Edited by: George E. Billman, Ohio State University, USA
Reviewed by: Mika Tarvainen, University of Eastern Finland, Finland; Yael Yaniv, Technion – Israel Institute of Technology, Israel
*Correspondence: Juan Bolea
This article was submitted to Clinical and Translational Physiology, a section of the journal Frontiers in Physiology
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
The purpose of this study is to characterize and attenuate the influence of mean heart rate (HR) on nonlinear heart rate variability (HRV) indices (correlation dimension, sample, and approximate entropy) as a consequence of being the HR the intrinsic sampling rate of HRV signal. This influence can notably alter nonlinear HRV indices and lead to biased information regarding autonomic nervous system (ANS) modulation. First, a simulation study was carried out to characterize the dependence of nonlinear HRV indices on HR assuming similar ANS modulation. Second, two HR-correction approaches were proposed: one based on regression formulas and another one based on interpolating RR time series. Finally, standard and HR-corrected HRV indices were studied in a body position change database. The simulation study showed the HR-dependence of non-linear indices as a sampling rate effect, as well as the ability of the proposed HR-corrections to attenuate mean HR influence. Analysis in a body position changes database shows that correlation dimension was reduced around 21% in median values in standing with respect to supine position (
Heart rate (HR) variability (HRV) has been studied as a non-invasive technique to assess autonomic nervous system (ANS) regulation of the heart. Although, HRV analysis is still controversial (Karemaker,
During the last decades, HRV analysis has been extended including nonlinear indices based on chaos theory. These methodologies describe ANS in terms of regularity and complexity. Non-linear indices have been studied in a wide range of cardiovascular diseases revealing discriminant power for risk stratification (Maestri et al.,
However, the physiological interpretation of HRV as a marker of ANS activity may be blurred since several factors could affect how intrinsic pacemaker cells and ANS activity are expressed in HRV (Yaniv et al.,
The goal of this study is to assess and attenuate the HR influence as sampling rate on nonlinear HRV indices in order to provide insight in their physiological interpretation as markers of ANS modulation. To assess the influence of HR on nonlinear HRV indices, a simulation study is conducted in which changes in ANS modulation are independent of changes on mean HR. Based on simulation results, two approaches are proposed to attenuate this mean HR influence. Finally, HR-corrected nonlinear HRV indices are computed over a body position changes database to study their performance under ANS elicitation.
This database was developed collaboratively at Harvard Medical School, Massachusetts Institute of Technology, and the Favaloro Foundation Medical School. The whole cohort of short-term recordings comes from two data collecting studies. Further details of this database can be found in Sobh et al. (
Thirteen male subjects of age 21.6 ± 4.4 years (Mean ± SD; range, 19–38 years) with no history of cardiopulmonary disease participated in a study carried out at Clinical Research Center at the Massachusetts Institute of Technology, USA.
It comprises groups of subjects of different ages. Only the young group was included in our work (9 subjects, 26.7 ± 4.7 years; range, 20–35 years).
Thus, from the whole database we selected 22 subjects. Two recordings per subject were acquired containing 7-min electrocardiographic (ECG) and respiration (RP) signals, sampled at 360 Hz. The protocol included postural changes. First, ECG and RP signals were recorded while subjects were in supine position. Then, subjects changed to standing position and after 5 min, to allow reaching hemodynamic equilibrium, ECG and RP signals were recorded in standing position. Subjects were asked to breathe following an irregular sequence of tones (Sobh et al.,
Twenty young rigorously-screened healthy subjects underwent 120 min of supine resting while continuous ECG and RP signals were recorded at 250 Hz while watching the movie Fantasia, Disney 1940, to help maintain wakefulness. Further database information is available elsewhere (Iyengar et al.,
Because the reliability of the HRV analysis can be compromised by low sampling frequency of ECG recordings (Merri et al.,
Approximate, sample entropy and correlation dimension are methods that exploit the phase-space representation of a time series based on Taken's theorem (Takens,
Correlation dimension,
Non-linear indices estimation may be compromised when the amplitude value of time series appears discrete in a reduced set of values due to the lack of variation. A pre-processing stage is included and details can be found elsewhere (Bolea et al.,
A simulation study is conducted to assess the mathematical relationship between HR and nonlinear HRV indices. The simulation study was carried out based on a HRV representation through the IPFM model. This model assumes that the ANS influence on the sinoatrial node can be represented by a modulating signal,
Fantasia database was selected to compute modulating signals. Assuming that
Instantaneous heart rate
Spectral analysis was applied to 5-min modulating signals
Among all modulating signals, only those which presented one marked peak on each band (LF and HF band) were selected. Spectral indices such as the powers and the frequency peaks were used to generate synthetic modulating signals using an autoregressive moving average technique (ARMA; Orini et al.,
Then, the IPFM model was applied on each stochastic realization, varying the parameter
Another simulation was done based on the BPC database characteristics. However, since subjects were asked to breathe following an irregular sequence of tones, the HF band does not show a dominant peak. In this case, the low and high frequencies used to feed the ARMA model were placed in the middle of LF and HF band, respectively. Then, modulating signals were simulated from spectral indices derived from supine and upright positions. This extends the analysis of HRV dependence on HR under enhanced sympathetic conditions.
The methodology used to compute nonlinear HRV indices, considered in this study, is applied over linearly detrended and normalized RR time series. The detrending ensures that mean HR values are removed from the series whereas the normalization eliminates the influence of mean HR on HRV amplitude. Despite this fact, the effect of mean HR as sampling rate might still be present on them. In this section this effect is investigated on the simulation study, where changes in mean HR are independent from changes in ANS modulation. First, a mathematical relationship between nonlinear HRV indices and HRM is assessed by two regression formulas; then, a HR-correction is proposed based on these formulas. Second, interpolation of RR series is proposed to attenuate the sampling rate influence by mean HR on nonlinear HRV indices.
In order to explore the relationship between nonlinear HRV indices and HR the following regression models were proposed.
where X ∈ {
Based on the former models HR-correction formulas were obtained by projecting each nonlinear index onto a standard level of
where ξ is the correction factor.
Transformation of X_{C}_{1} or X_{C}_{2} and RR into linear relationship was used to compute Pearson correlation coefficient ρ. Then, optimization was assessed by total least squares providing correction factors by the Golden Cut Search satisfying ρ(ξ) = 0.
Correction factors were computed on each stochastic realization. Thus, subject-specific correction was defined considering the correction factors of the 50 stochastic realizations for each modulating signal and computing the median of the HR-corrected indices.
Furthermore, a unique correction parameter was computed considering all stochastic realizations for all modulating signals. The transformation and optimization technique described above was applied to median values for each nonlinear index, thus defining a median correction approach to obtain
RR series are unevenly sampled being the HR its sampling rate. This implies that the number of data information for the same time interval is dependent on HR. On the other hand, it is known that estimation of nonlinear indices such as correlation dimension, sample, and approximate entropy are dependent on data length (Havstad and Ehlers,
Kolmogorov–Smirnov test was used to test the normality of data distributions. Mann–Whitney
Bland–Altman plots were used to analyse the agreement of subject-specific vs. median correction formulas. The intra-classes coefficient (ICC) was computed by SPSS for Windows, Version 15.0. Chicago, SPSS Inc.
Non-linear HRV indices (
The relationship between nonlinear HRV indices and RR is assessed in the simulation study where RR is changed without changes in ANS modulation. Non-linear HRV indices computed from simulated data are illustrated in Figure
ρ | 0.959 ± 0.068 | 0.947 ± 0.1 | 0.949 ± 0.074 | |||
0.0002 ± 0.0015 | 0.0004 ± 0.0044 | 0.0003 ± 0.0022 | ||||
Median ± IQR | 4.26 ± 0.76 | 0.72 ± 0.30 | 0.98 ± 0.26 | |||
0.919±0.129 | 0.896±0.186 | 0.902±0.139 | 0.923±0.129 | 0.896±0.179 | 0.910±0.125 | |
ρ sub-spe (× 10^{−05}) | 0.013±0.20 | 0.016±0.21 | −0.0051±0.20 | −0.016±0.20 | 0.011±0.20 | 0.01±0.20 |
1±0 | 1±0 | 1±0 | 1±0 | 1±0 | 1±0 | |
Median ± |
3.88±0.07 | 0.59±0.02 | 0.85±0.04 | 3.85±0.02 | 0.59±0.01 | 0.84±0.03 |
0.997 | 0.988 | 0.970 | 0.999 | 0.990 | 0.982 | |
ρ_{Median} (× 10^{−05}) | −0.787 | −0.109 | −0.051 | 0.661 | 0.232 | 0.061 |
1 | 1 | 1 | 1 | 1 | 1 | |
ξ Correction factor | 2.39 | 0.93 | 0.75 | 0.39 | 0.84 | 0.54 |
Median ± IQR | 3.88±0.07 | 0.59±0.02 | 0.85±0.05 | 3.85±0.02 | 0.59±0.01 | 0.84±0.03 |
ρ_{I2} | −0.473 ± 1.41 | −0.39 ± 1.09 | −0.29 ± 0.77 | |||
0.0005 ± 0.044 | 0.008 ± 0.19 | 0.068 ± 0.37 | ||||
Median ± IQR | 3.85 ± 0.01 | 0.59 ± 0.002 | 0.83 ± 0.006 |
Regression formulas were applied to each simulated modulating signal (subject-specific approach) providing corrected indices with minimal mean HR correlation. The obtained HR-corrected nonlinear indices are shown in Figure
A set of correction factors (median approach) was obtained by considering the median of all nonlinear index values for each heart rate and computing global correction parameters (Table
The nonlinear indices were computed from simulated RR time series resampled at 2, 4, and 8 Hz. As shown in Figure
The proposed HR-corrections were evaluated in the BPC database. The results shown in Figure
5.61 (4.88|6.38) | 4.41 (3.64|4.88) | 0.0025 | |
5.10 (4.33|5.62) | 4.07 (3.41|4.57) | 0.0014 | |
4.85 (4.19|5.25) | 3.97 (3.31|4.46) | 0.0019 | |
4.66 (3.98|5.27) | 3.88 (3.24|4.42) | 0.0045 | |
4.47 (3.93|4.93) | 3.82 (3.25|4.32) | 0.0064 | |
3.67 (3.23|4.08) | 3.02 (2.84|3.64) | 0.024 | |
0.73 (0.53|0.83) | 0.48 (0.037|0.0.67) | 0.008 | |
0.28 (0.05|0.38) | 0.24 (0.15|0.37) | 0.73 | |
0.40 (0.28|0.44) | 0.33 (0.25|0.44) | 0.44 | |
0.333 (0.158|0.434) | 0.272 (0.185|0.424) | 0.39 | |
0.436 (0.344|0.488) | 0.364 (0.27|0.47) | 0.062 | |
0.50 (0.42|0.54) | 0.35 (0.26|0.42) | 0.0013 | |
1.11 (1.03|1.17) | 0.88 (0.77|0.95) | 0.008 | |
0.94 (0.91|1.01) | 0.88 (0.80|0.97) | 0.057 | |
0.94 (0.91|0.99) | 0.87 (0.79|0.96) | 0.038 | |
0.784 (0.684|0.838) | 0.775 (0.707|0.856) | 0.5 | |
0.783 (0.742|0.825) | 0.777 (0.713|0.838) | 0.94 | |
0.80 (0.74|0.85) | 0.71 (0.66|0.80) | 0.0098 |
In a first study, the value of the median correction factor ξ extracted from the simulation study was used. It is worth noting that after linear correction there was no significant difference in
In a second study, simulation of each recording's characteristics was computed to apply subject-specific correction, derived independently from supine, and standing recordings. HR-corrected
Finally, nonlinear HRV indices were computed on RR time series interpolated at 2, 4, and 8 Hz. We can conclude that the higher the interpolation order, the lower the nonlinear HRV values. In all cases HR-corrected nonlinear indices calculated by interpolation showed statistical differences between positions regardless of the interpolation order used (results of 4 and 8 Hz not included in the manuscript) being their range notably reduced.
HRV analysis has been widely used as a non-invasive technique to assess and quantify cardiac ANS modulation (Task Force of the ESC-NASPE,
Regression formulas are commonly used to characterize the relationship between two magnitudes such as ventricular repolarization and heart rate (Pueyo et al.,
Simulated RR time series were interpolated at 2, 4, and 8 Hz. The higher the interpolation rate, the lower the nonlinear index values. The addition of new data, resulting from interpolation, can be interpreted in terms of entropy as an increase in signal regularity being in concordance with a previous work in which electroencephalogram complexity through correlation dimension was evaluated varying the sampling rate (Jing and Takigawa,
Despite the dependence of nonlinear HRV indices on mean HR revealed in the simulation study, no HR-correction of nonlinear HRV indices is applied in most of the studies found in the literature, where mean HR values are even not provided in some cases (Penttilä et al.,
Classical nonlinear HRV indices evaluated in the BPC database showed around 21, 34, and 21% of reduction in median values from standing with respect to supine position for
In the BPC database, HR-corrected nonlinear indices were computed under supine and standing conditions and
On the other hand, all nonlinear HRV indices were found still significantly different when corrected by interpolation. It was found a statistically significant reduction in standing with respect to supine position of 18, 30, and 12% for
Although, regression formulas were studied as HR-correction approach, their suitability depends on simulation requirements. Possible mismatches of simulated data with respect to real data difficult their application and therefore, we propose to compute nonlinear indices over interpolated RR series to attenuate mean HR effect, since no simulation is required, it saves computational time and still differentiates between both positions. This correction may lead to better understanding complexity and regularity under ANS changes unbiased by mean HR as natural sampling rate of RR time series.
Note that, although HR-correction attenuates the effect of mean HR as sampling rate, HR-corrected nonlinear HRV indices may be still correlated with mean HR due to their physiological dependence. After HR-correction, nonlinear HRV indices are capable of capturing information about ANS modulation in response to body position changes.
HR-corrected nonlinear HRV indices addressed in this study, pointed out a reduction in the complexity of the underlying system and an increase in the HRV series regularity caused by an increase of the sympathetic activity, when changing from supine to standing position, being in agreement with previous works with similar conditions, considering tilt table test or even exercise (Osaka et al.,
In this work, changes in nonlinear HRV indices were studied under different sympathetic conditions where mean HR also changed. It is studied to what extend changes in nonlinear HRV indices are explained by HR ones. Correlation dimension, approximate and sample entropy dependence on mean HR as sampling rate is explored. A simulation study was carried out emulating ANS modulation no linked to mean HR. Simulation results showed that heart rate affects nonlinear indices as it is the intrinsic sampling rate of HRV even when considering the same data length. Two HR-correction methodologies, regression formulas and interpolation, were proposed. Their evaluation on a BPC database revealed a reduction of all studied HR-corrected nonlinear HRV indices in supine and standing positions. After HR-correction, nonlinear HRV indices are capturing changes in the sympathetic modulation by body position-induced changes. HR-correction by interpolation was found suitable to attenuate nonlinear HRV indices effect on mean HR and its application could represent an improvement in their applicability extending it in such cases of non-steady mean HR.
All authors equally contributed to the conception of the work, revising it critically for important intellectual content, final approval of the version to be published, and agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. EP and RB were supervisors of the research and MO gave methodological support. In addition, JB was responsible for drafting the work.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
This work was funded under projects TEC2013-42140-R, TIN2013-41998-R, and TIN2014-53567-R by MINECO (Spain) and by BSICOS Group (T96) from Government of Aragón, European Social Fund (EU) and by European Research Council (ERC-2014-StG 638284) to (EP). CIBER is a center of the Instituto de Salud Carlos III in assistance from the European Regional Development Fund. The computation was performed by the ICTS “NANBIOSIS,” more specifically by the High Performance Computing Unit of the CIBER in Bioengineering, Biomaterials, and Nanomedicine (CIBER-BBN) at the University of Zaragoza.
Let
Then, the amount of reconstructed vectors is
is the correlation sum where
In addition, due to the intrinsic characteristics of
Self-comparisons,
is the correlation sum not considering self-comparisons.
For deterministic systems,
Thus,
For increasing