Characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments

Scaling of seismic memory with earthquake size

It has been observed that discrete earthquake events possess memory, i.e., that events occurring in a particular location are dependent on the history of that location. We conduct an analysis to see whether continuous real-time data also display a similar memory and, if so, whether such autocorrelations depend on the size of earthquakes within close spatiotemporal proximity. We analyze the seismic wave form database recorded by 64 stations in Japan, including the 2011 "Great East Japan Earthquake," one of the five most powerful earthquakes ever recorded, which resulted in a tsunami and devastating nuclear accidents. We explore the question of seismic memory through use of mean conditional intervals and detrended fluctuation analysis (DFA). We find that the wave form sign series show power-law anticorrelations while the interval series show power-law correlations. We find size dependence in earthquake autocorrelations: as the earthquake size increases, both of these correlation behaviors strengthen. We also find that the DFA scaling exponent α has no dependence on the earthquake hypocenter depth or epicentral distance.

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.

Asymmetric properties of long-term and total heart rate variability

We report on two new physiological phenomena: the long-term and total heart rate asymmetry, which describe a significantly larger contribution of heart rate accelerations to long-term and total heart rate variability. In addition to the existing pair of indices, SD1(d); SD1(a); which are based on partitioning short-term variance, we introduce two other pairs of descriptors based on partitioning longterm (SD2(d); SD2(a)) and total (SDNN(d); SDNN(a)) heart rate variability. The new asymmetric descriptors are used to analyze RR intervals time series derived from the 30-min ECG recordings of 241 healthy subjects resting in supine position. It is shown that both new types of asymmetry are present in 76% of the subjects. The new phenomena reported here are real physiological findings rather than artifacts of the method since they vanish after data shuffling.

Distribution of natural trends in long-term correlated records: a scaling approach

We estimate the exceedance probability W(x,α;L) that, in a long-term correlated Gaussian-distributed (sub) record of length L characterized by a fluctuation exponent α between 0.5 and 1.5, a relative increase Δ/σ(t) of size larger than x occurs, where Δ is the total observed increase measured by linear regression and σ(t) is the standard deviation around the regression line. We consider L between 500 and 2000, which is the typical length scale of monthly local and reconstructed annual global temperature records. We use scaling theory to obtain an analytical expression for W(x,α;L). From this expression, we can determine analytically, for a given confidence probability Q, the boundaries ±x(Q)(α,L) of the confidence interval. In the presence of an external linear trend, the total observed increase is the sum of the natural and the external increase. An observed relative increase Δ/σ(t) is considered unnatural when it is above x(Q)(α,L). In this case, the size of the external relative increase is bounded by Δ/σ(t)±x(Q)(α,L). We apply this approach to various global and local climate data and discuss the different results for the significance of the observed trends.

Quantifying and modeling long-range cross correlations in multiple time series with applications to world stock indices

We propose a modified time lag random matrix theory in order to study time-lag cross correlations in multiple time series. We apply the method to 48 world indices, one for each of 48 different countries. We find long-range power-law cross correlations in the absolute values of returns that quantify risk, and find that they decay much more slowly than cross correlations between the returns. The magnitude of the cross correlations constitutes "bad news" for international investment managers who may believe that risk is reduced by diversifying across countries. We find that when a market shock is transmitted around the world, the risk decays very slowly. We explain these time-lag cross correlations by introducing a global factor model (GFM) in which all index returns fluctuate in response to a single global factor. For each pair of individual time series of returns, the cross correlations between returns (or magnitudes) can be modeled with the autocorrelations of the global factor returns (or magnitudes). We estimate the global factor using principal component analysis, which minimizes the variance of the residuals after removing the global trend. Using random matrix theory, a significant fraction of the world index cross correlations can be explained by the global factor, which supports the utility of the GFM. We demonstrate applications of the GFM in forecasting risks at the world level, and in finding uncorrelated individual indices. We find ten indices that are practically uncorrelated with the global factor and with the remainder of the world indices, which is relevant information for world managers in reducing their portfolio risk. Finally, we argue that this general method can be applied to a wide range of phenomena in which time series are measured, ranging from seismology and physiology to atmospheric geophysics.

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.

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.

Stratification pattern of static and scale-invariant dynamic measures of heartbeat fluctuations across sleep stages in young and elderly

Cardiac dynamics exhibit complex variability characterized by scale-invariant and nonlinear temporal organization related to the mechanism of neuroautonomic control, which changes with physiologic states and pathologic conditions. Changes in sleep regulation during sleep stages are also related to fluctuations in autonomic nervous activity. However, the interaction between sleep regulation and cardiac autonomic control remains not well understood. Even less is known how this interaction changes with age, as aspects of both cardiac dynamics and sleep regulation differ in healthy elderly compared to young subjects. We hypothesize that because of the neuroautonomic responsiveness in young subjects, fractal and nonlinear features of cardiac dynamics exhibit a pronounced stratification pattern across sleep stages, while in elderly these features will remain unchanged due to age-related loss of cardiac variability and decline of neuroautonomic responsiveness. We analyze the variability and the temporal fractal organization of heartbeat fluctuations across sleep stages in both young and elderly. We find that independent linear and nonlinear measures of cardiac control consistently exhibit the same ordering in their values across sleep stages, forming a robust stratification pattern. Despite changes in sleep architecture and reduced heart rate variability in elderly subjects, this stratification surprisingly does not break down with advanced age. Moreover, the difference between sleep stages for some linear, fractal, and nonlinear measures exceeds the difference between young and elderly, suggesting that the effect of sleep regulation on cardiac dynamics is significantly stronger than the effect of healthy aging. Quantifying changes in this stratification pattern may provide insights into how alterations in sleep regulation contribute to increased cardiac risk.

Levels of complexity in scale-invariant neural signals

Many physical and physiological signals exhibit complex scale-invariant features characterized by 1/f scaling and long-range power-law correlations, indicating a possibly common control mechanism. Specifically, it has been suggested that dynamical processes, influenced by inputs and feedback on multiple time scales, may be sufficient to give rise to 1/f scaling and scale invariance. Two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait. Here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable 1/f scaling, they still may belong to different complexity classes. Our analysis of the multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast to the multifractal behavior found in healthy heartbeat dynamics, gait time series exhibit less complex, close to monofractal behavior. Further, we find strong anticorrelations in the sign and close to random behavior for the magnitude of gait fluctuations at short and intermediate time scales, in contrast to weak anticorrelations in the sign and strong positive correlation for the magnitude of heartbeat interval fluctuations-suggesting that the neural mechanisms of cardiac and gait control exhibit different linear and nonlinear features. These findings are of interest because they underscore the limitations of traditional two-point correlation methods in fully characterizing physiological and physical dynamics. In addition, these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar 1/f scaling.

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

We review recent attempts to understand the influence of sleep and wake states, sleep-stage transitions during sleep and the endogenous circadian rhythms on the neuroautonomic regulation of cardiac dynamics as represented by the scale-invariant organization of heartbeat fluctuations. We find that the probability distribution, the long-range temporal correlations as well as the nonlinear properties of the heartbeat fluctuations are significantly altered with transition from sleep to wake state, across sleep-stages and circadian phases. These sleep and circadian mediated changes in cardiac dynamics occur simultaneously over a broad range of time scales, suggesting a more complex then previously known interaction between the neural systems of sleep and circadian regulation with the neuroautonomic cardiac control, beyond rhythmic modulation at a characteristic time scale.

Endogenous circadian rhythm in human motor activity uncoupled from circadian influences on cardiac dynamics

The endogenous circadian pacemaker influences key physiologic functions, such as body temperature and heart rate, and is normally synchronized with the sleep/wake cycle. Epidemiological studies demonstrate a 24-h pattern in adverse cardiovascular events with a peak at approximately 10 a.m. It is unknown whether this pattern in cardiac risk is caused by a day/night pattern of behaviors, including activity level and/or influences from the internal circadian pacemaker. We recently found that a scaling index of cardiac vulnerability has an endogenous circadian peak at the circadian phase corresponding to approximately 10 a.m., which conceivably could contribute to the morning peak in cardiac risk. Here, we test whether this endogenous circadian influence on cardiac dynamics is caused by circadian-mediated changes in motor activity or whether activity and heart rate dynamics are decoupled across the circadian cycle. We analyze high-frequency recordings of motion from young healthy subjects during two complementary protocols that decouple the sleep/wake cycle from the circadian cycle while controlling scheduled behaviors. We find that static activity properties (mean and standard deviation) exhibit significant circadian rhythms with a peak at the circadian phase corresponding to 5-9 p.m. ( approximately 9 h later than the peak in the scale-invariant index of heartbeat fluctuations). In contrast, dynamic characteristics of the temporal scale-invariant organization of activity fluctuations (long-range correlations) do not exhibit a circadian rhythm. These findings suggest that endogenous circadian-mediated activity variations are not responsible for the endogenous circadian rhythm in the scale-invariant structure of heartbeat fluctuations and likely do not contribute to the increase in cardiac risk at approximately 10 a.m.

Scaling analysis of paces of fetal breathing, gross-body and extremity movements

Using detrended fluctuation analysis (DFA), we studied the scaling properties of the time instances (occurrence) of the fetal breathing, gross-body, and extremity movements scored on a second by second basis from the recorded ultrasound measurements of 49 fetuses. The DFA exponent α of all the three movements of the fetuses varied between 0.63 and 1.1. We found an increase in α obtained for the movement due to breathing as a function of the gestational age while this trend was not observed for gross-body and extremity movements. This trend was argued as the indication of the maturation of lung and functional development of respiratory aspect of the fetal central nervous system. This result may be useful in discriminating normal fetuses from high-risk fetuses.

Fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age: a new mechanistic picture of cardiac control in healthy elderly

Heart beat fluctuations exhibit temporal structure with robust long-range correlations, fractal and nonlinear features, which have been found to break down with pathologic conditions, reflecting changes in the mechanism of neuroautonomic control. It has been hypothesized that these features change and even break down also with advanced age, suggesting fundamental alterations in cardiac control with aging. Here we test this hypothesis. We analyze heart beat interval recordings from the following two independent databases: 1) 19 healthy young (average age 25.7 yr) and 16 healthy elderly subjects (average age 73.8 yr) during 2 h under resting conditions from the Fantasia database; and 2) 29 healthy elderly subjects (average age 75.9 yr) during approximately 8 h of sleep from the sleep heart health study (SHHS) database, and the same subjects recorded 5 yr later. We quantify: 1) the average heart rate (<R-R>); 2) the SD sigma(R-R) and sigma(DeltaR-R) of the heart beat intervals R-R and their increments DeltaR-R; 3) the long-range correlations in R-R as measured by the scaling exponent alpha(R-R) using the Detrended Fluctuation Analysis; 4) fractal linear and nonlinear properties as represented by the scaling exponents alpha(sgn) and alpha(mag) for the time series of the sign and magnitude of DeltaR-R; and 5) the nonlinear fractal dimension D(k) of R-R using the fractal dimension analysis. We find: 1) No significant difference in (P > 0.05); 2) a significant difference in sigma(R-R) and sigma(DeltaR-R) for the Fantasia groups (P < 10(-4)) but no significant change with age between the elderly SHHS groups (P > 0.5); and 3) no significant change in the fractal measures alpha(R-R) (P > 0.15), alpha(sgn) (P > 0.2), alpha(mag) (P > 0.3), and D(k) with age. Our findings do not support the hypothesis that fractal linear and nonlinear characteristics of heart beat dynamics break down with advanced age in healthy subjects. Although our results indeed show a reduced SD of heart beat fluctuations with advanced age, the inherent temporal fractal and nonlinear organization of these fluctuations remains stable. This indicates that the coupled cascade of nonlinear feedback loops, which are believed to underlie cardiac neuroautonomic regulation, remains intact with advanced age.

Temporally resolved fluctuation analysis of sleep ECG

The correlation behavior in the heart beat rate significantly differs with respect to light sleep, deep sleep, and REM sleep. We investigate whether fluctuations of the heart beat rhythm may serve as a surrogate parameter for rapidly changing sleep phenomena, and if these changes are accessible by progressive beat-by-beat analysis of the sleep electrocardiogram (ECG).

Cardiovascular and respiratory dynamics during normal and pathological sleep

Sleep is an active and regulated process with restorative functions for physical and mental conditions. Based on recordings of brain waves and the analysis of characteristic patterns and waveforms it is possible to distinguish wakefulness and five sleep stages. Sleep and the sleep stages modulate autonomous nervous system functions such as body temperature, respiration, blood pressure, and heart rate. These functions consist of a sympathetic tone usually related to activation and to parasympathetic (or vagal) tone usually related to inhibition. Methods of statistical physics are used to analyze heart rate and respiration to detect changes of the autonomous nervous system during sleep. Detrended fluctuation analysis and synchronization analysis and their applications to heart rate and respiration during sleep in healthy subjects and patients with sleep disorders are presented. The observed changes can be used to distinguish sleep stages in healthy subjects as well as to differentiate normal and disturbed sleep on the basis of heart rate and respiration recordings without direct recording of brain waves. Of special interest are the cardiovascular consequences of disturbed sleep because they present a risk factor for cardiovascular disorders such as arterial hypertension, cardiac ischemia, sudden cardiac death, and stroke. New derived variables can help to find indicators for these health risks.

Sleep-wake identification in infants: heart rate variability compared to actigraphy

Heart rate variability and actigraphy offer alternative techniques for sleep-wake identification compared to manual sleep scoring from a polysomnograph. The advantages include high accuracy, simplicity of use, and low intrusiveness. These advantages are valuable for determining sleep-wake states in such highly sensitive groups as infants. A learning vector quantization neural network was tested as a predictor. The accuracy of the neural network was compared to "gold standard" hand-scored polysomnographs. The prediction results are in agreement with other studies, thus validating the suggested methodology.

Experimental evidence for phase synchronization transitions in the human cardiorespiratory system

Transitions in the dynamics of complex systems can be characterized by changes in the synchronization behavior of their components. Taking the human cardiorespiratory system as an example and using an automated procedure for screening the synchrograms of 112 healthy subjects we study the frequency and the distribution of synchronization episodes under different physiological conditions that occur during sleep. We find that phase synchronization between heartbeat and breathing is significantly enhanced during non-rapid-eye-movement (non-REM) sleep (deep sleep and light sleep) and reduced during REM sleep. Our results suggest that the synchronization is mainly due to a weak influence of the breathing oscillator upon the heartbeat oscillator, which is disturbed in the presence of long-term correlated noise, superimposed by the activity of higher brain regions during REM sleep.

Two statistical methods for resolving healthy individuals and those with congestive heart failure based on extended self-similarity and a recursive method

In this paper we introduce two methods for measuring irregularities in human heartbeat time series (HHTS). First we consider the multi-fractal structure of HHTS to distinguish healthy individuals and from those with congestive heart failure. In this way we modify the Extended Self-Similarity (ESS) method and apply it to HHTS. Our second approach is based on the recursive method, which we use to predict the duration of the next heartbeat by considering a few previous ones. We use standard physiological data and show that these approaches lead to very satisfactory methods to resolve the healthy and CHF individuals. These methods can be used potentially in portable electronic heart alarm systems.

Cross-correlation of instantaneous phase increments in pressure-flow fluctuations: applications to cerebral autoregulation

We investigate the relationship between the blood flow velocities (BFV) in the middle cerebral arteries and beat-to-beat blood pressure (BP) recorded from a finger in healthy and post-stroke subjects during the quasisteady state after perturbation for four different physiologic conditions: supine rest, head-up tilt, hyperventilation, and CO2 rebreathing in upright position. To evaluate whether instantaneous BP changes in the steady state are coupled with instantaneous changes in the BFV, we compare dynamical patterns in the instantaneous phases of these signals, obtained from the Hilbert transform, as a function of time. We find that in post-stroke subjects the instantaneous phase increments of BP and BFV exhibit well-pronounced patterns that remain stable in time for all four physiologic conditions, while in healthy subjects these patterns are different, less pronounced, and more variable. We propose an approach based on the cross-correlation of the instantaneous phase increments to quantify the coupling between BP and BFV signals. We find that the maximum correlation strength is different for the two groups and for the different conditions. For healthy subjects the amplitude of the cross-correlation between the instantaneous phase increments of BP and BFV is small and attenuates within 3-5 heartbeats. In contrast, for post-stroke subjects, this amplitude is significantly larger and cross-correlations persist up to 20 heartbeats. Further, we show that the instantaneous phase increments of BP and BFV are cross-correlated even within a single heartbeat cycle. We compare the results of our approach with three complementary methods: direct BP-BFV cross-correlation, transfer function analysis, and phase synchronization analysis. Our findings provide insight into the mechanism of cerebral vascular control in healthy subjects, suggesting that this control mechanism may involve rapid adjustments (within a heartbeat) of the cerebral vessels, so that BFV remains steady in response to changes in peripheral BP.

Fractionally integrated process with power-law correlations in variables and magnitudes

Motivated by the fact that many empirical time series--including changes of heartbeat intervals, physical activity levels, intertrade times in finance, and river flux values--exhibit power-law anticorrelations in the variables and power-law correlations in their magnitudes, we propose a simple stochastic process that can account for both types of correlations. The process depends on only two parameters, where one controls the correlations in the variables and the other controls the correlations in their magnitudes. We apply the process to time series of heartbeat interval changes and air temperature changes and find that the statistical properties of the modeled time series are in agreement with those observed in the data.

Quantifying signals with power-law correlations: a comparative study of detrended fluctuation analysis and detrended moving average techniques

Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals. We systematically study the performance of different variants of the DMA method when applied to artificially generated long-range power-law correlated signals with an a priori known scaling exponent alpha(0) and compare them with the DFA method. We find that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter. Further, we investigate the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent alpha(0) , and how this regime depends on the correlations in the signal. Finally, we develop a three-dimensional representation to determine how the stability of the scaling curves obtained from the DFA and DMA methods depends on the scale of analysis, the order of detrending, and the order of the moving average we use, as well as on the type of correlations in the signal.

Long-range temporal correlations in electroencephalographic oscillations: Relation to topography, frequency band, age and gender

Presence of long-range temporal correlations in neuronal oscillations is thought to be beneficial for a reliable transfer of information in neuronal networks. In the present study long-range temporal correlations in electroencephalographic (EEG) neuronal oscillations were characterized with respect to their topography, frequency-band specificity (alpha and beta oscillations), gender and age. EEG was recorded in 91 normal subjects (age 20-65 years) in a resting condition. The amplitude of ongoing alpha and beta oscillations was extracted with band-pass filtering and Hilbert transform, and long-range temporal correlations were analyzed with detrended fluctuation analysis. The topography of long-range temporal correlations was comparable for alpha and beta oscillations, showing largest scaling exponents in the occipital and parietal areas. This topography was partially similar to that of the power distribution and a weak positive correlation was observed between long-range temporal correlations and power of neuronal oscillations. Long-range temporal correlations were stronger in alpha than beta oscillations, but only in a few electrode locations in the left hemisphere. In both frequency bands long-range temporal correlations were stronger in males than in females and were largely unaffected by the age of the subjects. It is hypothesized that the idling state of the occipital areas in the closed-eyes condition may explain both large power values and pronounced long-range temporal correlations in this region.

Effect of nonlinear filters on detrended fluctuation analysis

When investigating the dynamical properties of complex multiple-component physical and physiological systems, it is often the case that the measurable system's output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms. Instead, the output signal is often a linear or nonlinear function of the quantity of interest. Here, we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal, using the detrended fluctuation analysis (DFA) which has been shown to accurately quantify power-law correlations in nonstationary signals. Specifically, we study the effect of three types of transforms: (i) linear ( y(i) =a x(i) +b) , (ii) nonlinear polynomial ( y(i) =a x(k)(i) ) , and (iii) nonlinear logarithmic [ y(i) =log ( x(i) +Delta) ] filters. We compare the correlation and scaling properties of signals before and after the transform. We find that linear filters do not change the correlation properties, while the effect of nonlinear polynomial and logarithmic filters strongly depends on (a) the strength of correlations in the original signal, (b) the power k of the polynomial filter, and (c) the offset Delta in the logarithmic filter. We further apply the DFA method to investigate the "apparent" scaling of three analytic functions: (i) exponential [exp (+/-x+a) ] , (ii) logarithmic [log (x+a) ] , and (iii) power law [ (x+a)(lambda) ] , which are often encountered as trends in physical and biological processes. While these three functions have different characteristics, we find that there is a broad range of values for parameter a common for all three functions, where the slope of the DFA curves is identical. We further note that the DFA results obtained for a class of other analytic functions can be reduced to these three typical cases. We systematically test the performance of the DFA method when estimating long-range power-law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider.

Endogenous circadian rhythm in an index of cardiac vulnerability independent of changes in behavior

There exists a robust day/night pattern in the incidence of adverse cardiac events with a peak at approximately 10 a.m. This peak traditionally has been attributed to day/night patterns in behaviors affecting cardiac function in vulnerable individuals. However, influences from the endogenous circadian pacemaker independent from behaviors may also affect cardiac control. Heartbeat dynamics under healthy conditions exhibit robust complex fluctuations characterized by self-similar temporal structures, which break down under pathologic conditions. We hypothesize that these dynamical features of the healthy human heartbeat have an endogenous circadian rhythm that brings the features closer to those observed under pathologic conditions at the endogenous circadian phase corresponding to approximately 10 a.m. We investigate heartbeat dynamics in healthy subjects recorded throughout a 10-day protocol wherein the sleep/wake and behavior cycles are desynchronized from the endogenous circadian cycle, enabling assessment of circadian factors while controlling for behavior-related factors. We demonstrate that the scaling exponent characterizing temporal correlations in heartbeat dynamics does exhibit a significant circadian rhythm (with a sharp peak at the circadian phase corresponding to approximately 10 a.m.), which is independent from scheduled behaviors and mean heart rate. Cardiac dynamics under pathologic conditions such as congestive heart failure also are associated with a larger value of the scaling exponent of the interbeat interval. Thus, the sharp peak in the scaling exponent at the circadian phase coinciding with the period of highest cardiac vulnerability observed in epidemiological studies suggests that endogenous circadian-mediated influences on cardiac control may be involved in the day/night pattern of adverse cardiac events in vulnerable individuals.

Nonlinear volatility of river flux fluctuations

We study the spectral properties of the magnitudes of daily river flux increments, the volatility. The volatility series exhibits (i) strong seasonal periodicity and (ii) power-law correlations for time scales less than 1 yr. We test the nonlinear properties of the river flux increment series by randomizing its Fourier phases and find that the surrogate volatility series (i) has almost no seasonal periodicity and (ii) is weakly correlated for time scales less than 1 yr. We quantify the degree of nonlinearity by measuring (i) the amplitude of the power spectrum at the seasonal peak and (ii) the correlation power-law exponent of the volatility series.

Comparison of two different approaches in the detection of intermittent cardiorespiratory coordination during night sleep

BACKGROUND

The objective was to evaluate and to compare two completely different detection algorithms of intermittent (short-term) cardiorespiratory coordination during night sleep. The first method is based on a combination of respiratory flow and electrocardiogram recordings and determines the relative phases of R waves between successive onsets of inspiration. Intermittent phase coordination is defined as phase recurrence with accuracy alpha over at least k heartbeats. The second, recently introduced method utilizes only binary coded variations of heart rate (acceleration = 1, deceleration = 0) and identifies binary pattern classes which can be assigned to respiratory sinus arrhythmia (RSA). It is hypothesized that RSA pattern class recurrence over at least k heartbeats is strongly related with the intermittent phase coordination defined above.

RESULTS

Both methods were applied to night time recordings of 20 healthy subjects. In subjects <45 yrs and setting k = 3 and alpha = 0.03, the phase and RSA pattern recurrence were highly correlated. Furthermore, in most subjects the pattern predominance (PP) showed a pronounced oscillation which is most likely linked with the dynamics of sleep stages. However, the analysis of bivariate variation and the use of surrogate data suggest that short-term phase coordination mainly resulted from central adjustment of heart rate and respiratory rate rather than from real phase synchronization due to physiological interaction.

CONCLUSION

Binary pattern analysis provides essential information on short-term phase recurrence and reflects nighttime sleep architecture, but is only weakly linked with true phase synchronization which is rare in physiological processes of man.