EEG from occipital sites (O1, O2) (p < 0.01). It is significant that the value of τe correlated with the value of φ1 (r = 0.75, p < 0.01) but not with the value of(0) (r = 0.19, p < 0.01). When both period and mean luminance were varied simultaneously, the values of τe, (0), and φ1 for the most preferred stimuli were larger than those for the less preferred stimuli. It is remarkable that the ratio of high to low preference in terms of the τe was larger than that of φ1 at the occipital sites (O1 and O2). This indicates that the τe of alpha wave, i.e. the persistence and temporal coherence of the alpha rhythm, reflects the subjective preference better than does the φ1, i.e. its amplitude. There were no clear differences in the factors extracted from the ACF except when the mean luminance was varied.

As shown in Figs. 15.1 and 15.2, the longer period was preferred when the amplitude sensitivity was higher in the mean-luminance range 7.5–120 cd/m2. When the period was varied, the preferred stimulus had a significantly larger τe than that of the least preferred stimulus, especially at the occipital sites. This kind of tendency for larger τe under the preferred conditions was commonly discovered in the auditorybrain system, when t1, Tsub of a music sound field and the tempo of a noise burst were varied. The τe signifies the degree of similar repetitive features included in the alpha wave. The fact that alpha wave has a significantly larger τe indicates that the brain repeats the rhythm for a longer time, on average, under the preferred conditions.

Because O1 (left hemisphere) and O2 (right hemisphere) are closely located, as shown in Fig. 15.4, the difference between their EEG signals was difficult to identify. But, the larger τe in the left hemisphere may reflect the specialization of the human brain, specifically, the left hemisphere dominance for temporal factors. To further test this hypothesis, that the left hemisphere activity is dominant in the processing of temporal factors in vision as well as in audition, we also measured MEG signals in response to flickering lights.

15.1.2 Spatial Extent of Alpha Rhythms

To determine the flow of alpha waves across the cerebral cortex and their possible relation to subjective preference, we compared pairs of EEG signals from several different scalp locations by analyzing their crosscorrelation functions (CCFs). First, PCT was performed to examine subjective preference for the flickering light. The EEG was then recorded from seven electrodes (10–20 International Electrode Placement System) during presentations of the most and least preferred flickering-light conditions. The maximum value of the CCF, |φ(τ)|max, between the alpha wave measured at different electrodes and its delay time, τm, was analyzed. Results show that the most preferred flickering light has a significantly larger |φ(τ)|max than that of the less preferred flickering light and that the value of |φ(τ)|max decreases with increasing distance between the reference (O1 or O2) and the test electrode. The delay time of the maximum value of the CCF, τm, increases in a stepwise manner with the distance between reference and test electrodes. This suggests that there are discrete nuclei in the central system.

Analysis techniques based on autocorrelation (ACF) and crosscorrelation (CCF) have been developed to describe the nature of the EEG (Braizer and Casby, 1952; Barlow, 1961; McLachlan and Shaw, 1965; Liske et al., 1967; Hoovey et al., 1972). The ACF is used to determine characteristics over time, that is, the degree of persistence of a signal. Crosscorrelation functions (CCFs) are used to measure mutual relationships between the signals that are detected at two electrode sites, including common frequency components and transmission delays between the two sites.

The alpha rhythm, which has the longest period of any EEG brain rhythm normally seen in the waking state, is thought to be associated with pleasant and comfortable feelings. The relationship between the subjective preference and the alpha wave on the scalp has been studied by using the ACF factor τe throughout this volume. In these studies, the effective duration of the envelope of the normalized ACF, τe, of EEG and MEG alpha waves was analyzed. Results showed that the τe value of the alpha waves is longer when the subject is presented with the preferred condition. The spread of alpha wave over the scalp has also been studied by using the CCF (Inoye et al., 1983; Sato et al., 2003). The propagation of the alpha wave from the right hemisphere to the left that corresponds to the change in the magnitude of IACC has been observed (see Section 4.3.3).

It is assumed that the subjective preference for visual stimuli is reflected in both the intrachannel and interchannel relations between the EEG alpha waves in the time domain. The relationship between the subjective preference and the alpha wave over the scalp was investigated by using CCF analysis. Experiments were conducted under three conditions: (1) variation of period with constant mean luminance fixed;

(2) variation of mean luminance with constant period; (3) variation of both period and mean luminance (Soeta et al., 2002b). The paired stimuli were set for each subject according to the scale value of the individual preference as indicated in Table 15.3.

Table 15.3 Paired stimuli and the differences between scale values of preference for each subject. These are presented under three conditions: (1) variation of period with constant mean luminance (ML); (2) variation of ML with constant period; (3) variation of both period and ML

Values in parentheses indicate (Period, ML), and the single value that follows signifies the difference between scale values of subjective preference of the pair (X)–(Y).

The EEG was recorded from both the left and right cerebral areas of the scalps of subjects by using silver electrodes (7 mm diameter) at points T3, T4, T5, T6, O1, O2, and in addition Cz as shown in Fig. 15.4. The normalized CCF between the alpha waves measured at electrode positions O1 or O2 (reference electrodes) and those at the other electrodes (test electrodes) was analyzed. Subjective preference corresponded well with the effective duration of the ACF, τe, at both O1 and O2 as discussed above. The integration interval for the CCF was the same (2.5 s) as had been used in the ACF analysis. An example of the normalized CCF is shown in Fig. 15.9. A positive lag (τ > 0) means that the activity at the reference electrode was delayed relative to that at the test electrode. |φ(τ)|max was defined as the maximum value of the CCF in the range of τ≥ 0, and τm was defined as its delay time.

Fig. 15.9 An example of the normalized crosscorrelation function CCF between two EEG alpha band signals recorded from different electrodes showing the definitions of the maximum correlation value |φ(τ )|max and its delay time τ m

Effects of the subjective preference and the test electrode position on the |φ(τ)|max values were examined for all 10 subjects by using two-way ANOVA as indicated in Table 15.4. Results clearly indicated that |φ(τ)|max values were significantly related to the subjective preference when the period alone was varied and when both the period and the mean luminance were varied. When the period was varied, the value of |φ(τ)|max was significantly greater for the most preferred stimulus than for the less preferred stimulus. This result is true for both reference electrode positions (O1 and O2), as is shown in Fig. 15.10. However, as is shown in Fig. 15.11, there were no clear differences between values of |φ(τ)|max when the mean luminance was varied. When both period and mean luminance were varied, the value of |φ(τ)|max was significantly greater for the most preferred stimulus than for the least preferred stimulus. This is shown in Fig. 15.12.

Figure 15.13 shows the cumulative frequency curves of log10τm for different test electrodes when the period was varied. The value of τm increased with the distance between the reference and test electrode under all three conditions regardless of subjective preference. Remarkably, a stepwise phenomenon in the τm values was

Fig. 15.10 Maximal crosscorrelation values |φ(τ )|max for EEG alpha band signals as a function of test electrode position in response to variation of the flicker period between preferred and less preferred conditions. (a) Reference electrode selected: O1. (b) Reference electrode selected: O2. Error bars represent 95% confidence. ◦ : Higher preference; •: lower preference

Fig. 15.11 Maximal crosscorrelation values |φ(τ )|max for EEG alpha band signals as a function of test electrode position in response to variation of mean luminance between preferred and less preferred conditions. (a) Reference electrode selected at O1. (b) Reference electrode selected at O2. Error bars represent 95% confidence. ◦ : Higher preference; •: lower preference

found under all three conditions. The values of τm discovered here were centered on about 10 ms (logτm = –2.0) and 50 ms (logτm = –1.3). This means that the alpha wave propagates stepwise in the delay time.

When the period is varied, the preferred stimulus induces a significantly greater value of the absolute value of normalized ACF |φ(τ)|max of the alpha waves than that

Fig. 15.12 Maximal crosscorrelation values |φ(τ )|max for EEG alpha band signals as a function of test electrode position in response to variation of both period and mean luminance between preferred and less preferred conditions. (a) Reference electrode selected: O1. (b) Reference electrode selected: O2. Error bars represent 95% confidence. ◦ : Higher preference; •: lower preference

of the less preferred stimulus. The |φ(τ)|max signifies the degree of similar repetitive features that appear in the alpha waves recorded at two spatially separated electrodes. Significantly greater values of |φ(τ)|max for the alpha wave signifies that the brain is repeating a similar rhythm over a wider area under a preferred condition.

As discussed in previous sections, a number of studies have found greater τe values of the ACF of the alpha wave at the preferred stimulus than those at a relatively less preferred one. Significantly larger values of τe that appear for the alpha wave indicate that the brain is repeating a similar rhythm under these preferred conditions. Thus, the brain repeats a similar rhythm over a wider range in both brain area and time under a preferred condition.

The CCF of the alpha wave clarified the movement of the alpha wave as being over the scalp from the occipital area (O1, O2) to the temporal area (T3, T4) and to the vertex area (Cz). The flow of the alpha waves in relation to |φ(τ)|max and τm under a preferred condition is shown in Fig. 15.14. It is clear that the alpha wave propagated from the reference electrode O1 to other regions. A similar tendency was found when the reference electrode was at O2. The values of |φ(τ)|max and of τm, therefore, depend on the distance between the reference and test electrodes.

Relationships between EEG-coherence and mental processes have been reported in numerous studies (e.g., Rappelsberger and Petsche, 1988; Hinrichs and Machleidt, 1992; Petsche, 1996). In all of these studies, the focus was on the interchannel relationships between the power spectra in terms of, for example, synchronization of alpha frequency. Here, we have concentrated on the factor in the time domain because some applications of the ACF and CCF have indicated their effectiveness as additional tools in gaining a deeper understanding of EEG dynamics.

Fig. 15.13 Cumulative frequency of observed interelectrode signal delays τ m (logarithmic scale) EEG alpha band signals as a function of test electrode position in response to variation of the flicker period under the preferred condition at (a) reference electrode: O1; (b) reference electrode: O2 and under the non-preferred condition at (c) reference electrode: O1; (d) reference electrode: O2. Test electrodes are indicated by O1 (◦ ); T5 ( ); T3 ( ); O2 (•); T6 ( ); T4 ( ); Cz (◦ )

The results here lead us to the following conclusions:

1.When the period of the flickering light is varied, the preferred stimulus has significantly greater values of |φ(τ)|max than those of the less preferred stimulus. Together with the result shown above, we conclude that in the preferred condition, the alpha wave repeats over a certain time and this activity spreads over a certain area of the brain.

2.The value of |φ(τ)|max decreases with increasing distance between the reference and test electrodes.

3.The value of τm increases in a stepwise fashion with the distance between the reference and test electrodes. This suggests there are discrete nuclei in the central system.