Scale-invariant aspects of cardiac dynamics. Observing sleep stages and circadian phases

Future of Sleep Medicine: Novel Approaches and Measures Derived from Physiologic Systems Dynamics (Part I)

We review recent progress in understanding fundamental aspects of physiologic regulation during wake and sleep based on modern data-driven, analytical, and computational approaches with a focus on the complex dynamics of individual physiologic systems. The presented empirical findings indicate that sleep-wake and circadian cycles do not simply modulate basic physiologic functions but influence physiologic systems dynamics simultaneously over a broad range of time scales. The reviewed empirical approaches and derived measures represent novel mechanistic aspects of sleep and wake regulation, and lay the foundation for a new class of diagnostic and prognostic biomarkers in clinical sleep medicine.

Role of the Locus Coeruleus Arousal Promoting Neurons in Maintaining Brain Criticality across the Sleep-Wake Cycle

Sleep control depends on a delicate interplay among brain regions. This generates a complex temporal architecture with numerous sleep-stage transitions and intermittent fluctuations to micro-states and brief arousals. These temporal dynamics exhibit hallmarks of criticality, suggesting that tuning to criticality is essential for spontaneous sleep-stage and arousal transitions. However, how the brain maintains criticality remains not understood. Here, we investigate θ- and δ-burst dynamics during the sleep-wake cycle of rats (Sprague-Dawley, adult male) with lesion in the wake-promoting locus coeruleus (LC). We show that, in control rats, θ- and δ-bursts exhibit power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, as well as power-law long-range temporal correlations (LRTCs)-typical of non-equilibrium systems self-organizing at criticality. Furthermore, consecutive θ- and δ-bursts durations are characterized by anti-correlated coupling, indicating a new class of self-organized criticality that emerges from underlying feedback between neuronal populations and brain areas involved in generating arousals and sleep states. In contrast, we uncover that LC lesion leads to alteration of θ- and δ-burst critical features, with change in duration distributions and correlation properties, and increase in θ-δ coupling. Notably, these LC-lesion effects are opposite to those observed for lesions in the sleep-promoting ventrolateral preoptic (VLPO) nucleus. Our findings indicate that critical dynamics of θ- and δ-bursts arise from a balanced interplay of LC and VLPO, which maintains brain tuning to criticality across the sleep-wake cycle-a non-equilibrium behavior in sleep micro-architecture at short timescales that coexists with large-scale sleep-wake homeostasis.

Simulating Dynamics of Circulation in the Awake State and Different Stages of Sleep Using Non-autonomous Mathematical Model With Time Delay

We propose a mathematical model of the human cardiovascular system. The model allows one to simulate the main heart rate, its variability under the influence of the autonomic nervous system, breathing process, and oscillations of blood pressure. For the first time, the model takes into account the activity of the cerebral cortex structures that modulate the autonomic control loops of blood circulation in the awake state and in various stages of sleep. The adequacy of the model is demonstrated by comparing its time series with experimental records of healthy subjects in the SIESTA database. The proposed model can become a useful tool for studying the characteristics of the cardiovascular system dynamics during sleep.

Entropy Analysis of RR-Time Series From Stress Tests

The RR-interval time series or tachograms obtained from electrocardiograms have been widely studied since they reflect the cardiac variability, and this is an indicative of the health status of a person. The tachogram can be seen as a highly non-linear and complex time series, and therefore, should be analyzed with non-linear techniques. In this work, several entropy measures, Sample Entropy (SampEn), Approximate Entropy (ApEn), and Fuzzy Entropy (FuzzyEn) are used as a measure of heart rate variability (HRV). Tachograms belonging to thirty-nine subjects were obtained from a cardiac stress test consisting of a rest period followed by a period of moderate physical activity. Subjects are grouped according to their physical activity using the IPAQ sedentary and active questionnaire, we work with youth and middle-aged adults. The entropy measures for each group show that for the sedentary subjects the values are high at rest and decrease appreciably with moderate physical activity, This happens for both young and middle-aged adults. These results are highly reproducible. In the case of the subjects that exercise regularly, an increase in entropy is observed or they tend to retain the entropy value that they had at rest. It seems that there is a possible correlation between the physical condition of a person with the increase or decrease in entropy during moderate physical activity with respect to the entropy at rest. It was also observed that entropy during longer physical activity tests tends to decrease as fatigue accumulates, but this decrease is small compared to the change that occurs when going from rest to physical activity.

Critical Dynamics and Coupling in Bursts of Cortical Rhythms Indicate Non-Homeostatic Mechanism for Sleep-Stage Transitions and Dual Role of VLPO Neurons in Both Sleep and Wake

Origin and functions of intermittent transitions among sleep stages, including brief awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing sleep on scales of seconds and minutes results from intrinsic non-equilibrium critical dynamics. We investigate θ- and δ-wave dynamics in control rats and in rats where the sleep-promoting ventrolateral preoptic nucleus (VLPO) is lesioned (male Sprague-Dawley rats). We demonstrate that bursts in θ and δ cortical rhythms exhibit complex temporal organization, with long-range correlations and robust duality of power-law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, features typical of non-equilibrium systems self-organizing at criticality. We show that such non-equilibrium behavior relates to anti-correlated coupling between θ- and δ-bursts, persists across a range of time scales, and is independent of the dominant physiologic state; indications of a basic principle in sleep regulation. Further, we find that VLPO lesions lead to a modulation of cortical dynamics resulting in altered dynamical parameters of θ- and δ-bursts and significant reduction in θ-δ coupling. Our empirical findings and model simulations demonstrate that θ-δ coupling is essential for the emerging non-equilibrium critical dynamics observed across the sleep-wake cycle, and indicate that VLPO neurons may have dual role for both sleep and arousal/brief wake activation. The uncovered critical behavior in sleep- and wake-related cortical rhythms indicates a mechanism essential for the micro-architecture of spontaneous sleep-stage and arousal transitions within a novel, non-homeostatic paradigm of sleep regulation.SIGNIFICANCE STATEMENT We show that the complex micro-architecture of sleep-stage/arousal transitions arises from intrinsic non-equilibrium critical dynamics, connecting the temporal organization of dominant cortical rhythms with empirical observations across scales. We link such behavior to sleep-promoting neuronal population, and demonstrate that VLPO lesion (model of insomnia) alters dynamical features of θ and δ rhythms, and leads to significant reduction in θ-δ coupling. This indicates that VLPO neurons may have dual role for both sleep and arousal/brief wake control. The reported empirical findings and modeling simulations constitute first evidences of a neurophysiological fingerprint of self-organization and criticality in sleep- and wake-related cortical rhythms; a mechanism essential for spontaneous sleep-stage and arousal transitions that lays the bases for a novel, non-homeostatic paradigm of sleep regulation.

Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture

Origin and functions of intermittent transitions among sleep stages, including short awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing the sleep-wake cycle results from an underlying non-equilibrium critical dynamics, bridging collective behaviors across spatio-temporal scales. We investigate θ and δ wave dynamics in control rats and in rats with lesions of sleep-promoting neurons in the parafacial zone. We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality. Crucially, such temporal organization relates to anti-correlated coupling between θ- and δ-bursts, and is independent of the dominant physiologic state and lesions, a solid indication of a basic principle in sleep dynamics.

The avalanche-like behaviour of large-scale haemodynamic activity from wakefulness to deep sleep

Increasing evidence suggests that responsiveness is associated with critical or near-critical cortical dynamics, which exhibit scale-free cascades of spatio-temporal activity. These cascades, or 'avalanches', have been detected at multiple scales, from in vitro and in vivo microcircuits to voltage imaging and brain-wide functional magnetic resonance imaging (fMRI) recordings. Criticality endows the cortex with certain information-processing capacities postulated as necessary for conscious wakefulness, yet it remains unknown how unresponsiveness impacts on the avalanche-like behaviour of large-scale human haemodynamic activity. We observed a scale-free hierarchy of co-activated connected clusters by applying a point-process transformation to fMRI data recorded during wakefulness and non-rapid eye movement (NREM) sleep. Maximum-likelihood estimates revealed a significant effect of sleep stage on the scaling parameters of the cluster size power-law distributions. Post hoc statistical tests showed that differences were maximal between wakefulness and N2 sleep. These results were robust against spatial coarse graining, fitting alternative statistical models and different point-process thresholds, and disappeared upon phase shuffling the fMRI time series. Evoked neural bistabilities preventing arousals during N2 sleep do not suffice to explain these differences, which point towards changes in the intrinsic dynamics of the brain that could be necessary to consolidate a state of deep unresponsiveness.

Multifractal Spectrum Curvature of RR Tachograms of Healthy People and Patients with Congestive Heart Failure, a New Tool to Assess Health Conditions

We calculate the multifractal spectra of heartbeat RR-interval time series (tachograms) of healthy subjects and patients with congestive heart failure (CHF). From these time series, we obtained new subseries of 6 h durations when healthy persons and patients were asleep and awake respectively. For each time series and subseries, we worked out the multifractal spectra with the Chhabra and Jensen method and found that their graphs have different shapes for CHF patients and healthy persons. We suggest to measure two parameters: the curvature around the maximum and the symmetry for all these multifractal spectra graphs, because these parameters were different for healthy and CHF subjects. Multifractal spectra of healthy subjects tend to be right skewed especially when the subjects are asleep and the curvature around the maximum is small compared with the curvature around the maximum of the CHF multifractal spectra; that is, the spectra of patients tend to be more pointed around the maximum. In CHF patients, we also have encountered differences in the curvature of the multifractal spectra depending on their respective New York Heart Association (NYHA) index.

Heart rate variability changes in major depressive disorder during sleep: Fractal index correlates with BDI score during REM sleep

We investigated the relationship between autonomic nervous system activity during each sleep stage and the severity of depressive symptoms in patients with major depressive disorder (MDD) and healthy control subjects. Thirty patients with MDD and thirty healthy control subjects matched for sex, age, and body mass index completed standard overnight polysomnography. Depression severity was assessed using the Beck Depression Inventory (BDI). Time- and frequency-domain, and fractal HRV parameters were derived from 5-min electrocardiogram segments during light sleep, deep sleep, rapid eye movement (REM) sleep, and the pre- and post-sleep wake periods. Detrended fluctuation analysis (DFA) alpha-1 values during REM sleep were significantly higher in patients with MDD than in control subjects, and a significant correlation existed between DFA alpha-1 and BDI score in all subjects. DFA alpha-1 was the strongest predictor for the BDI score, along with REM density as a covariate. This study found that compared with controls, patients with MDD show reduced complexity in heart rate during REM sleep, which may represent lower cardiovascular adaptability in these patients, and could lead to cardiac disease. Moreover, DFA alpha-1 values measured during REM sleep may be useful as an indicator for the diagnosis and monitoring of depression.

Differences in nonlinear heart dynamics during rest and exercise and for different training

OBJECTIVE

In this work we want to analyze differences in nonlinear properties between rest and exercise and also to study the permanent effects of physical exercise on heart rate dynamics.

APPROACH

It has been shown that physical exercise alters heart dynamics by increasing heart rate and decreasing variability, modifying spectral power and linear correlations, etc. We hypothesize that physical exercise should also reduce nonlinearity in the heartbeat time series. To quantify nonlinearity in the heartbeat time series, we use an index of nonlinearity recently proposed by Bernaola et al based on correlations of the magnitude time series.

MAIN RESULTS

Our results confirm our initial hypothesis of loss of nonlinearity during physical exercise. Moreover, regarding the permanent effects of physical exercise on heart rate dynamics, we also obtain that aerobic physical training tends to increase nonlinearity in heart dynamics during rest.

SIGNIFICANCE

It is well-known that heart dynamics are controlled by complex interactions between the sympathetic and parasympathetic branches of the autonomic nervous system. Moreover, these two branches act in a competing way, resulting in a clear parasympathetic withdrawal and sympathetic activation during physical exercise. We associate these interactions during physical exercise with a drastic loss of nonlinear properties in the heartbeat time series, revealing the importance of nonlinearity measures in the study of complex systems.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

Predictability of arousal in mouse slow wave sleep by accelerometer data

Arousals can be roughly characterized by punctual intrusions of wakefulness into sleep. In a standard perspective, using human electroencephalography (EEG) data, arousals are associated to slow-wave rhythms and K-complex brain activity. The physiological mechanisms that give rise to arousals during sleep are not yet fully understood. Moreover, subtle body movement patterns, which may characterize arousals both in human and in animals, are usually not detectable by eye perception and are not in general present in sleep studies. In this paper, we focus attention on accelerometer records (AR) to characterize and predict arousal during slow wave sleep (SWS) stage of mice. Furthermore, we recorded the local field potentials (LFP) from the CA1 region in the hippocampus and paired with accelerometer data. The hippocampus signal was also used here to identify the SWS stage. We analyzed the AR dynamics of consecutive arousals using recurrence technique and the determinism (DET) quantifier. Recurrence is a fundamental property of dynamical systems, which can be exploited to characterize time series properties. The DET index evaluates how similar are the evolution of close trajectories: in this sense, it computes how accurate are predictions based on past trajectories. For all analyzed mice in this work, we observed, for the first time, the occurrence of a universal dynamic pattern a few seconds that precedes the arousals during SWS sleep stage based only on the AR signal. The predictability success of an arousal using DET from AR is nearly 90%, while similar analysis using LFP of hippocampus brain region reveal 88% of success. Noteworthy, our findings suggest an unique dynamical behavior pattern preceding an arousal of AR data during sleep. Thus, the employment of this technique applied to AR data may provide useful information about the dynamics of neuronal activities that control sleep-waking switch during SWS sleep period. We argue that the predictability of arousals observed through DET(AR) can be functionally explained by a respiratory-driven modification of neural states. Finally, we believe that the method associating AR data with other physiologic events such as neural rhythms can become an accurate, convenient and non-invasive way of studying the physiology and physiopathology of movement and respiratory processes during sleep.

Modeling heart rate variability including the effect of sleep stages

We propose a model for heart rate variability (HRV) of a healthy individual during sleep with the assumption that the heart rate variability is predominantly a random process. Autonomic nervous system activity has different properties during different sleep stages, and this affects many physiological systems including the cardiovascular system. Different properties of HRV can be observed during each particular sleep stage. We believe that taking into account the sleep architecture is crucial for modeling the human nighttime HRV. The stochastic model of HRV introduced by Kantelhardt et al. was used as the initial starting point. We studied the statistical properties of sleep in healthy adults, analyzing 30 polysomnographic recordings, which provided realistic information about sleep architecture. Next, we generated synthetic hypnograms and included them in the modeling of nighttime RR interval series. The results of standard HRV linear analysis and of nonlinear analysis (Shannon entropy, Poincaré plots, and multiscale multifractal analysis) show that-in comparison with real data-the HRV signals obtained from our model have very similar properties, in particular including the multifractal characteristics at different time scales. The model described in this paper is discussed in the context of normal sleep. However, its construction is such that it should allow to model heart rate variability in sleep disorders. This possibility is briefly discussed.

Network Physiology: How Organ Systems Dynamically Interact

We systematically study how diverse physiologic systems in the human organism dynamically interact and collectively behave to produce distinct physiologic states and functions. This is a fundamental question in the new interdisciplinary field of Network Physiology, and has not been previously explored. Introducing the novel concept of Time Delay Stability (TDS), we develop a computational approach to identify and quantify networks of physiologic interactions from long-term continuous, multi-channel physiological recordings. We also develop a physiologically-motivated visualization framework to map networks of dynamical organ interactions to graphical objects encoded with information about the coupling strength of network links quantified using the TDS measure. Applying a system-wide integrative approach, we identify distinct patterns in the network structure of organ interactions, as well as the frequency bands through which these interactions are mediated. We establish first maps representing physiologic organ network interactions and discover basic rules underlying the complex hierarchical reorganization in physiologic networks with transitions across physiologic states. Our findings demonstrate a direct association between network topology and physiologic function, and provide new insights into understanding how health and distinct physiologic states emerge from networked interactions among nonlinear multi-component complex systems. The presented here investigations are initial steps in building a first atlas of dynamic interactions among organ systems.

Fractal Analysis and Hurst Parameter for Intrapartum Fetal Heart Rate Variability Analysis: A Versatile Alternative to Frequency Bands and LF/HF Ratio

Background

The fetal heart rate (FHR) is commonly monitored during labor to detect early fetal acidosis. FHR variability is traditionally investigated using Fourier transform, often with adult predefined frequency band powers and the corresponding LF/HF ratio. However, fetal conditions differ from adults and modify spectrum repartition along frequencies.

Aims

This study questions the arbitrariness definition and relevance of the frequency band splitting procedure, and thus of the calculation of the underlying LF/HF ratio, as efficient tools for characterizing intrapartum FHR variability.

Study Design

The last 30 minutes before delivery of the intrapartum FHR were analyzed.

Subjects

Case-control study. A total of 45 singletons divided into two groups based on umbilical cord arterial pH: the Index group with pH ≤ 7.05 (n = 15) and Control group with pH > 7.05 (n = 30).

Outcome Measures

Frequency band-based LF/HF ratio and Hurst parameter.

Results

This study shows that the intrapartum FHR is characterized by fractal temporal dynamics and promotes the Hurst parameter as a potential marker of fetal acidosis. This parameter preserves the intuition of a power frequency balance, while avoiding the frequency band splitting procedure and thus the arbitrary choice of a frequency separating bands. The study also shows that extending the frequency range covered by the adult-based bands to higher and lower frequencies permits the Hurst parameter to achieve better performance for identifying fetal acidosis.

Conclusions

The Hurst parameter provides a robust and versatile tool for quantifying FHR variability, yields better acidosis detection performance compared to the LF/HF ratio, and avoids arbitrariness in spectral band splitting and definitions.

The quantification of the QT-RR interaction in ECG signal using the detrended fluctuationanalysis and ARARX modelling

In this paper, the detrended fluctuation analysis DFA is used to investigate and quantify the QT-RR interaction in different pathologic cases in order to distinguish between them. The study is carried out on the ECG signals of MIT-BIH universal database. Different ECG signals related to cardiac pathological cases are concerned with this study. These are: Premature Ventricular Contraction (PVC) (9 cases), Right Bundle Branch Block (RBBB) (4 cases), Left Bundle Branch Block (LBBB) (2 cases), Atrial Premature Beat (APB) (4 cases), Paced Beat (PB) (4 cases), and other pathologic cases with different severity (10 cases). All this cases are compared to the 15 normal cases. The obtained results show that the DFA can identify the healthy subject from the pathologic cases according to the values of the scaling exponent α. The results indicate that α varies between 0.5 and 1 in all cases which means that there is a long range correlation in RR and QT series. The QT and RR series are also modelled using the ARARX model. The parameters of the model are then extracted. The power spectral density (PSD) is estimated by using these parameters in order to provide further information about the causal interactions within the signals and also to determine the power scaling exponent β. This scaling exponent confirms the relationship between RR and QT intervals in all the studied cases except in APB and PB cases where the behaviour is similar to that of the white noise. The QT variability degrees are calculated and the DFA is applied on it. The obtained results show a long range correlation between RR and QT intervals in all cases and an ambiguity in the APB case. The DFA is compared to the Poincaré method in order to evaluate the algorithm performance using the Fuzzy Sugeno classifier is used for this purpose.

Segmentation of time series with long-range fractal correlations

Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome.

Adaptive multiscale complexity analysis of fetal heart rate

Per partum fetal asphyxia is a major cause of neonatal morbidity and mortality. Fetal heart rate monitoring plays an important role in early detection of acidosis, an indicator for asphyxia. This problem is addressed in this paper by introducing a novel complexity analysis of fetal heart rate data, based on producing a collection of piecewise linear approximations of varying dimensions from which a measure of complexity is extracted. This procedure specifically accounts for the highly non-stationary context of labor by being adaptive and multiscale. Using a reference dataset, made of real per partum fetal heart rate data, collected in situ and carefully constituted by obstetricians, the behavior of the proposed approach is analyzed and illustrated. Its performance is evaluated in terms of the rate of correct acidosis detection versus the rate of false detection, as well as how early the detection is made. Computational cost is also discussed. The results are shown to be extremely promising and further potential uses of the tool are discussed. MATLAB routines implementing the procedure will be made available at the time of publication.

Effect of significant data loss on identifying electric signals that precede rupture estimated by detrended fluctuation analysis in natural time

Electric field variations that appear before rupture have been recently studied by employing the detrended fluctuation analysis (DFA) to quantify their long-range temporal correlations. These studies revealed that seismic electric signal (SES) activities exhibit a scale invariant feature with an exponent αDFA≈1 over all scales investigated (around five orders of magnitude). Here, we study what happens upon significant data loss, which is a question of primary practical importance, and show that the DFA applied to the natural time representation of the remaining data still reveals for SES activities an exponent close to 1.0, which markedly exceeds the exponent found in artificial (man-made) noises. This enables the identification of a SES activity with probability of 75% even after a significant (70%) data loss. The probability increases to 90% or larger for 50% data loss.

Aging effects on cardiac and respiratory dynamics in healthy subjects across sleep stages

STUDY OBJECTIVES

Respiratory and heart rate variability exhibit fractal scaling behavior on certain time scales. We studied the short-term and long-term correlation properties of heartbeat and breathing-interval data from disease-free subjects focusing on the age-dependent fractal organization. We also studied differences across sleep stages and night-time wake and investigated quasi-periodic variations associated with cardiac risk.

DESIGN

Full-night polysomnograms were recorded during 2 nights, including electrocardiogram and oronasal airflow.

SETTING

Data were collected in 7 laboratories in 5 European countries.

PARTICIPANTS

180 subjects without health complaints (85 males, 95 females) aged from 20 to 89 years.

INTERVENTIONS

None.

MEASUREMENTS AND RESULTS

Short-term correlations in heartbeat intervals measured by the detrended fluctuation analysis (DFA) exponent alpha1 show characteristic age dependence with a maximum around 50-60 years disregarding the dependence on sleep and wake states. Long-term correlations measured by alpha2 differ in NREM sleep when compared with REM sleep and wake, besides weak age dependence. Results for respiratory intervals are similar to those for alpha2 of heartbeat intervals. Deceleration capacity (DC) decreases with age; it is lower during REM and deep sleep (compared with light sleep and wake).

CONCLUSION

The age dependence of alpha1 should be considered when using this value for diagnostic purposes in post-infarction patients. Pronounced long-term correlations (larger alpha2) for heartbeat and respiration during REM sleep and wake indicate an enhanced control of higher brain regions, which is absent during NREM sleep. Reduced DC possibly indicates an increased cardiovascular risk with aging and during REM and deep sleep.

Autonomic dysfunction and risk stratification assessed from heart rate pattern

The modulation of the autonomic nervous system (ANS) under physiological and pathophysiological conditions is in focus of recent research. Many patients with cardio- and cerebrovascular diseases display features of sympathovagal dysregulation. Measuring specific ANS parameters could improve risk stratification. Thus, the early diagnosis of ANS dysfunction in these patients poses a great challenge with high prognostic relevance.The most relevant methods and measures of Heart Rate Variability (HRV) analysis and HRV monitoring will be described in detail in this chapter. The grown importance of these easily obtainable heart rate patterns in stratifying the risk of patients with myocardial infarction and heart failure as well as ischemic stroke will be demonstrated based on recent clinical studies. In order to perspectively improve clinical management of these patients further large scale clinical investigations on the role of ANS dysfunction will be useful.

Effect of extreme data loss on long-range correlated and anticorrelated signals quantified by detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is an improved method of classical fluctuation analysis for nonstationary signals where embedded polynomial trends mask the intrinsic correlation properties of the fluctuations. To better identify the intrinsic correlation properties of real-world signals where a large amount of data is missing or removed due to artifacts, we investigate how extreme data loss affects the scaling behavior of long-range power-law correlated and anticorrelated signals. We introduce a segmentation approach to generate surrogate signals by randomly removing data segments from stationary signals with different types of long-range correlations. The surrogate signals we generate are characterized by four parameters: (i) the DFA scaling exponent alpha of the original correlated signal u(i) , (ii) the percentage p of the data removed from u(i) , (iii) the average length mu of the removed (or remaining) data segments, and (iv) the functional form P(l) of the distribution of the length l of the removed (or remaining) data segments. We find that the global scaling exponent of positively correlated signals remains practically unchanged even for extreme data loss of up to 90%. In contrast, the global scaling of anticorrelated signals changes to uncorrelated behavior even when a very small fraction of the data is lost. These observations are confirmed on two examples of real-world signals: human gait and commodity price fluctuations. We further systematically study the local scaling behavior of surrogate signals with missing data to reveal subtle deviations across scales. We find that for anticorrelated signals even 10% of data loss leads to significant monotonic deviations in the local scaling at large scales from the original anticorrelated to uncorrelated behavior. In contrast, positively correlated signals show no observable changes in the local scaling for up to 65% of data loss, while for larger percentage of data loss, the local scaling shows overestimated regions (with higher local exponent) at small scales, followed by underestimated regions (with lower local exponent) at large scales. Finally, we investigate how the scaling is affected by the average length, probability distribution, and percentage of the remaining data segments in comparison to the removed segments. We find that the average length mu_{r} of the remaining segments is the key parameter which determines the scales at which the local scaling exponent has a maximum deviation from its original value. Interestingly, the scales where the maximum deviation occurs follow a power-law relationship with mu_{r} . Whereas the percentage of data loss determines the extent of the deviation. The results presented in this paper are useful to correctly interpret the scaling properties obtained from signals with extreme data loss.

Methodology for multifractal analysis of heart rate variability: from LF/HF ratio to wavelet leaders

The present contribution aims at proposing a comprehensive and tutorial introduction to the practical use of wavelet Leader based multifractal analysis to study heart rate variability. First, the theoretical background is recalled. Second, practical issues and pitfalls related to the selection of the scaling range or statistical orders, minimal regularity, parabolic approximation of spectrum and parameter estimation, are discussed. Third, multifractal analysis is connected explicitly to other standard characterizations of heart rate variability: (mono)fractal analysis, Hurst exponent, spectral analysis and the HF/LF ratio. This review is illustrated on real per partum fetal ECG data, collected at an academic French public hospital, for both healthy fetuses and fetuses suffering from acidosis.