A. Spectral Power
Spectral power describes how the power of a signal is distributed over different frequencies. In this research, it was calculated by computing the variance of the filtered signal in the 8 Hz frequency band. From this, a difference in spectral power between the entrained and relaxed states can be observed as shown in figure 1B for subject 1, as an example. To assess whether this difference is statistically significance, pair-wise Wilcoxon sign-rank (as normality of data was not tested) was computed. The hypothesis was set at 5 percent confidence level and was investigated whether the median spectral power exhibited by EEG signals in the binaural state were lower than that in the relaxed state. Figure 1E shows the p-values for the one-tailed signed-rank test. From this, it can be seen that for participants 1, 4 and 5, there is evidence to support that binaural beat entrainment had an effect. Given that 3 participants were affected, this provides evidence (at least for these participants) that the effect of binaural beat entrainment was a reduction in spectral power, especially in the frontal cortex. This means that the alpha frequency spectral power was lower in the binaural state than in the relaxed state. Participants 2 and 3 do not seem to have been affected by binaural entrainment. For these participants, binaural entrainment had increased the spectral power but only in channel O2.
Therefore, from the statistical test, it can be seen that 3 out of 5 participants have been affected by binaural beat entrainment. The binaural beat presented to the subjects was in the alpha (8 Hz) frequency band, typically associated with a reduced level of brain activity. This reduced activity could explain the reduction in power or amplitude in the entrained state as opposed to the normal state the participants would have been in at the start.
B. Asymmetry Ratio
Asymmetry ratio gives an indication of the degree of synchronisation between the left and right hemispheres of the brain. It is calculated by computing the power between two channels. To compare whether there was a greater degree of synchronisation in the entrained state versus the relaxed state, the asymmetry ratio was computed. The lower the ratio, the greater the inter-hemispheric synchronisation, and the higher the likelihood that entrainment had an effect on the participants. Figure 1F shows the mean values of the asymmetry ratio calculation for the participants in the relaxed and entrained states. From this, it is possible to observe that, for all participants, in general, asymmetry ratio was lower in the entrained state than in the relaxed state, which suggests that, for these participants, binaural entrainment had an effect. However, the difference was not statistically different.
The last row of figure 1F shows the values for the grand averaged ratios from 8 pairs of electrodes. The grand average values of the asymmetry ratios in the entrained state are lower than the values of the relaxed state asymmetry ratios for all the participants. Therefore, it can be said that binaural entrainment had an effect and increased inter-hemispheric synchronisation in the brain. This confirms that binaural entrainment does affect cortical synchronisation, which was also found in another study. The synchronisation starts from the auditory system and the inferior colliculus in the cortex, spreading across the brain, and, in turn, affecting the processes which depend on such synchronisation. Inter-hemispheric synchronisation often occurs in brain signals and as such, is widely believed to be a result of synchronisation of neuronal activity, reflecting changes of neuronal brain membrane potential. Asymmetry ratio provides both an indication of the degree of synchronisation between the left and right hemispheres of the brain and a good method to assess further the effect of binaural entrainment on the different participants in this study. The underlying idea is that brain activity is propagated via cortical oscillations, which is related to the information flow from one brain structure to another. Different frequency bands are considered to represent the messenger frequency of cognitive processes, and such processes are considered in terms of communication across different parts of the brain. Short-range communication in the brain is normally associated with neural synchronisation in the gamma frequency, while long-range communication is associated with neural synchronisation in the alpha/beta frequency bands. Taking this assertion further, it is possible to assess the effect of binaural entrainment by comparing the values in oscillations observed in the different hemispheres or parts of the brain between the entrained state and the relaxed state. The pair-wise asymmetry ratio for a given brain structure provides information about functional coupling between similar structures in a closed system. The ratio provides insight into the interaction of the different brain structures. More specifically, the higher the value of this ratio, the weaker the relation of a selected structure with another structure, and the less there is interhemispheric coherence, which is widely believed to be critical to mental processes. Considering the basic assumption, it can be seen from the results that all 5 participants exhibited a reduction in asymmetry ratio, which implies a greater degree of interhemispheric synchronisation in the entrained state relative to the relaxed state. This provides evidence that binaural entrainment does effect the information flow process in the brain, therefore providing further evidence on the effect of binaural beats on the brain.