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With
the advent of dense sensor arrays (64–256 channels) in
electroencephalography
and magnetoencephalography studies, the probability increases that some
recording channels are contaminated by artifact. If all channels are
required
to be artifact free, the number of acceptable trials may be
unacceptably low.
Precise artifact screening is necessary for accurate spatial mapping,
for current
density measures, for source analysis, and for accurate temporal
analysis based
on single-trial methods. Precise screening presents a number of
problems given
the large datasets.

Therefore, EMEGS uses a procedure for statistical correction
of
artifacts in dense array studies (SCADS), which (1) detects individual
channel
artifacts using the recording reference, (2) detects global artifacts
using the
average reference, (3) replaces artifact-contaminated sensors with
spherical
interpolation statistically weighted on the basis of all sensors, and
(4)
computes the variance of the signal across trials to document the
stability of
the averaged waveform.

This procedure is implemented via the programs 'PrePro' and 'EditAEM'.
During the preprocessing, statistical parameters for later artifact
detection are calculated. The EditAEM interface (shown
below) then lets the user choose the minimum acceptable data
quality.

**Introduction**

In
recent years it has become evident that accurate recording of electrical or magnetic brain fields often requires
adequate spatial
sampling to avoid spatial aliasing (Tucker, Liotti, Potts, Russell, & Posner, 1994;
Wikswo, Gevins,
& Williamson, 1993). Dense sensor array electroencephalogram (EEG) systems (64–256 channels are now used in many laboratories.
Estimates of the
spatial Nyquist frequency1 of the human EEG and averaged event-related
potential (ERP)
suggest that an intersensor distance of 2–3 cm is required to achieve
adequate
spatial sampling (Spitzer,
Cohen, Fabrikant, & Hallett, 1989; Srinivasan, Tucker, &
Murias, 1998). With an even distribution of sensors across the head
surface, a sampling
density of less than 3 cm requires 128 sensors, and a density of less
than 2 cm
requires 256 sensors (Tucker,
1993). Similarly,
magnetoencephalogram (MEG)
systems have been scaled whole-head coverage, and may now measure from
122 to
148 sensors
at a time and twice
as many in the near future. Both the correctness of the
scalp
topography and the localization of neural generators depend on a sufficient
spatial resolution (Junghöfer,
Elbert, Leiderer, Berg, & Rockstroh, 1997;
Tucker, 1993). However, recording from dense arrays presents new prob-
lems for
data acquisition. Although many creative theoretical approaches and
some
empirical studies have been advanced for the problem of electrical or
magnetic
source analysis, there has been little attention to the problems of
statistical
management of data quality in multichannel EEG and MEG systems. The
results of
topographical analysis as well as source analysis depend strongly on
the
quality of the data of each sensor that enters the analysis. The
likelihood of
errors due to noise or other artifacts increases with the number of
sensors.
If, in a given trial, arti- facts are restricted to a few sensors, the
trial
still contains valuable information. However, simply removing the
artefact sensors
contaminated sensors from the average will introduce a specific class
of
errors. We propose a method for averaging multichannel event-related
electromagnetic data that (1) optimizes data intake in high-resolution data
acquisition, (2) minimizes errors of topography, current density
analysis, or
source localization due to missing sensors, and (3) provides statistical information about the data
quality for each
channel in the array. ERP analysis typically begins with a
three-dimensional
matrix (trial
*X ** *sensor X time) EEG*n*, *s*,
*t *with *n *denoting the number of
trials or recording epochs, *s *the
number of sensors, and *t *the
number of time samples within a
trial. Although we focus on electrical recordings in the present
report, a
similar structure is used for event-related MEG analysis. Data
processing
then comprises the following steps:

1.First, the influence of
extraneous noise resulting from movement or sensor (electrode)
artifacts is
controlled by rejecting epochs with large amplitudes. A criterion is
set such
that within a given epoch *n *and
for a given sensor *s *the
range of
data points EEG*n*, *s*, *t *for
all time points *t *does
not exceed
a predefined absolute amplitude (for the EEG, for instance, a
range of 100 mV
is suggested; Elbert, Lutzenberger, Rockstroh, & Birbaumer,
1985).In case
of violation of this requirement, the data recorded from a particular
sensor
will be declared as artifact contaminated for that particular trial.^{2
}If
this problem recurs frequently in a given data set, the rejection
strategy may
be elaborated as follows: (a) If data of one or several identified
sensors turn
out to be of poor quality throughout a significant portion of the *N *trials, these sensors will
be rejected
completely from further analyses (from all trials). (b) Alternatively,
an EEG*n *, epoch is
rejected entirely if a
significant portion of the *S *sensors
turns out to be artifact contaminated.

2. Second, artifacts from eye movements and blinks, as determined by periorbital electrooculogram (EOG) channels, are detected. Trials with artifacts may be rejected, or algorithms may be used to subtract the ocular artifact from the EEG channels (as described, for instance, by Berg & Scherg, 1991; Elbert et al., 1985).

3. Third, the remaining trials are averaged for each sensor and the resulting averaged ERP is then analyzed further.

Although this procedure is commonly used, the selective elimination of artifactual trials or channels has significant drawbacks, particularly when applied to dense array data:

1. First, if a sensor is noise contaminated in some but not all trials, the experimenter has to decide whether the rejection of that particular sensor, or the rejection of the noisy trials, will be appropriate. Often this decision is based on a rule of thumb that is not tailored to the specific data set: For example, if more than 20% of the sensors on a trial are noisy reject the trial, otherwise reject the data from individual sensors. Both trial and individual sensor data rejections result in a loss of signal information, and both actions may introduce a bias into the results.

2. Second, according to the “all or none” excessive amplitude rule, that is, that a given amplitude range should not be exceeded at any sensor during a trial, all trials for which this criterion is not met will be rejected irrespective of how many sensors are problematic. Furthermore, because they have different positions in relation to skull conductivity and brain sources, different EEG sensors have different EEG signal amplitudes. This will result in different background EEG amplitudes, depending on their distance from the reference sensor, and this background EEG is considered the “noise” in ERP averaging. Artifactual amplitudes thus summate with different EEG amplitudes for different channels.

3.
Third, once averaging
has been accomplished, no statistical information about the noise
level for
particular sensors, or about the set of measurements as a whole, is
available.
As a consequence, data sets with different noise levels are
compared within
one statistical procedure. The lack of noise information limits the
power of
inverse source modelling methods such as the least squares (Press,
Flannery,
Teukolsky, & Vetterling, 1986), chisquare, maximum-likelihood
(Sikihara,
Ogura, & Hotta, 1992), or minimum-norm methods
(Hämäläinen & Ilmoniemi,
1984). All these techniques can make good use of information on noise
heterogeneity.

The
crudeness of artifact screening and signal averaging contrasts
with the effort
that is invested in further data analysis, such as MRI-constrained
source modelling
with realistic head models. Empirical research (Braun, Kaiser, Kinces,
&
Elbert, 1997) has shown that the accuracy of current source modelling
is highly
dependent on the noise level of the data.

**Overview **

Therefore, EMEGS uses the following method for statistical control of artifacts in dense array studies (SCADS). The analysis requires two passes at the data, the first with the data kept in the recording reference, and the second with the data transformed to the average reference.

The
first pass detects and rejects artifactual channels, in the recording
reference
(e.g., vertex referenced), to avoid contamination of all channels
by the
artifacts when transforming EEG data to the average reference. The
average
reference is computed by subtracting the potential average across
all *S *sensors at one
point of time from each
single sensor potential at this point of time. Therefore artifacts
of single
sensors will contaminate the average reference (and thus all other
sensors) by
a factor of 1/*S*.^{3
}Once this
pass is complete, the average reference may be computed to allow
accurate
topographic mapping and topographic waveform plots. An accurate average
reference is unique to dense array studies. It requires a minimum of 64
channels, distributed to the inferior head surface as well as the top
of the
head (Junghöfer, Elbert, Tucker, & Braun, 1999; Tucker et al.,
1994).

Some EEG analysis methods, such as source localization procedures, do not require transformation to the average reference (because the reference site may be modelled explicitly). In these cases, or in case of MEG data (which does not require a reference), the first stage can be omitted as it will be repeated in the second pass.

In
the second pass, based on the average reference, global artifacts may
be more
clearly identified because the reference bias has been removed.
Individual
artifactual sensors that were identified in the first pass may be
interpolated
and replaced to complete the dataset and avoid the biases introduced by
missing
data.

**Procedure **

After
outlining the steps of the analysis procedure, we will describe
each in
detail.

1.
First Pass — Based on the Recording Reference:

1.1. Filter, thereby attenuating or removing artifacts in frequency bands that are not of interest for the analysis

1.2. Construct editing data matrices

1.3. Detect and reject consistently contaminated sensors (i.e., sensors exceeding a criterion of contamination throughout the experimental session)

1.4. Reject contaminated sensors in specific trials (to avoid the contamination of entire epochs when transforming to average reference)

1.5. Transform the edited data to average reference (to minimize the dependence of signal and noise amplitudes on the distance between the sensor and the chosen reference site).

2. Second Pass — Based on the Average Reference:

2.1. Construct editing data matrices (as step 1.2);

2.2. Determine and reject contaminated sensors in specific trials (based on the given editing matrices);

2.3. Reject contaminated trials

2.4. Average the remaining epochs, using interpolated values for distinct contaminated sensors (to avoid a different number of averaged epochs for different sensors)

2.5. Compute the standard deviation across all trials included in the average.

**1. First Pass Based on the Recording Reference
**

*1.1. Filter *

The decision to reject a given trial from the average should proceed after band pass filtering within the frequency band of interest. For ERP studies, retention of near-DC variation is usually preferred because slow brain potential changes may be meaningful, and higher frequency information related to sensory potentials may also be important. It is therefore best to record with a broad band pass (e.g., 0.01–100 Hz), then filter digitally, such as with a band stop or notch to filter out the 50-or 60-Hz main power line.

The
filter can be applied before segmentation of the ongoing stream of data
into
trials. If trials are filtered, any artifact produced by a fixed filter
length
must be minimized or subtracted from the beginning of the trial.
Stimulus
artifacts, such as from an electrical stimulus, must be removed before
filtering. Otherwise, digital filtering will temporally smear the
artifact,
making its removal more difficult.

*1.2. Construct Editing Matrices *

Editing data matrices are constructed to remove or correct sensors that are artifact contaminated. For this matrix construction, the maximum absolute value over time, the standard deviation over time and the maximum of the gradient of values over time (first derivative) are determined for every epoch. These three parameters display different sensitivities for specific artifacts. For instance, a sensor that is noisy throughout the entire epoch may produce normal amplitude values, whereas the noise contamination would be apparent in the standard deviation. Furthermore, transient artifacts may become obvious only from examining the first derivative.

Three
*N *x *S *data matrices *M *are produced with elements *mns *for the *n*th
epoch or trial at the *s*th
sensor.
The elements *mns *of
the first
matrix contain the maximal absolute value of the sensor *s *and the trial *n *over time. The second matrix
comprises the standard
deviations across the trial time interval. The third matrix describes
the
maximal temporal gradient. If the time interval of interest does not
correspond
to the entire trial interval, for example, the analysis targets only
the first
part of a recorded epoch, the calculation of the elements *mns *should be based on the
targeted time
interval to avoid rejection of trials or sensors because of artifacts
occurring
in non targeted time segments. Moreover, it might be necessary to
exclude a
distinct time segment with obvious stimulus-induced or other
experiment-specific artifacts from this calculation to avoid rejection
of
trials or sensors just because of this specific artifact. The editing
matrices
thus allow a focused screening of the data for the unique conditions of
the
experiment.

Additional
criteria and matrices can be created. Coherent biological noise,
such as from
alpha waves, often poses a problem for ERP source modelling.
Therefore, alpha
power might be specified in a further editing matrix in order
to identify
trials with large amplitude alpha waves.

*1.3. Detect and Reject Consistently Contaminated
Sensors *

The
parameter ( *p*)
matrices computed
in step 1.2 (absolute maximum, standard deviation, and first
derivative) are
used to determine contaminated sensors by creating a statistical
measure of
the degree and consistency of the artifactual values. A confidence
coefficient
is introduced to weight this measure. Medians are used to avoid the
influence
of extreme values.

We
first calculate the corresponding boundary values for *Lim*±( *p*)
for each parameter matrix *p *(Figure
1B):

Since *a = med*_{N}* ^{s }*

is similar to
a standard deviation except that *a *is the median and not
the mean across all *S *median
values. The general form of the equation as a whole resembles a robust (because it is based on medians)
confidence interval, with the
confidence
coefficient replaced by l *p *and the *SE *replaced
by a median based *SE *equivalent.
In computing the confidence
intervals for each sensor, a physical property of the data recorded
with
respect to a common reference site must be considered. This property is
illustrated in Figure 1A: the sensors close to the reference will
measure only
a small potential difference from the reference site
(because there is only a small amount
of brain
tissue generating a voltage difference between the index sensor site
and the
reference site! In
the present example, the vertex sensor (Cz) served
as reference. Figure 1A plots the amplitude (medium of absolute maximum)
a teach sensor site as a function of
its polar angle
from the Cz reference, which was defined as zero
(the pole)
. A larger polar angle means more
brain tissue contributing
to the potential difference, and thus a larger channel amplitude
(sensor site minus reference site
potential). This reference-dependence effect occurs with any
(e.g., nose, mastoid, non cephalic)
reference, and the effect can vary in
a complex fashion
between subjects and experimental conditions
(Junghofer et al., in press).

To remove this
effect, and thus equate the confidence intervals across the recording
channels,
the sensors are arranged according to their polar angular distance from
Cz and
the resulting function *a*(*s*)
is interpolated using a second degree
polynomial
least square regression. The original data *a*(*s*)
are corrected to *c*(*s*) by the resulting spatial dependency *b*(*s*), such that *c*(*s*)
= *a*(*s*)
- *b*(*s*)
(see Figure 1B). Now the final confidence interval for each parameter *p *can be calculated:

If the spatial
corrected median across all trials for a given sensor *c*(*s*)
exceeds the confidence intervals for
any of the three
parameters, it would be rejected from the analysis. Based on the
analysis of a large
assortment of datasets a *p *independent
value of l
= 2 seems to be a good choice to
reject consistently
noisy sensors while keeping data from sensors that show large signals
that may be
just large amplitude RPs. Figure 1B illustrates the confidence interval
for an analysis
based on the absolute amplitude maximum (firstparameter). Sensors 91 and 114 can be seen to be contaminated by
artefacts through-out
the measurement interval, and are thus candidates for rejection and
replacement
by interpolation. Figure 2A illustrates a dataset from which only
sensor #82
(bottom of sensor array)
was rejected completely.

*1.4. Detect and Reject Contaminated Sensor
Epochs*

In the next step, the individual sensor epochs (i.e.,a single sensor channels for a single trial n) are removed if the value of one of the three parameters for the sensor epoch p(s,n) exceeds the following confidence interval (calculated across all trials for that sensor channel):

Again a p independent value of lambda = 2 is a good choice to select sensor epochs with excessive noise content.

** 1.5. Transform the Edited
Data to Average Reference **Trials for
which the
resulting number of sensors with adequate data is less than a specified
threshold are removed from further analysis. This threshold varies from
experiment to experiment. For a clinical study of dementia it may be
necessary
to accept data with 80 of 128 sensor channels with acceptable data; for
a
normal study with well trained volunteers it may be possible to require
128 of
128 sensor channels.At this point, the accepted data are trans formed
to the
average reference.

**2.Second
Pass Based on Average Reference**

* *

*2.1 Construct the Average-Referenced
Editing Matrices*

If step 1.2 is repeated using the average reference data, artefacts produced by the reference sensor can be taken into account. Furthermore, the dependency of signal and noise power on the distance from the reference is no longer relevant. All calculations up to this step are accomplished by an automatic computer algorithm without necessity of interactive control.

*2.2 Detect and Reject Artifact-Contaminated
Sensor Epochs*

Identifying distinct sensors from particular trials should be based on visual inspection—in contrast to the automated detection of the first stage—for the following reasons: Because the noise may not be normally distributed and signal amplitude may not be constant across the trial, the contour of the frequency distribution of a sensor does not clearly indicate its noise. However, trials with abnormal amplitudes can be identified—as illustrated in Figure 2B for one sensor selected from the whole-head array in Figure 2A. Outliers in the distribution typically result from artifacts such as eye blinks, eye movements, or body movement. The probability of such artifacts, as well as those resulting from marked drifts, increases with the number of channels and with the duration of the data acquisition period.

Figure 2B illustrates a frequency distribution of amplitude maxima (amplitude histogram) for a given sensor. These are created by selecting the data point in each trial with the largest absolute deviation from zero. The critical upper limit for the amplitude maxima was chosen based on inspection of the histogram. All trials with values above this limit (indicated by the dashed line in Figure 2B) are removed—in the given example this number amounts to 29, so that 451 (94%) trials remain for further analysis.

The
removal of individual sensor epochs is illustrated in Figure 2A.
The maximum
absolute amplitudes across trials are log normally distributed, that
is, they
are skewed toward lower amplitudes. In an interactive manner, the
experimenter
must determine the upper and lower boundaries between which the data
are acceptable.
If a distribution is extremely broad or exhibits multiple peaks, the
sensor may
be removed completely (although such sensors should have been
already removed
when applying step 1.2 of the suggested first pass data processing).
Under
certain circumstances, bimodal distributions for some sensors may
be observed.
In general, this bimodality could indicate that a sensor—for
instance due to
movement—has lost its skin contact in the course of the acquisition
period.
This disruption will produce an abrupt increase in noise
amplitude. In such
cases a good strategy is to define the boundary amplitudes just above
the
distribution with the lower signal amplitudes^{4}.

^{
}

Boundaries have to be determined for each of the three parameters (absolute maximum, largest standard deviation, largest gradient). We have observed that the standard deviation and temporal gradient distributions resemble the distribution of the maximum amplitudes illustrated in Figure 2. Sensor epochs for which one or more of the three measures is outside of the respective predefined boundaries are removed from further analysis, whereas all others are included in the average.

A
computerized automatic processing of this outlined step would be
desirable,
particularly to standardize the described criteria for rejection.
Automatic
processing would also be complex, because the distributions of the
three
editing matrices *M *depend
on the
unique characteristics of the signals.^{5
}

^{
}

*2.3. Reject Contaminated Trials *

To identify trials contaminated by artifacts at many or all sensors, a histogram of the distribution of artifact-contaminated trials per sensor is constructed (Figure 3). On the basis of the histogram, the experimenter determines a lower boundary for trial rejection. This procedure improves the accuracy of the subsequent sensor epoch interpolation.

^{
}

With
118 selected as the minimum number of good sensors per
trial, of all trials
showing more than 10 bad
sensors within one trial are
rejected from further data analysis. In the present example, 90 (23%)
of the
480 trials are rejected due to artifacts that affect at least 11
sensors. Even
if the boundary for trial rejection is lowered— for instance to 110
good
sensors per trial—only a few more trials would have been saved for
further
analysis, all of them with in complete sensor sets. In
experiments with many trials
per condi-tion, it is desirable to choose a high boundary, because the
loss of trials
will then have a tolerable effect on the signal-to-noise ratio.If a
distribution
with a clear peak, like the one in Figure 3, is not obtained, the
choice of the
lower boundary may be based on the number of remaining trials.

*2.4.
Average the Artifact-Free
Trials with Interpolated Values for the Artificia**l Sensor
Sites*

Before averaging the remaining trials (i.e., all trials with a suffi-cientnumber of intact sensors remaining at this step), all sensor epochs that have been identified above as artefact contaminated are replaced by interpolation. The interpolation is achieved with weighted spherical splines fit to the intact sensors. In contrast to nearest neighbour interpolation, spherical splines are fit to all remaining sensors, such that the influence of each sensor is weighted nonlinearly by the inverse of its distance to the missing sensor and by the specific noise level (i.e., more distant and/or noisier sensors are weighted less than closer and/or cleaner sensors). This estimation and reconstruction of rejected sensor epochs is of particular importance to maintaining the accuracy of the dense array representation. The complete dataset, including the estimated interpolated data, may be computed and stored if single-trial analyses (such as spectral, latency-adjusted averaging, or nonlinear analyses) are desirable. Otherwise, the estimation and reconstruction can proceed with the averaged ERP epochs. Accurate surface potential distributions are particularly important for estimating radial current source density (CSD) from the two-dimensional (2D) Laplacian of the potential. Assuming no sources in the scalp, the 2D (surface) Laplacian is proportional to the radial current flow in or out of the skull at the computed point. The estimation of CSD based on spherical spline interpolation of EEG scalp potentials was first developed by Perrin, Pernier, Ber-trand, and Echallier (1989).

The calculation of the weighted spherical spline interpolation and the algorithms for calculating both CSD and intracranial potential maps were described by Junghöfer et al. (1997). Using spherical splines, data for a rejected sensor may be interpolated accepting all valid sensors, with the contribution of each weighted according to its noise level. This interpolation allows estimates for sensor sites for which one or several neighbours are missing. In addition, the global noise level of the remaining sensor epochs is used to calculate the regularization or “smoothing” factor. As described by Whaba (1981) or Freeden (1981), larger values of the regularization or smoothing factor indicate a smaller contribution of a single sensor’s data relative to the other remaining sensors. A sufficient number of remaining sensors for accurate is guaranteed by the minimum threshold (as described ins teps 1.5, and 2.3); otherwise the trial would have been rejected before this point. Each sensor is weighted according to its signal-to-noise ratio, which is deduced from the histogram distributions in the editing matrices in step 2.2.

Figure
4 illustrates a typical interpolation for missing sensor epochs. The
noise-contaminated sensor epochs (marked with an asterisk) were
interpolated
trial-by-trial. A trial before (A) and after (B, detail view) single
trial
interpolation was chosen to illustrate the effect of channel resetting
(channel
91 in this example). This example illustrates how an
artifact-contaminated
sensor could influence all other sensors in the average reference
transformation.

*2.5.
Calculate the Standard Deviation Across All Included Trials *

Finally,
the standard deviation is computed (for each time point) across all of
the
trials included in the average. In this matrix each element roughly
describes
the quality of each time sample in the average waveform. The standard
deviation
allows a comparison of signal quality between differing time points or
differing sensors. This comparison could provide a cautionary note for
further
analysis.^{7 }This caution is of crucial significance whenever
the topographical
distribution of averaged data is mapped using weighted spline
interpolations.
It also allows comparison between different data sets. Finally, this
information on noise levels may help improve the accuracy of
source modeling.

Finally, artifacts from subtle yet systematic eye movements may survive the artifact rejection process and thus contaminate the averaged ERP. Therefore, specific artifact correction procedures should also be implemented, such as subtractive correction procedures (e.g., Elbert et al., 1985) or modeling approaches (Berg & Scherg, 1991).

To test the accuracy of interpolation against measured data, we selected four adjacent sensors with good data (no rejected trials) in a 200-trial visual ERP experiment. We then treated them as if they were artifactual, interpolated them according to the SCADS methodology described above, and compared the interpolations to the actual data. The overplot of interpolated vs. actual data are shown for the four sensors (marked with asterisks) in Figure 5A, and in detail in Figure 5B. Although the interpolation was not perfect, Figure 5B shows that the waveform was fairly well reconstructed even for this large missing region. The fact that the interpolation is only approximate indicates that sampling with lower sensor density (e.g., 64 or 32 channels) would not accurately reflect the spatial frequency of the scalp fields (Srinivasan et al., 1998).

The
major advantage of the interpolation method of SCADS can be emphasized
at this
point: Averaging of trials without substituting the rejected
sensor epochs by
interpolated values will result in different numbers of trials per
sensor site
in the averages. This method would produce a temporal and spatial
correlation
of signal and noise, which would not be equally distributed across
trials.

**Conclusion **

By interpolating the artifactual sensors in individual (raw EEG and MEG) trials of the ERP, the SCADS methodology maximizes the data yield in dense array ERP and MEG studies. Furthermore, SCADS avoids analysis artifacts caused by correlated signal and noise. However, this methodology requires both extensive computing and the attention of the experimenter, requiring on the order of 5–10 min per condition per recording session. This interactive processing might be automated if a large amount of data of the same kind are to be analyzed. However, the SCADS methodology clearly requires more experimenter time and computing resources than the conventional averaging method. This methodology may not be necessary for experiments such as from university subjects, most of whom can provide data with minimal artifacts. However, for experiments that are valuable and difficult to collect without artifacts, such as from children or clinical populations, the additional investment may be justified.

Another benefit of SCADS is the statistical information about data quality, which provides objective criteria for rejection or inclusion of the data from a subject. Finally, in the subsequent steps of surface field mapping and electrical and magnetic source analysis, the SCADS methodology may provide substantial information on the noise and the variance of the average as well as the average signal represented by the ERP.

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