A comparative analysis of spectral exponent estimation techniques for 1/f(β) processes with applications to the analysis of stride interval time series

Aperiodic and Hurst EEG exponents across early human brain development: A systematic review

In electroencephalographic (EEG) data, power-frequency slope exponents (1/f_β) can provide non-invasive markers of in vivo neural activity excitation-inhibition (E:I) balance. E:I balance may be altered in neurodevelopmental conditions; hence, understanding how 1/fβ evolves across infancy/childhood has implications for developing early assessments/interventions. This systematic review (PROSPERO-ID: CRD42023363294) explored the early maturation (0-26 yrs) of resting-state EEG 1/f measures (aperiodic [AE], power law [PLE] and Hurst [HE] exponents), including studies containing ≥1 1/f measures and ≥10 typically developing participants. Five databases (including Embase and Scopus) were searched during March 2023. Forty-two studies were identified (Nparticipants=3478). Risk of bias was assessed using the Quality Assessment with Diverse Studies tool. Narrative synthesis of HE data suggests non-stationary EEG activity occurs throughout development. Age-related trends were complex, with rapid decreases in AEs during infancy and heterogenous changes thereafter. Regionally, AE maxima shifted developmentally, potentially reflecting spatial trends in maturing brain connectivity. This work highlights the importance of further characterising the development of 1/f measures to better understand how E:I balance shapes brain and cognitive development.

Magnetic resonance insights into the heterogeneous, fractal-like kinetics of chemically recyclable polymers

Moving toward a circular plastics economy is a vital aspect of global resource management. Chemical recycling of plastics ensures that high-value monomers can be recovered from depolymerized plastic waste, thus enabling circular manufacturing. However, to increase chemical recycling throughput in materials recovery facilities, the present understanding of polymer transport, diffusion, swelling, and heterogeneous deconstruction kinetics must be systematized to allow industrial-scale process design, spanning molecular to macroscopic regimes. To develop a framework for designing depolymerization processes, we examined acidolysis of circular polydiketoenamine elastomers. We used magnetic resonance to monitor spatially resolved observables in situ and then evaluated these data with a fractal method that treats nonlinear depolymerization kinetics. This approach delineated the roles played by network architecture and reaction medium on depolymerization outcomes, yielding parameters that facilitate comparisons between bulk processes. These streamlined methods to investigate polymer hydrolysis kinetics portend a general strategy for implementing chemical recycling on an industrial scale.

Fluctuations in Upper and Lower Body Movement during Walking in Normal Pressure Hydrocephalus and Parkinson's Disease Assessed by Motion Capture with a Smartphone Application, TDPT-GT

We aimed to capture the fluctuations in the dynamics of body positions and find the characteristics of them in patients with idiopathic normal pressure hydrocephalus (iNPH) and Parkinson's disease (PD). With the motion-capture application (TDPT-GT) generating 30 Hz coordinates at 27 points on the body, walking in a circle 1 m in diameter was recorded for 23 of iNPH, 23 of PD, and 92 controls. For 128 frames of calculated distances from the navel to the other points, after the Fourier transforms, the slopes (the representatives of fractality) were obtained from the graph plotting the power spectral density against the frequency in log-log coordinates. Differences in the average slopes were tested by one-way ANOVA and multiple comparisons between every two groups. A decrease in the absolute slope value indicates a departure from the 1/f noise characteristic observed in healthy variations. Significant differences in the patient groups and controls were found in all body positions, where patients always showed smaller absolute values. Our system could measure the whole body's movement and temporal variations during walking. The impaired fluctuations of body movement in the upper and lower body may contribute to gait and balance disorders in patients.

Better than DFA? A Bayesian Method for Estimating the Hurst Exponent in Behavioral Sciences

Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical technique used to evaluate the strength of long-range correlations in empirical time series in terms of the Hurst exponent, H. Specifically, DFA quantifies the linear regression slope in log-log coordinates representing the relationship between the time series' variability and the number of timescales over which this variability is computed. We compared the performance of two methods of fractal analysis-the current gold standard, DFA, and a Bayesian method that is not currently well-known in behavioral sciences: the Hurst-Kolmogorov (HK) method-in estimating the Hurst exponent of synthetic and empirical time series. Simulations demonstrate that the HK method consistently outperforms DFA in three important ways. The HK method: (i) accurately assesses long-range correlations when the measurement time series is short, (ii) shows minimal dispersion about the central tendency, and (iii) yields a point estimate that does not depend on the length of the measurement time series or its underlying Hurst exponent. Comparing the two methods using empirical time series from multiple settings further supports these findings. We conclude that applying DFA to synthetic time series and empirical time series during brief trials is unreliable and encourage the systematic application of the HK method to assess the Hurst exponent of empirical time series in behavioral sciences.

On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

Measuring the temporal complexity of functional MRI (fMRI) time series is one approach to assess how brain activity changes over time. In fact, hemodynamic response of the brain is known to exhibit critical behaviour at the edge between order and disorder. In this study, we aimed to revisit the spatial distribution of temporal complexity in resting state and task fMRI of 100 unrelated subjects from the Human Connectome Project (HCP). First, we compared two common choices of complexity measures, i.e., Hurst exponent and multiscale entropy, and observed a high spatial similarity between them. Second, we considered four tasks in the HCP dataset (Language, Motor, Social, and Working Memory) and found high task-specific complexity, even when the task design was regressed out. For the significance thresholding of brain complexity maps, we used a statistical framework based on graph signal processing that incorporates the structural connectome to develop the null distributions of fMRI complexity. The results suggest that the frontoparietal, dorsal attention, visual, and default mode networks represent stronger complex behaviour than the rest of the brain, irrespective of the task engagement. In sum, the findings support the hypothesis of fMRI temporal complexity as a marker of cognition.

Examining feedback mechanisms of postural control in Chiari Malformation by average wavelet coefficient decomposition and the Hurst exponent

BACKGROUND

Chiari Malformation (CM) is a congenital disorder occurring when the cerebellar tonsils descend into the foramen magnum, inhibiting cerebrospinal fluid (CSF) flow, causing headaches, dizziness, difficulty swallowing, muscle weakness, and loss of neuromuscular coordination. While there is no cure, surgical decompression of the hindbrain is used to alleviate symptoms. Loss of postural control is a main symptom reported by these patients; however, no study has examined postural stability in this cohort of patients.

RESEARCH QUESTION

Do patients with CM exhibit impaired postural stability compared to healthy controls?.

METHODS

Twelve female participants diagnosed with CM performed a postural stability test where six participants had undergone decompression (CM-D) surgery while six had not (CM-ND). Participants stood in Romberg fashion on an AMTI force plate according to an IRB-approved protocol. Postural stability measures were quantified by computing Hurst exponents. These values were determined from the Average Wavelet Coefficient method using a level 12 Symlet-2 wavelet to analyze anterior-posterior (AP) center-ofpressure (COP) trajectories in MATLAB. Identical procedures and analyses were performed on healthy control participants with no known neuromuscular disorders.

RESULTS

CM participants displayed significantly impaired postural stability compared to healthy controls (p = 0.0002). CM-D participants displayed significantly impaired postural stability compared to CM-ND (p = 0.002). CM-D and CM-ND both displayed significantly impaired postural stability compared to controls (p < 0.0001 and p < 0.003, respectively).

SIGNIFICANCE

Loss of postural stability is considered a main symptom of CM, however no study has previously quantified human postural control in this cohort of patients. Quantifying this relationship can provide further insight to neurologists studying the disorder and to therapists planning rehabilitation and pain relief methods.

Multifractal Cross Correlation Analysis of Agro-Meteorological Datasets (Including Reference Evapotranspiration) of California, United States

The multifractal properties of six acknowledged agro-meteorological parameters, such as reference evapotranspiration (ET0), wind speed (U), incoming solar radiation (SR), air temperature (T), air pressure (P), and relative air humidity (RH) of five stations in California, USA were examined. The investigation of multifractality of datasets from stations with differing terrain conditions using the Multifractal Detrended Fluctuation Analysis (MFDFA) showed the existence of a long-term persistence and multifractality irrespective of the location. The scaling exponents of SR and T time series are found to be higher for stations with higher altitudes. Subsequently, this study proposed using the novel multifractal cross correlation (MFCCA) method to examine the multiscale-multifractal correlations properties between ET0 and other investigated variables. The MFCCA could successfully capture the scale dependent association of different variables and the dynamics in the nature of their associations from weekly to inter-annual time scales. The multifractal exponents of P and U are consistently lower than the exponents of ET0, irrespective of station location. This study found that joint scaling exponent was nearly the average of scaling exponents of individual series in different pairs of variables. Additionally, the α-values of joint multifractal spectrum were lower than the α values of both of the individual spectra, validating two universal properties in the MFCCA studies for agro-meteorological time series. The temporal evolution of cross-correlation determined by the MFCCA successfully captured the dynamics in the nature of associations in the P-ET0 link.

Lipid Hydroperoxidation Effect on the Dynamical Evolution of the Conductance Process in Bilayer Lipid Membranes: A Condition Toward Criticality

Cell membranes are one of the main targets of oxidative processes mediated by reactive oxygen species (ROS). These chemical species interact with unsaturated fatty acids of membrane lipids, triggering an autocatalytic chain reaction, producing lipid hydroperoxides (LOOHs) as the first relatively stable product of the ROS-mediated lipid peroxidation (LPO) process. Numerous biophysical and computational studies have been carried out to elucidate the LPO impact on the structure and organization of lipid membranes. However, although LOOHs are the major primary product of LPO of polyunsaturated fatty acids (PUFAs), to the best of our knowledge, there is no experimental evidence on the effects of the accumulation of these LPO byproducts on the electrical properties and the underlying dynamics of lipid membranes. In this work, bilayer lipid membranes (BLMs) containing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocoline (POPC) with increasing hydroperoxidized POPC (POPC-OOH) molar proportions (BLM_PC/PC-OOH) are used as model membranes to investigate the effect of LOOH-mediated LPO propagation on the electrical behavior of lipid bilayers. Voltage-induced ion current signals are analyzed by applying the fractal method of power spectrum density (PSD) analysis. We experimentally prove that, when certain LOOH concentration and energy threshold are overcome, oxidized membranes evolve toward a critical state characterized by the emergence of non-linear electrical behavior dynamics and the pore-type metastable structures formation. PSD analysis shows that temporal dynamics exhibiting "white" noise (non-time correlations) reflects a linear relationship between the input and output signals, while long-term correlations (β > 0.5) begin to be observed closely to the transition (critical point) from linear (Ohmic) to nonlinear (non-Ohmic) behavior. The generation of lipid pores appears to arise as an optimized energy dissipation mechanism based on the system's ability to self-organize and generate ordered structures capable of dissipating energy gradients more efficiently under stressful oxidative conditions.

Applying fMRI complexity analyses to the single subject: a case study for proposed neurodiagnostics

Nonlinear dynamic tools have been statistically validated at the group level to identify subtle differences in system wide regulation of brain meso-circuits, often increasing clinical sensitivity over conventional analyses alone. We explored the feasibility of extracting information at the single-subject level, illustrating two pairs of healthy individuals with psychological differences in stress reactivity. We applied statistical and nonlinear dynamic tools to capture key characteristics of the prefrontal-limbic loop. We compared single subject results with statistical results for the larger group. We concluded that complexity analyses may identify important differences at the single-subject level, supporting their potential towards neurodiagnostic applications.

Most suitable mother wavelet for the analysis of fractal properties of stride interval time series via the average wavelet coefficient method

Human gait is a complex interaction of many nonlinear systems and stride intervals exhibiting self-similarity over long time scales that can be modeled as a fractal process. The scaling exponent represents the fractal degree and can be interpreted as a "biomarker" of relative diseases. The previous study showed that the average wavelet method provides the most accurate results to estimate this scaling exponent when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for the average wavelet method. This paper presents a comparative numerical analysis of 16 mother wavelets using simulated and real fractal signals. Simulated fractal signals were generated under varying signal lengths and scaling exponents that indicate a range of physiologically conceivable fractal signals. The five candidates were chosen due to their good performance on the mean square error test for both short and long signals. Next, we comparatively analyzed these five mother wavelets for physiologically relevant stride time series lengths. Our analysis showed that the symlet 2 mother wavelet provides a low mean square error and low variance for long time intervals and relatively low errors for short signal lengths. It can be considered as the most suitable mother function without the burden of considering the signal length.

Nonlinear temperature effects on multifractal complexity of metabolic rate of mice

Complex physiological dynamics have been argued to be a signature of healthy physiological function. Here we test whether the complexity of metabolic rate fluctuations in small endotherms decreases with lower environmental temperatures. To do so, we examine the multifractal temporal scaling properties of the rate of change in oxygen consumption r(VO₂), in the laboratory mouse Mus musculus, assessing their long range correlation properties across seven different environmental temperatures, ranging from 0 °C to 30 °C. To do so, we applied multifractal detrended fluctuation analysis (MF-DFA), finding that r(VO₂) fluctuations show two scaling regimes. For small time scales below the crossover time (approximately 10² s), either monofractal or weak multifractal dynamics are observed depending on whether T_a < 15 °C or T_a > 15 °C respectively. For larger time scales, r(VO₂) fluctuations are characterized by an asymptotic scaling exponent that indicates multifractal anti-persistent or uncorrelated dynamics. For both scaling regimes, a generalization of the multiplicative cascade model provides very good fits for the Renyi exponents τ(q), showing that the infinite number of exponents h(q) can be described by only two independent parameters, a and b. We also show that the long-range correlation structure of r(VO₂) time series differs from randomly shuffled series, and may not be explained as an artifact of stochastic sampling of a linear frequency spectrum. These results show that metabolic rate dynamics in a well studied micro-endotherm are consistent with a highly non-linear feedback control system.

Assessing interactions among multiple physiological systems during walking outside a laboratory: An Android based gait monitor

Gait function is traditionally assessed using well-lit, unobstructed walkways with minimal distractions. In patients with subclinical physiological abnormalities, these conditions may not provide enough stress on their ability to adapt to walking. The introduction of challenging walking conditions in gait can induce responses in physiological systems in addition to the locomotor system. There is a need for a device that is capable of monitoring multiple physiological systems in various walking conditions. To address this need, an Android-based gait-monitoring device was developed that enabled the recording of a patient's physiological systems during walking. The gait-monitoring device was tested during self-regulated overground walking sessions of fifteen healthy subjects that included 6 females and 9 males aged 18-35 years. The gait-monitoring device measures the patient's stride interval, acceleration, electrocardiogram, skin conductance and respiratory rate. The data is stored on an Android phone and is analyzed offline through the extraction of features in the time, frequency and time-frequency domains. The analysis of the data depicted multisystem physiological interactions during overground walking in healthy subjects. These interactions included locomotion-electrodermal, locomotion-respiratory and cardiolocomotion couplings. The current results depicting strong interactions between the locomotion system and the other considered systems (i.e., electrodermal, respiratory and cardiovascular systems) warrant further investigation into multisystem interactions during walking, particularly in challenging walking conditions with older adults.

Cognitive tasks during walking affect cerebral blood flow signal features in middle cerebral arteries and their correlation to gait characteristics

Gait is a complex process involving both cognitive and sensory ability and is strongly impacted by the environment. In this paper, we propose to study of the impact of a cognitive task during gait on the cerebral blood flow velocity, the blood flow signal features and the correlation of gait and blood flow features through a dual task methodology. Both cerebral blood flow velocity and gait characteristics of eleven participants with no history of brain or gait conditions were recorded using transcranial Doppler on mid-cerebral artery while on a treadmill. The cognitive task was induced by a backward counting starting from 10,000 with decrement of 7. Central blood flow velocity raw and envelope features were extracted in both time, frequency and time-scale domain; information-theoretic metrics were also extracted and statistical significances were inspected. A similar feature extraction was performed on the stride interval signal. Statistical differences between the cognitive and baseline trials, between the left and right mid-cerebral arteries signals and the impact of the antropometric variables where studied using linear mixed models. No statistical differences were found between the left and right mid-cerebral arteries flows or the baseline and cognitive state gait features, while statistical differences for specific features were measured between cognitive and baseline states. These statistical differences found between the baseline and cognitive states show that cognitive process has an impact on the cerebral activity during walking. The state was found to have an impact on the correlation between the gait and blood flow features.

How to Sync to the Beat of a Persistent Fractal Metronome without Falling Off the Treadmill?

In rehabilitation, rhythmic acoustic cues are often used to improve gait. However, stride-time fluctuations become anti-persistent with such pacing, thereby deviating from the characteristic persistent long-range correlations in stride times of self-paced walking healthy adults. Recent studies therefore experimented with metronomes with persistence in interbeat intervals and successfully evoked persistent stride-time fluctuations. The objective of this study was to examine how participants couple their gait to a persistent metronome, evoking persistently longer or shorter stride times over multiple consecutive strides, without wandering off the treadmill. Twelve healthy participants walked on a treadmill in self-paced, isochronously paced and non-isochronously paced conditions, the latter with anti-persistent, uncorrelated and persistent correlations in interbeat intervals. Stride-to-stride fluctuations of stride times, stride lengths and stride speeds were assessed with detrended fluctuation analysis, in conjunction with an examination of the coupling between stride times and stride lengths. Stride-speed fluctuations were anti-persistent for all conditions. Stride-time and stride-length fluctuations were persistent for self-paced walking and anti-persistent for isochronous pacing. Both stride times and stride lengths changed from anti-persistence to persistence over the four non-isochronous metronome conditions, accompanied by an increasingly stronger coupling between these gait parameters, with peak values for the persistent metronomes. These results revealed that participants were able to follow the beat of a persistent metronome without falling off the treadmill by strongly coupling stride-length fluctuations to the stride-time fluctuations elicited by persistent metronomes, so as to prevent large positional displacements along the treadmill. For self-paced walking, in contrast, this coupling was very weak. In combination, these results challenge the premise that persistent metronomes in gait rehabilitation would evoke stride-to-stride dynamics reminiscent of self-paced walking healthy adults. Future studies are recommended to include an analysis of the interrelation between stride times and stride lengths in addition to the correlational structure of either one in isolation.

The influence of auditory-motor coupling on fractal dynamics in human gait

Humans exhibit an innate ability to synchronize their movements to music. The field of gait rehabilitation has sought to capitalize on this phenomenon by invoking patients to walk in time to rhythmic auditory cues with a view to improving pathological gait. However, the temporal structure of the auditory cue, and hence the temporal structure of the target behavior has not been sufficiently explored. This study reveals the plasticity of auditory-motor coupling in human walking in relation to 'complex' auditory cues. The authors demonstrate that auditory-motor coupling can be driven by different coloured auditory noise signals (e.g. white, brown), shifting the fractal temporal structure of gait dynamics towards the statistical properties of the signals used. This adaptive capability observed in whole-body movement, could potentially be harnessed for targeted neuromuscular rehabilitation in patient groups, depending on the specific treatment goal.