiment, the sample was submerged in a
tank with balanced salt solution.

5.3 Results and Discussion
The calculated axial and lateral resolution at different depths were shown in Table 4-1.
The results indicate that the array based elastography system has the capability to
distinguish small structure tissue at hundred micron level. Therefore, applying this system
to image gelatin phantom with over 10 mm thickness and posterior sclera (over 1 mm
average thickness) is sufficient.

Table 5-1. The FWHM spatial resolution of the linear array transducer.
Imaging depth
(mm)
Axial resolution
(µm)
Lateral resolution
(µm)
5 94.33 126.72
6 98.03 121.14
7 101.27 117.9
8 100.85 119.13
9 101.54 121.89
10 101.77 126.53
11 103.27 132.54
12 106.25 139.45
13 109.36 148.51
14 110.21 158.96
15 110.93 169.4
16 113.8 180.77
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17 115.49 192.92
18 117.32 201.82
19 119.29 212.49
20 123.42 225.31

Figure. 5-3 shows the imaging results of homogenous gelatin phantom and posterior
sclera. The B-mode image of gelatin phantom had a uniform scatter distribution. Regarding
of the posterior segment of the eye, the retina, sclera and periorbital fat tissue underneath
were clearly observed in B-mode structural image. The second column of images showed
the shear wave propagation at different time series. Owing to higher stiffness of sclera
tissue than the fabricated gelatin phantom, the plotting time interval is different between
phantom (400 µ m interval plotting time) and sclera (225 µ m interval plotting time). The
Young’s modulus of the phantom calculated from shear wave speed is 15.75± 0.89 kPa
which is close to its designed parameter – 17 kPa, demonstrate the accuracy of our array
based elastography imaging system. The reconstructed Young’s modulus of posterior
sclera is around 70 kPa.
These results demonstrate the capability of using dual frequency array based
elastography system to characterize the biomechanical properties of soft tissues non-
invasively and at high frame rate. There are still some limitations in this study. The
frequency of the array is not optimal, we need to evaluate the best frequency for imaging
the posterior sclera using the whole eye globe. In addition, the size of the linear array
transducer is too large, which is difficult to co-register with the ring-shape transducer.
91

Figure 5-3. The B-mode image and shear wave propagation at three time-series of (a) the 6% gelatin
concentration tissue-mimicking phantom, and (b) one ex vivo posterior segment of porcine eyeball. The shear
wavefronts were clearly observed along all directions of phantom and the curvature of posterior sclera.
According to the shear wavefront location and propagation time, the Young’s modulus of phantom/posterior
sclera was reconstructed from the estimated shear wave speed. The arrow in the figures showed that the
region of the applied ARF force and the dash line described the boundary of the sclera tissue observed from
B-mode image.

92

Chapter 6 Summary and Future Work
6.1 Summary
In this research, ultrasonic micro-elastography imaging system has been successfully
developed to provide the biomechanical properties of soft tissues both qualitatively (via
ARFI) and quantitatively (via SWEI). The spatial resolution, image contrast, imaging field
of view of elastography system were experimentally calculated and measured using layer
structure gelatin based tissue mimicking phantom. These results show our system has the
capability to mapping the tissue stiffness in tiny scales.
Then we applied this technology to thin-layer tissue – the cornea. To fully investigate
the relationship between the cornea biomechanics and some ocular diseases such as
keratoconus and glaucoma, we performed the test under two experimental conditions,
including corneal cross linking (linked with keratoconus) and various intraocular pressures
(linked with glaucoma). Instead of using group velocity of the shear wave under the
assumption of a pure elastic material in chapter 2, phase velocity with the consideration of
shear wave dispersion issue was implemented in chapter 3 in order to represent the
viscoelastic properties of the cornea. However, for thin-layer tissues, shear wave
propagation suffers from boundary conditions such as multiple reflections, which may lead
to bias estimation. In chapter 4, we proposed a Lamb wave model to provide a more
accurate estimation of tissue elasticity and viscosity.
One of the limitations of the single-element based elastography system is the imaging
frame rate restricted by the low mechanical scanning speed. Array transducer with
electronic scanning has the ability to provide the high frame with while maintaining good
93

spatial resolution. In Chapter 5, we proposed dual frequency array-based elastography
system. The compounding plane wave technique and beamforming are involved.

6.2 Future Work
The work presented in this thesis is a proof of principle of ultrasonic micro-elastography
concept and show its favorable prospect on some clinical applications such as ocular tissues
and the artery. In addition, we have shown a demo on array-based elastography imaging
system with the implementation of high frame rate plane wave imaging technology. The
future development of ultrasonic micro-elastography will lie in two aspects.
The first aspect is regarding of the pushing transducer. In either current single-element
or newly developed array based elastography system, the pushing transducer used for
inducing tissue deformation is still a ring-shape single element transducer. The fixed focal
depth, beamwidth limited its capability into clinical study. The future system will integrate
with an array transducer to dynamic control the region of excitation.
The second aspect is to develop and improve high frequency ultrasound array. The array
we used in our previous studies is an 18 MHz commercial linear array. However, the length
of the array (over 13 mm) limits its ability to co-register with our ring-shape pushing
transducer. A customized small size array is desired. In addition, 1D array only track the
shear wave propagation in 2D space instead of its propagation in 3D. To track the shear
wave propagation in 3D would enhance its capability to reveal some important parameters
such as anisotropy. Therefore, 2D high frequency array is the future direction of high
resolution ultrasound elstography system.
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BIBLIOGRAPHY
Achenbach J 2012 Wave propagation in elastic solids vol 16: Elsevier)
Adie S G, Liang X, Kennedy B F, John R, Sampson D D and Boppart S A 2010 Spectroscopic
optical coherence elastography Optics express 18 25519-34
Ahmad A, Kim J, Sobh N A, Shemonski N D and Boppart S A 2014 Magnetomotive optical
coherence elastography using magnetic particles to induce mechanical waves Biomedical
optics express 5 2349-61
Ambroziński Ł, Song S, Yoon S J, Pelivanov I, Li D, Gao L, Shen T T, Wang R K and O’Donnell
M 2016 Acoustic micro-tapping for non-contact 4D imaging of tissue elasticity Scientific
Reports 6
Andreassen T T, Simonsen A H and Oxlund H 1980 Biomechanical properties of keratoconus and
normal corneas Experimental eye research 31 435-41
Babar N, Kim M, Cao K, Shimizu Y, Kim S-Y, Takaoka A, Trokel S L and Paik D C 2015 Cosmetic
preservatives as therapeutic corneal and scleral tissue cross-linking agents Investigative
ophthalmology & visual science 56 1274-82
Bercoff J, Tanter M and Fink M 2004 Supersonic shear imaging: a new technique for soft tissue
elasticity mapping IEEE transactions on ultrasonics, ferroelectrics, and frequency control
51 396-409
Bernal M, Nenadic I, Urban M W and Greenleaf J F 2011 Material property estimation for tubes
and arteries using ultrasound radiation force and analysis of propagating modes The
Journal of the Acoustical Society of America 129 1344-54
Binder P S 2007 Analysis of ectasia after laser in situ keratomileusis: risk factors Journal of
Cataract & Refractive Surgery 33 1530-8
Blacher J, Guerin A P, Pannier B, Marchais S J and London G M 2001 Arterial calcifications,
arterial stiffness, and cardiovascular risk in end-stage renal disease Hypertension 38 938-
42
Cartwright N E K, Tyrer J R and Marshall J 2011 Age-related differences in the elasticity of the
human cornea Investigative ophthalmology & visual science 52 4324-9
Catheline S, Gennisson J-L, Delon G, Fink M, Sinkus R, Abouelkaram S and Culioli J 2004
Measurement of viscoelastic properties of homogeneous soft solid using transient
elastography: An inverse problem approach The Journal of the Acoustical Society of
America 116 3734-41
Chen S, Fatemi M and Greenleaf J F 2004 Quantifying elasticity and viscosity from measurement
of shear wave speed dispersion The Journal of the Acoustical Society of America 115 2781-
5
Chen S, Urban M W, Pislaru C, Kinnick R, Zheng Y, Yao A and Greenleaf J F 2009 Shearwave
dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity
IEEE transactions on ultrasonics, ferroelectrics, and frequency control 56 55-62
Chiu Y C, Arand P W, Shroff S G, Feldman T and Carroll J D 1991 Determination of pulse wave
velocities with computerized algorithms American heart journal 121 1460-70
Cook J R, Bouchard R R and Emelianov S Y 2011 Tissue-mimicking phantoms for photoacoustic
and ultrasonic imaging Biomedical optics express 2 3193-206
Couade M, Pernot M, Prada C, Messas E, Emmerich J, Bruneval P, Criton A, Fink M and Tanter
M 2010a Quantitative assessment of arterial wall biomechanical properties using shear
wave imaging Ultrasound in medicine and biology 36 1662-76
Couade M, Pernot M, Prada C, Messas E, Emmerich J, Bruneval P, Criton A, Fink M and Tanter
M 2010b Quantitative assessment of arterial wall biomechanical properties using shear
wave imaging Ultrasound in medicine & biology 36 1662-76
95

Curatolo A, Villiger M, Lorenser D, Wijesinghe P, Fritz A, Kennedy B F and Sampson D D 2016
Ultrahigh-resolution optical coherence elastography Optics letters 41 21-4
Deol M, Taylor D A and Radcliffe N M 2015 Corneal hysteresis and its relevance to glaucoma
Current opinion in ophthalmology 26 96
Dias J, Diakonis V F, Lorenzo M, Gonzalez F, Porras K, Douglas S, Avila M, Yoo S H and Ziebarth
N M 2015 Corneal stromal elasticity and viscoelasticity assessed by atomic force
microscopy after different cross linking protocols Experimental eye research 138 1-5
Doherty J R, Trahey G E, Nightingale K R and Palmeri M L 2013 Acoustic radiation force elasticity
imaging in diagnostic ultrasound IEEE transactions on ultrasonics, ferroelectrics, and
frequency control 60 685-701
Doyley M M and Parker K J 2014 Elastography: general principles and clinical applications
Ultrasound clinics 9 1-11
Duprez D A and Cohn J N 2007 Arterial stiffness as a risk factor for coronary atherosclerosis
Current atherosclerosis reports 9 139-44
Elsheikh A, Alhasso D and Rama P 2008 Biomechanical properties of human and porcine corneas
Experimental eye research 86 783-90
Elsheikh A, Geraghty B, Rama P, Campanelli M and Meek K M 2010 Characterization of age-
related variation in corneal biomechanical properties Journal of the Royal Society Interface
rsif20100108
Elsheikh A, McMonnies C W, Whitford C and Boneham G C 2015 In vivo study of corneal
responses to increased intraocular pressure loading Eye and Vision 2 20
Elsheikh A, Wang D and Pye D 2007 Determination of the modulus of elasticity of the human
cornea Journal of refractive surgery 23 808-18
Famaey N and Sloten J V 2008 Soft tissue modelling for applications in virtual surgery and surgical
robotics Computer methods in biomechanics and biomedical engineering 11 351-66
Fung Y-c 2013 Biomechanics: mechanical properties of living tissues: Springer Science &
Business Media)
Garcia M and Kassab G S 2009 Right coronary artery becomes stiffer with increase in elastin and
collagen in right ventricular hypertrophy Journal of Applied Physiology 106 1338-46
Garrard J, Ummur P, Nduwayo S, Kanber B, Hartshorne T, West K, Moore D, Robinson T and
Ramnarine K 2015 Shear wave elastography may be superior to greyscale median for the
identification of carotid plaque vulnerability: A comparison with histology Ultraschall in
der Medizin-European Journal of Ultrasound 36 386-90
Gundiah N, Matthews P B, Karimi R, Azadani A, Guccione J, Guy T S, Saloner D and Tseng E E
2008 Significant material property differences between the porcine ascending aorta and
aortic sinuses Journal of Heart Valve Disease 17 606
Hall T J, Bilgen M, Insana M F and Krouskop T A 1997 Phantom materials for elastography ieee
transactions on ultrasonics, ferroelectrics, and frequency control 44 1355-65
Hamaoui M, Tahi H, Chapon P, Duchesne B, Fantes F, Feuer W and Parel J-M 2001 Corneal
preparation of eye bank eyes for experimental surgery Cornea 20 317-20
Han Z, Aglyamov S R, Li J, Singh M, Wang S, Vantipalli S, Wu C, Liu C-h, Twa M D and Larin
K V 2015a Quantitative assessment of corneal viscoelasticity using optical coherence
elastography and a modified Rayleigh–Lamb equation Journal of biomedical optics 20
020501-
Han Z, Li J, Singh M, Aglyamov S R, Wu C, Liu C-h and Larin K V 2015b Analysis of the effects
of curvature and thickness on elastic wave velocity in cornea-like structures by finite
element modeling and optical coherence elastography Applied physics letters 106 233702
Han Z, Li J, Singh M, Wu C, Liu C-h, Raghunathan R, Aglyamov S R, Vantipalli S, Twa M D and
Larin K V 2017 Optical coherence elastography assessment of corneal viscoelasticity with
a modified Rayleigh-Lamb wave model Journal of the mechanical behavior of biomedical
materials 66 87-94
96

Han Z, Li J, Singh M, Wu C, Liu C-h, Wang S, Idugboe R, Raghunathan R, Sudheendran N and
Aglyamov S R 2015c Quantitative methods for reconstructing tissue biomechanical
properties in optical coherence elastography: a comparison study Physics in medicine and
biology 60 3531
Han Z, Tao C, Zhou D, Sun Y, Zhou C, Ren Q and Roberts C J 2014 Air puff induced corneal
vibrations: theoretical simulations and clinical observations Journal of Refractive Surgery
30 208-13
Hollman K W, Emelianov S Y, Neiss J H, Jotyan G, Spooner G J, Juhasz T, Kurtz R M and
O'Donnell M 2002 Strain imaging of corneal tissue with an ultrasound elasticity
microscope Cornea 21 68-73
Hollman K W, Shtein R M, Tripathy S and Kim K 2013 Using an ultrasound elasticity microscope
to map three-dimensional strain in a porcine cornea Ultrasound in medicine & biology 39
1451-9
Hong J, Xu J, Wei A, Deng S X, Cui X, Yu X and Sun X 2013 A New Tonometer—The Corvis
ST Tonometer: Clinical Comparison with Noncontact and Goldmann Applanation
TonometersIOP Measurement with Corvis ST, NCT, and GAT Investigative
ophthalmology & visual science 54 659-65
Huang C-C, Shih C-C, Liu T-Y and Lee P-Y 2011 Assessing the viscoelastic properties of thrombus
using a solid-sphere-based instantaneous force approach Ultrasound in medicine & biology
37 1722-33
Huang C C, Chen P Y, Peng P H and Lee P Y 2017 40 MHz high ‐frequency ultrafast ultrasound
imaging Medical Physics 44 2185-95
Huang C C, Chen P Y and Shih C C 2013 Estimating the viscoelastic modulus of a thrombus using
an ultrasonic shear ‐wave approach Medical physics 40
Huang D, Swanson E A, Lin C P, Schuman J S, Stinson W G, Chang W, Hee M R, Flotte T,
Gregory K and Puliafito C A 1991 Optical coherence tomography Science (New York, NY)
254 1178
Ishikawa H and Schuman J S 2004 Anterior segment imaging: ultrasound biomicroscopy
Ophthalmology Clinics of North America 17 7
Kampmeier J, Radt B, Birngruber R and Brinkmann R 2000 Thermal and biomechanical
parameters of porcine cornea Cornea 19 355-63
Karpiouk A B, Aglyamov S R, Ilinskii Y A, Zabolotskaya E A and Emelianov S Y 2009
Assessment of shear modulus of tissue using ultrasound radiation force acting on a
spherical acoustic inhomogeneity IEEE transactions on ultrasonics, ferroelectrics, and
frequency control 56
Kennedy B F, Liang X, Adie S G, Gerstmann D K, Quirk B C, Boppart S A and Sampson D D
2011 In vivo three-dimensional optical coherence elastography Optics express 19 6623-34
Kennedy K M, Chin L, McLaughlin R A, Latham B, Saunders C M, Sampson D D and Kennedy
B F 2015 Quantitative micro-elastography: imaging of tissue elasticity using compression
optical coherence elastography Scientific reports 5
Kennedy K M, Kennedy B F, McLaughlin R A and Sampson D D 2012 Needle optical coherence
elastography for tissue boundary detection Optics letters 37 2310-2
Kirwan C and O’Keefe M 2008 Corneal hysteresis using the Reichert ocular response analyser:
findings pre ‐and post ‐LASIK and LASEK Acta ophthalmologica 86 215-8
Kling S, Remon L, Pé rez-Escudero A, Merayo-Lloves J and Marcos S 2010 Corneal biomechanical
changes after collagen cross-linking from porcine eye inflation experiments Investigative
ophthalmology & visual science 51 3961-8
Konofagou E E and Hynynen K 2003 Localized harmonic motion imaging: theory, simulations and
experiments Ultrasound in medicine & biology 29 1405-13
97

Krouskop T A, Wheeler T M, Kallel F, Garra B S and Hall T 1998 Elastic moduli of breast and
prostate tissues under compression Ultrasonic imaging 20 260-74
Kuo P-L, Charng C-C, Wu P-C and Li P-C 2017 Shear-wave elasticity measurements of three-
dimensional cell cultures for mechanobiology J Cell Sci 130 292-302
Laurent S, Katsahian S, Fassot C, Tropeano A-I, Gautier I, Laloux B and Boutouyrie P 2003 Aortic
stiffness is an independent predictor of fatal stroke in essential hypertension Stroke 34
1203-6
Liedtke C, Luedde T, Sauerbruch T, Scholten D, Streetz K, Tacke F, Tolba R, Trautwein C,
Trebicka J and Weiskirchen R 2013 Experimental liver fibrosis research: update on animal
models, legal issues and translational aspects Fibrogenesis & tissue repair 6 1
Liu J and Roberts C J 2005 Influence of corneal biomechanical properties on intraocular pressure
measurement: quantitative analysis Journal of Cataract & Refractive Surgery 31 146-55
Lubinski M A, Emelianov S Y and O'Donnell M 1999 Speckle tracking methods for ultrasonic
elasticity imaging using short-time correlation IEEE transactions on ultrasonics,
ferroelectrics, and frequency control 46 82-96
Luce D A 2005 Determining in vivo biomechanical properties of the cornea with an ocular response
analyzer Journal of Cataract & Refractive Surgery 31 156-62
Ma T, Qian X, Chiu C T, Yu M, Jung H, Tung Y-S, Shung K K and Zhou Q 2015 High-resolution
harmonic motion imaging (HR-HMI) for tissue biomechanical property characterization
Quantitative imaging in medicine and surgery 5 108
Maksuti E, Bini F, Fiorentini S, Blasi G, Urban M W, Marinozzi F and Larsson M 2017 Influence
of wall thickness and diameter on arterial shear wave elastography: a phantom and finite
element study Physics in medicine and biology 62 2694
Maksuti E, Widman E, Larsson D, Urban M W, Larsson M and Bjä llmark A 2016 Arterial stiffness
estimation by shear wave elastography: validation in phantoms with mechanical testing
Ultrasound in medicine & biology 42 308-21
Matthews P B, Azadani A N, Jhun C-S, Ge L, Guy T S, Guccione J M and Tseng E E 2010
Comparison of porcine pulmonary and aortic root material properties The Annals of
thoracic surgery 89 1981-8
McLaughlin J and Renzi D 2006 Shear wave speed recovery in transient elastography and
supersonic imaging using propagating fronts Inverse Problems 22 681
Mezerji H H, Van den Broek W and Bals S 2011 A practical method to determine the effective
resolution in incoherent experimental electron tomography Ultramicroscopy 111 330-6
Mikula E, Hollman K, Chai D, Jester J V and Juhasz T 2014 Measurement of corneal elasticity
with an acoustic radiation force elasticity microscope Ultrasound in Medicine and Biology
40 1671-9
Montaldo G, Tanter M, Bercoff J, Benech N and Fink M 2009 Coherent plane-wave compounding
for very high frame rate ultrasonography and transient elastography IEEE transactions on
ultrasonics, ferroelectrics, and frequency control 56 489-506
Munnerlyn C R, Koons S J and Marshall J 1988 Photorefractive keratectomy: a technique for laser
refractive surgery Journal of Cataract & Refractive Surgery 14 46-52
Muthupillai R, Lomas D, Rossman P and Greenleaf J F 1995 Magnetic resonance elastography by
direct visualization of propagating acoustic strain waves Science 269 1854
Nenadic I Z, Urban M W, Aristizabal S, Mitchell S A, Humphrey T C and Greenleaf J F 2011a On
Lamb and Rayleigh wave convergence in viscoelastic tissues Physics in medicine and
biology 56 6723
Nenadic I Z, Urban M W, Aristizabal S, Mitchell S A, Humphrey T C and Greenleaf J F 2011b On
Lamb and Rayleigh wave convergence in viscoelastic tissues Physics in Medicine &
Biology 56 6723
98

Nenadic I Z, Urban M W, Bernal M and Greenleaf J F 2011c Phase velocities and attenuations of
shear, Lamb, and Rayleigh waves in plate-like tissues submerged in a fluid (L) The Journal
of the Acoustical Society of America 130 3549-52
Nenadic I Z, Urban M W, Mitchell S A and Greenleaf J F 2011d Lamb wave dispersion ultrasound
vibrometry (LDUV) method for quantifying mechanical properties of viscoelastic solids
Physics in medicine and biology 56 2245
Nenadic I Z, Urban M W, Mitchell S A and Greenleaf J F 2011e Lamb wave dispersion ultrasound
vibrometry (LDUV) method for quantifying mechanical properties of viscoelastic solids
Physics in Medicine & Biology 56 2245
Nguyen T-M, Arnal B, Song S, Huang Z, Wang R K and O’Donnell M 2015 Shear wave
elastography using amplitude-modulated acoustic radiation force and phase-sensitive
optical coherence tomography Journal of biomedical optics 20 016001-
Nguyen T-M, Song S, Arnal B, Huang Z, O’Donnell M and Wang R K 2014 Visualizing
ultrasonically induced shear wave propagation using phase-sensitive optical coherence
tomography for dynamic elastography Optics letters 39 838-41
Nightingale K, McAleavey S and Trahey G 2003 Shear-wave generation using acoustic radiation
force: in vivo and ex vivo results Ultrasound in medicine & biology 29 1715-23
Nightingale K, Palmeri M and Trahey G 2006 Analysis of contrast in images generated with
transient acoustic radiation force Ultrasound in medicine & biology 32 61-72
Nightingale K, Soo M S, Nightingale R and Trahey G 2002 Acoustic radiation force impulse
imaging: in vivo demonstration of clinical feasibility Ultrasound in medicine & biology 28
227-35
Nightingale K R, Palmeri M L, Nightingale R W and Trahey G E 2001 On the feasibility of remote
palpation using acoustic radiation force The Journal of the Acoustical Society of America
110 625-34
Ophir J, Cespedes I, Ponnekanti H, Yazdi Y and Li X 1991 Elastography: a quantitative method
for imaging the elasticity of biological tissues Ultrasonic imaging 13 111-34
Ou R J, Shaw E L and Glasgow B J 2002 Keratectasia after laser in situ keratomileusis (LASIK):
evaluation of the calculated residual stromal bed thickness American journal of
ophthalmology 134 771-3
Pallikaris L G, Papatzanaki M E, Stathi E Z, Frenschock O and Georgiadis A 1990 Laser in situ
keratomileusis Lasers in surgery and medicine 10 463-8
Palmeri M L, Deng Y, Rouze N C and Nightingale K R Ultrasonics Symposium (IUS), 2014 IEEE
International,2014), vol. Series): IEEE) pp 1105-8
Palmeri M L, McAleavey S A, Fong K L, Trahey G E and Nightingale K R 2006 Dynamic
mechanical response of elastic spherical inclusions to impulsive acoustic radiation force
excitation IEEE transactions on ultrasonics, ferroelectrics, and frequency control 53 2065-
79
Palmeri M L and Nightingale K R 2011 Acoustic radiation force-based elasticity imaging methods
Interface Focus rsfs20110023
Palmeri M L, Rouze N C, Wang M H, Ding X and Nightingale K R 2010 IEEE International
Ultrasonics Symposium,2010), vol. Series): IEEE) pp 13-6
Palmeri M L, Sharma A C, Bouchard R R, Nightingale R W and Nightingale K R 2005 A finite-
element method model of soft tissue response to impulsive acoustic radiation force IEEE
transactions on ultrasonics, ferroelectrics, and frequency control 52 1699-712
Palmeri M L, Wang M H, Dahl J J, Frinkley K D and Nightingale K R 2008 Quantifying hepatic
shear modulus in vivo using acoustic radiation force Ultrasound in medicine & biology 34
546-58
Parker K J, Doyley M and Rubens D 2010 Imaging the elastic properties of tissue: the 20 year
perspective Physics in medicine and biology 56 R1
99

Pinton G F, Dahl J J and Trahey G E 2006 Rapid tracking of small displacements with ultrasound
IEEE transactions on ultrasonics, ferroelectrics, and frequency control 53 1103-17
Potsaid B, Baumann B, Huang D, Barry S, Cable A E, Schuman J S, Duker J S and Fujimoto J G
2010 Ultrahigh speed 1050nm swept source/Fourier domain OCT retinal and anterior
segment imaging at 100,000 to 400,000 axial scans per second Optics express 18 20029-
48
Qi W, Li R, Ma T, Li J, Kirk Shung K, Zhou Q and Chen Z 2013 Resonant acoustic radiation force
optical coherence elastography Applied physics letters 103 103704
Qi W, Li R, Ma T, Shung K K, Zhou Q and Chen Z 2014 Confocal acoustic radiation force optical
coherence elastography using a ring ultrasonic transducer Applied physics letters 104
123702
Qian X, Ma T, Yu M, Chen X, Shung K K and Zhou Q 2017 Multi-functional Ultrasonic Micro-
elastography Imaging System Scientific Reports 7 1230
Qu Y, Ma T, He Y, Zhu J, Dai C, Yu M, Huang S, Lu F, Shung K K and Zhou Q 2016a Acoustic
radiation force optical coherence elastography of corneal tissue IEEE Journal of Selected
Topics in Quantum Electronics 22 288-94
Qu Y, Ma T, He Y, Zhu J, Dai C, Yu M, Huang S, Lu F, Shung K K, Zhou Q and Chen Z 2016b
Acoustic radiation force optical coherence elastography of corneal tissue IEEE Journal of
Selected Topics in Quantum Electronics 22 288-94
Ramnarine K V, Garrard J W, Dexter K, Nduwayo S, Panerai R B and Robinson T G 2014 Shear
wave elastography assessment of carotid plaque stiffness: in vitro reproducibility study
Ultrasound in medicine & biology 40 200-9
Righetti R, Ophir J and Ktonas P 2002 Axial resolution in elastography Ultrasound in medicine &
biology 28 101-13
Righetti R, Srinivasan S and Ophir J 2003 Lateral resolution in elastography Ultrasound in
medicine & biology 29 695-704
Roberts C J and Dupps W J 2014 Biomechanics of corneal ectasia and biomechanical treatments
Journal of Cataract & Refractive Surgery 40 991-8
Rouviere O, Yin M, Dresner M A, Rossman P J, Burgart L J, Fidler J L and Ehman R L 2006 MR
elastography of the liver: preliminary results Radiology 240 440-8
Rouze N C, Wang M H, Palmeri M L and Nightingale K R 2012 Parameters affecting the resolution
and accuracy of 2-D quantitative shear wave images IEEE transactions on ultrasonics,
ferroelectrics, and frequency control 59 1729-40
Ruberti J W, Sinha Roy A and Roberts C J 2011 Corneal biomechanics and biomaterials Annual
review of biomedical engineering 13 269-95
Sarvazyan A, J Hall T, W Urban M, Fatemi M, R Aglyamov S and S Garra B 2011 An overview
of elastography-an emerging branch of medical imaging Current medical imaging reviews
7 255-82
Sarvazyan A P, Rudenko O V, Swanson S D, Fowlkes J B and Emelianov S Y 1998 Shear wave
elasticity imaging: a new ultrasonic technology of medical diagnostics Ultrasound in
medicine & biology 24 1419-35
Sarvazyan A P, Urban M W and Greenleaf J F 2013 Acoustic waves in medical imaging and
diagnostics Ultrasound in medicine & biology 39 1133-46
Shih C-C, Huang C-C, Zhou Q and Shung K K 2013 High-resolution acoustic-radiation-force-
impulse imaging for assessing corneal sclerosis IEEE transactions on medical imaging 32
1316-24
Shung K K 2015 Diagnostic ultrasound: Imaging and blood flow measurements: CRC press)
Silverman R H 2009 High ‐ resolution ultrasound imaging of the eye–a review Clinical &
experimental ophthalmology 37 54-67
Simons P C, Algra A, Bots M L, Grobbee D E and van der Graaf Y 1999 Common carotid intima-
media thickness and arterial stiffness Circulation 100 951-7
100

Smith S W 1997 The scientist and engineer's guide to digital signal processing
Srinivasan S, Righetti R and Ophir J 2003 Trade-offs between the axial resolution and the signal-
to-noise ratio in elastography Ultrasound in medicine & biology 29 847-66
Stehouwer C, Henry R and Ferreira I 2008 Arterial stiffness in diabetes and the metabolic syndrome:
a pathway to cardiovascular disease Diabetologia 51 527
Sunagawa K and Kanai H 2005 Measurement of shear wave propagation and investigation of
estimation of shear viscoelasticity for tissue characterization of the arterial wall Journal of
Medical Ultrasonics 32 39-47
Syversveen T, Brabrand K, Midtvedt K, Strø m E H, Hartmann A, Jakobsen J A and Berstad A E
2011 Assessment of renal allograft fibrosis by acoustic radiation force impulse
quantification–a pilot study Transplant international 24 100-5
Tanter M, Bercoff J, Athanasiou A, Deffieux T, Gennisson J-L, Montaldo G, Muller M, Tardivon
A and Fink M 2008 Quantitative assessment of breast lesion viscoelasticity: initial clinical
results using supersonic shear imaging Ultrasound in medicine & biology 34 1373-86
Tanter M and Fink M 2014 Ultrafast imaging in biomedical ultrasound IEEE transactions on
ultrasonics, ferroelectrics, and frequency control 61 102-19
Tanter M, Touboul D, Gennisson J-L, Bercoff J and Fink M 2009 High-resolution quantitative
imaging of cornea elasticity using supersonic shear imaging IEEE transactions on medical
imaging 28 1881-93
Torr G 1984 The acoustic radiation force American Journal of Physics 52 402-8
Tryfonopoulos D, Anastasiou E, Protogerou A, Papaioannou T, Lily K, Dagre A, Souvatzoglou E,
Papamichael C, Alevizaki M and Lekakis J 2005 Arterial stiffness in type 1 diabetes
mellitus is aggravated by autoimmune thyroid disease Journal of endocrinological
investigation 28 616-22
Urs R, Lloyd H O and Silverman R H 2014 Acoustic Radiation Force for Noninvasive Evaluation
of Corneal Biomechanical Changes Induced by Cross ‐ linking Therapy Journal of
Ultrasound in Medicine 33 1417-26
Vappou J, Luo J and Konofagou E E 2010 Pulse wave imaging for noninvasive and quantitative
measurement of arterial stiffness in vivo American journal of hypertension 23 393-8
Vlachopoulos C, Aznaouridis K and Stefanadis C 2010 Prediction of cardiovascular events and all-
cause mortality with arterial stiffness: a systematic review and meta-analysis Journal of
the American College of Cardiology 55 1318-27
W Urban M, Chen S and Fatemi M 2012 A review of shearwave dispersion ultrasound vibrometry
(SDUV) and its applications Current medical imaging reviews 8 27-36
Wang M H, Palmeri M L, Guy C D, Yang L, Hedlund L W, Diehl A M and Nightingale K R 2009
In vivo quantification of liver stiffness in a rat model of hepatic fibrosis with acoustic
radiation force Ultrasound in medicine & biology 35 1709-21
Wang S and Larin K V 2014 Shear wave imaging optical coherence tomography (SWI-OCT) for
ocular tissue biomechanics Optics letters 39 41-4
Widman E, Maksuti E, Amador C, Urban M W, Caidahl K and Larsson M 2016a Shear wave
elastography quantifies stiffness in ex vivo porcine artery with stiffened arterial region
Ultrasound in medicine & biology 42 2423-35
Widman E, Maksuti E, Amador C, Urban M W, Caidahl K and Larsson M 2016b Shear wave
elastography quantifies stiffness in ex vivo porcine artery with stiffened arterial region
Ultrasound in Medicine and Biology 42 2423-35
Wilson A, Marshall J and Tyrer J R 2016 The role of light in measuring ocular biomechanics Eye
30 234-40
Wollensak G, Aurich H, Pham D-T and Wirbelauer C 2007 Hydration behavior of porcine cornea
crosslinked with riboflavin and ultraviolet A Journal of Cataract & Refractive Surgery 33
516-21
101

Wollensak G, Spoerl E and Seiler T 2003 Stress-strain measurements of human and porcine corneas
after riboflavin–ultraviolet-A-induced cross-linking Journal of Cataract & Refractive
Surgery 29 1780-5
Yeh C-L, Chen B-R, Tseng L-Y, Jao P, Su T-H and Li P-C 2015 Shear-wave elasticity imaging of
a liver fibrosis mouse model using high-frequency ultrasound IEEE transactions on
ultrasonics, ferroelectrics, and frequency control 62 1295-307
Zhai L, Madden J, Foo W-C, Mouraviev V, Polascik T J, Palmeri M L and Nightingale K R 2010
Characterizing stiffness of human prostates using acoustic radiation force Ultrasonic
imaging 32 201-13
Zhang W, Chen H Y and Kassab G S 2007 A rate-insensitive linear viscoelastic model for soft
tissues Biomaterials 28 3579-86
Zhang X, Kinnick R R, Fatemi M and Greenleaf J F 2005 Noninvasive method for estimation of
complex elastic modulus of arterial vessels IEEE transactions on ultrasonics,
ferroelectrics, and frequency control 52 642-52
Zhou B, Sit A J and Zhang X 2017 Noninvasive measurement of wave speed of porcine cornea in
ex vivo porcine eyes for various intraocular pressures Ultrasonics 81 86-92
Zhu J, Qu Y, Ma T, Li R, Du Y, Huang S, Shung K K, Zhou Q and Chen Z 2015 Imaging and
characterizing shear wave and shear modulus under orthogonal acoustic radiation force
excitation using OCT Doppler variance method Optics letters 40 2099-102

Abstract (if available)

Abstract Based on the fact that a pathological process alters the elastic properties of the involved tissue, the biomechanical properties of the soft tissue therefore provide an additional contrast and clinically relevant information for disease diagnosis and tissue characterization. To measure the tissue biomechanics, a medical imaging modality called elastography, has been the focus of intense research activity since the mid-1990s. ❧ Acoustic radiation force (ARF) based ultrasonic elastography methods, such as acoustic radiation force impulse (ARFI) imaging, shear wave elasticity imaging (SWEI), and supersonic shear imaging (SSI), capitalizing on the advantage of synchronization of ARF excitation and ultrasonic detection, have been used to characterize the tissue biomechanical properties in a more effective and accurate manner. However, most of the current ultrasonic elastography studies, utilizing the standard clinical frequency range (1-20 MHz), could only provide spatial resolution up to sub-millimeter level and significantly narrows some clinical applications that needs micron-scale level visualization. For example, thin layer tissues such as the artery and ocular tissues. ❧ The work presented in this dissertation investigates an ultrasonic micro-elastography imaging technique utilizing the dual frequency configuration to fill the gaps between conventional ultrasound elastography and optical coherence elastography (OCE) on imaging resolution and penetration depth. The low frequency transducer which can sustain high voltage and long duration has the ability to generate enough “pushing force”, and high frequency transducer with good spatial resolution is used to map elasticity distribution. The developed system was first calibrated through gelatin mimicking phantoms, and then implemented on a thin layer tissue—the cornea. In addition, an advanced model—Lamb wave model is proposed to increase the accuracy of the reconstructed Young’s modulus by considering the shear wave dispersion issue. All these results demonstrate the capability of the developed ultrasonic micro-elastography imaging system on potential clinical application—thin layer tissue. Lastly, due to the low frame rate of single-element based micro-elastography system, we have improved this technique using high frequency array transducer which has both high resolution and high frame rate. The preliminary studies has been shown on posterior sclera tissue.

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Asset Metadata

Creator Qian, Xuejun (author)

Core Title High frequency ultrasound elastography and its biomedical applications

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 03/13/2019

Defense Date 12/19/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag elastography,high frequency ultrasound,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Zhou, Qifa (committee chair)

Creator Email jevonsqian@gmail.com,xuejunqi@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-133601

Unique identifier UC11676909

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Legacy Identifier etd-QianXuejun-7159.pdf

Dmrecord 133601

Document Type Dissertation

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Rights Qian, Xuejun

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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