Common multifractality in the heart rate variability and brain activity of healthy humans

Nonlinear Statistical Analysis of Normal and Pathological Infant Cry Signals in Cepstrum Domain by Multifractal Wavelet Leaders

Multifractal behavior in the cepstrum representation of healthy and unhealthy infant cry signals is examined by means of wavelet leaders and compared using the Student t-test. The empirical results show that both expiration and inspiration signals exhibit clear evidence of multifractal properties under healthy and unhealthy conditions. In addition, expiration and inspiration signals exhibit more complexity under healthy conditions than under unhealthy conditions. Furthermore, distributions of multifractal characteristics are different across healthy and unhealthy conditions. Hence, this study improves the understanding of infant crying by providing a complete description of its intrinsic dynamics to better evaluate its health status.

Admission Heart Rate Variability Is Associated With Poststroke Depression in Patients With Acute Mild-Moderate Ischemic Stroke

BACKGROUND

Stroke has been shown to cause cardiac autonomic dysfunction. Depression is common complication after acute ischemic stroke (AIS). The purpose of this study was to investigate whether decreased heart rate variability (HRV) was related to poststroke depression (PSD) in patients with mild-moderate AIS.

METHODS

In this study, we assessed autonomic function of ischemic stroke patients within 72 h from symptom onset by fractal dimension (FD). 503 patients (mean age 65.93 ± 10.19) with mild-moderate AIS underwent FD test after admission. Depressive symptoms were assessed using 17-item Hamilton Depression Rating Scale (HDRS) at baseline (within 7 days) and 3 months. Depression were defined if HDRS >6 points. According to the data of FD, we investigated association with early-onset PSD status and 3-month PSD.

RESULTS

59.24% (293/503) of patients had early-onset PSD status at baseline, and 38.66% (184/476) of patients had PSD at 3 months. ROC curve analysis shown that the optimal cut point of FD for early-onset PSD status and 3-month PSD were FD ≤ 1.27 and FD ≤ 1.19, respectively. In fully adjusted models, higher NIHSS [adjusted odd ratios (OR), 1.15; 95% confidence interval (CI), 1.05-1.27; P=0.005], younger age (adjusted OR, 1.18; 95% CI, 1.01-1.13; P=0.046), and FD ≤ 1.27 (adjusted OR, 3.31; 95% CI, 2.23-4.92; P<0.001) were associated with increased risk of early-onset PSD status. Higher NIHSS (adjusted OR, 1.21; 95% CI, 1.09-1.43; P<0.001) and FD ≤ 1.19 (adjusted OR, 2.68; 95% CI, 1.79-4.03; P=0.000) were associated with increased risk of 3-month PSD.

CONCLUSIONS

PSD is common after mild-moderate AIS and is highly correlated with decreased HRV, FD could serve as an objective tool to help in prediction of PSD.

Multifractal analysis of financial markets: a review

Multifractality is ubiquitously observed in complex natural and socioeconomic systems. Multifractal analysis provides powerful tools to understand the complex nonlinear nature of time series in diverse fields. Inspired by its striking analogy with hydrodynamic turbulence, from which the idea of multifractality originated, multifractal analysis of financial markets has bloomed, forming one of the main directions of econophysics. We review the multifractal analysis methods and multifractal models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. We survey the cumulating evidence for the presence of multifractality in financial time series in different markets and at different time periods and discuss the sources of multifractality. The usefulness of multifractal analysis in quantifying market inefficiency, in supporting risk management and in developing other applications is presented. We finally discuss open problems and further directions of multifractal analysis.

A healthy dose of chaos: Using fractal frameworks for engineering higher-fidelity biomedical systems

Optimal levels of chaos and fractality are distinctly associated with physiological health and function in natural systems. Chaos is a type of nonlinear dynamics that tends to exhibit seemingly random structures, whereas fractality is a measure of the extent of organization underlying such structures. Growing bodies of work are demonstrating both the importance of chaotic dynamics for proper function of natural systems, as well as the suitability of fractal mathematics for characterizing these systems. Here, we review how measures of fractality that quantify the dose of chaos may reflect the state of health across various biological systems, including: brain, skeletal muscle, eyes and vision, lungs, kidneys, tumours, cell regulation, skin and wound repair, bone, vasculature, and the heart. We compare how reports of either too little or too much chaos and fractal complexity can be damaging to normal biological function, and suggest that aiming for the healthy dose of chaos may be an effective strategy for various biomedical applications. We also discuss rising examples of the implementation of fractal theory in designing novel materials, biomedical devices, diagnostics, and clinical therapies. Finally, we explain important mathematical concepts of fractals and chaos, such as fractal dimension, criticality, bifurcation, and iteration, and how they are related to biology. Overall, we promote the effectiveness of fractals in characterizing natural systems, and suggest moving towards using fractal frameworks as a basis for the research and development of better tools for the future of biomedical engineering.

Assessing mood symptoms through heartbeat dynamics: An HRV study on cardiosurgical patients

BACKGROUND

Heart Rate Variability (HRV) is reduced both in depression and in coronary heart disease (CHD) suggesting common pathophysiological mechanisms for the two disorders. Within CHD, cardiac surgery patients (CSP) with postoperative depression are at greater risk of adverse cardiac events. Therefore, CSP would especially benefit from depression early diagnosis. Here we tested whether HRV-multi-feature analysis discriminates CSP with or without depression and provides an effective estimation of symptoms severity.

METHODS

Thirty-one patients admitted to cardiac rehabilitation after first-time cardiac surgery were recruited. Depressive symptoms were assessed with the Center for Epidemiologic Studies Depression Scale (CES-D). HRV features in time, frequency, and nonlinear domains were extracted from 5-min-ECG recordings at rest and used as predictors of "least absolute shrinkage and selection" (LASSO) operator regression model to estimate patients' CES-D score and to predict depressive state.

RESULTS

The model significantly predicted the CES-D score in all subjects (the total explained variance of CES-D score was 89.93%). Also it discriminated depressed and non-depressed CSP with 86.75% accuracy. Seven of the ten most informative metrics belonged to non-linear-domain.

LIMITATIONS

A higher number of patients evaluated also with a structured clinical interview would help to generalize the present findings.

DISCUSSION

To our knowledge this is the first study using a multi-feature approach to evaluate depression in CSP. The high informative power of HRV-nonlinear metrics suggests their possible pathophysiological role both in depression and in CHD. The high-accuracy of the algorithm at single-subject level opens to its translational use as screening tool in clinical practice.

Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces

When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover the intrinsic power-law cross correlations between two simultaneously recorded time series in the presence of nonstationarity after removing the effects of other time series acting as common forces. The DPXA method is a generalization of the detrended cross-correlation analysis that takes into account partial correlation analysis. We demonstrate the method by using bivariate fractional Brownian motions contaminated with a fractional Brownian motion. We find that the DPXA is able to recover the analytical cross Hurst indices, and thus the multiscale DPXA coefficients are a viable alternative to the conventional cross-correlation coefficient. We demonstrate the advantage of the DPXA coefficients over the DCCA coefficients by analyzing contaminated bivariate fractional Brownian motions. We calculate the DPXA coefficients and use them to extract the intrinsic cross correlation between crude oil and gold futures by taking into consideration the impact of the U.S. dollar index. We develop the multifractal DPXA (MF-DPXA) method in order to generalize the DPXA method and investigate multifractal time series. We analyze multifractal binomial measures masked with strong white noises and find that the MF-DPXA method quantifies the hidden multifractal nature while the multifractal DCCA method fails.

Correlations between the signal complexity of cerebral and cardiac electrical activity: a multiscale entropy analysis

The heart begins to beat before the brain is formed. Whether conventional hierarchical central commands sent by the brain to the heart alone explain all the interplay between these two organs should be reconsidered. Here, we demonstrate correlations between the signal complexity of brain and cardiac activity. Eighty-seven geriatric outpatients with healthy hearts and varied cognitive abilities each provided a 24-hour electrocardiography (ECG) and a 19-channel eye-closed routine electroencephalography (EEG). Multiscale entropy (MSE) analysis was applied to three epochs (resting-awake state, photic stimulation of fast frequencies (fast-PS), and photic stimulation of slow frequencies (slow-PS)) of EEG in the 1–58 Hz frequency range, and three RR interval (RRI) time series (awake-state, sleep and that concomitant with the EEG) for each subject. The low-to-high frequency power (LF/HF) ratio of RRI was calculated to represent sympatho-vagal balance. With statistics after Bonferroni corrections, we found that: (a) the summed MSE value on coarse scales of the awake RRI (scales 11–20, RRI-MSE-coarse) were inversely correlated with the summed MSE value on coarse scales of the resting-awake EEG (scales 6–20, EEG-MSE-coarse) at Fp2, C4, T6 and T4; (b) the awake RRI-MSE-coarse was inversely correlated with the fast-PS EEG-MSE-coarse at O1, O2 and C4; (c) the sleep RRI-MSE-coarse was inversely correlated with the slow-PS EEG-MSE-coarse at Fp2; (d) the RRI-MSE-coarse and LF/HF ratio of the awake RRI were correlated positively to each other; (e) the EEG-MSE-coarse at F8 was proportional to the cognitive test score; (f) the results conform to the cholinergic hypothesis which states that cognitive impairment causes reduction in vagal cardiac modulation; (g) fast-PS significantly lowered the EEG-MSE-coarse globally. Whether these heart-brain correlations could be fully explained by the central autonomic network is unknown and needs further exploration.

Classification of prolapsed mitral valve versus healthy heart from phonocardiograms by multifractal analysis

Phonocardiography has shown a great potential for developing low-cost computer-aided diagnosis systems for cardiovascular monitoring. So far, most of the work reported regarding cardiosignal analysis using multifractals is oriented towards heartbeat dynamics. This paper represents a step towards automatic detection of one of the most common pathological syndromes, so-called mitral valve prolapse (MVP), using phonocardiograms and multifractal analysis. Subtle features characteristic for MVP in phonocardiograms may be difficult to detect. The approach for revealing such features should be locally based rather than globally based. Nevertheless, if their appearances are specific and frequent, they can affect a multifractal spectrum. This has been the case in our experiment with the click syndrome. Totally, 117 pediatric phonocardiographic recordings (PCGs), 8 seconds long each, obtained from 117 patients were used for PMV automatic detection. We propose a two-step algorithm to distinguish PCGs that belong to children with healthy hearts and children with prolapsed mitral valves (PMVs). Obtained results show high accuracy of the method. We achieved 96.91% accuracy on the dataset (97 recordings). Additionally, 90% accuracy is achieved for the evaluation dataset (20 recordings). Content of the datasets is confirmed by the echocardiographic screening.

Integrated central-autonomic multifractal complexity in the heart rate variability of healthy humans

PURPOSE OF STUDY

The aim of this study was to characterize the central-autonomic interaction underlying the multifractality in heart rate variability (HRV) of healthy humans.

MATERIALS AND METHODS

Eleven young healthy subjects participated in two separate ~40 min experimental sessions, one in supine (SUP) and one in, head-up-tilt (HUT), upright (UPR) body positions. Surface scalp electroencephalography (EEG) and electrocardiogram (ECG) were collected and fractal correlation of brain and heart rate data was analyzed based on the idea of relative multifractality. The fractal correlation was further examined with the EEG, HRV spectral measures using linear regression of two variables and principal component analysis (PCA) to find clues for the physiological processing underlying the central influence in fractal HRV.

RESULTS

We report evidence of a central-autonomic fractal correlation (CAFC) where the HRV multifractal complexity varies significantly with the fractal correlation between the heart rate and brain data (P = 0.003). The linear regression shows significant correlation between CAFC measure and EEG Beta band spectral component (P = 0.01 for SUP and P = 0.002 for UPR positions). There is significant correlation between CAFC measure and HRV LF component in the SUP position (P = 0.04), whereas the correlation with the HRV HF component approaches significance (P = 0.07). The correlation between CAFC measure and HRV spectral measures in the UPR position is weak. The PCA results confirm these findings and further imply multiple physiological processes underlying CAFC, highlighting the importance of the EEG Alpha, Beta band, and the HRV LF, HF spectral measures in the supine position.

DISCUSSION AND CONCLUSION

The findings of this work can be summarized into three points: (i) Similar fractal characteristics exist in the brain and heart rate fluctuation and the change toward stronger fractal correlation implies the change toward more complex HRV multifractality. (ii) CAFC is likely contributed by multiple physiological mechanisms, with its central elements mainly derived from the EEG Alpha, Beta band dynamics. (iii) The CAFC in SUP and UPR positions is qualitatively different, with a more predominant central influence in the fractal HRV of the UPR position.

Modified permutation-entropy analysis of heartbeat dynamics

Heart rate variability (HRV) contains important information about the modulation of the cardiovascular system. Various methods of nonlinear dynamics (e.g., estimating Lyapunov exponents) and complexity measures (e.g., correlation dimension or entropies) have been applied to HRV analysis. Permutation entropy, which was proposed recently, has been widely used in many fields due to its conceptual and computational simplicity. It maps a time series onto a symbolic sequence of permutation ranks. The original permutation entropy assumes the time series under study has a continuous distribution, thus equal values are rare and can be ignored by ranking them according to their order of emergence, or broken by adding small random perturbations to ensure every symbol in a sequence is different. However, when the observed time series is digitized with lower resolution leading to a greater number of equal values, or the equalities represent certain characteristic sequential patterns of the system, it may not be rational to simply ignore or break them. In the present paper, a modified permutation entropy is proposed that, by mapping the equal value onto the same symbol (rank), allows for a more accurate characterization of system states. The application of the modified permutation entropy to the analysis of HRV is investigated using clinically collected data. Results show that modified permutation entropy can greatly improve the ability to distinguish the HRV signals under different physiological and pathological conditions. It can characterize the complexity of HRV more effectively than the original permutation entropy.

Multifractal detrending moving-average cross-correlation analysis

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross correlations. The multifractal detrended cross-correlation analysis (MFDCCA) approaches can be used to quantify such cross correlations, such as the MFDCCA based on the detrended fluctuation analysis (MFXDFA) method. We develop in this work a class of MFDCCA algorithms based on the detrending moving-average analysis, called MFXDMA. The performances of the proposed MFXDMA algorithms are compared with the MFXDFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving-average processes, and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents h(xy) extracted from the MFXDMA and MFXDFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross correlation is independent of the cross-correlation coefficient between two time series, and the MFXDFA and centered MFXDMA algorithms have comparative performances, which outperform the forward and backward MFXDMA algorithms. For two-component autoregressive fractionally integrated moving-average processes, we also find that the MFXDFA and centered MFXDMA algorithms have comparative performances, while the forward and backward MFXDMA algorithms perform slightly worse. For binomial measures, the forward MFXDMA algorithm exhibits the best performance, the centered MFXDMA algorithms performs worst, and the backward MFXDMA algorithm outperforms the MFXDFA algorithm when the moment order q<0 and underperforms when q>0. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MFXDMA algorithm gives the best estimates of h(xy)(q) since its h(xy)(2) is closest to 0.5, as expected, and the MFXDFA algorithm has the second best performance. For the volatilities, the forward and backward MFXDMA algorithms give similar results, while the centered MFXDMA and the MFXDFA algorithms fail to extract rational multifractal nature.

Multifractal nature of ocular aberration dynamics of the human eye

Ocular monochromatic aberrations display dynamic behavior even when the eye is fixating on a stationary stimulus. The fluctuations are commonly characterized in the frequency domain using the power spectrum obtained via the Fourier transform. In this paper we used a wavelet-based multifractal analytical approach to provide a more in depth analysis of the nature of the aberration fluctuations. The aberrations of five subjects were measured at 21 Hz using an open-view Shack-Hartmann sensor. We show that the aberration dynamics are multifractal. The most frequently occurring Hölder exponent for the rms wavefront error, averaged across the five subjects, was 0.31 ± 0.10. This suggests that the time course of the aberration fluctuations is antipersistant. Future applications of multifractal analysis are discussed.