Because the root frequency is much smaller than the sampling frequency, the result of sin−1x can be approximated by x. For example, the α rhythm having a higher frequency of 12Hz results in a normalized radian frequency of 0.12π (assume fs = 200Hz). The approximation only causes a 2.35% deviation from the true value. Note that output2~output6 are the results of downsampling (Figure 4), the root frequency fr,i should be further divided by 2i. According to equations (10) to (13), root frequency of each subband component depends on γx[0], ]γx[1 , and γx[2].
Tracking the root frequency of each subband component provides an efficient way to illus-trate the time evolution of characteristic frequency in meditation EEG. The following section presents two algorithms for the EEG feature extraction and the signal segmentation based on the ideas and methods introduced in this section.
IV. RESULTS
(A) Alpha-blocking phenomenon in meditation EEG:
Bursts of high-frequency beta (above 20Hz) are observed when the meditators enter into deep meditation. In our meditation EEG recordings, a few subjects even had significant beta ac-tivities since the beginning meditation. This phenomenon arouses our interest in further investi-gating the potential mechanism. After performing a few studies on different subjects, however, we noted a significant correlation between perception of the inner light and the alpha blocking.
Subject A, a healthy 48-year-old man, had been practicing the orthodox Zen Buddhism for more than 11 years. While meditating with eyes closed, his EEG was mainly characterized by the low alpha (8~9 Hz) activities. A close examination showed that the tiny, high-frequency beta jig-gling mingled in the alpha rhythms. When subject A signaled the event of perceiving the light, alpha blocking occurred and the EEG turned into low-amplitude beta (Figure 5). Subject B was a healthy 40-year-old female who had been practicing the Zen-Buddhism meditation since 1994.
For more than five years, she had never fallen ill. Like most Zen-Buddhism practitioners, she had an appearance and physiological status ten-year younger than her age. Her EEG in medita-tion switched between low-frequency (≈8Hz), high-power alpha and global beta activities, with larger amplitude in the frontal regions (F3, F4). As illustrated in Fig. 4, there always occurred the alpha blocking in succession to the signaling of perceiving the light (Figure 6).
Our experiment encountered one major difficulty— missing signals from the subjects. It is comprehensible since the subject at the meditating state beyond normal consciousness often 'forgets' the experimental protocol. In the circumstances, the EEG events cannot be correlated with the meditating process via subjective expression.
In the second part of this experiment, EEG changes under blessing is discussed. Blessing is mostly comprehended as the benediction, ritual, or manner conveying best wishes to someone.
Blessing in the orthodox Zen Buddhism, on the other hand, indicates a substantial benefaction from the master. A true master in the orthodox Zen Buddhism is required to attain the Buddha-hood Trinity full attainment of Buddha’s three bodies, the emanation body (Nirmanakaya 應 化身), the truth body (Dharmakaya 法身), and the blessedness body (Sambhogakaya 報身、佛
身). With the true energy (light) of life in nature, he is thus able to help disciples.
In our blessing experiment (Lo, Huang, and Chang 2003), master Miao Tien of the Zen-Buddhism Sect was invited to perform the blessing. It had been reported that blessing from master Miao Tien had cured many people. To avoid the possibility of placebo effect, the sub-jects did not know that they were to be blessed during the EEG recording. Master Miao Tien was not in the same room where the experiment was conducted. The mechanism of performing far-field blessing is still unknown from the scientific viewpoint. As stated by the Zen master, it was the truth body (Dharmakaya) that performed the blessing, and this blessing energy was be-stowed upon the true self. Both the experimental group (Zen-Buddhism practitioners) and the control group followed the same procedure: they were asked to sit, with eyes closed, in the normal relaxed position for 30 minutes. The EEG under blessing was compared with the normal background EEG.
To illustrate the EEG evolution during the entire session, the running Fourier spectral power based on short-time Fourier transform (STFT) was analyzed and percentage of power in each rhythmic band was depicted by different gray shade (Figure 7). The STFT was computed with a 2-second frame, shifted with a step of 1 second each time. The result was filtered twice by a lowpass moving averager of order 11 to smooth the jiggling. As shown in Figure 7, sig-nificant alpha blocking was observed in experimental subjects (C and D) during the blessing period. This alpha blocking phenomenon was highly correlated with the fact that the subjects saw the light, according to our post-experimental interview. In the blessing period, there ac-companied the slower rhythmic activities (theta and delta). The large power of low-frequency EEG rhythms prevails over the small-amplitude beta so that the emergence of beta rhythm can-not be discriminated in the running power-percentage analysis. Apparently, there was no sig-nificant change in EEG evolution in the non-meditating control subject (E) under blessing. Their EEGs contained a large proportion of alpha power in the entire record.
The above experiment somehow reveals the essence of Zen-Buddhism practicing one can only sense the light of truth after years of preparation for eventually being in resonance with the inner light. On the way of preparation, the human body itself changes its characteristics and is gradually adjusted to a state of being able to perceive this non-physical, spiritual power of blessing.
(B) Meditation EEG scenarios:
Meditation EEG scenarios nonlinear dynamics and complexity index:
The meditation EEG records collected from the Zen-Buddhist disciples exhibit some char-acteristic features that have been constantly observed. Figure 8 profiles those features from 5 meditators who appear certain pattern frequently. In Figure 8(a), the top tracing characterizes the deep meditation (also called ‘samadhi’ or ‘transcendence’) EEG that may be correlated with the Alaya (eighth) conscious state. The EEG at this stage was found to be featured by the “si-lent” pattern (to be symbolized by Φ in this paper). The second tracing, mainly composed of fast β rhythm with small amplitude, was observed mostly when the meditator entered into a peaceful, body-mind unified, and somehow beyond normal consciousness states. The slow α (4th tracing) relates to the mind-concentrating status of the sixth conscious state. West reported their finding of slower α (8~10Hz) with larger amplitude in the beginning of meditation (West, 1980). In the
the beginning to release themselves from flight of the imagination. We found that the EEG of a few subjects at this meditating stage exhibited a large portion of slow α rhythm. As the Zen meditation proceeds, much slower θ and ∆ rhythms may appear in some subjects. According to the subjective narration by meditators, they may feel drowsy or enter the seventh consciousness (sub-consciousness). In Figure 8(b), the 2D (two-dimensional) phase trajectories are constructed from the EEG epochs in Figure 8(a) using a delay of 5 samples (0.025 second). Apparently, the silent and β patterns have the phase trajectories of shrinking dynamical extent, yet with higher degree of irregularity. The α trajectory exhibits harmonious orbital patterns with high coherence.
Both the θ and ∆ trajectories involve dynamics of multi-modes, that is, the system dynamics are governed by two or more nonlinear mechanisms with different degrees of freedom. In Figure 8(b), the θ and ∆ trajectories apparently travel different spans in the phase space. This phe-nomenon is mostly caused by the simultaneous emergence of multiple EEG rhythms, for in-stance, the ∆ accompanied by β rhythm. In the case, outer orbits track the ∆ activity, while the inner orbits follow the β rhythm. This phenomenon results in two distinct estimates for the com-plexity index δ. First, small K indicates that the di,KNN (KNN distance), obtained after searching all the orbital points, most likely characterizes orbits of the same attribute. As K becomes large, the di,KNN, on the other hand, may represent the inter-distance between two orbital points that track different EEG rhythms.
Meditation EEG scenarios subband-AR-EEG-Viewer for tracking slow α:
Frequency of α rhythm ranges from 8Hz to 12Hz. The slow α is a particular pattern, nor-mally below 10Hz, that is observed in some experimental subjects at the mind-focusing stage of meditation. The Subband-AR-EEG-Viewer, designed to track the slow-α, can be reduced to the structure shown in Figure 9(a), with the algorithm illustrated in Figure 9(b). According to ana-lytical reasoning and practical experience, output1 in combination with output3 highly enhances the effectiveness of slow-α detection. Note that the fr,1 acts as an index of screening out the high-frequency component, and the fr,3 is employed in the classification as a major reference.
The algorithm (Figure 9(b)) depicts that slow-α pattern is detected when both root frequencies satisfy the following criteria:
fr,1 < 14Hz, and 8Hz < fr,3 <10Hz.
While only examining output1 (up to 30Hz) with the criterion 8Hz < fr,1 <10Hz, the model often fails to identify the noise-contaminated slow-α activities. Figure 10 demonstrates the
noise-immunization capability of our model. When a pure 9Hz sinusoid (Figure 10(a)) is par-tially contaminated by a uniformly distributed random noise (Figure 10(b)), the AR model does not recognize the noise-contaminated slow-α segment based on the criterion 8Hz<fr,1<10Hz (Figure 10(c)). Note that the epoch identified as the slow α is indicated by a black bar above the signal. Result in Figure 10(d) shows that the proposed model successfully detects the slow α under poor environment (SNR=8dB).
To justify the performance, we first analyze a simulated signal of 4-second duration. The signal shown in Figure 11(d) is generated by connecting three short-duration,
ampli-tude-modulated sinusoids, respectively, with frequencies 9Hz, 15Hz, and 5Hz (Figure
11(a)~(c)). The window length is 0.5 second (100 samples), moving at a step of 0.25 second. As shown in Figure 11(d), the algorithm effectively detects the occurrence of slow-α pattern.
Next, the algorithm is applied to the meditation EEGs (channel O1). A 10-second segment shown in Figure 12 is analyzed with the same implementing parameters as which used in Figure 11. A dark bar above the signal indicates the slow-α detected. As shown in Figure 12(a), ampli-tude variation often affects the recognizability of slow-α. It results in a crack in the first dark bar. On the other hand, a transient slow-α may be of little significance. We thus design a post-processor to further refine the result. It removes segments of duration shorter than 0.3 sec-ond and fuses a crack smaller than 0.3 secsec-ond (Figure 12(b)).
Detection of specific EEG patterns is important in identifying various meditation states. In addition, it may serve as a preprocessing stage in such tasks like the EEG segmentation or inter-pretation. Based on the Subband-AR-EEG-Viewer, we devised a particular scheme for medita-tion EEG interpretamedita-tion. Details are illustrated below.
Meditation EEG scenariosSubband-AR-EEG-Viewer for long-term interpretation:
Changes of the characteristic frequency in meditation EEG may be a key feature for under-standing various states of consciousness during meditation. We therefore develop a logical strategy implemented in a computerized algorithm to segment the EEG into sections with dif-ferent frequencies. The results illustrated by a running gray-scale chart indicate the evolution of characteristic frequency during meditation. In the following study, we present the result of in-terpreting the meditation EEG based on five spectral features frequently observed during meditation. The five features include: (1) slow waveform intermixing with high-frequency rhythms (symbolized by ‘χ’), (2) ∆, (3) θ, (4) α, and (5) β. The χ feature mostly appears at the transition from one EEG rhythm to another. To provide a long-term legible illustration, five spectral features are displayed by different grays. The gray tones from the darkest to the brightest colors indicate, respectively, the χ, ∆, θ, α, and β feature. In this task, the structure of Subband-AR-EEG Viewer can be reduced to that shown in Figure 13.
The algorithm examines each windowed segment to check the following criteria in order:
Criterion-χ: fr,3<7Hz<fr,1 and p3>0.7;
Criterion-∆: fr,1<7Hz and fr,4<3.5Hz;
Criterion-θ: fr,1<7Hz;
Criterion-α: fr,1<14Hz and 7Hz<fr,3; Criterion-β: 7Hz<fr,1;
where p3 is the AR(2)’s pole of output3. The criteria checkup is ordered according to a sound logic realizing the subband filtering scheme. The root frequency fr,1 is used to differentiate be-tween 0~7Hz and 7~30Hz EEG bands, while the fr,3 , fr,4 and p3 are employed in the subse-quent discrimination process. The length of p3 can be considered as an indication of the signifi-cance of the root frequency. Because the χ wave represents an intermixed signal composed of both low- and high-frequency components, we impose restrictions on the range of p3 to en-sure the significance of the low frequency component.
To verify the effectiveness of feature recognition, the algorithm is firstly applied to a simu-lated signal. As displayed in Figure 14(e), the signal is constituted by connecting five segments of ∆, θ, χ, α, and β patterns, respectively. Assume the sampling rate is 200Hz. This signal can
be simulated by the pole placement method, that is, placing each pole in the corresponding fre-quency band and adding Gaussian noise. Transition from θ to β normally results in such a com-pound pattern like χ. The running gray-scale chart (Figure 14(e)) above the simulated sequence successfully signals the temporal patterns.
The above simulation demonstrates the feasibility of the model and algorithm in Figures 8 and 9 for automatically identifying different EEG rhythms and revealing its time-varying schema. In empirical data, more complex rhythmic patterns involved may result in discrepancy between experienced EEG interpreters. Methodology development thus focuses on reliable rec-ognition of some key features in meditation EEG analysis. Figure 15 demonstrates the robust-ness of the Subband-AR-EEG Viewer for identifying even the little jittering of β rhythms em-bedded in the high-amplitude slow activity.
When applied to the long-term meditation EEG, this method is particularly robust for automatic interpretation with no need to determine the implementing parameters. Figure 16 dis-plays three running gray-scale charts for two experimental subjects (Figures 16(a) and (b)) and one control subject (Figure 16(c)). The error rate is approximately 8.7% in comparison with the results of naked-eye examination by an experienced EEG interpreter. Both meditators have been practicing the Zen-Buddhist meditation for more than eight years. Subjects of the control group sat in a normal, relaxed position with eyes closed. During the 10-minute meditation session, two meditators exhibited different meditation scenarios. Meditation EEG of subject 2k1019p is ap-parently dominated by β rhythm, sometimes transforming into short-duration α’s. According to the post-experimental interview, the subject did not always stay in the Alaya consciousness and occasionally got back to normal consciousness. The chart in Figure 16(a) evidently reveals this scenario. In Figure 16(b), subject 2k0830a exhibited a large portion of χ activities. In our medi-tation EEG study, EEG signals of some meditators indeed were found to be characterized by large-amplitude, slow-drifting rhythms interwoven with high-frequency tiny jiggles. Meditators with this kind of EEG characteristics normally have their meditation process wandering among normal consciousness, subconsciousness (subliminal consciousness), and Alaya consciousness (Lo, Huang, Chang 2003). Compared with the experimental group, EEG’s collected from the control subjects are normally dominated by α rhythm, as illustrated in Figure 16(c). Note that this subject drowsed in the experiment, resulting in occurrence of θ and ∆ rhythms.
(C) Spatio-temporal characteristics of meditation EEG:
In (Lo and Huang 2004), we demonstrated the running δ chart analyzed for selected 8-channel EEGs, including channels F3, F4, C3, C4, P3, P4, O1, and O2 for three experimental subjects and one control subject . We notice that the beginning five-minute EEGs are pretty much the same for the control subjects and the group-M2 meditators on the occipital brain re-gion. That is, α-rhythm dominates the EEG activities. This phenomenon is almost spatially un-biased for some control subjects. The α-rhythm appears at all the recording sites on the scalp, without limiting to the occipital region. Nonetheless, group-M2 meditators exhibit lower com-plexity in brain dynamics corresponding to the slow (θ+∆) activities. The Φ/β-dominated EEG of groups M2 and M3 is evident in the 8-channel δ charts. Group-M2 EEG, yet, reveals in-termittently emergence of (θ+∆) (dark gray) and α (mid gray) activities on the background Φ/β.
The 8-channel δ chart of group M2 shows higher δ ’s on the occipital and parietal regions, indicating the occurrence of significant Φ/β. Group-M3 subjects have an extraordinary EEG during the entire meditation session consistent Φ/β activities spreading all over the scalp.
Brain dynamics of high dimension and high complexity might be referred to the transcendental
state of consciousness. After twenty-minute recording, the δ charts differ a lot among the four groups. The gray-scale chart for the group-C1 control subjects remains about the same.
Group-M1 EEG basically is composed of the same rhythmic patterns, yet with increasing pro-portion of α rhythms on the parietal and occipital regions. Group-M2 subjects enter into the high-complexity brain dynamics (Φ/β), as that of group M3, all over the scalp during the last few minutes.
Note that the group-M1 meditators were fully awake though a large amount of θ and ∆ rhythms appeared. We attempt to hypothesize the occurrence of slow waves according to the quintessence and the ultimate aim of the orthodox Zen-Buddhist practice attaining an eternal state called the Buddhahood by firstly proving the most original true-self that embeds the light of the supreme wisdom, the noumenal energy, and the natural powers. Gradually, the human life system enters a unique status in harmony with the nature and the universe. The physical body thoroughly changes its constitution and, thus, becomes totally free from diseases. The medita-tors in group M3 are special. Their EEGs have been steady all the way through the meditation course. Particularly, α rhythm even has never appeared since the beginning of meditation. The meditators in this particular group said that their brain and mentality had been totally different from what before practicing the Zen-Buddhist meditation. They are now so calm, serene and peaceful when they are not in use. This status makes the meditators better preserve their mental power and body energy. On the other hand, they perform much better in their work or study be-cause, without the interference from “mental noise,” they feel more concentrated.
According to the above illustration, the meditation EEG evidently involves both spatial and temporal information. For investigating the spatial localization, the brain mappings of one-minute averaging δ in Figure 17, reconstructed from the 30-channel EEGs, demonstrate an interesting spatio-temporal phenomenon (Lo and Huang 2004). Control subjects exhibit global α activities in the first and last five-minute intervals. Group M1 begins with a bright-gray mapping and transits into a mid-tone one indicating the occurrence of α rhythm, whereas the brain mapping of group M2 evolves in the reverse course. As for group M3, The mapping fur-ther demonstrates the phenomenon of global quiet electrical activities in deep, transcendental Zen meditation.