Technology and Health Care 22 (2014) 885–894 DOI 10.3233/THC-140853 IOS Press

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Correlation study in respiration fluctuations during sleep stages Yanjun Zhanga,b , Xiangmin Zhangc , Chengwen Yand , Wenhui Liub, Enjia Yuc and Yuxi Luoa,∗ a School

of Engineering, Sun Yat-Sen University, Guangdong, China University, Guangdong, China c Sleep-Disordered Breathing Center of the 6th Affiliated Hospital of Sun Yat-Sen University, Guangdong, China d Department of Mechanical, Electro-Mechanical Engineering National Sun Yat-Sen University, Kaohsiung, Taiwan b Jinan

Received 27 May 2014 Accepted 17 July 2014 Abstract. BACKGROUND: Healthy sleep can be characterized by several stages: wake, light, SWS, and REM sleep. The clinical experts find that the breath of subjects is different in these sleep stages, but such observation is lacking data supporting, The statistical research about investigating breathing patterns during sleep process will be helpful for the sleep and breathing domain. OBJECTIVE: The objective of the paper is to statistically analyze the respiratory characteristics during different sleep stages. METHODS: Firstly, we calculated the mean value and standard deviation of respiratory rates of these stages, in which the respiratory rates were obtained by the autocorrelation method. Then the detrended fluctuation analysis (DFA) algorithm was applied to analyze long-range correlation of respiratory rates of sleep stages. RESULTS: The mean and standard deviation of respiratory rates are wake: 16.62 ± 2.43 cycles per minute (CPM), light: 15.15 ± 1.53 CPM, SWS: 15.06 ± 0.96 CPM and REM: 16.37 ± 2.03 CPM, respectively. The scaling exponent applied by detrended fluctuation analysis (DFA) algorithm reached about 0.7 for each stage. CONCLUSION: Results of the mean and standard deviation of respiratory rates show that different sleep stages lead to different autonomic regulations of breathing and exhibit different respiratory rates and fluctuations. And the DFA results demonstrate that respiratory rates are all long-range correlated in these stages although they lead to different fluctuation. Keywords: Sleep stages, autocorrelation, detrended fluctuation analysis (DFA)

1. Introduction Healthy sleep can be characterized by several stages: wake sleep, light sleep, SWS sleep, and REM sleep. According to the experience of clinical experts, the breath of subjects is quickly and fluctuatedly in wake and REM sleep stage; while as the deepening of sleep process, it will gradually become slowly and steadily in light and SWS sleep. Researches found that sleep stages can be speculated from respiratory information [1–8], while ventilated control strategy can be designed according to sleep structures and ∗ Corresponding author: Yuxi Luo, School of Engineering, Sun Yat-Sen University, Guangdong 510006, China. Tel.: +86 13631462576; E-mail: [email protected].

c 2014 – IOS Press and the authors. All rights reserved 0928-7329/14/$27.50 

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Fig. 1. Sleep-breathing monitoring of subjects applied Alice 5 PSG, Philips, Inc in the clinical experiment; (a) nose thermistor and nose pressure; (b) thorax belt and abdomen belt. (Colours are visible in the online version of the article; http://dx. doi.org/10.3233/THC-140853)

conditions [9,10]. Nevertheless, no reliable statistical data support this assertion so far. Thus, this paper statistically analyzes the breathing patterns during sleep process. There are many methods to obtain respiratory rates in previous literatures [11–13]. But these reported methods usually can not precisely identify the peak values of respiratory signals. By combining the advantages of previous literatures [11–13] and the clinical situations, we used the autocorrelation method to obtain the average respiratory rate of each epoch (30 seconds). Sleep physiological information, especially respiratory signals, is not only the complex and nonlinear, but also non-stationary and stochastic. So the physiological information gets much more complicated in many cases and the signals are hard to be directly analyzed by typical linear analysis methods. Common nonlinear methods, such as calculating the correlation dimension and lyapunov exponent, also require steady or quasi-steady conditions which is hardly possible for physiological signals processing [11–13]. In summary, some statistical methods should be combined to conduct an all-around analysis. Recently, a method of statistical physics – detrended fluctuation analysis (DFA) had been introduced into the analysis of physiological signals and had achieved initial success [13–15]. It is suitable for a number of non-stationary time series studies of long-range power function correlation. DFA algorithm can systematically remove different trends caused by external factors and lower the noise level due to imperfect measurements. Finally, DFA can successfully verify whether the sequence is long range-correlation. Therefore, we calculated the mean value and standard deviation of respiratory rates of different sleep stages and then applied DFA method to shed light on respiratory characteristics of each sleep stage. Previous literatures had also done some research on respiration and heart beat events during sleep process [13–15]. Gih Sung Chung et al. [13] identified the REM sleep with the characteristics extracted from breathing, the accuracy rate of recognition reaching up to about 87%. The research was merely distinguishing between REM and non-REM sleep [13]. In reference [14,15] correlation researches on sleep stages and respiration, and which on sleep stages and heartbeat had been done, while they simply conducted DFA correlation analysis of sleep physiological signals. In this study, experts used AASM rules for sleep staging [16,17], which was more suitable than R&K rules [18]. This study tries to explain the correlation problems of respiration and sleep stages, and to get different laws of respiration in different stages. The results can be benefit for sleep and breathing domain, such as improving the flexibility study of sleep ventilator, or estimating sleep stages without disturbing sleep, etc.

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T-Flow P-Flow THO ABD EEG EOG EMG 0

3

6

Time/s

9

12

15

Fig. 2. Respiratory signal oscillogram of four routines of 15 seconds. Note: T-Flow, nose thermistor; P-Flow, nose pressure; THO, thorax belt; ABD, abdom belt; EEG, Electroencephalogram; EOG, Electrooculogram; EMG, Electromyogram.

Fig. 3. Schematic representation of this study.

2. General solution and experimental data In this study, all-night polysomnographic (PSG) sleep recordings were obtained from 30 healthy subjects (22 males and 8 females) ranging from 31 to 65 years old (mean = 46.6 ± 12.8 years). These measurements were approved by the ethics committee of the 6th affiliated hospital of Sun Yat-Sen University. The subjects were interviewed about their sleep quality, medical history and all subjects reported no history of neurological or psychological disorders. The all-night PSGs were recorded in the Sleepdisordered Breathing Center of the 6th affiliated hospital of Sun Yat-Sen University (by Alice 5 PSG, Philips, Inc.). There was also no outside interference during data collection, and no medications were utilized to cause sleep. Figure 1 shows the details of data collection in the experimental. PSG is a systematic method which records the biophysiological signals that take place in the sleep process. The standard of visual sleep staging is based on the R&K rules, which is firstly proposed by Rechtschaffen and Kales in 1968 [18]. According to the R&K rules, each epoch (i.e., 30 s of data) is divided into each sleep stage, including wakefulness (wake), non-rapid eye movement (stages 1–4, from light to deep sleep) and rapid eye movement (REM). Stages 1 and 2 are usually called as light sleep stage, and stages 3 and 4 are commonly combined as the slow wave sleep (SWS) stage. Instead of the R&K rules, the scoring rules developed by the AASM have become the clinical standard in recent years [16, 17]. Figure 2 presents the typical PSG respiratory signals and the main sleep interpretation signals (gold standard) respectively.

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Thirty PSG sleep recordings were visually scored by sleep specialists using the AASM rules with a 30-s interval (termed the epoch). Of the twenty-eight channels of recordings obtained via PSG that we used to represent sleep and respiration, respiration was obtained from four channels, which are nose thermistor and nose pressure placed near the nose, and the thorax belt and abdomen belt signals related to volume changes of the thorax and abdomen, respectively. The nose thermocouple is a common sensor for obtaining a clear respiratory rate. And during some sleep events, the belt sensor can be a supplement under the condition that the thermocouple falls off. Figure 3 presents the flowchart of our method. 3. Autocorrelation method and DFA algorithm 3.1. Estimation of respiratory rate by autocorrelation method Since the respiratory signal is highly susceptible to external noise and interference, autocorrelation method was used to obtain the respiratory rates of each epoch (30 seconds) by following equation [11– 13]: Rxx(i,n) (τ ) =

1 N

N −τ −1

s(i,n) [m]s(i,n) [m + τ ]

(1)

m=0

where s, τ and N denote the respiratory signal, time delay and total number of samples in an epoch respectively. Autocorrelation, calculated from the raw respiratory signal, fluctuates periodically in an average respiration interval. Following the detection of the first peak, the respiratory rate was determined by using the following formula: frate =

fs

(2)

τpeak

where τpeak represents the delay of the first peak, and fs and frate denote the sampling and estimate respiratory rates, respectively. The mean value of the respiratory rates can be extracted by fratem =

M 1  fratei M

(3)

i=1

where frate is the respiratory rate array and fratem denotes the mean value of the respiratory rate array of an epoch. 3.2. Detrended Fluctuation Analysis (DFA) algorithm Here, we apply the detrended fluctuation analysis (DFA) to analyze the sleep signals [19–21]. One reason is that DFA can avoid spurious detection of correlation which is artefacts on nonstationarities in the time series. Let respiration time series be x(i) and length be N . Then the scaling exponent α is calculated according to the following steps: (1) Constructing sum sequence of the demeaned value. i  Y (i) = xk − x, i = 1, 2 · · · , N (4) k=1

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(2) We divided the sum sequence Y (i) into several non-overlapping segments with the length s. The number of the segment is Ns , which is int (N /s). Since the length N in the data may be not a multiple of the time scale s, a short part of the data may remain. In order not to disregard this part of the data, the same procedure was repeated starting from the opposite end of Y (i). Thereby, 2Ns segments were obtained altogether. (3) Calculating the local trend for each of the 2Ns segments. Ys (i) = Y (i) − pv (i) (5) Here, pv (i) is the fitting polynomial of the v-th segment. The order n of the polynomial can be 1 (linear), 2 (square), 3 (cube) or higher. (4) We calculated the root-mean-square of the 2Ns detrended segments, that is, the fluctuation function. s  2  1 2 Fs (v) = Ys (i) = Ys2 [(v − 1) s + i] (6) s i=1



2N 1 s 2 F (S) = Fs (v) 2Ns

1/2 (7)

v=1

Fluctuation function F (S), obtained from different detrended orders n, presented as F (n) (s). Then the dependency between F (n) (S) and s was calculated. Apparently, F (S) will increase with the increasing of s. If the original sequence x(i) is related to the long-range power-law, then F (S) increases by means of the power function: F (n) (s) ∝ sa (8) Here, α (=1/2) is called the scaling exponent. (5) Drawing the function relationship of F (S) and s by log-log scales and calculating the slope of the curve, which is the value of α by linear fitting. 4. Experiment The sampling rates of EEG, EOG and EMG signals were 500 samples per second. The signals sampling rate was decreased to 250 samples per second to reduce computational load. The sampling rate of respiratory signals was 100 samples per second. Respiratory rate was continuously measured during an all-night PSG in a sleep laboratory using nose thermistor and nose pressure, thorax and abdomen belt. The continuous time signals were divided into continuous 30 s epochs. The sleep stages have been determined by visual evaluation of PSG recordings. The mean respiratory rate in one-night sleep process of a healthy subject was represented in Fig. 4. The largest rate fluctuation usually occurred at the transitions between sleep stages and wake stages, often associated with body movements. To eliminate these large fluctuations representing local trends, we analyzed the sleep stages separately and skipped the unrealistic and disturbed epochs whose average respiratory rate went far beyond normal respiratory scope. 4.1. Statistical results We obtained the all-night respiratory rates via autocorrelation method as mentioned above. Then according to sleep stages, we classified respiratory rates of different sleep stages. Finally, the mean value

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Fig. 4. Representative one-night record of sleep stages and respiratory rates for a healthy subject.

and standard deviation of respiratory rates in wake, light, SWS, REM stages and all-night sleep were calculated and were shown in Table 1. Statistical results in Table 1 showed that respiratory condition are autonomic for each stage, in which is that wake: 16.62 ± 2.43 cycles per minute (CPM), light: 15.15 ± 1.53 CPM, SWS: 15.06 ± 0.96 CPM and REM: 16.37 ± 2.03 CPM, respectively. The mean values and standard deviations of wake and REM ˇ stages are larger than other stagesïijNwhich proves that the respiratory rhythms are quicker and more fluctuated. The mean values and standard deviations of light and SWS are becoming lower, indicating that from light sleep to deep sleep, the respiratory rhythms are slow and breath is becoming steady. It also can be observed that there are differences and fluctuations between the mean values and standard deviations of respiratory rates in wake, light, SWS and REM stages. Thus, we need to further prove whether this will influence the long range-correlation and the autonomic regulation of each stage.

4.2. DFA analysis DFA algorithm was adopted to compute the long-range correlation of relevant cases and the trend of respiratory rate in each stage. Figure 5 shows the analysis results of respiratory rate of one subject. From Fig. 5 long-range correlations (α > 0.5) occur during all these sleep states. The fitting trend error of DFA1 is larger. The effect of DFA2 and higher order is good and consistent. However, the polynomial fitting of DFA3 and higher order consist large amount of calculation. Thus, the experiment used DFA2 for data analysis which is recommended [19–21]. With the analysis of respiratory rates of each continuous sleep stages by DFA, we obtained, α = 0.72 in wake stage, α = 0.72 in light stage, α = 0.71 in SWS stage and α = 0.76 in REM stage, respectively. The all-night correlation rate was 0.69. Results in wake, light, SWS and REM stages conformed to the law of autonomic regulation in a variety of samples. Experimental results showed that respiration in sleep stages was long-range correlation.

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Table 1 Mean value and standard deviation of respiratory rates, cycles per minute (CPM), in wake, light, SWS, REM stages and all-night sleep of 30 subjects Subject 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Mean of 30 subjects

Wake mean S.D. 17.22 2.8 16.26 1.24 14.38 2.32 19.64 3.02 17.66 1.74 17.42 3.4 15.68 1.88 18.12 2.68 21.34 1.6 17.34 2.78 16.68 2.62 15.46 2.66 14.2 1.28 13.08 1.62 19.06 2.08 17.56 2.62 16.66 2.32 14.36 2.28 12.96 2.06 15.7 2.94 17.14 2.46 16.88 2.62 20.28 3.24 15.9 2.26 17.12 2.88 15.52 2.82 14.08 2.3 16.28 3.02 18.26 2.34 16.52 3.22 16.62 2.43

Light mean S.D. 14.46 1.46 16.96 1.44 12.9 1.52 14.94 1.4 14.6 1.48 15.18 2.28 16.54 1.52 15.22 2 20 1.86 15.16 1.86 15.42 1.26 15 1.54 14.82 1.08 13.58 1.02 17.54 1.22 15.82 1 16.3 1.96 14.86 1.46 11.48 0.8 11.74 1.7 15.7 1.54 16.1 1.26 16.98 1.46 13.7 1.74 15.3 1.52 14.4 1.38 13.52 1.4 17.2 2.34 16.58 1.54 12.74 2 15.15 1.53

SWS mean S.D. 14.62 0.44 18.44 0.46 13.32 1.32 15.14 0.86 14.48 0.9 16.04 1.46 17.66 0.98 16.04 1.48 18.42 1.52 15.16 1.12 16.06 0.98 15.28 0.66 15.08 0.84 13.28 0.8 17.38 0.76 16.28 0.46 15.3 0.98 14.08 0.98 11.38 0.54 11.2 0.8 15.32 0.88 16.14 0.9 16.14 0.66 13.32 1.08 14.12 0.52 14.84 0.66 12 1.06 16.38 2.42 16.08 0.82 12.84 1.48 15.06 0.96

REM mean S.D. 15.6 2.04 16.76 1.86 14.04 1.9 16.58 2 17.78 2.66 16.42 2.5 17.6 2.14 16.28 1.92 20.48 1.9 16.64 3.12 16.14 1.56 16.2 1.92 16.64 1.84 15.56 1.86 18.22 1.68 17.44 1.52 17.34 2.44 15.54 2.2 12.18 1.56 14.34 1.74 17.88 1.52 16.84 2.42 18.4 2.1 15.88 1.92 15.52 2 14.46 1.98 13.72 1.8 17.64 2.74 19.06 2.04 14.12 2.22 16.37 2.03

All-night mean S.D. 14.92 1.84 16.92 1.56 13.24 1.74 15.9 2.42 15.44 2.16 15.98 2.76 16.92 2 16 2.48 20.2 1.9 15.84 2.38 15.88 1.68 15.16 1.74 14.74 1.3 13.9 1.54 17.8 1.48 16.44 1.58 16.38 2.1 14.72 1.92 12.14 1.06 12.86 1.44 17.18 2.08 16.36 1.9 17.5 2.16 15.16 1.88 15.92 2.12 14.18 2.12 13.34 1.86 17.2 2.84 16.98 2 15.28 2.2 15.68 1.94

5. Discussion The experiment adopted the clinical data from the Sleep-disordered Breathing Center, which often associated with great noise but truly reflecting practical situations. Accurate sleep staging is the basis for the research of all sleep respiratory events. Experts used AASM rules (clinical interpretation) to conduct accurate sleep staging [16,17] in this paper. And autocorrelation method used in this paper can identify the peak values of respiratory signals to calculate respiratory rates [11–13]. The physiological signal of sleep and breathing is complex and unsteady, so it is not easy to carry out statistical research. According to previous literatures [19–21], detrended fluctuation analysis (DFA) analysis was applied to study both heart rates and respiratory characteristics during sleep process. But these researches lacked the systematical correlation analysis of sleep-breathing physiological signals between the subjects clinical situation [13–15]. In our study, we did the statistical work of the sleepbreathing signal in some different accepts. Firstly, we calculated the mean value and standard deviation of respiratory rates of these sleep stages. Results show that these sleep stages lead to different autonomic regulations of breathing and different sleep stages show different respiratory rhythms and fluctuations. Simultaneously, detrended fluctuation analysis (DFA) was employed to explore long-range correlation

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Y. Zhang et al. / Correlation study in respiration fluctuations during sleep stages Table 2 DFA statistical results of 18 subjects: Respiratory rate analysis of wake, light, SWS, REM stages and all-night sleep

Subject 1 2 3 4 5 6 7 8 9 Mean

Wake 0.8 0.66 0.85 0.72 0.66 0.71 0.71 0.71 0.72 0.72

Light 0.79 0.72 0.66 0.69 0.76 0.65 0.73 0.67 0.73 0.72

SWS 0.66 0.55 0.86 0.71 0.77 0.73 0.81 0.74 0.82 0.71

REM 0.82 0.82 0.65 0.69 0.86 0.76 0.69 0.76 0.73 0.76

All-night 0.74 0.72 0.64 0.7 0.81 0.61 0.62 0.61 0.7 0.69

Subject 10 11 12 13 14 15 16 17 18

5

Wake 0.68 0.8 0.77 0.77 0.71 0.65 0.67 0.72 0.73

Light 0.71 0.73 0.69 0.75 0.73 0.73 0.78 0.75 0.73

SWS 0.67 0.64 0.75 0.63 0.72 0.73 0.79 0.55 0.78

REM 0.72 0.82 0.76 0.73 0.81 0.78 0.79 0.65 0.87

All-night 0.71 0.75 0.71 0.69 0.63 0.65 0.73 0.75 0.71

3

DFA1 DFA2 DFA3

DFA1 DFA2 DFA3 1

F(s)/s

α

1

0.1

0.1

(a)

2

(b)

7

DFA1 DFA2 DFA3

1

DFA1 DFA2 DFA3

1

0.1 0.07

0.2 4

10

scale (s)

(c)

55

4

10

scale (s)

55

(d)

Fig. 5. DFA for the respiratory rate of the representative subject. (a) wake, (b) light, (c) SWS and (d) REM sleep. (Colours are visible in the online version of the article; http://dx.doi.org/10.3233/THC-140853)

of respiratory rates due to the different respiratory fluctuations of each stage. As a result, we found that respiratory rates were all long-range correlated in these stages although they lead to different autonomic regulation. This statistically testified the clinical situation, that is, respiration of subjects boasted different characteristics in wake, light, SWS, REM stages. Such results proved that in clinic the breath is quick

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and fluctuated in wake and REM sleep; while as sleep process deepens, breath will gradually becomes slow and steady in light and SWS sleep [11–15]. The results can be benefit for sleep and breathing domain. Based on the results in this paper, it may obtain sleep depth from respiration without disturbing sleep. In addition, OSAS events are related to sleep depth. We suppose respiratory rates may be used to predict the OSAS events, and sleep ventilator can provide suitable pressure according to the prediction. Correlation laws of respiratory rates in sleep stages obtained by this paper are compared with previous literatures, and result was similar to some extent [14]. Such similarities may be a result of synchronizing with heart rate coupling, or maybe they derived from the same source such as the role of sympathetic nerve. The statistical result supported the latter opinion mentioned above, that is, the coupling and differences in values may be caused by the same source, i.e. sympathetic nerve activity, that sympathetic nerve activity is different in sleep stages while heartbeat and respiration is not affected by sympathetic nerve activity in wake stage. The standard deviations of respiratory rates followed the relation that wake>light>SWS as the deepening of sleep process, the mean respiratory rates follow a similar relation, but in REM sleep such fluctuation returned as larger as wake sleep. Subjects breathe in active conscious state in REM and wake stages because of the effect of sympathetic nerve. We speculate that in REM stage, subjects are in the dream, so the respiration is also regulated by active consciousness of nerve activity and is led to big fluctuation again [13–15]. Then from light to SWS stage, sleep shifted from light to deep, gradually weakening the leading role of consciousness towards breathing. This is an interesting clinical phenomenon that can be explained by the statistical results in this paper. Electroencephalogram (EEG) signals is the golden standard for sleep staging. Whether the relation between EEG entrory and respiration can explain our results need further research. 6. Conclusion This paper obtained the mean value, standard deviation and DFA correlation of respiratory rates in sleep stages. Statistical results showed that under the condition that respiratory rates exhibited longrange correlation, sleep stages that wake, light, SWS and REM led to different autonomic regulations of breathing and different sleep stages exhibited different respiratory rhythms and fluctuations. In wake and REM stages subjects breathe quickly and fluctuatedly; while as the deepening of sleep process, breath will gradually turn slowly and steadily in light and SWS sleep. Conflict of interest The authors indicated no potential conflicts of interest. Acknowledgments The authors would like to thank the Sleep-disordered Breathing Center of the 6th affiliated hospital of Sun Yat-Sen University for providing the PSG recording data and supervising our methods. And the authors appreciate the support from the National Natural Science Foundation of China (No. 51205421) and the Key Laboratory of Sensing Technology and Biomedical Instruments of Guangdong province (2011A060901013 ).

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Correlation study in respiration fluctuations during sleep stages.

Healthy sleep can be characterized by several stages: wake, light, SWS, and REM sleep. The clinical experts find that the breath of subjects is differ...
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