Detrended Fluctuation Analysis Values Research Articles

Behavioral state-dependent associations between EEG temporal correlations and depressive symptoms

Previous studies have shown abnormal long-range temporal correlations in neuronal oscillations among individuals with Major Depressive Disorders, occurring during both resting states and transitions between resting and task states. However, the understanding of this effect in preclinical individuals with depression remains limited. This study investigated the association between temporal correlations of neuronal oscillations and depressive symptoms during resting and task states in preclinical individuals, specifically focusing on male action video gaming experts. Detrended fluctuation analysis (DFA), Lifetimes, and Waitingtimes were employed to explore temporal correlations across long-range and short-range scales. The results indicated widespread changes from the resting state to the task state across all frequency bands and temporal scales. Rest-task DFA changes in the alpha band exhibited a negative correlation with depressive scores at most electrodes. Significant positive correlations between DFA values and depressive scores were observed in the alpha band during the resting state but not in the task state. Similar patterns of results emerged concerning maladaptive negative emotion regulation strategies. Additionally, short-range temporal correlations in the alpha band echoed the DFA results. These findings underscore the state-dependent relationships between temporal correlations of neuronal oscillations and depressive symptoms, as well as maladaptive emotion regulation strategies, in preclinical individuals.

Heart-brain Rhythmic Synchronization during Meditation: A Nonlinear Signal Analysis.

Heart-brain synchronization is the integration of mind, body, and spirit. It occurs when the electrical activity of the heart and brain is synchronized. In recent years, there has been mounting curiosity to investigate the effects of meditation on heart-brain synchronization with respect to mental and emotional health and well-being. The current investigation aims to explore the rhythmic synchronicity between the brain and the heart during heartfulness meditation (HM) practice. The study was performed on 45 healthy volunteers who were categorized into three equal groups: long-term meditators (LTMs), short-term meditators (STMs), and nonmeditators (NMs). The electroencephalogram (EEG) signals were recorded to measure the prefrontal activity, and electrocardiogram (ECG) signals were recorded to measure the cardiac activity. The data were recorded in four states: baseline, meditation, transmission, and posttransmission. The detrended fluctuation analysis (DFA) method was used for the analysis of EEG and ECG signals. The result indicates that DFA values of EEG and ECG declined during meditation and transmission states as compared to pre- and postmeditation states. Significant results were obtained for the LTM group in all the states. A positive correlation was also observed between DFA of the heart and brain for the LTM group and no significant correlations were observed for the STM and NM groups. The shreds of evidence suggest that heart-brain synchronization facilitates mental and emotional stability. HM practice has the potential to regulate the fluctuation of the mind. Regular meditation practice may result in physiological synchrony between cardiac and neural behavior, which can be considered a quality index for meditation practice.

Deterministic Brownian-like Motion: Electronic Approach

Brownian motion is a dynamic behavior with random changes over time (stochastic) that occurs in many vital functions related to fluid environments, stock behavior, or even renewable energy generation. In this paper, we present a circuit implementation that reproduces Brownian motion based on a fully deterministic set of differential equations. The dynamics of the electronic circuit are characterized using four well-known metrics of Brownian motion, namely: (i) Detrended Fluctuation Analysis (DFA), (ii) power law in the power spectrum, (iii) normal probability distribution, and (iv) Mean Square Displacement (MSD); where traditional Brownian motion exhibits linear time growth of the MSD, a Gaussian distribution, a −2 power law of the frequency spectrum, and DFA values close to 1.5. The obtained results show that for a certain combination of values in the deterministic model, the dynamics in the electronic circuit are consistent with the expectations for a stochastic Brownian behavior. The presented electronic circuit improves the study of Brownian behavior by eliminating the stochastic component, allowing reproducibility of the results through fully deterministic equations, and enabling the generation of physical signals (analog electronic signals) with Brownian-like properties with potential applications in fields such as medicine, economics, genetics, and communications, to name a few.

Insight into the hierarchical control governing leg stiffness during the stance phase of running

Leg stiffness plays a key role in the storage and release of elastic energy during stance. However, the extent to which a runner is able to reuse stored energy remains a limiting factor in determining their running effectiveness. In this study, ten habitual rearfoot strikers and ten habitual forefoot strikers were asked to run on a treadmill in three footwear conditions: traditional, neutral, and minimal running shoes. We examined the effect of habitual foot strike pattern and footwear on leg stiffness control within three task-relevant phases of stance (i.e. touch-down, loading, unloading). Control was quantified using stride-to-stride leg stiffness time-series and the coefficient of variability and detrended fluctuation analysis (DFA). The results are interpreted within a theoretical framework that blends dynamic systems theory and optimal feedback control. Results indicate that leg stiffness control is tightly regulated by an active control process during the loading period of stance. In contrast, the touch-down and unloading phases are driven mostly by passive allometric control mechanisms. The effect of footwear on leg stiffness control was inconclusive due to inconsistent trends across three shoe types. However, stiffness control was affected by landing technique. Habitual rearfoot strike runners have reduced DFA values during the touch-down and unloading phases. These sub-phases are associated with an allometric control process and suggests that rearfoot strike runners express a reduction in system complexity for leg stiffness control and hence, a less adaptable system.

A Comparison of Global Surface Air Temperature Over the Oceans Between CMIP5 Models and NCEP Reanalysis

By utilizing eight CMIP5 model outputs in historical experiment that simulated daily mean sea surface temperature (SST) and NCEP reanalysis data over 12 ocean basins around the world from 1960 to 2005, this paper evaluates the performance of CMIP5 models based on the detrended fluctuation analysis (DFA) method. The results of National Centers for Environmental Prediction (NCEP) data showed that the SST in most ocean basins of the world had long-range correlation (LRC) characteristics. The DFA values of the SST over ocean basins are large in the tropics and small in high latitudes. In spring and autumn, the zonal average DFA of SST are basically distributed symmetrically in the Northern and Southern Hemispheres. In summer, the zonal average values of DFA in the Northern Hemisphere are larger than those in the southern hemisphere, and vice versa in winter. The performance of HadGEM2-AO, CNRM-CM5, and IPSL-CM5A-MR are all relative well among the eight models in simulating SST over most regions of the global ocean.

Non-linear analysis of heart rate variability for evaluating the acute effects of caffeinated beverages in young adults – ERRATUM

Caffeinated beverages are the most consumed substances in the world. High rate of uptake of these beverages leads to various cardiovascular disorders ranging from palpitations to coronary failure. The objective of the study is to ascertain how the complexity parameters of heart rate variability are affected by acute consumption of caffeinated beverages in young adults.Electrocardiogram measurements were performed before consuming drinks. After consuming the drinks, measurements were done again at 30 minutes and 60 minutes. Heart rate variability signals were acquired from electrocardiogram signals. Also, the signals were reconstructed in the phase space and largest Lyapunov exponent, correlation dimension, approximate entropy, and detrended fluctuation analysis values were calculated.Heart rate increased for energy drink and cola groups but not in coffee group. Non-linear parameter values of energy drink, coffee, and cola group are increased within 60 minutes after drink consumption. This change is statistically significant just for energy drink group.Energy drink consumption increases the complexity of the cardiovascular system in young adults significantly. Coffee and cola consumption have no significant effect on the non-linear parameters of heart rate variability.

Intrinsic activity temporal structure reactivity to behavioural state change is correlated with depressive symptoms.

The brain's intrinsic activity plays a fundamental role in its function. In normal conditions this activity is responsive to behavioural context, changing as an individual switches between directed tasks and task-free conditions. A key feature of such changes is the movement of the brain between corresponding critical and sub-critical states, with these dynamics supporting efficient cognitive processing. Breakdowns in processing efficiency can occur, however, in brain disorders such as depression. It was therefore hypothesised that depressive symptoms would be related to reduced intrinsic activity responsiveness to changes in behavioural state. This was tested in a mixed group of major depressive disorder patients (n=26) and healthy participants (n=37) by measuring intrinsic EEG activity temporal structure, quantified with detrended fluctuation analysis (DFA), in eyes-closed (EC) and eyes-open task-free states and contrasting between the conditions. The degree to which DFA values changed between the states was found to correlate negatively with depressive symptoms. DFA values did not differ between states in those with higher symptom levels, meaning that the brain remained in a less flexible sub-critical condition. This sub-critical condition in the EC state was further found to correlate with levels of maladaptive rumination. This may reflect a general cognitive inflexibility resulting from a lack in neural activity reactivity that may predispose people to overly engage in self-directed attention. These results provide an initial link between intrinsic activity reactivity and psychological features found in psychiatric disorders.

Non-linear analysis of heart rate variability for evaluating the acute effects of caffeinated beverages in young adults.

Caffeinated beverages are the most consumed substances in the world. High rate of uptake of these beverages leads to various cardiovascular disorders ranging from palpitations to coronary failure. The objective of the study is to ascertain how the complexity parameters of heart rate variability are affected by acute consumption of caffeinated beverages in young adults.Electrocardiogram measurements were performed before consuming drinks. After consuming the drinks, measurements were done again at 30 minutes and 60 minutes. Heart rate variability signals were acquired from electrocardiogram signals. Also, the signals were reconstructed in the phase space and largest Lyapunov exponent, correlation dimension, approximate entropy, and detrended fluctuation analysis values were calculated.Heart rate increased for energy drink and cola groups but not in coffee group. Non-linear parameter values of energy drink, coffee, and cola group are increased within 60 minutes after drink consumption. This change is statistically significant just for energy drink group.Energy drink consumption increases the complexity of the cardiovascular system in young adults significantly. Coffee and cola consumption have no significant effect on the non-linear parameters of heart rate variability.

Effect of sampling frequency on fractal fluctuations during treadmill walking.

The temporal dynamics of stride-to-stride fluctuations in steady-state walking reveal important information about locomotor control and can be quantified using so-called fractal analyses, notably the detrended fluctuation analysis (DFA). Gait dynamics are often collected during treadmill walking using 3-D motion capture to identify gait events from kinematic data. The sampling frequency of motion capture systems may impact the precision of event detection and consequently impact the quantification of stride-to-stride variability. This study aimed i) to determine if collecting multiple walking trials with different sampling frequency affects DFA values of spatiotemporal parameters during treadmill walking, and ii) to determine the reliability of DFA values across downsampled conditions. Seventeen healthy young adults walked on a treadmill while their gait dynamics was captured using different sampling frequency (60, 120 and 240 Hz) in each condition. We also compared data from the highest sampling frequency to downsampled versions of itself. We applied DFA to the following time series: step length, time and speed, and stride length, time and speed. Reliability between experimental conditions and between downsampled conditions were measured with 1) intraclass correlation estimates and their 95% confident intervals, calculated based on a single-measurement, absolute-agreement, two-way mixed-effects model (ICC 3,1), and 2) Bland-Altman bias and limits of agreement. Both analyses revealed a poor reliability of DFA results between conditions using different sampling frequencies, but a relatively good reliability between original and downsampled spatiotemporal variables. Collectively, our results suggest that using sampling frequencies of 120 Hz or 240 Hz provide similar results, but that using 60 Hz may alter DFA values. We recommend that gait kinematics should be collected at around 120 Hz, which provides a compromise between event detection accuracy and processing time.

Movement variability emerges in gait as adaptation to task constraints in dynamic environments

Background: Motor variability has been related to motor control playing a functional role in human adaptive behaviours. However, the direction of the relationship between variability and motor control can be unclear. The specific relations that exist between task constraints and movement (re)organization could explain some of this controversy.Research question: This study sought to understand whether manipulation of task constraints result in changes in the magnitude or structure of motor system variability observed in a basic walking task. We also investigated the relationship between performance in achieving task goals and the structure of motor variability.Methods: Twenty volunteers walked around a circular track with binary combinations of 3 task constraints, providing 8 conditions. The manipulated task constraints were: 1) track width; 2) surface stiffness; and 3), walking direction. Performance was analysed using standard deviation (SD) of sacral displacement and its mean velocity (MV). Fuzzy Entropy (FE) and Detrended Fluctuation Analysis (DFA) were used to assess the kinematic variability structure.Results: Individuals showed lower SD and MV walking on the narrower track. These changes were also followed by higher DFA values, indicating a more auto-correlated structure of variability. The foam surface was also associated with an increase in amplitude, velocity and irregularity (FE) of movement.Significance: Results of this study describe how specific task constraints, such as the width of the walking track and the surface stiffness, shape emergent movement coordination patterns as participants search for functional information from the environment to regulate performance behaviors. Changes in variability structure could reveal the search for adaptive strategies during walking. Smaller movement fluctuations and higher velocity in gait patterns are related to greater irregularity and lower autocorrelation in the kinematic variability structure, demonstrating that a specific relationship emerges between system variability and movement performance, which is driven by task constraints.

The detrended fluctuation and cross-correlation analysis of EEG signals

The detrended fluctuation analysis (DFA) and detrended cross-correlation analysis (DCCA) are the widely used methods for analysis of non-stationary time series. The detrended fluctuation and cross-correlation analysis of the EEG signals pre- and post-meditation (mindfulness) intervention are compared. It is observed that the EEG data obtained from seven subjects out of total 11 subjects shows reduction in the DFA and DCCA exponent values. The reduction in DFA exponent value represents the lower intrinsic fluctuation in the EEG time series, which is a measure of better (higher) complexity of these vital rhythms. The reduced DFA exponent values after 8-weeks of focused attention (mindfulness) meditation practice in more number of subjects indicate that the meditation practice enhances the ability to handle complexity. The detrended cross-correlation analysis (DCCA) of EEG signals shows that the EEG signals of electrode pair of two brain lobe hemispheres obeys the power-law relationship, and the DCCA exponent is reduced in value after the meditation intervention. The reduced DFA and DCCA exponents indicate improved neuronal functioning of these subjects.

Single channel EEG analysis for detection of depression

Abstract Purpose This study is aimed at finding a simple method for detection of depression based on the analysis of single channel short-term EEG signals. Materials and methods The accuracy of linear, spectral asymmetry index (SASI), and nonlinear, detrended fluctuation analysis (DFA), methods for differentiating depressive and healthy subjects was compared. The eyes closed EEG was recorded from 18 common reference (Cz) channels for 34 subjects (17 depressive and 17 control). The signals were stored at 400 Hz sampling frequency and digitally filtered with cutoff frequencies at 0.5 Hz and at 40 Hz. The first 5 min of each recording was selected for further analysis. Results The experiments indicated maximum difference for SASI values in channel Pz and for DFA values in channels Pz and O2. Therefore, channel Pz was selected for comparison of two methods. The results of statistical analysis show that SASI values are significantly higher for depressive than for control group (p = 3.577e–05), while DFA values are significantly lower for depressive group (p = 0.033). SASI has superior discrimination ability with classification accuracy of 76.5%, while the classification accuracy of DFA was 70.6%. Linear combination of SASI and DFA resulted in 91.2% classification accuracy. Conclusions Our results demonstrate that the analysis of single channel signal can provide high accuracy of differentiation depression EEG.

Variations in task constraints shape emergent performance outcomes and complexity levels in balancing.

This study investigated the extent to which specific interacting constraints of performance might increase or decrease the emergent complexity in a movement system, and whether this could affect the relationship between observed movement variability and the central nervous system's capacity to adapt to perturbations during balancing. Fifty-two healthy volunteers performed eight trials where different performance constraints were manipulated: task difficulty (three levels) and visual biofeedback conditions (with and without the center of pressure (COP) displacement and a target displayed). Balance performance was assessed using COP-based measures: mean velocity magnitude (MVM) and bivariate variable error (BVE). To assess the complexity of COP, fuzzy entropy (FE) and detrended fluctuation analysis (DFA) were computed. ANOVAs showed that MVM and BVE increased when task difficulty increased. During biofeedback conditions, individuals showed higher MVM but lower BVE at the easiest level of task difficulty. Overall, higher FE and lower DFA values were observed when biofeedback was available. On the other hand, FE reduced and DFA increased as difficulty level increased, in the presence of biofeedback. However, when biofeedback was not available, the opposite trend in FE and DFA values was observed. Regardless of changes to task constraints and the variable investigated, balance performance was positively related to complexity in every condition. Data revealed how specificity of task constraints can result in an increase or decrease in complexity emerging in a neurobiological system during balance performance.

Glucose series complexity in hypertensive patients

Nonlinear methods have been applied to the analysis of biological signals. Complexity analysis of glucose time series may be a useful tool for the study of the initial phases of glucoregulatory dysfunction. This observational, cross-sectional study was performed in patients with essential hypertension. Glucose complexity was measured with detrended fluctuation analysis (DFA), and glucose variability was measured by the mean amplitudes of glycemic excursion (MAGE). We included 91 patients with a mean age of 59 ± 10 years. We found significant correlations for the number of metabolic syndrome (MS)-defining criteria with DFA (r = 0.233, P = .026) and MAGE (r = 0.396, P < .0001). DFA differed significantly between patients who complied with MS and those who did not (1.44 vs. 1.39, P = .018). The MAGE (f = 5.3, P = .006), diastolic blood pressures (f = 4.1, P = .018), and homeostasis model assessment indices (f = 4.2, P = .018) differed between the DFA tertiles. Multivariate analysis revealed that the only independent determinants of the DFA values were MAGE (β coefficient = 0.002, 95% confidence interval: 0.001–0.004, P = .001) and abdominal circumference (β coefficient = 0.002, 95% confidence interval: 0.000015–0.004, P = .048). In our population, DFA was associated with MS and a number of MS criteria. Complexity analysis seemed to be capable of detecting differences in variables that are arguably related to the risk of the development of type 2 diabetes.

Quantitative Evaluation of Movement Disorders by Specified Analysis According to Actigraphy Records

Aim: To evaluate whether the specified analytical objective scale represents disease severity for neurological movement disorders according to the physical activity of the patients. Methods: Eighty-one patients with Parkinsonʹs disease (PD) and sixty-one patients with acute cerebral infarction (ACI) combined with upper limb motor function disorder at the Shuguang hospital, affiliated with the Shanghai TCM university. PD patients and ACI patients were treated according to the international medication guiding principle for PD or ACI respectively. We analysed the power-law exponent (PLE) and the detrended fluctuation analysis (DFA) of the actigraphy records, which were taken on 2 occasions (before drug administration for two groups, 24-38 days for PD patients and 28 days for ACI patients). Efficacy was evaluated by the Unified Parkinson Disease Rating Scale (UPDRS) for PD and by Fugl-Meyer Assessment (FMA) and the Functional Independence Measure (FIM) for ACI patients. We also evaluated the correlation between any changed rates of UPDRS scores and PLE for PD patients, and FMA and FIM scores and DFA for ACI patients. Results: The UPDRS scores and PLE values for PD, and the FMA and FIM scores with the DFA score for ACI were improved after the drug administration; they yielded a linear correlation coefficient of 0.699 and 0.823 between the improvement rates of the total UPDRS scores and the PLE values, and between the UPDRS Part III score and the PLE values, while it yielded a linear correlation coefficient of 0.638 and 0.712 between the improvement rates of the FMA scores and the DFA, and the FIM scores and the DFA respectively. There was no correlation between the UPDRS scores and the DFA values for the PD patients or between the FIM score or the FMA score and the PLE values for ACI patients. Conclusion: Actigraphy records and the analysis of its PLE or DFA might provide useful objective and specific information for controlling PD or ACI patients and for monitoring drug administration respectively.

Nonlinear Analysis of Ambulatory Activity Patterns in Community-Dwelling Older Adults

The natural ambulatory activity patterns of older adults are not well understood. User-worn monitors illuminate patterns of ambulatory activity and generate data suitable for analysis using measures derived from nonlinear dynamics. Ambulatory activity data were collected continuously from 157 community-dwelling older adults for 2 weeks. Participants were separated post hoc into groups based on the mean number of steps per day: highly active (steps > or = 10,000), moderately active (5,000 < or = steps < 10,000 steps), and inactive (steps <5,000 steps). Detrended fluctuation analysis (DFA), entropy rate (ER), and approximate entropy (ApEn) were used to examine the complexity of daily time series composed of 1-minute step count values. Coefficient of variation was used to examine time series variability. Between-group differences for each parameter were evaluated using analysis of variance. All groups displayed patterns of fluctuating step count values containing complex temporal structure. DFA, ER, and ApEn parameter values increased monotonically and significantly with increasing activity level (p < .001). The variability of step count fluctuations did not differ among groups. Highly active participants had more complex patterns of ambulatory activity than less active participants. The results supported the idea that, in addition to the volume of activity produced by an individual, patterns of ambulatory activity contain unique information that shows promise for offering insights into walking behavior associated with healthy aging.