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Heart rate variability analysis during hypnosis using wavelet transformation
Biomedical Signal Processing and Control 31 (2017) 1–5
Contents lists available at ScienceDirect
Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Heart rate variability analysis during hypnosis using wavelet transformation Xiuwen Chen a , Rongqian Yang a,∗ , Lulu Ge b , Lei Zhang c , Ruixue Lv c a b c
Department of Biomedical Engineering, South China University of Technology, Guangzhou, China Guangzhou Municipal Public Security Bureau, Guangzhou, China Shenzhen Sayes Medical Technology Co., Ltd., Shenzhen, China
a r t i c l e
i n f o
Article history: Received 19 April 2016 Received in revised form 19 June 2016 Accepted 7 July 2016 Keywords: Autonomic nervous system Heart rate variability Hypnosis Wavelet transformation
a b s t r a c t Hypnosis can act on the autonomic nervous system which can be presented by heart rate variability (HRV). So HRV implies many information related to hypnosis. Because HRV signal is time-variant and non-stationary, the traditional methods, such as Fourier transform and AR spectral estimation, are unable to analyze it. Hence, wavelet time-frequency analysis is applied here to not only offer superior time and frequency resolution, but also detect sudden amplitude and frequency jumps. The electrocardiograms of subjects were recorded under hypnosis, from which the corresponding HRV signals are obtained. The instant parameters including HRV, very low frequency (VLF), low frequency (LF), high frequency (HF), and the ratio of LF to HF (LF/HF) components of each HRV signal are then computed. Furthermore, mean, coefficient of variation, skewness, and kurtosis of independent frequency components in four hypnotic states (resting state, inducing state, imagining state and awaking state) were also obtained from the instant parameters to describe variation during hypnosis. The experiment results show that the parameters of HRV can reflect some physiological features of hypnosis, e.g., the LF/HF was more concentrative and steady in imagining state. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Clinical hypnosis is a mind-body technique that operates at the intersection of subjective perceptions and objective physiological changes. Many researches illustrated that hypnosis can be characterized by a decreased sympathetic tone and an increased parasympathetic activity [1], where sympathetic nervous system (SNS) and parasympathetic nervous system (PNS) are the two main branches of autonomic nervous system (ANS). In addition, autonomic cardiac tone was significantly modified during hypnosis by shifting the balance of the ANS toward an enhanced PNS modulation, accompanied by a reduction of the SNS tone and a decreased short-range similarity but without a concomitant change in heart rate [2]. Heart rate variability (HRV) is often used to assess function of ANS [3]. The measure of the ANS response to hypnosis can be obtained from analyzing the HRV parameters of frequency domain [4]. Low frequency (LF) component of HRV signal is influenced by both SNS and PNS and it may reflect the thermal control and barore-
∗ Corresponding author. E-mail address: [email protected] (R. Yang). http://dx.doi.org/10.1016/j.bspc.2016.07.004 1746-8094/© 2016 Elsevier Ltd. All rights reserved.
flex control of blood pressure through HRV. High frequency (HF) component is controlled by PNS and it is associated with respiratory activity. Although respiratory sinus arrhythmia occurs within the HF band, this condition can also occur at other frequencies. The ratio of LF and HF (LF/HF) is considered to reflect balance between SNS and PNS [5–7]. Some traditional methods, such as Auto-regressive (AR) spectral estimation and Fourier transformation, are the most popular methods to analyze HRV [8]. These methods to estimate spectrum presupposed that HRV is stationary and time-invariant signal. However, HRV is non-stationary signal in the long term, especially in hypnosis. The different stages of hypnosis results in the change of HRV parameters due to the individual received different external stimulus. The HRV parameters still vary even in the same stage. Therefore, traditional methods are not effective to analyze hypnotic HRV signal. On the other hand, traditional methods can only quantify the amplitude of heart rate oscillations, without providing temporal information [9]. The variability of instantaneous power of independent frequency components under hypnosis is extremely valuable, which maybe imply some important information. Compared with traditional methods, wavelet transformation (WT) can not only analyze non-stationary signal like hypnotic HRV and offer superior time and frequency resolution, but also has the
2
X. Chen et al. / Biomedical Signal Processing and Control 31 (2017) 1–5
ability to detect sudden amplitude and frequency jumps [10]. There are three main classes of wavelet analysis: Continuous Wavelet Transform (CWT), Discrete Wavelet Transform (DWT), and Wavelet Packet Transform (WPT). DWT and WPT are useful for compact representation of data, particularly for noise reduction, and can also for analyzing power spectrum of HRV [11–14]. However, DWT and WPT do not have subtle frequency resolution in terms of timefrequency analysis. Whereas, the CWT is the best one for feature extraction [15]. Only CWT is studied here because we are interested in extracting low s/n ratio signals in time series. We recorded and analyzed the changes of independent frequency components of subjects who were under hypnosis. Then some statistical features are computed by assessing the short-time variation of frequency components including mean, coefficient of variation, skewness and kurtosis of instantaneous power of independent frequency components at all the four states (resting state, inducing state, imagining state, and awaking state). It will indicate the change rule of frequency components of HRV under hypnosis and further compare the statistical features of these components in different hypnotic conditions. 2. Statistical feature extraction using Wavelet technique 2.1. Acquisition of HRV signal There are four states during hypnotic test. First, in resting state, subjects breathe normally with their eyes closed and lie quietly without moving before hypnosis. Second, in inducing state, subjects are guided to relax progressively and respond suggestions. Subjects are considered to be hypnotized when roving eye movements are observed or the subject respond by a hand movement that he or she feels to be hypnotized [16]. Third, in imagining state, subjects are invited to imagine pleasant and peaceful scene, and they are instructed to feel their subconscious and positive energy. This process is an alteration in perception, sensation, emotion, thought, or behavior through imagination and suggestion. Four, in awaking state, subjects return to waking state with completion of hypnosis. They breathe normally with their eyes closed and lay quietly without movement. Electrocardiography (ECG) signals and videos of subjects in the whole tests are recorded in all the four states. The subjects are documented with a video camera for detailed analysis after recording ECG. ECG is recorded in supine position by using three-limb ECG leads (ECG-B; SAYES, Shenzhen, China) through Red DotTM Ag/AgCl disposable electrodes placed in accordance with a sample rate at 500 Hz. Then the peaks of this ECG are extracted and resampled at 4 Hz to obtain HRV signal h(t). h(t) is segmented into four part hi (t) according the four hypnotic states, i = 1, 2, 3, 4. 2.2. Time-frequency analysis of HRV signal After the hi (t) is obtained, WT is used to compute its wavelet power coefficients WT(t,a) as follows 1 WT (a, b) = √ a
=
t−b hi (t) ∗ ( )dt a √
a
ejwt hi (w) ∗ (aw)dw
(1)
(2)
where * represents conjugate, the scaling factor a and shifting factor b are real and a > 0, the w is the angular frequency. hi (t) is the HRV signal in the ith state and (t) is the Morlet wavelet. After WT, a data matrix containing time, scale, and wavelet coefficients is obtained. Actually, the WT is not a function of time and frequency but time and the scaling factor a. Because scale is related
to frequency,PWT (t,a) is called the scalogram and it defines a joint density of time and scale [17], 1 |WT (t, a) |2 2Ca2
PWT (t, a) =
1 2Ca2
The factor
(3)
is inserted for proper normalization. The constant
C is chosen to obtain the energy by using WT,
C=
2
| (w)| dw |w|
(4)
A reference frequency wr is chosen from w = wr /a to obtain a time-frequency density. Finally, wavelet time-frequency analysis can be expressed by [18] wr PWT w2
PWT (t, w) = =
1 |WT 2Cwr
t, a =
w r t,
w
|
wr w
(5)
2
(6)
Then, the instantaneous power PWT (t, w) is obtained from Eq. (6), which contains the messages of time and frequency. For assessing the instantaneous power of independent frequency components of HRV, the frequency spectrum is divided into three parts: very low frequency (VLF, 0.003–0.04 Hz):
0.04
PVLF (t) =
PWT (t, f ) df
(7)
0.003
where f=2/w, frequency interval is related to the scaling factor a, and the frequency range from 0 to 2 Hz. Low frequency (LF, 0.04–0.15 Hz) spectrum is:
0.15
PLF (t) =
PWT (t, f ) df
(8)
0.04
and high frequency (HF, 0.15–0.40 Hz) spectrum is:
0.40
PHF (t) =
PWT (t, f ) df
(9)
0.15
2.3. Statistical analysis of independent frequency components In the process of hypnosis, the instantaneous power of independent frequency components changes with the time. In order to describe this variation, four parameters of statistical features are used: mean, coefficient of variation, skewness, and kurtosis. Mean represents mean value of instantaneous power at each hypnotic state. Coefficient of variation is defined as the ratio of standard deviation to mean, which shows the extent of variability in relation to the mean of the population [19]. Coe[X] =
(10)
where X represents instantaneous power of independent frequency components, represents mean value and represents standard deviation. Skewness can reflect the degree of asymmetry in the histogram of instantaneous power: Skew[X] = E
X − 3
=
E X 3 − 3 2 − 3 3
(11)
where E is the expectation operator. If the histogram is symmetrical, the skewness is zero. If the left hand tail is longer, the skewness will be negative. If the right hand tail is longer, the skewness will
X. Chen et al. / Biomedical Signal Processing and Control 31 (2017) 1–5
3
be positive [20]. Kurtosis is a measure for the degree of flatness or peakedness in the variable distribution: Kurt[X] =
2
E (X − )3 E (X − )2
(12)
High kurtosis tends to have a distinct peak near the mean, decline rather rapidly, and have heavy tails, while low kurtosis tends to have a flat top near the mean rather than a sharp peak. The standard normal curve of instantaneous power has a kurtosis of zero [20,21]. Mean, coefficient of variation, skewness, and kurtosis are the effective statistical features which are able to describe the variation of instantaneous power of independent frequency components changed over time. 3. Experimental results 3.1. Subjects and data recording
Fig. 1. The tridimensional plot of time, frequencies, and wavelet coefficients in the resting, inducing, imagining, and awaking states of a subject under hypnosis.
After informed consents, 12 subjects were enrolled in this study (9 female and 3 male, with mean age of 31.1 ± 5.4 years, mean height of 163.6 ± 6.3 cm, and mean weight of 57.8 ± 5.4 kg). None of the subjects reported any history of myocardial infarction, arrhythmia, alcohol abuse, head injury, or epilepsy. Moreover, these subjects had not consumed caffeine-containing drinks in the last 24 h before hypnosis. Two subjects dropped out because they did not reach a trance state. The remained 10 subjects met the requirement of this study, who did have the abnormal ECG, such as a heart rate of <50 beats per minute, or the presence of conduction disturbance. Subjects were individually hypnotized by an experienced hypnotist. In this hypnotic test, subjects experienced four states (resting state, inducing state, imagining state, and awaking state). ECG signals and videos of them were recorded. After peak extracting and resampling of ECG signal, HRV signal h(t) was obtained. According to Eq. (2), wavelet power coefficients WT(t,a) were calculated and the instantaneous power PWT (t, w) is obtained in Eq. (6). Instantaneous power of independent frequency components PVLF (t), PLF (t), and PHF (t) were calculated from Eq. (7)–(9). The ratio of LF and HF: LF/HF(t) = PLF (t)/PHF (t). Then the statistical features (mean, coefficient of variation, skewness and kurtosis) of frequency components were calculated in four hypnotic states by Eq. (10)–(12). 3.2. Statistical analysis The statistical analysis of all the results was performed. Due to the relationship between resting state, inducing state, imagining state, and awaking state differences between these states were analyzed using a non-parametric test (Friedman test). Statistical significance was defined as p < 0.05. Values were presented as mean and standard deviation. 3.3. Results 10 subjects met the requirements of this study and experienced trance states. We found a significant (p < 0.05) change of HRV parameters in these four states. The major difference between the resting state, inducing state, imagining state, and awaking state was in LF/HF: coefficient of variation (p=0.045), kurtosis (p=0.016) and skewness (p=0.040) of LF/HF were significantly different between these four states. Especially, compared to the other three states, coefficient of variation, kurtosis, and skewness of LF/HF were lower in imagining state. In addition, these results show no significant change in HRV and other independent frequency components such as VLF, LF, and HF.
Fig. 2. Global heart rate variability, independent frequency (VLF, LF, HF) and the LF/HF in the four hypnotic states of a subject.
The tridimensional plot of time, frequency, and, wavelet coefficients data in the resting state, inducing state, imagining state, and awaking state of a representative subject under hypnosis was exhibited in Fig. 1. Wavelet coefficients decreased when subject in inducing and imagining states, and increased in awaking state. As to a subject described in Fig. 1, the global HRV, independent frequency (VLF, LF, and HF) and LF/HF in the four hypnotic states were drawn in Fig. 2. HRV was steadier in inducing and imagining states but it fluctuated in waking state. Compared to the resting state, HF in imagining state was significantly increased and fluctuated. In addition, when subject was returning to waking state from imagining state, the curves of LF, HF, and LF/HF changed suddenly. Table 1 summarizes the mean, coefficient of variation, kurtosis, and skewness of HRV, VLF, LF, HF and LF/HF between the four hypnotic states. The coefficient of variation, kurtosis, and skewness of LF/HF differed significantly (p < 0.05) in these four states.
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Table 1 Comparisons of mean, coefficient of variation (CV), skewness (SKE), and kurtosis (KUR) of heart rate variability (HRV), very low frequency (VLF), low frequency (LF), high frequency (HF) and the ratio of LF to HF (LF/HF) components between the four hypnotic states. rest HRV mean HRV CV HRV KUR HRV SKE VLF mean VLF CV VLF KUR VLF SKE LF mean LF CV LF KUR LF SKE HF mean HF CV HF KUR HF SKE LF/HF mean LF/HF CV LF/HF KUR LF/HF SKE
751.6 0.05 2.86 −0.15 763.6 0.38 2.69 0.41 735.6 0.39 5.78 0.97 307.7 0.46 4.60 0.91 3.03 0.61 10.62 2.21
induce ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
40.8 0.01 0.38 0.35 246.9 0.16 0.72 0.61 283.1 0.10 5.96 1.00 136.0 0.14 2.88 0.44 1.95 0.13 3.51 0.49
790.1 0.06 3.30 0.08 670.8 0.41 2.53 0.60 553.3 0.47 3.11 0.69 418.2 0.47 4.55 1.15 1.75 0.61 8.07 1.76
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
imagine 48.0 0.02 0.76 0.57 285.0 0.14 0.76 0.40 281.5 0.14 1.34 0.48 190.9 0.12 1.72 0.58 1.16 0.17 6.12 0.85
813.9 0.05 3.34 −0.09 541.9 0.25 2.61 0.04 651.2 0.37 2.76 0.49 508.3 0.38 3.11 0.66 1.51 0.46 4.98 1.08
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
awake 38.0 0.01 0.65 0.68 124.8 0.12 0.61 0.43 187.9 0.13 0.74 0.48 189.1 0.10 0.94 0.40 0.70 0.08 2.67 0.56
815.4 0.07 2.78 0.11 1046.0 0.29 2.19 0.04 1056.7 0.44 2.87 0.80 583.7 0.47 4.07 0.91 2.26 0.63 7.96 1.87
p ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
58.1 0.03 0.48 0.44 313.6 0.13 0.41 0.35 488.4 0.17 0.81 0.30 293.7 0.17 1.23 0.56 1.44 0.23 2.39 0.42
0.057 0.072 0.137 0.316 0.334 0.481 0.532 0.108 0.254 0.316 0.091 0.481 0.115 0.532 0.352 0.644 0.352 0.045* 0.016* 0.040*
Note. *Friedman test, p < 0.05.
4. Discussion and conclusions In this study, the wavelet time-frequency analysis was used to separately analyze the regularity of the different frequency components of HRV in subjects who were under hypnosis. Parameters of statistical features (mean, coefficient of variation, skewness, and kurtosis) were used to describe the changes of independent frequency components under hypnosis. The experimental results show that the coefficient of variation, kurtosis, and skewness of LF/HF in imagining state are lower than the other three states. It is possible that the statistical feature can be extracted using wavelet time-frequency analysis and further applied to study the physiological variety in hypnosis. Compared to AR spectral estimation and Fourier transform, the advantages of the wavelet time-frequency analysis are that it can be applied on non-stationary time series and offer time and frequency resolution [10,22]. Assessing HRV signal with DWT, we can observe the changes of frequency with time, just like Fig. 1. The changes of independent frequency components under hypnosis like Fig. 2 can be obtained using wavelet time-frequency analysis. The mean, coefficient of variation, skewness, and kurtosis of HRV and independent frequency components (VLF, LF, HF, LF/HF) in four hypnotic states were calculated by the statistical features in Table 1. Although, the mean of independent frequency components could be obtain through AR spectral estimation or Fourier transform, the parameters which are able to describe variation, such as coefficient of variation, skewness and kurtosis can only be obtained through wavelet time-frequency analysis. HRV is a physiological signal related to functions of ANS and the measurement of HRV is a sensitive method to assess ANS [23]. The results show that the HRV, VLF, LF, HF exhibit spontaneous fluctuations even at rest that reflect the influence of the ANS. The coefficient of variation, kurtosis, and skewness of LF/HF were significantly different between these four states. In the imagining state, coefficient of variation, kurtosis, and skewness of LF/HF were lower than in the other three states, which indicated that LF/HF was more concentrative and steady in imagining state. Seeing, feeling, smelling and thinking of person under hypnosis will change according to hypnotist’s suggestions. Hypnosis might result in metabolic, cardiac, and cognitive activations [16]. Our results suggest that there is physiological variety during hypnosis. LF/HF can be considered to reflect the balance between SNS
and PNS and used as a measure of this balance. LF/HF is more concentrative and steady in imagining state, which would imply an increased modulation of ANS, especially of the enhanced PNS and reduced SNS. It proved that hypnosis is associated with a decreased sympathetic tone and an increased parasympathetic activity, and the balance between SNS and PNS is shifted. This study effectively applied wavelet time-frequency analysis to extract the statistical features of HRV under hypnosis which can imply that the balance of ANS is modulated under hypnosis. It indicated the changing regularity of HRV, independent frequency (VLF, LF, and HF) and LF/HF in the four hypnotic states. The LF/HF was more concentrative and steady in imagining state. The further research may apply wavelet time-frequency analysis to study the change of HRV of depression patients under hypnosis because hypnosis is adjuvant treatment method of depression and HRV of depression patients behaves abnormality. There are important clinical significance for studying the change rule of HRV and evaluating the effect of hypnotic treating depression. Acknowledgments This research was funded by the Shenzhen Science and Technology Program under Grant No. CXZZ20140903161225943 and No. CXZZ20150529144549687, the Guangdong Provincial Science and Technology Program under Grant No. 2016A020220011, the Guangzhou Science and Technology Program under Grant No. 201604020107. References [1] G. DeBenedittis, M. Cigada, A. Bianchi, M.G. Signorini, S. Cerutti, Autonomic changes during hypnosis: a heart rate variability power spectrumanalysis as a marker of sympatho-vagal balance, Int. J. Clin. Exp. Hypn. 42 (42) (1994) 140–152. [2] A.E. Aubert, B. Verheyden, F. Beckers, J. Tack, J. Vandenberghe, Cardiac autonomic regulation under hypnosis assessed by heart rate variability: spectral analysis and fractal complexity, Neuropsychobiology 60 (2) (2009) 104–112. [3] A.E. Aubert, D. Ramaekers, Neurocardiology: the benefits of irregularity. The basics of methodology, physiology and current clinical applications, Acta Cardiol. 54 (3) (1999) 107–120. [4] S.G. Diamond, O.C. Davis, R.D. Howe, Heart-rate variability as a quantitative measure of hypnotic depth, Int. J. Clin. Exp. Hypn. 56 (1) (2008) 1–18. [5] G.G. Berntson, D.L. Lozano, Y.J. Chen, Filter properties of root mean square successive difference (RMSSD) for heart rate, Psychophysiology 42 (2) (2005) 246–252.
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Contents lists available at ScienceDirect
Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc
Heart rate variability analysis during hypnosis using wavelet transformation Xiuwen Chen a , Rongqian Yang a,∗ , Lulu Ge b , Lei Zhang c , Ruixue Lv c a b c
Department of Biomedical Engineering, South China University of Technology, Guangzhou, China Guangzhou Municipal Public Security Bureau, Guangzhou, China Shenzhen Sayes Medical Technology Co., Ltd., Shenzhen, China
a r t i c l e
i n f o
Article history: Received 19 April 2016 Received in revised form 19 June 2016 Accepted 7 July 2016 Keywords: Autonomic nervous system Heart rate variability Hypnosis Wavelet transformation
a b s t r a c t Hypnosis can act on the autonomic nervous system which can be presented by heart rate variability (HRV). So HRV implies many information related to hypnosis. Because HRV signal is time-variant and non-stationary, the traditional methods, such as Fourier transform and AR spectral estimation, are unable to analyze it. Hence, wavelet time-frequency analysis is applied here to not only offer superior time and frequency resolution, but also detect sudden amplitude and frequency jumps. The electrocardiograms of subjects were recorded under hypnosis, from which the corresponding HRV signals are obtained. The instant parameters including HRV, very low frequency (VLF), low frequency (LF), high frequency (HF), and the ratio of LF to HF (LF/HF) components of each HRV signal are then computed. Furthermore, mean, coefficient of variation, skewness, and kurtosis of independent frequency components in four hypnotic states (resting state, inducing state, imagining state and awaking state) were also obtained from the instant parameters to describe variation during hypnosis. The experiment results show that the parameters of HRV can reflect some physiological features of hypnosis, e.g., the LF/HF was more concentrative and steady in imagining state. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction Clinical hypnosis is a mind-body technique that operates at the intersection of subjective perceptions and objective physiological changes. Many researches illustrated that hypnosis can be characterized by a decreased sympathetic tone and an increased parasympathetic activity [1], where sympathetic nervous system (SNS) and parasympathetic nervous system (PNS) are the two main branches of autonomic nervous system (ANS). In addition, autonomic cardiac tone was significantly modified during hypnosis by shifting the balance of the ANS toward an enhanced PNS modulation, accompanied by a reduction of the SNS tone and a decreased short-range similarity but without a concomitant change in heart rate [2]. Heart rate variability (HRV) is often used to assess function of ANS [3]. The measure of the ANS response to hypnosis can be obtained from analyzing the HRV parameters of frequency domain [4]. Low frequency (LF) component of HRV signal is influenced by both SNS and PNS and it may reflect the thermal control and barore-
∗ Corresponding author. E-mail address: [email protected] (R. Yang). http://dx.doi.org/10.1016/j.bspc.2016.07.004 1746-8094/© 2016 Elsevier Ltd. All rights reserved.
flex control of blood pressure through HRV. High frequency (HF) component is controlled by PNS and it is associated with respiratory activity. Although respiratory sinus arrhythmia occurs within the HF band, this condition can also occur at other frequencies. The ratio of LF and HF (LF/HF) is considered to reflect balance between SNS and PNS [5–7]. Some traditional methods, such as Auto-regressive (AR) spectral estimation and Fourier transformation, are the most popular methods to analyze HRV [8]. These methods to estimate spectrum presupposed that HRV is stationary and time-invariant signal. However, HRV is non-stationary signal in the long term, especially in hypnosis. The different stages of hypnosis results in the change of HRV parameters due to the individual received different external stimulus. The HRV parameters still vary even in the same stage. Therefore, traditional methods are not effective to analyze hypnotic HRV signal. On the other hand, traditional methods can only quantify the amplitude of heart rate oscillations, without providing temporal information [9]. The variability of instantaneous power of independent frequency components under hypnosis is extremely valuable, which maybe imply some important information. Compared with traditional methods, wavelet transformation (WT) can not only analyze non-stationary signal like hypnotic HRV and offer superior time and frequency resolution, but also has the
2
X. Chen et al. / Biomedical Signal Processing and Control 31 (2017) 1–5
ability to detect sudden amplitude and frequency jumps [10]. There are three main classes of wavelet analysis: Continuous Wavelet Transform (CWT), Discrete Wavelet Transform (DWT), and Wavelet Packet Transform (WPT). DWT and WPT are useful for compact representation of data, particularly for noise reduction, and can also for analyzing power spectrum of HRV [11–14]. However, DWT and WPT do not have subtle frequency resolution in terms of timefrequency analysis. Whereas, the CWT is the best one for feature extraction [15]. Only CWT is studied here because we are interested in extracting low s/n ratio signals in time series. We recorded and analyzed the changes of independent frequency components of subjects who were under hypnosis. Then some statistical features are computed by assessing the short-time variation of frequency components including mean, coefficient of variation, skewness and kurtosis of instantaneous power of independent frequency components at all the four states (resting state, inducing state, imagining state, and awaking state). It will indicate the change rule of frequency components of HRV under hypnosis and further compare the statistical features of these components in different hypnotic conditions. 2. Statistical feature extraction using Wavelet technique 2.1. Acquisition of HRV signal There are four states during hypnotic test. First, in resting state, subjects breathe normally with their eyes closed and lie quietly without moving before hypnosis. Second, in inducing state, subjects are guided to relax progressively and respond suggestions. Subjects are considered to be hypnotized when roving eye movements are observed or the subject respond by a hand movement that he or she feels to be hypnotized [16]. Third, in imagining state, subjects are invited to imagine pleasant and peaceful scene, and they are instructed to feel their subconscious and positive energy. This process is an alteration in perception, sensation, emotion, thought, or behavior through imagination and suggestion. Four, in awaking state, subjects return to waking state with completion of hypnosis. They breathe normally with their eyes closed and lay quietly without movement. Electrocardiography (ECG) signals and videos of subjects in the whole tests are recorded in all the four states. The subjects are documented with a video camera for detailed analysis after recording ECG. ECG is recorded in supine position by using three-limb ECG leads (ECG-B; SAYES, Shenzhen, China) through Red DotTM Ag/AgCl disposable electrodes placed in accordance with a sample rate at 500 Hz. Then the peaks of this ECG are extracted and resampled at 4 Hz to obtain HRV signal h(t). h(t) is segmented into four part hi (t) according the four hypnotic states, i = 1, 2, 3, 4. 2.2. Time-frequency analysis of HRV signal After the hi (t) is obtained, WT is used to compute its wavelet power coefficients WT(t,a) as follows 1 WT (a, b) = √ a
=
t−b hi (t) ∗ ( )dt a √
a
ejwt hi (w) ∗ (aw)dw
(1)
(2)
where * represents conjugate, the scaling factor a and shifting factor b are real and a > 0, the w is the angular frequency. hi (t) is the HRV signal in the ith state and (t) is the Morlet wavelet. After WT, a data matrix containing time, scale, and wavelet coefficients is obtained. Actually, the WT is not a function of time and frequency but time and the scaling factor a. Because scale is related
to frequency,PWT (t,a) is called the scalogram and it defines a joint density of time and scale [17], 1 |WT (t, a) |2 2Ca2
PWT (t, a) =
1 2Ca2
The factor
(3)
is inserted for proper normalization. The constant
C is chosen to obtain the energy by using WT,
C=
2
| (w)| dw |w|
(4)
A reference frequency wr is chosen from w = wr /a to obtain a time-frequency density. Finally, wavelet time-frequency analysis can be expressed by [18] wr PWT w2
PWT (t, w) = =
1 |WT 2Cwr
t, a =
w r t,
w
|
wr w
(5)
2
(6)
Then, the instantaneous power PWT (t, w) is obtained from Eq. (6), which contains the messages of time and frequency. For assessing the instantaneous power of independent frequency components of HRV, the frequency spectrum is divided into three parts: very low frequency (VLF, 0.003–0.04 Hz):
0.04
PVLF (t) =
PWT (t, f ) df
(7)
0.003
where f=2/w, frequency interval is related to the scaling factor a, and the frequency range from 0 to 2 Hz. Low frequency (LF, 0.04–0.15 Hz) spectrum is:
0.15
PLF (t) =
PWT (t, f ) df
(8)
0.04
and high frequency (HF, 0.15–0.40 Hz) spectrum is:
0.40
PHF (t) =
PWT (t, f ) df
(9)
0.15
2.3. Statistical analysis of independent frequency components In the process of hypnosis, the instantaneous power of independent frequency components changes with the time. In order to describe this variation, four parameters of statistical features are used: mean, coefficient of variation, skewness, and kurtosis. Mean represents mean value of instantaneous power at each hypnotic state. Coefficient of variation is defined as the ratio of standard deviation to mean, which shows the extent of variability in relation to the mean of the population [19]. Coe[X] =
(10)
where X represents instantaneous power of independent frequency components, represents mean value and represents standard deviation. Skewness can reflect the degree of asymmetry in the histogram of instantaneous power: Skew[X] = E
X − 3
=
E X 3 − 3 2 − 3 3
(11)
where E is the expectation operator. If the histogram is symmetrical, the skewness is zero. If the left hand tail is longer, the skewness will be negative. If the right hand tail is longer, the skewness will
X. Chen et al. / Biomedical Signal Processing and Control 31 (2017) 1–5
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be positive [20]. Kurtosis is a measure for the degree of flatness or peakedness in the variable distribution: Kurt[X] =
2
E (X − )3 E (X − )2
(12)
High kurtosis tends to have a distinct peak near the mean, decline rather rapidly, and have heavy tails, while low kurtosis tends to have a flat top near the mean rather than a sharp peak. The standard normal curve of instantaneous power has a kurtosis of zero [20,21]. Mean, coefficient of variation, skewness, and kurtosis are the effective statistical features which are able to describe the variation of instantaneous power of independent frequency components changed over time. 3. Experimental results 3.1. Subjects and data recording
Fig. 1. The tridimensional plot of time, frequencies, and wavelet coefficients in the resting, inducing, imagining, and awaking states of a subject under hypnosis.
After informed consents, 12 subjects were enrolled in this study (9 female and 3 male, with mean age of 31.1 ± 5.4 years, mean height of 163.6 ± 6.3 cm, and mean weight of 57.8 ± 5.4 kg). None of the subjects reported any history of myocardial infarction, arrhythmia, alcohol abuse, head injury, or epilepsy. Moreover, these subjects had not consumed caffeine-containing drinks in the last 24 h before hypnosis. Two subjects dropped out because they did not reach a trance state. The remained 10 subjects met the requirement of this study, who did have the abnormal ECG, such as a heart rate of <50 beats per minute, or the presence of conduction disturbance. Subjects were individually hypnotized by an experienced hypnotist. In this hypnotic test, subjects experienced four states (resting state, inducing state, imagining state, and awaking state). ECG signals and videos of them were recorded. After peak extracting and resampling of ECG signal, HRV signal h(t) was obtained. According to Eq. (2), wavelet power coefficients WT(t,a) were calculated and the instantaneous power PWT (t, w) is obtained in Eq. (6). Instantaneous power of independent frequency components PVLF (t), PLF (t), and PHF (t) were calculated from Eq. (7)–(9). The ratio of LF and HF: LF/HF(t) = PLF (t)/PHF (t). Then the statistical features (mean, coefficient of variation, skewness and kurtosis) of frequency components were calculated in four hypnotic states by Eq. (10)–(12). 3.2. Statistical analysis The statistical analysis of all the results was performed. Due to the relationship between resting state, inducing state, imagining state, and awaking state differences between these states were analyzed using a non-parametric test (Friedman test). Statistical significance was defined as p < 0.05. Values were presented as mean and standard deviation. 3.3. Results 10 subjects met the requirements of this study and experienced trance states. We found a significant (p < 0.05) change of HRV parameters in these four states. The major difference between the resting state, inducing state, imagining state, and awaking state was in LF/HF: coefficient of variation (p=0.045), kurtosis (p=0.016) and skewness (p=0.040) of LF/HF were significantly different between these four states. Especially, compared to the other three states, coefficient of variation, kurtosis, and skewness of LF/HF were lower in imagining state. In addition, these results show no significant change in HRV and other independent frequency components such as VLF, LF, and HF.
Fig. 2. Global heart rate variability, independent frequency (VLF, LF, HF) and the LF/HF in the four hypnotic states of a subject.
The tridimensional plot of time, frequency, and, wavelet coefficients data in the resting state, inducing state, imagining state, and awaking state of a representative subject under hypnosis was exhibited in Fig. 1. Wavelet coefficients decreased when subject in inducing and imagining states, and increased in awaking state. As to a subject described in Fig. 1, the global HRV, independent frequency (VLF, LF, and HF) and LF/HF in the four hypnotic states were drawn in Fig. 2. HRV was steadier in inducing and imagining states but it fluctuated in waking state. Compared to the resting state, HF in imagining state was significantly increased and fluctuated. In addition, when subject was returning to waking state from imagining state, the curves of LF, HF, and LF/HF changed suddenly. Table 1 summarizes the mean, coefficient of variation, kurtosis, and skewness of HRV, VLF, LF, HF and LF/HF between the four hypnotic states. The coefficient of variation, kurtosis, and skewness of LF/HF differed significantly (p < 0.05) in these four states.
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X. Chen et al. / Biomedical Signal Processing and Control 31 (2017) 1–5
Table 1 Comparisons of mean, coefficient of variation (CV), skewness (SKE), and kurtosis (KUR) of heart rate variability (HRV), very low frequency (VLF), low frequency (LF), high frequency (HF) and the ratio of LF to HF (LF/HF) components between the four hypnotic states. rest HRV mean HRV CV HRV KUR HRV SKE VLF mean VLF CV VLF KUR VLF SKE LF mean LF CV LF KUR LF SKE HF mean HF CV HF KUR HF SKE LF/HF mean LF/HF CV LF/HF KUR LF/HF SKE
751.6 0.05 2.86 −0.15 763.6 0.38 2.69 0.41 735.6 0.39 5.78 0.97 307.7 0.46 4.60 0.91 3.03 0.61 10.62 2.21
induce ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
40.8 0.01 0.38 0.35 246.9 0.16 0.72 0.61 283.1 0.10 5.96 1.00 136.0 0.14 2.88 0.44 1.95 0.13 3.51 0.49
790.1 0.06 3.30 0.08 670.8 0.41 2.53 0.60 553.3 0.47 3.11 0.69 418.2 0.47 4.55 1.15 1.75 0.61 8.07 1.76
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
imagine 48.0 0.02 0.76 0.57 285.0 0.14 0.76 0.40 281.5 0.14 1.34 0.48 190.9 0.12 1.72 0.58 1.16 0.17 6.12 0.85
813.9 0.05 3.34 −0.09 541.9 0.25 2.61 0.04 651.2 0.37 2.76 0.49 508.3 0.38 3.11 0.66 1.51 0.46 4.98 1.08
± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
awake 38.0 0.01 0.65 0.68 124.8 0.12 0.61 0.43 187.9 0.13 0.74 0.48 189.1 0.10 0.94 0.40 0.70 0.08 2.67 0.56
815.4 0.07 2.78 0.11 1046.0 0.29 2.19 0.04 1056.7 0.44 2.87 0.80 583.7 0.47 4.07 0.91 2.26 0.63 7.96 1.87
p ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±
58.1 0.03 0.48 0.44 313.6 0.13 0.41 0.35 488.4 0.17 0.81 0.30 293.7 0.17 1.23 0.56 1.44 0.23 2.39 0.42
0.057 0.072 0.137 0.316 0.334 0.481 0.532 0.108 0.254 0.316 0.091 0.481 0.115 0.532 0.352 0.644 0.352 0.045* 0.016* 0.040*
Note. *Friedman test, p < 0.05.
4. Discussion and conclusions In this study, the wavelet time-frequency analysis was used to separately analyze the regularity of the different frequency components of HRV in subjects who were under hypnosis. Parameters of statistical features (mean, coefficient of variation, skewness, and kurtosis) were used to describe the changes of independent frequency components under hypnosis. The experimental results show that the coefficient of variation, kurtosis, and skewness of LF/HF in imagining state are lower than the other three states. It is possible that the statistical feature can be extracted using wavelet time-frequency analysis and further applied to study the physiological variety in hypnosis. Compared to AR spectral estimation and Fourier transform, the advantages of the wavelet time-frequency analysis are that it can be applied on non-stationary time series and offer time and frequency resolution [10,22]. Assessing HRV signal with DWT, we can observe the changes of frequency with time, just like Fig. 1. The changes of independent frequency components under hypnosis like Fig. 2 can be obtained using wavelet time-frequency analysis. The mean, coefficient of variation, skewness, and kurtosis of HRV and independent frequency components (VLF, LF, HF, LF/HF) in four hypnotic states were calculated by the statistical features in Table 1. Although, the mean of independent frequency components could be obtain through AR spectral estimation or Fourier transform, the parameters which are able to describe variation, such as coefficient of variation, skewness and kurtosis can only be obtained through wavelet time-frequency analysis. HRV is a physiological signal related to functions of ANS and the measurement of HRV is a sensitive method to assess ANS [23]. The results show that the HRV, VLF, LF, HF exhibit spontaneous fluctuations even at rest that reflect the influence of the ANS. The coefficient of variation, kurtosis, and skewness of LF/HF were significantly different between these four states. In the imagining state, coefficient of variation, kurtosis, and skewness of LF/HF were lower than in the other three states, which indicated that LF/HF was more concentrative and steady in imagining state. Seeing, feeling, smelling and thinking of person under hypnosis will change according to hypnotist’s suggestions. Hypnosis might result in metabolic, cardiac, and cognitive activations [16]. Our results suggest that there is physiological variety during hypnosis. LF/HF can be considered to reflect the balance between SNS
and PNS and used as a measure of this balance. LF/HF is more concentrative and steady in imagining state, which would imply an increased modulation of ANS, especially of the enhanced PNS and reduced SNS. It proved that hypnosis is associated with a decreased sympathetic tone and an increased parasympathetic activity, and the balance between SNS and PNS is shifted. This study effectively applied wavelet time-frequency analysis to extract the statistical features of HRV under hypnosis which can imply that the balance of ANS is modulated under hypnosis. It indicated the changing regularity of HRV, independent frequency (VLF, LF, and HF) and LF/HF in the four hypnotic states. The LF/HF was more concentrative and steady in imagining state. The further research may apply wavelet time-frequency analysis to study the change of HRV of depression patients under hypnosis because hypnosis is adjuvant treatment method of depression and HRV of depression patients behaves abnormality. There are important clinical significance for studying the change rule of HRV and evaluating the effect of hypnotic treating depression. Acknowledgments This research was funded by the Shenzhen Science and Technology Program under Grant No. CXZZ20140903161225943 and No. CXZZ20150529144549687, the Guangdong Provincial Science and Technology Program under Grant No. 2016A020220011, the Guangzhou Science and Technology Program under Grant No. 201604020107. References [1] G. DeBenedittis, M. Cigada, A. Bianchi, M.G. Signorini, S. Cerutti, Autonomic changes during hypnosis: a heart rate variability power spectrumanalysis as a marker of sympatho-vagal balance, Int. J. Clin. Exp. Hypn. 42 (42) (1994) 140–152. [2] A.E. Aubert, B. Verheyden, F. Beckers, J. Tack, J. Vandenberghe, Cardiac autonomic regulation under hypnosis assessed by heart rate variability: spectral analysis and fractal complexity, Neuropsychobiology 60 (2) (2009) 104–112. [3] A.E. Aubert, D. Ramaekers, Neurocardiology: the benefits of irregularity. The basics of methodology, physiology and current clinical applications, Acta Cardiol. 54 (3) (1999) 107–120. [4] S.G. Diamond, O.C. Davis, R.D. Howe, Heart-rate variability as a quantitative measure of hypnotic depth, Int. J. Clin. Exp. Hypn. 56 (1) (2008) 1–18. [5] G.G. Berntson, D.L. Lozano, Y.J. Chen, Filter properties of root mean square successive difference (RMSSD) for heart rate, Psychophysiology 42 (2) (2005) 246–252.
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