Pre screening study in progress for breast cancer detection using electrical impedance spectroscopy

1. A Support Vector Machine Designed to Identify Breasts at High Risk
Using Multi-probe Generated REIS Signals: A Preliminary
Assessment
David Gur 1 , Bin Zheng 1 , Dror Lederman 1 , Sreeram Dhurjaty 2 , Jules Sumkin 1 ,
Margarita Zuley 1
1
Department of Radiology, University of Pittsburgh, Pittsburgh, PA 15213
2
Dhurjaty Electronics Consulting LLC, Rochester, NY 14618
ABSTRACT
A new resonance-frequency based electronic impedance spectroscopy (REIS) system with multi-probes,
including one central probe and six external probes that are designed to contact the breast skin in a circular form with a
radius of 60 millimeters to the central (“nipple”) probe, has been assembled and installed in our breast imaging facility.
We are conducting a prospective clinical study to test the performance of this REIS system in identifying younger
women (< 50 years old) at higher risk for having or developing breast cancer. In this preliminary analysis, we selected a
subset of 100 examinations. Among these, 50 examinations were recommended for a biopsy due to detection of a highly
suspicious breast lesion and 50 were determined negative during mammography screening. REIS output signal sweeps
that we used to compute an initial feature included both amplitude and phase information representing differences
between corresponding (matched) EIS signal values acquired from the left and right breasts. A genetic algorithm was
applied to reduce the feature set and optimize a support vector machine (SVM) to classify the REIS examinations into
“biopsy recommended” and “non-biopsy” recommended groups. Using the leave-one-case-out testing method, the
classification performance as measured by the area under the receiver operating characteristic (ROC) curve was 0.816 ±
0.042. This pilot analysis suggests that the new multi-probe-based REIS system could potentially be used as a risk
stratification tool to identify pre-screened young women who are at higher risk of having or developing breast cancer.
Keywords: Electrical impedance spectroscopy (EIS), resonance frequency, risk stratification, breast cancer, support
vector machine, technology assessment.
I. INTRODUCTION
Developing a non-radiation based, low cost, easy to operate, and highly performing prescreening tool to
identify younger women (< 50 years old) with higher risk of having or developing breast cancer has been attracting
research interest for a long time. Electrical Impedance Spectroscopy (EIS) technology is one of the approaches that have
been explored for this purpose. When applying EIS technology to detect breast abnormalities, the system applies
alternating low power electric signals to the breast skin (tissue) and measures the tissue’s response. The breast tissue
impedance is determined by analyzing the difference between the applied “excitation” and the response electrical signals.
Differences in electrical conductivity and capacitance between neo-plastic and normal breast tissue have been shown in
the 1920s and have been assumed to be primarily the result of changes in cellular water content, amount of extracellular
fluid, and membrane proteins [1]. Cancer cells exhibit altered local dielectric properties as compared with normal cells.
A study performed in the 1980s reported that the conductivity and capacitance in malignant human breast tissue was 20
to 40 fold higher than the normal breast tissue. Based on such experimental results, a prototype EIS system was tested in
the hope of detecting breast abnormalities [2]. Since then, a number of studies followed and improved EIS systems that
include both system hardware and classification algorithms have been developed and reported [3-8]. A commercial EIS
system (T-Scan 2000, Mirabel Medical Systems, Austin, TX) was approved by the U.S. Food and Drug Administration
(FDA) as an adjunct modality to mammography and several laboratory and clinical studies have been conducted to
assess the performance and clinical utility of this EIS system [9, 10].

2. In the last several years, we have been working on developing and evaluating a different type of EIS technology
[11-13]. The EIS system consists of paired detection probes and produces continuous multi-frequency electrical pulse
sweeps over a wide range of frequencies. From the recorded EIS signal sweeps, we focus on using primarily EIS signals
specifically at and near the resonance frequency for the breast tissue being measured. Using these signals we build
machine learning classifiers to identify breasts depicting highly suspicious abnormalities. Hence, we termed our new
approach REIS (for the resonance frequency we focus on). In a previous study, we tested a prototype REIS system with
one pair of probes that enabled contact with the nipple and a single lateral contact point at the lateral mid-outer portion
of the breast skin with a fixed distance of 60 mm to the center (“nipple”) probe. We also built an EIS signal feature
based artificial neural network (ANN) to classify cases that ultimately warranted a biopsy due to detection of a highly
suspected abnormality during diagnostic imaging workups and cases that were not recommended for a biopsy. The
overall performance of that classifier as measured by the area under the ROC curve was 0.707 ± 0.033, which is
significantly better than chance [12]. After demonstrating the feasibility of using the single probe REIS based approach,
we developed, assembled, and installed a new multi-probe REIS system in our clinical imaging facility [13]. Under an
IRB-approved protocol, we are currently conducting a prospective clinical study to assess the performance of this new
multi-probe REIS system. In this preliminary analysis, we selected an initial set of 100 acquired REIS measurements
(examinations) with verified diagnostic results. This group includes women with negative screening examinations and
women recommended for a biopsy as a result of the diagnostic workup. An initial set of multi-probe based EIS features
(values) were used combined with a genetic algorithm to reduce the number of redundant values and build a support
vector machine (SVM) based classifier to classify these women into positive (“recommended for biopsy”) and negative
(“not recommended for biopsy”) groups. The experimental procedures and classification results are described and
reported herein.
II. MATERIALS AND METHODS
Under an exclusive contract between the
University of Pittsburgh and Dhurjaty Electronics
Consulting LLC (Rochester, NY), a multi-probe
based REIS system to measure and record multi-
channel EIS signal sweeps (including amplitude,
phase, and combined magnitude) was specially
designed, assembled, and installed in our clinical
breast imaging facility [13]. In brief, the system
consists of a mechanical support, an electronic box,
and two interchangeable sensor cups depending on
breast size. It is driven by a notebook computer
housing the programs to control the system and data
acquisition. The sensor cups include seven mounted
metallic probes with one probe located in the center
of the cup and the other six probes are distributed
along a circle located in the 12, 2, 4, 6, 8, and 10
o’clock positions, respectively (Fig. 1). The distance
between the external probes and the center probe is
60 mm. During an REIS examination, the center
probe makes contact with the nipple and the other
six probes make contact with six points on the breast
skin surface. The maximum electric voltage and
current applied to the sensor probes (breast skin) are
less than 1.5V and 30mA, respectively. The
application of this sensor cup to the breast is similar
to manually holding a 1.5V battery; hence, as
expected, and our previous study showed, that the
majority of participants (>98%) did not feel an
electrical tingling during the examination [13].

3. All REIS examinations are performed by trained health care professionals. During each examination a
technologist in our clinical imaging facility selects a sensor cup based on the participant’s breast size and adjusts the
sensor box position along a vertical rail of the REIS system to fit the height of the breast and then locks it in place. The
center probe is positioned slightly higher than the naturally positioned level of the participant’s nipple. The woman is
then asked to “lift” her breast with her hand and position the nipple to make sure it touches (makes good contact with)
the center probe and then to “pull herself” into the cup by holding one or both sidebars of the REIS system. The
technologist types in a digital ID number specific to the REIS examination in question. Once the system detects that all
seven probes have “satisfactory” contact with the breast, the measurement and signal acquisition starts. The complete
examination of each breast takes 12 seconds. The same measurement procedure is repeated on both breasts during each
REIS examination. The multiple REIS signal sweeps generated between different pairs of sensor probes are
automatically recorded and saved in a specific data file named with the test ID number in a database. Each EIS signal
sweep records 121 output signals including signal amplitude (a), signal phase (p), and signal magnitude
( I = a 2 + p 2 ) ranging from 200 KHz to 800 KHz at a 5 KHz increment. The resonance frequency of each EIS
signal sweep is detected at a frequency at which the signal magnitude reaches the minimum value and at this frequency
phase crosses the zero line (e.g. converting from negative to positive values).
Under an IRB approved protocol, we are currently acquiring REIS data aimed to enable an investigation of the
possible performance and reliability of applying this technology to classify young women (between ages of 30 and 50
years old) into “positive” and “negative” groups. The “positive” group represents the cases that had been recommended
for biopsy due to suspicious findings during the imaging based diagnostic workup, and the “negative” group represents
negative screening cases that had been rated “negative” during screening and/or a diagnostic workup. Because REIS is a
non-imaging type of examination, there is no restriction (nor identification) regarding the type of abnormality in question
(i.e., mass, micro-calcification clusters, asymmetry, and etc.), nor of the abnormality location within the breast (in
“positive” cases). This preliminary analysis included an initial dataset of 100 REIS examinations (cases). Among these,
half (50) were “positive” and the other half “negative”.
In each REIS examination multiple EIS signal sweeps are generated and recorded. To develop the machine
learning classifiers to classify test cases, we first computed a relatively large number of EIS signal features extracted
from six sets of EIS sweeps for all six pairs between the center probe and each of the six “external” probes (Fig. 1).
Based on the expectations that similar to the known symmetry between breast tissue patterns observed on mammograms;
hence, the two breasts of each woman should have a higher level of electrical impedance symmetry in the normal
(negative) cases than in the abnormal (positive) cases [8], we used EIS signal differences (subtraction) between the
corresponding signal values extracted from two matched EIS sweeps acquired from the left and right breasts (in a
location based mirrored fashion). Our initial feature pool included a total of 33 EIS signal related features. Most of these
features represented the absolute difference (subtraction) of two corresponding EIS signal values computed for the two
breasts. Using figures 2 and 3 as an example, we describe the definitions, computational methods, and resulting units for
the 33 EIS signal difference related features. We first identified the resonance frequency values of all six EIS signal
sweeps and computed the maximum range of these six resonance frequency values for each breast
( Δf = Max | f i − f j | , i ≠ j = 1,2, K ,6 ). Thus, feature 1 is defined as the absolute difference of these two values
computed from the left (L) and right (R) breasts ( F1 = | Δf L − Δf R | ). In the sweeps shown in Fig. 2, the maximum
resonance frequency ranges for the two breasts are Δf L = 420 – 280 = 140 KHz, and Δf R = 405 – 280 = 125 KHz.
Thus, F1 = (140 – 125) = 15 KHz.
The remaining 32 features are divided into two groups each containing 16 values. In the first group, we first
computed an average value of the six EIS signal values extracted from the six EIS signal sweeps acquired from one
breast. We then computed either average (1 value) or absolute differences (15 values) of the two matched averaged
signal values between the two breasts. Thus, the 16 features in this group can be described as follows:
6
1. We computed the average resonance frequency ( f = ( ∑ f i ) / 6 ) for each breast. As shown in Fig. 2 f L = (390 +
i =1
405 + 330 + 300 + 280 + 320) / 6 = 337.5 (KHz) and f R = (420 + 405 + 305 + 285 + 300 + 360) / 6 = 345.8 (KHz).

4. From these two average resonance frequency values, we defined two features. Feature 2 is the average of the two
values ( F2 = ( f L + f R ) / 2 ) representing the overall resonance frequency of the case and Feature 3 is the
absolute difference between the two values ( F3 = | f L − f R | ). In Fig. 2, F2 = 341.7 KHz and F3 = 8.3 KHz,
respectively.
(a) (b)
(c) (d)
Figure 2: Six sets of recorded EIS signal magnitude sweeps and six phase sweeps for the left and right breast of one
examination. The minimum, average, and maximum resonance frequencies of the six sweeps are shown for comparison
in (a) and (b), respectively. Six sets of EIS output signal phase sweeps of the right and left breast, as well as the
frequencies at which the phase signals reaches a plateau are shown in (c) and (d), respectively.

5. 2. We identified EIS signal magnitude ( I ( f ) ) at resonance frequencies and computed the average value
6
(I =( ∑ I ( f ) ) / 6 ) at all six resonance frequencies for each breast. We defined Feature 4 as the absolute
i =1
i
difference of the two averaged values between the two breasts: F4 = | I L − I R | . As shown in Fig. 2 (a) and (b),
I L = (5576 + 5384 + 5555 + 5439 + 5334 + 5202) / 6 = 5415 (mV), and I R = (5433 + 5187 + 5346 + 5351 + 5688
+ 5769) / 6 = 5462.3 (mV). Thus, F4 = 47.3 (mV).
(a) (b)
Figure 3: A mirror-matched pair of EIS signal sweeps (magnitude –left and phase –right) that have the largest difference
in resonance frequency between the right and left breasts as shown in Fig. 2.
3. Near the resonance frequency of each EIS sweep, we extracted six signal values of an EIS sweep ( I ( f i ) ) at six
specific frequencies. These included values at two frequencies that are lower by 5 and 10 KHz than the identified
resonance frequency ( f −10 = f − 10 KHz and f −5 = f − 5 KHz) and values at frequencies that are higher by 5,
10, 15 and 20 KHz than the identified resonance frequency (from f 5 = f + 5 KHz to f 20 = f + 20 KHz at 5
KHz increment). At each of these frequencies we computed the EIS signal magnitude value ( I ( f i ) ) and subtracted
these values from the EIS signal magnitude value at the resonance frequency ( I ( f i ) ). Specifically, we computed
the following six values ΔI i = I ( f i ) − I ( f ) , i = −10, − 5, 5, 10, 15, 20 KHz. After averaging the six EIS
6
signal magnitude differences ( ΔI i ) over the six probe pairs ( ΔI i = ∑ ( ΔI )
k =1
i k ), we defined six features (Features
5 to 10) by computing the absolute differences for the EIS signal magnitude values computed from the two breasts
( F j = | ΔI ( f i ) L − ΔI ( f i ) R | , where j = 5, 6, K10 and i = −10, − 5, 5, 10, 15, 20 KHz below and above
the resonance frequency). For example, at f −10 = f − 10 KHz the EIS signal magnitude values acquired from the
right breast (Fig. 2(a)) are 5670, 5286, 5503, 5475, 5993, and 5937 for the six EIS sweeps, respectively. After
subtracting EIS magnitude values at the resonance frequency [ I ( f ) ] for the same EIS sweep, we computed the

6. average magnitude difference among six EIS sweeps: ΔI ( f −10 ) R = (237 + 99 + 157 + 124 + 305 + 168) / 6 = 181.7
(mV). Using the same approach we computed the six corresponding EIS sweep magnitude values (5665, 5544, 5785,
5505, 5475, and 5373) from the signal of the left breast and computed ΔI ( f −10 ) L = (89 + 160 + 230 + 66 + 141 +
171) / 6 = 142.8 (mV) for the left breast (Fig. 2(b)). Thus, F5 = 38.9 (mV) and so on.
4. From the EIS signal phase sweeps (Fig. 2 (c) and (d)), we computed the following seven feature values. In each EIS
Max
phase sweep, we identified the frequency [ f ( p )] at which the EIS phase signal (p) reaches a “plateau”. We
6
then computed the average values ( f ( p
Max
) = ∑ f ( piMax ) / 6 ) of the six EIS phase sweeps for both the left and
i =1
right breast and defined Feature 11 as the absolute difference of the two values ( F11 = | f ( p L ) − f ( p R ) | ).
Max Max
Max
In the example we present (Fig. 2 (c) and (d)), f ( p L ) = (505 + 520 + 455 + 430 + 430 + 455) / 6 = 466 (KHz)
Max
for the left breast and f ( p R ) = (535 + 525 + 440 + 420 + 430 + 480) / 6 = 472 (KHz) for the right breast. Thus,
F11 = (472 – 466) = 6 (KHz).
5. Similar to feature values 5-10 we computed EIS signal phase value differences rather than the EIS signal magnitude
value differences for the same set of six frequencies of interest. Features 12 to 17 are defined as the absolute
differences of the two averaged phase values at the six specific frequencies between two breasts
( F j = | p ( f i ) L − p ( f i ) R | , where j = 12, 13, K17 , and i = −10, − 5, 5, 10, 15, 20 KHz. For example, to
compute feature F12 from the EIS phase sweeps shown in Fig. 2(c) and (d), we computed p ( f i ) R = [(-1525) + (-
1178) + (-1257) + (-923) + (-1558) + (-1364)] / 6 = -1300.8 (mV) and p ( f i ) L = [(-1147) + (-1377) + (-1415) + (-
1072) + (-1126) + (-1305)] / 6 = -1240.3 (mV). As a result, F12 = 60.5 (mV) and so on.
The second group of 16 feature values (18-33) is computed in a similar manner to feature values (2-17) with
the exception that only one mirror-matched pair of EIS signal sweeps (rather than averages of all six sweeps) from left
and right breasts is selected. The selected matched pair of EIS signal sweeps is the one that has the largest difference in
the two resonance frequency values as compared with all other five matched pairs. In the example shown in Fig. 2, the
matched pair of EIS sweeps at 10 o’clock on the left breast and 2 o’clock on the right breast has the maximum resonance
frequency difference (40 KHz). Discarding the other five EIS pairs, we plotted this matched pair of EIS sweeps in Fig. 3.
Similar to computing the 16 feature values from the difference of the averaged data of the six EIS sweeps, we computed
the second set of 16 EIS signal features using the same definitions albeit computed solely based on the selected matched
pair of EIS sweeps ( F18 to F33 ). For example, as shown in Fig. 3 (a), features 18 to 20 are computed as: F18 = (320 +
360) / 2 = 340 (KHz), F19 = (360 – 320) = 40 (KHz), and F20 = (5769 – 5202) = 567 (mV), respectively. Table I
summarizes the definitions of all 33 EIS signal based feature values selected as an initial pool.
To classify between “positive” and “negative” examinations (case based) we built a support vector machine
(SVM) based classifier. The SVM is a popular machine learning classifier based on statistical learning theory [14] which
has been used in a number of classifiers designed for computer-aided detection schemes [15]. We modified a publicly
available SVM software package (SVM-Light) [16] to build our classifier. The SVM-Light software package provides
for 10 model (kernel) options including linear, polynomial, radial basis, sigmoid, and others. In this analysis, a
polynomial function based statistic model [ s = ( a ∗ b + c ) ] was selected.
d
To select a small (“optimal”) set of effective features and remove (discard) redundant features in our initial
feature pool and to define an optimal parameter (d) used in the polynomial function, a genetic algorithm (GA) [17] was
applied. The binary coding method with 35 genes was applied to represent a GA chromosome in which the first 33
represent all initially computed EIS signal related feature values and the last two genes represent the parameter (d) used
in the polynomial function. In the first 33 genes, 1 indicates that the feature represented by this gene is selected and 0

7. indicates that the feature is discarded from the SVM classifier. The last two gene codes represent d value ranging from 2
to 5. A unique GA fitness function that includes the SVM learning and the ROC curve fitting was designed and
implemented. The performance summary index used to select (fitness index) highly performing GA chromosomes in
each training generation was the area under the ROC curve ( Az ). Chromosomes that produce higher Az values have
higher probabilities of being selected for generating new chromosomes using the crossover and mutation method. The
GA operation was terminated when it reached either a global maximum performance level or a pre-determined
maximum number of growth generations (i.e., 100). The best GA selected chromosome was used to build the SVM
classifier, the result of which are reported in this paper.
Table I: A list of the initial set of 33 EIS signal based features. With the exception of features #2 and #18 that represent
an average of two feature values computed from two breasts, all other features represent the absolute difference of two
corresponding EIS signal values computed from the signals obtained from two breasts.
Feature Feature Description Feature unit
1 Difference in the range of six resonance frequencies KHz
2 Average of two averaged resonance frequencies KHz
3 Difference of two averaged resonance frequencies KHz
4 Difference of two averaged EIS signal magnitude values at corresponding mV
resonance frequencies
5 - 10 Difference of two averaged EIS signal magnitude values near the resonance mV
frequency ranging from -10 to +20KHz at 5KHz increments
11 Difference of two averaged frequency values when EIS phase signal reaches a KHz
plateau
12 - 17 The difference of two averaged EIS signal phase values near the resonance mV
frequency ranging from -10 to +20KHz at 5KHz increments
18 Average of two resonance frequencies exhibiting the maximum resonance frequency KHz
difference between mirror-matched pair of probes
19 Difference between two resonance frequencies of the selected matched pair of KHz
probes
20 Difference between two EIS signal magnitude values at the two matched resonance mV
frequencies
21 - 26 Difference between two EIS signal magnitude values of the matched probe pair near mV
the resonance frequencies ranging from -10 to +20KHz at 5KHz increments
27 Difference between two frequency values when EIS phase signal reaches a plateau KHz
28 – 33 Difference between two EIS signal phase values of the matched probe pair near the mV
resonance frequencies ranging from -10 to +20KHz at 5KHz increments
Performance assessment of the classifier was performed using the leave-one-case-out testing method due to the
limited size of the REIS dataset. During each testing iteration, 99 examinations were used to train the coefficients using
the SVM classifier with a fixed number of EIS signal features and a given classification function while the remaining
examinations were used to test the SVM performance. This process was repeated 100 times, hence, each examination
was used once as a test case. As a result, 100 testing (classification) scores that indicate the likelihood of the case being
positive were generated. Using these classification scores the SVM overall performance level was measured as the area
under the ROC curve ( AZ value), which is frequently used for this purpose as a summary index, and was computed
using a publicly available ROC program (ROCKIT [18]).

8. III. RESULTS
A set of 12 EIS signal features were selected by the GA from the initial pool of 33 features. Thus, the SVM
based classifier built, tested, and presented in this study included 12 EIS signal related features and a parameter d = 2
for the polynomial function based classification hyper-plane. Among the 12 REIS selected features, seven were extracted
from the average values of the six probe pairs (the first group). These features included F2 , F4 , F6 , F8 , F9 , F10 , and
F12 . The remaining five features were computed from a single mirror-matched probe pair showing the largest difference
in resonance frequencies (the second group) and included F17 , F19 , F21 , F28 , and F32 . Two of the features were
related to frequency differences, seven were associated with EIS signal magnitude differences, and three were related to
the computed phase differences. The testing (classification) performance of the SVM classifier when applied to our
dataset of 100 examinations achieved an AZ = 0.816 ± 0.042 (Fig. 4). The 95% confidence interval of the computed
AZ for this dataset was [0.722, 0.887].
Figure 4: The SVM actual detection performance data points and the fitted ROC curve classifying between 50 positive
(biopsy) cases and 50 negative (non-biopsy) examinations. The area under ROC curve ( AZ ) is 0.816 ± 0.042.
IV. DISCUSSION
To date, EIS technology has attracted but limited interest as an adjunct examination modality to mammography
[9, 10]. We are focused on the development and assessment of a different approach to using EIS signals. The unique
characteristic of our approach is that it is primarily based on differences in measurements of multiple EIS signals at and
near the detected resonance frequencies. We have assembled and tested two REIS systems. The first prototype REIS
system consisted of only one pair of sensor probes (one EIS signal detection channel) and the second system includes

9. seven sensor probes that can result in multiple pairs of EIS signal detection channels. In our previous study we
demonstrated the feasibility of applying REIS signal related feature values for classifying “biopsy” recommended and
“non-biopsy” recommended examinations [12]. The purpose of developing and testing the current (multi-probe) REIS
system is to improve the clinical utility of the same underlying REIS concept. The new REIS system can not only
generate multi-channel EIS signal sweeps, but it was also much easier to use and more reliable operationally. The system
automatically detects the adequacy of all contacts thereby avoiding the need for repeated scans. The total EIS signal
scanning time for each breast is substantially reduced from approximately 48 seconds to 12 seconds using this system.
This helps reduce the impact of unexpected patient movement during the examination. However, as the new REIS
system generates and records a substantially larger number of data than the previous single probe pair based REIS
system, selection of a small set of effective features is more effort consuming, albeit the classification performance is
significantly better.
This paper describes the first preliminary study that assessed the possible use of a SVM based machine learning
classifier for this purpose. We note that the initial feature pool of 33 EIS signal related features was reduced to 12 that
were used to build the SVM classifier. Both EIS signal magnitude and phase values were ultimately included in the
SVM classifier. Although we cannot directly compare our performance level to that achieved in the previous study ( AZ
= 0.707 ± 0.033) [12] as different datasets were used, we believe that the multi-probe pair based REIS system has the
potential to achieve a substantially higher classification performance.
Our initial testing results are quite encouraging but we need to emphasize that this was a very preliminary study
with but a small set of 100 REIS examinations. Additional work and further tests of this REIS approach using a
significantly larger number of diverse cases combined with repeated optimization of feature selection are needed before
this technology can be seriously considered as acceptable for routine clinical use. The possible advantages of the REIS
system and approach are many, such as low-cost, non-radiation based, and easy to use, but the system’s possible use as a
prescreening risk stratification tool (e.g. an office based system to be used in conjunction with CBE) in identifying
younger women (i.e., ≤ 50 years old) with higher risk of having or developing breast cancer remains far from reality at
this point in the development.
V. ACKNOWLEDGEMENT
This work is supported in part by Grant 1R21/R33 CA127169 to the University of Pittsburgh from the National
Cancer Institute, National Institutes of Health. The authors also thank the Magee-Womens Research Institute &
Foundation, Glimmer of Hope Fund, for supporting this effort.
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