Chaotic global analysis of heart rate variability following power spectral adjustments during exposure to traffic noise in healthy adult women

Aim. Previous studies have described the substantial impact of different types of noise on the linear behaviour of heart rate variability (HRV). Yet, there are limited studies about the complexity or nonlinear dynamics of HRV during exposure to traffic noise. Here, we evaluated the complexity of HRV during traffic noise exposure via six power spectra and, when adjusted by the parameters of the Multi-Taper Method (MTM). Material and methods. We analysed 31 healthy female students between 18 and 30 years old. Subjects remained at rest, seated under spontaneous breathing for 20 minutes with an earphone turned off and then the volunteers were exposed to traffic noise through an earphone for a period of 20 minutes. The traffic noise was recorded from a busy urban street and the sound involved car, bus, trucks engineers and horn sounds (71-104 dB). Results. The results stipulate that CFP3 and CFP6 are the best metrics to distinguish the two groups. The most appropriate power spectra were, Welch and MTM. Increasing the DPSS parameter of MTM increased the performance of both CFP3 and CFP6 as mathematical markers. Adaptive was the preferred type for Thomson’s nonlinear combination method. Conclusion. CFP3 with the adaptive option for MTM, and increased DPSS is designated as the best mathematical marker on the basis of five statistical tests.

Traffic noise exposure can be unpleasant and distracting, which may have effects on physiological variables. It is often found in hazardous situations as a result of industrialization and urbanization [1]. Hence, the scientific research literature has previously investigated the effects of different types of noise on autonomic nervous system (ANS) by investigating heart rate variability (HRV) [1].
The consecutive heart beats (RR-intervals) derived from the electrocardiograph (ECG) have been demonstrated to fluctuate in an irregular and chaotic manner [2]. Here, the objective is to estimate the possible pathological risks that traffic noise exposure during driving in women poses to the individual by evaluating the heart rate variability (HRV). To complete this we enforced the Shannon Entropy [3] and Detrended Fluctuation Analysis (DFA) [4] algorithms to six alternate power spectra to understand which exhibited the greatest parametric sensitivity. At the outset, Garner and Ling [5] computed the spectral Entropy 5and spectral Detrended Fluctuation Analysis (sDFA) [5], and these were based on the Welch power spectrum [6,7]. Later, the high spectral Entropy (hsEntropy) [8] and high spectral Detrended Fluctuation Analysis (hsDFA) [8]; were formulated founded on the Multi-Taper Method (MTM) power spectrum [9]. Yet, here further parameters based on Covariance [10], Burg [10], Yule-Walker [11] and the Periodogram [12] are computed. By implementing six different power spectra we hope to accomplish results of greater significance by parametric and non-parametric statistics and, the three effect sizes (discussed later) when equating the control subjects to those experiencing exposure to traffic noise via an earphone. It would then be possible to reach a clinical diagnosis quicker and provide the required treatment earlier.
Chaotic global techniques are more responsive to erraticism in dynamical systems than those based on linear, time-domain, geometric methods, frequency domain or the nonlinear measurements [2]. Chaotic behaviour in biological systems typically indicates normal physiological status; while a reduction of chaotic tendencies could be a pathophysiological marker [13]. Such computations are beneficial when assessing surgical patients [13], particularly if sedated [14,15] or incapable of indicating discomfort as with sleep apnea [16] or those with "air hunger" [17,18]. We expected the subjects exposed to traffic noise to perform in a nonlinear manner equivalent to persons with cardiac arrest [19], epileptic seizures [20,21], chronic obstructive pulmonary disease (COPD) [22] or attention deficit hyperactivity disorder (ADHD) [8].
The advantage for constructing the correlation with HRV is that it can provide a benchmark of the potential risks of the dynamical diseases [23] in the traffic noise exposure group. HRV is a simple, reliable and inexpensive technique to continuously record the ANS. Therefore, we aimed to evaluate nonlinear HRV through chaotic global analysis during exposure to traffic noise.

Material and methods
All method and materials were exactly as in the study by Alves M, et al. [24], which followed the STROBE (STrengthening the Reporting of OBservational studies in Epidemiology) guidelines. Our study previously published [24] described information regarding setting, variables, study design, participants, measurements, data sources, quantitative variables description, statistical methods and potential sources of bias.
Ethical approval and informed consent. All procedures were performed in accordance with the 466/2012 resolution of the National Health Council of December 12th 2012 and all subjects signed a confidential informed consent letter. All experimental protocols were inspected and approved by the Research Ethics Committee in Research of UNESP/Marilia through the Brazilian online platform (Number 5406).
Six Power Spectra. Formerly, we computed the Welch and Multi-Taper Method (MTM) power spectras. De Souza NM, et al. [25] described the application of the Welch power spectrum to achieve chaotic globals in subjects with type I diabetes mellitus. Yet, it was anticipated that since the MTM is an adaptive and nonlinear technique, and as such has a reduced amount of spectral leakage it would potentially be more sensitive to chaotic responses. The high spectral Entropy (hsEntropy) and high spectral Detrended Fluctuation Analysis (hsDFA) via the MTM power spectrum have been applied in studies on malnutrition [26], youth obesity [27] and ADHD [8]. Throughout all of the studies we applied the MTM power spectrum to generate the third parameter spectral Multi-Taper Method (sMTM) [5]. This quantifies the extent of broadband noise in the system associated with increasing chaotic response. This parameter remains unchanged throughout all the subsequent analysis.
In this study, when calculating spectral Entropy (hsEntropy for MTM) or spectral DFA (hsDFA for MTM) we enforce six different power spectra (Welch, MTM, Covariance, Burg, Yule-Walker and Periodogram) to give six variants of these parameters. There are seven different non-trivial permutations of three chaotic globals. The Chaotic Forward Parameters (CFP1 to CFP7) enables seven different combinations of chaotic globals to be applied to ensure optimum chaotic response. Initially whilst assessing the effects of the six power spectra all three chaotic global values have equal weighting of unity. The settings for these six power spectra are described next.
When we compute spectral Entropy and sDFA via Welch's method the parameters are set at: (i) sampling frequency of 1Hz, (ii) 50% overlap, (iii) a Hamming window and the number of discrete Fourier transform (DFT) point to use in the power spectral density (PSD) estimate is the greater of 256 or the next power of two greater than the length of the segments, and (iv) there is no detrending.
Then, with MTM, the parameters are set as the following: (i) sampling frequency of 1Hz; (ii) time bandwidth for the discrete prolate spheroidal sequences (DPSS) often referred to as slepian sequences [28] is 3; (iii) FFT is the larger of 256 and the next power of two greater than the length of the segment (iv) Thomson's adaptive nonlinear combination method to combine individual spectral estimates is applied.
The Periodogram power spectral density estimate is a nonparametric estimate of a wide-sense stationary random process using a rectangular window. The number of points in the discrete Fourier transform (DFT) is a maximum of 256 or the next power of two greater than the signal length.
Finally, for the Covariance, Burg and Yule-Walker methods the order is of the autoregressive model (AR) used to produce the power spectra density estimate and is set to 16. A default discrete Fourier transform (DFT) length of 256 is applied.

Nonlinear & statistical analysis
Chaotic Globals & CFP1 to CFP7. Spectral Entropy [5] (hsEntropy for the MTM) is an algorithm founded on the unevenness of the amplitude and frequency of the power spectrums peaks. Shannon entropy [3] is the function applied to the cited power spectrum. We compute the Shannon entropy for three values attained from three various power spectra. So, the power spectra at three test settings: (a) a sine wave, (b) uniformly distributed random variables, and (c) the oscillating signal from the subjects exposed to traffic noise. The three values are reduced proportionately so that their sum of squares is equal to one. Spectral Entropy (hsEntropy for the MTM) is the median value of the three.
DFA was derived in 1995 [4]. It can be executed on time-series where the mean, variance and autocorrelation adjust with time. sDFA (or, hsDFA for MTM) is where DFA is applied to the frequency rather than time. To acquire sDFA (or, hsDFA for MTM) we estimate the spectral adaptation in precisely the same manner as with Spectral Entropy (or, hsEntropy for MTM). Yet, DFA is the algorithm enforced onto the appropriate power spectrum.
Spectral Multi-Taper Method (sMTM) [5] is derived from elevated broadband noise intensities generated in MTM power spectra by irregular and often chaotic signals. sMTM is the area beneath the power spectrum but above the baseline.
CFP1 to CFP7 are applied to RR-intervals from the control subjects and those undergoing traffic noise exposure. sDFA (and hsDFA) respond to chaos contrariwise to the others, so we subtract its value from unity. There are seven non-trivial permutations of the three chaotic globals [8].

One-Way Analysis Of Variance & Kruskal-Wallis Tests.
Parametric statistics accept that datasets are normally distributed, so they use the mean as a measure of central tendancy. If we are unable to normalize the data we should not compare means. To prove normality we assessed the Anderson-Darling [29], Ryan-Joiner [30] and Lilliefors [29] tests. The Anderson-Darling test for normality applies an empirical cumulative distribution function, but the Ryan-Joiner test is a correlation-based test comparable to Shapiro-Wilk [31]. The Lilliefors test is particularly useful when studies have small sample sizes. Yet, in this study results were inconclusive throughout so we cannot declare that the observations are normally or non-normally distributed. So, we apply parametric and non-parametric tests of significance. Those chosen were the one-way analysis of variance (ANOVA1) [32] and the Kruskal-Wallis [33] tests of significance, respectively.
Cohen's d s , Hedges's g s and Glass's ∆ Tests. Cohen's d s [34] is the leading subcategory of effect sizes. It refers to the standardized mean difference between two groups of independent observations for the appropriate sample [35]. It is founded on the sample means and gives a biased estimate of the population effect size [36].
In the algebraic formula for Cohen's d s , the numerator is the variation between the means of two groups of observations. The denominator is the pooled standard deviation. These differences are squared. Then, they are summed and divided by the number of observations minus one for bias (hence, Bessel's correction) in the estimate of the population variance. Finally, the square root is applied.
Cohen's d s is often denoted as the uncorrected effect size. The corrected effect size is unbiased and may be termed Hedges's g s [37]. The difference between Cohen's d s and Hedges's g s is tiny especially in sample sizes greater than 20 [38]. Its algebraic formula is beneath. The same subscript letter in Hedges's g s is applied to distinguish the different calculations; as is the case here for Cohen's d s .
Hedges's g s = Cohen's d s x 3 1 -4(n 1 +n 2 )-9 Finally, when the standard deviations differ substantially between conditions, Glass's ∆ delta may be suitable [39]. This calculates the control group's standard deviation alone, and the experimental group is avoided.

CFP3 & CFP6 -MTM Spectrum only Thomson's nonlinear combination methods & DPSS.
Now we assess the outcome of manipulating Thomson's nonlinear combination settings on the MTM spectra. There are three options. They are "adapt", "eigen", or "unity" and are the weights on individual tapered power spectral density (PSD) estimates. The default "adapt" is the adaptive frequency-dependent weights. The "eigen" method weights each tapered PSD estimate by the eigenvalue (frequency concentration) of the corresponding Slepian taper. The "unity" method weights each tapered PSD estimate equally [41].
Moreover, we simultaneously assess the effect of changing the settings of the DPSS from 2 to 13. A DPSS equal to 1, indicates the conventional Blackman and Tukey [42,43] Fast Fourier Transform (FFT), so is excluded. DPSS affects the adaptation properties of the tapers with the intention of reducing spectral leakage. Whilst assessing the outcomes of the Thomson's nonlinear combinations settings and the levels of DPSS on the chaotic response the sampling frequency is fixed at 1Hz for the MTM and Fast Fourier Transform of length 256 is enforced. We assessed the outcomes of DPSS (2 to 13) and Thomson's nonlinear combinations ("adaptive", "eigen" and "unity"). Throughout the analysis there are 500 RRintervals. We assessed CFP3 and CFP6. These are the only groupings significant under the default conditions and with all six power spectra.

ANOVA1, Kruskal-Wallis & Effect Sizes
We have computed the seven permutations of the three chaotic globals CFP1 to CFP7 for 31 female subjects; both controls and those exposed to traffic noise via the earphone. We achieved this with 500 RR intervals throughout. The statistical results are illustrated in the six boxplots, one for each power spectrum as in Figure 1.
As of Table 1 we detected that the combinations CFP3 and CFP6 behave equally during all six power spectra. All CFP3 and CFP6 for Welch, MTM, Covariance, Burg, Yule-Walker and Periodogram have similar reponses. They have a p<0,001 for the ANOVA1 and Kruskal-Wallis tests of significance and, have large to very large effect sizes by all three measures -Glass's ∆ Delta, Hedges g s and Cohen's d s . They demonstrate an increase in chaotic response when comparing the controls to the traffic noise exposed group.
With MTM and Welch power spectra there are also significant results for CFP2 (p<0,05, medium effect sizes) and CFP5 (p<0,01, large effect sizes). Be that as it may, as revealed by the negative effect sizes the traffic noise exposed subjects exhibit a decrease in response when comparing control to the traffic noise exposed subjects. The Welch and MTM power spectra perform similarly throughout. MTM has the slightly better levels of significance when compared by the three effect sizes. It is not possible to distinguish between the two on the basis of the ANOVA1 and Kruskal-Wallis tests as the both give p<0,001. This is the advantage of calculating the effect sizes in this study.
Next the Periodogram power spectra has a significant result for CFP5 (p<0,01, medium effect size), yet the effect size value is negative and so responds in the opposite direction to those it calculated for CFP3 and CFP6. Those values which give negative values for the effect sizes can be ignored. They are responding incorrectly and have the lesser significances than CFP3 and CFP6. Now we assess the consequence that the DPSS has on the significance of the results. We use the three effect sizes (Glass's ∆ Delta, Hedges g s and Cohen's d s ) here, as when we calculate the ANOVA1 and Kruskal-Wallis they all perform equally with p<0,001. Therefore, it is very difficult to distinguish which values perform best. The range of statistical outcomes is unable to discriminate between their results.
When we calculate the effect sizes the values are similar throughout with all values greater than 1,08 (large effect size) and the majority over 1,20 (very large effect size). It is evident that the values for both CFP3 and CFP6 and for the three options of Thomson's nonlinear combination methods to combine individual spectral estimates ("adapt", "eigen" and "unity"), increase slightly with increasing DPSS. Effect sizes for CFP3 are greater and therefore more significant than CFP6. So increasing DPSS increases the significance of the results. So a DPSS of 13 where there is a reduced amount of spectral leakage and more adaptation (compared to FFT of Blackman-Tukey, DPSS of 1), is able to distinguish between the two groups in a more statistically significant manner. The mathematical markers are more efficient. Note: the properties of the discrete prolate spheroidal sequences (DPSS) value (2 to 13) on the effect sizes Glass's ∆ Delta, Hedges g s and Cohen's d s when comparing chaotic globals CFP3 and CFP6 for control subjects and those undergoing traffic noise exposure (both n=31). The remaining parameters are set as (a) sampling frequency of 1Hz; is (b) a discrete Fourier transform (DFT) length of 256 or the next power of two greater than the length of the segment (c) Thomson's "adaptive" nonlinear combination method to combine individual spectral estimates is applied. 500 RR-intervals were assessed thoughout.

Discussion
We can recognize from the results above that the most robust parameters throughout are CFP3 and CFP6. This was the situation for all six power spectra. MTM, Welch and Periodogram did have other groups which were significant but they responded in the inappropriate manner regarding their chaotic response.
So, for three of the power spectra -Welch, MTM and Periodogram all predicated on the Fast Fourier Transform, and all are non-parametric methods. It is expected that CFP3 would be the most statistically robust parameter. It has the best values when assessed by the three effect sizes.
It is notable that the Welch and MTM power spectra perform very similarly, as would be expected. A Periodogram spectrum is able to give consistent results with higher noise levels than the other two. But it is the least sophisticated algorithm that we applied in this study [12]. Despite the Periodogram matching the MTM and Welch it is rejected because, it is a blunt tool; the MTM and Welch have more parameters which can be modified to achieve better responses. The main ones we assessed are for MTM and are the DPSS (2 to 13) and Thomson's nonlinear combination methods to combine individual spectral estimates ("adapt", "eigen" and "unity").  Table  2 with the exception that Thomson's "eigen" nonlinear combination method to combine individual spectral estimates is applied. Again, 500 RR-intervals were used for the calculations throughout. Note: the effects of discrete prolate spheroidal sequences (DPSS) value (2 to 13) on Glass's ∆ Delta, Hedges g s and Cohen's d s when relating chaotic globals CFP3 and CFP6 for control subjects (n=31) and those undergoing traffic noise exposure (n=31). We used 500 RR-intervals throughout. The remaining parameters are as with Table 2 and 3 with the exception that Thomson's "unity" nonlinear combination method to combine individual spectral estimates is applied.
For the other three power spectra, all are parametric methods -Burg, Covariance and Yule-Walker and the results are mostly comparable, marginally less significant when assessed by effect sizes. The order of the power spectra has little influence over the results. Here we set the orders to 16. These are more computer processor intensive algorithms, and so slower to calculate. It is recommended where possible to use the non-parametric techniques.
Returning to MTM we call these derivatives high spectral Entropy (hsEntropy) and high spectral Detrended Fluctuation Analysis (hsDFA) and they do slightly outperform those derived from the Welch power spectrum. Yet, the MTM power spectrum excels with regards to the various parameters which define the spectrum. For instance, the time bandwidth for the DPSS can be adjusted and Thomson's "adaptive" nonlinear combination method to combine individual spectral estimates can be attuned to the "eigenvalue" or "unity" settings.
This flexiblity enables the possibility of increasing the significance of CFP3 and CFP6 derived from MTM power spectra. It is statistically valuable to increase the DPSS to 13 and, thus outperformed those with lower DPSS when compared by the three effect sizes (see Tables 2 to 4). Adjustments of Thomson's nonlinear combinations method appears limited but "adapt" is the slightly better performer on the three effect sizes (also, Tables 2 to 4). Having time-series which are longer, and increasing the number of subjects for both control and traffic noise exposed subjects could be advantageous.
The chaotic global metrics CFP3 (and CFP6), imposed on the HRV of women exposed to traffic noises and compared to the control groups are capable of statistically discriminating the variation between them. They demonstrate an increase in chaotic response when comparing the controls to the traffic noise exposed group. The results are more significant for CFP3 than CFP6, and the best performers are the Welch and MTM power spectra. When the DPSS is elevated for the MTM power spectrum the mathematical marker is improved; with increased effect sizes. The MTM power spectra is advocated as the best way of calculating chaotic globals with highest DPSS set at 13. The three Thomson's nonlinear combination methods to combine individual spectral estimates settings had a minimal consequence, but the "adapt" option was slightly improved on the basis of the three effect sizes. It is accepted that longer timeseries and increasing the number of subjects could be useful and, likely increase the statistical significance of the results.

Conclusion
Nonlinear HRV analysis through global chaotic approach detected changes in heart rhythm during traffic noise exposure, indicating increased nonlinear HRV during auditory stimulation.

Relationships and Activities.
This study received financial support from FAPESP (Process number 2012/01366-6). Dr. Vitor E. Valenti receives financial support from the National Council for Scientific and Technological Development, an entity linked to the Ministry of Science, Technology, Innovations and Communications from Brazil (Process number 302197/2018-4).