Degeneracy and long-range correlations

Effects of overground gait training assisted by a wearable exoskeleton in patients with Parkinson's disease

BACKGROUND

In the recent past, wearable devices have been used for gait rehabilitation in patients with Parkinson's disease. The objective of this paper is to analyze the outcome of a wearable hip orthosis whose assistance adapts in real time to the patient's gait kinematics via adaptive oscillators. In particular, this study focuses on a metric characterizing natural gait variability, i.e., the level of long-range autocorrelations (LRA) in series of stride durations.

METHODS

Eight patients with Parkinson's disease (Hoehn and Yahr stages 1[Formula: see text]2.5) performed overground gait training three times per week for four consecutive weeks, assisted by a wearable hip orthosis. Gait was assessed based on performance metrics such as the hip range of motion, speed, stride length and duration, and the level of LRA in inter-stride time series assessed using the Adaptive Fractal Analysis. These metrics were measured before, directly after, and 1 month after training.

RESULTS

After training, patients increased their hip range of motion, their gait speed and stride length, and decreased their stride duration. These improvements were maintained 1 month after training. Regarding long-range autocorrelations, the population's behavior was standardized towards a metric closer to the one of healthy individuals after training, but with no retention after 1 month.

CONCLUSION

This study showed that an overground gait training with adaptive robotic assistance has the potential to improve key gait metrics that are typically affected by Parkinson's disease and that lead to higher prevalence of fall.

TRIAL REGISTRATION

ClinicalTrials.gov Identifer NCT04314973. Registered on 11 April 2020.

Adaptive walking assistance does not impact long-range stride-to-stride autocorrelations in healthy people

Many studies have demonstrated in the past that the level of long-range autocorrelations in series of stride durations, characterizing natural gait variability, is impacted by external constraints, such as treadmill or metronome, or by pathologies, such as Parkinson's or Huntington's disease. Nevertheless, no one has analyzed the effects on this metric of a gait constrained by a robot-mediated walking assistance, which intrinsically tends to normalize the gait pattern. This paper focuses on the influence of a wearable active pelvis orthosis on the level of long-range autocorrelations in series of stride durations. Ten healthy participants, aged between 55 and 77 yr, performed four overground walking sessions, wearing this orthosis, and with different assistive parameters. This study showed that the adaptive assistance provided by this device has the potential of improving gait metrics that are typically affected by aging, such as the hip range of motion, walking speed, stride length, and stride duration, without impacting natural gait variability, i.e., the level of long-range autocorrelations in series of stride durations. This combination is virtuous toward the design of an assistive device for people with locomotion disorders resulting in deteriorated levels of long-range autocorrelations, such as patients with Parkinson's disease.NEW & NOTEWORTHY This study is the first that investigates the effects of a wearable active pelvis orthosis using an oscillator-based adaptive assistance on the level of long-range autocorrelations in series of stride durations during overground walking. It is also the first to compare the effects of different assistance settings on spatiotemporal gait metrics.

Relationship between gait complexity and pain attention in chronic low back pain

ABSTRACT

Clinical models of chronic low back pain (cLBP) highlight the role of excessive attention to pain and kinesiophobia on the origin of disability. At the motor control level, various mechanisms are involved in the impairments observed in patients with cLBP. We aimed to assess the role of maladaptative attentional behaviors by using a complex systems approach and a visual display as a distraction during walking. Sixteen patients with cLBP with no previous surgery or significant leg pain and 16 healthy matched controls were included. Patients walked on a treadmill at preferred walking speed with and without distraction. Stride time (ST) fractal complexity was assessed using detrended fluctuation analysis. A two-way analysis of variance with repeated measures on distraction was performed on fractal exponents. We found a significant group × distraction interaction effect on fractal complexity of ST series (F(1,30) = 9.972, P = 0.004). Post hoc analysis showed that, without distraction, patients with cLBP had significantly lower ST complexity than controls, but when distracted, they regained gait complexity, recovering the level of controls. Our results suggest that excessive attention to pain causes loss of complexity and adaptability in cLBP and explain alterations of motor control with pain. Fractal analysis seems to be a promising method to explore movement variability and individual adaptability in musculoskeletal disorders.

The Relation Between Complexity and Resilient Motor Performance and the Effects of Differential Learning

Complex systems typically demonstrate a mixture of regularity and flexibility in their behavior, which would make them adaptive. At the same time, adapting to perturbations is a core characteristic of resilience. The first aim of the current research was therefore to test the possible relation between complexity and resilient motor performance (i.e., performance while being perturbed). The second aim was to test whether complexity and resilient performance improve through differential learning. To address our aims, we designed two parallel experiments involving a motor task, in which participants moved a stick with their non-dominant hand along a slider. Participants could score points by moving a cursor as fast and accurately as possible between two boxes, positioned on the right- and left side of the screen in front of them. In a first session, we determined the complexity by analyzing the temporal structure of variation in the box-to-box movement intervals with a Detrended Fluctuation Analysis. Then, we introduced perturbations to the task: We altered the tracking speed of the cursor relative to the stick-movements briefly (i.e., 4 s) at intervals of 1 min (Experiment 1), or we induced a prolonged change of the tracking speed each minute (Experiment 2). Subsequently, participants had three sessions of either classical learning or differential learning. Participants in the classical learning condition were trained to perform the ideal movement pattern, whereas those in the differential learning condition had to perform additional and irrelevant movements. Finally, we conducted a posttest that was the same as the first session. In both experiments, results showed moderate positive correlations between complexity and points scored (i.e., box touches) in the perturbation-period of the first session. Across the two experiments, only differential learning led to a higher complexity index (i.e., more prominent patterns of pink noise) from baseline to post-test. Unexpectedly, the classical learning group improved more in their resilient performance than the differential learning group. Together, this research provides empirical support for the relation between complexity and resilience, and between complexity and differential learning in human motor performance, which should be examined further.

Fast Hand Movements Unveil Multifractal Roots of Adaptation in the Visuomotor Cognitive System

Beyond apparent simplicity, visuomotor dexterity actually requires the coordination of multiple interactions across a complex system that links the brain, the body and the environment. Recent research suggests that a better understanding of how perceptive, cognitive and motor activities cohere to form executive control could be gained from multifractal formalisms applied to movement behavior. Rather than a central executive "talking" to encapsuled components, the multifractal intuition suggests that eye-hand coordination arises from multiplicative cascade dynamics across temporal scales of activity within the whole system, which is reflected in movement time series. Here we examined hand movements of sport students performing a visuomotor task in virtual reality (VR). The task involved hitting spatially arranged targets that lit up on a virtual board under critical time pressure. Three conditions were compared where the visual search field changed: whole board (Standard), half-board lower view field (LVF) and upper view field (UVF). Densely sampled (90 Hz) time series of hand motions captured by VR controllers were analyzed by a focus-based multifractal detrended fluctuation analysis (DFA). Multiplicative rather than additive interactions across temporal scales were evidenced by testing comparatively phase-randomized surrogates of experimental series, which confirmed nonlinear processes. As main results, it was demonstrated that: (i) the degree of multifractality in hand motion behavior was minimal in LVF, a familiar visual search field where subjects correlatively reached their best visuomotor response times (RTs); (ii) multifractality increased in the less familiar UVF, but interestingly only for the non-dominant hand; and (iii) multifractality increased further in Standard, for both hands indifferently; in Standard, the maximal expansion of the visual search field imposed the highest demand as evidenced by the worst visuomotor RTs. Our observations advocate for visuomotor dexterity best described by multiplicative cascades dynamics and a system-wide distributed control rather than a central executive. More importantly, multifractal metrics obtained from hand movements behavior, beyond the confines of the brain, offer a window on the fine organization of control architecture, with high sensitivity to hand-related control behavior under specific constraints. Appealing applications may be found in movement learning/rehabilitation, e.g., in hemineglect people, stroke patients, maturing children or athletes.

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.

Fractal auditory stimulation has greater benefit for people with Parkinson's disease showing more random gait pattern

BACKGROUND

Healthy gait dynamics are characterized by the presence of fractal, persistent stride-to-stride variations, which become more random with Parkinson's disease (PD). Rhythmic auditory stimulation with fractal beat-to-beat variations can change gait dynamics in people with PD toward more persistence.

RESEARCH QUESTION

How does gait in people with PD change when synchronizing steps with fractal melodic metronomes with different step-to-beat ratios, and which stimulus do they prefer?

METHODS

In this cross-sectional study, 15 people with PD and 15 healthy older adults walked over-ground in three conditions: self-paced, paced by a fractal auditory stimulus with a 1:1 step-to-beat ratio ('metronome'), and fractal auditory stimulus with a 1:2 step-to-beat ratio ('music'). Gait dynamics were recorded with instrumented insoles, and detrended fluctuation analysis (DFA) was applied to the series of stride time intervals. Stimuli preference was assessed using Likert-like scales and open-ended questions. ANOVAs were used to compare mean, coefficient of variation, α-DFA, and the responses from the continuous Likert scales. Pearson correlations were used to assess the relationship between 'music' and 'metronome' enjoyment or difficulty with gait outcomes, and to determine the association between baseline α-DFA and changes due to the stimuli.

RESULTS

Our major findings are that (i) stride-to-stride variations were more persistent with the 'metronome' compared to baseline for both groups, (ii) the effect was greater for people with lower α-DFA at baseline (i.e., more random stride-to-stride variations), and (iii) both groups found the 'metronome' less difficult to synchronize with.

SIGNIFICANCE

This study showed that people with PD and healthy older adults walk with higher statistical persistence in their stride-to-stride variations when instructed to synchronize their steps with a fractal stimulus. Participants with lower persistence at baseline benefited the most from the fractal 'metronome', highlighting the importance to develop patient-centered tests and interventions.

When Coordinating Finger Tapping to a Variable Beat the Variability Scaling Structure of the Movement and the Cortical BOLD Signal are Both Entrained to the Auditory Stimuli

Rhythmic actions are characterizable as a repeating invariant pattern of movement together with variability taking the form of cycle-to-cycle fluctuations. Variability in behavioral measures is atypically random, and often exhibits serial temporal dependencies and statistical self-similarity in the scaling of variability magnitudes across timescales. Self-similar (i.e. fractal) variability scaling is evident in measures of both brain and behavior. Variability scaling structure can be quantified via the scaling exponent (α) from detrended fluctuation analysis (DFA). Here we study the task of coordinating thumb-finger tapping to the beats of constructed auditory stimuli. We test the hypothesis that variability scaling evident in tap-to-tap intervals as well as in the fluctuations of cortical hemodynamics will become entrained to (i.e. drawn toward) manipulated changes in the variability scaling of a stimulus's beat-to-beat intervals. Consistent with this hypothesis, manipulated changes of the exponent α of the experimental stimuli produced corresponding changes in the exponent α of both tap-to-tap intervals and cortical hemodynamics. The changes in hemodynamics were observed in both motor and sensorimotor cortical areas in the contralateral hemisphere. These results were observed only for the longer timescales of the detrended fluctuation analysis used to measure the exponent α. These findings suggest that complex auditory stimuli engage both brain and behavior at the level of variability scaling structures.

Impact of Healthy Aging on Multifractal Hemodynamic Fluctuations in the Human Prefrontal Cortex

Fluctuations in resting-state cerebral hemodynamics show scale-free behavior over two distinct scaling ranges. Changes in such bimodal (multi) fractal pattern give insight to altered cerebrovascular or neural function. Our main goal was to assess the distribution of local scale-free properties characterizing cerebral hemodynamics and to disentangle the influence of aging on these multifractal parameters. To this end, we obtained extended resting-state records (N = 2¹⁴) of oxyhemoglobin (HbO), deoxyhemoglobin (HbR) and total hemoglobin (HbT) concentration time series with continuous-wave near-infrared spectroscopy technology from the brain cortex. 52 healthy volunteers were enrolled in this study: 24 young (30.6 ± 8.2 years), and 28 elderly (60.5 ± 12.0 years) subjects. Using screening tests on power-law, multifractal noise, and shuffled data sets we evaluated the presence of true multifractal hemodynamics reflecting long-range correlation (LRC). Subsequently, scaling-range adaptive bimodal signal summation conversion (SSC) was performed based on standard deviation (σ) of signal windows across a range of temporal scales (s). Building on moments of different order (q) of the measure, σ(s), multifractal SSC yielded generalized Hurst exponent function, H(q), and singularity spectrum, D(h) separately for a fast and slow component (the latter dominating the highest temporal scales). Parameters were calculated reflecting the estimated measure at s = N (focus), degree of LRC [Hurst exponent, H(2) and maximal Hölder exponent, h_max] and measuring strength of multifractality [full-width-half-maximum of D(h) and ΔH₁₅ = H(−15)−H(15)]. Correlation-based signal improvement (CBSI) enhanced our signal in terms of interpreting changes due to neural activity or local/systemic hemodynamic influences. We characterized the HbO-HbR relationship with the aid of fractal scale-wise correlation coefficient, r_σ(s) and SSC-based multifractal covariance analysis. In the majority of subjects, cerebral hemodynamic fluctuations proved bimodal multifractal. In case of slow component of raw HbT, h_max, and Ĥ(2) were lower in the young group explained by a significantly increased r_σ(s) among elderly at high temporal scales. Regarding the fast component of CBSI-pretreated HbT and that of HbO-HbR covariance, h_max, and focus were decreased in the elderly group. These observations suggest an attenuation of neurovascular coupling reflected by a decreased autocorrelation of the neuronal component concomitant with an accompanying increased autocorrelation of the non-neuronal component in the elderly group.

Concurrent Changes of Brain Functional Connectivity and Motor Variability When Adapting to Task Constraints

In behavioral neuroscience, the adaptability of humans facing different constraints has been addressed on one side at the brain level, where a variety of functional networks dynamically support the same performance, and on the other side at the behavioral level, where fractal properties in sensorimotor variables have been considered as a hallmark of adaptability. To bridge the gap between the two levels of observation, we have jointly investigated the changes of network connectivity in the sensorimotor cortex assessed by modularity analysis and the properties of motor variability assessed by multifractal analysis during a prolonged tapping task. Four groups of participants had to produce the same tapping performance while being deprived from 0, 1, 2, or 3 sensory feedbacks simultaneously (auditory and/or visual and/or tactile). Whereas tapping performance was not statistically different across groups, the number of brain networks involved and the degree of multifractality of the inter-tap interval series were significantly correlated, increasing as a function of feedback deprivation. Our findings provide first evidence that concomitant changes in brain modularity and multifractal properties characterize adaptations underlying unchanged performance. We discuss implications of our findings with respect to the degeneracy properties of complex systems, and the entanglement of adaptability and effective adaptation.

Gait Dynamics in Parkinson's Disease: Short Gait Trials "Stitched" Together Provide Different Fractal Fluctuations Compared to Longer Trials

The fractal analysis of stride-to-stride fluctuations in walking has become an integral part of human gait research. Fractal analysis of stride time intervals can provide insights into locomotor function and dysfunction, but its application requires a large number of strides, which can be difficult to collect from people with movement disorders such as Parkinson's disease. It has recently been suggested that "stitching" together short gait trials to create a longer time series could be a solution. The objective of this study was to determine if scaling exponents from "stitched" stride time series were similar to those from continuous, longer stride time series. Fifteen young adults, fourteen older adults, and thirteen people with Parkinson's disease walked around an indoor track in three blocks: one time 15 min, five times 3 min, and thirty times 30 s. Stride time intervals were determined from gait events recorded with instrumented insoles, and the detrended fluctuation analysis was applied to each stride time series of 512 strides. There was no statistically significant difference between scaling exponents in the three blocks, but intra-class correlation revealed very low between-blocks reliability of scaling exponents. This result challenges the premise that the stitching procedure could provide reliable information about gait dynamics, as it suggests that fractal analysis of stitched time series does not capture the same dynamics as gait recorded continuously. The stitching procedure cannot be considered as a valid alternative to the collection of continuous, long trials. Further studies are recommended to determine if the application of fractal analysis is limited by its own methodological considerations (i.e., long time series), or if other solutions exists to obtain reliable scaling exponents in populations with movement disorders.

Frequency-Specific Fractal Analysis of Postural Control Accounts for Control Strategies

Diverse indicators of postural control in Humans have been explored for decades, mostly based on the trajectory of the center-of-pressure. Classical approaches focus on variability, based on the notion that if a posture is too variable, the subject is not stable. Going deeper, an improved understanding of underlying physiology has been gained from studying variability in different frequency ranges, pointing to specific short-loops (proprioception), and long-loops (visuo-vestibular) in neural control. More recently, fractal analyses have proliferated and become useful additional metrics of postural control. They allowed identifying two scaling phenomena, respectively in short and long timescales. Here, we show that one of the most widely used methods for fractal analysis, Detrended Fluctuation Analysis, could be enhanced to account for scalings on specific frequency ranges. By computing and filtering a bank of synthetic fractal signals, we established how scaling analysis can be focused on specific frequency components. We called the obtained method Frequency-specific Fractal Analysis (FsFA) and used it to associate the two scaling phenomena of postural control to proprioceptive-based control loop and visuo-vestibular based control loop. After that, convincing arguments of method validity came from an application on the study of unaltered vs. altered postural control in athletes. Overall, the analysis suggests that at least two timescales contribute to postural control: a velocity-based control in short timescales relying on proprioceptive sensors, and a position-based control in longer timescales with visuo-vestibular sensors, which is a brand-new vision of postural control. Frequency-specific scaling exponents are promising markers of control strategies in Humans.

Center of Pressure Motion After Calf Vibration Is More Random in Fallers Than Non-fallers: Prospective Study of Older Individuals

Aging is associated with changes in balance control and elderly take longer to adapt to changing sensory conditions, which may increase falls risk. Low amplitude calf muscle vibration stimulates local sensory afferents/receptors and affects sense of upright when applied in stance. It has been used to assess the extent the nervous system relies on calf muscle somatosensory information and to rapidly change/perturb part of the somatosensory information causing balance unsteadiness by addition and removal of the vibratory stimulus. This study assessed the effect of addition and removal of calf vibration on balance control (in the absence of vision) in elderly individuals (>65 years, n = 99) who did (n = 41) or did not prospectively report falls (n = 58), and in a group of young individuals (18-25 years, n = 23). Participants stood barefoot and blindfolded on a force plate for 135 s. Vibrators (60 Hz, 1 mm) attached bilaterally over the triceps surae muscles were activated twice for 15 s; after 15 and 75 s (45 s for recovery). Balance measures were applied in a windowed (15 s epoch) manner to compare center-of-pressure (CoP) motion before, during and after removal of calf vibration between groups. In each epoch, CoP motion was quantified using linear measures, and non-linear measures to assess temporal structure of CoP motion [using recurrence quantification analysis (RQA) and detrended fluctuation analysis]. Mean CoP displacement during and after vibration did not differ between groups, which suggests that calf proprioception and/or weighting assigned by the nervous system to calf proprioception was similar for the young and both groups of older individuals. Overall, compared to the elderly, CoP motion of young was more predictable and persistent. Balance measures were not different between fallers and non-fallers before and during vibration. However, non-linear aspects of CoP motion of fallers and non-fallers differed after removal of vibration, when dynamic re-weighting is required. During this period fallers exhibited more random CoP motion, which could result from a reduced ability to control balance and/or a reduced ability to dynamically reweight proprioceptive information. These results show that non-linear measures of balance provide evidence for deficits in balance control in people who go on to fall in the following 12 months.

Four Principles Regarding an Effective Treatment of Aging

The question whether aging is a disease or not, has been asked by many professionals who are involved in the study of age-related degeneration. However, not only an agreement on this remains elusive, but also effective clinical treatments against human aging have not been forthcoming. In this Opinion paper I suggest that the complexity involved in aging is such that we need to remodel our thinking to involve a much more 'systems-oriented' approach. I explore four main principles which should be employed by those who are working on finding treatments against agerelated degeneration. First, I discuss the problems encountered in translating laboratory research into effective therapies for humans. Second, I propose that a 'systems-thinking' method needs to be more extensively employed, instead of relying exclusively on the current reductionist one. Third, it is submitted that we must learn from the history of life-extension research, and not blindly follow contemporary paradigms, which may lead us into yet more 'dead ends' with regards to therapies. Finally, I suggest that, we may need to employ certain universal notions and use these in order to gain insights into the mechanics of a possible therapy against age-related degeneration. Examples may be the principle of hormesis, those of degeneracy, exaptation, and others from cybernetic or systems science domains. By using this four-pronged approach we liberate our thinking from the shackles of existing common mistakes and fallacies, and we open the way for a fresh approach that may lead us towards entirely new paradigms for providing clinically effective therapies against agerelated degeneration.

Seeking Temporal Predictability in Speech: Comparing Statistical Approaches on 18 World Languages

Temporal regularities in speech, such as interdependencies in the timing of speech events, are thought to scaffold early acquisition of the building blocks in speech. By providing on-line clues to the location and duration of upcoming syllables, temporal structure may aid segmentation and clustering of continuous speech into separable units. This hypothesis tacitly assumes that learners exploit predictability in the temporal structure of speech. Existing measures of speech timing tend to focus on first-order regularities among adjacent units, and are overly sensitive to idiosyncrasies in the data they describe. Here, we compare several statistical methods on a sample of 18 languages, testing whether syllable occurrence is predictable over time. Rather than looking for differences between languages, we aim to find across languages (using clearly defined acoustic, rather than orthographic, measures), temporal predictability in the speech signal which could be exploited by a language learner. First, we analyse distributional regularities using two novel techniques: a Bayesian ideal learner analysis, and a simple distributional measure. Second, we model higher-order temporal structure—regularities arising in an ordered series of syllable timings—testing the hypothesis that non-adjacent temporal structures may explain the gap between subjectively-perceived temporal regularities, and the absence of universally-accepted lower-order objective measures. Together, our analyses provide limited evidence for predictability at different time scales, though higher-order predictability is difficult to reliably infer. We conclude that temporal predictability in speech may well arise from a combination of individually weak perceptual cues at multiple structural levels, but is challenging to pinpoint.

Learning, motor skill, and long-range correlations

Long-range correlations have been evidenced in a number of experiments, generally using overlearned and overpracticed tasks. The authors hypothesized that long-range correlation could represent the byproduct of learning. They analyzed the series of periods produced by a group of expert and a group of novices during prolonged trials on a ski simulator. Results showed a very low variability in expert's series, as compared to novices. Fractal analyses showed that fluctuations were significantly more structured and correlated in experts. These results suggest that learning could be conceived as the progressive installation of complexity in the system.