Detrended Fluctuation Analysis Exponent Research Articles

The Between-Day Reliability of Correlation Properties of Heart Rate Variability During Running.

The short-term scaling exponent of detrended fluctuation analysis (DFA-a1) of heart rate variability may be a helpful tool to assess autonomic balance as a prelude to daily, individualized training. For this concept to be useful, between-session reliability should be acceptable. The aim of this study was to explore thereliability of DFA-a1 during a low-intensity exercise session in both a non-fatigued and a fatigued condition in healthy males and females. Ten participants completed two sessions with each containing an exhaustive treadmill ramp protocol. Before and after the fatiguing ramp, a standardized submaximal low-intensity exercise bout was performed during which DFA-a1, heart rate, and oxygen consumption (VO2) were measured. We compared between-session reliability of all metrics prior to the ramps (i.e., non-fatigued status) and after the first ramp (i.e., fatigued status). Intraclass correlation coefficients (ICC) with 95% confidence intervals (CI), the standard error of measurement, and the smallest worthwhile change (SWC) were determined. The ICC and SWC pre fatiguing ramp were 0.85 (95% CI 0.39-0.96) and 5.5% for DFA-a1, 0.85 (0.38-0.96) and 2.2% for heart rate, and 0.84 (0.31-0.96) and 3.1% for VO2. Post fatiguing ramp, the ICC and SWC were 0.55 (0.00-0.89) and 7.9% for DFA-a1, 0.91 (0.62-0.98) and 1.6% for heart rate, and 0.80 (0.17-0.95) and 3.0% for VO2. DFA-a1 shows generally acceptable to good between-session reliability with a SWC of 0.06 and 0.07 (5.5-7.9%) during non-fatigued and fatigued conditions. This suggests that this metric may be useful to inform on training readiness.

Exploration of the Severity of Hepatic Encephalopathy Deterioration Process Through Dynamics of the EEG Band Power time series.

Cirrhosis is a liver disease that could impair the functionality of the neural system, limiting cognitive processes and reduce mobility, possibly because alterations on dynamics of neural communications. In this study the dynamics of band power fluctuations on ß and γ bands were studied on three groups: control, patients with cirrhosis and patients diagnosed with minimal hepatic encephalopathy. EEG signals were recorded on an oddball paradigm and analyzed to obtain the latency and amplitude of the P300 wave and Detrended Fluctuation Analysis (DFA) exponent values over ß and γ band power time series for each channel. As expected, the latency of the P300 wave was significantly different for control subjects ( ). Amplitudes were not as different, but they tend to decrease for cirrhosis and minimal hepatic encephalopathy groups. DFA exponent values also tends to describe a more regular process and seems to be related with presence of symptoms of hepatic encephalopathy. These subtle changes could be produced by the mechanisms of a mild neurological impairment and be used, if it is confirmed, as an index to evaluate such deterioration.

Heart Rate Variability in Healthy Subjects During Monitored, Short-Term Stress Followed by 24-hour Cardiac Monitoring.

Heart Rate Variability (HRV) can be a useful metric to capture meaningful information about heart function. One of the non-linear indices used to analyze HRV, Detrended Fluctuation Analysis (DFA), finds short and long-term correlations in RR intervals to capture quantitative information about variability. This study focuses on the impact of visual and mental stimulation on HRV as expressed via DFA within healthy adults. Visual stimulation can activate the automatic nervous system to directly impact physiological behavior such as heart rate. In this investigation of HRV, 70 participants (21 males) viewed images on a screen followed by a math and recall task. Each viewing segment lasted 2 min and 18 s. The math and memory recall task segment lasted 4 min total. This process was repeated 9 times during which the participants’ electrocardiogram was recorded. 37 participants (12 males) opted in for an additional 24-h Holter recording after the viewing and task segments of the study were complete. Participants were randomly assigned to either a pure (organized image presentation) or mixed (random image presentation) image regime for the viewing portion of the study to investigate the impact of the external environment on HRV. DFA α1 was extracted from the RR intervals. Our findings suggest that DFA α1 can differentiate between the viewing [DFA α1 range from 0.96 (SD = 0.25) to 1.08 (SD = 0.22)] and the task segments [DFA α1 range from 1.17 (SD = 0.21) to 1.26 (SD = 0.25)], p < 0.0006 for all comparisons. However, DFA α1 was not able to distinguish between the two image regimes. During the 24-hour follow up, participants had an average DFA α1 = 1.09 (SD = 0.14). In conclusion, our findings suggest a graded response in DFA during short term stimulation and a responsiveness in participants to adjust physiologically to their external environment expressed through the DFA exponent.

Comparing adaptive fractal and detrended fluctuation analyses of stride time variability: Tests of equivalence

BackgroundFractal analyses quantify self-similarities in stride-to-stride fluctuations over different time scales. Fractal exponents can be measured with adaptive fractal analysis (AFA) or detrended fluctuation analysis (DFA), though measurements obtained with the algorithms have not been directly compared. Research questionAre stride time fractal exponents measured with AFA and DFA algorithms equivalent? MethodsData from 50 participants with Parkinson’s Disease (n = 15), age-similar healthy adults (n = 15) and healthy young adults (n = 20) were analyzed in this cross-sectional, observational study. Participants completed 6-min walks at self-selected speeds overground on a straight walkway and on a treadmill. Stride times were measured with inertial measurement units. Fractal exponents in stride time data were processed using AFA and DFA algorithms and compared with two one-sided tests of equivalence. Mixed ANOVAs were used to compare exponents between groups and conditions. ResultsFractal exponents computed with AFA and DFA were equivalent neither in the overground (0.796 & 0.830, respectively, p = .587) nor treadmill conditions (0.806 & 0.882, respectively, p = .122). Fractal exponents measured with DFA were higher than when measured with AFA. Standard errors were 22% lower when measured with AFA. Additionally, a group × condition interaction was statistically significant when fractal exponents were processed with the AFA algorithm (F(2,47) = 11.696, p < .001), whereas the group × condition interaction was not statistically significant when DFA exponents were compared (F(2, 47) = 2.144, p = .129). SignificanceAFA and DFA do not produce equivalent estimates of the fractal exponent α in stride time dynamics. Estimates of the fractal exponent α obtained with AFA or DFA algorithms therefore should not be used interchangeably. Standard errors were lower when derived with AFA. Fractal exponents calculated with AFA may be more sensitive to conditions that influence stride time fractal dynamics than are measures calculated with DFA.

Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set.

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.

Altered Temporal Structure of Neural Phase Synchrony in Patients With Autism Spectrum Disorder.

Functional connectivity, quantified by phase synchrony, between brain regions is known to be aberrant in patients with autism spectrum disorder (ASD). Here, we evaluated the long-range temporal correlations of time-varying phase synchrony (TV-PS) of electrocortical oscillations in patients with ASD as well as typically developing people using detrended fluctuation analysis (DFA) after validating the scale-invariance of the TV-PS time series. By comparing the DFA exponents between the two groups, we found that those of the TV-PS time series of high-gamma oscillations were significantly attenuated in patients with ASD. Furthermore, the regions involved in aberrant TV-PS time series were mainly within the social ability and cognition-related cortical networks. These results support the notion that abnormal social functions observed in patients with ASD may be caused by the highly volatile phase synchrony states of electrocortical oscillations.

Computational characteristics of interictal EEG as objective markers of epileptic spasms

ObjectiveFavorable neurodevelopmental outcomes in epileptic spasms (ES) are tied to early diagnosis and prompt treatment, but uncertainty in the identification of the disease can delay this process. Therefore, we investigated five categories of computational electroencephalographic (EEG) measures as markers of ES. MethodsWe measured 1) amplitude, 2) power spectra, 3) Shannon entropy and permutation entropy, 4) long-range temporal correlations, via detrended fluctuation analysis (DFA) and 5) functional connectivity using cross-correlation and phase lag index (PLI). EEG data were analyzed from ES patients (n = 40 patients) and healthy controls (n = 20 subjects), with multiple blinded measurements during wakefulness and sleep for each patient. ResultsIn ES patients, EEG amplitude was significantly higher in all electrodes when compared to controls. Shannon and permutation entropy were lower in ES patients than control subjects. The DFA intercept values in ES patients were significantly higher than control subjects, while DFA exponent values were not significantly different between the groups. EEG functional connectivity networks in ES patients were significantly stronger than controls when based on both cross-correlation and PLI. Significance for all statistical tests was p < 0.05, adjusted for multiple comparisons using the Benjamini-Hochberg procedure as appropriate. Finally, using logistic regression, a multi-attribute classifier was derived that accurately distinguished cases from controls (area under curve of 0.96). ConclusionsComputational EEG features successfully distinguish ES patients from controls in a large, blinded study. SignificanceThese objective EEG markers, in combination with other clinical factors, may speed the diagnosis and treatment of the disease, thereby improving long-term outcomes.

Towards Embedded Computation with Building Materials

We present results showing the capability of concrete-based information processing substrate in the signal classification task in accordance with in materio computing paradigm. As the Reservoir Computing is a suitable model for describing embedded in materio computation, we propose that this type of presented basic construction unit can be used as a source for “reservoir of states” necessary for simple tuning of the readout layer. We present an electrical characterization of the set of samples with different additive concentrations followed by a dynamical analysis of selected specimens showing fingerprints of memfractive properties. As part of dynamic analysis, several fractal dimensions and entropy parameters for the output signal were analyzed to explore the richness of the reservoir configuration space. In addition, to investigate the chaotic nature and self-affinity of the signal, Lyapunov exponents and Detrended Fluctuation Analysis exponents were calculated. Moreover, on the basis of obtained parameters, classification of the signal waveform shapes can be performed in scenarios explicitly tuned for a given device terminal.

Analysis of intentional lethal violent crimes: A sliding windows approach

This paper analyzes the fluctuations in time series of intentional lethal violent crime rates in Salvador, Bahia, Brazil from 2012 to 2018. The modeling proposed was performed with two main strategies: first, the descriptive of the series under study was defined using the sliding window approach, as determined by autocorrelation from Detrended Fluctuation Analysis (DFA), also with sliding window. Results of this research indicate that the series of DFA exponents, depending on the window (365 or 1000 days) and period, have oscillated between persistent, antipersistent and out of memory. Descriptive analysis identified reduction in the average crime rates from 2013 and a behavioral pattern among other moments. These findings will serve as another methodological proposal for monitoring, control and management of criminal indicators and research on them.

Trends and Persistence of Dry–Wet Conditions in Northeast Brazil

We analyze trend and persistence in Standardized Precipitation Index (SPI) time series derived from monthly rainfall data at 133 gauging stations in Pernambuco state, Brazil, using a suite of complementary methods to address the spatially explicit tendencies, and persistence. SPI was calculated for 1-, 3-, 6-, and 12-month time scales from 1950 to 2012. We use Mann–Kendall test and Sen’s slope to determine sign and magnitude of the trend, and detrended fluctuation analysis (DFA) method to quantify long-term correlations. For all time scales significant negative trends are obtained in the Sertão (deep inland) region, while significant positive trends are found in the Agreste (intermediate inland), and Zona da Mata (coastal) regions. The values of DFA exponents show different scaling behavior for different time scales. For short-term conditions described by SPI-1 the DFA exponent is close to 0.5 indicating weak persistency and low predictability, while for medium-term conditions (SPI-3 and SPI-6) DFA exponents are greater than 0.5 and increase with time scale indicating stronger persistency and higher predictability. For SPI-12 that describes long-term precipitation patterns, the values of DFA exponents for inland regions are around 1, indicating strong persistency, while in the shoreline the value of the DFA exponent is between 1.0 and 1.5, indicating anti-persistent fractional Brownian motion. These results should be useful for agricultural planning and water resource management in the region.

Noise suppression for magnetotelluric using variational mode decomposition and detrended fluctuation analysis

Noise suppression is significant for magnetotelluric (MT) data analysis, especially in the face of strong human electromagnetic interference. Variational mode decomposition (VMD) is a novel signal processing method, and the selection of proper decomposition layers plays a key role in its signal processing effects. In view of the fact that detrended fluctuation analysis (DFA) is an evaluation criterion capable of selecting the appropriate number of sub-signals, we propose a noise suppression method for MT by combing VMD with DFA. We firstly estimate the scaling exponent range of MT noisy data and decompose it into a given series of K-order intrinsic mode functions (IMFs). Then, a criterion based on DFA is designed to select the mode number K with the purpose to improve the decomposition accuracy of VMD. The scaling exponent of DFA is used to define the relevant modes for the construction of filtered signals. In this research, the MT data is collected from Qinghai test site and added with strong interference for comprehensive analysis by the remote reference method, VMD method, and the proposed VMD-DFA method. The results have shown that the proposed method could greatly improve the accuracy of signal decomposition and the reliability of the reconstructed signal by adaptively selecting suitable K-order IMFs for different types of interference. Consequently, strong interference is effectively eliminated, and the obtained apparent resistivity-phase curve is stable and smooth. Moreover, the denoised MT data will further strengthen the interpretability of geoelectric information.

Long-memory traces in $$\hbox {PM}_{10}$$ time series in Athens, Greece: investigation through DFA and R/S analysis

This paper investigates the existence of chaos in concentration dynamics of particulate matter with an aerodynamic diameter less than or equal to $$10\,\upmu \hbox {m}$$ ( $$\hbox {PM}_{10}$$ ) in the greater Athens area (GAA), Greece. It reports findings on three 16-year $$\hbox {PM}_{10}$$ time series recorded by three different air pollution monitoring stations located in GAA and examines if critical fractal epochs with long memory exist. Detrended Fluctuation Analysis (DFA) and Rescaled Range (R/S) Analysis were used via sliding windows of approximately 1-month duration. In all $$\hbox {PM}_{10}$$ time series, several segments were found with critical fractal behaviour and hidden long-memory patterns. All these segments exhibited Hurst exponents above 0.75 and DFA exponents above 1.75. Twelve $$\hbox {PM}_{10}$$ segments with fractality and long memory were commonly identified by both techniques. In one case, long memory was identified concurrently across all three air pollution monitoring stations and in another case, across two stations. The importance of the agreement between two different and independent chaos-analysis techniques is discussed in association with the proper selection of threshold values. This is the second time to address chaos in $$\hbox {PM}_{10}$$ data series in GAA, and the first time to combine two widely accepted techniques, DFA and R/S analysis.

Effects of Mental and Physical Fatigue Inducing Tasks on Balance and Gait Characteristics

150-Word AbstractFatigue may reduce human performance and increase injury risk. This study investigated the effects of mental and physical fatigue inducing tasks (MF and PF) on balance and gait cha...

Complexity and uncertainty analysis of financial stock markets based on entropy of scale exponential spectrum

Research on complexity and uncertainty of nonlinear signals has great significance in dynamic system analysis. In order to further analyze the detailed information from the financial data to acquire deeper insight into the complex system and improve the ability of prediction, we propose the entropy of scale exponential spectrum (EOSES) as a new measure. Combined with multiscale theory, we get multiscale EOSES. The scale exponential spectrum (SES) is derived from the scale exponent of detrended fluctuation analysis. As for the entropy, we choose Renyi entropy and fractional cumulative residual entropy to compare and analyze the results. Simulated data and financial time series are used to obtain further in-depth information on the EOSES. Compared with traditional methods, we find that Renyi EOSES over moving window can provide more details of complexity which include fractal structure and scale properties. Also, it reduces the influence of degree of fitting polynomial and has higher noise immunity. In addition, through the SES and EOSES, we can better research the properties and stages of stock markets and distinguish stock markets with different characteristics.

The critical role of respiratory sinus arrhythmia on temporal cardiac dynamics.

Temporal cardiac properties provide alternative information in analyzing heart rate variability (HRV), which may be disregarded by the standard HRV analyses. Patients with congestive heart failure (CHF) are known to have distinct temporal features from the healthy individuals. However, the underlying mechanism leading to the variation remains unclear. Whether or not these parameters can finely classify the severity for CHF patients is uncertain as well. In this work, an electrocardiogram was monitored in advanced CHF patients using 24-h Holter in four conditions, including baseline, one and three months after atenolol therapy, and healthy individuals. Slope and area under the curve (AUC) of multiscale entropy (MSE) curve over short (scales 1-5) and long (scales 6-20) scales, and detrended fluctuation analysis (DFA) scaling exponents at short (4-11 beats) and intermediate (>11 beats) window sizes were calculated. The results show that short-time scale MSE-derived parameters (slope: -0.08 ± 0.10, -0.03 ± 0.10, 0.02 ± 0.06, 0.08 ± 0.06; AUC: 4.03 ± 2.11, 4.69 ± 1.28, 4.73 ± 0.94, and 6.17 ± 1.23) and short-time scale DFA exponent (0.79 ± 0.16, 0.95 ± 0.22, 1.11 ± 0.19, and 1.35 ± 0.20) can hierarchically classify all four conditions. More importantly, simulated R-R intervals with different fractions and amplitude of respiratory sinus arrhythmia (RSA) components were examined to validate our hypothesis regarding the essentiality of RSA in the improvement of cardiovascular function, and its tight association with unpredictability and fractal property of HRV, which is in line with our hypothesis that RSA contributes significantly to the generation of the unpredictability and fractal behavior of HR dynamics.NEW & NOTEWORTHY Temporal cardiac properties provide useful diagnostic parameters for patients with congestive heart failure (CHF). Our study hierarchically classified CHF patients with β-blocker treatment by using multiscale entropy and detrended fluctuation analysis. Also, we provided the evidence to validate the critical role of respiratory sinus arrhythmia in the fractal properties of heart rate variability.

Inference on Long-Range Temporal Correlations in Human EEG Data

Detrended Fluctuation Analysis (DFA) is a statistical estimation algorithm used to assess long-range temporal dependence in neural time series. The algorithm produces a single number, the DFA exponent, that reflects the strength of long-range temporal correlations in the data. No methods have been developed to generate confidence intervals for the DFA exponent for a single time series segment. Thus, we present a statistical measure of uncertainty for the DFA exponent in electroencephalographic (EEG) data via application of a moving-block bootstrap (MBB). We tested the effect of three data characteristics on the DFA exponent: (1) time series length, (2) the presence of artifacts, and (3) the presence of discontinuities. We found that signal lengths of ∼5 minutes produced stable measurements of the DFA exponent and that the presence of artifacts positively biased DFA exponent distributions. In comparison, the impact of discontinuities was small, even those associated with artifact removal. We show that it is possible to combine a moving block bootstrap with DFA to obtain an accurate estimate of the DFA exponent as well as its associated confidence intervals in both simulated data and human EEG data. We applied the proposed method to human EEG data to (1) calculate a time-varying estimate of long-range temporal dependence during a sleep-wake cycle of a healthy infant and (2) compare pre- and post-treatment EEG data within individual subjects with pediatric epilepsy. Our proposed method enables dynamic tracking of the DFA exponent across the entire recording period and permits within-subject comparisons, expanding the utility of the DFA algorithm by providing a measure of certainty and formal tests of statistical significance for the estimation of long-range temporal dependence in neural data.

Attenuated long-range temporal correlations of electrocortical oscillations in patients with autism spectrum disorder

The aim of this study was to investigate the long-range temporal correlations (LRTCs) of instantaneous amplitude of electrocortical oscillations in patients with autism spectrum disorder (ASD). Using the resting-state electroencephalography (EEG) of 15 patients with ASD (aged between 5˜18 years, mean age = 11.6 years, SD = 4.4 years) and 18 typical developing (TD) people (aged between 5˜18 years, mean age = 8.9 years, SD = 2.4 years), we estimated the LRTCs of neuronal oscillations amplitude of 84 predefined cortical regions of interest using detrended fluctuation analysis (DFA) after confirming the presence of scale invariance. We found that the DFA exponents of instantaneous amplitude of beta and low-gamma oscillations were significantly attenuated in patients with ASD compared to TD participants. Moreover, the regions with attenuated DFA exponent were mainly located in social functions related cortical networks, including the default mode network (DMN), the mirror neuron system (MNS) and the salience network (SN). These findings suggest that ASD is associated with highly volatile neuronal states of electrocortical oscillations, which may be related to social and cognitive dysfunction in patients with ASD.

Effect of EKG Sampling Rate on Heart Rate Variability Analysis.

We studied the effect of EKG sampling rate on heart rate variability (HRV) analysis. We acquired EKG from four term hypoxic-ischemic encephalopathic infants undergoing therapeutic hypothermia. The EKG signal was acquired continuously for 4 days from the cardiorespiratory monitor through the analog port. The following HRV metrics were calculated: normalized low-frequency (nLF), normalized high-frequency (nHF), low-frequency (LF), high-frequency (HF), short-term detrended fluctuation analysis (DFA) exponent (αs), long-term DFA exponent (αL), root mean square (RMS) short (RMSS), and RMS long (RMSL). In addition, heart rate was used. These metrics were calculated for EKG acquired at 1 KHz (served as reference, EKGref) as well as from EKGs downsampled at 500 Hz (EKG500), 250 Hz (EKG250), and 125 Hz (EKG125). The bedside monitors were simultaneously sending the EKG to a data warehouse, storing the EKG (EKGDWH) at 250 Hz. All HRV metrics were also calculated for the EKGDWH. The comparison between HRV metrics calculated from EKGref and downsampled EKG (EKG500, EKG250, EKG125) was made with intraclass correlation coefficient (r). The comparisons of HRV metrics between EKG250 and EKGDWH were also made with ICC. Our results show that HRV calculated with EKGref and from downsampled EKG were highly correlated (r>0.8 for all comparisons, P<; 0.001). HRV metrics from EKG250 and EKGDWH were also significantly correlated (r=0.7, P<; 0.001) for all metrics except for HF (r=0.276). These data show that HF power is compromised in the EKGDWH signal and caution must be exercised in interpreting the HF power calculated from this EKG.

Pre-processing of Photoplethysmographic Waveform for Amplitude Regularization

This study is aimed to develop a post-processing method to regularize amplitude of PPG waveforms and evaluate the performance of the algorithm. The proposed procedure for regularizing amplitude consists of extracting the signal envelopes based on time-domain filtering, generating a compensation curve, and reconstructing the waveform. The proposed technique was evaluated with respect to dispersion and waveform fluctuation by means of coefficients of variation (CV) and a scaling exponent of detrended fluctuation analysis (DFA). Other criteria included the detection performances of major features such as upper and lower fiducial points and maximum dV/dt. In developing this method, we used a clinical dataset that comprised 74,225 beats. By applying reconstruction algorithm, the %CV and the scaling exponent of DFA were significantly decreased from 115.4 to 71.4 and from 1.029 to 0.836, respectively in peak amplitude. In valley amplitude, they were also decreased from 38.3 to 13.2 and from 0.993 to 0.713, respectively. Moreover, sensitivity of maximum dV/dt point, upper and lower peak detection are increased by 8.50, 2.72 and 5.21% after reconstruction, respectively. Our results clearly showed that the proposed reconstruction technique could reduce amplitude fluctuation and improve detection of fiducial points.

Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: Continuously varying exponents mimic M/EEG results.

We revisit the CROS (“CRitical OScillations”) model which was recently proposed as an attempt to reproduce both scale-invariant neuronal avalanches and long-range temporal correlations. With excitatory and inhibitory stochastic neurons locally connected in a two-dimensional disordered network, the model exhibits a transition where alpha-band oscillations emerge. Precisely at the transition, the fluctuations of the network activity have nontrivial detrended fluctuation analysis (DFA) exponents, and avalanches (defined as supra-threshold activity) have power law distributions of size and duration. We show that, differently from previous results, the exponents governing the distributions of avalanche size and duration are not necessarily those of the mean-field directed percolation universality class (3/2 and 2, respectively). Instead, in a narrow region of parameter space, avalanche exponents obtained via a maximum-likelihood estimator vary continuously and follow a linear relation, in good agreement with results obtained from M/EEG data. In that region, moreover, the values of avalanche and DFA exponents display a spread with positive correlations, reproducing human MEG results.