## Abstract

To examine whether heart rate variability (HRV) during daily life shows power law behavior independently of age and interindividual difference in the total power, log-log scaled coarse-graining spectra of the nonharmonic component of 24-h HRV were studied in 62 healthy men (age 21–79 yr). The spectra declined with increasing frequency in all subjects, but they appeared as broken lines slightly bending downward, particularly in young subjects with a large total power. Regression of the spectrum by a broken line with a single break point revealed that the spectral exponent (β) was greater in the region below than above the break point (1.63 ± 0.23 vs. 0.96 ± 0.21,*P* < 0.001). The break point frequency increased with age (*r* = 0.51, *P* < 0.001) and β correlated with age negatively below the break point (*r* = 0.39) and positively above the break point (*r* = 0.70). The contribution to interindividual difference in total power was greater from the differences in the power spectral density at frequencies closer to both ends of the frequency axis and minimal from that at −3.25 log(Hz), suggesting hingelike movement of the spectral shape at this frequency with the difference in total power. These characteristics of the 24-h HRV spectrum were simulated by an artificial signal generated by adding two noises with different β values. Given that the power law assumption is fundamental to the analysis of dynamics through the log-log scaled spectrum, our observations are substantial for physiological and clinical studies of the heartbeat dynamic during daily life and suggest that the nonharmonic component of HRV in normal subjects during daily life may include at least two 1/*f*
^{β} fluctuations that differ in dynamics and age dependency.

- power spectral analysis
- fractal
- nonlinear
- complex system
- ambulatory electrocardiogram

the power spectrum of the nonharmonic component of heart rate variability (HRV), when plotted as the logarithm of power spectral density (PSD) on the logarithm of frequency (log-log scaled spectrum), has been reported to show a linear decay with increasing frequency (8, 15). This phenomenon is referred to as power law behavior and known as a feature of 1/*f*
^{β}fluctuation. When power law behavior is observed in the output signal from a dynamic system, the complexity of the system can be estimated by the steepness of the slope of the log-log scaled spectrum, i.e., spectral exponent (β): the steeper the slope, the lesser the complexity of the system (11). An earlier observation showed that the spectral exponent of short-term (5-min) HRV increased with age, suggesting an age-related loss of complexity in the heartbeat regulation system (10). Also, an increase in the spectral exponent of HRV in 24-h ambulatory recording has been reported to be an increased risk for mortality in the elderly population (6). Because HRV is thought to be an output signal from the complex information network of the cardiovascular regulation system (7), analysis of the HRV dynamics and their changes with aging would provide useful information about the characteristics of the cardiovascular regulation system and its aging.

However, the appearance of the log-log scaled spectrum of 24-h HRV during daily activities is not necessarily straightly linear but similar to a broken line that bends slightly downward in healthy subjects, particularly in young subjects or those with a large total power of HRV. The HRV during daily life could include the responses to various daily stimuli and activities as well as the fluctuations originating from the cardiovascular regulation system. Thus they could be the mixture of multiple fluctuations that differ from each other in the dynamics and in the responses to various factors, such as aging.

In the present study we examined whether the conventional power law assumption applies to the heartbeat dynamics in normal subjects during daily life, particularly when the effects of aging and interindividual difference in the total power are considered. Our initial questions in this study were as follows: *1*) Are the spectral exponents of the nonharmonic component of HRV and the effects of aging on the spectral exponent invariant throughout the frequency range of the 24-h spectrum?*2*) Is the total power of the 24-h HRV contributed by PSD at each frequency as a linear function of the frequency or as a nonlinear function with certain frequency specificity; in other words, is the fundamental shape of log-log scaled power spectrum of 24-h HRV always straightly linear independently of age and total power? Given that the power law assumption is fundamental to the analysis of dynamics through the log-log scaled spectrum, the results of this study would be substantial for the physiological and clinical investigations of heartbeat dynamics during daily life.

## METHODS

#### Subjects.

We studied 62 healthy men [age 21–79 yr, 50 ± 18 (SD) yr] who had been rigorously screened for latent disorders through medical history, physical examinations, blood cell count, blood biochemistry, and electrocardiogram (ECG). Elderly subjects (≥65 yr old) had also been screened for occult cardiovascular disease by exercise tolerance test. None was taking any medications for >2 wk preceding the study. Seven (11%) subjects were current smokers. Ambulatory ECG were recorded continuously for 48 h (*days 1* and*2*) in 43 subjects and for 24 h (*day 1*) in 19 subjects. The ambulatory ECG data from *day 1* were used for the main analysis of this study, and those from*day 2* were used to examine reproducibility of measures. The ECG in all subjects were in sinus rhythm. The maximum number of ectopic beats observed in these recordings was 110/24 h. None of them showed significant ST segment changes, atrioventricular block, or bundle branch block. The protocol of this study was in accordance with the Ethical Guidelines of Nagoya City University Medical School, and all subjects gave their written informed consent.

#### Data collection.

The ambulatory ECG was recorded on FM tape (1 tape/24 h) with a portable tape recorder (model DMC-3253, Nihon Kohden, Tokyo, Japan), with each subject performing usual daily activities. All tapes were played back with a Holter ECG scanner (model DMC-4100, Nihon Kohden) at a rate 240 times faster than real time and digitized to 12-bit data at a sampling frequency of 128 Hz. The effect of wow flutter was canceled by a crystal-oscillator signal simultaneously recorded on a timing track. All QRS complexes in each tape were detected and labeled automatically. The results of the automatic analysis were reviewed, and any errors in R wave detection and QRS labeling were edited manually. The 24-h sequence of the label of each QRS complex with the preceding R-R interval was transferred to a computer workstation (model S-7/7000U, Fujitsu, Tokyo, Japan).

#### Time series analysis.

The R-R interval time series was defined as the 24-h sequence of the intervals between two successive R waves of sinus rhythm. To avoid the adverse effects of remaining errors in the detection of supraventricular ectopic beats on the analysis, all abrupt large changes in the R-R interval (>20% of moving average of R-R intervals) were reviewed interactively until all errors were corrected. The R-R interval sequence was interpolated by a linear step function; i.e., the value of the function between two successive R waves was assumed to be constant at a value equal to the R-R interval, and the value during a gap resulting from artifacts, noises, and exclusions of ectopic beats was considered equal to the R-R interval subsequent to the gap. The length of interpolated gaps relative to the total length of the recording was 0.024 ± 0.026% (median 0.016%, range 0.001–0.127%), which showed no correlation with age (*r* = 0.02).

To evaluate exclusively the nonharmonic components of 24-h HRV without the harmonic components, we used coarse-graining spectral analysis (CGSA) (21). The interpolated time series were submitted to the CGSA algorithm of Time Series Statistical Analysis System (version 3.01.01b) developed by Yamamoto and Hughson (21). The principle and algorithm of this method have been described elsewhere in detail (21, 22). Briefly, the extraction of nonharmonic components was achieved by the cross-correlations between the original and the rescaled data; the data were rescaled twice with different methods: once by sampling every second data point and once by sampling every data point twice. The power spectrum was obtained as the geometric mean of two cross spectra between the original and two sets of the rescaled data thus obtained. Only nonharmonic components were preserved after the cross-correlations because of their property known as “self-similarity” or “scale invariance,” whereas the harmonic components were lost. The magnitude of fluctuation at each frequency was expressed as PSD. Namely, power was multiplied by the number of spectral data points and divided by the width of the frequency band for each data point.

#### Analysis of spectral characteristics.

The characteristics of the nonharmonic component were evaluated by plotting log(PSD) vs. log(frequency). The spectral exponent was defined as the value that satisfies the following equation
where*P* is PSD,*f* is frequency, β is the spectral exponent, and *C* is a proportionality constant (15). By taking the logarithms of both sides of the equation, this equation can be rewritten as
which shows that β can be estimated by linear regression analysis of log(PSD) on log(frequency). The interpolated 24-h R-R interval function was resampled equidistantly so that 2^{17} data points were obtained. In the rescaling process of CGSA, every second data point was sampled, resulting in a 2^{16}-point symmetrical power spectrum. We used the method of Saul et al. (15) to avoid the effects of uneven density of spectral data points along the log(frequency) axis. Briefly, the log(frequency) axis was divided into equally spaced bins. Log(PSD) was averaged over each bin. If bins included no data point, particularly in the lower-frequency range, the average values for such bins were obtained by interpolation.

Two different bin widths were used according to the purposes of analysis. A bin width of 0.00882 log(Hz) (512 bins for the entire frequency band of the 24-h log-log scaled power spectrum) was used for the regression analysis of log(PSD) on log(frequency), by which we examined whether the spectral exponents and the effect of aging on the spectral exponent are identical throughout the spectral region (*question 1*). A bin width of 0.1 log(Hz) (10 bins/decade) was used for the correlation and linear regression analysis of the relationships between the log(total power) and log(PSD) at different frequencies, by which we examine whether the interindividual difference in total power is contributed by PSD at each frequency as a linear function of frequency or as a nonlinear function with certain frequency specificity (*question 2*). Because the estimated PSD for the lowest frequency was unreliable, datum of the first bin was excluded from regression analysis in both analyses.

To examine whether the log-log scaled spectrum is considered as a straight line or as a broken line bending to a consistent direction, each spectrum in the frequency range from 6.1 × 10^{−5} to 4.0 × 10^{−2} Hz [−4.2 to −1.4 log(Hz)] was regressed by a broken line that was composed of two least-square straight lines connecting at a break point (Fig. 1). The broken line best fitting the spectra was determined as follows. All possible break points {( *f*
_{B},*P*
_{B})‖ −4.2 log(Hz) ≤*f*
_{B} ≤ −1.4 log(Hz), 2 log(ms^{2}/Hz) ≤*P*
_{B} ≤ 9 log(ms^{2}/Hz)} were examined with a resolution of 0.01 log(Hz) for*f*
_{B} and 0.01 log(ms^{2}/Hz) for*P*
_{B}, where*f*
_{B} is frequency and *P*
_{B} is PSD of the break point. For each possible (* f*
_{B},*P*
_{B}), two least-square regression lines crossing at ( *f*
_{B},*P*
_{B}) were determined for the spectral regions above and below*f*
_{B}, respectively, and the residual mean squares for the least-square regression lines were calculated for the corresponding spectral regions. The best broken line was determined as the broken line that minimized the sum of the two residual mean squares weighted by the numbers of data points regressed, i.e., the number of data points above and below*f*
_{B}, respectively. Two spectral exponents (β_{a} and β_{b}) were determined as the slopes of two least-square regression lines for the spectral regions above and below*f*
_{B}, respectively, in each subject.

#### Statistical analysis.

The Statistical Analysis System program package (SAS Institute, Cary, NC) was used for statistical evaluations. The difference in the spectral exponent between two different frequency regions was evaluated by paired *t*-test. The effects of aging on power spectral variables were assessed by Pearson’s correlation coefficients and also by ANOVA after subjects were divided into three age groups: 21–39 yr (*group Y*), 40–59 yr (*group M*), and 60–79 yr (*group O*). Bonferroni’s test was used for post hoc multiple comparisons. To visualize changes in the shape of the log-log scaled spectrum with age, the ensemble averages of log-log scaled spectra were calculated for the three age groups. The effect of log(total power) on log(PSD) for each bin was assessed by Pearson’s correlation coefficients and linear regression analysis by means of SAS correlation and regression procedures. Reproducibility of the spectral characteristics (break point and spectral exponents) was evaluated through intraclass correlation coefficients for one-way random-effects ANOVA, with defining subjects as the random factor (19) and the coefficient of repeatability of Bland and Altman (2). Values are means ± SD. *P* < 0.05 was considered statistically significant.

## RESULTS

#### Characteristics of the log-log scaled power spectrum.

The log-log scaled spectra of the nonharmonic component of 24-h HRV obtained by CGSA showed a monotonous decline with increasing frequency in all subjects. Closer observations, however, revealed that the spectra appeared as a broken line bending downward about −3 log(Hz) in most subjects, particularly in young subjects and in subjects with a large total power (Fig. 1). The regression analysis by a broken line with a single break point revealed that a break point existed at*f*
_{B} of −2.89 ± 0.16 log(Hz) and that the spectral exponents above*f*
_{B}(β_{a}; 0.96 ± 0.21) were significantly smaller than the spectral exponents below*f*
_{B}(β_{b}; 1.63 ± 0.23,*P* < 0.001). As shown in Table 1, the difference between β_{a} and β_{b} was significant, even when analyzed separately in the groups divided by age. This indicates that the log-log scaled spectrum of the nonharmonic component of 24-h HRV showed a significant downward bending.

#### Effects of aging.

The ensemble averages of the log-log scaled spectrum for the three age groups are presented in Fig. 2. As shown in Fig. 2 and Table 1,*f*
_{B} was higher in*group O* than in *group Y* (*P* < 0.001). Interestingly, while β_{a} was greater in *group O* than in*group M*, which was in turn greater than in *group Y*(*P* < 0.001), β_{b} was smaller in*group O* than in *group Y* (*P* = 0.03), although the difference in β_{b} was not discernible in Fig. 2. The relationships between age and spectral parameters in each subject are presented in Fig.3, which showed that*f*
_{B} correlated positively with age (*r* = 0.51,*P* < 0.001). Although β_{a} correlated positively with age (*r* = 0.70,*P* <0.001), β_{b} correlated negatively (*r* = −0.39,*P* = 0.001); consequently, the difference between them (β_{b}− β_{a}), which reflected the degree of bending of the spectrum, decreased with age (*r* = −0.60,*P* < 0.001).

#### Effects of interindividual difference in total power.

The total power in all subjects ranged from 8.37 to 11.08 log(ms^{2}) [10.08 ± 0.59 log(ms^{2}) (SD)] and correlated negatively with age (*r* = −0.52, *P* < 0.001). Correlation and linear regression analysis of the relationships between the log(total power) and log(PSD) at different frequency bins showed significant positive correlations for all frequency bins from −4 to −1 log(Hz) (*P* < 0.001). Interestingly, however, the correlation coefficients and linear regression coefficients showed distributions similar to the letter “V,” with a clear dip at −3.25 log(Hz) (Fig.4). Thus the interindividual difference in total power was contributed more strongly by the differences in PSD at frequencies closer to both ends of the frequency axis and minimally at −3.25 log(Hz), suggesting that the spectrum shows hingelike movement at this frequency with the interindividual difference in total power.

#### Reproducibility.

Among 43 subjects subjected to ECG recordings for 2 consecutive days, the spectral parameters showed good within-individual reproducibility:*f*
_{B}, β_{a}, and β_{b} for *day 1* were −2.89 ± 0.16 log(Hz), 0.95 ± 0.22, and 1.63 ± 0.24, respectively, and those for *day 2* were −2.90 ± 0.15log(Hz), 0.96 ± 0.21, and 1.60 ± 0.24, respectively. The intraclass correlations (0.44, 0.92, and 0.62 for*f*
_{B}, β_{a}, and β_{b}, respectively,*P* < 0.001 for all) indicated good within-subject reproducibility over 2 consecutive days for β_{a} and β_{b}. The intraclass correlation for *f*
_{B} was relatively low because of small interindividual variance; however, the coefficient of repeatablity of Bland and Altman (2) for*f*
_{B} was acceptable [0.33 log(Hz)].

#### Simulation study.

Our observations showed that the log-log scaled spectrum of 24-h HRV during daily life appeared as a broken line bending downward and that the degree of the bending (β_{b}− β_{a}) decreased with aging. To examine whether these characteristics of the power spectra are explained as the results of a combination of two 1/*f*
^{β}fluctuations differing in dynamics and its age dependency, we performed simulation studies (Fig. 5).

We generated a combined noise signal by adding fractal noise to square-wave noise simulating adaptive responses of the R-R interval during daily life. As shown in Fig.5
*F*, a broken-line log-log scaled spectrum similar to those observed in *group Y* was obtained from the combined noise signal composed of fractal noise (β = 0.7, total power = 3,114 ms^{2}; Fig.5
*A*) and square-wave noise (total power = 28,355 ms^{2}; Fig.5
*C*). Additionally, as shown in Fig.5
*L*, the effects of aging observed in the characteristics of the log-log scaled spectrum in*group O* were simulated by an increase in β (1.2) and a decrease in total power (1,463 ms^{2}) of the fractal noise (Fig.5
*G*) and a decrease in total power (7,423 ms^{2}) of the square-wave noise (Fig. 5
*I*).

## DISCUSSION

In healthy men we studied the power law behavior of the nonharmonic component in 24-h HRV during daily life and the effects of aging and total power on the behavior. The major findings of this study are as follows: *1*) the log-log scaled spectrum of the nonharmonic component of the 24-h HRV was considered as a broken line bending downward at around −2.9 log(Hz) (1.3 × 10^{−3} Hz), and the shape of the spectrum was stable over 2 consecutive days within each individual, *2*) the spectral exponents above and below the break-point frequency changed to opposite directions with aging so that the degree of bending decreased with aging, whereas the break-point frequency itself increased with age by 0.27 log(Hz) per decade, *3*) the shape of the spectrum was affected also by interindividual difference in total power and showed hingelike movement at a break point of −3.25log(Hz), and *4*) the spectral characteristics and their age-related changes were simulated by the model composed of two different 1/*f*
^{β}fluctuations. These findings are inconsistent with the conventional power law assumption that ascribes the nonharmonic component of 24-h HRV to a single 1/*f*
^{β}fluctuation, but, conversely, they support the hypothesis that 24-h HRV may be composed of at least two 1/*f*
^{β}fluctuations differing from each other in dynamics and age dependency.

Analysis of the spectral exponent has been used as a method for estimating the complexity of HRV. Kobayashi and Musha (8) studied the log-log scaled power spectrum of 10-h HRV in an awake normal young man during bed rest. They reported that in a frequency range of 1.0 × 10^{−4}–2.0 × 10^{−2} Hz, the shape of the spectrum was straightly linear with a spectral exponent near 1. Their observation was confirmed by Saul et al. (15). Lipsitz et al. (10) compared the spectral exponent of 5-min HRV between 12 healthy young (18–35 yr) and 10 healthy older (71–94 yr) subjects and reported that the spectral exponent was greater in the older subjects than in the young subjects. They suggested that aging may be associated with a loss of dimensionality due to reduced autonomic responsiveness.

Analysis of the spectral exponent of HRV may also have clinical significance. Bigger et al. (1) reported that the spectral exponent of 24-h HRV in a frequency range of 4.0 × 10^{−4}–1.0 × 10^{−2} Hz was increased in patients after acute myocardial infarction, and the degree of the increase was an independent predictor for death. Butler et al. (3) reported that the spectral exponent of a 256-beat HRV was greater in patients with heart failure than in healthy men. Recently, Huikuri et al. (6), adopting the same frequency range used by Bigger et al. for calculating the spectral exponent of 24-h HRV, reported that a spectral exponent >1.5 was an independent predictor for cardiac and cerebrovascular death in a randomly selected elderly population. These earlier studies were based on the assumption that the nonharmonic component of HRV is ascribed to a single 1/*f*
^{β}fluctuation; however, the validity of this simple power law assumption has not been examined for 24-h HRV.

Estimation of the characteristics of the nonharmonic component, such as the spectral exponent, may be confounded by concomitantly existing harmonic components at various frequencies (12, 13, 16, 18). Contamination of the power of harmonic components could result in a spurious bending of the log-log scaled spectrum. Because the power of high- and low-frequency components, well-known harmonic components of HRV, decreases with aging (4, 9, 17), the contamination of power of these components may also result in an age-related increase in the spectral exponent of the frequency band including these components. To resolve these problems, we adopted CGSA, which extracted the nonharmonic component from the harmonic components (21). Using CGSA, we observed that the log-log scaled spectrum of the nonharmonic component of 24-h HRV was a broken line bending downward, although the result was basically the same when we used conventional fast Fourier transformation in the analysis (data not shown).

To examine whether the spectra are straightly linear or bending, we performed regression analysis by a broken line with a single break point. The statistical requirement to indicate that a spectrum is bending, in general, is a significant reduction in the residual variance with broken-line regression compared with simple linear regression. We determined the broken line, inasmuch as that minimized the residual variance, and our method included straight-line regressions as a part of the solution; the difference in the residual variance between the broken line and the straight line did not reach a significant level (data not shown). Nevertheless, our observation of the statistically significant difference in the spectral exponent between the regions above and below the break point (β_{a} > β_{b}) seems enough to indicate that the spectra were significantly bending downward; if the spectra were straightly linear, the null hypothesis of β_{a} = β_{b} would not be rejected statistically.

Two hypotheses may be considered for the mechanisms of the broken-line spectrum of 24-h HRV. One is that 24-h HRV does not have characteristics of 1/*f*
^{β}fluctuation. This possibility seems unlikely, however, because downward bending of the log-log scaled spectrum of 24-h HRV was observed, even with CGSA, in which only nonharmonic components with scale-invariant properties were preserved. The other and more likely hypothesis is that 24-h HRV is composed of multiple 1/*f*
^{β}fluctuations with different spectral characteristics.

It seems possible that nonharmonic components of 24-h HRV during daily life have multiple origins with different dynamics. The cardiovascular regulation system is thought to be a multiplex information network with many strata, i.e., molecular, genomic, cellular, organic, and whole body levels (7). Given that HRV is an output signal from such a complex system, it could show fractal noiselike fluctuation with a spectral exponent close to 1. On the other hand, the cardiovascular regulation system needs to adapt to the changes in circulatory demands caused by internal and external stimuli, such as sleep-wakefulness rhythm, food intake, physical and psychological activities, and social and environmental conditions. One may speculate that adaptive responses to these stimuli could result in a high degree of long-range temporal correlation in heart rate dynamics, which could result in nonharmonic fluctuation with a spectral exponent near 2. Indeed, a broken-line spectrum similar to that of actual 24-h HRV was simulated by the artificial noise generated by adding time series of fractal noise and time series simulating adaptive responses (Fig. 5,*A–F*).

In this study we observed that not only the spectral exponent but also its age-related changes were different between frequency regions. Lipsitz et al. (10), who found an age-related increase in the spectral exponent of 5-min HRV, suggested that their findings may reflect a loss of dimensionality because of reduced autonomic responsiveness with age. Our result indicates that β_{a}increases with age, whereas β_{b}decreases with age. Thus the concept of loss of dimensionality/complexity with aging may explain only a part of the age-related changes in 24-h heartbeat dynamics during daily life.

Although the mechanisms of the age-related decrease in β_{b} cannot be deduced from the present study, this phenomenon indicates an age-related decrease in the degree of long-range temporal correlation in the lower-frequency region. One may speculate that age-related changes in the adaptive responses, including an indistinct day-night contrast and decreased autonomic responses to postural changes and exercise in the elderly (10, 17, 20, 23), might be involved in this phenomenon. We observed that the age-related decrease in β_{b} was simulated by the combination of decreased magnitude of the adaptive responses as well as increased spectral exponent and decreased power of the fractal noise (Fig. 5, *G–L*).

The mechanisms for the age-related increase in*f*
_{B} may be more complex. In the simulation model we proposed, the position of the break point could be a function of four independent variables, i.e., the spectral exponents and the total powers of the two sets of time series that were added. Although the detailed mechanism is unknown, Fig. 2 and simulation data suggest that an age-related increase in the spectral exponent and/or a decrease in the total power in the fractal noise-like fluctuation may primarily contribute to the age-related increase in*f*
_{B}.

#### Limitations.

Although we observed that aging affected the spectral characteristics of the nonharmonic component of 24-h HRV, we studied only men. Because a gender difference in HRV has been reported (9, 14), our findings may not be applicable to women. Also, all subjects in this study were rigorously screened for medical problems, but the exercise tolerance test was performed only in elderly (≥65-yr-old) subjects. We cannot exclude the possible effects of occult cardiovascular diseases in our subjects. Additionally, our subjects included seven smokers. Smoking has been reported to affect HRV through acute and chronic impairment of autonomic function (5). Comparisons of spectral characteristics between the 7 smokers and 55 nonsmokers showed no significant difference, even when the effects of age were taken into account (data not shown); however, the statistical power seems insufficient to draw any conclusions. Studies in larger populations are necessary.

### Perspectives

We found that a simple power law assumption does not apply to the heartbeat dynamics in normal subjects during daily life. The log-log scaled power spectrum of 24-h HRV during daily life was not straightly linear but similar to a broken line bending downward. Furthermore, the spectral exponents above and below the break-point frequency changed to opposite directions with aging. These observations and the results of the simulation suggest that the nonharmonic component of 24-h HRV in normal subjects may include at least two 1/*f*
^{β}fluctuations that differ in dynamics and age dependency. The potential values of our findings are substantial, considering the growing interests in the clinical values of the nonharmonic component in HRV. Our study raises concerns about the interpretation of earlier observations demonstrating an increased spectral exponent in patients with heart failure (3), high-risk patients after acute myocardial infarction (1), and an elderly population with an increased risk for cardiovascular death (6). These studies differed not only in the method of spectral analysis but also in the frequency band analyzed, both of which could affect the obtained spectral exponent. Nonharmonic components of HRV observed in different frequency regions could differ from each other not only in mathematical properties but also in physiological origins.

## Acknowledgments

This study was supported in part by Research Grants for Aging and Health (1996, 1997, and 1998) from the Ministry of Health and Welfare of Japan (to J. Hayano).

## Footnotes

Address for reprint requests and other correspondence: S. Sakata, Third Dept. of Internal Medicine, Nagoya City University Medical School, 1 Kawasumi, Mizuho-cho Mizuho-ku, Nagoya 467-8601, Japan (E-mail:sakata{at}med.nagoya-cu.ac.jp).

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- Copyright © 1999 the American Physiological Society