EEG was performed in a group of 27 patients who varied in age and sex (23 females, 4 males; mean age: 29.9 ± 11.5 years), and consisted primarily of ambulatory patients with headache, fainting, loss of consciousness, or epilepsy. Patient EEG data were included in analyses if they demonstrated adequate expression of alpha waves.

EEG data were acquired with the sampling frequency of 250 Hz in a standard 10–20 system of electrode placement using ELMIKO EEG DigiTrack™ Recording System with 19 EEG channels: Fp1, Fp2, F7, F3, Fz, F4, F8, T7, C3, Cz, C4, T8, P7, P3, Pz, P4, P8, O1, O2. Depending on the specified recording conditions, the original EEG signal was recorded using four different reference electrodes: linked earlobes (A1–A2), neck (NK), chin (S1), and frontal (AFz).

Then, the data were re-referenced using average reference electrode (AVERAGE) (Nunez and Srinivasan, 2006) and reference electrode standardization techniques (REST) (Yao, 2001; Zhai and Yao, 2004; Yao et al., 2005). REST is a method that allows for the transformation of original EEG data—with the reference electrode placed at an arbitrary point on the head—to a new dataset with the reference at infinity and the potential at zero or a constant. This transformation was performed using the freely available REST Toolbox (http://www.neuro.uestc.edu.cn/rest/). The procedure is based on the calculation of the leadfield matrix for the canonical concentric-three-spheres head model.

Next, the current source density (CSD) or scalp surface Laplacian was estimated from the transformed EEG data to reduce the impact of volume conduction (Kayser and Tenke, 2006a,b, 2015; Kayser, 2009). These calculations were performed using a spherical spline algorithm (Perrin et al., 1989, 1990; Jurcak et al., 2007) in the CSD Toolbox (http://psychophysiology.cpmc.columbia.edu/Software/CSDtoolbox/).

Spatiotemporal maps of EEG patterns were analyzed using the EEG Time-Potential Mapping Module of ELMIKO EEG DigiTrack™ Recording System, which is widely used in clinical practice (Sobieszek, 2009, 2013, 2015).

The power spectrum density (PSD) of EEG signal for each channel was calculated in the range of alpha band from 8 to 13 Hz. Maps of relative spectral power were estimated for different frequency ranges (theta: 4–7 Hz; alpha: 7–8, 8–10, 10–13 Hz; beta: 13–25 Hz).

DTF is a measure based on Granger Causality, but is defined in the frequency domain (Kaminski and Blinowska, 1991).

For a multivariate k-channel process, X(t) = [X₁(t), X₂(t),…, X_k(t)]^T, the multivariate autoregressive model takes the form:

where E(t) is a k–dimensional vector, A^ is a square k × k matrix.

We can rewrite (Equation 1) in the form;

Transforming the multivariate autoregressive model to the frequency domain, we obtain:

The matrix of coefficients H(f) is called the transfer matrix.

The DTF is defined as a normalized version of the transfer matrix:

In the calculation of DTF, the product of the model order and the number of EEG channels must be several times smaller than the number of the samples in the analyzed signal (Blinowska and Kaminski, 2006). In this study, the model order was equal to 10 and the number of EEG channels was 19. The DTF was calculated for 2-, 4-, and 8-s segments sampled with frequency of 250 Hz, and the rule was found to be satisfied.

The power spectrum and DTF have the following relationship (Blinowska et al., 2004):

where V = E(f)E⁺(f) is the spectral matrix of input white noise processes that does not depend on frequency; + refers to the Hermitean transpose, i.e., the composition of transposition and complex conjugation of a matrix.

The power spectrum, S(f), depends only on the EEG amplitude. The power spectrum does not depend on the phase of the signal, which gives information about the time relations between signals, and therefore enables the estimation of directionality of the EEG activity propagation. Moreover, the source of EEG activity does not necessarily have to be located at the power spectrum maximum (Kaminski et al., 1997). Thus, the DTF provides additional information to the spectral analysis regarding the localization of generators and the directionality of signal propagation.

The multivariate model used in the DTF calculation already includes all EEG signals and their relations. Thus, the method provides the whole spectral matrix at once, with auto-spectra on the diagonal and cross-spectra on the off-diagonal. The power spectra presented in this paper correspond to the auto-spectra derived from the DTF method.

In graph theory, the brain is modeled as a graph composed of nodes, representing brain regions (i.e., the EEG channels, here), and links between the nodes, representing functional connections (i.e., the magnitude and directionality of DTF, here).

For each of the obtained graphs, three indices were calculated: density, degree, and strength (Rubinov and Sporns, 2010). The degree of an individual node is equal to the number of links connected to that node, and reflects the relative importance of a node in the network. The mean network degree is commonly used as a measure of the graph density, or the total “wiring cost” of the network. The directed variant of the degree distinguishes the number of inward links from the number of outward links, while the weighted variant of the degree, termed the strength, is defined as the sum of all neighboring link weights.

Figures 1A,B illustrates that patterns of spectral power distribution (SPD) depend on choice of window size. EEG was recorded in three window durations: 2-, 4-, and 8-s. Figures 1A,B shows the relative SPD in the first patient, a 27-year-old woman. The split in higher alpha (10–13 Hz) is clearly visible in the shorter, 2-s window. In the longer, 8-s window however, two peaks were observed in the SPD with maximum at electrodes O2 and T4 in theta and low alpha bands, and a broad SPD in the higher alpha range (see Figure 1B). Maps of the relative power spectra are shown separately in five frequency bands (theta: 4–7 Hz; alpha: 7–8, 8–10, 10–13 Hz; beta: 13–25 Hz) in Figure 1C. Increased level of relative power spectrum can be seen clearly at electrodes T4 and O2 in theta (4–7 Hz) and low alpha (7–8 Hz) ranges (areas marked with yellow and red color in Figure 1C). Moreover, high level of relative power spectrum is observed in the posterior part of the brain, with dominance in the right hemisphere at electrode O2 in the higher alpha band (10–13 Hz).

Next, we tested the importance of the location of the reference electrode. Figure 2 shows a comparison of EEG patterns recorded from a second patient (28-year-old woman) using two montages: bipolar (BIP) and monopolar. Four different reference electrodes were evaluated in the examined patients: linked earlobes (A1–A2), neck (nk), chin (S1), and frontal (AFz). Only the monopolar montages allowed for the correct localization of alpha waves' generators. The effect of split alpha is clearly observed in the PSD for both montages. However, comparing the PSD obtained with the bipolar montage (see Figure 2A) with that obtained with the monopolar one (c.f. Figure 2B) revealed the existence of hemispheric asymmetry with dominance of lower frequency alpha in the left hemisphere, and higher frequency alpha in the right hemisphere. The highest relative power spectrum was observed in the posterior part of brain (O1, O2) in higher alpha band (10–13 Hz). A dominance of lower alpha band (8–10 Hz) in the left hemisphere is also evident (see Figure 2C).

Inspection of the spatiotemporal map of the EEG pattern in one patient revealed the existence of two sources of alpha waves, localized mainly in the occipital derivations (O1 or O2; see Figure 3). Slightly different oscillation frequencies suggest that the right hemisphere is more likely to generate the alpha rhythm. The segment was divided into six parts (see a–f in Figure 3C). The first cycle (designated with the numbers from 1 to 4 in Figure 3A) started with the minimum EEG amplitude at O2 (marked as a blue spot) and ended with the maximum amplitude at O1 (marked as a red spot). The next cycle (marked with the numbers from 5 to 7) ended with the maximal amplitude at the second generator, localized at O2. The synchronization of both sources subsequently occurred (at points 8 and 9). Of note, this system is not stable due to slowing of activity in the left hemisphere, which is clearly visible in the amplitude changes marked with the numbers from 16 to 21 (cf. Figure 3B). The activity at O2 (at point 16, 18, and 20) occurs before activity at O1 (at point 17, 19, and 21), suggesting that the source located at this electrode acts as a driver of the process. This was verified by analyzing the connectivity pattern using the DTF (data not shown).

Both cases discussed above illustrate the existence of generators localized in posterior areas, particularly at derivations O1 and O2. Alpha rhythms can be also generated in other parts of the brain. The coexistence of several generators was demonstrated in the third patient, a 54-year-old woman (see Figure 4). The localization of generators depends on the choice of the reference electrode. The EEG signal was first registered to a reference electrode placed on the neck. This registration showed a maximum of the relative power spectrum of alpha band (8–10 Hz) in frontal and left occipital regions of the brain (see Figure 4). The same signal was then re-referenced to the linked earlobes reference (A1–A2). Here, the maximum of the relative power spectrum was localized to the posterior part of brain in left and right hemispheres, which was accompanied by a decrease of the relative power spectrum in frontal cortex. Next, the DTF was calculated to localize the generators and identify the directionality of EEG activity propagation and DTF strength (c.f. Figures 6A,B). The DTF was presented in each 1 Hz-frequency interval in the range of alpha bands. The dominance of the generator at O1 for both montages was verified (see graphs in Figures 6A,B). In addition, other generators were identified when the reference was placed on the neck, with one at P8 (with maximum strength at 9–10 Hz) and another at O2 (with maximum strength at 11–12 Hz). These DTF results changed dramatically when the signal was re-referenced to the linked earlobes (cf. Figure 6B). A second generator was identified at electrode Pz, which dominated for frequency of 10 Hz. Therefore, our data show that generators do not necessarily need to be localized in occipital or frontal parts of the brain, as was predicted by the Robinson et al. model (Robinson et al., 2001, 2003).

The effect of data re-referencing is illustrated in Figures 5, 6. The power spectral density (PSD) of the 4-s segment of original EEG recorded in the third patient (54-year-old woman) is shown separately for each of four reference electrodes (NK, A1-A2, AVERAGE, and REST) in Figure 5. The frequency of split alpha peaks and the spatial distribution over the scalp surface are influenced strongly by choice of reference electrode.

The original data were re-referenced from the neck (NK) to the linked earlobes (A1–A2). The data referenced to the linked earlobes revealed two split alpha patterns: one in the occipital-parietal regions of brain and the second in frontal-central regions of brain. These patterns demonstrated a common dominant frequency of 9.5 Hz, but differed in the frequency of the second peak (8.5 Hz in the frontal-central lobe and 10 Hz in the occipital-parietal lobe; see Figures 5A,B).

The application of other reference electrodes (AVERAGE and REST) resulted in the reduction of low-frequency peak in frontal channels, and a sharpening of the peak at 9.5 Hz frequency (see Figures 5C,D). For the REST, the low-frequency alpha peak at the left and right temporal-parietal derivations (T7, T8, P7, P8) was appeared (see Figure 5D). Thus, it is likely that split alpha may result from an interaction between the occipital and temporo-parietal areas, rather than between left and right occipital hemispheres. However, this hypothesis can only be verified by applying REST to a high-density EEG dataset.

The strength of outward connections calculated from the adjacency matrices of DTF is presented for each of the four reference electrodes in Figure 6. Re-referencing the original EEG data to the linked earlobes reference (A1–A2) caused a reduction in strength at right parieto-occipital derivations (P4, P8, and O2), and an increase in strength at the central derivations (see Fz and Pz in Figures 6A,B). The results for the average reference also highlight the role of right frontal and parietal derivations (see F4, F8, and P8 in Figure 6C). The most outstanding results were obtained using the REST (cf. Figure 6D). The strength at electrode P8 was much higher than strength observed at other derivations. Interestingly, strength at occipital derivations was significantly reduced, reaching levels in both hemispheres that were comparable to levels observed in other channels in posterior brain regions.

The spatial distribution of the strongest 60% of connections between EEG channels are presented in graphs in Figure 6, for three frequencies (7, 8, and 10 Hz).

The impact of volume conduction on the identification of split alpha is illustrated in Figure 7. The PSD of transformed data using the CSD transformation of the original EEG with the reference electrode placed at NK is showed in Figure 7B. The characteristic pattern of split alpha was completely abolished by the application of the CSD transform. In addition, although a few peak frequencies were still visible, their spatial distribution became disjointed. Comparing the PSD of the original EEG (see Figure 5A) with that of the transformed data (cf. Figure 7B), there was a shift in the dominant frequency of 9.5 Hz from the occipital lobe (the last seven channels: P7, P3, Pz, P4, P8, O1, O2) to the frontal lobe. In addition, the high-frequency alpha (10 Hz) was replaced by the low-frequency alpha (8.5–9 Hz).

Pearson correlation coefficients (R) between the PSD calculated for the CSD and the PSD for the four reference electrodes (NK, A1-A2, AVERAGE, REST) are presented in Figure 7C. The highest R values were between CSD and AVERAGE at almost all EEG derivations, and only at a few electrode locations did REST correlated with the CSD better than the AVERAGE (F3, Fz, T7, P3).

Figure 7D shows the average strength of outward links calculated with the transformed data using the CSD transform and with the four reference electrodes. These graphs were created by averaging the strength of outward links over all frequencies in the alpha band (from 7 to 13 Hz) shown in Figure 7A. Evaluating the results presented in Figure 7, reduction of volume conduction by applying the CSD transform resulted in an increase in strength of connections, particularly at the frontal derivations (Fp1, Fp2, F7), and a decrease in strength at central posterior derivation (Pz). Statistically significant differences (p < 0.05) between the CSD and each of the four reference electrodes were found for almost all EEG derivations, excluding C4, P4, and O1 for NK, T7, and C3 for A1–A2, T7, C3, O1, and O2 for AVERAGE.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.