Comparison of Detrended Fluctuation Analysis

8/2/2019 Comparison of Detrended Fluctuation Analysis

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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003 1143

Comparison of Detrended Fluctuation Analysis andSpectral Analysis for Heart Rate Variability in Sleep

and Sleep ApneaThomas Penzel* , Member, IEEE, Jan W. Kantelhardt, Ludger Grote, Jrg-Hermann Peter, and Armin Bunde

AbstractSleep has been regarded as a testing situation forthe autonomic nervous system, because its activity is modulatedby sleep stages. Sleep-related breathing disorders also influencethe autonomic nervous system and can cause heart rate changesknown as cyclical variation. We investigated the effect of sleepstages and sleep apnea on autonomic activity by analyzing heartrate variability (HRV). Since spectral analysis is suited for theidentification of cyclical variations and detrended fluctuationanalysis can analyze the scaling behavior and detect long-rangecorrelations, we compared the results of both complementarytechniques in 14 healthy subjects, 33 patients with moderate,

and 31 patients with severe sleep apnea. The spectral parametersVLF, LF, HF, and LF/HF confirmed increasing parasympatheticactivity from wakefulness and REM over light sleep to deep sleep,which is reduced in patients with sleep apnea. Discriminanceanalysis was used on a person and sleep stage basis to determinethe best method for the separation of sleep stages and sleep apneaseverity. Using spectral parameters 69.7% of the apnea severityassignments and 54.6% of the sleep stage assignments werecorrect, while using scaling analysis these numbers increased to74.4% and 85.0%, respectively. We conclude that changes in HRVare better quantified by scaling analysis than by spectral analysis.

Index TermsHeart rate, human research, long-range correla-tions, polysomnography, scaling analysis, sleep, sleep apnea, spec-tral analysis.

I. INTRODUCTION

SLEEP as the absence of wakefulness and the missing abilityto react on external stimuli is regarded as a unbiased testsituation for the autonomic nervous system [1]. Sleep is not

just a constant state controlled by metabolic needs for the body

being at rest. Instead, sleep consists of different well-defined

sleep stages [2] which follow a well-structured temporal order

in normal restorative sleep [3]. Heart rate and heart rate vari-

ability (HRV) vary with the sleep stages, and their normal vari-

ability is affected in sleep disorders.

Manuscript received April 4, 2002; revised February 27, 2003. Asterisk indi-cates corresponding author.

*T. Penzel is with the Division of Pulmonary Diseases, Department of In-ternal Medicine, Hospital of Philipps-University, Baldingerstrasse 1, D-35033Marburg, Germany (e-mail: [email protected]).

J. W. Kantelhardt and A. Bunde are with the Institut fr Theoretische PhysikIII, Justus-Liebig-Universitt, D-35392 Giessen, Germany.

L. Grote is with the Department of Clinical Pharmacology, Sahlgrenska Uni-versity Hospital, Gothenburg, Sweden. He is also with the Division of Pul-monary Diseases, Department of Internal Medicine, Hospital of Philipps-Uni-versity, D-35033 Marburg, Germany.

J.-H. Peter is with the Division of Pulmonary Diseases, Department of In-ternal Medicine, Hospital of Philipps-University, D-35033 Marburg, Germany.

Digital Object Identifier 10.1109/TBME.2003.817636

It has been shown that autonomic activity changes from

waking to sleep. Big differences were found between non-REM

and REM sleep [4]. Sympathetic tone drops progressively

from wakefulness over sleep stage 1 to 4. In contrast, REM

sleep was characterized by increased sympathetic tone [5].

Parasympathetic tone increases from wakefulness to non-REM

sleep. Periods of wakefulness during sleep were found to have

an intermediate position between non-REM and REM sleep

[6].

Sleep apnea affects HRV during sleep described as cyclicalvariation of heart rate [7]. The recording of cyclical variation of

heart rate together with snoring has been used in order to de-

tect obstructive sleep apnea with ambulatory recording devices

[8]. It can be assumed that the cyclical variation of heart rate

can be detected by spectral analysis if the appropriate frequency

range is investigated. The pattern of bradycardia and tachycardia

during apnea has been attributed to an effective parasympa-

thetic control of heart rate during sleep [9] interrupted by sym-

pathetic activation accompanying the intermittent apnea-termi-

nating arousals.

Spectral analysis of HRV is well established and provides a

quantitative evaluation of sympathetic and parasympathetic ac-

tivation of the heartbeat [10]. Three major oscillatory compo-nents were identified. The physiological interpretation of the

very-low-frequency (VLF) component ( ) is still dis-

cussed, the low-frequency (LF) component (0.040.15 Hz) re-

flects baroreflex sympathetic control of blood pressure, and the

high-frequency (HF) component (0.150.4 Hz) reflects respi-

ratory rhythm and is believed to be related to parasympathetic

control of heart rate [11]. The changes of the frequency com-

ponents during wakefulness and sleep stages were compared in

healthy controls and patients with ischemic heart disease [12].

This method has been used continuously to evaluate heart rate

during sleep in healthy males and females [5] and to investigate

differences between stage 4 and REM sleep [6].

In recent years, the detrended fluctuation analysis (DFA)method [13] has become a widely-used technique for the de-

tection of long-range correlations in noisy, nonstationary time

series [14][16]. In the biomedical context, it has successfully

been applied to diverse fields such as DNA sequences, neuron

spiking, human gait, and heart rate dynamics [17][19]. In the

DFA method, long-range correlations between interbeat inter-

vals separated by several beats are detected by investigating the

scaling behavior of the heartbeat fluctuations on different time

scales disregarding trends and nonstationarities in the data.

One reason we employed the DFA method is to avoid spurious

0018-9294/03$17.00 2003 IEEE
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1144 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 10, OCTOBER 2003

TABLE IRESULTS OF SLEEP STAGE SCORING AND EVALUATION OF BREATHING ARE

GIVEN FOR HEALTHY PERSONS AND THE TWO SLEEP APNEA GROUPS. BMI,AHI, AND TST ARE LISTED

detection of correlations that are artifacts of nonstationarities in

the heartbeat time series. In order to determine correlations on

long time scales, we cannot split the data into short stationary

segments. We have to analyze long, nonstationary data. For

these, the correlation behavior cannot be determined from the

scaling of the autocorrelation function or the power spectrum,

since both are affected by artifacts caused by nonstationarities.

If scaling behavior on large time scales is not investigated, the

time series can be split into shorter, quasi-stationary segments,

and power in the frequency bands can be calculated from the

power spectrum.

This study was performed on existing sleep recordings to

compare spectral analysis of heart rate and DFA in their ability

to distinguish sleep stages in normal and sleep apnea subjects.

We also wanted to see whether sleep apnea severity can be dis-

tinguished using parameters derived from spectral analysis and

DFA and which one performs better.

II. METHODS

A. Subjects

Sixty-four patients with symptoms of excessive daytime

sleepiness and arterial hypertension were recruited. Patients

had to be free of any cardiovascular medication. Patients with

apparent cardiac arrhythmias were excluded. 33 patients with

mild to moderate obstructive sleep apnea with an apnea-hy-

popnea index (AHI) events/h and 31 patients with severe

sleep apnea AHI events/h according to Grote et al. [20]

were selected for this study. In order to compare our results

with normal subjects, 14 healthy persons participated in the

study. These normal controls had no symptoms of sleepinessand no sleep apnea. Anthropometric data were presented in

Table I.

B. Sleep Recording

All subjects underwent two subsequent nights of

polysomnography with electroencephalogram (EEG), elec-

trooculogram, electromyogram, recording of oro-nasal airflow,

respiratory movements, snoring, oxygen saturation, and elec-

trocardiogram (ECG) as required for sleep studies [21]. Signals

were analogue amplified with a polygraph (Schwarzer poly-

graph, Neurocard, Mnchen, Germany) digitized with 100 Hz

and were recorded in a computer for subsequent analysis. Sleep

Fig. 1. (a) Representative one-night record for a healthy subject. The values

represent averages of the heartbeat intervals over 30 heartbeats (left axis).The sleep phases (right axis) have been determined by visual evaluation ofelectrophysiological recordings of brain activity [2]. Non-REM sleep stages 1and 2 are indicated as light sleep, and stages 3 and 4 as deep sleep. (b) Resultsof the scaling analysis with second-order DFA (DFA2) for the data shown in(a). In the double logarithmic plot, the fluctuation function F ( t ) is plotted as afunction of segment size(timescale) t forthe three sleep stagesand compared tothe result for wake during the night. The slopes of the curves correspond to thevalue of the fluctuation scaling exponent . For comparison, a dotted straightline with slope = 0 : 5 and a dashed straight line with slope = 1 are alsoshown.

was evaluated according to Rechtschaffen and Kales [2]. For

subsequent analysis some sleep stages were grouped together.

We distinguished light sleep (stage 1 and 2), deep sleep

(stage 3 and 4), REM sleep, and wakefulness. Figs. 1(a)and 2(a) present two examples.

C. Evaluation of Respiration

Oro-nasal airflow was recorded by thermistors at the nos-

trils and the mouth. Respiratory movements were recorded with

a chest and abdominal belt using inductive plethysmography

(Respitrace, Studley Data Systems, Oxford, U.K.). Oxygen sat-

uration was recorded using a pulseoximetry monitor (Ohmeda

Biox 3700, Boulder, CO). Respiratory signals were evaluated

according to American Academy of Sleep Medicine criteria [21]

and sleep-related breathing disorders were scored as follows:

apneas were scored as cessations of respiratory flow for at least10 s and hypopneas were scored when the sum of signals ob-

tained from Respitrace was below 50% of normal breathing am-

plitude and was accompanied by a drop of oxygen saturation by

at least 4%. Based on the sum of apneas and hypopnoeas we cal-

culated an apnea-hypopnea index (AHI) as the number of events

per hour during total sleep time (TST). Normal subjects were re-

quired to have an AHI events/h during the sleep recording.

D. Heart Rate Analysis

Together with theothersignals ECG lead II hadbeen digitized

at 100 Hz for patients and 200 Hz for normal subjects. The inter-

beat intervals were derived from the ECG as RR intervals using
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PENZEL et al.: COMPARISON OF DETRENDED FLUCTUATION ANALYSIS AND SPECTRAL ANALYSIS FOR HRV IN SLEEP AND SLEEP APNEA 1145

Fig. 2. The calculation of the spectral parameters using FFT in 5-min segments was performed separately for the sleep stages. The summed spectra for eachsleep stage were plotted and used to calculate the spectral bands. The figure depicts the heart rate and the sleep stage records as well as the power spectra for lightsleep, deep sleep, REM sleep, and wake for a patient with moderate sleep apnea. For the spectra the y -axis for light sleep has a different scale in order to show thepronounced VLF peak being characteristic for sleep apnea during light sleep.

an R-wave detector referenced as DF1 in the comparative paper

of Friesen et al. [22]. Forsubsequent analysis of RR intervalswe

reduced the 200 Hz derived resolution to 100 Hz by arithmeticrounding of interval values. The time series were obtained for

the entire duration of the sleep recording. All annotated periods

of wakefulness, light sleep, deep sleep and REM sleep were an-

alyzed separately. Based on discussions with our cardiologist on

arrhythmia-related artifacts in interbeat time series we chose the

following practical criteria for automatic preprocessing: sleep

recordings from our patients were excluded from our retrospec-

tive analysis, if more than 1% of the interbeat intervals failed to

meet the following criteria: s interbeat interval s

and 0.66 s maximum difference from the previous interbeat in-

terval. All recording epochs, where one sleep stage persisted

shorter than 3 min or had more than 1% of RR intervals vio-

lating the criteria were excluded. In addition, the violating in-

tervals in accepted epochs were also excluded, concatenating

the remaining parts of the series. In order to investigate cleansleep stage effects on HRV without sleep stage transition ef-

fects and nonstationarities associated with them we removed

the initial and the final 45 seconds of each sleep stage period.

Time domain and frequency domain measures were calculated

according to standard definitions [11]. Mean RR intervals and

the standard deviation of all RR intervals (SDNN) were calcu-

lated in the time domain.

For the calculation of the power spectra, the RR interval

time series was resampled at 3.41 Hz using linear interpolation.

Consecutive segments of 5 min (1024 points) inside each sleep

stage were analyzed by spectral analysis [fast Fourier transform

(FFT)] separately. No windowing function was applied. Only
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the segment mean value was subtracted from the time series

before applying the FFT. In case of having less than 5 min of

RR intervals in one segment, zero-padding was used. Spectral

analysis requires stationarity, which can be only partially ful-

filled for physiological data. We regarded the individual sleep

stages as stable in a physiological sense. Of course this does

not mean stationarity in a mathematical sense. Furthermore,

it is very difficult to distinguish long-range correlations fromslight nonstationarities, and we do not want to introduce a bias

against regimes with strong long-range correlations. Hence,

we have to assume stationarity for the carefully cleaned 5-min

segments separated for the different sleep stages. It is not pos-

sible to prove and assure mathematical stationarity of our data

since the segments of the sleep stages are too short. However

the sleep stages can be regarded as more homogeneous than

data covering one night or 24 h. The absence of a mathematical

proof for stationarity is a limitation of our study.

The spectral analysis and the interpolation routine were im-

plemented using Matlab 6.1 (The Mathworks Inc, Natick, MA).

We calculated total power, VLF ( ), LF (0.040.15

Hz), HF (0.150.4 Hz), and the ratio LF/HF for the individualsleep stages separately. Since the length of each segment is 5

min corresponding to a resolution of 0.003 Hz, reliable values

for the VLF band ( ) can be calculated, if several full

segments are analyzed for each type of sleep. We calculated

the average value for each type of sleep and each subject using

all possible segments and considering the number of seconds

in each segment as a weight factor in the averaging procedure.

This processing is illustrated for the example of one patient with

sleep apnea in Fig. 2.

E. Detrended Fluctuation Analysis of Heart Rate

A DFA was applied to the time series of heartbeat intervalsfor the different sleep stages [19].

The DFA procedure [13], [15], [16] consists of four steps.

Step 1: Determine the profile

of the data series of length . Sub-

traction of the mean is not compul-

sory, since it would be eliminated by the

later detrending in step 3. An example ofa profile of heartbeat intervals is

shown in Fig. 3.

Step 2: Divide the profile into

nonoverlapping segments of

equal length . The procedure is illus-

trated for two values of in Fig. 3(a)

and (b). Since the length of the series

is often not a multiple of the considered

time scale , a short part at the end of

the profile may remain. In order not to

disregard this part of the series, the

same procedure is repeated starting from

Fig. 3. Illustration of the detrending procedure in the second-order DFA(DFA2). The profile Y ( i ) (dashed lines) calculated by summation of the timeseries in step 1 is split into nonoverlapping segments of equal duration (timescale) t in step 2. This process is illustrated for t = 1 0 0 heartbeats in (a)and for t = 2 0 0 heartbeats in (b) for the same 800 interbeat intervals from ahealthy subject. In step 3, least square quadratic fits to the profile (continuouslines) are calculated in each segment. The squares of the differences betweenthe profile and the fits are used to calculate the fluctuation function F ( t ) instep 4 of the DFA procedure.

the opposite end. Thereby, segments

are obtained altogether.

Step 3: Calculate the local trend for

each of the segments by a least-square fit

of the data. Then determine the variance

for each segment , . Here,

is the fitting polynomial in segment .

Linear, quadratic, cubic, or higher order

polynomials can be used in the fitting

procedure (conventionally called DFA1,

DFA2, DFA3, ). For DFA2 the quadratic

fitting polynomials are illustrated in

Fig. 3(a) and (b).

Step 4: Average over all segments and

take the square root to obtain the fluctu-

ation function

In order to determine how depends on the time scale ,

steps 2 to 4 must be repeated for several time scales . This must

be done for at least 30 time scales, although only two exemplary

scales are shown in Fig. 3. We have used 60 scales between

and . It is apparent that will increase

with increasing , since the deviations from the fits will become
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TABLE IIITHE SIGNIFICANCE LEVELS WERE GIVEN FOR THE GROUP DIFFERENCES

BETWEEN SLEEP STAGES USING THE BONFERRONI TEST. EACH LINE LISTS THERESULTS FOR THE COMPARISON OF THE STAGES NAMED IN COLUMNS 1 AND 2

different classes. We used discriminance analysis as provided

by SPSS version 10. We treated the parameters taken from each

subject and each sleep stage equally. The model derived by

discriminance analysis creates hyperplanes in the hyperspace.

The hyperplanes for the independent variables were applied

to predict the correct assignment of each single subject into

the corresponding class of sleep and apnea (corresponding

to the segment in the hyperspace). The numbers of correct

assignments were calculated in percent.

III. RESULTS

Descriptive results for all spectral components and the two

DFA parameters are given in Table II for healthy subjects ( ),

moderate sleep apnea ( ), and the severe sleep apnea patients

( ).

A. MANOVA Analysis

The analysis of variance did show high significance for the

effects of sleep stages, the effects of apnea severity and thecombination of sleep stages and apnea severity for both sets

of parameters stemming from spectral analysis and from DFA

( ).

When checking the individual group differences using the

Bonferroni test most spectral components did show significant

differences between the different sleep stages. We also checked

the and calculated with DFA2 using the Bonferroni test.

The individual results were summarized in Table III. We also

checked the group differences for the apnea severity groups. The

individual results are summarized in Table IV. For the apnea

severity we found significant differences for but no signifi-

cant differences for .

B. Discriminance Analysis

By applying discriminance analysis which separates the

hyperspace created by the dependent parameters with hyper-

planes we could prove that separation of sleep stages was

performed best using and derived by DFA. 78.4%

of sleep assignments were correct. If mean RR intervals and

SDNN were added, the correct assignments increased to 85.0%.

The assignments of sleep stages based on spectral analysis

parameters resulted in 51.4%. If mean RR interval and SDNN

were added 54.6% of correct assignments were reached for

sleep stages.

TABLE IVTHE SIGNIFICANCE LEVELS WERE GIVEN FOR THE GROUP DIFFERENCES

BETWEEN SLEEP APNEA SEVERITY GROUPS USING THE BONFERRONI TEST

Separation of apnea severity based on spectral parameters

performed better than based on DFA parameters. 63.6% of

apnea severity assignments were correct. If mean RR intervals

and SDNN were added to the discriminance analysis model,

the correct assignments increased to 69.7%. The assignments

of apnea severity based on DFA parameters resulted in 60.1%.

If mean RR interval and SDNN were added 74.4% of assign-

ments were correct. This was slightly better than the spectral

parameter set together with time domain parameters.

If both classes were separated at the same time, and the cor-

responding discriminant model was applied, DFA analysis was

better with 54.9% of correct assignments compared to spectralparameters with 36.3% correct assignments. In both cases, mean

RR intervals and SDNN were included in the model.

As a last test, all variables, derived by DFA, the spectral pa-

rameters, mean RR intervals, and SDNN were taken together.

Then we achieved 84.1% correct assignments for sleep, 72.9%

for apnea and 56.1% for separating both classes at the same

time.

IV. DISCUSSION

This is the first study which systematically compared the

method of spectral analysis of HRV and DFA in a defined

population. We used both methods to compare the abilityto discriminate sleep stages and sleep apnea severity. The

separation of sleep stages was performed best using the two

parameters derived by DFA together with time domain mea-

sures. The separation of apnea severity was also better using the

parameters derived by DFA taken together with time domain

measures. If only spectral parameters were compared to DFA

parameters, they were better in the case of apnea severity. The

results indicate that DFA derived parameters reflect heart rate

regulation properties which complement time domain measures

and their combination performs better than spectral measures

when we want to distinguish sleep stage and apnea severity.

In the study, we used a relatively low resolution for the in-

terbeat time series of 0.01 s. A correct detection of R peaksof the QRS complexes is believed to require a sampling rate

of 5001000 Hz [11], which is usually not available for sleep

recordings. Not having data with this high sampling rate is a

limitation of this study. In order to check the influence of the

limited resolution, we repeated the entire analysis for the normal

subjects, this time using the full resolution of the ECG that had

been digitized at 200 Hz. We found no changes for the final DFA

and spectral analysis results. When any changes were found in

the final values presented in Table II they were below 1%. It is

expected that the slightly incorrect determination of the posi-

tion of some R-peaks can only affect the short-range correlation

properties up to several heartbeats and the highest frequencies in
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the power spectrum. The long-range correlations and the lower

frequency ranges where we are most interested in will not be

affected.

When comparing our results with previous studies on HRV

during apnea, we can confirm several aspects with existing

results. HRV during sleep had been investigated in several

studies [4][6], [12], [26]. The changes in power spectral

components have been described. The LF component decreasesfrom wakefulness to light sleep and further to deep sleep. It

increases during REM sleep to values near wakefulness [26].

This was confirmed in our study. The HF component increases

from wakefulness to light sleep and further to deep sleep. It is

lower again during REM sleep [26]. Our data did not show sig-

nificant differences for HF and did not show an increase from

light sleep to deep sleep. But our data had a high variability in

all instances. The autonomic balance LF/HF is shifted toward

parasympathetic predominance during deep sleep.

In our patients with moderate and severe sleep apnea we

found decreased HF activity during all sleep stages and wake-

fulness. Only during REM sleep in the severe sleep apnea

patients HF activity was not lower than in the control subjects.Wiklund et al. [27] investigated spectral components during

various tests in awake patients with sleep apnea. They also

found significant decreases of HF activity and conclude that

an autonomic dysfunction is present in patients with sleep

apnea. HRV during sleep was not investigated in the study of

Wiklund et al.. Another study on HRV in patients with sleep

apnea tried to overcome the limitations of standard spectral

measures by employing an autoregressive modeling to partition

the RR interval time series into a respiration-dependent and an

independent component [28]. In this study, the modified com-

ponents and LF/HF were investigated for six normal subjects

and seven sleep apnea subjects during wakefulness and sleep

stage 2. The LF/HF was significantly higher in sleep apnea

both during wakefulness and sleep stage 2, as was confirmed in

our study. This shows a stronger decrease of parasympathetic

activity than the decrease of sympathetic activity in sleep apnea

patients during all stages of sleep (Table II).

The meaning of is related to short-range correlations due

to the effect of breathing on heart rate and could be related

to effects of slower brain functions such as sleep regulation on

heart rate. As isalways larger than wedo see strongercor-

relations on short time scales up to 70 heartbeats. Seventy heart-

beats corresponds to the usual duration of a single sleep apnea

event. Based on these results we can speculate, that the con-

trol of heart rate in the range of respiration-related time scales,which are breathing (35 heartbeats) and apnea events (3070

heartbeats) is much tighter than the control of heart rate on long

time scales, which are sleep stages or the circadian rhythm.

The DFA method was previously used to analyze long-term

ECG recordings of patients with congestive heart failure (CHF)

compared to healthy controls [17]. Average scaling exponents

of and were found for

the CHF patients and and

for the healthy subjects. The differences did allow to distinguish

the two groups. In the study, however, neither day and night nor

sleep stages were investigated separately, and DFA1 was used

instead of DFA2 in our study. Nevertheless, the values for the

healthy subjects are very similar to our results for and for

our healthy subjects during wakefulness, see Table II.

The scaling properties of heartbeat intervals during daytime

and nighttime were compared in [18], and an exponent corre-

sponding to was calculated with DFA1. During daytime, av-

erage values of were found for healthy sub-

jects. Again, this valueis consistent with ourfindings forhealthy

subjects during wakefulness. During the night, the values ofbecome significantly smaller, and was

found by Ivanov et al. [18]. The value is larger than our result

for healthy subjects during all sleep stages.

The reason is that the short intermediate wake states during the

night as well as transition regimes between sleep stages signif-

icantly affect the fluctuations of the heart rate occurring during

the night and lead to a higher scaling exponent , if these por-

tions of the time series are not eliminated. Bonnet et al. [29] had

previously reported sleep stage transition effects on HRV. In our

analysis, we took care to remove sleep stage transition effects.

The first results we have published on the scaling behavior of

the heartbeat and the values for healthy subjects during the

different sleep stages [19] are also consistent with the results re-ported here. In that study we compared results for different or-

ders of DFA and found no significant differences between DFA2

to DFA4 and only slightly increased for DFA1 in some cases

with strong trends. Nevertheless, we cannot exclude the possi-

bility that our results presented here for DFA2 can change if an-

other detrending order is employed. It has been shown recently

[30] that removing some noisy and unreliable parts from contin-

uous recordings and stitching together the remaining parts does

not modify the DFA results, unless significantly more than 10%

of the data is removed or the fluctuation exponent is smaller than

0.5 (so called anti-correlations). Since no more than 1% of the

data was removed in the sleep stages we used and our is not

smaller than 0.5 we can neglect the effects of the exclusion and

the concatenation procedure.

In the present study, we confirmed that for REM sleep

is consistently larger than for light sleep and deep sleep which

proves the existence of long-range correlations for REM sleep.

The values for almost reach values for wakefulness. This

shows that the autonomic activity during REM sleep differs

completely from non-REM sleep and this finding remains to

be the same in patients with different severity of sleep apnea.

REM sleep has to be regarded a totally different state of the au-

tonomic nervous system which even persists in disorders with a

strong effects on heart rate regulation.

A limitation of our study is that the age and body mass indexof our healthy control subjects (employees of the hospital) is

considerably lower than age and body mass index of our pa-

tients. Both factors play a role in heart rate regulation [31], [32].

Our patients had no other cardiac or pulmonary disorder beside

sleep apnea. Age and body mass index are very typical for sleep

apnea patients. As the influence of age and BMI on our results

cannot be completely excluded this presents a limitation of our

study.

Our results do indicate that it might be possible to improve

heart rate analysis in such a way that it is possible to recognize

the severity of sleep apnea in rough classes and sleep stages in a

general way which distinguishes wake, light sleep, deep sleep,
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and REM sleep. In order to prove these hypotheses, prospec-

tive studies with implementations of the discriminance func-

tions must be performed.

ACKNOWLEDGMENT

The authors would like to thank W. Althaus and R. Conradtfor sleep stage and respiratory event scoring. They would also

like to thank T. Ploch for statistical advice and providing the

statistical tests. The sleep recordings of healthy subjects were

performed as part of the Siesta project funded by the European

Commission (under Grant Biomed 2 BMH-97-2040). The sleep

recordings of patients were baseline studies with a study sup-

ported by Roche (under Grant G-5001 and M-21222).

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Thomas Penzel (M92) was born in 1958 in Ham-burg, Germany. He studied physics, mathematics,and physiology in Gttingen, Berlin and Marburg.He graduated in theoretical physics (1986), receivedthe doctorate degree in human biology (1991), andthe habilitation in physiology (1995).

He was appointed Professor in 2001 at the medicalfaculty of the University of Marburg. Since 1982, heis with the sleep laboratory at the University of Mar-burg. His research interests include biosignal analysisof EEG, ECG, respiration, and telemedicine applica-

tions.He was a member of the board of the German Sleep Society in 19932001.

Since 2001 he is the president of the International Society on Biotelemetry.


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Jan W. Kantelhardt was born in 1970 in Giessen,Germany. He studied physics and mathematics inGiessen and Berlin, graduated in 1996, and receivedthe doctorate degree in theoretical physics in 1999.

Since 1995, he has been with the Institute for The-oretical Physics IIIat theUniversityof Giessen,inter-rupted by several stays abroad in Israel (Physics De-partment, Bar-Ilan University, Ramat-Gan)and in theUSA (Center for Polymer Studies, Boston University,

Boston, MA) for about two years. His research inter-ests include the vibrational and electrical propertiesof disordered materials (glasses and semiconductors) and applications of statis-tical physics in physiology and medicine.

Ludger Grote was born 1964 in Meppen, Germany.He studied medicine at theUniversityof Marburgandat the University of Hamburg. In 2001, he receivedhis habilitation. He specialized in internal medicine.

Since 1990, he has been a Physician with themedical faculty and at the Institute of Physiologyin Marburg. Today he is a Physician with the SleepDisorders Center of the Sahlgrenska UniversityHospital, Sweden. His work and research interestfocuse on sleep-related breathing disorders, sleepapnea, and cardiovascular risks.

Jrg-Hermann Peter was born in 1945 in Treis-bach, Germany. He studied medicine and psychologyin Marburg, received the M.D. degree in 1971 andthe doctorated degree in pychology with emphasison pychophysiology in 1980. He specialized ininternal medicine and received the habilitation ininternal medicine in 1986.

He worked as Scientific Assistantwith theInstitutefor Psychology in Marburg and was Supervisor in

biostatistics for various scientific studies. In 1981, hefounded the Sleep Laboratory of Marburg. As Headof the lab, he was appointed professor in1993 at the medical faculty of the Uni-versity of Marburg. From 1995 to 1998, he was President of the German SleepSociety. He established and advanced sleep medicine as a medical specialty inGermany. His research interest focuses on sleep apnea, cardiovascular risks, andnocturnal hypertension.

Armin Bunde was born in 1947 in Giessen, Ger-many. He studied physics in Giessen and Stuttgart,graduated in 1970 and received the doctorate degreein theoretical physics in 1974. He received the ha-bilitation in Konstanz in 1982 and he was awarded aHeisenberg Fellowship in 1983.

From 19871993, he was Professor of TheoreticalPhysics at the Universityof Hamburg, Hamburg,Ger-many. Since 1994, he is Head of the Institute of The-oretical Physics IIIat theUniversityof Giessen. He iseditor of several books on glass science, percolation

theory,fractals, and applications of statistical physics in climatology, hydrology,biology, and medicine. These topics also represent his present main area of re-search.

Documents

Comparison of Detrended Fluctuation Analysis