Correlated and uncorrelated regions in heart-rate fluctuations during sleep

Cardiovascular and respiratory dynamics in patients with sleep apnea

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. 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.

Extensive studies on linear growth processes with spatiotemporally correlated noise in arbitrary substrate dimensions

An extensive analytical and numerical study on a class of growth processes with spatiotemporally correlated noise in arbitrary dimension is undertaken. In addition to the conventional investigation on the interface morphology and interfacial widths, we pay special attention to exploring the characteristics of the slope-slope correlation function S(r,t) and the [Q]-th degree residual local interfacial width w[Q](l,t), whose importance has been somewhat overlooked in the literature. Based on the above analysis, we give a plausible theoretical explanation about the various experimental observations of kinetically and thermodynamically unstable surface growth. Furthermore, through explicit examples, we show that the statistical methods of calculating the exponents (including the dynamic exponent z, the global roughness exponent α, and the local roughness exponent α(loc)), based on the scaling of S(r,t) and w[Q](l,t), are very reliable and rarely influenced by the finite time and/or finite-size effects. Another important issue we focus on in this paper is related to numerical calculation. For the specific class of growth processes discussed in this paper, we develop a very efficient and accurate algorithm for numerical calculation of the dynamics of interface configuration, the structure factor, the various correlation functions, the interfacial width and its variants in arbitrary dimensions, even with very large system size and very late time. The proposed systematical algorithm can be easily generalized to other linear processes and some special nonlinear processes.

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.

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

The influence from the central nervous system on the human multifractal heart rate variability (HRV) is examined under the autonomic nervous system perturbation induced by the head-up-tilt body maneuver. We conducted the multifractal factorization analysis to factor out the common multifractal factor in the joint fluctuation of the beat-to-beat heart rate and electroencephalography data. Evidence of a central link in the multifractal HRV was found, where the transition towards increased (decreased) HRV multifractal complexity is associated with a stronger (weaker) multifractal correlation between the central and autonomic nervous systems.

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.

Singular behavior of slow dynamics of single excitable cells

In various kinds of cultured cells, it has been reported that the membrane potential exhibits fluctuations with long-term correlations, although the underlying mechanism remains to be elucidated. A cardiac muscle cell culture serves as an excellent experimental system to investigate this phenomenon because timings of excitations can be determined over an extended time period in a noninvasive manner through visualization of contractions, although the properties of beat-timing fluctuations of cardiac muscle cells at the single-cell level remains to be fully clarified. In this article, we report on our investigation of spontaneous contractions of cultured rat cardiac muscle cells at the single-cell level. It was found that single cells exhibit several typical temporal patterns of contractions and spontaneous transitions among them. Detrended fluctuation analysis on the time series of interbeat intervals revealed the presence of 1/f(beta) noise at sufficiently large timescales. Furthermore, multifractality was also found in the time series of interbeat intervals. These experimental trends were successfully explained using a simple mathematical model, incorporating correlated noise into ionic currents. From these findings, it was established that singular fluctuations accompanying 1/f(beta) noise and multifractality are intrinsic properties of single cardiac muscle cells.

Detecting specific health-related events using an integrated sensor system for vital sign monitoring

In this paper, a new method for the detection of apnea/hypopnea periods in physiological data is presented. The method is based on the intelligent combination of an integrated sensor system for long-time cardiorespiratory signal monitoring and dedicated signal-processing packages. Integrated sensors are a PVDF film and conductive fabric sheets. The signal processing package includes dedicated respiratory cycle (RC) and QRS complex detection algorithms and a new method using the respiratory cycle variability (RCV) for detecting apnea/hypopnea periods in physiological data. Results show that our method is suitable for online analysis of long time series data.

Analysis of blood pressure-heart rate feedback regulation under non-stationary conditions: beyond baroreflex sensitivity

The feedback regulation of blood pressure and heart rate is an important indicator of human autonomic function usually assessed by baroreflex sensitivity (BRS). We suggest a new method yielding a higher temporal resolution than standard BRS methods. Our approach is based on a regression analysis of the first differences of inter-heartbeat intervals and blood pressure values. Data are recorded from 23 patients with hypertension and sleep apnoea, 22 patients with diabetes mellitus and 23 healthy subjects. Using the proposed method for 3 min data segments, we obtain average regression coefficients of 9.1 and 3.5 ms mmHg(-1) for healthy subjects in supine and orthostatic positions, respectively. In patients with hypertension, we find them to be 3.8 and 2.6 ms mmHg(-1). The diabetes patients with and without autonomic neuropathy are characterized by 3.1 and 6.1 ms mmHg(-1) in the supine position compared with 1.7 and 3.3 ms mmHg(-1) in the orthostatic position. The results are highly correlated with conventional BRS measures; we find r > 0.9 for the dual sequence method. Therefore, we suggest that the new method can quantify BRS. It is superior in distinguishing healthy subjects from patients both in supine and orthostatic positions for short-term recordings. It is suitable for non-stationary data and has good reproducibility. Besides, we cannot exclude that other regulatory mechanisms than BRS may also contribute to the regression coefficients between the first differences.

Eliminating finite-size effects and detecting the amount of white noise in short records with long-term memory

Long-term memory is ubiquitous in nature and has important consequences for the occurrence of natural hazards, but its detection often is complicated by the short length of the considered records and additive white noise in the data. Here we study synthetic Gaussian distributed records x_{i} of length N that consist of a long-term correlated component (1-a)y_{i} characterized by a correlation exponent gamma , 0<gamma<1 , and a white-noise component aeta_{i} , 0< or =a< or =1 . We show that the autocorrelation function C_{N}(s) has the general form C_{N}(s)=[C_{infinity}(s)-E_{a}]/(1-E_{a}) , where C_{infinity}(0)=1 , C_{infinity}(s>0)=B_{a}s;{-gamma} , and E_{a}={2B_{a}/[(2-gamma)(1-gamma)]}N;{-gamma}+O(N;{-1}) . The finite-size parameter E_{a} also occurs in related quantities, for example, in the variance Delta_{N};{2}(s) of the local mean in time windows of length s : Delta_{N};{2}(s)=[Delta_{infinity};{2}(s)-E_{a}]/(1-E_{a}) . For purely long-term correlated data B_{0} congruent with(2-gamma)(1-gamma)/2 yielding E_{0} congruent withN;{-gamma} , and thus C_{N}(s)=[(2-gamma)(1-gamma)/2s;{-gamma}-N;{-gamma}]/[1-N;{-gamma}] and Delta_{N};{2}(s)=[s;{-gamma}-N;{-gamma}]/[1-N;{-gamma}] . We show how to estimate E_{a} and C_{infinity}(s) from a given data set and thus how to obtain accurately the exponent gamma and the amount of white noise a .

Statistical analysis of the overnight and daytime return

We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open), and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 New York Stock Exchange stocks for the 20 year period from 1988 to 2007. The tail distribution of the volatility, the long-term memory in the sequence, and the cross correlation between different returns are analyzed. Our results suggest that (i) the two component returns and volatilities have features similar to that of the total return and volatility. The tail distribution follows a power law for all volatilities, and long-term correlations exist in the volatility sequences but not in the return sequences. (ii) The daytime return contributes more to the total return. Both the tail distribution and the long-term memory of the daytime volatility are more similar to that of the total volatility, compared to the overnight records. In addition, the cross correlation between the daytime return and the total return is also stronger. (iii) The two component returns tend to be anticorrelated. Moreover, we find that the cross correlations between the three different returns (total, overnight, and daytime) are quite stable over the entire 20 year period.

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.

Cross-modulated amplitudes and frequencies characterize interacting components in complex systems

The dynamics of complex systems is characterized by oscillatory components on many time scales. To study the interactions between these components we analyze the cross modulation of their instantaneous amplitudes and frequencies, separating synchronous and antisynchronous modulation. We apply our novel technique to brain-wave oscillations in the human electroencephalogram and show that interactions between the alpha wave and the delta or beta wave oscillators as well as spatial interactions can be quantified and related with physiological conditions (e.g., sleep stages). Our approach overcomes the limitation to oscillations with similar frequencies and enables us to quantify directly nonlinear effects such as positive or negative frequency modulation.

Automated synchrogram analysis applied to heartbeat and reconstructed respiration

Phase synchronization between two weakly coupled oscillators has been studied in chaotic systems for a long time. However, it is difficult to unambiguously detect such synchronization in experimental data from complex physiological systems. In this paper we review our study of phase synchronization between heartbeat and respiration in 150 healthy subjects during sleep using an automated procedure for screening the synchrograms. We found that this synchronization is significantly enhanced during non-rapid-eye-movement (non-REM) sleep (deep sleep and light sleep) and is reduced during REM sleep. In addition, we show that the respiration signal can be reconstructed from the heartbeat recordings in many subjects. Our reconstruction procedure, which works particularly well during non-REM sleep, allows the detection of cardiorespiratory synchronization even if only heartbeat intervals were recorded.

Theoretical basis for identification of different anesthetic states based on routinely recorded EEG during operation

In this paper, we present a new method to identify anesthetic states based on routinely recorded electroencephalogram (EEG). The identification of anesthesia stages are conducted using fast Fourier transform (FFT) and modified detrended fluctuation analysis (DFA) method. Simulation results demonstrate that this new method can clearly discriminate all five anesthesia states: very deep anesthesia, deep anesthesia, moderate anesthesia, light anesthesia and awake.

Comparison of wavelet transform modulus maxima and multifractal detrended fluctuation analysis of heart rate in patients with systolic dysfunction of left ventricle

BACKGROUND

In recent years the WTMM (wavelet transform modulus maxima) and MDFA (multifractal detrended fluctuation analysis) methods have become widely used techniques for the determination of nonlinear, multifractal heart rate (HR) dynamics. The purpose of our study was to compare multifractal parameters of heart rate calculated using both methods in a group of 90 patients with reduced left ventricular systolic function (rlvs group) and in a group of 39 healthy persons (nsr group).

METHODS

For each subject from the rlvs group (LVEF < or =40%) and the nsr group, a 24-hour ECG Holter monitoring was performed. The width of the multifractal spectrum and global Hurst exponent were calculated by means of WTMM and MDFA methods for 5-hour daytime and nighttime subsets.

RESULTS

The width of the multifractal spectrum was significantly lower and the Hurst exponent was significantly higher in rlvs group in comparison to nsr group both during diurnal activity and nocturnal rest according to MDFA and only during diurnal activity according to WTMM method. In both groups we observed significant differences of the multifractal spectrum width and the global Hurst exponent between the nighttime and daytime recordings.

CONCLUSIONS

MDFA seems to be more sensitive as compared with WTMM method in differentiation between multifractal properties of the heart rate in healthy subjects and patients with left ventricular systolic dysfunction.

Efficient scheme for parametric fitting of data in arbitrary dimensions

We propose an efficient scheme for parametric fitting expressed in terms of the Legendre polynomials. For continuous systems, our scheme is exact and the derived explicit expression is very helpful for further analytical studies. For discrete systems, our scheme is almost as accurate as the method of singular value decomposition. Through a few numerical examples, we show that our algorithm costs much less CPU time and memory space than the method of singular value decomposition. Thus, our algorithm is very suitable for a large amount of data fitting. In addition, the proposed scheme can also be used to extract the global structure of fluctuating systems. We then derive the exact relation between the correlation function and the detrended variance function of fluctuating systems in arbitrary dimensions and give a general scaling analysis.

Human heart beat analysis using a modified algorithm of detrended fluctuation analysis based on empirical mode decomposition

How to quantify the complexity of a physiological signal is a crucial issue for verifying the underlying mechanism of a physiological system. The original algorithm of detrended fluctuation analysis (DFA) quantifies the complexity of signals using the DFA scaling exponent. However, the DFA scaling exponent is suitable only for an integrated time series but not the original signal. Moreover, the method of least squares line is a simple detrending operation. Thus, the analysis results of the original DFA are not sufficient to verify the underlying mechanism of physiological signals. In this study, we apply an innovative timescale-adaptive algorithm of empirical mode decomposition (EMD) as the detrending operation for the modified DFA algorithm. We also propose a two-parameter scale of randomness for DFA to replace the DFA scaling exponent. Finally, we apply this modified algorithm to the database of human heartbeat interval from Physiobank, and it performs well in identifying characteristics of heartbeat interval caused by the effects of aging and of illness.

Long-range correlation of renal sympathetic nerve activity in both conscious and anesthetized rats

In this study we employed both detrended fluctuation analysis (DFA) and multiscale entropy (MSE) measurements to compare the long-range temporal correlation (LRTC) of multifibre renal sympathetic nerve activity (RSNA) between conscious and anesthetized Wistar rats. It was found that both methods showed the obvious LRTC properties in conscious state. Moreover, the scaling exponent of the RSNA in conscious rats was significantly higher than that in anesthetized rats. The results of MSE analysis showed that the entropy values, derived from the conscious group, increased on small time scales and then stabilized to a relatively constant value whereas the entropy measure, derived from anesthetized animals, almost monotonically decreased. This suggests that the fractal properties of underlying dynamics of the system have been reduced by anesthesia. The results demonstrate that apparently random fluctuations in multifibre RSNA are dictated by a complex deterministic process that imparts "long-term" memory to the dynamic system. However, this memory is significantly weakened by anesthesia.

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.

Volatility: a hidden Markov process in financial time series

Volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is a time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data by assuming that it is described by a hidden Markov process which together with the price forms a two-dimensional diffusion process. We derive a maximum-likelihood estimate of the volatility path valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are that (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model, (ii) the estimated volatility is related to trading volume by a power law of the form sigma proportional, variant V0.55, and (iii) future returns are proportional to the current volatility, which suggests some degree of predictability for the size of future returns.

Fluctuation and synchronization of gait intervals and gait force profiles distinguish stages of Parkinson's disease

We study the effects of Parkinson's disease (PD) on the long-term fluctuation and phase synchronization properties of gait timing (series of interstride intervals) as well as gait force profiles (series characterizing the morphological changes between the steps). We find that the fluctuations in the gait timing are significantly larger for PD patients and early PD patients, who were not treated yet with medication, compared to age-matched healthy controls. Simultaneously, the long-term correlations and the phase synchronization of right and left leg are significantly reduced in both types of PD patients. Surprisingly, long-term correlations of the gait force profiles are relatively weak for treated PD patients and healthy controls, while they are significantly larger for early PD patients. The results support the idea that timing and morphology of recordings obtained from a complex system can contain complementary information.

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).

Relation between volatility correlations in financial markets and Omori processes occurring on all scales

We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period is characterized by the Omori law, which describes the decay in the rate of aftershocks of a given size with time t by a power law with exponent close to 1. A shock followed by such a power law decay in the rate is here called Omori process. We find self-similar features in the volatility. Specifically, within the aftercrash period there are smaller shocks that themselves constitute Omori processes on smaller scales, similar to the Omori process after the large crash. We call these smaller shocks subcrashes, which are followed by their own aftershocks. We also show that the Omori law holds not only after significant market crashes as shown by Lillo and Mantegna [Phys. Rev. E 68, 016119 (2003)], but also after "intermediate shocks." By appropriate detrending we remove the influence of the crashes and subcrashes from the data, and find that this procedure significantly reduces the memory in the records. Moreover, when studying long-term correlated fractional Brownian motion and autoregressive fractionally integrated moving average artificial models for volatilities, we find Omori-type behavior after high volatilities. Thus, our results support the hypothesis that the memory in the volatility is related to the Omori processes present on different time scales.

Sleep stage dependent patterns of nonlinear heart rate dynamics in postmenopausal women

OBJECTIVE

To study the effects of sleep stage changes on nocturnal nonlinear heart rate variability (HRV) in postmenopausal women.

DESIGN

A prospective study.

POPULATION

Seventy-one healthy postmenopausal women.

METHODS

The women underwent two separate sleep studies four months apart. One steady state epoch per night of the awake state, stage 2 (light) non-REM sleep, stage 3-4 (deep) non-REM sleep and REM sleep were extracted. From the ECG, the fractal scaling exponents alpha(1) and alpha(2), approximate entropy (ApEn), the Poincaré plot variability coefficients SD1 and SD2, along with the low (LF) and high frequency (HF) bands of linear HRV as well as the LF/HF ratio were calculated.

RESULTS

None of the spectral measures of HRV changed significantly during the non-REM sleep compared to awake state. However, in non-REM sleep, alpha(2) (p<0.001) decreased significantly compared to the awake state, while alpha(1) and ApEn remained unchanged. SD1 was slightly increased in stage 2 sleep (p<0.05), while SD2 decreased in slow wave sleep (p<0.001). In REM sleep, alpha(2) values returned to the awake values, while ApEn and alpha(1) increased above the awake levels (p<0.01 for all variables), and SD1 decreased (p<0.01). HF spectral component decreased slightly (p<0.05 compared to stage 2 sleep) and LF/HF ratio increased during REM sleep (p<0.001). ApEn and alpha(2) had no correlations with any of the spectral measures of HRV, and alpha(1) had a modest correlation with the LF/HF ratio only during sleep.

CONCLUSIONS

We found that nonlinear indices of HRV describe specific features in HR dynamics during various sleep stages that are not detected by traditional spectral HRV indices.

Utilization of biomechanical modeling in design of robotic arm for rehabilitation of stroke patients

Stroke is one of the leading causes for long-term disability in the United States. Robot-aided rehabilitation has facilitated the functional recovery of chronic stroke victims. In this study, two models were developed to aid the design of a rehabilitation robot driven by pneumatic muscle (PM) actuators, which will be applied in the treatment of the upper-limb sensorimotor deficits of stroke patients. A biomechanical model of the musculoskeletal system with exoskeleton robot powered by PM was implemented to examine the initial parameters of PM based on the kinematics and dynamics of PM assisted arm-reaching and self-feeding tasks. The outputs of the model provided guidelines for the optimal design of robot's structure. Additionally, the model can determine the necessary auxiliary force and the activation timing pattern of each PM during multi-joint coordinated movement for the robot's dynamic control. Inverse-dynamics biomechanical model generates the joint torques required to perform the movement. In addition to the musculoskeletal model, we propose a simple method to estimate the self-generated net muscle torques, therefore, to provide quantitative assessment of motor improvement of stroke patients during the therapy.

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.

Prenatal RR fluctuations dynamics: detecting fetal short-range fractal correlations

OBJECTIVE

Several studies have suggested that the analysis of heart rate variability (HRV) during gestation provides indications of the development or maturation of fetal cardiovascular regulatory mechanisms. In this study, we evaluate the existence of short-range fractal-like correlations in fetal RR fluctuations data from the second half of human gestation.

METHODS

Fifty-six short-term abdominal ECG recordings were obtained from low-middle-risk pregnant women. Gestational age varied from estimated 21 weeks to term. For comparison, RR-interval data of 51 healthy adults were also analysed.

RESULTS

Principal findings along the gestational period explored were the existence of fractal RR dynamics in prenatal fetal data as revealed by the short-range scaling exponent alpha(1). No significant differences of alpha(1) (p = 0.4770) were found between fetal (median 1.2879) and adult data (median 1.3214), either between the fetal cases before or after 24 weeks (p = 0.6116) despite observing more variation at early stages. However, fetal RR data did involve lower magnitude in comparison with adults as we found significant differences in pNN20 and SDNN values.

CONCLUSION

The fetal short-range fractal behaviour of RR data could then be linked to the functional development of the parasympathetic activity, which appears to become manifested before 21 weeks of gestation.

Detecting mental EEG properties using detrended fluctuation analysis

Based on detrended fluctuation analysis (DFA), we explore the characteristics of multichannel electroencephalogram (EEG), which is recorded from many subjects performing different mental tasks. The results show that mental EEG exhibits long-range power-law correlations by calculating its scaling exponents (alpha), which can reflect the kinds of mental tasks. The scaling exponent of letter-composing is different from that of multiplication especially at positions C3 and C4, and at positions O1 and O2 the scaling exponent of rotation is also different distinctively from that of multiplication. Detrended fluctuation analysis exhibits its robustness against noises in our works. We could benefit more from the results of this paper in designing mental tasks and selecting brain areas in brain-computer interface systems.

Nonlinear analyses of cell proliferation in the central nervous system reveal stochastic and deterministic components

This paper analyzes the dynamics of cell proliferation in the developing central nervous system. Three different algorithms, Fano factor, Allan factor and detrended fluctuations analysis, are used to estimate de scaling exponent of space numerical series obtained by recording the number and position of proliferating cells along the cephalic-caudal axis of the system. It can be concluded that the dynamics of proliferation involves two component: (a) a random noncorrelated stochastic component representing a basal proliferating activity uniformly distributed along the cephalic-caudal axis and (b) a deterministic nonstationary component that imposes a defined global trend to the process. The deterministic nonstationary trend can be interpreted as the effect of a controlling influence operating along the cephalic-caudal axis. This result indicates that the proliferative activity is spatially organized along the cephalic-caudal axis of the system.

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.

Statistics of return intervals in long-term correlated records

We consider long-term correlated data with several distribution densities (Gaussian, exponential, power law, and log normal) and various correlation exponents gamma (0<gamma<1) , and study the statistics of the return intervals r_{j} between events above some threshold q . We show that irrespective of the distribution, the return intervals are long-term correlated in the same way as the original record, but with additional uncorrelated noise. Due to this noise, the correlations are difficult to observe by the detrended fluctuation analysis (which exhibits a crossover behavior) but show up very clearly in the autocorrelation function. The distribution P_{q}(r) of the return intervals is characterized at large scales by a stretched exponential with exponent gamma , and at short scales by a power law with exponent gamma-1 . We discuss in detail the occurrence of finite-size effects for large threshold values for all considered distributions. We show that finite-size effects are most pronounced in exponentially distributed data sets where they can even mask the stretched exponential behavior in records of up to 10;{6} data points. Finally, in order to quantify the clustering of extreme events due to the long-term correlations in the return intervals, we study the conditional distribution function and the related moments. We find that they show pronounced memory effects, irrespective of the distribution of the original data.

Detecting REM sleep from the finger: an automatic REM sleep algorithm based on peripheral arterial tone (PAT) and actigraphy

Scoring of REM sleep based on polysomnographic recordings is a laborious and time-consuming process. The growing number of ambulatory devices designed for cost-effective home-based diagnostic sleep recordings necessitates the development of a reliable automatic REM sleep detection algorithm that is not based on the traditional electroencephalographic, electrooccolographic and electromyographic recordings trio. This paper presents an automatic REM detection algorithm based on the peripheral arterial tone (PAT) signal and actigraphy which are recorded with an ambulatory wrist-worn device (Watch-PAT100). The PAT signal is a measure of the pulsatile volume changes at the finger tip reflecting sympathetic tone variations. The algorithm was developed using a training set of 30 patients recorded simultaneously with polysomnography and Watch-PAT100. Sleep records were divided into 5 min intervals and two time series were constructed from the PAT amplitudes and PAT-derived inter-pulse periods in each interval. A prediction function based on 16 features extracted from the above time series that determines the likelihood of detecting a REM epoch was developed. The coefficients of the prediction function were determined using a genetic algorithm (GA) optimizing process tuned to maximize a price function depending on the sensitivity, specificity and agreement of the algorithm in comparison with the gold standard of polysomnographic manual scoring. Based on a separate validation set of 30 patients overall sensitivity, specificity and agreement of the automatic algorithm to identify standard 30 s epochs of REM sleep were 78%, 92%, 89%, respectively. Deploying this REM detection algorithm in a wrist worn device could be very useful for unattended ambulatory sleep monitoring. The innovative method of optimization using a genetic algorithm has been proven to yield robust results in the validation set.

Analysis of non-stationary data for heart-rate fluctuations in terms of drift and diffusion coefficients

We describe a method for analyzing the stochasticity in non-stationary data for the beat-to-beat fluctuations in the heart rates of healthy subjects, as well as those with congestive heart failure. The method analyzes the return time series of the data as a Markov process, and computes the Markov time scale, i.e., the time scale over which the data are a Markov process. We also construct an effective stochastic continuum equation for the return series. We show that the drift and diffusion coefficients, as well as the amplitude of the return time series for healthy subjects are distinct from those with CHF. Thus, the method may potentially provide a diagnostic tool for distinguishing healthy subjects from those with congestive heart failure, as it can distinguish small differences between the data for the two classes of subjects in terms of well-defined and physically-motivated quantities.

Detrended fluctuation analysis in x-ray photon correlation spectroscopy for determining coarsening dynamics in alloys

We study the dynamics of precipitate coarsening in phase-separating alloys at late stages of phase separation by x-ray photon correlation spectroscopy (XPCS). For analyzing time series of fluctuating speckle intensities from small-angle scattering of coherent x rays, the method of detrended fluctuation analysis (DFA), which is ideal for determining power-law correlations, is applied. We discuss the application of DFA with respect to XPCS data by means of simulated time series. In particular, the effects of different signal-to-noise ratios are examined. Results from measurements of the two model systems Al-6 at. % Ag at 140 degrees C and Al-9 at. % Zn at 0 degrees C are presented. Since the DFA effectively removes adulterating trends in the data, quantitative agreement with Monte Carlo simulations is obtained. It is verified that two different coarsening mechanisms are predominant in the two systems--coarsening either by diffusion of single atoms or by movement of whole precipitates.

Dependence of heart rate variability on heart period in disease and aging

The aim of this study was to compare the dependence of heart rate variability (HRV) on heart period (RR interval length) under different physiological and pathological states in order to detect changes in HR modulation. The dependence of HRV on the RR interval length in healthy elderly subjects, congestive heart failure (CHF) patients and one patient with a transplanted heart (T) was compared with healthy young subjects. Spectral powers, sample entropy (SampEn) and short-term fractal scaling exponent (alpha1) were determined from 24 h free-running recordings. For the same HR, HRV measures were different in different groups. In healthy subjects HRV measures depended on RR interval length and all spectral powers were highly correlated, although reduced in elderly subjects. SampEn at high HR was the most sensitive quantity to changes induced by aging. In disease, CHF and T, an achievable HR range was decreased, all spectral powers were reduced, but correlated, and the dependence of HRV measures on RR was lost. There was an evident difference in the dependence of nonlinear on linear measures between young subjects and all the other studied groups. In disease the reduction in autonomic control was associated with the decrease in short-range correlation and regularity in RR series. We have concluded that the analysis of HRV measures as functions of RR interval length can reveal important aspects of HR control that might be lost in averaging.

Ultrafast intermolecular zero quantum spectroscopy

Clinical magnetic resonance spectroscopy is typically limited by magnetic inhomogeneities which destroy spectral resolution, but intermolecular zero quantum coherences (iZQCs) are insensitive to such inhomogeneities. iZQC resolution in vivo, however, has been hampered by physiological fluctuations over the time scale of the two-dimensional acquisition. A faster iZQC sequence will allow us to average away these fluctuations, and thus we present a new approach to ultrafast two-dimensional spectroscopy. This communication reports iZQC experiments acquiring up to 31 t1-points per scan, as well as extensions to a broad range of other 2D sequences.

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.