** Abstract: The
problem to find an optimal EEG reference is the actual topic for discussion
over 60 years. We have studied topographical differences in averaged EEG
amplitudes in alpha domain recorded in 10–20 system during “eyes closed”
test. These differences appeared due to the use of 13 reference schemes:
top and bottom of the chin (Ch1, Ch2); nose (N); top and bottom of the
neck (Nc1, Nc2); upper back (Bc); united electrodes at the base of the
neck anteriorly and posteriorly (2Nc); united, ipsilateral, and individual
ear electrodes (A12, Sym, A1, A2); vertex (Cz); and averaged reference
(AR). Six experiments for each of the ten subjects were carried out with
grounded and ungrounded states of three distant basic references Ch2, Bc,
2Nc. Pairwise comparisons of topographic consistency of 13 reference schemes
were carried out on the proposed complex of three independent indicators
with evaluative criterion, followed by centroid-based clustering of the
reference schemes and its discriminant verification. As a result, we have
established: (1) that most coordinated topography is provided by the following
reference electrodes — A12, P1, P2, Sym; (2) reference electrodes A1, Sh2,
A2, Sh1, AR, Cz are characterized by individually varying topography, which
may lead to contradictory conclusions obtained when they are used; (3)
no significant reasons have been found for preferring the grounded (neutral)
states of reference electrodes, that makes the search for or mathematical
construct of an infinitely remote neutral reference electrode less important;
(4) numerous distortions of EEG topography by reference electrode standardization
technique (REST) raise serious doubts about its proclaimed advantages in
EEG studies.**
* Key
words:* EEG, reference electrode, reference
at infinity, neutral reference, spectral analysis, cluster analysis, discriminant
analysis, topographical analysis, REST reference electrode standardization
technique..

**1. Introduction**

**2. Material and methods**

** (1) Ttwelve Pearson
correlation coefficients r _{ij} were calculated between Vi(Amean)
of i-reference and Vj(Amean) of each other j-reference. Then the mean correlation
Mi(r_{ij}) for i-reference is calculated by averaging of all its
rij. Mi(r_{ij}) are used to estimate the integral topographic differences
or similarities of each i-reference concerning all other references [18,
19]. The following two indicators assess the differential differences in
two orthogonal directions.**

**3. Results**
**3.1. Effect of the basic reference
electrode grounding**

**A**

**B**
**Fig. 1. Mean EEG spectral amplitudes
[mV] of alpha domain at 16 electrodes ordered
along sagittally meridians (horizontal axis). Six diagrams for chosen examinee
represent 6 records performed using three basic references in their ungrounded
state: at chin (Ch2), at back (Bc) and “united neck” (2Nc) and in their
grounded state (Ch2g, Bcg, 2Ncg) in two consecutive records (A, B). The
legends are on fig.1A.**

** Let us for each subject,
record and reference calculate M(Amean)-value by averaging of Amean over
the scalp. Fig.2 shows the changes of M(Amean) for three basic reference
electrodes, their two states (grounded/ungrounded), ten subjects and two
consecutive records for each subject. We can see that the data are characterized
by a strong interindividual variability. It also demonstrates (when comparing
two values for two consecutive records) the presence of intraindividual
variability, which is significantly lower in comparison with the interindividual
variability.**

**Fig. 2. Diagrams of mean spectral amplitudes
averaged over scalp [mV] in alpha domain for
ten subjects (horizontal axis) in six experiments using three basic reference
electrodes in their ungrounded and grounded states. For each subject, two
adjacent points on the diagrams, connected by bold lines, belong to two
consecutive records. The legends are similar to fig.1. Thin lines play
a supporting role for the connecting of the points of each of the six diagrams.**

** First, let us consider
the ratios between references in respect of their average tendencies. The
mean values and standard deviations of twenty M(Amean)-values calculated
for twenty records of each basic reference are: Bc=4.54±2.21, Bcg=5.88±3.67,
Ch2=4.1±2.87, Ch2g=4.42±2.5, 2Nc=3.4±0.87, 2Ncg=3.35±0.75. Thus, the greatest
average amplitude M(Amean) is observed for reference on back, then for
reference on chin and lowest one for “united neck” reference. The ratios
between these three references in grounded state are approximately double
that can be seen from statistics on their differences: Bcg-Ch2g=0.95±1.9,
Ch2g-2Ncg =0.88±2.55. Two-sample t-test does not find the differences between
Bcg and Ch2g, Ch2g and 2Ncg, Bc and Ch2, Ch2 and 2Nc at significance levels
p = 0.15, 0.07, 0.59, 0.31, t-values = 1.47, 1.85, 0.55, 1.03, DOF = 38,
22, 38, 22 (someone with Welch correction).**
** The statistics for
differences between grounded and ungrounded conditions: Bcg-Bc=1.33±2.38,
Ch2g-Ch2=0.32±1.93, 2Ncg-2Nc=-0.05±0.28 shows that increasing of averaged
EEG activation take its place for grounding state of references on back
and on chin. No significant differences between Bcg and Bc, Ch2g
and Ch2, 2Ncg and 2Nc were found at significance levels p = 0.17, 0.7,
0.8, t-values = 1.40, 0.39, 0.23, DOF = 31, 38, 38 (the first with Welch
correction).**
** The analysis of the
differences between grounded and ungrounded state of basic references requires
considering that the raw data are not simultaneously recorded, so the intraindividual
variability can affect the results of the comparison, and the extent of
this influence should be assessed in advance. The presence of two successive
records performed in each experiment helps to distinguish the correlations
determined by the intraindividual variability and by the influence of the
grounding factor (GF). Three above-described primary topographical indicators
Amean, DAmean1, DAmean2
are separately used as the raw data. The correlation between the presence/absence
of grounding was calculated for each parameter and ten subjects and for
two consecutive records reflecting the impact of intraindividual variability.**
** If the grounding
actually has a significant effect on the topography change, topograms for
grounded and ungrounded states would have greater differences than in the
case of natural intraindividual variability (appearing as a random and
less significant factor). Then, the correlations between the same primary
topographical indicators would be repeatedly weaker than in the case of
intraindividual variability. Therefore, the effect of GF can be detected
by pairwise comparing the mean values in the samples relating to GF and
intraindividual variability.**
** We explain the procedure
on the example of Amean values for grounded/ungrounded state. Pearson correlation
was calculated between Amean of 21 scalp derivations for each pair of Ch2-Ch2g,
Bc-Bcg 2Nc-2Ncg basic references records. Thus, the sample of 60 correlations
is formed, i.e. 3 basic references * 2 consecutive records * 10 subjects
= 60. This sample reflects GF. Similarly, the second sample of 60 correlations
between Amean values of the first and second consecutive records is formed,
i.e. 3 basic references * 2 grounded/ungrounded state * 10 subjects. The
second sample reflects intraindividual variability of Amean. For three
indicators Amean, DAmean1, DAmean2
we get three pairs of such samples.**
** Let us consider the
descriptive statistics (mean ± standard deviation) for the three pairs
of samples: 0.9 ± 0.12 and 0.92 ± 0.09 (correlations with Amean); 0.82±0.2
and 0.84±0.15 (DAmean1); 0.67±0.33 and 0.76±0.21
(DAmean2). The mean values of the correlations
related to GF, as expected, are slightly lower compared to intraindividual
variability (the difference of 2%, 2%, 14%, respectively) in all three
cases. However, t-test for correlations transformed by Fisher Z-normalization
Z(r)=0.5ln((1+r)/(1–r)) did not reveal significant differences between
means at significance levels ð = 0.89, 0.67, and 0.98. Therefore, these
three indicators were not affected by GF beyond the effect of intraindividual
variability.**
** We can go the other
way. Our three pairs of samples represent two factors: 1-st factor with
two levels: GF - intraindividual variability, and 2-nd factor with three
levels: Amean, DAmean1, and DAmean2.
Sixty repeated values were measured for each factor level, but it is not
the third within-subjects factor because records in each pair of samples
are different. So we have the two-factors repeated measures model with
fixed-effects. This ANOVA got the results: 1-st factor effect: F(1,354)=0.292,
p=0.768; 2-nd factor effect: F(2,354)=12.67, p=0.00004; inter-factor effect:
F(2,354)=0.063, p=0.94. Thus, GF is not significant again.**
** These results are
further confirmed by cross correlations within the triad of the analyzed
samples related to Amean and ?Amean1, Amean and ?Amean2, ?Amean1 and ?Amean2.
These cross correlations affected by GF are 0.68, 0.63, 0.69, and effected
by intraindividual variability are 0.55, 0.31, 0.54. As we can see, the
former are repeatedly higher; i.e., GF correlations between the three pairs
of samples are more coordinated than those related to intraindividual variability.
Therefore, in this case, there is also no reducing effect of GF on the
correlations.**
** Conclusion.
Based on the results described above, grounded and ungrounded states of
reference electrodes can be considered equivalent in terms of preserving
the EEG topography.. This result in a certain degree reduces the relevance
of the problem to find or construct an infinitely remote neutral reference.
Indeed, why mathematically construct different virtual neutral references,
if the real neutral reference can be obtained under grounded electrode
on human body?**

**3.2. Topographic differences
between references**

** The final aim of our study is to find the
reliable classification of examined references according to their topographical
coherency was carried out using the following technique:**
**(1) Mi(r _{ij}) values were
transformed to uniform range by its ranking for better comparability.**

** The clustering into
two, three, four, and five classes was tested. The only statistically significant
classification (p<0.0001 for the null hypothesis “the intercluster distance
is zero” or more popular “the classification is not valid”) includes the
three classes (cf. “Class” row in table 2). Number of class increases with
increasing of topographic incoherence of reference schemes. Two bottom
lines of the table show the Mahalanobis distance Di2 of each i-reference
scheme to its cluster center and the significance p of the null hypothesis
“Di2=0” meaning “the reference scheme belongs to this cluster.” All null
hypotheses are accepted at the highest significance levels p=0.57-0.89.
For relative estimation of references the table also includes their averaged
ranks (cf. “Mean rank” row).**
** Thus, the following
three classes of reference schemes were found:**
** (1) Reference electrodes
A12, Ch1, Ch2, and Sym (average ranks of 9.7, 8.6, 8.3, and 7.2) are characterized
by the highest similarity of their topography among themselves and in relation
to other references.**
** (2) Reference electrodes
2Nc, Bc, Ns, A1, Nc2, A2, and Nc1 (ranks 6.7, 6.6, 6.5, 5.4, 5.4, 4.9,
and 4.6) are characterized by less coherent topography.**
** (3) Reference electrodes
AR and Cz (ranks 4.4 and 2.1) are characterized by the least coherent topography.**

**3.3. Comparison with the standardized
reference**

** As it can be seen
from fig. 4A the REST leads to the significant decrease of EEG amplitudes.
The average values of two source records are 2.67±0.83 and 2.69±0.73
compare to the REST values 2.18±0.49 and 2.19±0.52. In addition, REST brings
considerable topographical distortion, namely:**
**• the sharp decrease of C3 and C4 amplitudes
relative to all other electrodes;**
**• the significant decrease of P3 and P4 amplitudes
relative to O1 and O2; of T3 and T4 amplitudes relative to F7 and
F8;**
**• the significant increase of Fp1, Fp2, F3
and F4 amplitudes relative to P3, P4, O1 and O2; of T5 amplitude relative
to T6; of O1 amplitude relative to O2;**
**• the inversion of amplitude difference between
first and second records in Fp1, F7, F8, F3, F4, T6, O1, O2 electrodes;**
**• change the asymmetry sign: 1) in first record
between F3–F4, C3–C4, T5–T6 pairs of electrodes; 2) in second record between
Fp1–Fp2, F7–F8, F3–F4, C3–C4 pairs of electrodes.**
** Let us perform the
calculation of the absolute differences between the first and second records
for normalized date (fig. 4B). For the source records we receive smaller
difference 0.15±0.13 that differ 1.67 times from the results of REST standardization
0.25±0.18. One-sample Wilcoxon W-test (both samples belong to the same
sequence of derivations and the samples are not normally distributed according
chi-square test p=0.012) reveals the significant differences of these samples
p=0.013. Thus the differences between REST results significantly exceed
the intra-individual variability.**
** It should be also
noted that REST software contains a number of bags in its transformations
and processing, in import/export procedures, it is very poorly and fragmentary
documented, it supports only three schemes strictly fixed and very peculiar
sequence of 16, 64 and 128 EEG electrodes. So the use of this program is
only possible after a series of personal consultations with the authors.
These problems cause additional distrust of this method.**
** Thus, the REST method
brings the significant distortions in typical EEG topography provided using
the real neutral reference. Therefore, the advantages of REST method proclaimed
in numerous publications give raise to serious doubts.**

**4. Discussion**

**5. Conclusion**