Introduction

The interactions between brain areas are certainly key to the computational power of the cortex. For normal individuals, the principal technique to estimate brain activity is EEG and its derivatives in the fast time domain [ 1 ].

Visual evoked potential (VEP) is an averaged response recorded from the occipital area of the brain, elicited simultaneously with the presentation of pattern-reversal checkerboard visual stimulation. VEP response consists of a small negativity at 75 milliseconds, which is called (N75), followed by a positivity appearing at 100 milliseconds, which is called (P100). The latest component is considered the main peak of VEP [ 2 ].

Coherence analysis estimates the linear directions between two independent sources [ 3 , 4 ]. Besides, the linear dependency is inefficient for the complex or nonlinear analysis of bioelectronics signals [ 5 ]. Therefore, cortico-muscular coherence is influenced by the emphasis on the precision of behavioral presentation [ 6 ]. Additionally, coherence may either be absent or weak in some subjects . Coherence across EEG channels is predominantly used to assess functional connectivity over different brain regions [ 1 ]. An algorithm is used based on auto cross-correlation applied across both hemispheres to examine intra hemispheric coherence of EEG to diagnose various forms of dysfunction in the brain [ 3 ].

Mutual information across brain channels may present the relationship between electroencephalogram and electromyogram or any other recorded signals using a nonlinear method .

The important studies used global coherence analysis based on the surface Laplacian scheme and spectral analysis to track the anesthetic level of brain. They also used spatiotemporal dynamics, which measures the radial current density at each electrode position. The spectral analysis results show an increase in alpha and delta wave activity on the frontal lobe and an increase and a decrease in delta activity and alpha activity, respectively, in the occipital lobe. While the coherence analysis predicts a strong alpha activity in the occipital lobe during alertness of the subject and moves later to the frontal lobe during unconscious. Coherence was weak in the delta frequency range in both unconscious and awake conditions [ 12 ]. EEG spectrum of range (0-64) Hz is used, covering delta to gamma wave. The use of coherence on the patients revealed that the particular pairs of electrodes, which are symmetrical on the cortex, are dramatically differed in specific areas of damage [ 3 ]. However, coherence is related to brain disease, such as epilepsy and Alzheimer’s disease [ 13 - 16 ].

Current research further used coherence analysis horizontally, vertically, and diagonally for the discrimination and elicitation of how the coherency of VEP responses differs from the age of subjects. The study of coherence with respect to the age between multi-brain locations in different directions provides a pre-step of study brain connectivity. Such research provides valuable information for the research line clinically and anatomically.

Material and Methods

Experimental and analysis implementation investigates the visual evoked potential response with respect to the age of the subject. Cross-coherence analysis techniques are employed to assess the strength of connectivity between different brain lobes, particularly those associated with VEP in the frontal and occipital regions, in various spatial directions (horizontal, vertical, and diagonal). Furthermore, cross-coherence has been examined in both the time and frequency domains.

Samples Data and Recording

The sample data is collected for the human healthy subjects, classified into two groups. The first group is called the matured group with an average age of 25±2.6 SD years old. The second group is called the young group with an average age of 10±2.6 SD years old. A written statement confirmed that the subject has neither been diagnosed with nor is currently suffering from any physiological, neurological, psychological, or ophthalmological disorders. For correcting the degree of vision of some subjects, they were wearing glasses during the data recording. The subject was trained to set stable on the experiment chair with a gap of about 100 cm from the display screen [ 17 , 18 ]. Full-field visual stimulation was used to activate the visual pathway. Specifically, a high-contrast pattern reversal checkerboard, composed of alternating black and white checks arranged in a tessellated pattern, was presented at a reversal frequency of 1 Hz [ 2 ].

The data were collected using a KT88-2400 EEG machine following standard protocols for recording both EEG and VEP. A head cap was securely attached to the scalp to facilitate accurate data acquisition [ 19 , 20 ]. The electrodes distributed in the scalp follow the 10-20 electrode system [ 21 ]. The cap consists of 19 channels covering all the brain lobes (frontal, parietal, central, temporal, and occipital) and referenced to the earlobe (Figure 1).

VEP Cross Coherence Analysis

The quantitative assessment of linear dependency across different brain regions is referred to as coherence analysis. EEG records brain activity, and coherence analysis illustrates the interactions between electrode sites [ 22 ]. In fact, the correlation between any pair of EEG signals in the frequency domain gives the coherency. However, the correlation between signals calculated the ratio using equation (1) [ 23 ]. Where the mean square value is the sum of squares of the signal divided by the corresponding degrees of freedom.

$\begin{array}{cc}\mathrm{co}=\frac{E\left(\mathrm{xy}\right)}{\sqrt{E\left(x^2\right)\times E\left(y^2\right)}}& \mathrm{(1)}\end{array}$

Where, E(xy) is the mean product of two signals x and y, and E(x²) and E(y²) are the mean square values of the first and the second signal, respectively.

Alternatively, the correlation can be expressed in terms of covariance, as shown in Equation (2). Here, variance measures the extent to which each value in the signal deviates from its average, and it is commonly referred to as the power of the signal.

$\begin{array}{cc}\mathrm{co}=\frac{E\left(\mathrm{xy}\right)}{\sqrt{\mathrm{Var}\left(x\right)\times \mathrm{Var}\left(y\right)}}& \mathrm{(2)}\end{array}$

Where COV(x,y) is the coberence of the signals, Var(x) and Var(y) are the variance of the first and second signal respectively [ 23 ].

Current research investigates the coherence across the brain hemispheres horizontally, vertically, and diagonally (Figure 1). The horizontal coherence is compared in both age groups for the frontal lobe (Fp1 - Fp2) and occipital lobe (O1 - O2). Also, the vertical coherence is compared for both groups for left and right hemispheres, between occipital and frontal lobes (Fp1 – O1) and (Fp2 – O2). In addition, the diagonal coherence is compared for both age groups between (Fp1 – O2) and (Fp2 – O1).

Figure 1. Horizontal (blue), vertical (red), and diagonal (green) coherence across the brain hemisphere for the frontal and occipital lobe

Results

VEP Response Result

Visual evoked potentials are recorded for 19 electrodes attached to the brain for both groups. The group analysis of averaged VEP recorded from 19 channels and 20 subjects was studied for each age group. However, a prominent response was clearly observed in the frontal and occipital regions of the brain, as shown in Figures 2 (a, b, c and d). This result is consistent with previously reported findings [ 2 ].

Figure 2. The visual evoked potentials response using pattern reversal checkerboard stimulation for young and matured groups (a) and (b) in the frontal lobe and (c) and (d) for the occipital lobe. The amplitude of the prominent peak of Visual evoked potential (VEP) at 100 ms is much higher in the young group than in matured in the electrode site of the frontal and occipital lobes.

In Figure 2, the prominent peak of VEPs is recorded in the frontal and occipital areas of the brain. Therefore, these areas are logically used to study the coherence across the brain for comparison purposes between age groups.

Cross Coherence Analysis Result

The coherence is compared between cross-hemisphere frontal and occipital electrode sites (Fp1, Fp2, O1, and O2). Coherence has been investigated in two age groups for the time and frequency domains. The cross coherence represents horizontal coherence versus the time domain of the frontal and occipital lobes between electrode positions Fp1, Fp2, O1, and O2 for matured and young age groups, Figures 3 (a, b, c, and d).

Figure 3. Horizontal coherence of the frontal and occipital lobes between electrodes positions in time domain (a) Fp1 and Fp2 for matured, (b) Fp1 and Fp2 young age groups, (c) O1 and O2 for matured and (d) O1 and O2 young age groups and in the frequency domain (e) Fp1 and Fp2 for matured, (f) Fp1 and Fp2 young age groups, (g) O1 and O2 for matured and (h) O1 and O2 young age groups

It is observed that coherence varies with time, exceeding 0.5 in the occipital lobe in both mature and young age groups (Figures 3c and 3d). In contrast, the coherence value is approximately 0.2 in the frontal lobe for both age groups (Figures 3a and b).

In the mature group (Figures 3a and c), the fluctuation in coherence was clearly proportional to the epochs of the recorded (VEPs). Specifically, within each time window, an increase in coherence was observed to correspond with the prominent VEP peak. However, this pattern was not discernible in the younger age group, where fluctuations in coherence exhibited no clear association with the time windows of the VEP response (Figures 3b and d).

The variation of horizontal coherence versus frequency bands of VEP is shown in Figure 3 (e, f, g, and h). The coherence between the left and right frontal lobes shows a frequency response at 15 Hz, representing Alpha wave is seen in both matured and young age groups (Figures 3e and f). While this response is only seen in the matured gropes in the coherency of the occipital lobe ( Figure 3g and h). The alpha wave disappears in the occipital lobe from the young age group.

The vertical coherency in the time domain, for the left side of the brain between Fp1-O1 and the right side of the brain between Fp2-O2 are mostly similar in both mature and young age groups (Figures 4a, b, c, and d). Since there is no significant difference or indicator to differentiate between these groups.

Figure 4. Left and right vertical coherence between electrodes positions in time domain (a) Fp1 and O1 for matured, (b) Fp1 and O1 for young age groups, (c) Fp2 and O2 for matured and (d) Fp2 and O2 young age group and in the frequency domain (e) Fp1 and O1 for matured, (f) Fp1 and O1 for young age groups, (g) Fp2 and O2 for matured and (h) Fp2 and O2 young age group

The vertical coherence with frequency bands is shown in Figure 4 (e, f, g, and h). The frequency vertical coherence in the matured age group between Fp1-O1 shows an extra peak in the range of late Alpha wave at 25 Hz compared to that in the young age group. All other frequency peaks are almost the same for all coherence and groups as in Figure 4 (e, f, g, and h).

Similar to vertical coherence in the time domain, diagonal coherence across brain hemispheres displays a similar pattern, as demonstrated in Figures 5 (a, b, c, and d). Notably, coherence values in the young age group were slightly lower than those in the mature age group. In the mature group, the coherence exceeded 0.5, while in the young group, it was approximately 0.4. This slight difference may serve as an indicator of neural maturity.

Figure 5. Diagonal coherence between electrodes positions in time domain (a) Fp1 and O2 for matured, (b) Fp1 and O2 for young age groups, (c) Fp2 and O1 for matured and (d) Fp2 and O1 for young age groups and in frequency domain (e) Fp1 and O2 for matured, (f) Fp1 and O2 for young age groups, (g) Fp2 and O1 for matured and (h) Fp2 and O1 for young age groups

The diagonal coherence in the frequency domain shows the frequency peak of the Alpha wave at 15 Hz in the matured age group. While the young group shows the late Alpha wave at around 25 Hz, as shown in Figures 5 (e, f, g, and h). The two frequencies, early and late alpha waves, are clearly indicated in both cross coherence between left and right brain hemispheres and frontal and occipital brain lobes.

Discussion

In the result section, an important finding is highlighted through the investigation of VEP responses and cross-coherence analysis. As shown in Figure 2, the VEP response was noticed clearly in the frontal and occipital lobes of the brain across the brain hemispheres. As a comparison between age groups, the pattern reversal VEP showed no differences in latency; the main P100 peak consistently appeared at 100 ms after the onset of visual stimulation for both groups. In contrast, significant differences were observed in the amplitude of the VEP responses. In the frontal regions, specifically at electrodes Fp1 and Fp2, the amplitude in the young age group exceeded 3×10^-3 μV, whereas it was less than 2×10^-3 μV in the mature group. Similarly, in the occipital regions (O1 and O2), which are critical for visual processing, the amplitude of the P100 component in the young subjects was approximately twice as high as that in the mature subjects.

On the other hand, as discussed in Figure 3, horizontal coherence illustrates the relationship between the left and right brain hemispheres by comparing connectivity within the same lobe. As expected, the horizontal coherence results in normal subjects should be symmetric within the same lobes, given that the VEP response serves as a test of the visual pathway [ 24 ]. In contrast, diagonal coherence successfully revealed age-related variations (Figure 5), with coherence values in the mature group surpassing those in the young group. This finding suggests stronger interconnections between different brain lobes and hemispheres in the mature group, indicating a more advanced level of neural development.

Furthermore, coherence in the frequency domain demonstrated a marked distinction between the age groups: the mature group exhibited a dominant coherence peak at approximately 15 Hz, while the younger group showed a peak around 25 Hz. This observation suggests that a decrease in frequency is indicative of increased neural maturity. This may correlate with more advanced levels of thinking, decision-making, and perception. These results are consistent with previous EEG age-related studies [ 25 ] that reported decreased coherence in the theta and alpha bands in younger individuals. Our findings also revealed two prominent peaks in the early and late alpha frequency ranges, with strong coherence in some brain regions related to the VEP response and diminished coherence in others. Examining coherence across various brain lobes and directions will enhance our understanding of brain connectivity, particularly as the number of electrodes, components, and nodes increases.

Conclusion

Cross-coherence is a statistical approach used to quantify the relationship between two signal sources. This study aimed to compare horizontal, vertical, and diagonal coherence across brain hemispheres, as well as between the frontal and occipital lobes, in both mature and young age groups. In the time domain, horizontal coherence was observed to be higher between the occipital lobes than between the frontal lobes. Diagonal coherence in the younger age group was below 0.4, whereas it exceeded 0.4 in the time domain and 0.5 in the frequency domain for the mature group. These findings suggest that diagonal coherence effectively distinguishes between age groups, unlike vertical coherence, which did not show significant differences. In the frequency domain, horizontal coherence between the left and right occipital lobes in the mature group displayed an alpha wave peak at 15 Hz, a feature absents in the younger group. Furthermore, vertical coherence between Fp1 and O1 in the mature group exhibited an additional peak in the late alpha range at 25 Hz, while diagonal coherence revealed a 15 Hz peak for the mature group compared to a 25 Hz peak for the younger group.

Acknowledgment

The authors are grateful to the College of Science, Al-Muthanna University for unlimited support towards this research. Also special thanks to the Department of Physics, Faculty of Science, Universiti Teknologi Malaysia for their support during data recording.

Ethical Approval

Ethical Approval is obtained before data recording. Data management follows ethical guidelines. The personal information of all participants is protected and secured.

Informed Consent

This study was approved by the Al-Muthanna University, College of Science in the scientific plan and Informed consent was also obtained.

Funding

This research is self-funded.

Conflict of Interest

None

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