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Detrended fluctuation analysis of short-term heart rate variability in late pregnant women
Autonomic Neuroscience: Basic and Clinical 150 (2009) 122–126
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Autonomic Neuroscience: Basic and Clinical j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a u t n e u
Detrended fluctuation analysis of short-term heart rate variability in late pregnant women Rong-Guan Yeh a, Jiann-Shing Shieh a, Gau-Yang Chen b,c,⁎, Cheng-Deng Kuo d a
Institute of Mechanical Engineering, Yuan Ze University, Tao-Yuan, Taiwan Department of Internal Medicine, Ten-Chen General Hospital, Yangmei, Tao-Yuan, Taiwan Institute of Biomedical Engineering, National Yang-Ming University, Taipei, Taiwan d Laboratory of Biophysics, Department of Research and Education, Taipei Veterans General Hospital, Taipei. Taiwan b c
a r t i c l e
i n f o
Article history: Received 12 October 2008 Received in revised form 11 March 2009 Accepted 4 May 2009 Keywords: Heart rate variability Detrended fluctuation analysis Pregnancy
a b s t r a c t Spectral analysis of heart rate variability using short or long time series is a common method in the assessment of autonomic nervous activity. Nonlinear method such as detrended fluctuation analysis was proposed and proved to be useful for the possible non-stationary and nonlinear characteristics in the time series of heart period. In this study, we investigated the detrended fluctuation analysis and conventional heart rate variability measures in 16 late pregnant women before and 3 months after delivery and in 16 healthy controls. Global and discrete, short-term (≤ 11 beats, α1) and long-term (N 11 beats, α2), scaling exponent were calculated in detrended fluctuation analysis. We found that the late pregnant women have elevated global scaling exponent, elevated short-term scaling exponent and lower heart rate variability measures in the low and high frequency ranges than those of the healthy controls and 3 months after delivery. The deranged measures recovered 3 months after delivery. In addition, the detrended fluctuation scaling exponent did not correlate with most conventional time and frequency domain measures of heart rate variability. Our study suggested that the global and short-term detrended fluctuation scaling exponents might be new and independent measures of heart rate variability in late pregnancy, in addition to those conventional time and frequency domain measures. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Power spectral analysis has been used in the evaluation of heart rate variation responding to external or internal control mechanism. The autonomic cardiovascular regulation can be quantitatively and noninvasively assessed by the power distribution in the high-frequency and low-frequency ranges (Akselrod et al., 1981; Nakamura et al., 2005). The measures of spectral heart rate variability (HRV) have been demonstrated to have diagnostic and prognostic value in many physiological conditions and disease states. However, the fluctuations in heart rate often are non-stationary and nonlinear in many physiological and pathological conditions. Therefore, nonlinear methods were proposed to dissect the complex control of heart rate dynamics (Huikuri et al., 2003; Seely and Macklem, 2004). Detrended fluctuation analysis (DFA) method was developed from a modified root mean square analysis of a random walk to exclude the local trend induced by characteristic time scales from the fluctuations of the multi-component systems, and get a long-range correlation (Peng et al., 1995; Stanley et al., 1999; Rodriguez
⁎ Corresponding author. Department of Internal Medicine, Ten-Chen General Hospital, 356, Sec 1, Chung-Sun N Rd, Yangmei, Tao-Yuan 326, Taiwan. Tel.: +886 34782350; fax: +886 34784879. E-mail address: [email protected] (G.-Y. Chen). 1566-0702/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.autneu.2009.05.241
et al., 2007). This method has been applied to heart rate dynamics and other physiological systems such as DNA sequences (Peng et al., 1992), neuron spiking (Blesić et al., 1999; Bahar et al., 2001), and human gait analysis (Hausdorff et al., 1997). Both long-term and short-term spectral analyses of HRV have been proved to be valuable in the delineation of the complex control of heart rate (Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, 1996). Although a long-term data was originally suggested in the calculation of the correlation properties of DFA, a short-term scaling exponent from 256 heart periods can also demonstrate significant difference in the comparison between supine and standing postures in the healthy subjects (Vuksanović and Gal, 2005). A short-term index would be more clinically practical than that of long-term index if the application of DFA could be extended to a short-term data, since the clinical decision often should be made in a short period of time. In the previous studies, we demonstrated that the women in late pregnancy had a decreased HRV (Kuo et al., 1997) that might be related to the aortocaval compression, and that the depressed HRV recovered after delivery (Chen et al., 1999; Kuo et al., 2000). Since a long-term recording in a late pregnant woman may be impractical or impossible when a severe aortocaval compression or hypotension develops, it is necessary to evaluate the short-term scaling exponent of DFA in late
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high-frequency power ratio (LHR=LFP/HFP) as the index of sympathyvagal balance (Pomeranz et al., 1985; Pagani et al., 1986).
Table 1 The clinical data of the control and late pregnant women group. Variable
Age (yr) Body height (cm) Body weight (kg) Gestational age (weeks)
Control (N = 16) 29.8 ± 4.5 159.6 ± 5.2 52.4 ± 7.4
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Pregnant women Before delivery (N = 16) 30.9 ± 3.9 157.1 ± 3.9 62.1 ± 6.9⁎† 35.9 ± 2.5
After delivery (N = 16)
52.5 ± 4.9
Values are expressed as mean ± standard deviation. ⁎p b 0.05 between control and late pregnant women; †p b 0.05 before and after delivery in late pregnant women.
pregnant women and its relation to conventional time and frequency domain measures of HRV. 2. Materials and methods 2.1. Study subjects Sixteen late pregnant and 16 healthy age-matched nonpregnant women were studied. Subjects who had alcohol, smoking, medical illness or medications were excluded. Twelve of the 16 late pregnant women were from our previous study (Chen et al., 1999). All late pregnant women included in this study had singleton vertex fetus, and gestational age between 30 and 38 weeks without apparent cardiopulmonary distress or complications of pregnancy. The healthy age-matched nonpregnant women were recruited from the community. The Institutional Review Board of the Hospital has approved this study, and written informed consent was obtained from each subject before the study. 2.2. Time- and frequency-domain HRV analysis The study protocol and HRV analysis were similar to that of our previous study (Kuo et al., 1997). In brief, all subjects were requested not to drink caffeinated beverages for at least 24 h before electrocardiographic recording. After a 5 minute rest in supine position, a continuous analog signal of lead II electrocardiogram was picked up by a bedside electrocardiographic monitor (Model 90621A, Spacelabs Inc., Redmond, WA), and was transmitted to a personal computer for recording for 15 min. The sampling frequency for electrocardiographic signals was 500 Hz. A repeated electrocardiographic recording was performed around 3 months after delivery when the postpartum woman had a better restoration. The recorded electrocardiographic signals were retrieved afterwards to measure the consecutive RR intervals by using a software for the detection of R waves. Sinus pause and atrial or ventricular arrhythmias were deleted and the last 660 stationary RR intervals were obtained for DFA and HRV analysis. If the percentage of deletion was greater than 5%, then the subject was excluded from the study. The time domain measures of HRV including mean RR intervals, standard deviation, coefficient of variation, and root mean square of successive difference of the RR intervals were calculated by using standard formulae. The power spectra of 660 RR intervals were obtained by means of discrete Fourier transformation (Matlab, The MathWorks Inc., Massachusetts, USA). Direct current component was excluded before the calculation of power spectra. The area under the spectral peaks within the ranges of 0.01–0.04 Hz, 0.04–0.15 Hz, 0.15–0.4 Hz, and 0.01–0.4 Hz were defined as the very low-frequency power (VLFP), lowfrequency power (LFP), high-frequency power (HFP), and total power (TP), respectively. The normalized high-frequency power (nHFP = 100 × HFP/TP) was used as the index of cardiac vagal modulation, the normalized low-frequency power (nLFP = 100 × LFP/TP) as the index of combined cardiac sympathetic and vagal modulation, and the low-/
2.3. Detrended fluctuation analysis (DFA) The DFA algorithm was similar to that of our previous study (Yeh et al., 2006). In brief, the time series (total length 660) was first integrated and divided into segments of length n (4≤n ≤ 165). Each segment was then detrended by subtracting the best linear fit. The fluctuation function F(n) was then calculated as the root mean square of the detrended time series as a function of the segment size n. If the time series is self-similar, a relationship indicates the presence of power law (fractal) scaling F(n) ~nα. The scaling exponent α can be estimated by a linear fit on the log–log plot of F(n) versus n. The α value represents the correlation properties of the time series. The global scaling exponent α value was calculated within the range of n between n = 4 and n = 165. In addition, short-term correlation exponent α1 was calculated within the range between n = 4 and n = 11 (Mäkikallio et al., 1997, 1998); whereas the long-term correlation exponent α2 was calculated within the range of n between n = 12 and n = 165. In this method, a fractal-like time series can result in a global scaling exponent α = 1, a white Gaussian noise (totally random time series) α = 0.5, and a Brownian noise time series α = 1.5 (Press, 1978; Montroll and Shlesinger, 1984; Peng et al., 1995). 3. Statistical analysis All data are expressed as means ± standard deviation. A paired ttest was used if the measure compared was normally distributed or Wilcoxon signed-rank test (SigmaStat statistical software, SPSS Inc., Chicago, Illinois, USA) was used if the measure compared was distribution free in the comparison of HRV and DFA measures before and after delivery in the late pregnant women. A t-test was used if the measure compared was normally distributed or Mann-Whitney rank sum test was used if the measure compared was distribution free in Table 2 Heart rate variability and detrended fluctuation analysis in the control and late pregnant women. Variable
Mean RRI (ms) SDRR (ms) CVRR (%) RMSSD (ms) TP (ms2) VLFP (ms2) LFP (ms2) HFP (ms2) nVLFP (nu) nLFP (nu) nHFP (nu) LHR α α1 α2
Control (N = 16) 839.14 ± 77.92 44.21 ± 14.50 5.21 ± 1.46 37.25 ± 15.94 808.67 ± 541.44 252.20 ± 189.97 240.07 ± 223.50 316.40 ± 227.99 32.73 ± 13.01 28.86 ± 7.44 38.41 ± 15.25 0.92 ± 0.53 0.76 ± 0.08 0.86 ± 0.22 0.70 ± 0.11
Pregnant women Before delivery (N = 16)
After delivery (N = 16)
654.27 ± 83.03⁎† 35.82 ± 14.31 5.45 ± 2.08 13.84 ± 7.50⁎† 257.85 ± 159.43⁎† 139.28 ± 94.79⁎ 71.87 ± 44.47⁎† 46.70 ± 52.36⁎† 54.71 ± 4.30⁎†
784.43 ± 101.99 40.43 ± 20.38 5.17 ± 2.84 28.73 ± 14.77 513.06 ± 343.37 169.00 ± 121.22 148.56 ± 121.16 195.50 ± 147.84 34.31 ± 13.76 30.03 ± 8.88 35.67 ± 17.94 1.70 ± 2.43 0.76 ± 0.12 0.87 ± 0.23 0.69 ± 0.12
28.73 ± 9.50 16.56 ± 11.16⁎† 2.94 ± 2.45⁎ 0.86 ± 0.13⁎† 1.13 ± 0.32⁎† 0.75 ± 0.15
Values are expressed as mean ± standard deviation. Nu, normalized unit; RRI, RR interval; SDRR, standard deviation of RR interval; CVRR, coefficient of variation of RR interval; RMSSD, root mean square of successive difference; TP, total power; VLFP, very low-frequency power; LFP, low-frequency power; HFP, high-frequency power; nVLFP, normalized very lower-frequency power; nLFP, normalized lower-frequency power; nHFP, normalized high-frequency power; LHR, low-/high-frequency power ratio; DFA, detrended fluctuation analysis; α, DFA value at scales between n = 4 and n = 165; α1, DFA value at scales between n = 4 and n = 11; α2, DFA value at scales between n = 12 and n = 165. ⁎p b 0.05 between control and late pregnant women before delivery; †p b 0.05 before and after delivery in late pregnant women; ‡p b 0.05 between control and after delivery women.
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the comparison of HRV and DFA measures between late pregnant women and age-matched nonpregnant women. A Pearson product moment correlation analysis was used if the data analyzed was normally distributed, or Spearman rank order correlation analysis was used if the data analyzed for distribution free data in the correlation analysis between HRV measures and DFA measures. A p value b 0.05 was considered statistically significant.
4. Results 4.1. Baseline characteristics of the study subjects None of the study subjects had N5% arrhythmia in the electrocardiographic recording. Thus, all study subjects were included in the final statistical analysis. The baseline data of the study subjects are shown in Table 1. The late pregnant women had higher body weight than those of the controls, as expected.
Table 3 The correlation coefficient between heart rate variability and detrended fluctuation analysis in the control and pregnant women group. Variable
Control (N = 16)
Pregnant women Before delivery (N = 16)
After delivery (N = 16)
DFA value (α) Mean RRI (ms) SDRR (ms) CVRR (%) RMSSD (ms) TP (ms2) VLFP (ms2) LFP (ms2) HFP (ms2) nVLFP (nu) nLFP (nu) nHFP (nu) LHR
0.511⁎ 0.069 − 0.080 0.045 0.053 0.311 − 0.066 − 0.068 0.373 − 0.048 − 0.295 0.076
0.267 0.841⁎ 0.838⁎
0.042 0.549⁎ 0.536⁎
0.446 0.836⁎ 0.939⁎ 0.662⁎ 0.284 0.179 − 0.165 − 0.089 0.242
0.164 0.450 0.677⁎ 0.392 0.168 0.642⁎ 0.092 − 0.538⁎ 0.375
DFA value (α1) Mean RRI (ms) SDRR (ms) CVRR (%) RMSSD (ms) TP (ms2) VLFP (ms2) LFP (ms2) HFP (ms2) nVLFP (nu) nLFP (nu) nHFP (nu) LHR
− 0.433 − 0.097 − 0.007 − 0.084 0.037 − 0.206 0.084 0.177 − 0.272 0.031 0.217 0.076
− 0.073 0.342 0.396 − 0.095 − 0.072 0.113 − 0.294 − 0.173 0.138 − 0.141 − 0.057 0.300
− 0.156 0.394 0.470 0.087 0.041 0.081 − 0.161 0.160 − 0.120 − 0.309 0.245 − 0.073
DFA value (α2) Mean RRI (ms) SDRR (ms) CVRR (%) RMSSD (ms) TP (ms2) VLFP (ms2) LFP (ms2) HFP (ms2) nVLFP (nu) nLFP (nu) nHFP (nu) LHR
0.583⁎ 0.103 − 0.052 0.085 0.102 0.327 0.019 − 0.049 0.293 0.017 − 0.258 0.080
0.373 0.768⁎ 0.723⁎ 0.536⁎ 0.889⁎ 0.919⁎ 0.815⁎ 0.351 0.031 0.008 − 0.047 0.170
0.148 0.462 0.407 0.197 0.533⁎ 0.684⁎ 0.563⁎ 0.214 0.530⁎ 0.254 − 0.532⁎ 0.386
Values expressed are correlation coefficient. Abbreviations are as in the Table 2. ⁎ p b 0.05 between heart rate variability measures and detrended fluctuation analysis value are correlated by Pearson product moment correlation for normally distribution data or Spearman rank order correlation for distribution free data.
4.2. HRV and DFA between late pregnant women and controls Table 2 tabulates the HRV and DFA measures before and after delivery in late pregnant women and controls. The mean RR interval and root mean square of successive difference in the time domain, TP, VLFP, LFP, HFP, and nHFP were all significantly decreased, whereas the normalized very low-frequency power (nVLFP), LHR in the frequency domain, and DFA values α and α1 were significantly increased in late pregnant women, as compared with those of the controls. After delivery, the mean RR interval and root mean square of successive difference in the time domain, and TP, LFP, HFP, and nHFP in the frequency domain were all significantly increased, whereas the nVLFP and DFA value α and α1 were significantly decreased as compared with those before delivery. There were no significant differences in all HRV and DFA measures between controls and the women after delivery. 4.3. Correlation between HRV and DFA in late pregnant women The standard deviation and coefficient of variation of RR interval in the time domain, and TP, VLFP, and LFP in the frequency domain correlated significantly and positively with DFA value α and α2 in late pregnant women (Table 3). These correlation coefficients were decreased in the women after delivery. Significant correlations were still found between DFA value α and the standard deviation, coefficient of variation of RR interval, and VLFP, and between DFA value α2 and TP, VLFP, and LFP after delivery. The mean RRI in the control group correlated significantly and positively with DFA value α and α2, whereas the nHFP in the women 3 months after delivery correlated significantly and negatively with DFA values α and α2. All HRV measures did not correlate significantly with all DFA values in the controls. The DFA value α1 did not correlate significantly with conventional HRV measures in all study subjects (Table 3). 5. Discussions We demonstrated in this study that the DFA values α and α1 were increased in late pregnant women before delivery and returned to the level of healthy controls 3 months after delivery. A decreased HRV measures in individual frequency ranges in the late pregnant women have been reported before (Chen and Kuo, 1997; Kuo et al. 1997; Speranza et al., 1998; Kuo et al., 2000; Matsuo et al., 2007) and in this study. The decreased HRV measures and vagal modulation during late pregnancy might be a result of the aortocaval compression induced by the enlarged gravid uterus in late pregnant stage. The DFA value has been reported to be dependent on various physiological situations such as body posture (Vuksanović and Gal, 2005; Castiglioni et al., 2007), age (Rajendra et al., 2004; Vuksanović and Gal, 2005), gender (Francis et al., 2002), sleep stages (Penzel et al., 2003; Staudacher et al., 2005), and physical activity level (Tulppo et al., 2001; Castiglioni et al., 2007). The finding that the DFA values α and α1 were increased in late pregnant women and their recovery to that of controls 3 months after delivery implied a reduction in the heart rhythm complexity in the late pregnant women. The aortocaval compression might have compromised the hemodynamics of the late pregnant women, leading to a reduced complexity of the heart beating. In addition, a fetal-maternal heart rate synchronization or coordination has been observed before (Cerutti et al. 1986; Ferrazzi et al., 1989; Van Leeuwen et al., 2003). The synchronicity between the mother and fetus cardiovascular systems might also be responsible for the more regular heart rhythm behavior in the late pregnant women. The DFA was developed originally as a long-term correlation using a 24 h time series (Peng et al., 1995; Stanley et al., 1999). A long-term index up to 24 h duration has inherent limitation in its application to various clinical situations, especially in emergent or critical care unit where a short-term index will be more clinically practical or when a
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long-term recording is impossible such as the supine position in late pregnant women. Although a series of long-term data was originally suggested in the calculation of DFA (Peng et al., 1995; Stanley et al., 1999), a short length time series of 3 min to 30 min has been tried and proved to be useful in discriminating supine from standing position in healthy subjects (Vuksanović and Gal, 2005), in detecting changes at high intensity levels of exercise when the conventional HRV measures cannot be applied (Hautala et al., 2003), and in patients with heart failure from healthy controls (Rodriguez et al., 2007). According to the Nyquist-Shannon sampling theorem (Miao, 2007), the sampling frequency must be at least twice the signal bandwidth, or in other words, the sampling interval must be less than half signal period, to avoid the loss of information in reconstructing the original signal. In our study, the signal period was 660 RR intervals. The use of sampling interval of 4 to 165 RR intervals in the calculation of α or 4 to 11 RR intervals in the calculation of α1 does not violate the rule that the maximum sampling interval must be less than half signal period, i.e. 330 RR intervals. Our result offered additional evidence that the DFA from a short length of time series might be extended to late pregnant women. No consensus was reported on the minimum length of time series required in the calculation of the DFA α1. The dependence of the length of time series on stability of DFA α1, a sampling effects or an authentic physiological condition, would be an interesting and practical topic. All conventional HRV measures did not correlate significantly with DFA value α1 in the controls and late pregnant women before or 3 months after delivery, similar to the results in patients with coronary disease (Mäkikallio et al., 1998) and in healthy subjects of various ages (Pikkujämsä et al., 1999). Conventional spectral methods measure the magnitude of each frequency component (i.e., oscillation mode). On the other hand, correlation analysis, as made by DFA, focuses on how these oscillation modes are arranged. Thus, DFA scaling exponents will not correlate with most HRV measures theoretically. However, DFA α1 was reported to be theoretically approximated by 2 LHR/(1+LHR) and a very high correlation coefficient between DFA α1 and 2 LHR/(1+LHR) up to 0.97 in healthy subjects and patients with congestive heart failure has been reported (Willson et al., 2002). The correlation coefficient between DFA α1 and LHR was found to be much lower, for instances, 0.90 (Hautala et al., 2003), 0.84 (Tulppo et al., 2001), 0.76 (Mäkikallio et al., 1998), 0.69 (Shin et al., 2006), 0.43 in supine position (Vuksanović and Gal, 2005), or even not correlated, 0.09 in standing position (Vuksanović and Gal, 2005), 0.49 (Perkiomaki JS et al., 2002), and –0.07, 0.30, 0.08 in the postpartum, before delivery and age-matched healthy nonpregnant controls in the present study. The high correlation might reflect the regularity of the breathing rhythm rather than the heart rhythm phenomena since a high correlation between DFA α1 and LHR has been reported in controlled breathing (Tulppo et al., 2001; Hautala et al., 2003). However, a low correlation result in controlled breathing (Perkiomaki et al., 2002) and a high correlation result in no breathing control (Willson et al., 2002; Shin et al., 2006) suggested that other factors might be responsible for the inconsistent results between DFA α1 and LHR. The physiological basis of the DFA and its relation to conventional HRV measures need further evaluation. The DFA value α1 might be a new and independent measure of HRV, in addition to the conventional time and frequency domain HRV measures. With the previous successful applications of the DFA to many physiological systems such as DNA sequences, neuron spiking, and human gait analysis (Peng et al., 1992; Hausdorff et al., 1997; Blesić et al., 1999; Bahar et al., 2001), more applications of DFA in clinical medicine can be expected in the future. Similar to α1, the DFA values α and α2 did not correlate with conventional HRV measures in the healthy controls, whereas they correlate positively with global HRV measures including standard deviation and coefficient of variation of RR interval, the TP, VLFP, and LFP in the late pregnant women. Though the conventional HRV measures and all DFA values were not significantly different from those of the healthy controls, the correlation still exists for some HRV
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Autonomic Neuroscience: Basic and Clinical j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / a u t n e u
Detrended fluctuation analysis of short-term heart rate variability in late pregnant women Rong-Guan Yeh a, Jiann-Shing Shieh a, Gau-Yang Chen b,c,⁎, Cheng-Deng Kuo d a
Institute of Mechanical Engineering, Yuan Ze University, Tao-Yuan, Taiwan Department of Internal Medicine, Ten-Chen General Hospital, Yangmei, Tao-Yuan, Taiwan Institute of Biomedical Engineering, National Yang-Ming University, Taipei, Taiwan d Laboratory of Biophysics, Department of Research and Education, Taipei Veterans General Hospital, Taipei. Taiwan b c
a r t i c l e
i n f o
Article history: Received 12 October 2008 Received in revised form 11 March 2009 Accepted 4 May 2009 Keywords: Heart rate variability Detrended fluctuation analysis Pregnancy
a b s t r a c t Spectral analysis of heart rate variability using short or long time series is a common method in the assessment of autonomic nervous activity. Nonlinear method such as detrended fluctuation analysis was proposed and proved to be useful for the possible non-stationary and nonlinear characteristics in the time series of heart period. In this study, we investigated the detrended fluctuation analysis and conventional heart rate variability measures in 16 late pregnant women before and 3 months after delivery and in 16 healthy controls. Global and discrete, short-term (≤ 11 beats, α1) and long-term (N 11 beats, α2), scaling exponent were calculated in detrended fluctuation analysis. We found that the late pregnant women have elevated global scaling exponent, elevated short-term scaling exponent and lower heart rate variability measures in the low and high frequency ranges than those of the healthy controls and 3 months after delivery. The deranged measures recovered 3 months after delivery. In addition, the detrended fluctuation scaling exponent did not correlate with most conventional time and frequency domain measures of heart rate variability. Our study suggested that the global and short-term detrended fluctuation scaling exponents might be new and independent measures of heart rate variability in late pregnancy, in addition to those conventional time and frequency domain measures. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Power spectral analysis has been used in the evaluation of heart rate variation responding to external or internal control mechanism. The autonomic cardiovascular regulation can be quantitatively and noninvasively assessed by the power distribution in the high-frequency and low-frequency ranges (Akselrod et al., 1981; Nakamura et al., 2005). The measures of spectral heart rate variability (HRV) have been demonstrated to have diagnostic and prognostic value in many physiological conditions and disease states. However, the fluctuations in heart rate often are non-stationary and nonlinear in many physiological and pathological conditions. Therefore, nonlinear methods were proposed to dissect the complex control of heart rate dynamics (Huikuri et al., 2003; Seely and Macklem, 2004). Detrended fluctuation analysis (DFA) method was developed from a modified root mean square analysis of a random walk to exclude the local trend induced by characteristic time scales from the fluctuations of the multi-component systems, and get a long-range correlation (Peng et al., 1995; Stanley et al., 1999; Rodriguez
⁎ Corresponding author. Department of Internal Medicine, Ten-Chen General Hospital, 356, Sec 1, Chung-Sun N Rd, Yangmei, Tao-Yuan 326, Taiwan. Tel.: +886 34782350; fax: +886 34784879. E-mail address: [email protected] (G.-Y. Chen). 1566-0702/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.autneu.2009.05.241
et al., 2007). This method has been applied to heart rate dynamics and other physiological systems such as DNA sequences (Peng et al., 1992), neuron spiking (Blesić et al., 1999; Bahar et al., 2001), and human gait analysis (Hausdorff et al., 1997). Both long-term and short-term spectral analyses of HRV have been proved to be valuable in the delineation of the complex control of heart rate (Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology, 1996). Although a long-term data was originally suggested in the calculation of the correlation properties of DFA, a short-term scaling exponent from 256 heart periods can also demonstrate significant difference in the comparison between supine and standing postures in the healthy subjects (Vuksanović and Gal, 2005). A short-term index would be more clinically practical than that of long-term index if the application of DFA could be extended to a short-term data, since the clinical decision often should be made in a short period of time. In the previous studies, we demonstrated that the women in late pregnancy had a decreased HRV (Kuo et al., 1997) that might be related to the aortocaval compression, and that the depressed HRV recovered after delivery (Chen et al., 1999; Kuo et al., 2000). Since a long-term recording in a late pregnant woman may be impractical or impossible when a severe aortocaval compression or hypotension develops, it is necessary to evaluate the short-term scaling exponent of DFA in late
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high-frequency power ratio (LHR=LFP/HFP) as the index of sympathyvagal balance (Pomeranz et al., 1985; Pagani et al., 1986).
Table 1 The clinical data of the control and late pregnant women group. Variable
Age (yr) Body height (cm) Body weight (kg) Gestational age (weeks)
Control (N = 16) 29.8 ± 4.5 159.6 ± 5.2 52.4 ± 7.4
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Pregnant women Before delivery (N = 16) 30.9 ± 3.9 157.1 ± 3.9 62.1 ± 6.9⁎† 35.9 ± 2.5
After delivery (N = 16)
52.5 ± 4.9
Values are expressed as mean ± standard deviation. ⁎p b 0.05 between control and late pregnant women; †p b 0.05 before and after delivery in late pregnant women.
pregnant women and its relation to conventional time and frequency domain measures of HRV. 2. Materials and methods 2.1. Study subjects Sixteen late pregnant and 16 healthy age-matched nonpregnant women were studied. Subjects who had alcohol, smoking, medical illness or medications were excluded. Twelve of the 16 late pregnant women were from our previous study (Chen et al., 1999). All late pregnant women included in this study had singleton vertex fetus, and gestational age between 30 and 38 weeks without apparent cardiopulmonary distress or complications of pregnancy. The healthy age-matched nonpregnant women were recruited from the community. The Institutional Review Board of the Hospital has approved this study, and written informed consent was obtained from each subject before the study. 2.2. Time- and frequency-domain HRV analysis The study protocol and HRV analysis were similar to that of our previous study (Kuo et al., 1997). In brief, all subjects were requested not to drink caffeinated beverages for at least 24 h before electrocardiographic recording. After a 5 minute rest in supine position, a continuous analog signal of lead II electrocardiogram was picked up by a bedside electrocardiographic monitor (Model 90621A, Spacelabs Inc., Redmond, WA), and was transmitted to a personal computer for recording for 15 min. The sampling frequency for electrocardiographic signals was 500 Hz. A repeated electrocardiographic recording was performed around 3 months after delivery when the postpartum woman had a better restoration. The recorded electrocardiographic signals were retrieved afterwards to measure the consecutive RR intervals by using a software for the detection of R waves. Sinus pause and atrial or ventricular arrhythmias were deleted and the last 660 stationary RR intervals were obtained for DFA and HRV analysis. If the percentage of deletion was greater than 5%, then the subject was excluded from the study. The time domain measures of HRV including mean RR intervals, standard deviation, coefficient of variation, and root mean square of successive difference of the RR intervals were calculated by using standard formulae. The power spectra of 660 RR intervals were obtained by means of discrete Fourier transformation (Matlab, The MathWorks Inc., Massachusetts, USA). Direct current component was excluded before the calculation of power spectra. The area under the spectral peaks within the ranges of 0.01–0.04 Hz, 0.04–0.15 Hz, 0.15–0.4 Hz, and 0.01–0.4 Hz were defined as the very low-frequency power (VLFP), lowfrequency power (LFP), high-frequency power (HFP), and total power (TP), respectively. The normalized high-frequency power (nHFP = 100 × HFP/TP) was used as the index of cardiac vagal modulation, the normalized low-frequency power (nLFP = 100 × LFP/TP) as the index of combined cardiac sympathetic and vagal modulation, and the low-/
2.3. Detrended fluctuation analysis (DFA) The DFA algorithm was similar to that of our previous study (Yeh et al., 2006). In brief, the time series (total length 660) was first integrated and divided into segments of length n (4≤n ≤ 165). Each segment was then detrended by subtracting the best linear fit. The fluctuation function F(n) was then calculated as the root mean square of the detrended time series as a function of the segment size n. If the time series is self-similar, a relationship indicates the presence of power law (fractal) scaling F(n) ~nα. The scaling exponent α can be estimated by a linear fit on the log–log plot of F(n) versus n. The α value represents the correlation properties of the time series. The global scaling exponent α value was calculated within the range of n between n = 4 and n = 165. In addition, short-term correlation exponent α1 was calculated within the range between n = 4 and n = 11 (Mäkikallio et al., 1997, 1998); whereas the long-term correlation exponent α2 was calculated within the range of n between n = 12 and n = 165. In this method, a fractal-like time series can result in a global scaling exponent α = 1, a white Gaussian noise (totally random time series) α = 0.5, and a Brownian noise time series α = 1.5 (Press, 1978; Montroll and Shlesinger, 1984; Peng et al., 1995). 3. Statistical analysis All data are expressed as means ± standard deviation. A paired ttest was used if the measure compared was normally distributed or Wilcoxon signed-rank test (SigmaStat statistical software, SPSS Inc., Chicago, Illinois, USA) was used if the measure compared was distribution free in the comparison of HRV and DFA measures before and after delivery in the late pregnant women. A t-test was used if the measure compared was normally distributed or Mann-Whitney rank sum test was used if the measure compared was distribution free in Table 2 Heart rate variability and detrended fluctuation analysis in the control and late pregnant women. Variable
Mean RRI (ms) SDRR (ms) CVRR (%) RMSSD (ms) TP (ms2) VLFP (ms2) LFP (ms2) HFP (ms2) nVLFP (nu) nLFP (nu) nHFP (nu) LHR α α1 α2
Control (N = 16) 839.14 ± 77.92 44.21 ± 14.50 5.21 ± 1.46 37.25 ± 15.94 808.67 ± 541.44 252.20 ± 189.97 240.07 ± 223.50 316.40 ± 227.99 32.73 ± 13.01 28.86 ± 7.44 38.41 ± 15.25 0.92 ± 0.53 0.76 ± 0.08 0.86 ± 0.22 0.70 ± 0.11
Pregnant women Before delivery (N = 16)
After delivery (N = 16)
654.27 ± 83.03⁎† 35.82 ± 14.31 5.45 ± 2.08 13.84 ± 7.50⁎† 257.85 ± 159.43⁎† 139.28 ± 94.79⁎ 71.87 ± 44.47⁎† 46.70 ± 52.36⁎† 54.71 ± 4.30⁎†
784.43 ± 101.99 40.43 ± 20.38 5.17 ± 2.84 28.73 ± 14.77 513.06 ± 343.37 169.00 ± 121.22 148.56 ± 121.16 195.50 ± 147.84 34.31 ± 13.76 30.03 ± 8.88 35.67 ± 17.94 1.70 ± 2.43 0.76 ± 0.12 0.87 ± 0.23 0.69 ± 0.12
28.73 ± 9.50 16.56 ± 11.16⁎† 2.94 ± 2.45⁎ 0.86 ± 0.13⁎† 1.13 ± 0.32⁎† 0.75 ± 0.15
Values are expressed as mean ± standard deviation. Nu, normalized unit; RRI, RR interval; SDRR, standard deviation of RR interval; CVRR, coefficient of variation of RR interval; RMSSD, root mean square of successive difference; TP, total power; VLFP, very low-frequency power; LFP, low-frequency power; HFP, high-frequency power; nVLFP, normalized very lower-frequency power; nLFP, normalized lower-frequency power; nHFP, normalized high-frequency power; LHR, low-/high-frequency power ratio; DFA, detrended fluctuation analysis; α, DFA value at scales between n = 4 and n = 165; α1, DFA value at scales between n = 4 and n = 11; α2, DFA value at scales between n = 12 and n = 165. ⁎p b 0.05 between control and late pregnant women before delivery; †p b 0.05 before and after delivery in late pregnant women; ‡p b 0.05 between control and after delivery women.
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the comparison of HRV and DFA measures between late pregnant women and age-matched nonpregnant women. A Pearson product moment correlation analysis was used if the data analyzed was normally distributed, or Spearman rank order correlation analysis was used if the data analyzed for distribution free data in the correlation analysis between HRV measures and DFA measures. A p value b 0.05 was considered statistically significant.
4. Results 4.1. Baseline characteristics of the study subjects None of the study subjects had N5% arrhythmia in the electrocardiographic recording. Thus, all study subjects were included in the final statistical analysis. The baseline data of the study subjects are shown in Table 1. The late pregnant women had higher body weight than those of the controls, as expected.
Table 3 The correlation coefficient between heart rate variability and detrended fluctuation analysis in the control and pregnant women group. Variable
Control (N = 16)
Pregnant women Before delivery (N = 16)
After delivery (N = 16)
DFA value (α) Mean RRI (ms) SDRR (ms) CVRR (%) RMSSD (ms) TP (ms2) VLFP (ms2) LFP (ms2) HFP (ms2) nVLFP (nu) nLFP (nu) nHFP (nu) LHR
0.511⁎ 0.069 − 0.080 0.045 0.053 0.311 − 0.066 − 0.068 0.373 − 0.048 − 0.295 0.076
0.267 0.841⁎ 0.838⁎
0.042 0.549⁎ 0.536⁎
0.446 0.836⁎ 0.939⁎ 0.662⁎ 0.284 0.179 − 0.165 − 0.089 0.242
0.164 0.450 0.677⁎ 0.392 0.168 0.642⁎ 0.092 − 0.538⁎ 0.375
DFA value (α1) Mean RRI (ms) SDRR (ms) CVRR (%) RMSSD (ms) TP (ms2) VLFP (ms2) LFP (ms2) HFP (ms2) nVLFP (nu) nLFP (nu) nHFP (nu) LHR
− 0.433 − 0.097 − 0.007 − 0.084 0.037 − 0.206 0.084 0.177 − 0.272 0.031 0.217 0.076
− 0.073 0.342 0.396 − 0.095 − 0.072 0.113 − 0.294 − 0.173 0.138 − 0.141 − 0.057 0.300
− 0.156 0.394 0.470 0.087 0.041 0.081 − 0.161 0.160 − 0.120 − 0.309 0.245 − 0.073
DFA value (α2) Mean RRI (ms) SDRR (ms) CVRR (%) RMSSD (ms) TP (ms2) VLFP (ms2) LFP (ms2) HFP (ms2) nVLFP (nu) nLFP (nu) nHFP (nu) LHR
0.583⁎ 0.103 − 0.052 0.085 0.102 0.327 0.019 − 0.049 0.293 0.017 − 0.258 0.080
0.373 0.768⁎ 0.723⁎ 0.536⁎ 0.889⁎ 0.919⁎ 0.815⁎ 0.351 0.031 0.008 − 0.047 0.170
0.148 0.462 0.407 0.197 0.533⁎ 0.684⁎ 0.563⁎ 0.214 0.530⁎ 0.254 − 0.532⁎ 0.386
Values expressed are correlation coefficient. Abbreviations are as in the Table 2. ⁎ p b 0.05 between heart rate variability measures and detrended fluctuation analysis value are correlated by Pearson product moment correlation for normally distribution data or Spearman rank order correlation for distribution free data.
4.2. HRV and DFA between late pregnant women and controls Table 2 tabulates the HRV and DFA measures before and after delivery in late pregnant women and controls. The mean RR interval and root mean square of successive difference in the time domain, TP, VLFP, LFP, HFP, and nHFP were all significantly decreased, whereas the normalized very low-frequency power (nVLFP), LHR in the frequency domain, and DFA values α and α1 were significantly increased in late pregnant women, as compared with those of the controls. After delivery, the mean RR interval and root mean square of successive difference in the time domain, and TP, LFP, HFP, and nHFP in the frequency domain were all significantly increased, whereas the nVLFP and DFA value α and α1 were significantly decreased as compared with those before delivery. There were no significant differences in all HRV and DFA measures between controls and the women after delivery. 4.3. Correlation between HRV and DFA in late pregnant women The standard deviation and coefficient of variation of RR interval in the time domain, and TP, VLFP, and LFP in the frequency domain correlated significantly and positively with DFA value α and α2 in late pregnant women (Table 3). These correlation coefficients were decreased in the women after delivery. Significant correlations were still found between DFA value α and the standard deviation, coefficient of variation of RR interval, and VLFP, and between DFA value α2 and TP, VLFP, and LFP after delivery. The mean RRI in the control group correlated significantly and positively with DFA value α and α2, whereas the nHFP in the women 3 months after delivery correlated significantly and negatively with DFA values α and α2. All HRV measures did not correlate significantly with all DFA values in the controls. The DFA value α1 did not correlate significantly with conventional HRV measures in all study subjects (Table 3). 5. Discussions We demonstrated in this study that the DFA values α and α1 were increased in late pregnant women before delivery and returned to the level of healthy controls 3 months after delivery. A decreased HRV measures in individual frequency ranges in the late pregnant women have been reported before (Chen and Kuo, 1997; Kuo et al. 1997; Speranza et al., 1998; Kuo et al., 2000; Matsuo et al., 2007) and in this study. The decreased HRV measures and vagal modulation during late pregnancy might be a result of the aortocaval compression induced by the enlarged gravid uterus in late pregnant stage. The DFA value has been reported to be dependent on various physiological situations such as body posture (Vuksanović and Gal, 2005; Castiglioni et al., 2007), age (Rajendra et al., 2004; Vuksanović and Gal, 2005), gender (Francis et al., 2002), sleep stages (Penzel et al., 2003; Staudacher et al., 2005), and physical activity level (Tulppo et al., 2001; Castiglioni et al., 2007). The finding that the DFA values α and α1 were increased in late pregnant women and their recovery to that of controls 3 months after delivery implied a reduction in the heart rhythm complexity in the late pregnant women. The aortocaval compression might have compromised the hemodynamics of the late pregnant women, leading to a reduced complexity of the heart beating. In addition, a fetal-maternal heart rate synchronization or coordination has been observed before (Cerutti et al. 1986; Ferrazzi et al., 1989; Van Leeuwen et al., 2003). The synchronicity between the mother and fetus cardiovascular systems might also be responsible for the more regular heart rhythm behavior in the late pregnant women. The DFA was developed originally as a long-term correlation using a 24 h time series (Peng et al., 1995; Stanley et al., 1999). A long-term index up to 24 h duration has inherent limitation in its application to various clinical situations, especially in emergent or critical care unit where a short-term index will be more clinically practical or when a
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long-term recording is impossible such as the supine position in late pregnant women. Although a series of long-term data was originally suggested in the calculation of DFA (Peng et al., 1995; Stanley et al., 1999), a short length time series of 3 min to 30 min has been tried and proved to be useful in discriminating supine from standing position in healthy subjects (Vuksanović and Gal, 2005), in detecting changes at high intensity levels of exercise when the conventional HRV measures cannot be applied (Hautala et al., 2003), and in patients with heart failure from healthy controls (Rodriguez et al., 2007). According to the Nyquist-Shannon sampling theorem (Miao, 2007), the sampling frequency must be at least twice the signal bandwidth, or in other words, the sampling interval must be less than half signal period, to avoid the loss of information in reconstructing the original signal. In our study, the signal period was 660 RR intervals. The use of sampling interval of 4 to 165 RR intervals in the calculation of α or 4 to 11 RR intervals in the calculation of α1 does not violate the rule that the maximum sampling interval must be less than half signal period, i.e. 330 RR intervals. Our result offered additional evidence that the DFA from a short length of time series might be extended to late pregnant women. No consensus was reported on the minimum length of time series required in the calculation of the DFA α1. The dependence of the length of time series on stability of DFA α1, a sampling effects or an authentic physiological condition, would be an interesting and practical topic. All conventional HRV measures did not correlate significantly with DFA value α1 in the controls and late pregnant women before or 3 months after delivery, similar to the results in patients with coronary disease (Mäkikallio et al., 1998) and in healthy subjects of various ages (Pikkujämsä et al., 1999). Conventional spectral methods measure the magnitude of each frequency component (i.e., oscillation mode). On the other hand, correlation analysis, as made by DFA, focuses on how these oscillation modes are arranged. Thus, DFA scaling exponents will not correlate with most HRV measures theoretically. However, DFA α1 was reported to be theoretically approximated by 2 LHR/(1+LHR) and a very high correlation coefficient between DFA α1 and 2 LHR/(1+LHR) up to 0.97 in healthy subjects and patients with congestive heart failure has been reported (Willson et al., 2002). The correlation coefficient between DFA α1 and LHR was found to be much lower, for instances, 0.90 (Hautala et al., 2003), 0.84 (Tulppo et al., 2001), 0.76 (Mäkikallio et al., 1998), 0.69 (Shin et al., 2006), 0.43 in supine position (Vuksanović and Gal, 2005), or even not correlated, 0.09 in standing position (Vuksanović and Gal, 2005), 0.49 (Perkiomaki JS et al., 2002), and –0.07, 0.30, 0.08 in the postpartum, before delivery and age-matched healthy nonpregnant controls in the present study. The high correlation might reflect the regularity of the breathing rhythm rather than the heart rhythm phenomena since a high correlation between DFA α1 and LHR has been reported in controlled breathing (Tulppo et al., 2001; Hautala et al., 2003). However, a low correlation result in controlled breathing (Perkiomaki et al., 2002) and a high correlation result in no breathing control (Willson et al., 2002; Shin et al., 2006) suggested that other factors might be responsible for the inconsistent results between DFA α1 and LHR. The physiological basis of the DFA and its relation to conventional HRV measures need further evaluation. The DFA value α1 might be a new and independent measure of HRV, in addition to the conventional time and frequency domain HRV measures. With the previous successful applications of the DFA to many physiological systems such as DNA sequences, neuron spiking, and human gait analysis (Peng et al., 1992; Hausdorff et al., 1997; Blesić et al., 1999; Bahar et al., 2001), more applications of DFA in clinical medicine can be expected in the future. Similar to α1, the DFA values α and α2 did not correlate with conventional HRV measures in the healthy controls, whereas they correlate positively with global HRV measures including standard deviation and coefficient of variation of RR interval, the TP, VLFP, and LFP in the late pregnant women. Though the conventional HRV measures and all DFA values were not significantly different from those of the healthy controls, the correlation still exists for some HRV
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measures 3 months after delivery in the pregnant women, implying that the heart rate dynamics may still be different in these subjects. In conclusion, the DFA values α and α1 were increased in late pregnant women before delivery and returned to the level of healthy controls 3 months after delivery, similar to those of conventional HRV measures. In addition, the DFA value α1 did not correlate with all HRV measures in all study subjects, and the FDA value α and α2 did not correlate with most HRV measures in the healthy controls. The DFA might thus be a new and independent measure of HRV in late pregnancy, in addition to the conventional time and frequency domain HRV measures. References Akselrod, S., Gordon, D., Ubel, F.A., Shannon, D.C., Barger, A.C., Cohen, R.J., 1981. Power spectral analysis of heart rate fluctuation: a quantitative probe of beat-to-beat cardiovascular control. Science 213, 220–222. 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