Multifractality and heart rate variability

Multifractal analysis of heart rate variability in pregnancy during sleep

Understanding the complex dynamics of heart rate variability (HRV) during pregnancy is crucial for monitoring both maternal well-being and fetal health. In this study, we use the Multifractal Detrended Fluctuations Analysis approach to investigate HRV patterns in pregnant individuals during sleep based on RR interval maxima (MM fluctuations). In addition, we study the type of multifractality within MM fluctuations, that is, if it arises from a broad probability density function or from varying long-range correlations. Furthermore, to provide a comprehensive view of HRV changes during sleep in pregnancy, classical temporal and spectral HRV indices were calculated at quarterly intervals during sleep. Our study population consists of 21 recordings from nonpregnant women, 18 from the first trimester (early-pregnancy) and 18 from the second trimester (middle-pregnancy) of pregnancy. Results. There are statistically significant differences ( p -value < 0.05) in mean heart rate, rms heart rate, mean MM fluctuations, and standard deviation of MM fluctuations, particularly in the third and fourth quarter of sleep between pregnant and non-pregnant states. In addition, the early-pregnancy group shows significant differences ( p -value < 0.05) in spectral indices during the first and fourth quarter of sleep compared to the non-pregnancy group. Furthermore, the results of our research show striking similarities in the average multifractal structure of MM fluctuations between pregnant and non-pregnant states during normal sleep. These results highlight the influence of different long-range correlations within the MM fluctuations, which could be primarily associated with the emergence of sleep cycles on multifractality during sleep. Finally, we performed a separability analysis between groups using temporal and spectral HRV indices as features per sleep quarter. Employing only three features after Principal Component Analysis (PCA) to the original feature set, achieving complete separability among all groups appears feasible. Using multifractal analysis, our study provides a comprehensive understanding of the complex HRV patterns during pregnancy, which holds promise for maternal and fetal health monitoring. The separability analysis also provides valuable insights into the potential for group differentiation using simple measures such as mean heart rate, rms heart rate, and mean MM fluctuations or in the transformed feature space based on PCA.

Multifractal Heart Rate Value Analysis: A Novel Approach for Diabetic Neuropathy Diagnosis

Type 2 diabetes mellitus (T2DM) is characterized by several complications, such as retinopathy, renal failure, cardiovascular disease, and diabetic neuropathy. Among these, neuropathy is the most severe complication, due to the challenging nature of its early detection. The linear Hearth Rate Variability (HRV) analysis is the most common diagnosis technique for diabetic neuropathy, and it is characterized by the determination of the sympathetic-parasympathetic balance on the peripheral nerves through a linear analysis of the tachogram obtained using photoplethysmography. We aimed to perform a multifractal analysis to identify autonomic neuropathy, which was not yet manifest and not detectable with the linear HRV analysis. We enrolled 10 healthy controls, 10 T2DM-diagnosed patients with not-full-blown neuropathy, and 10 T2DM diagnosed patients with full-blown neuropathy. The tachograms for the HRV analysis were obtained using finger photoplethysmography and a linear and/or multifractal analysis was performed. Our preliminary results showed that the linear analysis could effectively differentiate between healthy patients and T2DM patients with full-blown neuropathy; nevertheless, no differences were revealed comparing the full-blown to not-full-blown neuropathic diabetic patients. Conversely, the multifractal HRV analysis was effective for discriminating between full-blown and not-full-blown neuropathic T2DM patients. The multifractal analysis can represent a powerful strategy to determine neuropathic onset, even without clinical diagnostic evidence.

Characterization of autonomic states by complex sympathetic and parasympathetic dynamics

Assessment of heartbeat dynamics provides a promising framework for non-invasive monitoring of cardiovascular and autonomic states. Nevertheless, the non-specificity of such measurements among clinical populations and healthy conditions associated with different autonomic states severely limits their applicability and exploitation in naturalistic conditions. This limitation arises especially when pathological or postural change-related sympathetic hyperactivity is compared to autonomic changes across age and experimental conditions. In this frame, we investigate the intrinsic irregularity and complexity of cardiac sympathetic and vagal activity series in different populations, which are associated with different cardiac autonomic dynamics. Sample entropy, fuzzy entropy, and distribution entropy are calculated on the recently proposed sympathetic and parasympathetic activity indices (SAI and PAI) series, which are derived from publicly available heartbeat series of congestive heart failure patients, elderly and young subjects watching a movie in the supine position, and healthy subjects undergoing slow postural changes. Results show statistically significant differences between pathological/old subjects and young subjects in the resting state and during slow tilt, with interesting trends in SAI- and PAI-related entropy values. Moreover, while CHF patients and healthy subjects in upright position show the higher cardiac sympathetic activity, elderly and young subjects in resting state showed higher vagal activity. We conclude that quantification of intrinsic cardiac complexity from sympathetic and vagal dynamics may provide new physiology insights and improve on the non-specificity of heartbeat-derived biomarkers.

Brain entropy, fractal dimensions and predictability: A review of complexity measures for EEG in healthy and neuropsychiatric populations

There has been an increasing trend towards the use of complexity analysis in quantifying neural activity measured by electroencephalography (EEG) signals. On top of revealing complex neuronal processes of the brain that may not be possible with linear approaches, EEG complexity measures have also demonstrated their potential as biomarkers of psychopathology such as depression and schizophrenia. Unfortunately, the opacity of algorithms and descriptions originating from mathematical concepts have made it difficult to understand what complexity is and how to draw consistent conclusions when applied within psychology and neuropsychiatry research. In this review, we provide an overview and entry-level explanation of existing EEG complexity measures, which can be broadly categorized as measures of predictability and regularity. We then synthesize complexity findings across different areas of psychological science, namely, in consciousness research, mood and anxiety disorders, schizophrenia, neurodevelopmental and neurodegenerative disorders, as well as changes across the lifespan, while addressing some theoretical and methodological issues underlying the discrepancies in the data. Finally, we present important considerations when choosing and interpreting these metrics.

Evaluation of non-linear heart rate variability using multi-scale multi-fractal detrended fluctuation analysis in mice: Roles of the autonomic nervous system and sinoatrial node

Nonlinear analyses of heart rate variability (HRV) can be used to quantify the unpredictability, fractal properties and complexity of heart rate. Fractality and its analysis provides valuable information about cardiovascular health. Multi-Scale Multi-Fractal Detrended Fluctuation Analysis (MSMFDFA) is a complexity-based algorithm that can be used to quantify the multi-fractal dynamics of the HRV time series through investigating characteristic exponents at different time scales. This method is applicable to short time series and it is robust to noise and nonstationarity. We have used MSMFDFA, which enables assessment of HRV in the frequency ranges encompassing the very-low frequency and ultra-low frequency bands, to jointly assess multi-scale and multi-fractal dynamics of HRV signals obtained from telemetric ECG recordings in wildtype mice at baseline and after autonomic nervous system (ANS) blockade, from electrograms recorded from isolated atrial preparations and from spontaneous action potential recordings in isolated sinoatrial node myocytes. Data demonstrate that the fractal profile of the intrinsic heart rate is significantly different from the baseline heart rate in vivo, and it is also altered after ANS blockade at specific scales and fractal order domains. For beating rate in isolated atrial preparations and intrinsic heart rate in vivo, the average fractal structure of the HRV increased and multi-fractality strength decreased. These data demonstrate that fractal properties of the HRV depend on both ANS activity and intrinsic sinoatrial node function and that assessing multi-fractality at different time scales is an effective approach for HRV assessment.

Fractal Structure of Brain Electrical Activity of Patients With Mental Disorders

This work was aimed at a comparative analysis of the degree of multifractality of electroencephalographic time series obtained from a group of healthy subjects and from patients with mental disorders. We analyzed long-term records of patients with paranoid schizophrenia and patients with depression. To evaluate the properties of multifractal scaling of various electroencephalographic time series, the method of maximum modulus of the wavelet transform and multifractal analysis of fluctuations without a trend were used. The stability of the width and position of the singularity spectrum for each of the test groups was revealed, and a relationship was established between the correlation and anticorrelation dynamics of successive values of the electroencephalographic time series and the type of mental disorders. It was shown that the main differences between the multifractal properties of brain activity in normal and pathological conditions lie in the different width of the multifractality spectrum and its location associated with the correlated or anticorrelated dynamics of the values of successive time series. It was found that the schizophrenia group is characterized by a greater degree of multifractality compared to the depression group. Thus, the degree of multifractality can be included in a set of tests for differential diagnosis and research of mental disorders.

Intrinsic Complexity of Sympathetic and Parasympathetic Dynamics from HRV series: a Preliminary Study on Postural Changes

The analysis of complex heartbeat dynamics has been widely used to characterize heartbeat autonomic control in healthy and pathological conditions. However, underlying physiological correlates of complexity measurements from heart rate variability (HRV) series have not been identified yet. To this extent, we investigated intrinsic irregularity and complexity of cardiac sympathetic and vagal activity time series during postural changes. We exploited our recently proposed HRV-based, time-varying Sympathetic and Parasympathetic Activity Indices (SAI and PAI) and performed Sample Entropy, Fuzzy Entropy, and Distribution Entropy calculations on publicly-available heartbeat series gathered from 10 healthy subjects undergoing resting state and passive slow tilt sessions. Results show significantly higher entropy values during the upright position than resting state in both SAI and PAI series. We conclude that an increase in HRV complexity resulting from postural changes may derive from sympathetic and vagal activities with higher complex dynamics.

Meditation-Induced Coherence and Crucial Events

In this paper we emphasize that 1/f noise has two different origins, one compatible with Laplace determinism and one determined by unpredictable crucial events. The dynamics of heartbeats, manifest as heart rate variability (HRV) time series, are determined by the joint action of these different memory sources with meditation turning the Laplace memory into a strongly coherent process while exerting an action on the crucial events favoring the transition from the condition of ideal 1/f noise to the Gaussian basin of attraction. This theoretical development affords a method of statistical analysis that establishes a quantitative approach to the evaluation of the stress reduction realized by the practice of Chi meditation and Kundalini Yoga.

Bidirectional Cardio-Respiratory Interactions in Heart Failure

We investigated cardio-respiratory coupling in patients with heart failure by quantification of bidirectional interactions between cardiac (RR intervals) and respiratory signals with complementary measures of time series analysis. Heart failure patients were divided into three groups of twenty, age and gender matched, subjects: with sinus rhythm (HF-Sin), with sinus rhythm and ventricular extrasystoles (HF-VES), and with permanent atrial fibrillation (HF-AF). We included patients with indication for implantation of implantable cardioverter defibrillator or cardiac resynchronization therapy device. ECG and respiratory signals were simultaneously acquired during 20 min in supine position at spontaneous breathing frequency in 20 healthy control subjects and in patients before device implantation. We used coherence, Granger causality and cross-sample entropy analysis as complementary measures of bidirectional interactions between RR intervals and respiratory rhythm. In heart failure patients with arrhythmias (HF-VES and HF-AF) there is no coherence between signals (p < 0.01), while in HF-Sin it is reduced (p < 0.05), compared with control subjects. In all heart failure groups causality between signals is diminished, but with significantly stronger causality of RR signal in respiratory signal in HF-VES. Cross-sample entropy analysis revealed the strongest synchrony between respiratory and RR signal in HF-VES group. Beside respiratory sinus arrhythmia there is another type of cardio-respiratory interaction based on the synchrony between cardiac and respiratory rhythm. Both of them are altered in heart failure patients. Respiratory sinus arrhythmia is reduced in HF-Sin patients and vanished in heart failure patients with arrhythmias. Contrary, in HF-Sin and HF-VES groups, synchrony increased, probably as consequence of some dominant neural compensatory mechanisms. The coupling of cardiac and respiratory rhythm in heart failure patients varies depending on the presence of atrial/ventricular arrhythmias and it could be revealed by complementary methods of time series analysis.

Sign and magnitude scaling properties of heart rate variability in patients with end-stage renal failure: Are these properties useful to identify pathophysiological adaptations?

The scaling properties of heart rate variability data are reliable dynamical features to predict mortality and for the assessment of cardiovascular risk. The aim of this manuscript was to determine if the scaling properties, as provided by the sign and magnitude analysis, can be used to differentiate between pathological changes and those adaptations basically introduced by modifications of the mean heart rate in distinct manoeuvres (active standing or hemodialysis treatment, HD), as well as clinical conditions (end stage renal disease, ESRD). We found that in response to active standing, the short-term scaling index (α₁) increased in healthy subjects and in ESRD patients only after HD. The sign short-term scaling exponent (α_1sign) increased in healthy subjects and ESRD patients, showing a less anticorrelated behavior in active standing. Both α₁ and α_1sign did show covariance with the mean heart rate in healthy subjects, while in ESRD patients, this covariance was observed only after HD. A reliable estimation of the magnitude short-term scaling exponent (α_1magn) required the analysis of time series with a large number of samples (>3000 data points). This exponent was similar for both groups and conditions and did not show covariance with the mean heart rate. A surrogate analysis confirmed the presence of multifractal properties (α_1magn > 0.5) in the time series of healthy subjects and ESDR patients. In conclusion, α₁ and α_1sign provided insights into the physiological adaptations during active standing, which revealed a transitory impairment before HD in ESRD patients. The presence of multifractal properties indicated that a reduced short-term variability does not necessarily imply a declined regulatory complexity in these patients.

Sudden Cardiac Risk Stratification with Electrocardiographic Indices - A Review on Computational Processing, Technology Transfer, and Scientific Evidence

Great effort has been devoted in recent years to the development of sudden cardiac risk predictors as a function of electric cardiac signals, mainly obtained from the electrocardiogram (ECG) analysis. But these prediction techniques are still seldom used in clinical practice, partly due to its limited diagnostic accuracy and to the lack of consensus about the appropriate computational signal processing implementation. This paper addresses a three-fold approach, based on ECG indices, to structure this review on sudden cardiac risk stratification. First, throughout the computational techniques that had been widely proposed for obtaining these indices in technical literature. Second, over the scientific evidence, that although is supported by observational clinical studies, they are not always representative enough. And third, via the limited technology transfer of academy-accepted algorithms, requiring further meditation for future systems. We focus on three families of ECG derived indices which are tackled from the aforementioned viewpoints, namely, heart rate turbulence (HRT), heart rate variability (HRV), and T-wave alternans. In terms of computational algorithms, we still need clearer scientific evidence, standardizing, and benchmarking, siting on advanced algorithms applied over large and representative datasets. New scenarios like electronic health recordings, big data, long-term monitoring, and cloud databases, will eventually open new frameworks to foresee suitable new paradigms in the near future.

Significance of using a nonlinear analysis technique, the Lyapunov exponent, on the understanding of the dynamics of the cardiorespiratory system in rats

BACKGROUND/AIM

Pneumocardiography (PNCG) is the recording method of cardiac-induced tracheal air flow and pressure pulsations in the respiratory airways. PNCG signals reflect both the lung and heart actions and could be accurately recorded in spontaneously breathing anesthetized rats. Nonlinear analysis methods, including the Lyapunov exponent, can be used to explain the biological dynamics of systems such as the cardiorespiratory system.

MATERIALS AND METHODS

In this study, we recorded tracheal air flow signals, including PNCG signals, from 3 representative anesthetized rats and analyzed the nonlinear behavior of these complex signals using Lyapunov exponents.

RESULTS

Lyapunov exponents may also be used to determine the normal and pathological structure of biological systems. If the signals have at least one positive Lyapunov exponent, the signals reflect chaotic activity, as seen in PNCG signals in rats; the largest Lyapunov exponents of the signals of the healthy rats were greater than zero in this study.

CONCLUSION

A method was proposed to determine the diagnostic and prognostic values of the cardiorespiratory system of rats using the arrangement of the PNCG and Lyapunov exponents, which may be monitored as vitality indicators.

Advances in heart rate variability signal analysis: joint position statement by the e-Cardiology ESC Working Group and the European Heart Rhythm Association co-endorsed by the Asia Pacific Heart Rhythm Society

Following the publication of the Task Force document on heart rate variability (HRV) in 1996, a number of articles have been published to describe new HRV methodologies and their application in different physiological and clinical studies. This document presents a critical review of the new methods. A particular attention has been paid to methodologies that have not been reported in the 1996 standardization document but have been more recently tested in sufficiently sized populations. The following methods were considered: Long-range correlation and fractal analysis; Short-term complexity; Entropy and regularity; and Nonlinear dynamical systems and chaotic behaviour. For each of these methods, technical aspects, clinical achievements, and suggestions for clinical application were reviewed. While the novel approaches have contributed in the technical understanding of the signal character of HRV, their success in developing new clinical tools, such as those for the identification of high-risk patients, has been rather limited. Available results obtained in selected populations of patients by specialized laboratories are nevertheless of interest but new prospective studies are needed. The investigation of new parameters, descriptive of the complex regulation mechanisms of heart rate, has to be encouraged because not all information in the HRV signal is captured by traditional methods. The new technologies thus could provide after proper validation, additional physiological, and clinical meaning. Multidisciplinary dialogue and specialized courses in the combination of clinical cardiology and complex signal processing methods seem warranted for further advances in studies of cardiac oscillations and in the understanding normal and abnormal cardiac control processes.

n-Order and maximum fuzzy similarity entropy for discrimination of signals of different complexity: Application to fetal heart rate signals

This paper presents two new concepts for discrimination of signals of different complexity. The first focused initially on solving the problem of setting entropy descriptors by varying the pattern size instead of the tolerance. This led to the search for the optimal pattern size that maximized the similarity entropy. The second paradigm was based on the n-order similarity entropy that encompasses the 1-order similarity entropy. To improve the statistical stability, n-order fuzzy similarity entropy was proposed. Fractional Brownian motion was simulated to validate the different methods proposed, and fetal heart rate signals were used to discriminate normal from abnormal fetuses. In all cases, it was found that it was possible to discriminate time series of different complexity such as fractional Brownian motion and fetal heart rate signals. The best levels of performance in terms of sensitivity (90%) and specificity (90%) were obtained with the n-order fuzzy similarity entropy. However, it was shown that the optimal pattern size and the maximum similarity measurement were related to intrinsic features of the time series.

Multifractality in heartbeat dynamics in patients undergoing beating-heart myocardial revascularization

BACKGROUND

The multifractal approach of HRV analysis offers new insight into the mechanisms of autonomic modulation of the diseased hearts and has a potential to depict subtle changes in cardiac autonomic nervous control not revealed by conventional linear and non-linear analyses in various conditions like heart failure or stable angina pectoris. The aim of this study was to employ the multifractality approach in cardiac surgery patients and evaluate the multifractality before and after beating-heart myocardial revascularization (off-pump CABG).

METHODS

Twenty-four hour Holter recordings were performed pre- and postoperatively in 60 patients undergoing off-pump CABG. Selected conventional time- and frequency-domain linear HRV indices were calculated from the 24h and 5 min ECG segments, and preselected multifractal parameters τ(q=2), τ(q=3), h_top and Δh were determined for daytime (12:00-18:00) and nighttime (00:00-06:00) periods of the ECG recordings using Ivanov's method. Mean differences over time were tested using paired-samples t-test and exact Wilcoxon matched-pairs test. The results are reported as mean ± SD and median with interquartile range. A p value of <0.05 was considered statistically significant.

RESULTS

All selected conventional linear HRV parameters decreased significantly after off pump CABG (p from <0.001-0.015). Preoperatively, multifractal parameter τ(q=2) was -0.60 ± 0.12 and -0.54 ± 0.12, τ(q=3) -0.52 ± 0.18 and -0.49 ± 0.17, h_top 0.20 ± 0.07 and 0.15 ± 0.07 and Δh 0.31 ± 0.14 and 0.17 ± 0.14 for daytime and nighttime periods, respectively. Postoperatively, τ(q=2) and τ(q=3) were significantly higher for daytime (-0.49 ± 0.15, p<0.001 and -0.43 ± 0.23, p=0.015), whereas h_top and Δh were significantly higher for both daytime and nighttime (0.25 ± 0.07, p<0.001 and 0.19 ± 0.06, p=0.002 for h_top and 0.41 ± 0.20, p=0.003 and 0.31 ± 0.19, p < 0.001 for Δh, respectively). All pre- and postoperative parameters, except τ(q=2) and τ(q=3) preoperatively, were significantly lower for nighttime as compared to daytime periods.

CONCLUSIONS

A significant breakdown of multifractal complexity and anti-correlation behavior with a significant sympathetic overdrive and a concomitant parasympathetic withdrawal occurs after off-pump CABG. The circadian pattern of multifractality regains its day-night variation in the first week after the surgical procedure.

Coarse-grained multifractality analysis based on structure function measurements to discriminate healthy from distressed foetuses

This paper proposes a combined coarse-grained multifractal method to discriminate between distressed and normal foetuses. The coarse-graining operation was performed by means of a coarse-grained procedure and the multifractal operation was based on a structure function. The proposed method was evaluated by one hundred recordings including eighty normal foetuses and twenty distressed foetuses. We found that it was possible to discriminate between distressed and normal foetuses using the Hurst exponent, singularity, and Holder spectra.

Mathematical biomarkers for the autonomic regulation of cardiovascular system

Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance.

Beyond long memory in heart rate variability: an approach based on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

Heart Rate Variability (HRV) series exhibit long memory and time-varying conditional variance. This work considers the Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors. ARFIMA-GARCH models may be used to capture and remove long memory and estimate the conditional volatility in 24 h HRV recordings. The ARFIMA-GARCH approach is applied to fifteen long term HRV series available at Physionet, leading to the discrimination among normal individuals, heart failure patients, and patients with atrial fibrillation.

Time-frequency analysis of the endocavitarian signal in paroxysmal atrial fibrillation

We apply the time-frequency analysis to the endocavitarian signal of patients suffering from paroxysmal atrial fibrillation. The time-frequency spectrum reveals the components of the endocavitarian signal. These components are located in the regions of the time-frequency domain that differ for in-rhythm and in-atrial fibrillation signals. By using experimental data, we perform a statistical study of these regions, and we obtain their average value. The difference in the shape of these regions is caused by the re-entry circuits that characterize atrial fibrillation. We propose a propagation model for atrial fibrillation based on the re-entry circuits, which explains the shape of the time-frequency spectrum.

Advances in monitoring cardiovascular signals. Contribution of nonlinear signal processing

Monitoring procedures are the basis to evaluate the clinical state of patients and to assess changes in their status, thus providing necessary interventions in time. To obtain this important objective it is necessary to integrate technological development with systems performing biomedical knowledge extraction and classification. Methods extracting non linear characteristics from HRV signal are presented and discussed to stress that integrated and multiparametric signal processing approaches can contribute to new diagnostic and classification indices. Examples report heart rate variability analysis in long periods in patients with cardiovascular disease. Fetal ECG monitoring is another example. In this case, coupling nonlinear parameters and linear time and frequency techniques increases diagnostic power and reliability of the monitoring. The paper shows that integrated signal analysis is very helpful to describe pathophysiological mechanisms involved in the cardiovascular and neural system control. It is a reliable basis to set up knowledge-based monitoring systems.

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.

Computing the multifractal spectrum from time series: an algorithmic approach

We show that the existing methods for computing the f(alpha) spectrum from a time series can be improved by using a new algorithmic scheme. The scheme relies on the basic idea that the smooth convex profile of a typical f(alpha) spectrum can be fitted with an analytic function involving a set of four independent parameters. While the standard existing schemes [P. Grassberger et al., J. Stat. Phys. 51, 135 (1988); A. Chhabra and R. V. Jensen, Phys. Rev. Lett. 62, 1327 (1989)] generally compute only an incomplete f(alpha) spectrum (usually the top portion), we show that this can be overcome by an algorithmic approach, which is automated to compute the D(q) and f(alpha) spectra from a time series for any embedding dimension. The scheme is first tested with the logistic attractor with known f(alpha) curve and subsequently applied to higher-dimensional cases. We also show that the scheme can be effectively adapted for analyzing practical time series involving noise, with examples from two widely different real world systems. Moreover, some preliminary results indicating that the set of four independent parameters may be used as diagnostic measures are also included.

Introduction to controversial topics in nonlinear science: is the normal heart rate chaotic?

In June 2008, the editors of Chaos decided to institute a new section to appear from time to time that addresses timely and controversial topics related to nonlinear science. The first of these deals with the dynamical characterization of human heart rate variability. We asked authors to respond to the following questions: Is the normal heart rate chaotic? If the normal heart rate is not chaotic, is there some more appropriate term to characterize the fluctuations (e.g., scaling, fractal, multifractal)? How does the analysis of heart rate variability elucidate the underlying mechanisms controlling the heart rate? Do any analyses of heart rate variability provide clinical information that can be useful in medical assessment (e.g., in helping to assess the risk of sudden cardiac death)? If so, please indicate what additional clinical studies would be useful for measures of heart rate variability to be more broadly accepted by the medical community. In addition, as a challenge for analysis methods, PhysioNet [A. L. Goldberger et al., "PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals," Circulation 101, e215-e220 (2000)] provided data sets from 15 patients of whom five were normal, five had heart failure, and five had atrial fibrillation (http://www.physionet.org/challenge/chaos/). This introductory essay summarizes the main issues and introduces the essays that respond to these questions.