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White
Red
Red
Plasma
Plasma
20
10
0
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Red
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No of Occurrences
No of Occurrences
30
10
20
10
0
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20
No of Occurrences
No of Occurrences
20
10
0
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No of Occurrences
No of Occurrences
30
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maginitude
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start
Partition samples
into clusters.
Compute the mean
of each cluster.
Reassign samples to
cluster with nearest µ.
yes
Cluster
change?
no
stop
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80
60
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Cluster 1
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100
Ca
FT
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No of Occurrences
80
60
40
20
0
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Cluster 1
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Red
Red
Plasma
Plasma
1
feature f49
feature f47
1
0
-1
0
-1
-2
-2
-1
0
feature f7
1
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-2
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2
.
0 0
feature f7
1
2
0
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1
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2
2
White
White
Red
Red
Plasma
Plasma
1
feature f3
1
feature f2
-1
0
-1
0
-1
-2
-2
-1
0
feature f7
1
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0
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2
2
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White
Red
Red
Plasma
Plasma
1
feature f11
feature f10
1
0
-1
0
-1
-2
-2
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feature f7
1
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1
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2
2
White
White
Red
Red
Plasma
Plasma
1
feature f17
feature f15
1
0
-1
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-2
2
0
-1
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0
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1
2
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30
White
Red
No of Occurrences
Plasma
20
10
0
Cluster 0
Cluster 1
Cluster 2
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Intravascular Ultrasound Image Interpretation
William H Nailon , Stephen McLaughlin , Timothy Spencer , M Pauliina Ramo ,
The University of Edinburgh, Dept. of Electrical Eng., Edinburgh EH9 3JL, Scotland, UK,
Tel/Fax +44
[31] 650 5655 / 650 6554. e-mail: whn@ee.ed.ac.uk
Departments of Medical Physics and Cardiology, Western General Hospital,
Crewe Road South, Edinburgh EH4 2XU, Scotland, UK.
Abstract
resolution image information is to investigate the textural
properties of the image, as the texture contains information
on the spatial distribution of tonal variations within ROIs.
Here, two approaches were used to characterise image texture. These were,
In this study, statistical and fractal texture analysis was
used to assess the ability of 30MHz Intravascular Ultrasound (IVUS) data, in raw and scan-converted form, to
characterise atherosclerotic plaque. Data from 3 different plaque groups was assessed in the study, these were,
loose fibrotic tissue (LFT), dense fibrotic tissue (DFT) and
calcium (CA). The composition of each group was verified
from histo-pathological analysis, providing a Gold Standard from which results were verified. Scan-converted images were used to locate 33 regions of interest (ROI) within
areas of known tissue composition. Fractal and Statistical
textural features were computed on ROI data in raw and
scan-converted form. The results show the ability of the
method to discriminate between groups, but in particular,
they highlight the advantage of using the raw data over the
scan-converted data to assess coronary artery disease.
1. Statistical Texture Analysis;
2. Fractal Texture Analysis.
2. Statistical Texture Analysis
Grey-tone spatial dependence matrices [3] were used to
compute meaningful features relating to arterial plaque composition, by examining the textural properties contained in
the selected ROIs from the raw and scan-converted data. In
this, a second order statistical analysis technique, each spatial dependence matrix entry is the probability of finding a
pixel which has grey-tone at a distance and angle from
a pixel which has grey-tone . A fundamental premise in
using this conceptual framework for analysing image texture, is that the image segment to be analysed is rectangular,
containing resolution cells horizontally and resolution cells vertically. This results in horizontal and vertical
spatial domains of,
1. Introduction
Currently, one of the leading causes of death in the industrialised world is cardiovascular disease. Diagnostic ultrasound has been used extensively over the past two decades
to assess this condition [1]. More recently, IVUS was developed through a need for more detailed assessment of cardiovascular disease at the level of the disease process itself.
The unique assessment of arterial disease offered
by IVUS, through viewing coronary artery interiors, is realised by insertion of a high frequency ultrasound transducer,
incorporated into the tip of a catheter, into the vessel. The
high resolution image information provided by IVUS can be
used to classify arterial plaque in diseased coronary arteries by objective plaque characterisation [4] [5]. The key to
characterising atherosclerotic plaque composition from high
1 2 (1)
1 2 (2)
Furthermore, to reduce the computation involved, the greytones within a given image segment must be quantised to
have ! grey levels. To derive the texture content contained within a given image segment, it is also essential to
consider each pixel as having eight nearest neighbours connected to it, except at the periphery of the segment. The
neighbours can be grouped into the four categories shown
in Figure 1. We may then assume, that all of the texture
information is contained in the probability density functions
"$#
"$#
%& : ')( , where each
%* : +,( is the probability
1 This study was supported by the Northern and Yorkshire Regional
Health Authority (N.H.S. Executive R&D project: Ic8), the EPSRC and
the Royal Society.
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O
1 & 5,
3 & 7,
4 & 8,
2 & 6,
3. Fractal Texture Analysis
O
90
O
135
45
6
7
8
5
X
1
4
3
2
O
There are many techniques frequently used to describe
the texture of natural surfaces. Fractals have proved useful in describing natural and irregular surfaces by a single
measure [7]. This measure, the fractal dimension, describes
the degree of irregularity in the surface texture. The rougher
or more irregular the structure, the greater its fractal dimension. Here, we investigate the use of the fractal dimension
as a single measure to characterise atherosclerotic plaque.
To do this, it is essential to construct an intensity surface for
the ROI, from which the fractal dimension may be measured
to provide a measure of image texture. This was achieved
by regarding the pixel intensity at a point
, as the
height above a plane . A typical random intensity surface
constructed in this manner is shown in Figure 2.
O
HORIZONTAL NEIGHBOURS
VERTICAL NEIGHBOURS
RIGHT DIAGONAL NEIGHBOURS
LEFT DIAGONAL NEIGHBOURS
Figure 1. Nearest neighbour resolution cells.
8
with which two neighbouring pixels, one with grey-tone
and the other with grey-tone occur, when separated by a
distance and an angle . Such a matrix is a grey-tone spatial dependence matrix, of which there are four in a single
texture data set, corresponding to the four nearest neighbour
categories. More formally, for angle quantised to 45 o intervals, the estimated probability density functions are defined
by equations 3, 4, 5 and 6.
z
0o ! "# where %$& 0 (' $ ' )
* : 45o+, * #! -!# where %$& $ $ .$& $ $ )
or
* : 90o /0 * #! 1!# where ' ,$& ' $ 0)
5 76 4
I(x,y)
y
(3)
x
Figure 2. Intensity surface representation.
(4)
3.1. Fractional Brownian Motion and the Fractal
Dimension
Fractional Brownian motion, an extension of Brownian
motion, provides a useful model for describing natural random fractals [2]. In this estimation concept, the intensity
surface is regarded as a fractional Brownian surface enveloped in three dimensional space. The fractal dimension is
found from this method by considering the absolute intensity difference of pixel pairs at different scales. It can be
shown that for a fractional Brownian surface, the following
relationship must be satisfied,
(5)
* : 135o/20 3 (6)
1 where .$& $ .$& $ $ $ )
or
where, in all cases, is the spatial location of the pixel
is the spatial location of the pixel
with grey-tone ,
with grey-tone and denotes the number of elements in
9" '(4 1 $ 4 2 ' /: ; 5 2 $<5 1>= 6 2 $ 6 1? (7)
where, 4 1 and 4 2 refer to the pixel intensity at two
5
9 is the mean and @ is the Hurst
separate points 6 ,
coefficient. To simplify, if we write,
A C4 BD E' 4 5 2 6 2 $
A#F ; 5 2 $G5 1>=
the set. A set of 13 local textural features were computed
in the spatial domain from the grey-tone spatial dependence
matrices.
¦ hK=
4 5 1 7 6 1 ' 6 2 $ 6 1
(8)
(9)
D^$*<@ 10$D0-V"$.
(10)
of such a surface, may be
3 (11)
using
this
procedure
is
The first step
in
estimating
for various . The next step is to plotto
calculate
! " versus ! " . The slope of the best fitting
#
$ % to #'&)( is over
line through the data from
the chosen range, from which * can be estimated using
equation 11 .
DFT or CA
where, the fractal dimension
determined from,
LFT
Catheter
Vessel Wall
4. In Vitro Data Acquisition
The IVUS data used in this study was obtained from
coronary arteries obtained immediately after post-mortem
examination and imaged within 30 minutes of being dissected from the heart. The excised vessels were mounted in
a flow phantom for imaging, where physiological pressure
was maintained through closed loop saline injection. The
positions at which the image data was captured were marked
with silk suture for histological analysis, used to verify the
composition of plaque within the ROIs. In total, 33 ROIs
were used in the study, 15 LFT, 10 DFT and 8 CA.
The modified IVUS imaging system used in the study [6],
allowed real-time collection of the raw ultrasound signals,
240 for one complete 360o scan of the transducer from the
radio frequency (RF) output of the Hewlett Packard intravascular machine. Each line of raw ultrasound was captured by
a Tektronix RTD720A real-time digitiser, and sampled with
a sampling period of 4ns with 8 bit vertical resolution. This
resulted in 2048 sample points per line and a scan depth of
6mm for
1540 ms 1 .
Once captured, images were formed from the raw data
set of 2048 sample points by 240 lines. From each raw
image, a 512x512 scan-converted image was constructed
for orientation within the vessel and to locate the 33 ROIs.
The ROIs selected were matched with their corresponding
sections in the raw data to form the data set used in the
study. Figure 3 shows a section taken from a digitised
RF data image. Figure 4 shows one of the scan-converted
images used in the analysis with ROIs marked.
+
,
Figure 4. Scan-converted image.
4.1. Atherosclerotic Plaque Composition
Atherosclerosis involves the formation and deposit of
fatty substances such as cholesterol, cellular waste products,
calcium and fibrin in the inner lining of an artery. Depending
on their composition, atherosclerotic plaques can be identified using IVUS due to their unique response to ultrasound.
DFT and CA, composed largely of extra-cellular collagen,
have a very similar ultrasound appearance. They are easily
identified by their high echogenicity and shadow in their
wake. This is due to their ability to reflect most of the incident ultrasound as a result of their dense structure. LFT,
composed of collagen fibres forms diffusely in the arterial
wall. It is identified by IVUS as echogenic specular regions,
clearly differentiable from blood.
-
5. Results
The statistical and fractal techniques used to assess the
textural properties of the raw and scan-converted data resulted in a large amount of data being generated. Statistical
inference from the data, on the ability of the techniques to
discriminate plaque groups, was carried out by Analysis of
Variance (ANOVA). Tables 1 and 2 summarise the F-values
and their significance (P-value), for the fractal and statistical features computed on the raw and scan-converted data.
Those features obtained from the GTSDM able to discriminate plaque types from the raw and scan-converted data are
shown in Figures 5 to 7, where, only F-values for those
features found to have significance levels less than 5% are
shown. Figure 8 shows the results of using the fractal dimension as a single measure to discriminate plaque types
from the raw and scan-converted data. Only F-values found
significant at the 5% significance level are plotted.
Figures 5 and 6 show that it is possible to discrimin-
sample
points
lines
Figure 3. Raw data section.
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measure, that it is capable of equalling the discriminative
power of the GTSDM. However, one of the inherent uncertainty factors of the chosen technique, is in the choice
and
.
of limiting scales for fractal geometry,
Here, the range was chosen to be equal to the smallest dimension, length or width, of the ROI.
The results present good evidence to suggest that the
treatment of the raw RF data in image form, is a more robust
means of quantifying atherosclerotic plaque than analysis
of the scan-converted image data. Undoubtedly, this is due
to the degree of post-processing required on the RF data to
form a scan-converted image, which is essential to identify
ROIs.
ate between LFT and DFT (LFT/DFT), and between LFT
and CA (LFT/CA) using specific features derived from the
GTSDM. However, examining the results more closely highlights the significantly better discriminative properties of
features derived from the raw data rather than the scanconverted data.
Figure 7 shows the limited ability of GTSDM features in
discriminating between DFT and CA (DFT/CA) using the
raw and the scan-converted data. Only 2 features derived
from the raw data and 1 from the scan-converted data hold
discriminative properties.
The effectiveness of using the fractal dimension to discriminate between LFT/DFT and between LFT/CA is shown
in Figure 8. As with the GTSDM features, the performance
of the method was best when working with the raw data,
however, unlike the GTSDM which showed marginal discriminative properties between DFT/CA, the fractal dimension was unable to partition these groups.
7. Conclusion
The use of IVUS as a clinical aid in imaging cardiovascular disease has appreciated substantially the level of diagnostic information available for describing arterial morphology. While the morphological information available to
the clinician is a powerful aid in assisting diagnosis, providing information relating to tissue types within normal and
diseased vessels would make a significant contribution to
the choice of treatment. The techniques proposed in this
study show, through preliminary results, promise towards
the goal of providing the interventional cardiologist with
this aid using the raw data.
6. Discussion
The results manifest the superiority of using the raw data
to discriminate LFT/DFT and LFT/CA using the proposed
statistical and fractal based texture analysis techniques.
They show the difficulty in differentiating between DFT/CA,
a phenomenon reflected in differentiating DFT/CA from
videodensitometric data.
From the GTSDM raw data results of LFT/DFT and
LFT/CA, it is evident that some of the features used display
redundant information. This is clearly visible in features
f4, f5, f8 and f13, where, f4 is a measure of the ROI variance; f5 measures the local homogeneity; f8 measures the
degree of randomness and f13 measures the linearity within
the chosen ROI. Since all of these features are related to
the homogeneity of a particular ROI, it is not surprising that
they show enormous merit in discriminating LFT from DFT
and CA. This is due to the greater density of collagen in
the latter 2 groups making them homogeneous and accounting for their highly echogenic appearance when viewed in
scan-converted form (Figure 4). Feature f7, the sum variance measure and f9 the entropy measure relating to the
randomness contained in the ROI have small discriminative
power in the raw data between LFT/DFT and none between
LFT/CA. This is due to their dependence on f8, the sum
entropy feature. The small changes in f8 between plaque
groups, provides adequate discrimination when used alone,
however, when linked with f7 and f9 the numerical value
of f8 does not emphasise the discriminative properties of f7
and f9. With these points in mind, it should be possible to
optimise the feature set to reduce the prohibitive amount of
computation involved in finding the GTSDM.
As an instrument for discriminating between groups, the
fractal dimension shows, with the advantage of a single
Acknowledgements
The authors are extremely grateful to Dr. D.M. Salter for
providing the expertise required in histological analysis of
the vessels. In providing the necessary enthusiasm, guidance and expertise in the project, the authors would like to
thank Prof. W.N. McDicken and Dr. G.R. Sutherland.
References
[1] D. M. Cavaye, R. A. White, and G. E. Kopchok. Intraluminal
ultrasound: basic principles, techniques and applications. In
D. M. Cavaye and R. M. White, editors, A text and atlas of
arterial imaging: modern and developing technology, pages
109–123. Chapman and Hall medical, 1993.
[2] C. Chen, J. S. Daponte, and M. D. Fox. Fractal feature analysis
and classification in medical imaging. IEEE Transactions on
Medical Imaging, 8(2):133–142, June 1989.
[3] R. M. Haralick, K. Shanmugam, and I. Dinstein. Texture features for image classification. IEEE Transactions on Systems,
Man, and Cybernetics, SMC-3(6):610–621, November 1973.
[4] P. P. Kearney, I. R. Sharkey, and G. R. Sutherland. Intracoronary ultrasound: current state of the art. British Heart Journal
(Supplement 2), 73:16–25, 1995.
[5] R. J. G. Peters, W. E. M. Kok, H. Bot, and C. A. Visser. Characterisation of plaque components with intracoronary ultrasound
¦ hU£
D^$*<@ 10$D0-V"$.
F-values for features able to discriminate LFT/CA
250
200
F-value
150
RAW
SCAN
100
F13
F12
F11
F9
F10
F8
F7
F6
F5
F4
F3
0
F2
50
F1
imaging: An in vitro quantitative study with videodensitometry. American Society of Echocardiography, 7:616–623,
1994.
[6] T. Spencer, M. P. Ramo, D. M. Salter, T. Anderson, P. P. Kearney, G. R. Sutherland, K. A. A. Fox, and W. N. McDicken.
Characterisation of athersoclerotic plaque by spectral analysis
of intravascular ultrasound: an in vitro study with histological and radiological validation. Ultrasound in Medicine and
Biology. submitted for review.
[7] D. Stoyan and H. Stoyan. Fractals, random shapes and point
fields: methods of geometrical statistics. John Wiley and Sons,
1994.
Feature number
Feature
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
F11
F12
F13
Fractal Dim.
LFT/DFT
F-value
P-value
LFT/CA
F-value
P-value
41.442
9.6940
39.245
98.592
81.136
12.336
5.0000
78.630
5.0630
43.789
34.676
20.086
105.61
34.257
31.107
24.107
72.080
126.47
129.34
31.544
1.3750
98.166
0.0210
54.364
71.305
20.876
225.68
23.145
0.000
0.005
0.000
0.000
0.000
0.002
0.035
0.000
0.034
0.000
0.000
0.000
0.000
0.000
DFT/CA
F-value
P-value
0.000
0.000
0.000
0.000
0.000
0.000
0.254
0.000
0.886
0.000
0.000
0.000
0.000
0.000
4.558
1.401
0.854
4.429
1.478
1.076
3.657
0.705
2.387
0.200
0.001
0.645
5.483
0.289
0.049
0.254
0.369
0.051
0.242
0.315
0.074
0.413
0.142
0.660
0.976
0.434
0.032
0.598
Figure 6. Discrimination of LFT/CA with GTSDM.
F-values for features able to discriminate DFT/CA
6
5
Table 1. F and P values for Raw data.
RAW
SCAN
2
0.185
0.591
0.185
0.582
0.057
0.746
0.926
0.042
0.991
0.576
0.338
0.153
0.055
0.376
F13
F12
F11
F10
0
F9
1
F8
1.923
0.300
1.922
0.315
4.213
0.108
0.009
4.905
0.000
0.325
0.976
2.256
4.301
0.829
F7
0.858
0.000
0.112
0.532
0.951
0.006
0.000
0.044
0.000
0.702
0.466
0.880
0.136
0.020
F6
0.033
52.84
2.759
0.403
0.004
9.476
87.17
4.575
148.9
0.150
0.553
0.023
2.399
6.361
F5
0.281
0.000
0.673
0.249
0.018
0.007
0.000
0.442
0.000
0.324
0.678
0.137
0.495
0.001
3
F4
1.2210
28.315
0.1830
1.4000
6.5170
8.7010
36.258
0.6110
29.914
1.0140
0.1770
2.3710
0.4810
15.274
DFT/CA
F-value
P-value
F3
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
F11
F12
F13
Fractal Dim
LFT/CA
F-value
P-value
F2
LFT/DFT
F-value
P-value
F1
Feature
F-value
4
Feature number
Figure 7. Discrimination of DFT/CA with GTSDM.
Table 2. F and P values for Scan-converted data.
F-values for fractal dimension between groups
35
F-values for features able to discriminate LFT/DFT
30
120
F-value
25
100
F-value
80
20
RAW
SCAN
15
10
60
RAW
SCAN
40
5
0
LFT / DFT
DFT / CA
F13
F12
F11
F9
F10
F8
F7
F6
F5
F4
F3
F2
F1
0
LFT / CA
Plaque
20
Feature number
Figure 8. Discrimination with the fractal dimension.
Figure 5. Discrimination of LFT/DFT with GTSDM.
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F-values for FOS on raw data
F-values for FOS on scan-converted data
600
600
"FO_W_P_raw.dat"
"FO_W_R_raw.dat"
"FO_P_R_raw.dat"
"FO_W_P_scan.dat"
"FO_P_R_scan.dat"
"FO_W_R_scan.dat"
500
400
400
300
300
F-value
F-value
500
200
200
100
100
0
0
-100
-100
F1
F2
F3
F4
Feature number
F5
F6
F7
F1
"!#%$'&()+*-,(./(021435(67098)-(0;:/<>='?2@
F2
F-values for NGTDM on raw data
F5
F6
F7
F-values for NGTDM on scan-converted data
100
"NGTDM_W_P_raw.dat"
"NGTDM_P_R_raw.dat"
"NGTDM_W_R_raw.dat"
80
"NGTDM_W_P_scan.dat"
"NGTDM_P_R_scan.dat"
"NGTDM_W_R_scan.dat"
80
60
F-value
60
F-value
F4
Feature number
CY![Z $&()4*,-(./(021+35(6708)-(0;:/<>=>?2@
100
40
40
20
20
0
0
F1
F2
F3
Feature number
F4
F5
F1
"!BAC$'&()+*-,(.D(021+35(67098)-(0;:/EDFBG&IH@
F2
F3
Feature number
F4
F5
\ Y![] $&()4*,-(./(021+35(6^08\)(0;:DE/F[G_&KH@
F-values for GTSDM on raw data
F-values for GTSDM on scan-converted data
1800
1800
"GTSDM_W_P_raw.dat"
"GTSDM_W_R_raw.dat"
"GTSDM_P_R_raw.dat"
1600
1400
"GTSDM_W_P_scan.dat"
"GTSDM_W_R_scan.dat"
"GTSDM_P_R_scan.dat"
1600
1400
1200
1200
1000
1000
F-value
F-value
F3
800
800
600
600
400
400
200
200
0
0
F1
F2
F3
F4
F5
F6 F7 F8 F9 F10 F11 F12 F13 F14
Feature number
F1
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F2
F3
F4
F5
F6 F7 F8 F9 F10 F11 F12 F13 F14
Feature number
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Vessel Wall for 3 fractal features (f=3)
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LFT
240 lines
No of Occurences
20
B
B
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