Detrended fluctuation analysis in a simple spreadsheet as a tool for teaching fractal physiology

Running gait produces long range correlations: A systematic review

BACKGROUND

Walking and running are common forms of locomotion, both of which exhibit variability over many gait cycles. Many studies have investigated the patterns generated from that ebb and flow, and a large proportion suggests human gait exhibits Long Range Correlations (LRCs). LRCs refer to the observation that healthy gait characteristic, like stride times, are positively correlated to themselves over time. Literature on LRCs in walking gait is well known but less attention has been given to LRCs in running gait.

RESEARCH QUESTION

What is the state of the art concerning LRCs in running gait?

METHODS

We conducted a systematic review to identify the typical LRC patterns present in human running gait, in addition to disease, injury, and running surface effects on LRCs. Inclusion criteria were human subjects, running related experiments, computed LRCs, and experimental design. Exclusion criteria were studies on animals, non-humans, walking only, non-running, non-LRC analysis, and non-experiments.

RESULTS

The initial search returned 536 articles. After review and deliberation, our review included 26 articles. Almost every article produced strong evidence for LRCs apparent in running gait and in all running surfaces. Additionally, LRCs tended to decrease due to fatigue, past injury, increased load carriage and seem to be lowest at preferred running speed on a treadmill. No studies investigated disease effects on LRCs in running gait.

SIGNIFICANCE

LRCs seem to increase with deviations away from preferred running speed. Previously injured runners produced decreased LRCs compared to non-injured runners. LRCs also tended to decrease due to an increase in fatigue rate, which has been associated with increased injury rate. Lastly, there is a need for research on the typical LRCs in an overground environment, for which the typical LRCs found in a treadmill environment may or may not transfer.

Correlation between heart rate variability and polysomnography-derived scores of obstructive sleep apnea

Obstructive sleep apnea (OSA) is one of the most common sleep disorders and affects nearly a billion people worldwide. Furthermore, it is estimated that many patients with OSA are underdiagnosed, which contributes to the development of comorbidities, such as cardiac autonomic imbalance, leading to high cardiac risk. Heart rate variability (HRV) is a non-invasive, widely used approach to evaluating neural control of the heart. This study evaluates the relationship between HRV indices and the presence and severity of OSA. We hypothesize that HRV, especially the nonlinear methods, can serve as an easy-to-collect marker for OSA early risk stratification. Polysomnography (PSG) exams of 157 patients were classified into four groups: OSA-free (N = 26), OSA-mild (N = 39), OSA-moderate (N = 37), and OSA-severe (N = 55). The electrocardiogram was extracted from the PSG recordings, and a 15-min beat-by-beat series of RR intervals were generated every hour during the first 6 h of sleep. Linear and nonlinear HRV approaches were employed to calculate 32 indices of HRV. Specifically, time- and frequency-domain, symbolic analysis, entropy measures, heart rate fragmentation, acceleration and deceleration capacities, asymmetry measures, and fractal analysis. Results with indices of sympathovagal balance provided support to reinforce previous knowledge that patients with OSA have sympathetic overactivity. Nonlinear indices showed that HRV dynamics of patients with OSA display a loss of physiologic complexity that could contribute to their higher risk of development of cardiovascular disease. Moreover, many HRV indices were found to be linked with clinical scores of PSG. Therefore, a complete set of HRV indices, especially the ones obtained by the nonlinear approaches, can bring valuable information about the presence and severity of OSA, suggesting that HRV can be helpful for in a quick diagnosis of OSA, and supporting early interventions that could potentially reduce the development of comorbidities.

Adaptive Capacities and Complexity of Heart Rate Variability in Patients With Chronic Obstructive Pulmonary Disease Throughout Pulmonary Rehabilitation

Introduction

The complexity of bio-signals, like R-R intervals, is considered a reflection of the organism's capacity to adapt. However, this association still remains to be consolidated. We investigated whether the complexity of R-R intervals at rest and during perturbation [6-minute walking test (6MWT)], yielded information regarding adaptive capacities in Chronic Obstructive Pulmonary Disease (COPD) patients during pulmonary rehabilitation (PR).

Methods

In total, 23 COPD patients (64 ± 8 years, with forced expiratory volume in 1 s of 55 ± 19% predicted) were tested three times at the start (T1), middle (T2), and end (T3) of 4 weeks PR. Each time, R-R intervals were measured at rest and during 6MWT. The complexity of R-R intervals was assessed by evenly spaced Detrended Fluctuations Analysis and evaluated by the fractal exponent α and deviation from maximal complexity |1-α|.

Results

The 6MWT distance was significantly increased at T2 and T3 compared to T1. Neither α nor |1-α| at rest and during perturbation significantly changed throughout PR, nor were they consistently associated with 6MWT distances at each time. Throughout the PR program, complexity during the 6MWT was significantly lower compared to the rest. The level of α during 6MWT at T1 was positively correlated with the improvement of the 6MWT distance throughout the PR program.

Discussion

Reduced complexity in COPD patients during acute perturbation at the beginning of PR supports a decreased improvement of the 6MWT distance throughout PR. This result seems consistent with the notion that the complexity reflects the patients' adaptive capacities and could therefore become a clinical indicator in an applied perspective.

Multifractal Dynamics in Executive Control When Adapting to Concurrent Motor Tasks

There is some evidence that an improved understanding of executive control in the human movement system could be gained from explorations based on scale-free, fractal analysis of cyclic motor time series. Such analyses capture non-linear fractal dynamics in temporal fluctuations of motor instances that are believed to reflect how executive control enlist a coordination of multiple interactions across temporal scales between the brain, the body and the task environment, an essential architecture for adaptation. Here by recruiting elite rugby players with high motor skills and submitting them to the execution of rhythmic motor tasks involving legs and arms concurrently, the main attempt was to build on the multifractal formalism of movement control to show a marginal need of effective adaptation in concurrent tasks, and a preserved adaptability despite complexified motor execution. The present study applied a multifractal analytical approach to experimental time series and added surrogate data testing based on shuffled, ARFIMA, Davies&Harte and phase-randomized surrogates, for assessing scale-free behavior in repeated motor time series obtained while combining cycling with finger tapping and with circling. Single-tasking was analyzed comparatively. A focus-based multifractal-DFA approach provided Hurst exponents (H) of individual time series over a range of statistical moments H(q), q = [−15 15]. H(2) quantified monofractality and H(-15)-H(15) provided an index of multifractality. Despite concurrent tasking, participants showed great capacity to keep the target rhythm. Surrogate data testing showed reasonable reliability in using multifractal formalism to decipher movement control behavior. The global (i.e., monofractal) behavior in single-tasks did not change when adapting to dual-task. Multifractality dominated in cycling and did not change when cycling was challenged by upper limb movements. Likewise, tapping and circling behaviors were preserved despite concurrent cycling. It is concluded that the coordinated executive control when adapting to dual-motor tasking is not modified in people having developed great motor skills through physical training. Executive control likely emerged from multiplicative interactions across temporal scales which puts emphasis on multifractal approaches of the movement system to get critical cues on adaptation. Extending such analyses to less skilled people is appealing in the context of exploring healthy and diseased movement systems.

Test-Retest Reliability and the Effects of Walking Speed on Stride Time Variability During Continuous, Overground Walking in Healthy Young Adults

Studies have investigated the reliability and effect of walking speed on stride time variability during walking trials performed on a treadmill. The objective of this study was to investigate the reliability of stride time variability and the effect of walking speed on stride time variability, during continuous, overground walking in healthy young adults. Participants completed: (1) 2 walking trials at their preferred walking speed on 1 day and another trial 2 to 4 days later and (2) 1 trial at their preferred walking speed, 1 trial approximately 20% to 25% faster than their preferred walking speed, and 1 trial approximately 20% to 25% slower than their preferred walking speed on a separate day. Data from a waist-mounted accelerometer were used to determine the consecutive stride times for each trial. The reliability of stride time variability outcomes was generally poor (intraclass correlations: .167-.487). Although some significant differences in stride time variability were found between the preferred walking speed, fast, and slow trials, individual between-trial differences were generally below the estimated minimum difference considered to be a real difference. The development of a protocol to improve the reliability of stride time variability outcomes during continuous, overground walking would be beneficial to improve their application in research and clinical settings.

Investigating fractal dimension, heart rate variability, and memory during different image sequencing regimes in young adults

The goal of this study is to investigate patterns that emerge in brain and heart signals in response to external stimulating image regimes. Data were collected from 84 subjects of ages 18-22. Subjects viewed a series of both neutrally and negatively arousing pictures during 2-min and 18-s-long segments repeated nine times. Both brain [electroencephalogram (EEG)] and heart signals [electrocardiogram (EKG)] were recorded for the duration of the study (ranging from 1.5 to 2.5 h) and analyzed using nonlinear techniques. Specifically, the fractal dimension was computed from the EEG to determine how this voltage trace is related to the image sequencing. Our results showed that subjects visually stimulated by a series of mixed images (a randomized set of neutrally or negatively arousing images) had a significantly higher fractal dimension compared to subjects visually triggered by pure images (an organized set of either all neutral or all negatively arousing images). In addition, our results showed that subjects who performed better on memory recall had a higher fractal dimension computed from the EEG. Analysis of EKG also showed greater heart rate variability in subjects who viewed a series of mixed images compared to subjects visually triggered by pure images. Overall, our results show that the healthy brain and heart are responsive to environmental stimuli that promote adaptability, flexibility, and agility.

Assessment of diurnal variation of stride time variability during continuous, overground walking in healthy young adults

BACKGROUND

There is emerging evidence that gait variability outcomes provide unique insights regarding the status of an individual's locomotor control system; however, there is currently limited evidence on the within-day reliability of stride time variability (STV) outcomes, or whether they demonstrate diurnal variation, when measured during continuous, overground walking in healthy young adults.

RESEARCH QUESTIONS

1) Are STV outcomes measured in the morning and afternoon during continuous, overground walking significantly different in healthy young adults? 2) What is the within-day reliability of STV outcomes measured during continuous, overground walking in healthy young adults?.

METHODS

Thirty-one healthy young adults (20.8 ± 3.7 years) completed two 10-minute continuous, overground walking trials on the same day (9:00-11:00am and 3:00-5:00pm) at their preferred walking speed. Data from a waist-mounted tri-axial accelerometer were used to determine the series of consecutive stride times for each trial.

RESULTS

There were no significant differences between sessions for average walking speed, average stride time, or STV. The within-day reliability was excellent for average walking speed and stride time, and generally poor to fair for STV.

SIGNIFICANCE

Healthy young adults do not appear to demonstrate diurnal variation in STV outcomes during continuous, overground walking; however, the development of a protocol to improve their reliability, as well as the establishment of normative ranges for such outcomes, would be beneficial to improve their application and interpretation in research and clinical settings.

Detrended Fluctuation, Coherence, and Spectral Power Analysis of Activation Rearrangement in EEG Dynamics During Cognitive Workload

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1-5.8 Hz), θ2 (5.9-7.4 Hz), β1 (13-19.9 Hz), and β2 (20-25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future.