Correspondence: Byung-Hwan Yang, MD, Department of Neuropsychiatry, College of Medicine & The Mental Health Research Institute, Hanyang University, 17 Haengdang-dong, Seongdong-gu, Seoul 133-791, Korea 
Tel: +82-2-2290-8422, Fax: +82-2-2298-2055, E-mail: bhyang@hanyang.ac.kr

Introduction

The construct of hypnosis has traditionally been associated with the idea of profound, suggestion-induced alterations in subjective experience. The most commonly used index of experiential change, and that which has been the center of theoretical debate, is verbal report. In an effort to avoid the potential biases and inaccuracies of subjective reports, investigators have adopted electrophysiological methods to examine responses to the hypnotic situation, as well as to identify the physiological markers of those persons responsive under such conditions. The rationale for the application of these methods has grown out of the traditional belief that the hypnotic condition differs from the waking condition¹.
Numerous studies have been performed to investigate whether the electroencephalogram (EEG) correlates with the hypnotic process itself. However, the electrophysio logical correlates of hypnosis remain controversial and the neural mechanisms underlying the hypnotic experience and the responses to hypnotic suggestions are largely unknown². 
Today, with the availability of more sophisticated signal processing approaches, it is possible to reconsider and update previous attempts to describe the EEG correlates of hypnosis. Recent work suggests that applying measures from nonlinear dynamics (popularly called "chaos") can provide an important insight into EEG³. Chaotic measures, such as fractal dimensions, Hausdorff dimensions, Lyapunov exponents, Kolmogorov entropy and others, suggest that the complex activity generated by the brain, and considered by some to be noise, may not be random, but may indeed contain information concerning the underlying processes of the brain, albeit in an ordered but nonpredictable pattern referred to as chaotic⁴. 
In recent years, the technique of detrended fluctuation analysis (DFA) invented by Peng et al⁵ has established itself as an important fractal analysis tool for the detection of long-range (auto-) correlations in time series with non-stationarities. The advantages of DFA over conventional methods (e.g. power spectral analysis) are that it permits the detection of long-range correlations embedded in a seemingly non-stationary time series, and also avoids the spurious detection of apparent long-range correlations that are an artifact of non-stationarity⁶. 
Recently, several studies have been performed in an attempt to detect long-range correlations in EEG by DFA^7,8,9. These studies suggested that the dynamics of EEG have long-range correlations. Just as these attempts permit the detection of long-term trends in EEG, fractal analysis could be used to distinguish the hypnotic condition from the waking condition and to investigate further issues relating to hypnosis. 
This study analyzes the trends of EEG signals in the waking condition and the hypnotic condition using fractal analysis for the preliminary definition of the physio-logical concomitants of hypnosis. 

Materials and Methods 

Subjects 
The data were collected between June 2002 and August 2003 from 9 consecutive psychiatric outpatients seeking hypnotherapy in a hospital-based hypnosis clinic located in Goyang, Korea. Only patients who completed a Korean Version of the Hypnotic Induction Profile (HIP-K)¹⁰ were included in this study. This scale was developed from the original HIP¹¹ by a process of translation and back-translation and revision by the original author. The HIP includes both qualitative and quantitative scores of hypnotizability, standardized on a patient population in a clinical setting,¹¹ in which the qualitative score is called the "profile score" and the quantitative score is called the "induction score." The regular zero profile and decrement profile of the HIP were excluded, because these two patterns serve to show the inability of the patient to experience hypnosis. A single hypnotist administered the scale of hypnotizability, namely J.S. Lee, one of the authors of this study, who is a psychiatrist with extensive experience in hypnosis and HIPK. This process was always part of the patients' treatment. These data were collected primarily to facilitate the treatment process. 
Six right-handed (self-reported) individuals with a mean age of 33.4 13.8 were included in this study, all of whom were females who met the inclusion and exclusion criteria for hypnotizability, who were in good medical condition, and who had no history of alcohol or drug abuse, head trauma, epileptic episodes or other systemic disease that might affect brain functions Table 1. The hypnotherapy was repeatedly administered until a target symptom improved or the subjects wanted to quit. All of the data from their hypnosis sessions were included for individuals who visited the clinic for more than one hypnotherapy episode. The mean number of hypnotherapy sessions was 5. Twenty-five sets of data were analyzed. 

Procedure 
The subjects were first shown the hypnosis-treatment setting, including the EEG monitoring equipment. Afterwards, electrodes were attached to each subject, who sat in a comfortable armchair in a sound-attenuated, dimly lit EEG room, with the hypnotist nearby. Hypnosis was induced using the modified HIP technique, with only involves eye-roll and instructional arm levitation. After the completion of the hypnotic induction, including instructional arm levitation, the hypnotist conducted an unstructured therapeutic interview. The hypnosis treatment consisted of 4 conditions, with a minimum of 5 minutes each, namely: (1) quiet wakefulness (eyes closed); (2) beginning of hypnotic induction; (3) hypnotic condition (completed instructional-arm levitation); and (4) end of hypnotic condition (suggestion of wakening and eye opening). The first-stage and third-stage data were used in the analysis. 

EEG recordings 
The EEG data were acquired by means of a Telefactor EEG-monitoring device in the EEG recording room. To avoid any disturbances or interferences, the recording room was shielded with copper. The EEG recordings were made using silver-silver chloride cup electrodes (Ag-AgCl) attached by collodion at 19 scalp sites (international 10/20 electrode system Fp1/2, F3/4, C3/4, P3/4, O1/2, F7/8, T7/8, P7/8, Fz, Cz and Pz), with Cz being used as a reference point. The EEG-measurement-device settings were as follows: 200-Hz sampling rate, 16-bit resolution, 1-Hz high-pass filter, 70-Hz lowpass filter and 60-Hz notch filter. Using the EEG recording, the hypnotist noted the annotations for the following objective changes in the subjects throughout the entire hypnosis session: waking condition, initial hypnotic induction, completed instructional-arm levitation, and the end of the hypnotic condition. 

Fractal analysis of EEG time series 
The acquired EEG data during the waking and hypnotic conditions was analyzed using DFA. DFA is a fractal analysis method which is used for quantifying the correlation property in a non-stationary time series, by computing a scaling exponent by means of a modified root mean square analysis of a random walk. 
Briefly, the time series to be analyzed (with N samples) is first integrated. where x(i) [i=1,..., N] is a timeseries and M is the average value of the series x(i). 
Next, the integrated time series is divided into boxes of equal length, n. In each box of length n, a least squares line is fit to the data (representing the trend in that box). The y coordinate of the straight-line segments is denoted by yn(k). Next, the integrated time series, y(k), is detrended by subtracting the local trend, yn(k), in each box. 

            Equation 1.                                          Equation 2.

The root-mean-square fluctuation of this integrated and detrended time series is calculated using the following equation: 
This computation is repeated over all time scales (box sizes) to determine the variation of F(n), the average fluctuation, as a function of the box size. Typically, F(n) increases with (Note - I think it would otherwise need to say "relationship between ... and ...) increasing box size, n. A linear relationship on a log-log plot indicates the presence of scaling (self-similarity), which means that the fluctuations in small boxes are related to the fluctuations in larger boxes in a power-law fashion. The slope of the line relating log F(n) to log n determines the scaling exponent (self-similarity parameter), which is the result of DFA^5,12. 
It is known that when the scaling exponent is 0.5, (the fluctuations are referred to as?) "white noise." In this event, the value at one instant is not correlated with any of the previous values, and the integrated value, y(k), corresponds to a random work¹³. The case where the scaling exponent=1 is a special one, which corresponds to 1/f noise¹⁴. A scaling exponent=1.5 indicates Brownian noise, which is the integration of white noise. When 015. A scaling exponent greater than 0.5 and less than or equal to 1.0 indicates persistent long-range power-law correlations. Finally, in the case where the scaling exponent is greater than 1, correlations of the original (non-integrated) signal exist, but cease to be have the power-law form¹². It is these scaling exponents that are of interest in this study. 
The scaling exponent can also be viewed as an indicator of the "roughness" of the original time series. The larger the value of the scaling exponent, the smoother the time series is. In this context, 1/f noise can be interpreted as a compromise or "trade-off" between the complete unpredictability of white noise (very rough "landscape") and the much smoother landscape of Brownian noise¹⁶. 
The average measuring time± standard deviation for one session was 32±11 minutes, and x(i) signifies the recorded EEG data. Although, DFA is the optimum fractal analysis technique to use for determining the whole trend in long-term EEG, the application of DFA took about 25-48 hours to yield results for one case. This could be considered to demonstrate the weakness of DFA, particularly for long-term analyses such as hypnotic analysis. To compensate for this deficiency, Gotman's wave simplifying method¹⁷ was employed and this technique successfully allowed the number of data analyzed to be reduced to 20% of the original data Figure 1. 
According to the classical method of wave analysis, the EEG signal is broken down into segments, or the sections between two consecutive extremes of amplitude. Segments are characterized by their individual duration, amplitude, and direction and, hence, alternate in direction. An example is given in Figure 1(b). Moreover, we designed a way of regrouping segments into sequences, recreating the slow-frequency wave in the presence of low-amplitude, fast activity. A sequence ends when a segment not belonging to it is found. A sequence of direction X (up or down) is not allowed to include a segment S of direction -X larger than either of the two segments immediately adjacent to S. Furthermore, a sequence of direction X may not include a segment of direction -X of a duration equal to or larger than 30 m/sec. This is to ensure that a sequence of direction X only includes small segments of direction -X. Figure 1. gives examples of the regrouping of segments into sequences. If the EEG wave of Figure 1(a). was acquired at 256 points per second (sampling rate), segmentation can simplify this to 12 points per second, and sequencing will subsequently reduce this to 4 points per second. After these processes, DFA was applied to the simplified and sequenced data, and the scaling exponent, also a result of DFA, was statistically analyzed for each channel of each subject. 

Statistical analysis 
The scaling exponent at each channel of each subject was statistically analyzed. The paired t-test was used to determine if there were any differences between the means of the conditions. 
All statistical procedures were performed using SPSS 10 for Windows. Statistical significance was determined at a=0.05 for all analyses. 

Results 

    Table 2 shows the means and standard deviations of the scaling exponent for each channel and the results of the paired t-test. All of the scaling exponents in the waking and hypnosis states were greater than 0.5 and less than 1.5, regardless of the condition, which means that the original data had correlations. The scaling exponent in the waking condition, such as that in example F7 which was 1.22±0.31, was situated between the values of 1/f noise and Brownian noise. On the other hand, the scaling exponent in the hypnotic condition, which for example F7 was 0.95±0.35, was situated between the values of 1/f noise and white noise. Similar results were observed in all of the other channels. Significant differences were found between the scaling exponents during the waking and hypnotic conditions in most of the channels (except, Fp1 and F4). 
Subsequently, the individual changes in each subject resulting from the number of hypnotic trials were analyzed Table 3. Four subjects who had taken hypnotic therapy at least three times were selected for this experiment. In all of the trials, the scaling exponents displayed similar values and the differences among the scaling exponents of each trial were statistically nonsignificant. In the following experiment, the symmetrical characteristics of the left and right hemisphere were examined. However, the examination of the symmetries did not yield any statistically significant differences Figure 2. 

Discussion 

Do electrophysiological differences that distinguish hypnotic conditions from waking conditions exist? Is there a psychophysiological index that distinguishes between waking and hypnotic conditions? Studies conducted in the last three decades in an attempt to answer these questions have resulted in contradictory findings. In this study, the fractal analysis technique was used to analyze EEG time series, in order to determine the possible EEG correlates of the hypnotic state. 
It was found that the results of the fractal analysis for the waking and hypnotic EEG conditions were significantly different from each other in most EEG channels. All of the scaling exponents, however, were greater than 0.5 and less than 1.5, regardless of the condition. Thus, the EEG data are not random, like white noise, nor are they the outcome of a process with short-term correlations. Instead, the EEG rhythm is related to its earlier rhythm, and this scaling occurs in a scale-invariant, fractal like manner at each condition. For most channels, the scaling exponents of the fractal analysis were signifi-cantly different between the hypnotic condition and the waking condition. The values of the scaling exponents during the hypnotic condition were situated between the values of 1/f noise and white noise. In contrast, the values of the waking condition were situated between the values of 1/f noise and Brownian noise. The reduction of the scaling exponents during the hypnotic condition demonstrates that hypnotic influences can override the normally present long-range correlations, and that hypnosis is not simply a result of social-psychological interchange. 
In addition, previous studies have shown that the scaling exponent of EEG increases as the brain activity descends toward the level of deep sleep^7,8. Lee et al⁷ found that the mean value of the scaling exponent was 0.99947 during the waking condition, 1.0353 during REM sleep, 1.1054 during stage-1 sleep, 1.1429 during stage-2 sleep, 1.221 during stage-3 sleep, and 1.3729 during stage-4 sleep. These values matched the results of the present study. These findings indicate that the dynamics of EEG becomes increasingly similar to Brownian noise during the sleep stage, suggesting that the dynamics of the brain become less random and more correlated at this time. On the other hand, the dynamics of EEG during the hypnotic condition had opposite char-acteristics. This finding also demonstrates that hypnosis is not the same thing as sleep. 
Several standardized measures, with good psychometric characteristics, are available to reliably assess hypnotizability. For example, the Stanford Hypnotic Susceptibility scales^18,19 and Hypnotic Induction Profile^11,20 have excellent test-retest reliability after long intervals. Although such terms as hypnotic susceptibility, responsiveness, suggestibility and depth embrace possess some subtle nuances, they are typically used inter-changeably to indicate the quantifiable rating of a sub-ject's response to hypnotic suggestions under standard conditions. It is common to classify people as lowly or highly hypnotizable, depending on their performance on a particular scale. However, some researchers have attempted to change hypnotic susceptibility using programs that enhance it²¹ Thus, individual changes were analyzed in each subject resulting from the number of hypnotic trials. Four subjects who had undergone hypnotic therapy at least three times before were selected. In all trials, the scaling exponents displayed similar values and the differences among the values of each trials were statistically nonsignificant. This indicates that it is difficult to change individual sensitivities to hypnosis by repeated hypnotic induction. 
In people that are difficult to hypnotize in the waking state, the more rational, cognitive left hemisphere is responsible for the processing of incoming signals and shows higher electrical activity. On the other hand, in highly hypnotizable people, the holistic, emotional, spatial right hemispheric activity is accentuated. This is why hypnosis is mentioned in the literature as a "right hemispheric" phenomenon²². Some studies have reported that there is an important difference between the activities of the two cerebral hemispheres^23,24. However, Sabourin et al 25 . did not find such a relationship. Furthermore, Crawford and Gruzelier²⁶ concluded their review of this issue by suggesting that highly-susceptible people do not exhibit greater specificity in the right hemisphere. Does this mean "people who are highly-susceptible to hypnosis"? I'm not sure whether this would be clear or not for the informed reader. 
Consistent with this view, this study examined the symmetries between the two cerebral hemispheres and did not find in any statistically significant difference. No statistically significant difference between the frontal and the occipital lobe could be found either. It has been suggested that hypnosis is a change of organization of neural activity in the whole brain network rather than a "specific area" phenomenon. 
In this context, our results suggested that the thalamus is critical in inducing hypnosis. Numerous investigators, including Dempsey and Morison²⁷ and Adrian²⁸ , showed that significant EEG activity is generated by neuronal pools within the thalamus. The thalamus (a Greek word that means "inner chamber" or "bedroom") is an important processing station in the center of the brain. It is often thought of as the major sensory-relay station, especially during pain. In addition to sensory information, the thalamus also conveys nearly all other inputs to the cortex, including motor inputs from the cerebellum and basal ganglia, limbic inputs, widespread modulatory inputs involved in behavioral arousal and sleep-wake cycles, and other inputs that are connected to the characteristic phenomenon of hypnosis²⁹ . Thus, it is reasonable to assume that the thalamus is critical in inducing hypnosis and in generating the degradation of the long-range correlations during the hypnotic condition. 
In conclusion, in the present study, we found that the fractal analysis technique can be used to demonstrate the electrophysiological correlation of the hypnotic influence on cerebral activity. The scaling exponents of the fractal analysis are reduced towards white noise during the hypnotic condition, and this differentiates the hypnotic condition from the waking condition. In this study, we also examined the symmetries between the two cerebral hemispheres, but did not found any statistically significant difference. No statistically significant difference could be found between the frontal and occipital lobes either. This results suggests that the thalamus is critical in inducing hypnosis and in generating these long-range correlations during the hypnotic condition. However, to define the hypnotic condition, the results of this fractal analysis still leave much to be explained. At present, more cases and data suitable for this form of analysis are being collected, and we hope that this will eventually lead to more significant results.

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