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For Peer Review
Three
-
dimensional visualization of
ultrasound backscatter
statistics by window-modulated compounding Nakagami
imaging
Journal:
Ultrasonic Imaging
Manuscript ID
UIX-17-0011.R1
Manuscript Type:
Technical Article
Date Submitted by the Author:
31-May-2017
Complete List of Authors:
Zhou, Zhuhuang; Beijing University of Technology, College of Life Science
and Bioengineering
Wu, Shuicai; Beijing University of Technology, Biomedical Engineering
Lin, Man-Yen; Chang Gung University, Department of Medical Imaging and
Radiological Sciences
Fang, Jui; Chang Gung University, Ph.D. Program in Biomedical
Engineering
Liu, Hao-Li
Tsui, Po-Hsiang; Chang Gung University, Department of Medical Imaging
and Radiological Sciences
Keywords:
backscatter statistics, Nakagami imaging, three-dimensional imaging,
window-modulated compounding, ultrasound tissue characterization
Abstract:
In this study, the window-modulated compounding (WMC) technique was
integrated into three-dimensional (3D) ultrasound Nakagami imaging for
improving the spatial visualization of backscatter statistics. A 3D WMC
Nakagami image was produced by summing and averaging a number of 3D
Nakagami images (number of frames denoted as N) formed using sliding
cubes with varying side lengths ranging from 1 to N times the transducer
pulse. To evaluate the performance of the proposed 3D WMC Nakagami
imaging method, agar phantoms with scatterer concentrations ranging
from 2 to 64 scatterers/mm3 were made, and six stages of fatty liver (0, 1,
2, 4, 6, and 8 weeks) were induced in rats by methionine-choline-deficient
diets (3 rats for each stage, total n = 18). A mechanical scanning system
with a 5-MHz focused single-element transducer was used for ultrasound
radiofrequency data acquisition. The experimental results showed that 3D
WMC Nakagami imaging was able to characterize different scatterer
concentrations with performance similar to that of conventional 3D
Nakagami imaging. Backscatter statistics were visualized with various
numbers of frames; N = 5 reduced the estimation error of 3D WMC
Nakagami imaging in visualizing the backscatter statistics. Compared with
conventional 3D Nakagami imaging, 3D WMC Nakagami imaging improved
the image smoothness without significant image resolution degradation,
and it can thus be used for describing different stages of fatty liver in rats.
The proposed 3D WMC Nakagami imaging strategy may be used as an
enhanced image-based pathological model for visual and quantitative
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tissue characterization.
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Three-dimensional visualization of ultrasound backscatter statistics by 1
window-modulated compounding Nakagami imaging 2
3
4
Zhuhuang Zhou
1,2
, Shuicai Wu
1
, Man-Yen Lin
3
, Jui Fang
4
, Hao-Li Liu
3,*
, and 5
Po-Hsiang Tsui
5,6,7,*
6
7
8
1
College of Life Science and Bioengineering, Beijing University of Technology, 9
Beijing, China 10
2
Faculty of Information Technology, Beijing University of Technology, Beijing, 11
China 12
3
Department of Electrical Engineering, Chang-Gung University, Taoyuan, Taiwan 13
4
Ph.D. Program in Biomedical Engineering, College of Engineering, Chang Gung 14
University, Taoyuan, Taiwan 15
5
Department of Medical Imaging and Radiological Sciences, College of Medicine, 16
Chang Gung University, Taoyuan, Taiwan 17
6
Medical Imaging Research Center, Institute for Radiological Research, Chang Gung 18
University and Chang Gung Memorial Hospital at Linkou, Taoyuan, Taiwan 19
7
Department of Medical Imaging and Intervention, Chang Gung Memorial Hospital at 20
Linkou, Taoyuan, Taiwan 21
22
Corresponding authors: 23
Po-Hsiang Tsui (tsuiph@mail.cgu.edu.tw) and Hao-Li Liu 24
(haoliliu@mail.cgu.edu.tw) 25
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Acknowledgements 27
28
This work was supported by the Ministry of Science and Technology (Taiwan) under 29
Grant No. MOST 103-2221-E-182-001-MY3 and the Chang Gung Memorial Hospital 30
(Linkou, Taiwan) under Grant Nos. CIRPD1E0022 and CMRPD1F0311. This work 31
was also supported in part by the National Natural Science Foundation of China 32
(Grant No. 71661167001) and the Young Innovative Talents of the Beijing 33
Educational Committee (Grant No. CIT & TCD 201404053). 34
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Three-dimensional visualization of ultrasound backscatter statistics by 1
window-modulated compounding Nakagami imaging 2
3
Abstract 4
5
In this study, the window-modulated compounding (WMC) technique was integrated 6
into three-dimensional (3D) ultrasound Nakagami imaging for improving the spatial 7
visualization of backscatter statistics. A 3D WMC Nakagami image was produced by 8
summing and averaging a number of 3D Nakagami images (number of frames 9
denoted as N) formed using sliding cubes with varying side lengths ranging from 1 to 10
N times the transducer pulse. To evaluate the performance of the proposed 3D WMC 11
Nakagami imaging method, agar phantoms with scatterer concentrations ranging from 12
2 to 64 scatterers/mm
3
were made, and six stages of fatty liver (0, 1, 2, 4, 6, and 8 13
weeks) were induced in rats by methionine-choline-deficient diets (3 rats for each 14
stage, total n = 18). A mechanical scanning system with a 5-MHz focused 15
single-element transducer was used for ultrasound radiofrequency data acquisition. 16
The experimental results showed that 3D WMC Nakagami imaging was able to 17
characterize different scatterer concentrations. Backscatter statistics were visualized 18
with various numbers of frames; N = 5 reduced the estimation error of 3D WMC 19
Nakagami imaging in visualizing the backscatter statistics. Compared with 20
conventional 3D Nakagami imaging, 3D WMC Nakagami imaging improved the 21
image smoothness without significant image resolution degradation, and it can thus be 22
used for describing different stages of fatty liver in rats. 23
Keywords: backscatter statistics, Nakagami imaging, three-dimensional imaging, 24
window-modulated compounding, ultrasound tissue characterization 25
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Introduction 26
27
Ultrasound imaging has been widely used in routine diagnostics because of its low 28
cost, nonionizing radiation, and real-time capability.
1,2
Because B-mode images are 29
constructed from ultrasound echo signals of particular amplitude, they have particular 30
drawbacks; specifically, they are qualitative (affected by several signal/image 31
processing parameters such as dynamic range) and operator dependent.
1
To 32
complement B-mode imaging for quantitative analysis, studies have investigated 33
quantitative ultrasound (QUS) that is based on analyzing the properties of the 34
frequency, phase, or statistical information of backscattered signals.
3–10
In the context 35
of QUS, parameters including backscatter coefficients, acoustic attenuation, speed of 36
sound, backscatter statistics, and tissue elasticity can be estimated for tissue 37
characterization.
4,11,12
38
In general, a biological tissue can be modeled as a collection of acoustic 39
scatterers. Different scatterer concentrations and arrangements result in different 40
behaviors of ultrasound backscattering and correspondingly different radiofrequency 41
(RF) backscattered signals. Research has shown that the statistical distribution of 42
backscattered signals is associated with tissue microstructures and can be used to 43
characterize scatterers in tissues that are not resolvable in conventional B-mode 44
images.
4–10
Currently, the Nakagami distribution is the most frequently adopted 45
approximation for backscatter statistics because of its simplicity and low 46
computational complexity.
4
Hampshire
13
and Shankar
14
pioneered the use of the 47
Nakagami model in applications of medical ultrasound. Shankar demonstrated that the 48
Nakagami parameter estimated from the backscatter envelopes is able to differentiate 49
various scattering conditions (pre-Rayleigh, Rayleigh, and post-Rayleigh distributions) 50
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for tissue characterization.
14
Subsequently, Shankar proposed the concept of 51
ultrasound Nakagami imaging,
15
and a computational method based on a sliding 52
window technique was implemented and validated for visualizing backscatter 53
statistics to quantify the properties of scatterers.
16
Ultrasound Nakagami imaging has 54
been used systematically in various medical applications by different research 55
groups.
8,9,17–26
Concurrently, some technical issues have been investigated to improve 56
the performance of ultrasound Nakagami imaging, including three-dimensional (3D) 57
Nakagami imaging,
27
artifact reduction,
7,28
small-window Nakagami imaging,
29
and 58
window-modulated compounding (WMC) Nakagami imaging.
6
A literature review 59
indicated that image resolution and smoothness are two foci for research on Nakagami 60
imaging techniques. However, how to simultaneously enhance the resolution and 61
smoothness of 3D ultrasound Nakagami images needs further investigation. 62
Basically, increasing ultrasound frequency can improve the resolution of the 63
Nakagami image because it is commonly suggested that the side length of the sliding 64
window used to construct the Nakagami image be three times the pulse length.
16
65
Higher frequencies result in shorter pulse lengths, making the size of the sliding 66
window smaller (better resolution). Nevertheless, increasing the frequency is not 67
recommended in clinical applications due to the limitations of penetration. The use of 68
a 3D imaging approach was suggested as an alternative strategy to improve the 69
resolution of the Nakagami image because it allows the resolution to correspond to a 70
smaller window size (the side length is just two times the pulse length).
27,30
By 71
contrast, the WMC technique was recently proposed to enhance the smoothness of 72
ultrasound Nakagami images (please see the section on theoretical background and 73
algorithms for the details).
6
The WMC technique enables the Nakagami image to 74
visualize the backscatter statistics with an improved image smoothness, without 75
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affecting the resolution. 76
To update Nakagami imaging techniques, we assumed that combining 3D 77
Nakagami imaging and the WMC technique may allow simultaneous improvement of 78
image resolution and smoothness for 3D Nakagami images. In this study, our 79
objective was to develop a 3D WMC Nakagami imaging technique for visualizing 80
backscatter statistics with enhanced image quality. In the following sections, we 81
introduce the theoretical background, algorithms, and procedures involved in 82
performing phantom measurements and animal experiments of fatty liver in vitro for 83
validation. The experimental results showed that the 3D WMC Nakagami imaging 84
technique allows visualizing changes in backscatter statistics with improved image 85
resolution and smoothness for tissue characterization. 86
87
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Theoretical background and algorithms 101
102
Nakagami model 103
The probability distribution function of the ultrasound backscatter envelope R under 104
the Nakagami model is given by
14
105
(1) 106
where Γ(·) and U(·) are the gamma function and the unit step function, respectively. 107
Let E(·) denote the statistical mean. The scaling parameter Ω and Nakagami parameter 108
m can be respectively obtained from 109
(2) 110
and 111
(3) 112
The Nakagami parameter m, estimated using the backscatter envelopes, is the shape 113
parameter of the Nakagami distribution that fits well with the statistical distribution of 114
the backscatter envelopes. The variation of the Nakagami parameter from 0 to 1 115
indicates changes in the envelope statistics from pre-Rayleigh to Rayleigh 116
distributions. Any Nakagami parameters higher than 1 indicate that the distributions 117
of the backscatter statistics are post-Rayleigh distributions. Various backscatter 118
statistics can be quantified by the Nakagami parameter; therefore, the Nakagami 119
distribution may be treated as a general model for ultrasonic backscattering.
14
120
121
Ultrasound Nakagami imaging 122
A Nakagami image is constructed on the basis of a Nakagami parameter map by using 123
a square sliding window to process the envelope image. Some details of the Nakagami 124
imaging sliding window technique were updated in a recent study.
31
First, the raw 125
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beamformed RF signals (i.e., the scan lines of an image) are demodulated to yield the 126
envelope image without logarithmic compression
),(
ˆyxR
: 127
(4)
128
Subsequently, a window measuring kl
×
in size within the uncompressed envelope 129
image is used to obtain the local backscatter envelope R
w
: 130
(5)
131
where i and j indicate the location corresponding to the upper left corner of the 132
window. R
w
is used for estimating the local Nakagami parameter m
w
through Equation 133
(3), which is assigned as the new pixel located at the center of the window: 134
(6)
135
The sliding window then moves throughout
),(
ˆyxR
in steps of one pixel, and each 136
local m
w
value is filled into the corresponding pixel of the Nakagami parametric map. 137
An interpolated parametric map M is then created, whose size is the same as
),(
ˆyxR
: 138
(7) 139
To satisfy the requirements of an acceptable resolution and stable parameter 140
estimation, the minimum side length of the sliding window used for constructing the 141
two-dimensional (2D) Nakagami image is three times the pulse length of 142
the transducer.
6,16
143
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7
The concept of 3D Nakagami imaging is the same as that of 2D Nakagami 144
imaging. However, the difference is that the 3D Nakagami image is 145
constructed using a sliding cube that moves across the 3D envelope data [Figure 1(a)]. 146
According to a previous study, the required minimum side length of the sliding cube 147
that can satisfy the stable parameter estimation is just two times the pulse length, 148
which is smaller than that required in 2D Nakagami imaging to provide an improved 149
resolution.
27
150
151
WMC Nakagami imaging 152
In the context of visualizing backscatter statistics, the WMC technique was proposed 153
to incorporate the benefits of the large- and small-window-based Nakagami imaging 154
techniques.
6
Using a large window to construct a Nakagami image results in stable 155
parameter estimation and enhanced image smoothness. By contrast, a small window 156
(corresponding to a small spatial scale) enables achieving enhanced Nakagami 157
parametric image resolution. A WMC Nakagami image is defined as a compounding 158
Nakagami image obtained by summing and averaging Nakagami images formed using 159
sliding windows with varying side lengths ranging from 1 to N times the transducer 160
pulse length in steps of one pulse length: 161
(8) 162
N also represents the number of frames used for Nakagami-image compounding. A 163
previous study suggested using N = 10 to achieve minimal estimation error for 2D 164
WMC Nakagami imaging.
6
The WMC technique was shown to significantly improve 165
the smoothness of a Nakagami image without resolution degradation.
6
166
167
3D WMC Nakagami imaging 168
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The WMC technique and 3D Nakagami imaging are useful for improving smoothness 169
and resolution, respectively. Thus, the WMC technique can be combined with 3D 170
Nakagami imaging to realize 3D WMC Nakagami imaging that simultaneously 171
improves both image resolution and smoothness. Specifically, a 3D WMC Nakagami 172
image is constructed by summing and averaging several 3D Nakagami images, which 173
are generated using sliding cubes with varying slide lengths that range from 1 to N 174
times the transducer pulse length in steps of one pulse length, as represented by 175
Equation (11) and illustrated in Figure 1(b). 176
(9) 177
Here, N also indicates the number of frames used for 3D Nakagami-image 178
compounding. 179
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Materials and methods 194
195
This section describes phantom experiments conducted to explore the optimal frame 196
number N that allows 3D WMC Nakagami imaging with minimal estimation error. 197
The image resolution and smoothness were evaluated; then, an animal model of fatty 198
liver was used to evaluate the feasibility of 3D WMC Nakagami imaging for 199
ultrasound tissue characterization. 200
201
Phantom experiments 202
Phantoms containing scatterers at different concentrations were made by adding 203
different quantities of glass beads with diameters of 75 µm (Model 59200U, Supelco, 204
Bellefonte, PA, USA) into agar solution produced by dissolving 0.75 g of agar powder 205
in 100 mL of water. The scatterer concentration of the phantom (the number of 206
scatterers per cubic millimeter) was determined by 207
(10) 208
where M, r
g
, and ρ indicate the mass, radius, and density of the glass beads, 209
respectively, and V denotes the volume of the agar phantom. The number densities of 210
the scatterers were 2, 4, 8, 16, 32, and 64 scatterers/mm
3
. For each scatterer 211
concentration, five phantoms were made. 212
An ultrasound mechanical scanning system was used for 3D ultrasound scanning 213
(Figure 2). The system comprised a high-resolution motion stage driven by a 214
piezoelectric motor (Model HR8, Nanomotion, Yokneam, Israel), a single-element 215
transducer (Model V310, Panametrics-NDT; frequency: 5 MHz; pulse length: 0.3 216
mm), a pulser/receiver (Model 5072PR, Panametrics-NDT, Waltham, MA, USA), and 217
a data acquisition card (Model PXI-5152, National Instruments, Austin, TX, USA). 218
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The transducer was mechanically scanned using the motion stage and was connected 219
to a pulser/receiver for transmitting and receiving ultrasonic RF signals. The received 220
data were amplified by the amplifier built into the pulser/receiver and then digitized 221
by the data acquisition card for data storage and offline analysis on a personal 222
computer. 223
In each trial, the transducer and the phantom were immersed in a bath containing 224
distilled water at room temperature. The phantom was positioned at the focus of the 225
transducer (1.15 cm). For each phantom with a specific scatterer concentration, 100 226
2D frames were obtained for 3D data acquisition. The interval between each scan 227
frame was 0.1 mm, and each frame consisted of 100 A-lines of backscattered signals 228
obtained at a sampling rate of 50 MHz. Each backscattered signal corresponded to a 229
data length of approximately 10 mm. The interval between each A-line was 0.1 mm. 230
The Hilbert transform was conducted on each scan line of each 2D RF slice to get the 231
2D envelope slices. These 2D envelope slices were used to reconstruct the 3D 232
envelope data for 3D B-mode, Nakagami, and WMC Nakagami imaging. 233
Conventional 3D Nakagami images were constructed using a sliding cube with 234
side lengths of two times the pulse length.
27
The average m
w
parameter (i.e., the voxel 235
values in the 3D Nakagami image) as a function of the number density of scatterers 236
was plotted. Several 3D WMC Nakagami images with various N settings were 237
constructed for calculating the corresponding average m
wmc
parameter. The use of 238
large windows benefits stable estimations of the Nakagami parameter because it 239
provides sufficient envelope data for parameter estimation. Therefore, if N is large 240
enough, the m
wmc
parameter estimations associated with various number densities of 241
scatterers should be stable and should approach the m
w
parameters obtained from the 242
conventional 3D Nakagami images (as the ground truth). For this reason, the frame 243
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number N used for 3D Nakagami-image compounding is appropriate when 244
(11) 245
Given a reasonable control of the estimation error between the m
wmc
and m
w
246
parameters, it should be possible to satisfy Equation (13). The estimation error is 247
defined by 248
(12) 249
Image data processing was performed using MATLAB software (Version R2012a, 250
MathWorks, Inc., MA, USA). The 3D image display was implemented using AVIZO 251
software (Mercury Computer Systems, Chelmsford, MA, USA). 252
After the optimal value of N was determined, the resolution and smoothness of 253
3D WMC Nakagami images were compared with those of conventional 3D Nakagami 254
images. For each number density of scatterers, each frame in the 3D WMC and 255
conventional Nakagami images was used to calculate autocorrelation functions (ACFs) 256
for averaging. The width of an ACF, measured at the level at which it drops below its 257
maximal value, is a well-known criterion used to evaluate image resolution.
6
The 258
smoothness was evaluated by the full width at half maximum (FWHM) of the m
w
and 259
m
wmc
parameter distributions (bins = 40). A narrow FWHM denotes a small degree of 260
variation in estimating local parameters, corresponding to improved image 261
smoothness. Significant differences in resolution (i.e., ACF width) and smoothness 262
(the FWHM of the parameter distribution) between 3D WMC and conventional 263
Nakagami imaging results were identified by the p-value obtained from a paired t-test 264
< 0.05. The statistical analysis was performed using SigmaPlot software (Version 12.0, 265
Systat Software, Inc., CA, USA). 266
267
Animal experiments in vitro 268
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In vitro animal experiments were conducted to further evaluate the feasibility of using 269
3D WMC Nakagami imaging in practical ultrasound tissue characterization. 270
Six-week-old male Wistar rats (weight 228.81 ± 9.42 g) were used (n = 18). The use 271
of animals in this study was approved by the Institutional Animal Care and Use 272
Committee of Chang Gung University. The rats were bred and maintained in an 273
air-conditioned animal house (21–24 °C) with a relative humidity of 45%–70% and a 274
12-h light/dark cycle. The rats were fed with methionine-choline-deficient (MCD)
32
275
diets for 0 (used as the control group), 1, 2, 4, 6, and 8 weeks to induce fatty liver 276
(three rats in each group). For each group, all rats were sacrificed, and the middle lobe 277
of each rat’s liver was removed for 3D ultrasound scanning in vitro in a 0.9% saline 278
water environment using the same scanning system and the same data acquisition and 279
analysis procedure as the phantom experiments. The number of frames N used for 3D 280
WMC Nakagami imaging was determined according to the finding from the phantom 281
experiments. The average m
wmc
parameter as a function of time (weeks of MCD diets) 282
was plotted for correlation analysis using SigmaPlot software. 283
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Results 294
295
Phantom experiments 296
Figure 3(a) shows the typical 3D B-mode and Nakagami images of the phantoms. As 297
the number densities of scatterers increased from 2 to 64 scatterers/mm
3
, the shading 298
of the Nakagami images gradually varied from deep blue to light green, 299
corresponding to an increase in the average Nakagami parameter (m
w
) from 300
approximately 0.21 to 1.22, as shown in Figure 3(b). This means that the envelope 301
statistics vary from pre-Rayleigh (m < 1) to Rayleigh (m = 1) and to post-Rayleigh (m > 302
1) distributions when the number densities of scatterers in the transducer resolution 303
cell increase. The linear fitting curve of the m
w
parameter as a function of scatterer 304
concentration in Figure 3(b) reproduced the typical relationship between the 305
backscatter statistics and the scatterer concentration obtained using 3D Nakagami 306
imaging.
27
307
Figure 4 shows the 3D WMC Nakagami images of the phantoms constructed 308
using N values ranging from 1 to 10. The curves of the average m
wmc
parameter as a 309
function of N are shown in Figure 5. For different number densities of scatterers, the 310
corresponding m
wmc
parameter values decreased gradually and entered a stable phase 311
as N increased from 1 to 10, demonstrating that using large cube-based Nakagami 312
images during compounding moderates the parameter to alleviate overestimation 313
caused by small cube-based Nakagami images. Figure 6 shows the curves of the 314
estimation error between the m
w
and m
wmc
parameters for each number density of 315
scatterers. Overall, increasing N from 1 to 5 reduced the estimation error of the m
wmc
316
parameter. Using N > 5 increased the estimation error. This finding suggests that using 317
N = 5 as a criterion for 3D WMC Nakagami imaging produces estimations of the 318
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m
wmc
parameter close to those of the standard m
w
parameter. 319
Figure 7 shows the average m
wmc
parameter as a function of the number density 320
of scatterers (N = 5). The average m
wmc
parameter increased from approximately 0.20 321
to 1.23 when the number density of scatterers increased from 2 to 64 scatterers/mm
3
. 322
The results of the m
w
and m
wmc
parameters were compared, and correlation analysis 323
was performed based on the linear fitting curve in the form of y = ax + y
0
, as shown in 324
Figure 8(a). The m
wmc
parameter correlated well with the conventional m
w
parameter 325
(correlation coefficient r = 0.995), demonstrating that the proposed 3D WMC 326
Nakagami imaging has the ability to correctly reflect the backscatter statistics of 327
ultrasound signals corresponding to different number densities of scatterers. The 328
p-value between the m
w
and m
wmc
parameters was higher than 0.05, indicating no 329
significant difference between the two imaging modalities, as shown in Figure 8(b). 330
Figure 9 shows that the average FWHM values of the m
w
and m
wmc
parameter 331
distributions (N = 5) were 5.75 ± 1.41 and 3.22 ± 0.85, respectively. The widths of the 332
probability distribution of the m
wmc
parameter were narrower than those of the m
w
333
parameter for various number densities of scatterers. The p-value was lower than 0.05, 334
demonstrating that the smoothness of the 3D WMC Nakagami image was 335
significantly improved compared with that of the 3D conventional Nakagami image. 336
Figure 10 shows the autocorrelations of the 3D Nakagami images and WMC 337
Nakagami images (N = 5). The widths of the ACF images in the X-axis, Y-axis, and 338
Z-axis for the 3D WMC Nakagami images were 610.73 ± 295.87, 116.47 ± 73.51, and 339
11.43 ± 7.16 pixels, respectively. Without WMC processing (i.e., conventional 3D 340
Nakagami imaging), the widths of the ACF images in the X-axis, Y-axis, and Z-axis 341
were 532.60 ± 266.54, 96.27 ± 63.86, and 10.00 ± 6.42 pixels, respectively. For each 342
number density of scatterers, the p-values between the ACF widths obtained without 343
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and with WMC were higher than 0.05, signifying that no significant difference existed 344
between the resolutions of 3D Nakagami images constructed without and with WMC 345
processing. 346
347
Animal experiments 348
Figure 11 shows 3D B-mode and 3D WMC Nakagami images (constructed using N = 349
5) of rat livers for 0 to 8 weeks of MCD diets. Over that range of MCD diets, the 350
shading of the 3D WMC Nakagami images gradually varied to light green 351
corresponding to post-Rayleigh distributions. To confirm these observations, a volume 352
of interest (VOI) was manually selected for calculation of the average m
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parameter 353
of the liver parenchyma, as shown in Figure 12. The values of m
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for 0, 1, 2, 4, 6, 354
and 8 weeks of MCD diets were 0.69 ± 0.03, 0.76 ± 0.06, 0.98 ± 0.09, 1.12 ± 0.08, 355
1.23 ± 0.09, and 1.38 ± 0.03, respectively. This result shows that the global 356
backscatter statistics of rat livers varied from pre-Rayleigh to post-Rayleigh 357
distributions with changes in liver properties from normal to fatty stages. The results 358
obtained from animal experiments show that 3D WMC Nakagami imaging can 359
characterize tissues by visualizing the spatial changes in the backscatter statistics. 360
361
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363
364
365
366
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Discussion 369
370
Significance of this study 371
In this study, a 3D WMC Nakagami imaging technique was developed by integrating 372
the WMC technique into 3D Nakagami imaging and validated through phantom and 373
animal experiments. The experimental results indicate that 3D WMC Nakagami 374
imaging has several advantages over conventional Nakagami imaging in the following 375
aspects. (i) Resolution: No significant difference was found between the resolutions 376
of 3D Nakagami images obtained without and with WMC processing. This implies 377
that 3D WMC Nakagami imaging inherits the benefits of 3D Nakagami imaging; 378
specifically, 3D WMC Nakagami imaging provides higher-resolution images than 379
conventional 2D Nakagami imaging does. (ii) Smoothness: The smoothness of 3D 380
Nakagami images is also a critical issue in addition to image resolution, particularly 381
for characterizing homogeneous tissues. Using a sliding cube with the suggested size 382
is difficult to provide a smooth estimate of the parameter for 3D Nakagami imaging. 383
The number densities of scatterers in a homogeneous medium may differ locally, 384
resulting in local variations in backscattered statistics. On the other hand, this is also 385
because the lack of smoothness of the 3D Nakagami image produces larger variations 386
between local Nakagami parameters. Without resolution degradation, the 3D WMC 387
technique largely improved the smoothness of 3D Nakagami images. This is 388
attributed to the combined advantages of large- and small-cube-based 3D Nakagami 389
imaging to achieve empirically optimal performance. The 3D WMC Nakagami 390
imaging technique showed minimal estimation error when the number of frames N 391
was 5. (iii) Spatial tissue characterization: 3D WMC Nakagami imaging performs 392
well in detecting spatial changes in the backscatter statistics induced by fatty 393
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infiltration in rat livers. Compared with conventional 3D Nakagami imaging, 3D 394
WMC Nakagami imaging provided superior image quality in spatial tissue 395
characterization. 396
397
Effects of fatty liver in rats on the backscatter statistics 398
A normal liver parenchyma may be typically considered as a 3D arrangement of 399
considerable scatterers.
33,34
Under this condition, the statistics of the echo amplitudes 400
for normal liver tissues typically follow the Rayleigh distribution.
35-38
However, in 401
practical measurements, the Rayleigh distribution is not necessarily the ground truth 402
of the statistical properties of ultrasound backscattered echoes returned from normal 403
livers. Instead, the backscatter statistics of normal liver tissues tend to follow 404
pre-Rayleigh distributions because normal livers have blood vessels.
39
This 405
phenomenon has also been found in rat livers, indicating that the backscatter statistics 406
of normal rat livers follow pre-Rayleigh distributions.
30,32,40
The mechanisms by 407
which fatty liver tissue affects the statistical distribution of backscattered signals have 408
been widely discussed in previous studies.
32,41,42
In general, hepatic steatosis is 409
usually considered as macrovesicular steatosis (large droplet steatosis), in which a 410
single large vacuole of fat fills the hepatocyte and displaces the nucleus to the 411
periphery.
43
Therefore, an acoustic model for fatty liver may be simply simulated 412
using a scattering medium with numerous randomly distributed acoustic scatterers 413
(liver cells) in addition to scatterers with different echogenicities and sizes (fatty 414
vesicles).
42
This simplified model implies that the formation of fatty liver involves an 415
increasing number density of fatty vesicles in the liver parenchyma. Increasing the 416
number density of scatterers not only leads to a larger backscatter amplitude
44
but also 417
generates a stronger effect of constructive wave interference, which causes the echo 418
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amplitude distribution to vary away from a Rayleigh distribution.
32,41,42
419
420
Potential uses of 3D WMC Nakagami imaging in animal applications 421
Prior to clinical investigations using 3D WMC Nakagami imaging, future applications 422
may focus on quantitative analyses of tissues in animal models. This is because 423
researchers have typically used animal models for validating new pharmaceuticals or 424
investigating new medical issues. Accordingly, 3D ultrasound imaging has become a 425
very convenient noninvasive laboratory tool for morphology and volumetric analysis. 426
For example, Dawson et al. developed a highly accurate, reconstructive 3D ultrasound 427
imaging system for mouse hearts.
45
Further applications of 3D ultrasound imaging in 428
echocardiography for small animal studies were summarized.
46
In vivo volumetric 429
imaging of the rat lateral gastrocnemius muscle was made through the generation of 430
3D ultrasound biomicroscopic images.
47
Quantitative volumetric imaging of normal, 431
neoplastic, and hyperplastic mouse prostates was also implemented using 3D 432
ultrasound.
48
It should be noted that 3D ultrasound imaging has been widely applied 433
to morphology or volumetric measurements, but the literature details few applications 434
to tissue characterization. The current quantitative imaging of tissues in animal 435
models has unmet needs that must be satisfied. 436
The value of 3D WMC Nakagami imaging is different from that of general 3D 437
ultrasound B-mode imaging. Recall that 3D WMC Nakagami imaging can visualize 438
spatial changes in backscatter statistics with superior resolution and smoothness (i.e., 439
stable parameter estimation) for tissue characterization. Most liver diseases occur in 440
the liver parenchyma, and few structures exist in the liver. Therefore, 3D visualization 441
and quantitative analysis are paramount in characterizing liver parenchyma. In the 442
future, the 3D WMC Nakagami imaging algorithm may be combined with real-time 443
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systems, providing an image-based pathological model for in vivo tracking of the 444
growth and formation of liver disease in animals visually, without animal sacrifice. 445
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Conclusions 469
470
In this study, 3D WMC Nakagami imaging was developed and validated by phantom 471
and animal experiments on fatty liver in rats. The conclusions can be summarized as 472
follows: (i) The number of frames N = 5 was the optimal value for stable Nakagami 473
parameter estimations and reliable 3D WMC Nakagami imaging; (ii) when N = 5 was 474
used, the 3D WMC Nakagami images were able to demonstrate variations in the 475
number density of scatterers; (iii) 3D WMC Nakagami imaging inherits the 476
advantages of 3D Nakagami imaging, providing an enhanced resolution compared 477
with conventional 2D Nakagami imaging; (iv) the use of the WMC technique endows 478
3D Nakagami imaging with an improved smoothness for visualizing spatial changes 479
in backscatter statistics; (v) 3D WMC Nakagami imaging performed well in the 480
assessment of fatty liver in rats, and it thus has potential to act as an image-based 481
pathological model for visually characterizing liver diseases in animal studies. 482
483
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correlation algorithm to suppress artifacts in ultrasonic Nakagami images. 570
Ultrason Imaging. 2012;34:110–24. 571
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Symp Proc. 2011;1:887–90. 573
30. Ho MC, Tsui PH, Lee YH, Chen YS, Chen CN, Lin JJ, Chang CC. Early 574
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feasibility evaluation. Ultrasound Med Biol. 2014;40:2272–84. 576
31. Ma HY, Lin YH, Wang CY, Chen CN, Ho MC, Tsui PH. Ultrasound 577
window-modulated compounding Nakagami imaging: resolution improvement 578
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32. Ho MC, Lee YH, Jeng YM, Chen CN, Chang KJ, Tsui PH. Relationship between 581
ultrasound backscattered statistics and the concentration of fatty droplets in livers: 582
an animal study. PLoS One. 2013;8:e63543. 583
33. Yamaguchi T, Hachiya H. Modeling of the cirrhotic liver considering the liver 584
lobule structure. Jpn J Appl Phys. 1999;38:3388–92. 585
34. Hara T, Hachiya H. A new modeling for the changes in the distribution of 586
scatterers in cirrhotic liver. Jpn J Appl Phys. 2000;39:3262–5. 587
35. Tuthill TA, Sperry RH, Parker KJ. Deviations from Rayleigh statistics in 588
ultrasonic speckle. Ultrason Imaging. 1988;10:81–9. 589
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Kishimoto T, Matsubara H, Hachiya H, Ishikura H, Saisho H. A pilot approach 591
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37. Toyoda H, Kumada T, Kamiyama N, Shiraki K, Takase K, Yamaguchi T, 594
Hachiya H. B-mode ultrasound with algorithm based on statistical analysis of 595
signals: evaluation of liver fibrosis in patients with chronic hepatitis C. Am J 596
Roentgenol. 2009;193:1037–43. 597
38. Igarashi Y, Yamaguchi T, Hachiya H. Stability of quantitative evaluation method 598
of liver fibrosis using amplitude distribution model of fibrotic liver. Jpn J Appl 599
Phys. 2011;50:07HF17. 600
39. Son JY, Lee JY, Yi NJ, Lee KW, Suh KS, Kim KG, Lee JM, Han JK, Choi BI. 601
Hepatic steatosis: assessment with acoustic structure quantification of US 602
imaging. Radiology. 2016;278:257–64. 603
40. Ho MC, Lin JJ, Shu YC, Chen CN, Chang KJ, Chang CC, Tsui PH. Using 604
ultrasound Nakagami imaging to assess liver fibrosis in rats. Ultrasonics. 605
2012;52:215–22. 606
41. Wan YL, Tai DI, Ma HY, Chiang BH, Chen CK, Tsui PH. Effects of fatty 607
infiltration in human livers on the backscattered statistics of ultrasound imaging. 608
Proc Inst Mech Eng H. 2015;229:419–28. 609
42. Tsui PH, Wan YL. Effects of fatty infiltration of the liver on the Shannon entropy 610
of ultrasound backscattered signals. Entropy. 2016;18:341. 611
43. Tandra S, Yeh MM, Brunt EM, Vuppalanchi R, Cummings OW, Unalp-Arida A, 612
Wilson LA, Chalasani N. Presence and significance of microvesicular steatosis in 613
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Chang KJ. Use of Nakagami statistics and empirical mode decomposition for 616
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45. Dawson D, Lygate CA, Saunders J, Schneider JE, Ye X, Hulbert K, Noble JA, 619
Neubauer S. Quantitative 3-dimensional echocardiography for accurate and rapid 620
cardiac phenotype characterization in mice. Circulation. 2004;110:1632
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46. Ram R, Mickelsen DM, Theodoropoulos C, Blaxall BC. New approaches in small 622
animal echocardiography: imaging the sounds of silence. Am J Physiol Heart Circ 623
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47. Martins NSF, Carneiro LT, Dantas HM, Esperança C, Marroquim RC, Oliveira 625
LF, Machado JC. Generation of 3D ultrasound biomicroscopic images: technique 626
validation and in vivo volumetric imaging of rat lateral gastrocnemius. Res 627
Biomed Eng. 2015;31:85
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48. Singh S, Pan C, Wood R, Yeh CR, Yeh S, Sha K, Krolewski JJ, Nastiuk KL. 629
Quantitative volumetric imaging of normal, neoplastic and hyperplastic mouse 630
prostate using ultrasound. BMC Urol. 2015;15:97. 631
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Figure legends 644
645
Figure 1. (a) Sliding cube is moved across the three-dimensional (3D) envelope data 646
to calculate the local Nakagami parameters for a 3D Nakagami parametric image. (b) 647
Flowchart of the proposed 3D window-modulated compounding Nakagami imaging 648
strategy. 649
650
Figure 2. Mechanical scanning system with a single-element focused transducer for 651
ultrasound radiofrequency data acquisition. 652
653
Figure 3. (a) Three-dimensional (3D) B-mode and 3D conventional Nakagami images 654
of phantoms with different number densities of scatterers (ranging from 2 to 64 655
scatterers/mm
3
). (b) Linear fitting curve of the m
w
parameter as a function of number 656
density of scatterers (ranging from 2 to 64 scatterers/mm
3
) 657
658
Figure 4. Three-dimensional window-modulated compounding Nakagami images of 659
phantoms with different number densities of scatterers (2, 4, 6, 8, 16, 32, 64 660
scatterers/mm
3
) constructed using different settings of the number of frames N. 661
662
Figure 5. Parameter m
wmc
as a function of frame number N obtained from phantoms 663
with different number densities of scatterers (ranging from 2 to 64 scatterers/mm
3
). 664
665
Figure 6. Estimation error between the m
wmc
and the m
w
parameters as a function of 666
frame number N for different number densities of scatterers (ranging from 2 to 64 667
scatterers/mm
3
). 668
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669
Figure 7. Linear fitting curve of the m
wmc
parameter (N = 5) as a function of number 670
density of scatterers (ranging from 2 to 64 scatterers/mm
3
). 671
672
Figure 8. (a) Relationship between m
wmc
and m
w
parameters (correlation coefficient r 673
= 0.995). (b) Comparisons of the parameters between three-dimensional 674
window-modulated compounding and conventional Nakagami imaging. 675
676
Figure 9. Comparisons of the full width at half maximum of the parameter distribution 677
between three-dimensional window-modulated compounding and conventional 678
Nakagami imaging. 679
680
Figure 10. Comparisons of the autocorrelation function width of an image between 681
three-dimensional window-modulated compounding and conventional Nakagami 682
imaging on the (a) X-axis, (b) Y-axis, and (c) Z-axis. 683
684
Figure 11. Three-dimensional B-mode and window-modulated compounding 685
Nakagami images of rat livers at different weeks of methionine-choline-deficient 686
diets. 687
688
Figure 12. Linear fitting curve of the m
wmc
parameter (N = 5) as a function of weeks 689
of methionine-choline-deficient diets. 690
691
692
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695
Figure 1. (a) Sliding cube is moved across the three-dimensional (3D) envelope data 696
to calculate the local Nakagami parameters for a 3D Nakagami parametric image. (b) 697
Flowchart of the proposed 3D window-modulated compounding Nakagami imaging 698
strategy. 699
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Figure 2. Mechanical scanning system with a single-element focused transducer for 702
ultrasound radiofrequency data acquisition. 703
704
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Figure 3. (a) Three-dimensional (3D) B-mode and 3D conventional Nakagami images 707
of phantoms with different number densities of scatterers (ranging from 2 to 64 708
scatterers/mm
3
). (b) Linear fitting curve of the m
w
parameter as a function of number 709
density of scatterers (ranging from 2 to 64 scatterers/mm
3
) 710
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Figure 4. Three-dimensional window-modulated compounding Nakagami images of 713
phantoms with different number densities of scatterers (2, 4, 6, 8, 16, 32, 64 714
scatterers/mm
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) constructed using different settings of the number of frames N. 715
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Figure 5. Parameter m
wmc
as a function of frame number N obtained from phantoms 719
with different number densities of scatterers (ranging from 2 to 64 scatterers/mm
3
). 720
721
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Figure 6. Estimation error between the m
wmc
and the m
w
parameters as a function of 724
frame number N for different number densities of scatterers (ranging from 2 to 64 725
scatterers/mm
3
). 726
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Figure 7. Linear fitting curve of the m
wmc
parameter (N = 5) as a function of number 729
density of scatterers (ranging from 2 to 64 scatterers/mm
3
). 730
731
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739
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Figure 8. (a) Relationship between m
wmc
and m
w
parameters (correlation coefficient r 741
= 0.995). (b) Comparisons of the parameters between three-dimensional 742
window-modulated compounding and conventional Nakagami imaging. 743
744
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Figure 9. Comparisons of the full width at half maximum of the parameter distribution 754
between three-dimensional window-modulated compounding and conventional 755
Nakagami imaging. 756
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Figure 10. Comparisons of the autocorrelation function width of an image between 761
three-dimensional window-modulated compounding and conventional Nakagami 762
imaging on the (a) X-axis, (b) Y-axis, and (c) Z-axis. 763
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Figure 11. Three-dimensional B-mode and window-modulated compounding 767
Nakagami images of rat livers at different weeks of methionine-choline-deficient 768
(MCD) diets. 769
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Figure 12. Linear fitting curve of the m
wmc
parameter (N = 5) as a function of weeks 774
of methionine-choline-deficient diets. 775
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