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Am J Physiol Heart Circ Physiol 290: H2560-H2570, 2006. First published December 22, 2005; doi:10.1152/ajpheart.00903.2005
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Aging and nonlinear heart rate control in a healthy population

Frank Beckers, Bart Verheyden, and André E. Aubert

Laboratory of Experimental Cardiology, School of Medicine, Katholieke Universiteit Leuven, 3000 Leuven, Belgium

Submitted 23 August 2005 ; accepted in final form 22 December 2005


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
In recent years more studies are using nonlinear dynamics to describe cardiovascular control. Because of the large dispersion of physiological data, it is important to have large studies with both male and female participants to establish a range of physiological healthy values. This study investigated the effect of gender and age on nonlinear indexes. Nonlinear scaling properties were studied by using 1/f slope (where f is frequency), fractal dimension, and detrended fluctuation analysis short- and long-term correlations (DFA{alpha}1 and DFA{alpha}2, respectively). Nonlinear complexity was described with correlation dimension (CD), Lyapunov exponent (LE), and approximate entropy (ApEn). The population consisted of 135 women and 141 men (age, 18–71 yr). Twenty-four hour ECG recordings were obtained by using Holter monitoring. The recordings were split into daytime (8 AM–9 PM) and nighttime (11 PM–6 AM). A day-night variation was present in all nonlinear heart rate variability (HRV) indexes, except for the CD in the female population. During the night the percentage of CD values of surrogate data files differing from the CD value of the original data increased. All nonlinear indexes were significantly correlated with age. Deeper analysis per age category of 10 yr showed a stabilization in the age decline of the fractal dimension and ApEn at the age of ≥40 yr. The vagal pathways seemed to be more involved in the generation of nonlinear fluctuations. Higher nonlinear behavior was evident during the night. No clear difference between men and women was found in the nonlinear indexes. Nonlinear indexes decline with age. This can be related to the concept of decreasing autonomic modulation with advancing age.

heart rate variability; nonlinear dynamics; gender; circadian rhythm

THE PHYSIOLOGICAL BACKGROUND of heart rate fluctuations (heart rate variability; HRV) has been described extensively with the use of statistical methods and linear spectral analysis methods. The power spectral density description of HRV shows two distinct peaks: one in the so-called low-frequency (LF) band (0.04–0.15 Hz in humans) and another in the high-frequency (HF) band (0.16–0.4 Hz in humans). HF fluctuations have been attributed to vagal modulation, and LF fluctuations appear to be jointly mediated by sympathetic and vagal influences, together with the baroreflex mechanism (51a). It is well-known that time and frequency domain indexes quantifying HRV are reduced in many pathological conditions. Myocardial infarction (29), diabetes (17), coronary artery disease (21), and end-stage heart failure (18) are some of the most clearcut examples in which HRV was found to be associated with survival. The decreased autonomic modulation with advancing age is also reflected in a decrease in linear HRV indexes (10, 44, 45).

In healthy subjects, a significant difference between day and night HRV was reported (45), reflecting the higher vagal modulation during the night. In normal, healthy conditions, gender differences have been observed in HRV in various age classes (10, 23, 44, 45). Compared with men, women are at lower risk of coronary heart disease and of serious arrhythmias (58). Clinical manifestations of coronary artery disease in women lag by ~10 yr, and coronary events such as sudden cardiac death may lag as much as 20 yr (13). It has been suggested that a beneficial autonomic control of heart rate at ages <45 yr might be partly responsible for this advantage in the female population (45).

In recent years, new dynamic methods of HRV quantification have been used to uncover nonlinear fluctuations in heart rate that are otherwise not apparent. These nonlinear variations would enable the cardiovascular system to respond more quickly to changing conditions. Several methods have been proposed to quantify these fluctuations on the basis of the scaling properties of the heart rate variations [fractal dimension (FD) (28), 1/f slope (60) (where f is frequency), detrended fluctuation analysis (40)], the properties of the complex system in phase space [Lyapunov exponents (LE) (47), correlation dimension (CD) (8), pointwise CD (51), approximate entropy (ApEn) (5, 43)], or other nonlinear properties [recurrence plots (11, 35), Poincaré plots (53), and symbolic dynamics (56)].

Previous studies have tried to assess gender- and age-related differences in some nonlinear components of HRV (27, 42, 63). A decrease in nonlinear behavior was observed with increasing age (27, 42, 63), as were differences between day and night values (42, 63). However, most of these studies have major limitations, especially concerning the short-duration ECG recordings used (39, 48), but also the comparison of small groups (27) and the mix of male and female subjects (9) limit the use of these studies for comparison.

Analysis methods derived from nonlinear system dynamics have opened up a new approach for studying and understanding the characteristics of cardiovascular dynamics. Nonlinear analysis methods differ from the conventional HRV methods because they are not designed to assess the magnitude of variability but rather the quality, scaling, and correlation properties of the signals. A defining feature of healthy function is adaptability, the capacity to respond to unpredictable stresses and stimuli. A nonlinear responsiveness would offer greater flexibility than a linear responsiveness. The meaning of the indexes used for nonlinear dynamics is not as clearcut as those derived from spectral analysis. Future research will need to focus on determining clear physiological meanings for all indexes. Most studies conducted thus far have concluded that decreased nonlinear behavior of heart rate is associated with pathological states.

On the basis of smaller studies in different pathologies, one can indicate possible physiological links to the nonlinear indexes: FD is a measure of the regularity of a signal. It corresponds to the self-similarity of the signal. It has been linked to vagal modulation of heart rate (63). A 1/f slope of –1 is an indication that the tachograms represent scaling behavior. This slope has been associated with sympathetic modulation (20), although this was not found by others (59, 60). ApEn is an index of overall complexity and predictability of a time series. The more regular and predictable the time series, the lower will be the value of ApEn. On the other hand, a more random RR time series will lead to higher ApEn values. ApEn is mostly linked with vagal modulation (4). Detrended fluctuation analysis quantifies the fractal scaling properties of the time series. The scaling exponents obtained with detrended fluctuation analysis can be seen as self-similarity parameters, which are characteristic for fractal behavior. Values of these exponents of ~1 are an indication of scaling behavior. The long-range correlations should correspond to sympathetic modulation, whereas short-term correlations should correspond to both sympathetic and vagal modulation (57). The largest LE quantifies the sensitivity of the system to initial conditions. This is characterized by the average rate of divergence of two neighboring trajectories in phase space and gives a measure of predictability. A negative LE implies that the orbits approach a common fixed point. A LE of zero means that the trajectories maintain their relative position, and a positive LE implies that the orbits diverge, representing a chaotic attractor. In previous studies this index was believed to be uncorrelated to autonomic modulation (20). The CD is a quantitative measure of the phase space and describes the complexity of the system and has been moderately linked to both sympathetic and vagal modulation (26) or only vagal modulation (20).

The concept of "normal" or "control" values is difficult in HRV analysis. To label a patient with a reduced or increased HRV, baseline values before the onset of the pathology should be available, which is often not possible. Because of the large dispersion of physiological data (especially HRV data), it is important to have large studies with both male and female participants to establish a range of physiological healthy values.

The purpose of the present study was, first, to investigate the effect of gender and age on nonlinear indexes; second, to study day-night variations in nonlinear indexes; third, to correlate traditional time and frequency domain measures of HRV with methods derived from nonlinear dynamics to make physiological correlates; and fourth, to define a physiological range of these nonlinear indexes in a healthy population.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 REFERENCES
 
Population

A detailed medical history was obtained from all participants. Patients underwent a standard physiological examination. All patients presented with normal ECGs that were verified during analysis of the Holter recording. Patients were not on drug treatment. Only subjects with no history of diabetes, hypertension, cardiovascular, neurological, or psychiatric diseases were allowed to participate in this study. A total of 276 healthy subjects entered the study. They were recruited at two centers of occupational medicine (Medi Leuven and IDEWE) and in a group of volunteers of the Christelijke Mutualiteiten (health insurance institution). The population consisted of 135 women and 141 men between the age of 18 and 71 yr. All subjects gave informed consent to the protocol approved by the local Ethical Committee.

Data Acquisition

Twenty-four hour ECG recordings were obtained using Holter monitoring (ELA Medical, sample rate 200 Hz). Only recorders with time tracking were used. After RR peak detection and visual inspection by the operator for verifying the peak detection, a file containing the consecutive RR intervals was exported for later processing with HRV analysis software (3). The 24-h recordings were split into daytime (8 AM–9 PM) and nighttime (11 PM–6 AM).

Linear Analysis

Linear HRV parameters were calculated in agreement with the standards of measurement proposed by the Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology (51a). In case of ectopic beats, two linear filters were applied to correct for data points outside a limit interval (3).

Mean and SD of the RR tachogram (SD), the square root of the mean of the sum of the squares of differences between consecutive RR intervals (rMSSD), and the percentage of intervals that vary more than 50 ms from the previous interval (pNN50) were calculated in the time domain.

After resampling of the tachogram at 2 Hz with the use of a cubic spline approximation [for details, see Aubert et al. (3)] power spectra were obtained by using fast Fourier transformation. The direct current component was removed by subtracting the mean value of the data set. A Hanning window of 256 points (corresponding to 128 s, gliding window with 50% overlap) was used. Two frequency bands were defined: a LF band from 0.04 to 0.15 Hz and a HF band from 0.16 to 0.4 Hz. Within each frequency band the spectral power was expressed in absolute values of low, high, and total power (in ms2), a low-to-high ratio, and in normalized units {%LF = [LF/(total power)] x 100 and %HF= [HF/(total power)] x 100}.

To check the stationarity of the time series, the mean value and the SD of the total recording, as well as of each data segment of 256 points, were calculated. The variation of the mean value from one segment to another was kept <1 SD (3). Also, a nonparametric "run" test was used. In this case a criterion has to be fulfilled. Both procedures have been explained in detail previously (3). Only stationary parts of the signal were used for further spectral analysis.

Nonlinear Analysis

The nonlinear components of HRV were computed by using several methods.

Fractal dimension. The first method, fractal dimension or FD, is based on the algorithm of Katz (28). This algorithm describes the planar extend of the time series. The higher the FD, the more irrregular the signal.

1/f slope. The 1/f slope of the log(power)-log(frequency) plot was obtained from the linear regression from 10–4 to 10–2 Hz. The plots had an uneven density that might give greater weight for data in the higher-frequency range. Therefore, we used a logarithmic interpolation of the log-log plot, giving a balanced number of points for linear interpolation. A slope of –1 is an indication of scaling behavior.

ApEn. ApEn quantifies the entropy of the system (4). Entropy refers to system randomness, regularity, and predictability and allows systems to be quantified by rate of information loss or generation. ApEn more specifically measures the likelihood that runs of patterns that are close will remain close for subsequent incremental comparisons. It was calculated according to the formula of Pincus (43) with fixed input variables m = 2 and r = 15% as suggested by Goldberger et al. (15) (m being the length of compared runs, and r is a filter). Higher values of ApEn indicate a more complex structure in the time series.

Detrended fluctuation analysis. Detrended fluctuation analysis quantifies fractallike correlation properties of the time series and uncovers short-range and long-range correlations. The root-mean-square fluctuation of the integrated and detrended data are measured within observation windows of various sizes and then plotted against window size on a log-log scale (40). The scaling exponent DFA{alpha} indicates the slope of this line, which relates log(fluctuation) to log(window size). Both the short-term (4–11 beats) DFA{alpha}1 and the long-term (>11 beats) DFA{alpha}2 scaling exponents were calculated. The scaling exponent can be seen as a self-similarity parameter, which is characteristic of a fractal. Values of {alpha} around 1 are an indication of scaling behavior.

Correlation dimension. In the presence of chaos, an attractor in phase space characterizes the dynamics of the system, and its complexity can be quantified in terms of the properties of the attractor. In our study, the time delay for the reconstruction of the attractor was calculated for each recording separately with the method of the autocorrelation function (2). The correlation dimension or CD can be considered as a measure for the number of independent variables needed to define the total system in phase space (8). The embedding dimension was varied between 2 and 30. When a finite value is found for the CD of a time series, correlations are present in the signal. To conclude whether these correlations are linear or nonlinear, a surrogate time series needs to be calculated from the signal. The surrogate time series has a random phase but the same power spectrum as the original signal. A significant difference between the CD of the surrogate and the original time series indicates that there are nonlinear correlations present in the HRV signal. The difference between the CD of the original data and the CD of the surrogate data is defined by an S value. S values >2 indicate significant differences; S values <2 indicate no significant differences.

Largest Lyapunov exponent. Finally, the largest Lyapunov exponent LE was calculated on the basis of the algorithm of Rosenstein et al. (47), which allows the calculation of this parameter on short data sets. The trajectories of chaotic signals in phase space follow typical patterns. Closely spaced trajectories converge and diverge exponentially relative to each other. For dynamic systems, sensitivity to initial conditions is quantified by the LEs. LEs characterize the average rate of divergence of these neighboring trajectories. A positive LE can be taken as a definition of chaos provided the system is known to be deterministic (47). Larger values of the LE indicate more complex behavior.

Statistical Analysis

Statistical analysis was performed with SPSS Windows version 8.0 (Scientific Packages for Social Sciences, Chicago, IL). All data were tested for normality by using the Kolmogorov-Smirnov test. To correct for skewed distributions, a logarithmic transform was used on the spectral power indexes and rMSSD. pNN50 was transformed by using the square root.

Differences between groups were analyzed by Student's t-test or by ANOVA calculated for day and night in both men and women.

To test the association between the spectral and nonlinear indexes, we calculated a two-tailed Pearson correlation coefficient (r). Because HRV is known to decrease with age (45), partial correlation coefficients were calculated. Correlations between –0.25 and 0.25 were disregarded because they indicate only little or no relationship (12).


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 REFERENCES
 
Mean values for linear and nonlinear HRV indexes are listed in Tables 1 (male population) and 2 (female population). The influence of gender is depicted in Table 3 for all indexes. The male and female populations were similar in age distribution; however, men presented with an overall higher body mass index (BMI) compared with the women (24.9 ± 3.1 vs. 23.4 ± 3.8 kg/m2, respectively; P < 0.005).


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  		Table 1. Values of linear and nonlinear HRV indexes during the day and the night in males

 

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  		Table 2. Values of linear and nonlinear HRV indexes during the day and the night in females

 

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  		Table 3. Gender differences of the linear and nonlinear HRV indexes

 
Day-Night Variation

A day-night variation was present in all nonlinear HRV indexes except for the correlation dimension in the female population. The value of the largest LE was positive both in males and females, and both during daytime and nighttime. The value of the CD increased slightly during the night (3.97 ± 0.72 to 4.37 ± 1.30 in the male population; P < 0.05; 4.15 ± 0.75 to 4.41 ± 1.29 in the female population; P = NS). During the night the percentage of CD values of surrogate data files differing from the CD value of the original data increased in both populations (P = 0.001). The values of FD and DFA{alpha}1 increased significantly at daytime. DFA{alpha}2 (Fig. 1), ApEn, and the LE value increased during night hours, and the 1/f slope became less steep. The day-night variations were visible in both the male and the female population.


Figure 1
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  		Fig. 1. Night-day difference of high-frequency (HF) power and detrended fluctuation analysis long-term scaling exponent (DFA{alpha}2): all data. (***P < 0.001). Boxes represent the 75th percentile, median, and 25th percentile. Whiskers show the largest and smallest observed values.

 
All linear indexes showed a day-night variation, except SD and LF power did not show this in both our male and female population. Heart rate decreased during the night (P < 0.001). In general, daytime values of the linear indexes were lower than nighttime values. In both the male and female population, total power and HF power increased significantly during the night (both P < 0.001, Fig. 1). LF power showed a lower relative contribution compared with daytime values.

Gender Influence

Gender-related differences only existed in ApEn, DFA{alpha}1, and the LE. These differences showed as well during the day as during the night. Values of ApEn were higher in the female population, and the LE and DFA{alpha}1 were lower compared with the male population.

Heart rate in the female population was higher compared with the males both during the day and night. All absolute HRV indexes were higher in the male population. Frequency domain indexes showed a significantly lower HRV in female subjects. The gender difference was mainly caused by a difference in LF power. The relative contribution of LF power during the day was significantly higher in the male population compared with the female population (P < 0.01). During the night the gender difference in %LF power disappeared although LF power in absolute values in the male population was still significantly higher compared with the female population (P < 0.001). No significant gender differences were found in HRV indexes denoting vagal modulation (rMSSD, pNN50, and HF power) during the night. During daytime a small difference existed in rMSSD and pNN50 between the male and female subjects (both P < 0.05).

Age Dependence

All nonlinear indexes were significantly correlated with age (all P < 0.001) during daytime hours. This correlation was more pronounced in the female population. During the night the relation with age disappeared in some indexes, especially in the male population. (Tables 1 and 2).

Spectral powers, rMSSD, pNN50, FD, ApEn, DFA{alpha}1, CD, and LE decreased with increasing age. The 1/f slope became steeper. Only DFA{alpha}2 increased with increasing age (r = 0.45; P < 0.001, all data). Increasing age was associated with a higher heart rate only in the female population (day: r = 0.35; night: r = 0.27; both P < 0.001). For the nonlinear indexes, the age dependency was especially prominent during the daytime hours and more pronounced in the female population. FD was strongest related with age (r = –0.56; P < 0.001, all data, Fig. 2). Linear indexes in the male population were more strongly related with age than in the female population.


Figure 2
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  		Fig. 2. Decrease of the fractal dimension (FD) with age. In the male population (A), R2 = 0.34 (P < 0.001); in the female population (B), R2 = 0.34 (P < 0.001). Top and bottom lines represent 90% confidence intervals (CI).

 
Deeper analysis per age category of 10 yr showed a stabilization in the age decline of the FD and ApEn at the age of ≥40 yr. DFA{alpha}2 continued to increase up to 60 yr. The number of surrogate data with the original data remained stable over all ages (Fig. 3). The value of the 1/f slope became steeper, and the LE decreased at the age of >60 yr.


Figure 3
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  		Fig. 3. Percentage of recordings showing a difference between the correlation dimension value of the surrogate data sets and the original data in the different age classes in male population (A) and female population (B).

 
The day-night variation in most nonlinear indexes was also age dependent. Day-night differences in ApEn and DFA{alpha}1 were most prominent in the age classes of <50 yr, whereas in the LE it was more prominent in the >50 yr age categories.

Also the decline in linear indexes stabilized around the age category of 40 yr.

Values for the male and female population converged at higher ages, and the gender differences for ApEn, FD, the LE and the linear parameters (LF, HF and total power) disappeared at ages >40 yr (Fig. 4).


Figure 4
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  		Fig. 4. Disappearing gender differences from the age of 40 yr onward for approximate entropy (ApEn), FD, and low-frequency (LF) power during the night.

 
Influence of Resting Heart Rate

All linear HRV indexes were strongly related to HR (or mean RR). FD increased and DFA{alpha}2 decreased with increasing heart rate. The other nonlinear indexes are not influenced by heart rate. An inverse relation between heart rate and most linear HRV indexes existed. Only the percentages of LF and HF had a positive association with heart rate. Especially the indexes attributed to vagal modulation were strongly associated with heart rate (pNN50 and rMSSD: r = –0.72; HF: r = –0.64; all P < 0.001). This was also the case after examining the partial correlations for the male and female population separately.

After introducing mean RR as a covariate, gender differences during the night disappeared for the linear parameters. Only HF% and the LF/HF ratio showed a significant gender difference during the night. During the day the gender differences remained.

For the nonlinear indexes, correction for mean RR did not alter the gender differences. Introducing mean RR as a covariate in the day-night variation changes the significance levels both in the female and the male population (Tables 1 and 2).

Correlations Between Different HRV Indexes

Table 4 shows the partial Pearson's correlation coefficients, controlling for age, between nonlinear and linear HRV indexes.


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  		Table 4. Partial Pearson correlation coefficients between linear and nonlinear HRV indexes, controlling for age

 
ApEn was related with linear indexes describing vagal modulation after controlling for age [rMSSD, pNN50, and HF power in absolute and proportional (%) units; all r > 0.38; P < 0.001]. The FD was not related with linear HRV indexes. Without controlling for age, however, as is done in most studies, strong relations existed with LF and HF power (r = 0.48 and r = 0.43, respectively; P < 0.001). The 1/f slope was related to LF power (r = 0.29; P < 0.001). The short-term correlation parameter DFA{alpha}1 was related to almost every linear HRV parameter. The strongest association was found in the proportional contributions of LF and HF (r = 0.67 and r = –0.67, respectively; both P < 0.001) and LF/HF ratio (r = 0.72; P < 0.001). The long-term correlation index DFA{alpha}2 was only related to LF power in absolute and relative units (r = –0.27 and r = –0.64, respectively; both P < 0.001).

The CD showed only a link to %HF power (r = 0.28; P < 0.001), and the LE did not show any relation with the linear HRV indexes, even without controlling for age.

The FD is correlated with every other nonlinear index except for the CD. ApEn is related to the 1/f slope and the FD. DFA{alpha}1 was also related to the FD, ApEn, CD, and LE.


   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
REFERENCES
 
In this study the most commonly used nonlinear indexes (FD, ApEn, 1/f slope, CD, detrended fluctuation analysis, and the largest LE) were examined in a population of 276 healthy subjects between the age of 18 and 71 yr. We found a strong decrease in nonlinear behavior with advancing age. Gender differences in nonlinear dynamics were less pronounced.

Influence of Gender and Age

We did not find clear evidence of a higher nonlinear behavior of heart rate fluctuations in the female population. DFA{alpha}1 and the LE were slightly lower in the female population. ApEn, on the contrary, was higher in the female population. These findings agree with Pikkujämsä et al. (41).

The major difference between the male and female population is in LF modulation of heart rate. This was also found previously (7, 10, 23). LF modulation has been linked to sympathetic modulation of heart rate. This means that the male population has an overall higher sympathetic drive than women. Especially during the day, the larger proportion of LF power in men is striking. Higher sympathetic activity has been related to a higher susceptibility to fatal arrhythmia and to the development of coronary artery disease (50). Therefore, hypothetically, the reduced LF power in women could protect against the development and incidence of coronary artery disease and arrhythmia. The exact contribution of this difference in autonomic cardiac control remains to be elucidated.

The higher heart rate found in women and the lower sympathetic drive in women are seemingly contrasting. However, one should keep in mind that heart rate is not only determined by sympathetic modulation but is a result of a complex interplay between sympathetic influences, vagal influences, baroreflex, and even physical fitness. The higher heart rate in women can also be related to a lower stroke volume. In a previous study, we found no significant correlations between BMI and heart rate or HRV indexes for the female population, whereas higher BMI was related to lower HRV indexes in men (45). Also, in the female population, the menstrual cycle could have an influence on the HRV indexes. Guasti et al. (16) described in 1999 that sympathetic modulation can be influenced different in different phases of the ovulatory cycle. Also, others later described small changes in sympathetic activity with menstrual cycle (37, 49). Leicht et al. (32). on the contrary, could not find changes in HRV in the different menstrual cycles. Recently, Vellejo et al. (55) described that in HRV analysis in women, menstrual cycle was the least important factor influencing HRV. Age and BMI were more important factors (55). It should be noted that all these studies were performed in young female subjects (age <35 yr).

There was a strong correlation with age in most nonlinear indexes. Increasing age was associated with decreasing nonlinear behavior. This was shown in a decrease in FD, ApEn, CD, LE, and a steeper 1/f slope. The decrease with age was more prominent in the female population. Our results also show a convergence of the male and female data between the age of 40 and 50 yr, both for the linear and the nonlinear indexes. This has been attributed to the female hormone estrogen (45). Most women enter menopause during this age range. The age dependence of the linear HRV indexes was also observed by others (1, 10, 14, 31, 54, 63). Pikkujämsä et al. (41) did not find a relation with age for ApEn and DFA{alpha}1 in both men and women; however it should be noted that the range of ages in their study was very limited (40–59 yr). In a previous study (42) with a wider age distribution, they did find a strong decline in ApEn with age and the 1/f slope. DFA{alpha}2 also increased with advancing age, which is in accordance with our results. Iyengar et al. (24) found the opposite of our results for DFA{alpha}1 and DFA{alpha}2. Their mixed gender population (10 subjects) was measured while lying down, awake, and watching a movie. This and the small number of subjects can explain these different findings. Otsuka et al. (39) have reported a decrease in CD value with age in their male population, especially during the night hours. We also found a decrease in CD but only during the day. They used a constant time delay of 1.0 s for each recording, while we opted to calculate the optimal time delay for each recording separately. This could give different results. Yeragani et al. (63) also found a decreased FD in an elderly population, both in wake state and in sleep state. A decrease in cardiac nonlinear dynamics with age has also been observed by Kaplan et al. (27) in a limited population of 16 young and 16 old healthy subjects. The decrease in nonlinear behavior was also described by Acharya et al. (1) in a mixed population of male and female subjects.

The decrease of nonlinear behavior with increasing age can be related to the general concept of decreasing autonomic modulation with advancing age. Increasing age might thus result in an increased inability of the cardiac system to respond adequately to changing conditions.

Day-Night Variations

During the night there was a tendency for higher nonlinearity: the LE increased, the CD increased, the percentage in differences with surrogate data sets increased, DFA{alpha}2 increased, ApEn increased, and the 1/f slope came closer to real 1/f behavior. Only the FD and DFA{alpha}1 decreased. This was the case in both the male and the female population. Even after correction for mean RR there is a tendency toward increased nonlinearity during the night.

Time and frequency domain indexes support the previously observed increase in vagal modulation during the night: pNN50, rMSSD and the proportion of HF power increase during the night, while heart rate slows down. Although LF power increases in absolute value, its relative contribution decreases, again stressing the vagal dominance during the night. In this study, the transition phases of going to sleep and waking up were excluded from the analysis to provide data on relatively stable time periods. The morning and evening periods can also contain potentially important information. Especially the transition between sleep and awakening has been described previously as a time of high sympathetic activity and has been related to the occurrence of cardiac arrhythmia in this time frame (30). Future research will focus on the hourly day-night variations.

Relation with Linear Indexes

The influence of resting heart rate was also noted in our previous study (45). Also others (36, 42) later described the importance of considering the influence of resting heart rate and age in measuring HRV. The latter parameter should be taken into account when examining both linear and nonlinear HRV indexes.

ApEn was strongly related with indexes describing vagal modulation of heart rate. This was in accordance with observations in a previous study in heart failure patients (4). However, some studies did not find a relation with vagal indexes (52). Unlike previous reports (63), we did not find a relation of FD with HF power or other vagally related indexes. However, without controlling for age there was a strong relation with both HF and LF power. Previous studies have not taken age into account as a covariate. The 1/f slope was related to LF power, which seems logical because the 1/f power spectrum is largely determined by the LF power. Yamamoto and Hughson (59), however, suggested only a moderate influence of the sympathetic nervous system on the 1/f slope after experiments of beta-blockade. Yamamoto et al. (60) rather suggested an influence of the vagal system due to the influence of atropine on the 1/f slope. Hagerman et al. (20), on the contrary, found no influence of beta-blockade and cholinergic blockade on the 1/f slope. The CD was only moderately related to the proportion of HF power, while the LE seemed unrelated to any linear HRV index. The CD has also been studied by Kanters et al. (26) by using forced respiration. They concluded on a mixed influence of both sympathetic and vagal stimulation because no differences were found by using the forced respiration protocol. However, no comparison to surrogate data sets was made. The long-term correlation index was related to LF power, while the short-term correlation index was strongest related to the proportion of LF and HF power. This last relation was also found by Tulppo et al. (52) in baseline conditions and during head-up tilt and exercise. Our values of DFA{alpha}1 and DFA{alpha}2 are also in agreement with values found by Peng et al. (40) in a healthy population. These findings are also in full support of the article by Willson et al. (57), in which the DFA{alpha}1 and DFA{alpha}2 indexes where described as ratios of spectral powers. DFA{alpha}1 was related to 2/[1 + (HF/LF)], and DFA{alpha}2 was related to 2/[1 + (LF/VLF)], with VLF representing the power in the very low frequency region below 0.04 Hz. These formulas also describe the link with the LF/HF ratio for DFA{alpha}1 and the link with LF power for DFA{alpha}2 that we found.

Our results indicate that the nonlinear fluctuations in humans are only moderately influenced by the sympathetic nervous system but more by the vagal nerves. The majority of the nonlinear indexes show a clear relation with indexes representing vagal modulation (ApEn, DFA{alpha}1, and FD without correction for age). The 1/f slope and DFA{alpha}2 were more related to sympathetic modulation.

Practical Applications

In this study the nonlinear indexes have been linked to vagal modulation of heart rate control. The rationale behind the idea of nonlinear fluctuations is that the cardiovascular system would adapt easier and faster to necessary changes. For this the choice of the vagal (fast acting) pathways seems logical. Because the nonlinear control seems to be decreased during the day, it stresses the importance of the vagal pathways in enabling the nonlinear fluctuations to be expressed or even for the sympathetic system to inhibit the generation of the nonlinear fluctuations. The triggers of this increased need for nonlinear control during the night might come from the increased respiratory sinus arrhythmia, or even from changes linked to different sleep stages.

The use of nonlinear indexes as risk stratifiers might be an important future application. Already several studies have been published that demonstrate the huge potential of these methods. Mäkikallio et al. (34) found an increased risk in patients with decreased DFA{alpha}1 index and a steeper 1/f slope (–1.5 < beta < –1). This was later confirmed by Huikuri et al. (22). Promising results have been obtained in patients with panic disorders (46, 62). Yeragani et al. (61) recently proved that in panic disorder decreased baroreflex sensitivity and an increased blood pressure variability is accompanied by a higher degree of nonlinear complexity. Heart failure patients on the contrary have depressed nonlinear behavior compared with healthy subjects. Guzetti et al. (18) even demonstrated that the 1/f slope had prognostic value in this patient group. Earlier, Peng et al. (40) had already demonstrated a lower DFA{alpha}1 and a higher DFA{alpha}2 value in heart failure patients. Lin et al. (33) found beneficial effects of beta-blocker therapy in patients with advanced congestive heart failure, represented by a 1/f slope closer to –1 (–1.70 before therapy vs. –1.22 after therapy), representing the typical 1/f behavior and an increase in the DFA{alpha}1 parameter from 0.78 to 1.13 after beta-blocker therapy. Heart transplant patients presented a decreased system complexity (8, 19). Hypertension also leads to decreased nonlinear behavior of HRV (25), while blood pressure fluctuations in this group presented a lower degree of nonlinear control (38). It is becoming clear that nonlinear control is decreased in patients at higher risk of lethal arrhythmia. Risk assessment for patients after myocardial infarction or in heart failure or the prediction of lethal arrhythmia (22, 34, 51, 56) is important for clinical assessment of disease severity.

Study Limitations

1) No activity log was recorded during the 24-h Holter recording. This means that we have no information about possible differences in the young and the elderly population (6). The subjects were asked to refrain from intense physical activity to avoid interference from exercise episodes; also, no specific interventions to stimulate or block autonomic pathways were performed. 2) Respiration was not recorded during the 24-h Holter recording. We used visual inspection of the power spectra to verify the location of the respiratory component in the HF region. 3) No information about sleep (quality, hours of sleep) was recorded. Night hours were chosen the same for all subjects, ensuring the same data lengths for analysis. Hours were chosen from 11 PM to 6 AM, ensuring the inclusion of the periods with enhanced vagal modulation, and avoiding the waking up period.

Summary of Conclusions

We found evidence of the involvement of the autonomic nervous system in the generation of nonlinear fluctuations in healthy human subjects. The vagal pathways seemed to play a dominant role in the generation of these complex dynamics. This was expressed in higher nonlinear behavior during the night, when vagal influence is largest (higher HF power). No clear difference between men and women was found in the nonlinear indexes.

Nonlinear heart rate fluctuations also decline with age. This can be related to the general concept of decreasing autonomic modulation with advancing age. This again provides evidence for the involvement of the autonomic nervous system in the generation of these complex fluctuations.

We do not see the nonlinear analysis techniques as a replacement of the linear methods but rather as a completion of the model. The linear methods have an advantage over the nonlinear methods in that they are more suitable when shorter data sets are used. Spectral analysis is also superior in visually representing autonomic modulation. The interpretation of the spectral components is more intuitive and easier to understand. However, they cannot quantify the presence or absence of nonlinear behavior.

In our analysis of the nonlinear dynamic systems in 24-h Holter recordings, we have opted to calculate values for day and night separately and not to use the 24-h period as a whole because day-night fluctuations are present in autonomic control of heart rate. Analyzing the whole day as one period should therefore mask specific alterations caused by either sympathetic predominance (during the day) or vagal predominance (during the night).


   FOOTNOTES
 

Address for reprint requests and other correspondence: A. E. Aubert, Laboratory of Experimental Cardiology, School of Medicine, Katholieke Universiteit Leuven, UZ Gasthuisberg O-N, Herestraat 49, B-3000 Leuven, Belgium (e-mail: andre.aubert{at}med.kuleuven.be)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 

  1. Acharya UR, Kannathal N, Sing OW, Ping LY, and Chua T. Heart rate analysis in normal subjects of various age groups. Biomed Eng Online 3: 24, 2004.[CrossRef][Medline]
  2. Albano AM, Smilowitz L, Rapp PE, de Guzman GC, and Bashore TR. Physics of Phase Space, edited by Kim Y and Zachary WW. Berlin: Springer Verlag, 1987.
  3. Aubert AE, Ramaekers D, Beckers F, Breem R, Denef C, Van de Werf F, and Ector H. The analysis of heart rate variability in unrestrained rats. Validation of method and results. Comput Methods Programs Biomed 60: 197–213, 1999.[CrossRef][Web of Science][Medline]
  4. Beckers F, Ramaekers D, and Aubert AE. Approximate entropy of heart rate variability: validation of methods and application in heart failure. Cardiovasc Eng 1: 177–182, 2001.[CrossRef]
  5. Bernardi L, Valle F, Coco M, Calciati A, and Sleight P. Physical activity influences heart rate variability and very-low- frequency components in Holter electrocardiograms. Cardiovasc Res 32: 234–237, 1996.[Abstract/Free Full Text]
  6. Bigger JT Jr, Fleiss JL, Steinman RC, Rolnitzky LM, Schneider WJ, and Stein PK. RR variability in healthy, middle-aged persons compared with patients with chronic coronary heart disease or recent acute myocardial infarction. Circulation 91: 1936–1943, 1995.[Abstract/Free Full Text]
  7. Bogaert C, Beckers F, Ramaekers D, and Aubert AE. Analysis of heart rate variability with correlation dimension method in a normal population and in heart transplant patients. Auton Neurosci 90: 142–147, 2001.[CrossRef][Web of Science][Medline]
  8. Braun C, Kowallik P, Freking A, Hadeler D, Kniffki KD, and Meesmann M. Demonstration of nonlinear components in heart rate variability of healthy persons. Am J Physiol Heart Circ Physiol 275: H1577–H1584, 1998.[Abstract/Free Full Text]
  9. Cowan MJ, Pike K, and Burr RL. Effects of gender and age on heart rate variability in healthy individuals and in persons after sudden cardiac arrest. J Electrocardiol 27, Suppl: 1–9, 1994.[Web of Science][Medline]
  10. Dabire H, Mestivier D, Jarnet J, Safar ME, and Chau NP. Quantification of sympathetic and parasympathetic tones by nonlinear indexes in normotensive rats. Am J Physiol Heart Circ Physiol 275: H1290–H1297, 1998.[Abstract/Free Full Text]
  11. Dawson-Saunders B and Trapp RG. Interpreting correlation coefficients. In: Basic and Clinical Biostatistics. London: Prentice-Hall International, 1990, p. 54–56.
  12. Eastwood JA and Doering LV. Gender differences in coronary artery disease. J Cardiovasc Nurs 20: 340–351, 2005.[Medline]
  13. Fagard RH, Pardaens K, and Staessen JA. Influence of demographic, anthropometric and lifestyle characteristics on heart rate and its variability in the population. J Hypertens 17: 1589–1599, 1999.[Web of Science][Medline]
  14. Goldberger AL, Mietus JE, Rigney DR, Wood ML, and Fortney SM. Effects of head-down bed rest on complex heart rate variability: response to LBNP testing. J Appl Physiol 77: 2863–2869, 1994.[Abstract/Free Full Text]
  15. Guasti L, Grimoldi P, Mainardi LT, Petrozzino MR, Piantanida E, Garganico D, Diolisi A, Zanotta D, Bertolini A, Ageno W, Grandi AM, Cerutti S, and Venco A. Autonomic function and baroreflex sensitivity during a normal ovulatory cycle in humans. Acta Cardiol 54: 209–213, 1999.[Web of Science][Medline]
  16. Guo N, Lu Z, Xue X, Shu J, and Liu S. Assessment of autonomic function in patients with acute myocardial infarction or diabetes mellitus by heart rate variability, ventricular late potential and QT dispersion. Hypertens Res 23: 367–370, 2000.[Web of Science][Medline]
  17. Guzzetti S, Mezzetti S, Magatelli R, Porta A, De Angelis G, Rovelli G, and Malliani A. Linear and non-linear 24 h heart rate variability in chronic heart failure. Auton Neurosci 86: 114–119, 2000.[CrossRef][Web of Science][Medline]
  18. Guzzetti S, Signorini MG, Cogliati C, Mezzetti S, Porta A, Cerutti S, and Malliani A. Non-linear dynamics and chaotic indices in heart rate variability of normal subjects and heart-transplanted patients. Cardiovasc Res 31: 441–446, 1996.[CrossRef][Web of Science][Medline]
  19. Hagerman I, Berglund M, Lorin M, Nowak J, and Sylven C. Chaos-related deterministic regulation of heart rate variability in time- and frequency domains: effects of autonomic blockade and exercise. Cardiovasc Res 31: 410–418, 1996.[CrossRef][Web of Science][Medline]
  20. Huikuri HV. Heart rate variability in coronary artery disease. J Intern Med 237: 349–357, 1995.[Web of Science][Medline]
  21. Huikuri HV, Makikallio TH, Peng CK, Goldberger AL, Hintze U, and Moller M. Fractal correlation properties of R-R interval dynamics and mortality in patients with depressed left ventricular function after an acute myocardial infarction. Circulation 101: 47–53, 2000.[Abstract/Free Full Text]
  22. Huikuri HV, Pikkujamsa SM, Airaksinen KE, Ikaheimo MJ, Rantala AO, Kauma H, Lilja M, and Kesaniemi YA. Sex-related differences in autonomic modulation of heart rate in middle-aged subjects. Circulation 94: 122–125, 1996.[Abstract/Free Full Text]
  23. Iyengar N, Peng CK, Morin R, Goldberger AL, and Lipsitz LA. Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics. Am J Physiol Regul Integr Comp Physiol 271: R1078–R1084, 1996.[Abstract/Free Full Text]
  24. Kagiyama S, Tsukashima A, Abe I, Fujishima S, Ohmori S, Onaka U, Ohya Y, Fujii K, Tsuchihashi T, and Fujishima M. Chaos and spectral analyses of heart rate variability during head-up tilting in essential hypertension. J Auton Nerv Syst 76: 153–158, 1999.[CrossRef][Web of Science][Medline]
  25. Kanters JK, Hojgaard MV, Agner E, and Holstein-Rathlou NH. Influence of forced respiration on nonlinear dynamics in heart rate variability. Am J Physiol Regul Integr Comp Physiol 272: R1149–R1154, 1997.[Abstract/Free Full Text]
  26. Kaplan DT, Furman MI, Pincus SM, Ryan SM, Lipsitz LA, and Goldberger AL. Aging and the complexity of cardiovascular dynamics. Biophys J 59: 945–949, 1991.[Web of Science][Medline]
  27. Katz MJ. Fractals and the analysis of waveforms. Comput Biol Med 18: 145–156, 1988.[CrossRef][Web of Science][Medline]
  28. Kleiger RE, Miller JP, Bigger JT Jr, and Moss AJ. Decreased heart rate variability and its association with increased mortality after acute myocardial infarction. Am J Cardiol 59: 256–262, 1987.[CrossRef][Web of Science][Medline]
  29. Kozak M, Krivan L, and Semrad B. Circadian variations in the occurrence of ventricular tachyarrhythmias in patients with implantable cardioverter defibrillators. Pacing Clin Electrophysiol 26: 731–735, 2003.[CrossRef][Medline]
  30. Kuo TB, Lin T, Yang CC, Li CL, Chen CF, and Chou P. Effect of aging on gender differences in neural control of heart rate. Am J Physiol Heart Circ Physiol 277: H2233–H2239, 1999.[Abstract/Free Full Text]
  31. Leicht AS, Hirning DA, and Allen GD. Heart rate variability and endogenous sex hormones during the menstrual cycle in young women. Exp Physiol 88: 441–446, 2003.[Abstract]
  32. Lin LY, Lin JL, Du CC, Lai LP, Tseng YZ, and Huang SK. Reversal of deteriorated fractal behavior of heart rate variability by beta-blocker therapy in patients with advanced congestive heart failure. J Cardiovasc Electrophysiol 12: 26–32, 2001.[CrossRef][Web of Science][Medline]
  33. Makikallio TH, Hoiber S, Kober L, Torp-Pedersen C, Peng CK, Goldberger AL, and Huikuri HV. Fractal analysis of heart rate dynamics as a predictor of mortality in patients with depressed left ventricular function after acute myocardial infarction. TRACE Investigators TRAndolapril Cardiac Evaluation. Am J Cardiol 83: 836–839, 1999.[CrossRef][Web of Science][Medline]
  34. Mestivier D, Dabire H, Safar M, and Chau NP. Use of nonlinear methods to assess effects of clonidine on blood pressure in spontaneously hypertensive rats. J Appl Physiol 84: 1795–1800, 1998.[Abstract/Free Full Text]
  35. Migliaro ER, Contreras P, Bech S, Etxagibel A, Castro M, Ricca R, and Vicente K. Relative influence of age, resting heart rate and sedentary life style in short-term analysis of heart rate variability. Braz J Med Biol Res 34: 493–500, 2001.[Web of Science][Medline]
  36. Minson CT, Halliwill JR, Young TM, and Joyner MJ. Sympathetic activity and baroreflex sensitivity in young women taking oral contraceptives. Circulation 102: 1473–1476, 2000.[Abstract/Free Full Text]
  37. Osaka M, Kumagai H, Sakata K, Onami T, Chon KH, Watanabe MA, and Saruta T. Low-order chaos in sympathetic nerve activity and scaling of heartbeat intervals. Phys Rev E Stat Nonlin Soft Matter Phys 67: 041915, 2003.[Medline]
  38. Otsuka K, Cornelissen G, and Halberg F. Age, gender and fractal scaling in heart rate variability. Clin Sci (Colch) 93: 299–308, 1997.[Medline]
  39. Peng CK, Havlin S, Hausdorff JM, Mietus JE, Stanley HE, and Goldberger AL. Fractal mechanisms and heart rate dynamics. Long-range correlations and their breakdown with disease. J Electrocardiol 28, Suppl: 59–65, 1995.[Web of Science][Medline]
  40. Pikkujamsa SM, Makikallio TH, Airaksinen KE, and Huikuri HV. Determinants and interindividual variation of R-R interval dynamics in healthy middle-aged subjects. Am J Physiol Heart Circ Physiol 280: H1400–H1406, 2001.[Abstract/Free Full Text]
  41. Pikkujamsa SM, Makikallio TH, Sourander LB, Raiha IJ, Puukka P, Skytta J, Peng CK, Goldberger AL, and Huikuri HV. Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory. Circulation 100: 393–399, 1999.[Abstract/Free Full Text]
  42. Pincus SM. Approximate entropy as a measure of system complexity. Proc Natl Acad Sci USA 88: 2297–2301, 1991.[Abstract/Free Full Text]
  43. Ramaekers D, Ector H, and Aubert AE. The influence of age and gender on heart rate variability (HRV). J Am Coll Cardiol 33: 900–902, 1999.[CrossRef][Web of Science][Medline]
  44. Ramaekers D, Ector H, Aubert AE, Rubens A, and Van de Werf F. Heart rate variability and heart rate in healthy volunteers. Is the female autonomic nervous system cardioprotective? Eur Heart J 19: 1334–1341, 1998.[Abstract/Free Full Text]
  45. Rao RK and Yeragani VK. Decreased chaos and increased nonlinearity of heart rate time series in patients with panic disorder. Auton Neurosci 88: 99–108, 2001.[CrossRef][Web of Science][Medline]
  46. Rosenstein MT, Collins JJ, and De Luca CJ. A practical method for calculating the largest Lyapunov exponents from small data sets. Physica D 65: 117–134, 1993.[CrossRef]
  47. Ryan SM, Goldberger AL, Pincus SM, Mietus J, and Lipsitz LA. Gender- and age-related differences in heart rate dynamics: are women more complex than men? J Am Coll Cardiol 24: 1700–1707, 1994.[Abstract]
  48. Sato N, Miyake S, Akatsu J, and Kumashiro M. Power spectral analysis of heart rate variability in healthy young women during the normal menstrual cycle. Psychosom Med 57: 331–335, 1995.[Abstract/Free Full Text]
  49. Schwartz PJ, La Rovere MT, and Vanoli E. Autonomic nervous system and sudden cardiac death. Experimental basis and clinical observations for post-myocardial infarction risk stratification. Circulation 85: I77–I91, 1992.[Medline]
  50. Skinner JE, Pratt CM, and Vybiral T. A reduction in the correlation dimension of heartbeat intervals precedes imminent ventricular fibrillation in human subjects. Am Heart J 125: 731–743, 1993.[CrossRef][Web of Science][Medline]
  51. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heart rate variability: standards of measurement, physiological interpretation and clinical use. Circulation 93: 1043–1065, 1996.[Free Full Text]
  52. Tulppo MP, Hughson RL, Makikallio TH, Airaksinen KE, Seppanen T, and Huikuri HV. Effects of exercise and passive head-up tilt on fractal and complexity properties of heart rate dynamics. Am J Physiol Heart Circ Physiol 280: H1081–H1087, 2001.[Abstract/Free Full Text]
  53. Tulppo MP, Makikallio TH, Takala TE, Seppanen T, and Huikuri HV. Quantitative beat-to-beat analysis of heart rate dynamics during exercise. Am J Physiol Heart Circ Physiol 271: H244–H252, 1996.[Abstract/Free Full Text]
  54. Umetani K, Singer DH, McCraty R, and Atkinson M. Twenty-four hour time domain heart rate variability and heart rate: relations to age and gender over nine decades. J Am Coll Cardiol 31: 593–601, 1998.[Abstract/Free Full Text]
  55. Vallejo M, Marquez MF, Borja-Aburto VH, Cardenas M, and Hermosillo AG. Age, body mass index, and menstrual cycle influence young women's heart rate variability—a multivariable analysis. Clin Auton Res 15: 292–298, 2005.[CrossRef][Web of Science][Medline]
  56. Voss A, Kurths J, Kleiner HJ, Witt A, Wessel N, Saparin P, Osterziel KJ, Schurath R, and Dietz R. The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death. Cardiovasc Res 31: 419–433, 1996.[CrossRef][Web of Science][Medline]
  57. Willson K, Francis DP, Wensel R, Coats AJ, and Parker KH. Relationship between detrended fluctuation analysis and spectral analysis of heart-rate variability. Physiol Meas 23: 385–401, 2002.[CrossRef][Web of Science][Medline]
  58. Wilson PW and Evans JC. Coronary artery disease prediction. Am J Hypertens 6: 309S-313S, 1993.[Medline]
  59. Yamamoto Y and Hughson RL. On the fractal nature of heart rate variability in humans: effects of data length and beta-adrenergic blockade. Am J Physiol Regul Integr Comp Physiol 266: R40–R49, 1994.[Abstract/Free Full Text]
  60. Yamamoto Y, Nakamura Y, Sato H, Yamamoto M, Kato K, and Hughson RL. On the fractal nature of heart rate variability in humans: effects of vagal blockade. Am J Physiol Regul Integr Comp Physiol 269: R830–R837, 1995.[Abstract/Free Full Text]
  61. Yeragani VK, Mallavarapu M, Radhakrishna RK, Tancer M, and Uhde T. Linear and nonlinear measures of blood pressure variability: increased chaos of blood pressure time series in patients with panic disorder. Depress Anxiety 19: 85–95, 2004.[CrossRef][Web of Science][Medline]
  62. Yeragani VK, Nadella R, Hinze B, Yeragani S, and Jampala VC. Nonlinear measures of heart period variability: decreased measures of symbolic dynamics in patients with panic disorder. Depress Anxiety 12: 67–77, 2000.[CrossRef][Web of Science][Medline]
  63. Yeragani VK, Sobolewski E, Kay J, Jampala VC, and Igel G. Effect of age on long-term heart rate variability. Cardiovasc Res 35: 35–42, 1997.[Abstract/Free Full Text]



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