Local scale exponents of blood pressure and heart rate variability by detrended fluctuation analysis: effects of posture, exercise, and aging

Assessing cardiovascular stress based on heart rate variability in female shift workers: a multiscale-multifractal analysis approach

Introduction

Sleep-wake cycle disruption caused by shift work may lead to cardiovascular stress, which is observed as an alteration in the behavior of heart rate variability (HRV). In particular, HRV exhibits complex patterns over different time scales that help to understand the regulatory mechanisms of the autonomic nervous system, and changes in the fractality of HRV may be associated with pathological conditions, including cardiovascular disease, diabetes, or even psychological stress. The main purpose of this study is to evaluate the multifractal-multiscale structure of HRV during sleep in healthy shift and non-shift workers to identify conditions of cardiovascular stress that may be associated with shift work.

Methods

The whole-sleep HRV signal was analyzed from female participants: eleven healthy shift workers and seven non-shift workers. The HRV signal was decomposed into intrinsic mode functions (IMFs) using the empirical mode decomposition method, and then the IMFs were analyzed using the multiscale-multifractal detrended fluctuation analysis (MMF-DFA) method. The MMF-DFA was applied to estimate the self-similarity coefficients, α(q, τ), considering moment orders (q) between -5 and +5 and scales (τ) between 8 and 2,048 s. Additionally, to describe the multifractality at each τ in a simple way, a multifractal index, MFI(τ), was computed.

Results

Compared to non-shift workers, shift workers presented an increase in the scaling exponent, α(q, τ), at short scales (τ < 64 s) with q < 0 in the high-frequency component (IMF1, 0.15-0.4 Hz) and low-frequency components (IMF2-IMF3, 0.04-0.15 Hz), and with q> 0 in the very low frequencies (IMF4, < 0.04 Hz). In addition, at large scales (τ> 1,024 s), a decrease in α(q, τ) was observed in IMF3, suggesting an alteration in the multifractal dynamic. MFI(τ) showed an increase at small scales and a decrease at large scales in IMFs of shift workers.

Conclusion

This study helps to recognize the multifractality of HRV during sleep, beyond simply looking at indices based on means and variances. This analysis helps to identify that shift workers show alterations in fractal properties, mainly on short scales. These findings suggest a disturbance in the autonomic nervous system induced by the cardiovascular stress of shift work.

Bayesian at heart: Towards autonomic outflow estimation via generative state-space modelling of heart rate dynamics

Recent research is revealing how cognitive processes are supported by a complex interplay between the brain and the rest of the body, which can be investigated by the analysis of physiological features such as breathing rhythms, heart rate, and skin conductance. Heart rate dynamics are of particular interest as they provide a way to track the sympathetic and parasympathetic outflow from the autonomic nervous system, which is known to play a key role in modulating attention, memory, decision-making, and emotional processing. However, extracting useful information from heartbeats about the autonomic outflow is still challenging due to the noisy estimates that result from standard signal-processing methods. To advance this state of affairs, we propose a novel approach in how to conceptualise and model heart rate: instead of being a mere summary of the observed inter-beat intervals, we introduce a modelling framework that views heart rate as a hidden stochastic process that drives the observed heartbeats. Moreover, by leveraging the rich literature of state-space modelling and Bayesian inference, our proposed framework delivers a description of heart rate dynamics that is not a point estimate but a posterior distribution of a generative model. We illustrate the capabilities of our method by showing that it recapitulates linear properties of conventional heart rate estimators, while exhibiting a better discriminative power for metrics of dynamical complexity compared across different physiological states.

Scale-Fractal Detrended Fluctuation Analysis for Fault Diagnosis of a Centrifugal Pump and a Reciprocating Compressor

Reciprocating compressors and centrifugal pumps are rotating machines used in industry, where fault detection is crucial for avoiding unnecessary and costly downtime. A novel method for fault classification in reciprocating compressors and multi-stage centrifugal pumps is proposed. In the feature extraction stage, raw vibration signals are processed using multi-fractal detrended fluctuation analysis (MFDFA) to extract features indicative of different types of faults. Such MFDFA features enable the training of machine learning models for classifying faults. Several classical machine learning models and a deep learning model corresponding to the convolutional neural network (CNN) are compared with respect to their classification accuracy. The cross-validation results show that all models are highly accurate for classifying the 13 types of faults in the centrifugal pump, the 17 valve faults, and the 13 multi-faults in the reciprocating compressor. The random forest subspace discriminant (RFSD) and the CNN model achieved the best results using MFDFA features calculated with quadratic approximations. The proposed method is a promising approach for fault classification in reciprocating compressors and multi-stage centrifugal pumps.

Cardiorespiratory dynamics during respiratory maneuver in athletes

Introduction: The modern practice of sports medicine and medical rehabilitation requires the search for subtle criteria for the development of conditions and recovery of the body after diseases, which would have a prognostic value for the prevention of negative effects of training and rehabilitation tools, and also testify to the development and course of mechanisms for counteracting pathogenetic processes in the body. The purpose of this study was to determine the informative directions of the cardiorespiratory system parameters dynamics during the performing a maneuver with a change in breathing rate, which may indicate the body functional state violation.

Methods: The results of the study of 183 healthy men aged 21.2 ± 2.3 years who regularly engaged in various sports were analyzed. The procedure for studying the cardiorespiratory system included conducting combined measurements of indicators of activity of the respiratory and cardiovascular systems in a sitting position using a spiroarteriocardiograph device. The duration of the study was 6 min and involved the sequential registration of three measurements with a change in breathing rate (spontaneous breathing, breathing at 0.1 Hz and 0.25 Hz).

Results: Performing a breathing maneuver at breathing 0.1 Hz and breathing 0.25 Hz in comparison with spontaneous breathing leads to multidirectional significant changes in heart rate variability indicators–TP (ms2), LF (ms2), LFHF (ms2/ms2); of blood pressure variability indicators–TPDBP (mmHg2), LFSBP (mmHg2), LFDBP (mmHg2), HFSBP (mmHg2); of volume respiration variability indicators - LFR, (L×min-1)2; HFR, (L×min-1)2; LFHFR, (L×min-1)2/(L×min-1)2; of arterial baroreflex sensitivity indicators - BRLF (ms×mmHg-1), BRHF (ms×mmHg-1). Differences in indicators of systemic hemodynamics and indicators of cardiovascular and respiratory systems synchronization were also informative.

Conclusion: According to the results of the study, it is shown that during performing a breathing maneuver with a change in the rate of breathing, there are significant changes in cardiorespiratory parameters, the analysis of which the increments made it possible to determine of the changes directions dynamics, their absolute values and informative limits regarding the possible occurrence of the cardiorespiratory interactions dysregulation.

Cardiorespiratory dynamics during respiratory maneuver in athletes

Introduction: The modern practice of sports medicine and medical rehabilitation requires the search for subtle criteria for the development of conditions and recovery of the body after diseases, which would have a prognostic value for the prevention of negative effects of training and rehabilitation tools, and also testify to the development and course of mechanisms for counteracting pathogenetic processes in the body. The purpose of this study was to determine the informative directions of the cardiorespiratory system parameters dynamics during the performing a maneuver with a change in breathing rate, which may indicate the body functional state violation. Methods: The results of the study of 183 healthy men aged 21.2 ± 2.3 years who regularly engaged in various sports were analyzed. The procedure for studying the cardiorespiratory system included conducting combined measurements of indicators of activity of the respiratory and cardiovascular systems in a sitting position using a spiroarteriocardiograph device. The duration of the study was 6 min and involved the sequential registration of three measurements with a change in breathing rate (spontaneous breathing, breathing at 0.1 Hz and 0.25 Hz). Results: Performing a breathing maneuver at breathing 0.1 Hz and breathing 0.25 Hz in comparison with spontaneous breathing leads to multidirectional significant changes in heart rate variability indicators-TP (ms2), LF (ms2), LFHF (ms2/ms2); of blood pressure variability indicators-TPDBP (mmHg2), LFSBP (mmHg2), LFDBP (mmHg2), HFSBP (mmHg2); of volume respiration variability indicators - LFR, (L×min-1)2; HFR, (L×min-1)2; LFHFR, (L×min-1)2/(L×min-1)2; of arterial baroreflex sensitivity indicators - BRLF (ms×mmHg-1), BRHF (ms×mmHg-1). Differences in indicators of systemic hemodynamics and indicators of cardiovascular and respiratory systems synchronization were also informative. Conclusion: According to the results of the study, it is shown that during performing a breathing maneuver with a change in the rate of breathing, there are significant changes in cardiorespiratory parameters, the analysis of which the increments made it possible to determine of the changes directions dynamics, their absolute values and informative limits regarding the possible occurrence of the cardiorespiratory interactions dysregulation.

Multi-Scale Evaluation of Sleep Quality Based on Motion Signal from Unobtrusive Device

Sleep disorders are a growing threat nowadays as they are linked to neurological, cardiovascular and metabolic diseases. The gold standard methodology for sleep study is polysomnography (PSG), an intrusive and onerous technique that can disrupt normal routines. In this perspective, m-Health technologies offer an unobtrusive and rapid solution for home monitoring. We developed a multi-scale method based on motion signal extracted from an unobtrusive device to evaluate sleep behavior. Data used in this study were collected during two different acquisition campaigns by using a Pressure Bed Sensor (PBS). The first one was carried out with 22 subjects for sleep problems, and the second one comprises 11 healthy shift workers. All underwent full PSG and PBS recordings. The algorithm consists of extracting sleep quality and fragmentation indexes correlating to clinical metrics. In particular, the method classifies sleep windows of 1-s of the motion signal into: displacement (DI), quiet sleep (QS), disrupted sleep (DS) and absence from the bed (ABS). QS proved to be positively correlated (0.72±0.014) to Sleep Efficiency (SE) and DS/DI positively correlated (0.85±0.007) to the Apnea-Hypopnea Index (AHI). The work proved to be potentially helpful in the early investigation of sleep in the home environment. The minimized intrusiveness of the device together with a low complexity and good performance might provide valuable indications for the home monitoring of sleep disorders and for subjects’ awareness.

Heart Rate Variability from Wearable Photoplethysmography Systems: Implications in Sleep Studies at High Altitude

The interest in photoplethysmography (PPG) for sleep monitoring is increasing because PPG may allow assessing heart rate variability (HRV), which is particularly important in breathing disorders. Thus, we aimed to evaluate how PPG wearable systems measure HRV during sleep at high altitudes, where hypobaric hypoxia induces respiratory disturbances. We considered PPG and electrocardiographic recordings in 21 volunteers sleeping at 4554 m a.s.l. (as a model of sleep breathing disorder), and five alpine guides sleeping at sea level, 6000 m and 6800 m a.s.l. Power spectra, multiscale entropy, and self-similarity were calculated for PPG tachograms and electrocardiography R–R intervals (RRI). Results demonstrated that wearable PPG devices provide HRV measures even at extremely high altitudes. However, the comparison between PPG tachograms and RRI showed discrepancies in the faster spectral components and at the shorter scales of self-similarity and entropy. Furthermore, the changes in sleep HRV from sea level to extremely high altitudes quantified by RRI and PPG tachograms in the five alpine guides tended to be different at the faster frequencies and shorter scales. Discrepancies may be explained by modulations of pulse wave velocity and should be considered to interpret correctly autonomic alterations during sleep from HRV analysis.

Multiscale assessment of the degree of multifractality for physiological time series

Recent advancements in detrended fluctuation analysis (DFA) allow evaluating multifractal coefficients scale-by-scale, a promising approach for assessing the complexity of biomedical signals. The multifractality degree is typically quantified by the singularity spectrum width (W_SS), a method that is critically unstable in multiscale applications. Thus, we aim to propose a robust multiscale index of multifractality, compare it with W_SS and illustrate its performance on real biosignals. The proposed index is the cumulative function of squared increments between consecutive DFA coefficients at each scale n: α_CF(n). We compared it with W_SS calculated scale-by-scale considering monofractal/monoscale, monofractal/multiscale, multifractal/monoscale and multifractal/multiscale random processes. The two indices provided qualitatively similar descriptions of multifractality, but α_CF(n) differentiated better the multifractal components from artefacts due to crossovers or detrending overfitting. Applied on 24 h heart rate recordings of 14 participants, the singularity spectrum failed to always satisfy the concavity requirement for providing meaningful W_SS, while α_CF(n) demonstrated a statistically significant heart rate multifractality at night in the scale ranges 16-100 and 256-680 s. Furthermore, α_CF(n) did not reject the hypothesis of monofractality at daytime, coherently with previous reports of lower nonlinearity and monoscale multifractality during the day. Thus, α_CF(n) appears a robust index of multiscale multifractality that is useful for quantifying complexity alterations of physiological series. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Multifractal and Multiscale Detrended Fluctuation Analysis of Cardiovascular Signals: how the Estimation Bias Affects ShortTerm Coefficients and a Way to mitigate this Error

The Detrended Fluctuation Analysis (DFA) is a popular method for quantifying the self-similarity of the heart rate that may reveal complexity aspects in cardiovascular regulation. However, the self-similarity coefficients provided by DFA may be affected by an overestimation error associated with the shortest scales. Recently, the DFA has been extended to calculate the multifractal-multiscale self-similarity and some evidence suggests that overestimation errors may affect different multifractal orders. If this is the case, the error might alter substantially the multifractal-multiscale representation of the cardiovascular self-similarity. The aim of this work is 1) to describe how this error depends on the multifractal orders and scales and 2) to propose a way to mitigate this error applicable to real cardiovascular series.Clinical Relevance- The proposed correction method may extend the multifractal analysis at the shortest scales, thus allowing to better assess complexity alterations in the cardiac autonomic regulation and to increase the clinical value of DFA.

Asymmetric multiscale multifractal analysis (AMMA) of heart rate variability

Objective.The physiological activity of the heart is controlled and modulated mostly by the parasympathetic and sympathetic nervous systems. Heart rate variability (HRV) analysis is therefore used to observe fluctuations that reflect changes in the activity in these two branches. Knowing that acceleration and deceleration patterns in heart rate fluctuations are asymmetrically distributed, the ability to analyze HRV asymmetry was introduced into MMA.Approach. The new method is called asymmetric multiscale multifractal analysis (AMMA) and the analysis involved six groups: 36 healthy persons, 103 cases with aortic valve stenosis, 36 with hypertrophic cardiomyopathy, 32 with atrial fibrillation, 59 patients with coronary artery disease (CAD) and 13 with congestive heart failure.Main results. Analyzing the results obtained for the 6 groups of patients based on the AMMA method, i.e. comparing the Hurst surfaces for heart rate decelerations and accelerations, it was noticed that these surfaces differ significantly. And the differences occur in most groups for large fluctuations (multifractal parameterq > 0). In addition, a similarity was found for all groups for the AMMA Hurst surface for decelerations to the MMA Hurst surface-heart rate decelerations (lengthening of the RR intervals) appears to be the main factor determining the shape of the complete Hurst surface and so the multifractal properties of HRV. The differences between the groups, especially for CAD, hypertrophic cardiomyopathy and aortic valve stenosis, are more visible if the Hurst surfaces are analyzed separately for accelerations and decelerations.Significance. The AMMA results presented here may provide additional input for HRV analysis and create a new paradigm for future medical screening. Note that the HRV analysis using MMA (without distinguishing accelerations from decelerations) gave satisfactory screening statistics in our previous studies.

Entropy and Multifractal-Multiscale Indices of Heart Rate Time Series to Evaluate Intricate Cognitive-Autonomic Interactions

Recent research has clarified the existence of a networked system involving a cortical and subcortical circuitry regulating both cognition and cardiac autonomic control, which is dynamically organized as a function of cognitive demand. The main interactions span multiple temporal and spatial scales and are extensively governed by nonlinear processes. Hence, entropy and (multi)fractality in heart period time series are suitable to capture emergent behavior of the cognitive-autonomic network coordination. This study investigated how entropy and multifractal-multiscale analyses could depict specific cognitive-autonomic architectures reflected in the heart rate dynamics when students performed selective inhibition tasks. The participants (N=37) completed cognitive interference (Stroop color and word task), action cancellation (stop-signal) and action restraint (go/no-go) tasks, compared to watching a neutral movie as baseline. Entropy and fractal markers (respectively, the refined composite multiscale entropy and multifractal-multiscale detrended fluctuation analysis) outperformed other time-domain and frequency-domain markers of the heart rate variability in distinguishing cognitive tasks. Crucially, the entropy increased selectively during cognitive interference and the multifractality increased during action cancellation. An interpretative hypothesis is that cognitive interference elicited a greater richness in interactive processes that form the central autonomic network while action cancellation, which is achieved via biasing a sensorimotor network, could lead to a scale-specific heightening of multifractal behavior.

Sex Differences in Heart Rate Nonlinearity by Multifractal Multiscale Detrended Fluctuation Analysis

Recent developments of detrended fluctuation analysis (DFA) provide multifractal/multiscale (MFMS) descriptions of the heart rate self-similarity, a promising approach to cardiovascular complexity. However, it is unclear whether the MFMS DFA may also describe the nonlinear components of heart rate variability. Our aim is to define MFMS DFA indices for quantifying the short-term and long-term degree of the heart-rate nonlinearity and to apply these indices to detect possible sex-related differences.We recorded the inter-beat-interval (IBI) series in 42 male and in 42 female healthy participants sitting at rest for about 2 hours. For each series j, we generated 100 phase-randomized surrogate series. We applied the MFMS DFA to estimate the self-similarity coefficients α over scales τ between 8 and 512 s and moment orders q between -5 and +5, obtaining coefficients for the original series, α^O,j (q, τ), and for each surrogate, α^i,j (q, τ) with 1≤i≤100. We first evaluated π^j(q, τ), percentile of α^i,j (q, τ) distribution in which was α^O,j (q, τ). Then we calculated the percentages of scales where π^j(q, τ) was <5% for 8≤τ≤16 s (short-term nonlinearity index NL₁(q)) and for 16≤τ≤512 s (long-term nonlinearity index NL₂(q)). We found that NL₁(q) was generally greater than 50% at all q≥0 but q=2 (i.e., moment order of the monofractal DFA), while at q<0 it was high in males only, with significant sex differences at q=-1 and q=-2. Results indicate that the multifractal DFA may highlight nonlinear heart-rate components at the short scales that are not revealed by the traditional monofractal DFA and that appear related to gender differences.Clinical Relevance- This supports the use of MFMS DFA to integrate the linear information from traditional spectral methods of heart rate variability in clinical studies aimed at improving the stratification of the cardiovascular risk.

Can the Detrended Fluctuation Analysis Reveal Nonlinear Components of Heart Rate Variabilityƒ

The Detrended Fluctuation Analysis (DFA) is widely employed to quantify the fractal dynamics of R-R intervals (RRI). This is usually done by estimating a short- and a long-term coefficient, but it is still unclear how much the information provided by such a bi-scale DFA is independent of that of traditional spectral indices. However, more sophisticated DFA approaches have been recently proposed, including the multifractal-multiscale DFA and the DFA for magnitude and sign of RRI changes. The aim of our work is to investigate whether novel DFA approaches allow extracting the information on the nonlinear RRI dynamics that traditional spectral methods cannot retrieve.We selected 4-hour segments of beat-by-beat RRI series from a 24-hour Holter recording, one during daytime (wake), one at night (sleep) in a healthy volunteer. From the wake segment, we generated 100 surrogate series shuffling the phases but preserving the power spectrum, and then from each of the resulting RRI series, we generated the series of the sign and the series of the magnitude of successive RRI changes. We generated similar series from the sleep recording. Thus, we finally obtained 6 original beat-to-beat series to be compared with 600 surrogate series, each of 4-hour duration.The comparison between original and surrogate series showed that for this experimental setting, the traditional monofractal DFA provides the same information retrievable by the power spectrum. However, specific components of the multifractal DFA reveal information not detectable by the power spectrum, particularly in the sleep condition. Furthermore, the DFA of the magnitude of RRI changes reflects important nonlinear components. Therefore, these more sophisticated DFA approaches might effectively improve the clinical value of RRI variability analysis.

Day and Night Changes of Cardiovascular Complexity: A Multi-Fractal Multi-Scale Analysis

Recently, a multifractal-multiscale approach to detrended fluctuation analysis (DFA) was proposed to evaluate the cardiovascular fractal dynamics providing a surface of self-similarity coefficients α(q,τ), function of the scale τ, and moment order q. We hypothesize that this versatile DFA approach may reflect the cardiocirculatory adaptations in complexity and nonlinearity occurring during the day/night cycle. Our aim is, therefore, to quantify how α(q, τ) surfaces of cardiovascular series differ between daytime and night-time. We estimated α(q,τ) with -5 ≤ q ≤ 5 and 8 ≤ τ ≤ 2048 s for heart rate and blood pressure beat-to-beat series over periods of few hours during daytime wake and night-time sleep in 14 healthy participants. From the α(q,τ) surfaces, we estimated short-term (<16 s) and long-term (from 16 to 512 s) multifractal coefficients. Generating phase-shuffled surrogate series, we evaluated short-term and long-term indices of nonlinearity for each q. We found a long-term night/day modulation of α(q,τ) between 128 and 256 s affecting heart rate and blood pressure similarly, and multifractal short-term modulations at q < 0 for the heart rate and at q > 0 for the blood pressure. Consistent nonlinearity appeared at the shorter scales at night excluding q = 2. Long-term circadian modulations of the heart rate DFA were previously associated with the cardiac vulnerability period and our results may improve the risk stratification indicating the more relevant α(q,τ) area reflecting this rhythm. Furthermore, nonlinear components in the nocturnal α(q,τ) at q ≠ 2 suggest that DFA may effectively integrate the linear spectral information with complexity-domain information, possibly improving the monitoring of cardiac interventions and protocols of rehabilitation medicine.

Slow 0.1 Hz Breathing and Body Posture Induced Perturbations of RRI and Respiratory Signal Complexity and Cardiorespiratory Coupling

Objective: We explored the physiological background of the non-linear operating mode of cardiorespiratory oscillators as the fundamental question of cardiorespiratory homeodynamics and as a prerequisite for the understanding of neurocardiovascular diseases. We investigated 20 healthy human subjects for changes using electrocardiac RR interval (RRI) and respiratory signal (Resp) Detrended Fluctuation Analysis (DFA, α1RRI, α2RRI, α1Resp, α2Resp), Multiple Scaling Entropy (MSERRI1-4, MSERRI5-10, MSEResp1-4, MSEResp5-10), spectral coherence (CohRRI-Resp), cross DFA (ρ1 and ρ2) and cross MSE (XMSE1-4 and XMSE5-10) indices in four physiological conditions: supine with spontaneous breathing, standing with spontaneous breathing, supine with 0.1 Hz breathing and standing with 0.1 Hz breathing. Main results: Standing is primarily characterized by the change of RRI parameters, insensitivity to change with respiratory parameters, decrease of CohRRI-Resp and insensitivity to change of in ρ1, ρ2, XMSE1-4, and XMSE5-10. Slow breathing in supine position was characterized by the change of the linear and non-linear parameters of both signals, reflecting the dominant vagal RRI modulation and the impact of slow 0.1 Hz breathing on Resp parameters. CohRRI-Resp did not change with respect to supine position, while ρ1 increased. Slow breathing in standing reflected the qualitatively specific state of autonomic regulation with striking impact on both cardiac and respiratory parameters, with specific patterns of cardiorespiratory coupling. Significance: Our results show that cardiac and respiratory short term and long term complexity parameters have different, state dependent patterns. Sympathovagal non-linear interactions are dependent on the pattern of their activation, having different scaling properties when individually activated with respect to the state of their joint activation. All investigated states induced a change of α1 vs. α2 relationship, which can be accurately expressed by the proposed measure-inter-fractal angle θ. Short scale (α1 vs. MSE1-4) and long scale (α2 vs. MSE5-10) complexity measures had reciprocal interrelation in standing with 0.1 Hz breathing, with specific cardiorespiratory coupling pattern (ρ1 vs. XMSE1-4). These results support the hypothesis of hierarchical organization of cardiorespiratory complexity mechanisms and their recruitment in ascendant manner with respect to the increase of behavioral challenge complexity. Specific and comprehensive cardiorespiratory regulation in standing with 0.1 Hz breathing suggests this state as the potentially most beneficial maneuver for cardiorespiratory conditioning.

Decomposing the complexity of heart-rate variability by the multifractal-multiscale approach to detrended fluctuation analysis: an application to low-level spinal cord injury

OBJECTIVE

While several studies have assessed autonomic cardiovascular control after a spinal cord lesion using heart-rate variability (HRV) indices in the frequency and time domains, complexity measures have rarely been used, even if detrended fluctuation analysis (DFA) appeared promising. Recent developments in DFA decompose the multifractal contributions using temporal scales. Our aim is to evaluate the potential of these new DFA tools, considering as an example application the decomposition of HRV complexity in individuals with spinal cord injury (SCI) at a low lesion level, for whom alterations in traditional indices are not expected.

APPROACH

We enrolled 14 subjects with SCI with a lesion below the eleventh thoracic vertebra and 34 able-bodied (AB) controls. We recorded the R-R intervals (RRI) for 10 min in supine and sitting postures. We applied the multifractal-multiscale (MFMS) DFA to derive scale coefficients, α(q,τ), with function of the multifractal order q and scale τ, and evaluated a scale-coefficient dispersion index, α _SD(τ), as the standard deviation of α(q,τ) over q. We calculated the RRI increments, their magnitude and sign, estimating the MFMS DFA coefficients for the series of magnitude α _m(q,τ) and sign α _s(q,τ).

MAIN RESULTS

While sitting, differences between SCI and AB groups depended on q for coefficients 16  <  τ  <  32 s, so that α _SD(τ) was lower in individuals with SCI at τ  =  25 s. In the supine condition, short-term scales were greater in individuals with SCI for all q, and α _SD(τ) did not differ between groups. Group differences were found in α _s(q,τ) and not in α _m(q,τ) or in traditional HRV indices. The surrogate analysis showed AB-SCI differences in linear HRV components at scales τ  <  16 s and nonlinear components at larger scales.

SIGNIFICANCE

Complexity decomposition by DFA describes autonomic alterations in HRV in low-level paraplegia better than traditional indices, probably pointing out a loss of system complexity in the sitting posture and an impaired sympatho/vagal modulation in the supine position.

Application of an Improved Correlation Method in Electrostatic Gait Recognition of Hemiparetic Patients

Hemiparesis is one of the common sequelae of neurological diseases such as strokes, which can significantly change the gait behavior of patients and restrict their activities in daily life. The results of gait characteristic analysis can provide a reference for disease diagnosis and rehabilitation; however, gait correlation as a gait characteristic is less utilized currently. In this study, a new non-contact electrostatic field sensing method was used to obtain the electrostatic gait signals of hemiplegic patients and healthy control subjects, and an improved Detrended Cross-Correlation Analysis cross-correlation coefficient method was proposed to analyze the obtained electrostatic gait signals. The results show that the improved method can better obtain the dynamic changes of the scaling index under the multi-scale structure, which makes up for the shortcomings of the traditional Detrended Cross-Correlation Analysis cross-correlation coefficient method when calculating the electrostatic gait signal of the same kind of subjects, such as random and incomplete similarity in the trend of the scaling index spectrum change. At the same time, it can effectively quantify the correlation of electrostatic gait signals in subjects. The proposed method has the potential to be a powerful tool for extracting the gait correlation features and identifying the electrostatic gait of hemiplegic patients.

A Fast DFA Algorithm for Multifractal Multiscale Analysis of Physiological Time Series

Detrended fluctuation analysis (DFA) is a popular tool in physiological and medical studies for estimating the self-similarity coefficient, α, of time series. Recent researches extended its use for evaluating multifractality (where α is a function of the multifractal parameter q) at different scales n. In this way, the multifractal-multiscale DFA provides a bidimensional surface α(q,n) to quantify the level of multifractality at each scale separately. We recently showed that scale resolution and estimation variability of α(q,n) can be improved at each scale n by splitting the series into maximally overlapped blocks. This, however, increases the computational load making DFA estimations unfeasible in most applications. Our aim is to provide a DFA algorithm sufficiently fast to evaluate the multifractal DFA with maximally overlapped blocks even on long time series, as usually recorded in physiological or clinical settings, therefore improving the quality of the α(q,n) estimate. For this aim, we revise the analytic formulas for multifractal DFA with first- and second-order detrending polynomials (i.e., DFA₁ and DFA₂) and propose a faster algorithm than the currently available codes. Applying it on synthesized fractal/multifractal series we demonstrate its numerical stability and a computational time about 1% that required by traditional codes. Analyzing long physiological signals (heart-rate tachograms from a 24-h Holter recording and electroencephalographic traces from a sleep study), we illustrate its capability to provide high-resolution α(q,n) surfaces that better describe the multifractal/multiscale properties of time series in physiology. The proposed fast algorithm might, therefore, make it easier deriving richer information on the complex dynamics of clinical signals, possibly improving risk stratification or the assessment of medical interventions and rehabilitation protocols.

Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average

We present a bottom-up derivation of fluctuation analysis with detrending for the detection of long-range correlations in the presence of additive trends or intrinsic nonstationarities. While the well-known detrended fluctuation analysis (DFA) and detrending moving average (DMA) were introduced ad hoc, we claim basic principles for such methods where DFA and DMA are then shown to be specific realizations. The mean-squared displacement of the summed time series contains the same information about long-range correlations as the autocorrelation function but has much better statistical properties for large time lags. However, the scaling exponent of its estimator on a single time series is affected not only by trends on the data but also by intrinsic nonstationarities. We therefore define the fluctuation function as mean-squared displacement with weighting kernel. We require that its estimator be unbiased and exhibit the correct scaling behavior for the random component of a signal, which is only achieved if the weighting kernel implies detrending. We show how DFA and DMA satisfy these requirements and we extract their kernel weights.

Heart rate variability in mental stress: The data reveal regression to the mean

This data article aimed to assess whether there is a relationship between baseline heart rate variability (HRV) and mental stress-induced autonomic reactivity. Out of 1206 healthy subjects, 162 students were randomly selected to participate in this study. Participants were presented with a mental arithmetic task of 10 min duration. The task required serial subtraction of 7 from a randomly selected 3-digit number. During performance of this task as well as at baseline, ECG was recorded to acquire heart rate and HRV (high frequency, low frequency, the standard deviation of NN) data. Participants were divided into quartiles according to baseline HRV. Mental stress responses were compared across groups. We observed significant differences for autonomic reactivity scores between groups with high versus low baseline HRV. Linear regression results were consistent with the regression to the mean model and mental stress reaction (defined as mental stress value minus baseline value) negatively correlated with baseline values. Baseline-adjusted analyses did not demonstrate significant intergroup differences for changes in heart rate and HRV from rest to mental stress. These data suggest regression to the mean is a major source of variability of stress-related changes in heart rate variability.

Analysis for the Influence of ABR Sensitivity on PTT-Based Cuff-Less Blood Pressure Estimation before and after Exercise

An accurate and continuous measurement of blood pressure (BP) is of great importance for the prognosis of some cardiovascular diseases in out-of-hospital settings. Pulse transit time (PTT) is a well-known cardiovascular parameter which is highly correlated with BP and has been widely applied in the estimation of continuous BP. However, due to the complexity of cardiovascular system, the accuracy of PTT-based BP estimation is still unsatisfactory. Recent studies indicate that, for the subjects before and after exercise, PTT can track the high-frequency BP oscillation (HF-BP) well, but is inadequate to follow the low-frequency BP variance (LF-BP). Unfortunately, the cause for this failure of PTT in LF-BP estimation is still unclear. Based on these previous researches, we investigated the cause behind this failure of PTT in LF-BP estimation. The heart rate- (HR-) related arterial baroreflex (ABR) model was introduced to analyze the failure of PTT in LF-BP estimation. Data from 42 healthy volunteers before and after exercise were collected to evaluate the correlation between the ABR sensitivity and the estimation error of PTT-based BP in LF and HF components. In the correlation plot, an obvious difference was observed between the LF and HF groups. The correlation coefficient r for the ABR sensitivity with the estimation error of systolic BP (SBP) and diastolic BP (DBP) in LF was 0.817 ± 0.038 and 0.757 ± 0.069, respectively. However, those correlation coefficient r for the ABR sensitivity with the estimation error of SBP and DBP in HF was only 0.403 ± 0.145 and 0.274 ± 0.154, respectively. These results indicated that there is an ABR-related complex LF autonomic regulation mechanism on BP, PTT, and HR, which influences the effect of PTT in LF-BP estimation.

Multifractal multiscale dfa of cardiovascular time series: Differences in complex dynamics of systolic blood pressure, diastolic blood pressure and heart rate

The heart-rate fractal dynamics can be assessed by Detrended Fluctuation Analysis (DFA), originally proposed for estimating a short-term coefficient, α₁ (for scales n≤12 beats), and a long-term coefficient α₂ (for longer scales). Successively, DFA was extended to provide a multiscale α, i.e. a continuous function of n, α(n); or a multifractal α, i.e. a function of the order q of the fluctuations moment, α(q). Very recently, a multifractal-multiscale DFA was proposed for evaluating multifractality at different scales separately. Aim of this work is to describe the multifractal multiscale dynamics of three cardiovascular signals often recorded beat by beat in physiological and clinical settings: systolic blood pressure (SBP), diastolic blood pressure (DBP) and pulse interval (PI, inverse of the heart rate). We recorded SBP, DBP and PI for at least 90' in 65 healthy volunteers at rest, and adapted the previously proposed multifractal multiscale DFA to estimate α as function of the temporal scale, τ, between 15 and 450 s, and of the order q, between -5 and 5. We report, for the first time: 1) substantial differences among α(q,τ) surfaces of PI, SBP and DBP; 2) a strong dependency of the degree of multifractality on the temporal scale.

Effects of platooning on signal-detection performance, workload, and stress: A driving simulator study

Platooning, whereby automated vehicles travel closely together in a group, is attractive in terms of safety and efficiency. However, concerns exist about the psychological state of the platooning driver, who is exempted from direct control, yet remains responsible for monitoring the outside environment to detect potential threats. By means of a driving simulator experiment, we investigated the effects on recorded and self-reported measures of workload and stress for three task-instruction conditions: (1) No Task, in which participants had to monitor the road, (2) Voluntary Task, in which participants could do whatever they wanted, and (3) Detection Task, in which participants had to detect red cars. Twenty-two participants performed three 40-min runs in a constant-speed platoon, one condition per run in counterbalanced order. Contrary to some classic literature suggesting that humans are poor monitors, in the Detection Task condition participants attained a high mean detection rate (94.7%) and a low mean false alarm rate (0.8%). Results of the Dundee Stress State Questionnaire indicated that automated platooning was less distressing in the Voluntary Task than in the Detection Task and No Task conditions. In terms of heart rate variability, the Voluntary Task condition yielded a lower power in the low-frequency range relative to the high-frequency range (LF/HF ratio) than the Detection Task condition. Moreover, a strong time-on-task effect was found, whereby the mean heart rate dropped from the first to the third run. In conclusion, participants are able to remain attentive for a prolonged platooning drive, and the type of monitoring task has effects on the driver's psychological state.

The role of sympathetic and vagal cardiac control on complexity of heart rate dynamics

Analysis of heart rate variability (HRV) by nonlinear approaches has been gaining interest due to their ability to extract additional information from heart rate (HR) dynamics that are not detectable by traditional approaches. Nevertheless, the physiological interpretation of nonlinear approaches remains unclear. Therefore, we propose long-term (60 min) protocols involving selective blockade of cardiac autonomic receptors to investigate the contribution of sympathetic and parasympathetic function upon nonlinear dynamics of HRV. Conscious male Wistar rats had their electrocardiogram (ECG) recorded under three distinct conditions: basal, selective (atenolol or atropine), or combined (atenolol plus atropine) pharmacological blockade of autonomic muscarinic or β1-adrenergic receptors. Time series of RR interval were assessed by multiscale entropy (MSE) and detrended fluctuation analysis (DFA). Entropy over short (1 to 5, MSE1–5) and long (6 to 30, MSE6–30) time scales was computed, as well as DFA scaling exponents at short (αshort, 5 ≤ n ≤ 15), mid (αmid, 30 ≤ n ≤ 200), and long (αlong, 200 ≤ n ≤ 1,700) window sizes. The results show that MSE1–5 is reduced under atropine blockade and MSE6–30 is reduced under atropine, atenolol, or combined blockade. In addition, while atropine expressed its maximal effect at scale six, the effect of atenolol on MSE increased with scale. For DFA, αshort decreased during atenolol blockade, while the αmid increased under atropine blockade. Double blockade decreased αshort and increased αlong. Results with surrogate data show that the dynamics during combined blockade is not random. In summary, sympathetic and vagal control differently affect entropy (MSE) and fractal properties (DFA) of HRV. These findings are important to guide future studies.

NEW & NOTEWORTHY Although multiscale entropy (MSE) and detrended fluctuation analysis (DFA) are recognizably useful prognostic/diagnostic methods, their physiological interpretation remains unclear. The present study clarifies the effect of the cardiac autonomic control on MSE and DFA, assessed during long periods (1 h). These findings are important to help the interpretation of future studies.

Fractal analysis of heart rate variability reveals alterations of the integrative autonomic control of circulation in paraplegic individuals

The autonomic nervous system plays a major role in the integrative control of circulation, possibly contributing to the 'complex' dynamics responsible for fractal components in heart rate variability. Aim of this study is to evaluate whether an altered autonomic integrative control is identified by fractal analysis of heart rate variability. We enrolled 14 spinal cord injured individuals with complete lesion between the 5th and 11th thoracic vertebra (SCI_H), 14 with complete lesion between 12th thoracic and 5th lumbar vertebra (SCI_L), and 34 able-bodied controls (AB). These paraplegic subjects have an altered autonomic integrative regulation, but intact autonomic cardiac control and, as to SCI_L individuals, intact autonomic splanchnic control. Power spectral and fractal analysis (temporal spectrum of scale coefficients) were performed on 10 min tachograms. AB and SCI_L power spectra were similar, while the SCI_L fractal spectrum had higher coefficients between 12 and 48 s. SCI_H individuals had lower power than controls at 0.1 Hz; their fractal spectrum was morphologically different, diverging from that of controls at the largest scales (120 s). Therefore, when the lesion compromises the autonomic control of lower districts, fractal analysis reveals alterations undetected by power spectral analysis of heart rate variability.

The fractal structure of cardiovascular beat-to-beat series described over a broad range of scales: Differences between blood pressure and heart rate, and the effect of gender

The fractal characteristics of heart rate variability are usually assessed by estimating short- and long-term scale coefficients, α1 and α2, by detrended fluctuation analysis. Recently we extended this approach introducing a temporal spectrum of scale coefficients, α(τ), that describes the deviations of self-similarity from the bi-fractal model at each scale τ. Until now relatively short recordings were considered and α(τ) was characterized only for scales τ<;100 s. Aim of this work is to describe α(τ) of cardiovascular signals extending the range τ by an order of magnitude with respect to previous studies. We considered 2-hour recordings of systolic and diastolic blood pressure (SBP and DBP) and of pulse interval (PI) in 68 volunteers (26 males, 42 females) sitting at rest. The α(τ) spectra were estimated for 5s ≤τ ≤1000s and compared. We found important differences between α(τ) of SBP, DBP and PI. In particular, α(τ) of PI was lower than α(τ) of SBP at all the scales τ, with a relative maximum at τ =26 s and a minimum at τ =300 s that were completely missing in α(τ) of DBP. Significant differences were also found between α(τ) of males and females, probably linked to gender differences in the cardiovascular autonomic tone.

Evaluating the clinical value of oscillatory cardiopulmonary coupling in patients with obstructive sleep apnea hypopnea syndrome by impedance cardiogram

OBJECTIVES

For patients with obstructive sleep apnea hypopnea syndrome (OSAHS), chronic inflammation and hemodynamic oscillations caused by respiratory events contribute to cardiovascular disease (CVD). In this study, a physiological marker named oscillatory coupling factor (OCF) exacted from cardiac output (CO) was introduced. This study aimed to evaluate the clinical value of OCF and tentatively explore its predictive value of cardiovascular prognosis in OSAHS patients.

METHODS

An impedance cardiogram (ICG) was used to continuously obtain the participants' CO with simultaneous polysomnography. Participants were divided into three groups: an OSAHS-CVD- group (n = 19); an OSAHS + CVD- group (n = 34); and an OSAHS + CVD + group (n = 36). The OCF was exacted from the CO by using empirical mode decompensation-based detrended fluctuation analysis (EMD-DFA).

RESULTS

The OCF values were: OSAHS + CVD + group [1.20 (0.98-1.78)] > OSAHS + CVD- group [1.14 (1.02-1.94)] > OSAHS-CVD- group [0.95 (0.56-1.16)], (p = 0.001). A Spearman test showed that OCF was positively correlated with age, apnea/hypopnea index (AHI), microarousal index (MAI), oxygen desaturation index (ODI), and negatively correlated with the lowest SpO2. Ten participants were treated by one-night continuous positive airway pressure (CPAP): their AHI decreased from 44.9 (18.0-72.9)/hour to 1.25 (0.0-7.5)/hour, and their OCF fell from 1.17 (1.10-1.69) to 1.08 (0.96-1.23) (p = 0.038). Seventy-seven participants were effectively followed up. Seven participants developed CVD events or newly diagnosed CVD; their OCFs were distributed on a relatively high level [1.18 (1.01-1.56)].

CONCLUSION

The OSAHS participants had higher OCFs than those without OSAHS, while CVD made the OCFs even higher; CPAP could rectify this change. Oscillatory coupling factor may be a physiological marker of cardiopulmonary coupling and have potential cardiovascular prognostic value for people with OSAHS.

Assessing complexity of heart rate variability in people with spinal cord injury using local scale exponents

Detrended fluctuation analysis (DFA) has been widely used to study dynamics of heart rate variability (HRV), which provides a quantitative parameter, the scaling exponent a, to represent the correlation properties of RR interval series. However, it has been demonstrated that HRV exhibits complex behavior that cannot be fully described by a single exponent. This study aimed to investigate whether local scale exponent α(t) with t being the time scale can reveal new features of HRV that cannot be reflected by DFA coefficients. To accurately estimate α(t), we developed an approach for correcting a(t) at small scales and verified the approach using simulated signals. We studied HRV in 12 subjects with spinal cord injury and 14 able-bodied controls during sitting and prone postures. The results showed that α(t) provides complementary views of HRV, suggesting that it may be used to evaluate the effects of SCI-induced autonomic damage on HRV.

Adaptive correlation dimension method for analysing heart rate variability during the menstrual cycle

Correlation dimension (CD) is used for analysing the chaotic behaviour of the nonlinear heart rate variability (HRV) time series. In CD, the autocorrelation function is used to calculate the time delay. However, it does not provide optimum values of time delays, which leads to an inaccurate estimation of the HRV between phases of the menstrual cycle. Thus, an adaptive CD method is presented here to calculate the optimum value of the time delay based upon the information content in the HRV signal. In the proposed method, the first step is to divide the HRV signal into overlapping windows. Afterwards, the time delay is calculated for each window based on the features of the signal. This procedure of finding the optimum time delay for each window is known as adaptive autocorrelation. Then, the CD for each window is calculated using optimum time delays. Finally, adaptive CD is calculated by averaging the CD of all windows. The proposed method is applied on two data sets: (i) the standard Physionet dataset and (ii) the dataset acquired using BIOPAC(®)MP150. The results show that the proposed method can accurately differentiate between normal and diseased subjects. Further, the results prove that the proposed method is more accurate in detecting HRV variations during the menstrual cycles of 74 young women in lying and standing postures. Three statistical parameters are used to find the effectiveness of adaptive autocorrelation in calculating time delays. The comparative analysis validates the superiority of the proposed method over detrended fluctuation analyses and conventional CD.

Using local scale exponent to characterize heart rate variability in response to postural changes in people with spinal cord injury

Heart rate variability (HRV) is a promising marker for evaluating the remaining autonomic function in people with spinal cord injury (SCI). HRV is commonly assessed by spectral analysis and detrended fluctuation analysis (DFA). This study aimed to investigate whether local scale exponent α(t) can reveal new features of HRV that cannot be reflected by spectral measures and DFA coefficients. We studied 12 participants with SCI and 15 healthy able-bodied controls. ECG signals were continually recorded during 10 min sitting and 10 min prone postures. α(t) was calculated for scales between 4 and 60 s. Because α(t) could be overestimated at small scales, we developed an approach for correcting α(t) based on previous studies. The simulation results on simulated monofractal time series with α between 0.5 and 1.3 showed that the proposed method can yield improved estimation of α(t). We applied the proposed method to raw RR interval series. The results showed that α(t) in healthy controls monotonically decreased with scale at scales between 4 and 12 s (0.083–0.25 Hz) in both the sitting and prone postures, whereas in participants with SCI, α(t) slowly decreased at almost all scales. The sharp decreasing trend in α(t) in controls suggests a more complex dynamics of HRV in controls. α(t) at scales between 4 (0.25 Hz) and around 7 s (0.143 Hz) was lower in subjects with SCI than in controls in the sitting posture; α(t) at a narrow range of scales around 12 s (0.083 Hz) was higher in participants with SCI than in controls in the prone posture. However, none of normalized low frequency (0.04–0.15 Hz) power, the ratio of low frequency power to high frequency (0.15–0.4 Hz) power and long-term (>11 beats) DFA coefficient showed significant difference between healthy controls and subjects with SCI in the prone posture. Our results suggest that α(t) can reveal more detailed information in comparison to spectral measures and the standard DFA parameters.

Autonomic modulations of heart rate variability and performances in short-distance elite swimmers

PURPOSE

Endurance exercise is associated with high cardiac vagal tone, but how the cardiac autonomic control correlates with shorter anaerobic performances is unknown. Therefore, the aim of this study was to evaluate how autonomic modulations of heart rate (HR) variability (V) correlate with performances of short- (<1 min) and very short (<30 s) duration in elite athletes.

METHOD

Thirteen male swimmers, national-level crawl specialists in short (100-m) and very short (50-m) distances, were enrolled. HR was recorded during 15-min supine rest: (1) in the morning after wake up, (2) in the afternoon before sprint-oriented training sessions, (3) few minutes after training (first recovery phase after swimming cooldown). Heart rate variability (HRV) vagal and sympatho/vagal indices were calculated in time, frequency and complexity domains. Correlations of best seasonal times on 100- or 50-m distances with HRV indices and the velocity at blood lactate accumulation onset (V OBLA) were calculated.

RESULTS AND CONCLUSION

Vagal indices were highest in the morning where they positively correlated with very short-distance times (higher the index, worse is the 50-m performance). Sympatho/vagal indices were highest after training where they negatively correlated with short-distance times (higher the index, better is the 100-m performance). V OBLA did not correlate with the performances. Therefore, autonomic HRV indices and not V OBLA predict short and very short, most anaerobic, performances. Results also suggest that a strong cardiac vagal control has no effect on short performances and is even detrimental to very short performances, and that the capacity to powerfully increase the sympathetic tone during exercise may improve short, but not very short performances.

An equivalent circuit model for onset and offset exercise response

Background

The switching exercise (e.g., Interval Training) has been a commonly used exercise protocol nowadays for the enhancement of exerciser’s cardiovascular fitness. The current difficulty for simulating human onset and offset exercise responses regarding the switching exercise is to ensure the continuity of the outputs during onset-offset switching, as well as to accommodate the exercise intensities at both onset and offset of exercise.

Methods

Twenty-one untrained healthy subjects performed treadmill trials following both single switching exercise (e.g., single-cycle square wave protocol) and repetitive switching exercise (e.g., interval training protocol). During exercise, heart rate (HR) and oxygen uptake (VO ₂) were monitored and recorded by a portable gas analyzer (K4b ², Cosmed). An equivalent single-supply switching resistance-capacitor (RC) circuit model was proposed to accommodate the observed variations of the onset and offset dynamics. The single-cycle square wave protocol was utilized to investigate the respective dynamics at onset and offset of exercise with the aerobic zone of approximate 70% - 77% of HR _max, and verify the adaption feature for the accommodation of different exercise strengths. The design of the interval training protocol was to verify the transient properties during onset-offset switching. A verification method including Root-mean-square-error (RMSE) and correlation coefficient, was introduced for comparisons between the measured data and model outputs.

Results

The experimental results from single-cycle square wave exercises clearly confirm that the onset and offset characteristics for both HR and VO ₂ are distinctly different. Based on the experimental data for both single and repetitive square wave exercise protocols, the proposed model was then presented to simulate the onset and offset exercise responses, which were well correlated indicating good agreement with observations.

Conclusions

Compared with existing works, this model can accommodate the different exercise strengths at both onset and offset of exercise, while also depicting human onset and offset exercise responses, and guarantee the continuity of outputs during onset-offset switching. A unique adaption feature by allowing the time constant

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and steady state gain to re-shift back to their original states, more closely mimics the different exercise strengths during normal daily exercise activities.

Scaling analysis of stock markets

In this paper, we apply the detrended fluctuation analysis (DFA), local scaling detrended fluctuation analysis (LSDFA), and detrended cross-correlation analysis (DCCA) to investigate correlations of several stock markets. DFA method is for the detection of long-range correlations used in time series. LSDFA method is to show more local properties by using local scale exponents. DCCA method is a developed method to quantify the cross-correlation of two non-stationary time series. We report the results of auto-correlation and cross-correlation behaviors in three western countries and three Chinese stock markets in periods 2004-2006 (before the global financial crisis), 2007-2009 (during the global financial crisis), and 2010-2012 (after the global financial crisis) by using DFA, LSDFA, and DCCA method. The findings are that correlations of stocks are influenced by the economic systems of different countries and the financial crisis. The results indicate that there are stronger auto-correlations in Chinese stocks than western stocks in any period and stronger auto-correlations after the global financial crisis for every stock except Shen Cheng; The LSDFA shows more comprehensive and detailed features than traditional DFA method and the integration of China and the world in economy after the global financial crisis; When it turns to cross-correlations, it shows different properties for six stock markets, while for three Chinese stocks, it reaches the weakest cross-correlations during the global financial crisis.

A new algorithm for quadratic sample entropy optimization for very short biomedical signals: application to blood pressure records

This paper describes a new method to optimize the computation of the quadratic sample entropy (QSE) metric. The objective is to enhance its segmentation capability between pathological and healthy subjects for short and unevenly sampled biomedical records, like those obtained using ambulatory blood pressure monitoring (ABPM). In ABPM, blood pressure is measured every 20-30 min during 24h while patients undergo normal daily activities. ABPM is indicated for a number of applications such as white-coat, suspected, borderline, or masked hypertension. Hypertension is a very important clinical issue that can lead to serious health implications, and therefore its identification and characterization is of paramount importance. Nonlinear processing of signals by means of entropy calculation algorithms has been used in many medical applications to distinguish among signal classes. However, most of these methods do not perform well if the records are not long enough and/or not uniformly sampled. That is the case for ABPM records. These signals are extremely short and scattered with outliers or missing/resampled data. This is why ABPM Blood pressure signal screening using nonlinear methods is a quite unexplored field. We propose an additional stage for the computation of QSE independently of its parameter r and the input signal length. This enabled us to apply a segmentation process to ABPM records successfully. The experimental dataset consisted of 61 blood pressure data records of control and pathological subjects with only 52 samples per time series. The entropy estimation values obtained led to the segmentation of the two groups, while other standard nonlinear methods failed.

Multiscale multifractal analysis of traffic signals to uncover richer structures

Multifractal detrended fluctuation analysis (MF-DFA) is the most popular method to detect multifractal characteristics of considerable signals such as traffic signals. When fractal properties vary from point to point along the series, it leads to multifractality. In this study, we concentrate not only on the fact that traffic signals have multifractal properties, but also that such properties depend on the time scale in which the multifractality is computed. Via the multiscale multifractal analysis (MMA), traffic signals appear to be far more complex and contain more information which MF-DFA cannot explore by using a fixed time scale. More importantly, we do not have to avoid data sets with crossovers or narrow the investigated time scales, which may lead to biased results. Instead, the Hurst surface provides a spectrum of local scaling exponents at different scale ranges, which helps us to easily position these crossovers. Through comparing Hurst surfaces for signals before and after removing periodical trends, we find periodicities of traffic signals are the main source of the crossovers. Besides, the Hurst surface of the weekday series behaves differently from that of the weekend series. Results also show that multifractality of traffic signals is mainly due to both broad probability density function and correlations. The effects of data loss are also discussed, which suggests that we should carefully handle MMA results when the percentage of data loss is larger than 40%.

Detrended fluctuation analysis of blood pressure in preterm infants with intraventricular hemorrhage

Very preterm infants are at high risk of death and serious permanent brain damage, as occurs with intraventricular hemorrhage (IVH). Detrended fluctuation analysis (DFA) that quantifies the fractal correlation properties of physiological signals has been proposed as a potential method for clinical risk assessment. This study examined whether DFA of the arterial blood pressure (ABP) signal could derive markers for the identification of preterm infants who developed IVH. ABP data were recorded from a prospective cohort of 30 critically ill preterm infants in the first 1-3 h of life, 10 of which developed IVH. DFA was performed on the beat-to-beat sequences of mean arterial pressure (MAP), systolic blood pressure (SBP) and pulse interval, with short-term exponent (α1, for timescale of 4-15 beats) and long-term exponent (α2, for timescale of 15-50 beats) computed accordingly. The IVH infants were found to have higher short-term scaling exponents of both MAP and SBP (α1 = 1.06 ± 0.18 and 0.98 ± 0.20) compared to the non-IVH infants (α1 = 0.84 ± 0.25 and 0.78 ± 0.25, P = 0.017 and 0.038, respectively). The results have demonstrated that fractal dynamics embedded in the arterial pressure waveform could provide useful information that facilitates early identification of IVH in preterm infants.

Detection of co-regulation of local structure and magnitude of stride time variability using a new local detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a popular method to numerically define the persistent structure of stride time variability. The conventional DFA assumes that the persistent structure in stride time variability is consistent in time and can be numerically defined by a single DFA scaling exponent. However, stride time regulation has to be adaptive to both environmental and internal perturbations and consequently, the persistent structure of stride time variability will have to be modulated in time. The present article introduces a new local detrended fluctuation analysis (DFAloc) that is able to detect modulation in the structure of stride time variability generated by phase-couplings between temporal scales. DFAloc was used in a reanalysis of the data set of stride time variability of Hausdorff et al. and a data set available at www.physionet.org. The results showed that there were significant phase couplings between temporal scales that generate an inverse correlation (r=-0.54 to -0.83) between the local structure and local magnitude of the stride time variability. Furthermore, the modulation of the local structure was significantly influenced by gait speed, external pace making, and age (all p's<0.05). These results suggest several specific modifications of contemporary theories that have been suggested for the persistent structure of stride time variability found by the conventional DFA.

Effects of autonomic ganglion blockade on fractal and spectral components of blood pressure and heart rate variability in free-moving rats

Fractal analysis is a promising tool for assessing autonomic influences on heart rate (HR) and blood pressure (BP) variability. The temporal spectrum of scale coefficients, α(t), was recently proposed to describe the cardiovascular fractal dynamics. Aim of our work is to evaluate sympathetic influences on cardiovascular variability analyzing α(t) and spectral powers of HR and BP after ganglionic blockade. BP was recorded in 11 rats before and after autonomic blockade by hexamethonium infusion (HEX). Systolic and diastolic BP, pulse pressure and pulse interval were derived beat-by-beat. Segments longer than 5 min were selected at baseline and HEX to estimate power spectra and α(t). Comparisons were made by paired t-test. HEX reduced all spectral components of systolic and diastolic BP, the reduction being particularly significant around the frequency of Mayer waves; it induced a reduction on α(t) coefficients at t<2s and an increase on coefficients at t>8s. HEX reduced only slower components of pulse interval power spectrum, but decreased significantly faster scale coefficients (t<8s). HEX only marginally affected pulse pressure variability. Results indicate that the sympathetic outflow contributes to BP fractal dynamics with fractional Gaussian noise (α<1) at longer scales and fractional Brownian motion (α>1) at shorter scales. Ganglionic blockade also removes a fractional Brownian motion component at shorter scales from HR dynamics. Results may be explained by the characteristic time constants between sympathetic efferent activity and cardiovascular effectors. Therefore fractal analysis may complete spectral analysis with information on the correlation structure of the data.

Cardiac sounds from a wearable device for sternal seismocardiography

Seismocardiography is the body-surface recording of vibrations produced by the beating heart. A high frequency (HF) accelerometric component of the seismocardiogram (SCG) is related to the heart sounds generated by the closure of atrio-ventricular and semilunar valves. This paper evaluates the feasibility of recording the SCG component associated to cardiac sounds by means of a wearable device originally designed for monitoring ECG, respiratory movements, body accelerations and posture in freely moving subjects. The method is based on the averaging of the HF component of the acceleration vector measured by the wearable system, and on the subsequent extraction of features from its envelope. The method is applied on data recorded in healthy volunteers in different postures and during sleep. Results indicate that it is possible to reliably identify the time of occurrence of the first and second heart sound within the cardiac cycle. They also show significant differences in the HF component of SCG between supine and standing postures. Analyzing the HF SCG in a volunteer sleeping at high altitude (4554 m asl) substantial differences were also found among three body positions (lying supine or on the left or right side). These differences are likely to reflect changes in cardiac mechanics induced by different postures of the body.

Customization of entropy estimation measures for human arterial hypertension records segmentation

This paper describes a new application of the recently developed Coefficient of Sample Entropy (CosEn) measure. This entropy estimator is specially suited for cases where the length of the time series is extremely short. CosEn has already been used successfully to characterize and detect atrial fibrillation, using as few as 12 heartbeats. We have customized the methodology employed for heartbeat interval series to blood pressure hypertensive (BPHT) human records. Little can be found about BPHT records and its nonlinear regularity analysis. The method described in this paper provides a good segmentation between control and pathologic groups, based on the corresponding labeled BPHT records. The experimental dataset was drawn from the available records at the Hypertension Unit of the University Hospital of Mostoles, in Spain. The hypertension related variables studied were systolic blood pressure (SBP), diastolic blood pressure (DBP) and mean blood pressure (MBP). The hypothesis test yielded the following results in each case: acceptance probability of 0 for SBP, 0.005 for DBP and 0 for MBP. The confidence intervals for the three variables were nonoverlapping.

Characterization of detrended fluctuation analysis in the context of glycemic time series

There is a growing interest in the analysis of hyperglycemia and its relationship with other pathologies. The level of glucose in blood is regulated by the flux/reflux and controlled by hyperglycemia hormones and hypoglycemic insulin. Glycemic profiles are characterized by a nonlinear and nonstationary behavior but also influenced by circadian rhythms and patient daily routine which introduce quasi-periodic trends into them. This type of signals are commonly analyzed by Detrended Fluctuation Analysis (DFA) which states that the control system in charge of regulating the glucose level usually holds a long-range negative correlation. But there is an inconsistency about the windowing lengths, as no standard or rules are set. This work studies the influence of the windowing length sequence, and shows that there is a need for selecting the optimal values in order to obtain a good differentiation between different groups, and these values are somehow determined by signal characteristics.

Review and classification of variability analysis techniques with clinical applications

Analysis of patterns of variation of time-series, termed variability analysis, represents a rapidly evolving discipline with increasing applications in different fields of science. In medicine and in particular critical care, efforts have focussed on evaluating the clinical utility of variability. However, the growth and complexity of techniques applicable to this field have made interpretation and understanding of variability more challenging. Our objective is to provide an updated review of variability analysis techniques suitable for clinical applications. We review more than 70 variability techniques, providing for each technique a brief description of the underlying theory and assumptions, together with a summary of clinical applications. We propose a revised classification for the domains of variability techniques, which include statistical, geometric, energetic, informational, and invariant. We discuss the process of calculation, often necessitating a mathematical transform of the time-series. Our aims are to summarize a broad literature, promote a shared vocabulary that would improve the exchange of ideas, and the analyses of the results between different studies. We conclude with challenges for the evolving science of variability analysis.

Assessing the fractal structure of heart rate by the temporal spectrum of scale exponents: a new approach for detrended fluctuation analysis of heart rate variability

Detrended fluctuation analysis (DFA) is the most popular method for assessing the fractal characteristics of heart rate (HR). Traditionally, short-term and long-term scale coefficients, α(1) and α(2), are calculated from DFA. We recently showed that the traditional approach oversimplifies a more complex phenomenon better represented by a continuous spectrum of scale coefficients. In this paper we present a DFA based method for describing the HR fractal dynamics with a temporal spectrum of scale exponents, α(t), rather than by a model of lumped parameters, α(1) and α(2). Since α(t) is a function of the temporal scale, its interpretation is facilitated when conditions with different mean HR are compared. In this work, we reanalyze HR data, collected by our group in previous studies, by applying the proposed α(t) spectrum. We quantify the effects of gender, ageing, posture and activity level, and the alterations induced by exposure to high and very-high altitude hypoxia, on α(t). Most of the results may be interpreted in terms of changes of cardiac autonomic regulation, and indicate clearly that the new proposed DFA spectrum provides a more faithful and interpretable description of the HR fractal dynamics than traditional α(1) and α(2) scale coefficients.