Day-Night Variations In Nonlinear Heart Rate Variability Measures In A Large Healthy Population

Day-Night Variations In Nonlinear Heart Rate Variability Measures In A Large Healthy Population

Vandeput S

, Verheyden B

, Aubert AE

, Van Huffel S

1

Department of Electrical Engineering, ESAT-SCD, Katholieke Universiteit Leuven, Belgium,

Laboratory of Experimental Cardiology, Faculty of Medicine, Katholieke

Universiteit Leuven, Belgium steven.vandeput@esat.kuleuven.be

Abstract. Heart rate variability (HRV) measurements are used as markers of autonomic modulation of heart rate. Numerical noise titration was applied to a large healthy population and analyzed with respect to day-night variations. The transition phases of waking up and going to sleep were examined by an hourly analysis and resulted for many HRV measures in a clear circadian evolution. A higher nonlinear behaviour was observed during the night while nonlinear heart rate fluctuations decline with age. Both confirm the involvement of the autonomic nervous system in the generation of nonlinear and complex dynamics.

1 Introduction

Heart rate variability (HRV) measurements are used as markers of autonomic modulation of heart rate [1]. Standard time and frequency domain methods of HRV are well described by the Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology [2], but in the last decades, new dynamic methods of HRV quantification have been used to uncover apparent nonlinear fluctuations in heart rate. These nonlinear variations would enable the cardiovascular system to respond more quickly to changing conditions.

Conventional spectral analysis of HRV can provide analytical features of its cyclic variation, but fail to show the dynamic properties of the fluctuations. Nonlinear methods are typically designed to assess the quality, scaling and correlation properties, rather than to assess the magnitude of variability like conventional HRV methods do. Furthermore, it has been shown that the autonomic nervous system (ANS) control underlies the nonlinearity and the possible chaos of normal HRV [3]. Here the numerical noise titration technique [4] is used, which provides a highly sensitive test for deterministic chaos and a relative measure for tracking chaos of a noise-contaminated signal in short data segments

Other linear and nonlinear HRV measures are calculated too, giving the possibility to compare the results of this recently developed method with those of other techniques.

The purpose of this study, taking into account a sufficiently large number of healthy subjects between adolescence and old age, was to have an indication of the Noise Limit (NL) values, which are the output of the numerical noise titration technique, in normal healthy persons. So far, this method was only applied a few times and always to study relative differences between patient groups [5-6]. In addition, day-night differences in heart rate variability were investigated. In healthy subjects, a significant difference between day and night standard HRV was reported [7], reflecting the higher vagal modulation during the night.

We hypothesize now that RR interval time series at night are less chaotic compared to those at daytime.

2 Methods

2.1 Data acquisition

Twenty-four hour ECG recordings of 276 healthy subjects (135 women and 141 men

between 18 and 74 years of age) were obtained in Leuven (Belgium) using Holter monitoring. After R peak detection and visual inspection by the operator for verifying the peak detection, a file containing the consecutive RR intervals, called tachogram, was exported for later processing. The 24-h recordings were split into daytime (8–21h) and nighttime (23–6h). A detailed medical history was obtained from each participant. More details concerning the study population, monitoring and preprocessing are described in [7].

2.2 Linear HRV parameters

Linear HRV parameters were obtained in agreement with the standards of measurement, proposed by [2]. Mean and standard deviation (SD) of the tachogram, the standard deviation of the 5 minute average of RR intervals (SDANN), 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, power spectral density was computed by using fast Fourier transformation. In the frequency domain, low frequency power (0.04 – 0.15 Hz), high frequency power (0.16 – 0.40 Hz) and total power (0.01 – 1.00 Hz), as well as the ratio of low frequency over high frequency, were calculated. In addition, the power can be expressed in absolute values or in normalized units (NU).

2.3 Nonlinear HRV parameters

To assess the nonlinear HRV properties, several methods have been proposed in the past and are calculated here: 1/f slope [8], fractal dimension (FD) [9], detrended fluctuation analysis (DFA) [10], correlation dimension (CD) [11], approximate entropy (ApEn) [12] and Lyapunov exponent (LE) [13].

Numerical noise titration is a nonlinear data analysis technique that is a better alternative for the Lyapunov exponent (LE), which is a measure of the exponential divergence of nearby states. LE fails to specifically distinguish chaos from noise and can not detect chaos reliably unless the data series are inordinately lengthy and virtually free of noise, but those requirements are difficult, mostly even impossible, to fulfill for most empirical data. The different sections of the numerical noise titration algorithm are already well described in [14].

Modeling. For any heartbeat RR time series y

, n = 1, 2, …, N, a closed-loop version of the dynamics is proposed in which the output y

feeds back as a delayed input. The univariate time series are analysed by using a discrete Volterra autoregressive series of degree d and memory κ as a model to calculate the predicted time series y

:

2

0 1 1 2 2 1 1 2 1 2

1

1

( )

calc d

n n n n n n n M n

M m m m

y a a y a y a y a y a y y a y

a z n

    

        





        

 

 

(1)

where M = (κ + d)! / ( κ! d!) is the total dimension. Thus, each model is parameterised by κ and d which correspond to the embedding dimension and the degree of the nonlinearity of the model (i.e. d = 1 for linear and d > 1 for nonlinear model). The coefficients a

are recursively estimated from (1) by using the Korenberg algorithm.

Nonlinear detection (NLD). The goodness of fit of a model (linear vs. nonlinear) is measured by the normalised residual sum of squared errors:

     

 

2

2 1

2

1

, ,

N calc

n n

n N

n y

n

y d y

d

y



 















 ⁽²⁾

with

1

1

y n

n

N y





  ^{and    , d }

represents a normalised variance of the error residuals. The optimal model {κ

, d

} is the model that minimizes the Akaike information criterion:

  ^log   ^r

C r r

 N

  (3)

where ^{r }  ^{1, M}  is the number of polynomial terms of the truncated Volterra expansion from a certain pair ( κ, d).

Numerical noise titration. The NLD is used to measure the chaotic dynamics inherent in the RR series by means of numerical noise titration as follows:

1. Given a time series y

, apply the NLD to detect nonlinear determinism. If linear, then there is insufficient evidence for chaos.

2. If nonlinear, it may be chaotic or non-chaotic. To discriminate these possibilities, add a small (< 1% of signal power) amount of random white noise to the data and then apply NLD again to the noise corrupted data. If linear, the noise limit (NL) of the data is zero and the signal is non-chaotic.

3. If nonlinearity is detected, increase the level of added noise and again apply NLD.

4. Repeat the above step until nonlinearity can no longer be detected when the noise is too high (low signal-to-noise ratio). The maximum noise level (i.e. NL) that can be added to the data just before nonlinearity can no longer be detected, is directly related to the Lyapunov exponent (LE).

Decision tool. According to this numerical titration scheme, NL > 0 indicates the presence of chaos, and the value of NL gives an estimate of relative chaotic intensity. Conversely, if NL = 0, then the time series may be non-chaotic or the chaotic component is already neutralised by the background noise. Therefore, the condition NL > 0 provides a simple sufficient test for chaos. Details of NLD and numerical noise titration are discussed in [15- 16].

2.4 Analysis

After resampling the RR interval time series to the mean heart rate (Hz), the numerical noise titration was applied using a 300-second window and sliding the window every 30 seconds. All described HRV parameters were calculated during daytime (8-21h) and nighttime (23-6h) as well as for each hour of the day.

Statistical analysis was performed with SPSS Windows version 11.5 (Scientific Packages for Social Sciences, Chicago, IL, USA). Differences between day and night were analysed pairwise by the nonparametric Wilcoxon Signed Rank test. P < 0.05 was considered statistically significant.

3 Results

All values, expressed in mean ± standard deviation, for linear and nonlinear indices are listed in Tab. 1 , separately for day and night. The last column of Tab. 1 indicates for every HRV measure whether the day-night difference is statistically significant or not. During the night, heart rate was significantly lower (higher mean RR interval). In addition, a day-night variation was present in all linear and nonlinear HRV measures, except the Noise Limit (NL).

Concerning the time and frequency domain indices, measures related to vagal modulation

(pNN50, high frequency power) were higher. Low frequency power exhibited higher absolute

values during the night, but a higher relative contribution during the day. These variations

were present in both men and women and in all age categories as already found in a previous

study [12]. The relatively small differences in SD, SDANN and low frequency power,

however, did not always reach statistical significance in these smaller groups. Those day-

night changes in vagal modulation were linked to the day-night changes in basal heart rate

(correlation between differences in day-night heart rate and day-night high frequency power r

= -0.45, P < 0.001).

With respect to the nonlinear indices, significant day-night variation was visible in both male and female population for 1/f slope, FD, DFA α

DFA α

, ApEn and LE [17]. The value of CD increased slightly during the night, but not significantly for women.

Day Night Day-night difference Time domain HRV

Mean (ms) 724.2 ± 89.7 920.5 ± 125.9 ***

SD (ms) 104.3 ± 33.1 110.6 ± 40.1 *

SDANN (ms) 82.9 ± 31.3 74.9 ± 33.8 ***

rMSSD (ms) 31.5 ± 16.6 48.9 ± 29.9 ***

pNN50 (%) 7.4 ± 7.3 17.5 ± 15.5 ***

Freq domain HRV

LF power (ms

) 817 ± 572 1086 ± 983 ***

LF power (NU) 82.8 ± 8.7 74.8 ± 11.9 ***

HF power (ms

) 187 ± 246 433 ± 626 ***

HF power (NU) 17.2 ± 8.7 25.5 ± 11.9 ***

Total power (ms

) 2010 ± 1424 2846 ± 2319 ***

LF/HF 6.5 ± 3.5 4.0 ± 2.7 ***

Nonlinear HRV

1/f slope -1.19 ± 0.18 -1.12 ± 0.21 ***

FD 1.28 ± 0.09 1.22 ± 0.10 ***

DFA α

1.49 ± 0.14 1.42 ± 0.15 ***

DFA α

1.04 ± 0.11 1.14 ± 0.11 ***

CD 4.08 ± 0.76 4.41 ± 1.27 *

ApEn 0.77 ± 0.17 0.86 ± 0.19 ***

LE 0.26 ± 0.07 0.29 ± 0.09 ***

NL 4.09 ± 3.12 4.26 ± 3.99 NS

Tab 1. HRV measures (mean ± standard deviation) over complete population during day and night. For abbreviations, see Methods. Significance of day-night difference: *P<0.05,

**P<0.01, ***P<0.005, NS = non-significant.

SEX

Female Male

95% CI NL

6.0

5.5

5.0

4.5

4.0

3.5

3.0

night

day

Age

> 60 50-59 40-49 30-39

< 30

95% CI NL

6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0

night

day

Fig 1. Day-night variation by numerical noise titration (95% confidence interval around mean

NL), seperately for men and women (left) and per age category of 10 years (right).

Regarding the outcome of the noise titration technique, Fig. 1 shows that the day-night difference is larger in the male population compared to the female. In both groups, NL is higher at night although statistically not significant. Moreover, day-night variations were investigated according to age. Increasing age leads to a continuous decrease in NL during daytime, but this evolution can not be observed during night. Noise titration also shows an increasing diurnal variation for the categories of 40 years of age or more.

Being interested in the more subtle changes during the transitions between day and night, all HRV parameters were calculated for each of the 24 hours. For each linear (Fig. 2) and nonlinear (Fig. 3) HRV measure, mean and 95% confidence interval are plotted for each hour, for men as well as for women. In general, a good evolution over 24 hours can be seen.

Especially, the transitions between day and night are very valuable and instructive.

Fig 2. Evolution over 24 hours for several linear HRV parameters: mean, SD, rMSSD, pNN50, LF power (%), HF power (%), total power and LF/HF (from top to bottom and

from left to right). Bars represent mean and corresponding 95% confidence interval.

Concerning the standard HRV measures in time and frequency domain, these diurnal

variations can be seen in the male and female population. Sometimes there is a smooth

transition from night to day, spread over several hours while in other cases (in particular SD),

a strong change can be observed between two consecutive hours in the morning.

Fig 3.Evolution over 24 hours for several nonlinear HRV parameters: 1/f, FD, DFA α

DFA α

, CD, ApEn, LE and NL (from top to bottom and from left to right). Bars represent

mean and corresponding 95% confidence interval.

In the nonlinear HRV parameters, the same patterns can be seen, but for 1/f, ApEn, LE and NL, the evolution is less clear, mainly due to the larger 95% confidence bounds. The values of FD and DFA α

increased significantly at daytime while 1/f slope, DFA α

and CD increased during night hours. Men and women have the same diurnal variations, except for LE. However ApEn and NL show the same evolution for men and women, both measures have a higher gender difference compared to other nonlinear measures.

The noise titration technique did not obtain a significant day-night difference originally, although the analysis per hour give a rather clear 24h evolution, even better than the Lyapunov exponent or the approximate entropy. Looking at the transitions between day and night in all HRV measures, a change happens around 8 in the morning and 22 in the evening.

Investigating more in detail why NL failed to distinguish between day and night, mean NL

values for each hour are depicted by boxplots in Fig. 4(a). By grouping hours into day (9-

22h) or night (23-8h), mean NL can be calculated for both periods and for each person. In

Fig. 4(b) the blue line presents the mean NL for each hour while the red line indicates the

mean value over nighttime (13.23 ± 7.56) and daytime (10.96 ± 8.91). However the day-

night difference was not significant (p = 0.437) when using the original day (8-21h) and night

(23-6h) files as shown in Tab. 1, the new definition of day and night enables NL to make a

statistically significant (p = 5.17 E

) day-night variation by pairwise comparison for each

subject using Wilcoxon Signed Rank test.

(a) (b)

Fig 4. (a) Boxplot presenting NL values per hour of all 276 subjects. (b) Mean NL per hour (blue) compared to mean NL over nighttime (23-8h) and daytime (9-22h) (red).

Fig 5. Boxplot indicating statistical significance between day and night by numerical noise titration (NL) based on analysis per hour and defining day from 9 till 22h and night

from 23 till 8h.

4 Discussion

Heart rate variability is considered a parameter of cardiovascular health. In this study, all linear and the most commonly used nonlinear HRV measures (1/f slope, FD, DFA, CD, ApEn and LE) were examined in a population of 276 healthy subjects between 18 and 71 years of age. In addition, the recently developed method of numerical noise titration was applied leading to a new nonlinear HRV measure, called Noise Limit (NL). Nowadays, this technique is only applied a few times [5-6] and always to study relative differences between patient groups. Being interested in the NL values of normal persons and comparing them with other HRV measures, this study is performed in a large healthy population.

Concerning the day-night variation, time and frequency domain indices support the previously observed increase in vagal modulation during nighttime as described in [7].

pNN50 , rMSSD and the proportion of HF power increase during night, while heart rate

slows down. Although LF power increases in absolute value, its relative contribution

decreases, again stressing the vagal dominance at night.

During nighttime, there was a tendency for higher nonlinearity too as already described in [17]. LE, CD, DFA α

and ApEn increased while the 1/f slope came closer to real 1/f behaviour. Only FD and DFA α

decreased. This was the case in both the male and female population. Contrary to our hypothesis, even NL was higher at night meaning that in healthy persons there is more chaos during sleep than awake and that heart rate is not more predictable during night than by day. This confirms the higher nonlinearity in the tachogram at night.

Moreover, day-night variation by noise titration was investigated according to age.

Increasing age led to a continuous decrease in NL during daytime, but this evolution was not visible during night. This observation corresponds with previous studies in which a decrease of nonlinear behaviour with increasing age was found [18-21]. Increasing age might result in an increased inability of the cardiac system to respond adequately to changing conditions.

In this study, the transition phases of waking up and going to sleep were examined by the hourly analysis. The morning and evening periods can also contain potentially important information [22]. Some HRV measures had a smooth transition over several hours between night and day, while other ones showed a strong change over two consecutive hours in those periods. However ApEn and NL had the same circadion evolution for men and women, both measures had a higher gender difference compared to other nonlinear measures.

By grouping hours into day (9-22h) or night (23-8h), noise titration resulted in a strongly significant day-night difference while this was not the case when using the original day (8- 21h) and night (23-6h) files. Consequently, the technique seems to be very sensitive to the definition of day and night, more than most other nonlinear HRV parameters. Nevertheless, noise titration succeeds in presenting the circadian variation as efficiently as other nonlinear measures.

5 Conclusion

In summary, for the first time the numerical noise titration technique was applied to a large healthy population and analyzed with respect to day-night variations. The transition phases of waking up and going to sleep were examined by an hourly analysis and resulted for many HRV measures in a clear circadian evolution. A higher nonlinear behaviour was observed during the night while nonlinear heart rate fluctuations decline with age. Both confirm the involvement of the autonomic nervous system in the generation of nonlinear and complex dynamics.

Acknowledgement

Research supported by GOA-AMBioRICS, CoE EF/05/006, IUAP P5/22, FWO-G.0519.06 and ESA (Prodex-8 C90242).

Steven Vandeput and Bart Verheyden are supported by the Belgian Federal Office of Scientific Affairs (ESA-PRODEX).

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