Noise and complexity in human postural control: interpreting the different estimations of entropy

A Potential Mechanism Involved in the Regularity of Center-of-Pressure Displacements During Achieving Unipedal Equilibrium on Stable and Unstable Surfaces

Sample entropy (SampEn) is a widely used measure for estimating the regularity of center-of-pressure (COP) trajectories, with high COP regularity (low SampEn) commonly interpreted as ineffective postural control. The current study aimed to investigate one possible source of COP regularity-agonist-antagonist coactivation-resulting in joint stiffness or action stability. A cross-correlation analysis was conducted to determine the similarity (coactivation) level of 5 pairs of lower limb agonist-antagonist electromyographic signals. SampEn was applied to anteroposterior (ap) and mediolateral (ml) COP displacements. Electromyographic and COP signals were simultaneously derived from 25 active young adults (25.6 ± 4.0 years) during unipedal balancing on stable and multiaxial-unstable surfaces. Then, the correlation between individual agonist-antagonist cross-correlation coefficients and SampEn-COP was explored. The results show that only the tibialis anterior-peroneus longus (TA-PL) coactivations are negatively correlated with SampEn-COPap/ml (P ≤ .030) in both surface conditions, with greater TA-PL coactivation appearing with lower SampEn-COPap/ml. In addition, sex effects as one factor that might influence postural control were also tested. Women exhibited greater TA-PL coactivation (P = .017) and lower SampEn-COPap (P = .005) than men. Together, TA-PL coactivation could be one possible origin of COP regularity, but its effects might be detrimental to unipedal postural control, especially for women.

The use of nonlinear analysis in understanding postural control: A scoping review

Nonlinear analyses have emerged as an approach to unraveling the intricate dynamics and underlying mechanisms of postural control, offering insights into the complex interplay of physiological and biomechanical factors. However, achieving a comprehensive understanding of the application of nonlinear analysis in postural control studies remains a challenge due to the various nonlinear measurement methods currently available. Thus, this scoping review aimed to identify existing nonlinear analyses used to study postural control in both dynamic and quiet tasks, and to summarize and disseminate the available literature on the use of nonlinear analysis in postural control. For this purpose, a scoping review was conducted and reported following the PRISMA Extension for Scoping Reviews (PRISMA-ScR) Checklist and Explanation. Searches were conducted up to July 2023 on PubMed/Medline, Embase, CINAHL, Web of Science, and Google Scholar databases, resulting in the inclusion of 397 unique studies. The main classes employed among the studies were entropy-based, fractal-based, quantification of recurrence plots, and quantification of stability, with a total of 91 different algorithms distributed among these classes. The most common condition used to study postural control was quiet standing, followed by dynamic standing and gait tasks. Although various algorithms were utilized for this purpose, sample entropy was employed in 43% of studies to explore mechanisms related to postural control. Among them, 28% were in quiet standing, 3.27% were in dynamic standing, and 4.78% to study postural control during the gait. The results also provide insights into nonlinear analysis for future studies, concerning the complexity and interactions within the postural control system across various task demands.

Controlling posture to see the world: The integration of visual task demands and postural sway in sitting and standing infants

Our ability to integrate posture with visually demanding tasks is a critical aspect of motor behavior flexibility. When looking at a small object, excessive body movements impair an individual's ability to visually attend to the object. To overcome this problem, we adjust our postural sway to successfully focus on the object. The goal of the current study was to assess whether infants also adjust postural sway when engaged in a challenging visual task. The participants, 19 independently sitting infants (Sitters) and 21 newly independently standing infants (Standers), sat or stood on a force plate while viewing differently sized images displayed on a monitor (smaller images: 8 × 6.5 cm or 3 × 3 cm; larger images: 13 × 16 cm or 13 × 13 cm). Regardless of image size, Standers were less stable than Sitters with larger sway areas and faster sway velocities. Both Sitters and Standers adjusted sway area but not sway velocity, based on image size. Sitters and Standers differed in how they controlled sway dynamics. Standers but not Sitters altered sway dynamics based on image size. Overall, infants used posture-specific adaptive control strategies to make fine-grained adjustments based on image size. The development of the ability to integrate posture with a visually demanding task further emphasizes the capability of advanced complex motor behaviors during infancy, enabling infants to flexibly attend to important aspects of their environment at different postural positions.

Exercise makes better mind: a data mining study on effect of physical activity on academic achievement of college students

The effect of physical activity (PA) on academic achievement has long been a hot research issue in physical education, but few studies have been conducted using machine learning methods for analyzing activity behavior. In this paper, we collected the data on both physical activity and academic performance from 2,219 undergraduate students (Mean = 19 years) over a continuous period of 12 weeks within one academic semester. Based on students' behavioral indicators transformed from a running APP interface and the average academic course scores, two models were constructed and processed by CHAID decision tree for regression analysis and significance detection. It was found that first, to attain higher academic performance, it is imperative for students to not only exhibit exceptional activity regularity, but also sustain a reduced average step frequency; second, the students completing running exercise with an average frequency of 1 time/week and the duration of 16-25 min excelled over approximately 88 percentage of other students on academic performance; third, the processing validity and reliability of physical observation data in complex systems can be improved by utilizing decision tree as a leveraging machine learning tool and statistical method. These findings provide insights for educational practitioners and policymakers who will seek to enhance college students' academic performance through physical education programs, combined with data mining methods.

Integrating Motor Variability Evaluation Into Movement System Assessment

Common assessment tools for determining therapeutic success in rehabilitation typically focus on task-based outcomes. Task-based outcomes provide some understanding of the individual's functional ability and motor recovery; however, these clinical outcomes may have limited translation to a patient's functional ability in the real world. Limitations arise because (1) the focus on task-based outcome assessment often disregards the complexity of motor behavior, including motor variability, and (2) mobility in highly variable real-world environments requires movement adaptability that is made possible by motor variability. This Perspective argues that incorporating motor variability measures that reflect movement adaptability into routine clinical assessment would enable therapists to better evaluate progress toward optimal and safe real-world mobility. The challenges and opportunities associated with incorporating variability-based assessment of pathological movements are also discussed. This Perspective also indicates that the field of rehabilitation needs to leverage technology to advance the understanding of motor variability and its impact on an individual's ability to optimize movement.

IMPACT

This Perspective contends that traditional therapeutic assessments do not adequately evaluate the ability of individuals to adapt their movements to the challenges faced when negotiating the dynamic environments encountered during daily life. Assessment of motor variability derived during movement execution can address this issue and provide better insight into a patient's movement stability and maneuverability in the real world. Creating such a shift in motor system assessment would advance understanding of rehabilitative approaches to motor system recovery and intervention.

Relationship between backpack load location, sex, anthropometric and body composition factors with postural sway in healthy young adults

Objective

Evaluate the effect of backpack load location on postural sway and correlate sway path length (PL) to anthropometrics and body composition.

Methods

Fifteen participants aged 18-25 stood on a force plate with backpack load located high (LH), low (LL) or without backpack (NL). Body composition and anthropometric variables were correlated to PL.

Results

Load increased PL, 95% confidence ellipse, and mean velocity while it reduced mediolateral SampEn (p<0.05). Females had increased mean velocity and PL of sway (p<0.05). Larger phase angles correlated with reduced PL under NL. Taller individuals correlated with reduced PL under LL. Greater mass correlated with reduced PL under LH.

Conclusions

Load carriage regardless of load location increased postural sway metrics except mediolateral SampEn. Females had greater PL and mean velocity compared to males. Select anthropometric and body composition variables correlated with postural sway under different load conditions.

Recurrence quantification analysis of postural sway in patients with persistent postural perceptual dizziness

Background

Persistent postural perceptual dizziness (PPPD) is a common cause of chronic dizziness and imbalance. Emerging evidence suggests that changes in quantitative measures of postural control may help identify individuals with PPPD, however, traditional linear metrics of sway have yielded inconsistent results. Methodologies to examine the temporal structure of sway, including recurrent quantification analysis (RQA), have identified unique changes in dynamic structure of postural control in other patient populations. This study aimed to determine if adults with PPPD exhibit changes in the dynamic structure of sway and whether this change is modulated on the basis of available sensory cues.

Methods

Twelve adults diagnosed with PPPD and twelve age-matched controls, completed a standard battery of quiet stance balance tasks that involved the manipulation of visual and/or proprioceptive feedback. For each group, the regularity and complexity of the CoP signal was assessed using RQA and the magnitude and variability of the CoP signal was quantified using traditional linear measures.

Results

An overall effect of participant group (i.e., healthy controls vs. PPPD) was seen for non-linear measures of temporal complexity quantified using RQA. Changes in determinism (i.e., regularity) were also modulated on the basis of availability of sensory cues in patients with PPPD. No between-group difference was identified for linear measures assessing amount and variability of sway.

Conclusions

Participants with PPPD on average exhibited sway that was similar in magnitude to, but significantly more repeatable and less complex than, healthy controls. These data show that non-linear measures provide unique information regarding the effect of PPPD on postural control, and as a result, may serve as potential rehabilitation outcome measures.

Characterization of Physiological Noise in Complex Cardiovascular Variability Series

The cardiovascular system can be analyzed using spectral, nonlinear, and complexity metrics. Nevertheless, dynamical noise may significantly impact these quantifiers. To our knowledge, there has been no attempt to quantify the intrinsic cardiovascular system noise driving heartbeat dynamics. To this end, this study presents a novel, model-free framework to define and quantify physiological noise using nonlinear Approximate Entropy profile. The framework was tested using analytical noisy series and then applied to real Heart Rate Variability (HRV) series gathered from a publicly-available dataset of recordings from 19 young and 19 elderly subjects watching the movie "Fantasia". Results suggest that physiological noise may account for over 15% of cardiovascular dynamics and is influenced by aging, with decreased cardiac noise in the elderly compared to the young subjects. Our findings indicate that physiological noise is a crucial factor in characterizing cardiovascular dynamics, and current spectral, nonlinear, and complexity assessments should take into account underlying dynamical noise estimates.

Leg Dominance—Surface Stability Interaction: Effects on Postural Control Assessed by Smartphone-Based Accelerometry

The preferential use of one leg over another in performing lower-limb motor tasks (i.e., leg dominance) is considered to be one of the internal risk factors for sports-related lower-limb injuries. The current study aimed to investigate the effects of leg dominance on postural control during unipedal balancing on three different support surfaces with increasing levels of instability: a firm surface, a foam pad, and a multiaxial balance board. In addition, the interaction effect between leg dominance and surface stability was also tested. To this end, a tri-axial accelerometer-based smartphone sensor was placed over the lumbar spine (L5) of 22 young adults (21.5 ± 0.6 years) to record postural accelerations. Sample entropy (SampEn) was applied to acceleration data as a measure of postural sway regularity (i.e., postural control complexity). The results show that leg dominance (p < 0.001) and interaction (p < 0.001) effects emerge in all acceleration directions. Specifically, balancing on the dominant (kicking) leg shows more irregular postural acceleration fluctuations (high SampEn), reflecting a higher postural control efficiency or automaticity than balancing on the non-dominant leg. However, the interaction effects suggest that unipedal balancing training on unstable surfaces is recommended to reduce interlimb differences in neuromuscular control for injury prevention and rehabilitation.

Characterization of Postural Sway in Women with Osteoporosis and a Control Group by Means of Linear and Nonlinear Methods

The mechanisms underlying the altered postural control and risk of falling in patients with osteoporosis are not yet fully understood. The aim of the present study was to investigate postural sway in women with osteoporosis and a control group. The postural sway of 41 women with osteoporosis (17 fallers and 24 non-fallers) and 19 healthy controls was measured in a static standing task with a force plate. The amount of sway was characterized by traditional (linear) center-of-pressure (COP) parameters. Structural (nonlinear) COP methods include spectral analysis by means of a 12-level wavelet transform and a regularity analysis via multiscale entropy (MSE) with determination of the complexity index. Patients showed increased body sway in the medial–lateral (ML) direction (standard deviation in mm: 2.63 ± 1.00 vs. 2.00 ± 0.58, p = 0.021; range of motion in mm: 15.33 ± 5.58 vs. 10.86 ± 3.14, p = 0.002) and more irregular sway in the anterior–posterior (AP) direction (complexity index: 13.75 ± 2.19 vs. 11.18 ± 4.44, p = 0.027) relative to controls. Fallers showed higher-frequency responses than non-fallers in the AP direction. Thus, postural sway is differently affected by osteoporosis in the ML and AP directions. Clinically, effective assessment and rehabilitation of balance disorders can benefit from an extended analysis of postural control with nonlinear methods, which may also contribute to the improvement of risk profiles or a screening tool for the identification of high-risk fallers, thereby prevent fractures in women with osteoporosis.

Human Motor Noise Assessed by Electromagnetic Sensors and Its Relationship with the Degrees of Freedom Involved in Movement Control

Motor variability is a prominent feature of the human movement that, nowadays, can be easily measured through different sensors and analyzed using different types of variables, and it seems to be related to functional and adaptative motor behavior. It has been stated that motor variability is related to the system's flexibility needed to choose the right degrees of freedom (DoFs) to adapt to constant environmental changes. However, the potential relationship between motor variability and DoFs is unknown. The aim of this study was to analyze how motor variability, both the amount and structure, changes depending on the mechanical DoFs involved in the movement control. For this purpose, movement variability was assessed by a tracking sensor in five tasks with different DoFs, and the amount, using standard deviation, and the structure of variability, through fuzzy entropy and detrended fluctuation analysis, were also assessed. The results showed a higher amount of variability and a less predictable and more auto-correlated variability structure in the long-term when more mechanical DoFs are implied. The studies that analyze motor variability should consider the type of movement and the DoFs involved in the analyzed task since, as the findings have shown, both factors have a noticeable influence on the amount and the structure of motor variability.

Effect of sleep deprivation on postural control and dynamic stability in healthy young adults

BACKGROUND

Postural control results from non-linear interactions of multiple neuromusculoskeletal elements and contextual factors. The use of non-linear analyses that consider the temporal evolution of postural adjustments, such as sample entropy, could inform about the changes in postural control due to contextual disturbances such as sleep deprivation.

RESEARCH QUESTION

What are the effects of sleep deprivation on static postural control and dynamic stability in healthy young adults?

METHODS

A quasi-experimental study was performed with 17 healthy young males submitted to 24 h of monitored sleep deprivation. The postural control was measured using sample entropy, area, and total average velocity of the center of pressure on a force platform. The dynamic stability was measured using the Modified Star Excursion Balance Test (SEBTm) composite score for each lower limb. Repeated-measures analysis of variance (baseline × 12 h × 15 h × 18 h × 21 h × 24 h of sleep deprivation) verified the effect of sleep deprivation in the postural control variables. Paired t-test compared the composite score of the SEBTm between baseline and 24 h sleep deprivation.

RESULTS

Sample entropy decreased after 18 h of sleep deprivation (p = 0.032) and 24 h of sleep deprivation (p = 0.001). Despite the significant main effect for the area (p = 0.012) and speed (p = 0.007) of the center of pressure, no pairwise differences were identified in the post hoc analysis. The non-dominant lower limb SEBTm composite score was reduced after 24 h of sleep deprivation (p = 0.033), and no difference was observed in the dominant limb.

SIGNIFICANCE

Sleep deprivation reduced the adaptability in static postural control and dynamic stability of the non-dominant lower limb of healthy young male adults. Sample entropy seemed more sensitive to capture the effects of sleep deprivation than the classical postural control variables.

One-Leg Stance Postural Sway Is Not Benefited by Bicycle Motocross Practice in Elite Riders

Balance has been positioned as an important performance skill in sport. Differences in postural control have been found between levels of expertise. However, this statement remains unanswered in some cyclic sports. This work aimed to describe the one-leg balance performance of a sample of elite BMX riders-racing and freestyle-compared to a control group formed by recreational athletes. The center of pressure (COP) of nineteen international BMX riders (freestyle, n = 7; racing, n = 12) and twenty physically active adults was analyzed in a 30-s one-leg stance test on both legs. COP dispersion and velocity variables were analyzed. Non-linear dynamics of postural sway were evaluated through Fuzzy Entropy and Detrended Fluctuation Analysis. BMX athletes did not show differences between legs in any of the variables. The control group did show differences between the dominant and non-dominant leg in the magnitude of variability of the COP in the mediolateral axis. Group comparison revealed non-significant differences. International BMX athletes did not show better balance parameters than the control group in a one-leg stance balance task. The adaptations derived from BMX practice do not have a significant impact in one-leg stance balance performance.

Standing Posture in Motor and Cognitive Dual-Tasks during Smartphone Use: Linear and Nonlinear Analysis of Postural Control

Analysis of the center of pressure (CoP) during cognitive or motor dual-tasking is widely used to characterize postural control. Most studies use traditional measures of CoP to quantify postural control, but given its complexity, nonlinear analysis of CoP is of growing interest in the area. This study aims to analyze CoP behavior in healthy young adults during standing posture performance while simultaneously performing motor or cognitive tasks on a smartphone, using linear and nonlinear analysis of CoP. Thirty-six healthy participants (23.08 ± 3.92 years) were found eligible for this study. They performed a single task (ST), cognitive dual-task (cog-DT), and motor dual-task (mot-DT). The total excursion of CoP, displacement of CoP in the anterior-posterior and medial-lateral directions, mean total velocity of CoP, and mean anterior-posterior and medial-lateral velocities of CoP were measured with a force plate. Approximate entropy (ApEn) of the anterior-posterior (ApEn-AP) and medial-lateral (ApEn-ML) displacement of CoP were also calculated. The results showed that dual-task costs for the total excursion, displacement in the anterior-posterior direction, mean total velocity, and mean anterior-posterior velocity of CoP were greater during the cog-DT than the mot-DT (p < 0.05). In the nonlinear analysis of the CoP, there was no difference (p > 0.05) between the cog-DT and mot-DT for ApEn values of the anterior-posterior and medial-lateral time series of the CoP. Both linear and nonlinear analyses showed differences between the cog-DT and ST (p < 0.05), revealing a decline in postural control during the cog-DT compared with the ST. In conclusion, performing a cog-DT causes sway impairments and lower postural control efficacy compared with motor single and dual-tasks. Furthermore, both linear and nonlinear analyses were able to distinguish between conditions.

Cardio-Hypothalamic-Pituitary Coupling during Rest and in Response to Exercise

The objective of this study was to examine cardio hypothalamic-pituitary coupling and to better understand how the temporal relations between these systems are altered during rest and exercise conditions. An intensive within subjects study design was used. Seven adult males completed two visits, each consisting of either a 24 h period of complete rest or a 24 h period containing a high-intensity exercise bout. An intravenous catheter was used to collect serum samples every 10 min throughout the 24 h period (i.e., 145 samples/person/condition) to assess growth hormone (GH) dynamics throughout the 24 h period. Cardiac dynamics were also collected throughout the 24 h period and epoched into 3 min windows every 10 min, providing serial short-time measurements of heart rate variability (HRV) concurrent to the GH sampling. The standard deviation of the normal RR interval (SDNN), the root mean square of successive differences (rMSSD), and sample entropy (SampEn) was calculated for each epoch and used to create new profiles. The dynamics of these profiles were individually quantified using SampEn and recurrence quantification analysis (RQA). To address our central question, the coupling between these profiles with GH was assessed using cross-SampEn and cross-RQA (cRQA). A comparison between the epoched HRV profiles indicated a main effect between profiles for sample entropy (p < 0.001) and several measures from RQA. An interaction between profile and condition was observed for cross-SampEn (p = 0.04) and several measures from cRQA. These findings highlight the potential application of epoched HRV to assess changes in cardiac dynamics, with specific applications to assessing cardio hypothalamic-pituitary coupling.

Biathletes present repeating patterns of postural control to maintain their balance while shooting

Balance can be a main factor contributing to success in many disciplines, and biathlon is a representative example. A more stable posture may be a key factor for shooting scores. The center of foot pressure (COP) is commonly recorded when evaluating postural control. As COP measurements are highly irregular and non-stationary, non-linear deterministic methods, such as entropy, are more appropriate for the analysis of COP displacement. The aim of our study was to investigate whether the longitudinal effects of biathlon training can elicit specific changes in postural control. Eight national-level biathletes, 15 non-athletes who prior to the experiment took part in 3 months of shooting training, and 15 non-athletes with no prior rifle shooting experience took part in our study. The data was collected with the use of a force plate. Participants performed three balance tasks in quiet standing, the shooting position (internal focus-participants concentrated on maintaining the correct body position and rifle), and aiming at the target (external focus-participants concentrated on keeping the laser beam centered on the targets). Biathletes obtained significantly lower values of sample entropy compared to the other groups during the shooting and aiming at the target trials (p<0.05). External and internal focuses influenced the process of postural control among participants who had prior rifle shooting experience and the control group; they obtained significantly higher values of sample entropy while shooting and aiming at the target compared to the quiet standing trial (p<0.05). The biathletes obtained significantly lower values of sample entropy in the aiming at the target position compared to the quiet standing trial. Specific balance training is associated with the ability to deal with a more challenging, non-specific task. The biathletes seemed to employ a different motor control strategy than the beginners and control group, creating repeating patterns (more regular signal for COP) to keep one's balance during the shooting and aiming at the target positions.

Postural control strategies are revealed by the complexity of fractional components of COP

The complexity of the center of pressure (COP) provides important information regarding the underlying mechanisms of postural control. The relationships between COP complexity and balance performance are not fully established and might depend on the task constraints and the filtering decomposition of the COP signal. This study assessed COP complexity under different task constraints and it was assessed if emergent dynamics of COP fluctuations differ according to fractional components of COP related to peripheral or central adjustments. One hundred and sixty-two participants performed two sitting balance tasks. Accuracy was required by following a target that moved in the mediolateral (ML) or in the anteroposterior (AP) axis. Complexity dynamics of COP were addressed through Detrended Fluctuation Analysis (DFA) in the axis constrained by accuracy requirements and in the one non-constrained. Decomposition of COP components was applied by low-pass, band-pass and high-pass filters. DFA of low-pass and band-pass components of COP in the constrained axis were small-to-moderately related (r = .190 to .237) to balance performance. DFA of the high-pass component of the COP exhibited the opposite relationship (r = -.283 to -.453) in both axes (constrained and non-constrained). This study evidences that COP complexity is linked to better performance. This positive relationship complexity/performance is observed in the low- and mid-frequency components of the COP. These components might be related to central mechanisms of postural control. The lack of relationships between the different frequencies analyzed in the study suggests that they are capturing different components of postural control.

Effects of ECG Data Length on Heart Rate Variability among Young Healthy Adults

The relationship between the robustness of HRV derived by linear and nonlinear methods to the required minimum data lengths has yet to be well understood. The normal electrocardiography (ECG) data of 14 healthy volunteers were applied to 34 HRV measures using various data lengths, and compared with the most prolonged (2000 R peaks or 750 s) by using the Mann-Whitney U test, to determine the 0.05 level of significance. We found that SDNN, RMSSD, pNN50, normalized LF, the ratio of LF and HF, and SD1 of the Poincaré plot could be adequately computed by small data size (60-100 R peaks). In addition, parameters of RQA did not show any significant differences among 60 and 750 s. However, longer data length (1000 R peaks) is recommended to calculate most other measures. The DFA and Lyapunov exponent might require an even longer data length to show robust results. Conclusions: Our work suggests the optimal minimum data sizes for different HRV measures which can potentially improve the efficiency and save the time and effort for both patients and medical care providers.

Heart Rate Dynamics During Acute Recovery From Maximal Aerobic Exercise in Young Adults

INTRODUCTION

Resting heart rate (HRrest), heart rate variability (HRV), and HR recovery (HRR) from exercise provide valuable information about cardiac autonomic control. RR-intervals during acute recovery from exercise (RRrec) are commonly excluded from HRV analyses due to issues of non-stationarity. However, the variability and complexity within these trends may provide valuable information about changes in HR dynamics.

PURPOSE

Assess the complexity of RRrec and determine what physiologic and demographic information are associated with differences in these indices in young adults.

METHODS

RR-intervals were collected throughout maximal treadmill exercise and recovery in young adults (n = 92). The first 5 min of RRrec were (1) analyzed with previously reported methods that use 3-interval lengths for comparison and (2) detrended using both differencing(diff) and polynomial regression(res). The standard deviation of the normal interval (SDNN), root mean square of successive differences (rMSSD), root mean square (RMS) of the residual of regression, and sample entropy (SampEn) were calculated. Repeated measures analysis of covariance (ANCOVA) tested for differences in these indices for each of the methodological approaches, controlling for race, body fat, peak oxygen uptake (VO2p eak), and resting HR (HRrest). Statistical significance was set at p < 0.05.

RESULTS

VO2p eak and HRrest were significantly correlated with traditional measures of HRR and the variability surrounding RRrec. SampEndiff and SampEnres were correlated with VO2p eak but not HRrest or HRR. The residual-method provided a significantly (p = 0.04) lower mean standard error (MSE) (0.064 ± 0.042) compared to the differencing-method (0.100 ± 0.033).

CONCLUSIONS

Complexity analysis of RRrec provides unique information about cardiac autonomic regulation immediately following the cessation of exercise when compared to traditional measures of HRR and both HRrest and VO2peak influence these results.

Use of Virtual Reality to Assess Dynamic Posturography and Sensory Organization: Instrument Validation Study

Background

The Equitest system (Neurocom) is a computerized dynamic posturography device used by health care providers and clinical researchers to safely test an individual’s postural control. While the Equitest system has evaluative and rehabilitative value, it may be limited owing to its cost, lack of portability, and reliance on only sagittal plane movements. Virtual reality (VR) provides an opportunity to reduce these limitations by providing more mobile and cost-effective tools while also observing a wider array of postural characteristics.

Objective

This study aimed to test the plausibility of using VR as a feasible alternative to the Equitest system for conducting a sensory organization test.

Methods

A convenience sample of 20 college-aged healthy individuals participated in the study. Participants completed the sensory organization test using the Equitest system as well as using a VR environment while standing atop a force plate (Bertec Inc). The Equitest system measures the equilibrium index. During VR trials, the estimated equilibrium index, 95% ellipse area, path length, and anterior-posterior detrended fluctuation analysis scaling exponent alpha were calculated from center of pressure data. Pearson correlation coefficients were used to assess the relationship between the equilibrium index and center of pressure–derived balance measures. Intraclass correlations for absolute agreement and consistency were calculated to compare the equilibrium index and estimated equilibrium index.

Results

Intraclass correlations demonstrated moderate consistency and absolute agreement (0.5 < intraclass correlation coefficient < 0.75) between the equilibrium index and estimated equilibrium index from the Equitest and VR sensory organization test (SOT), respectively, in four of six tested conditions. Additionally, weak to moderate correlations between force plate measurements and the equilibrium index were noted in several of the conditions.

Conclusions

This research demonstrated the plausibility of using VR as an alternative method to conduct the SOT. Ongoing development and testing of virtual environments are necessary before employing the technology as a replacement to current clinical tests.

The Influence of Functional Flywheel Resistance Training on Movement Variability and Movement Velocity in Elite Rugby Players

The aim of this study was to identify the changes in movement variability and movement velocity during a six-week training period using a resistance horizontal forward-backward task without (NOBALL) or with (BALL) the constraint of catching and throwing a rugby ball in the forward phase. Eleven elite male rugby union players (mean ± SD: age 25.5 ± 2.0 years, height 1.83 ± 0.06 m, body mass 95 ± 18 kg, rugby practice 14 ± 3 years) performed eight repetitions of NOBALL and BALL conditions once a week in a rotational flywheel device. Velocity was recorded by an attached rotary encoder while acceleration data were used to calculate sample entropy (SampEn), multiscale entropy, and the complexity index. SampEn showed no significant decrease for NOBALL (ES = -0.64 ± 1.02) and significant decrease for BALL (ES = -1.71 ± 1.16; p < 0.007) conditions. Additionally, movement velocity showed a significant increase for NOBALL (ES = 1.02 ± 1.05; p < 0.047) and significant increase for BALL (ES = 1.25 ± 1.08; p < 0.025) between weeks 1 and 6. The complexity index showed higher levels of complexity in the BALL condition, specifically in the first three weeks. Movement velocity and complex dynamics were adapted to the constraints of the task after a four-week training period. Entropy measures seem a promising processing signal technique to identify when these exercise tasks should be changed.

Low back pain development differentially influences centre of pressure regularity following prolonged standing

Occupations requiring prolonged periods of static standing are associated with the development of low back pain (LBP). Certain individuals are susceptible to LBP development during prolonged standing (pain developers, PDs) while others are not (non-pain developers, NPDs). Linear centre of pressure (COP) measures suggest that standing balance control is negatively influenced following prolonged standing, and that PDs and NPDs may be differentially affected. The objective of this study was to determine if nonlinear standing balance control, quantified on COP, using sample entropy, is altered after 2-h of standing. Thirty two participants stood for 2-h. Separate 2-min standing trials, performed with eyes open and eyes closed, were collected before and after the 2-h standing protocol. Sample entropy, median power frequency and RMS amplitude of the COP time-series, was calculated from the 2-min standing trials for all participants. For comparison, participants were classified, post hoc, as PDs or NPDs according to visual analog scale pain scores. Sample entropy decreased after 2-h of standing for both PDs and NPDs, however, the decrease for NPDs was only 21% of the decrease observed in PDs. This study demonstrated that nonlinear control of upright standing changes after 2- hours of standing, resulting in an increase in COP regularity post 2- hours of standing for both PDs and NPDs. PDs displayed a greater change in COP regularity, which is supported by the theory that increased COP regularity occurs with pain/pathology.

Influence of sampling frequency and number of strides on recurrence quantifiers extracted from gait data

In this study, the influence of the sampling frequency and number of strides on recurrence quantifiers extracted from gait data was investigated in order to provide baseline values and preserve the system's non-linear dynamical characteristics expressed by these recurrence quantifiers. Recurrence quantifiers were extracted from a recurrence plot (RP), which required the reconstruction of a high-dimensional state space capable of reproducing the dynamical characteristics of the analyzed system. In this study, the following quantifiers were extracted: rate of recurrence (RR), determinism (DET), average diagonal lines length (AVG), maximum diagonal lines length (MaxL), Shannon entropy (EntD), and measure of trend (TREND). Data collected during treadmill walking were statistically analyzed to compare the distribution characteristics (mean, median, and standard deviation) and the quantifiers' correlation with those obtained from a control time series with an acquisition time corresponding to 150 strides and a 100-Hz sampling frequency, which are common values used in gait studies. It was not possible to reduce the number of strides for the MaxL or TREND. However, for the RR, DET, AVG, and EntD, it was possible to reduce the number of strides by 60% when analyzed together. The minimum sampling frequency required to extract all quantifiers simultaneously was 100 Hz. This potential reduction in the number of strides is appropriate for evaluating fast gait events, with short temporal localization in the RP, by applying the sliding window method to the recurrence plot.

A Mathematical Model to Examine Issues Associated With Using Portable Force-Measurement Technologies to Collect Infant Postural Data

Portable force-measurement technologies are becoming increasingly popular tools to examine the maturation of postural motor milestones, such as sitting and standing, in infants. These convenient, low-cost devices provide numerous opportunities to characterize postural development outside of the laboratory. However, it is important to understand the unique challenges and technical limitations associated with collecting center of pressure (CoP) data using portable force-measurement technologies in infant populations. This study uses a mathematical model to examine issues that emerge when using portable force-measurement technologies to collect sitting and standing postural data in infants. The results of our mathematical simulations demonstrate that the CoP errors from portable force-measurement technologies depend on the posture examined (e.g., sitting vs. standing), the anthropometrics of the person (e.g., height and weight), the frequency of body sway, and the experimental setup (e.g., an additional support surface being placed on top of the device). Recommendations are provided for developmental researchers interested in adopting these technologies in infant populations.

Characteristics of Serve, Reception and Set That Determine the Setting Efficacy in Men's Volleyball

The aim of this investigation was to establish the criteria of service, reception and set that determine setting efficacy in world-class top-level volleyball. The study sample consisted of 4.113 gaming actions (1.371 serve actions, 1.371 reception actions, and 1.371 set actions), corresponding to the observation of four matches for each of the 12 best ranked teams in the Volleyball World Championship - a total of 23 matches. The criteria were: in-game role of the server, serve zone, type of serve, striking technique and serve direction; receiver player, reception zone, and reception efficacy; setting zone, type of set, setting technique, setting efficacy, a set’s area, and set tempo. Multinomial logistic regression showed that criteria related to reception (reception efficacy) and to set (setting zone, type of set, a set’s area, and set tempo) determined set efficacy. Specifically, positive and negative receptions and settings from acceptable and non-acceptable zones reduced perfect setting. In contrast, the jump set toward zones three and six and the first and second tempo increased perfect setting. Serve criteria did not determine set efficacy. This study can guide trainers and players in the training process.

Comparison of a portable balance board for measures of persistence in postural sway

Measuring postural sway is important for determining functional ability or risk of falling. Gathering postural sway measures outside of controlled environments is desirable for reaching populations with limited mobility. Previous studies have confirmed the accuracy of the magnitude of postural sway using the Nintendo Wii Balance Board (WBB). However, it is unclear if the WBB can accurately measure persistence of postural sway, i.e., the pattern of center-of-pressure fluctuations over time. The purpose of this study was to compare measures of persistence of postural sway (through detrended fluctuation analysis) using WBB and a force platform (FP). Seventeen healthy individuals performed three standing conditions: eyes open, eyes closed, and one-leg standing. The WBB (30 Hz) was placed on top on the FP (600 Hz) to collect data simultaneously, then the FP data were downsampled to 100 Hz and 30 Hz. The agreement between WBB and FP for measures of postural sway were influenced by the sampling rate and postural sway direction. Intraclass correlation coefficient was excellent (range: 0.953-0.998) for long-term scaling regions in the anterior-posterior direction, but lower (range: 0.352-0.877) and inconsistent for medial-lateral direction and short-term scaling regions. The three comparison groups (WBB at 30 Hz, FP at 30 Hz, and FP at 100 Hz) showed dissimilar abilities in detecting differences in persistence of postural sway. In summary, the WBB is accurate for quantifying persistence of postural sway measurements in long-term scaling regions in the AP direction, but has limitations for short-term scaling regions and the ML direction.

Number of Trials Needed to Assess Postural Control of Young Adults in Single and Dual-Task

Despite its popularity, there is a lack of standardization when assessing postural control. This study aimed to suggest how many trials should be used when assessing young adults' postural control with a specific single-task and dual-task quiet stance protocol. Two groups of 15 participants performed 20 trials of 60 s (feet together, eyes open) with or without a dual-task. The number of trials needed to obtain two consecutive intra-class correlation coefficients (ICC(2,k)) ≥0.900 was then assessed for seven center of pressure variables. Although inconsistency was observed between variables and tasks, five trials seems to be a good compromise.

The Amount and Temporal Structure of Center of Pressure Fluctuations During Quiet Standing in Patients With Chronic Low Back Pain

The characteristics of postural sway were assessed in quiet standing under three different postural task conditions in 14 patients with nonspecific chronic low back pain and 12 healthy subjects using linear and nonlinear center of pressure parameters. The linear parameters consisted of area, the mean total velocity, sway amplitude, the SD of velocity, and the phase plane portrait. The nonlinear parameters included the Lyapunov exponent, sample entropy, and the correlation dimension. The results showed that the amount of postural sway was higher in the patients with low back pain compared with the healthy subjects. Assessing the nonlinear parameters of the center of pressure showed a lower sample entropy and a higher correlation dimension in the patients with low back pain compared with the healthy subjects. The results of this study demonstrate the greater regularity and higher dimensionality of the center of pressure fluctuations in patients with nonspecific chronic low back pain, which suggests that these patients adopt different postural control strategies to maintain an upright stance.

Fall Risk Prediction in Multiple Sclerosis Using Postural Sway Measures: A Machine Learning Approach

Numerous postural sway metrics have been shown to be sensitive to balance impairment and fall risk in individuals with MS. Yet, there are no guidelines concerning the most appropriate postural sway metrics to monitor impairment. This investigation implemented a machine learning approach to assess the accuracy and feature importance of various postural sway metrics to differentiate individuals with MS from healthy controls as a function of physiological fall risk. 153 participants (50 controls and 103 individuals with MS) underwent a static posturography assessment and a physiological fall risk assessment. Participants were further classified into four subgroups based on fall risk: controls, low-risk MS (n = 34), moderate-risk MS (n = 27), high-risk MS (n = 42). Twenty common sway metrics were derived following standard procedures and subsequently used to train a machine learning algorithm (random forest - RF, with 10-fold cross validation) to predict individuals' fall risk grouping. The sway-metric based RF classifier had high accuracy in discriminating controls from MS individuals (>86%). Sway sample entropy was identified as the strongest feature for classification of low-risk MS individuals from healthy controls. Whereas for all other comparisons, mediolateral sway amplitude was identified as the strongest predictor for fall risk groupings.

Task-specific adaptations of postural sway in sitting infants

When engaging in manual or visual tasks while sitting, infants modify their postural sway based on concurrent task demands. It remains unclear whether these modulations are sensitive to differences in concurrent task demands (holding a toy vs. looking at a toy being held by someone else), and whether the properties of the support surface impact these adaptations. We investigated infants' ability to modify postural sway when holding a toy or visually attending to a toy someone else was holding while sitting on different support surfaces. Twenty-six independently sitting infants sat on solid and compliant surfaces placed on a force plate while looking at or holding a toy. Measures of postural sway were calculated from the center of pressure data. Visually attending to a toy was associated with less sway and lower sway velocity than when holding a toy. Surprisingly, surface compliance did not affect sway and there were no interaction effects. Whereas sway modulations may facilitate infants' performance on both manual and visual concurrent tasks, the visual task placed more constraints on the postural system leading to greater adaptations in postural sway. These findings provide insights into how infants are allocating attention and coordinating perceptual-motor information in developing sitting skills.

Changed Temporal Structure of Neuromuscular Control, Rather Than Changed Intersegment Coordination, Explains Altered Stabilographic Regularity after a Moderate Perturbation of the Postural Control System

Sample entropy (SaEn) applied on center-of-pressure (COP) data provides a measure for the regularity of human postural control. Two mechanisms could contribute to altered COP regularity: first, an altered temporal structure (temporal regularity) of postural movements (H1); or second, altered coordination between segment movements (coordinative complexity; H2). The current study used rapid, voluntary head-shaking to perturb the postural control system, thus producing changes in COP regularity, to then assess the two hypotheses. Sixteen healthy participants (age 26.5 ± 3.5; seven females), whose postural movements were tracked via 39 reflective markers, performed trials in which they first stood quietly on a force plate for 30 s, then shook their head for 10 s, finally stood quietly for another 90 s. A principal component analysis (PCA) performed on the kinematic data extracted the main postural movement components. Temporal regularity was determined by calculating SaEn on the time series of these movement components. Coordinative complexity was determined by assessing the relative explained variance of the first five components. H1 was supported, but H2 was not. These results suggest that moderate perturbations of the postural control system produce altered temporal structures of the main postural movement components, but do not necessarily change the coordinative structure of intersegment movements.

Simple Degree-of-Freedom Modeling of the Random Fluctuation Arising in Human–Bicycle Balance

In this study, we propose a new simple degree-of-freedom fluctuation model that accurately reproduces the probability density functions (PDFs) of human–bicycle balance motions as simply as possible. First, we measure the time series of the roll angular displacement and velocity of human–bicycle balance motions and construct their PDFs. Next, using these PDFs as training data, we identify the model parameters by means of particle swarm optimization; in particular, we minimize the Kolmogorov–Smirnov distance between the human PDFs from the participants and the PDFs simulated by our model. The resulting PDF fitnesses were over 98.7 % for all participants, indicating that our simulated PDFs were in close agreement with human PDFs. Furthermore, the Kolmogorov–Smirnov statistical hypothesis testing was applied to the resulting human–bicycle fluctuation model, showing that the measured time responses were much better supported by our model than the Gaussian distribution.

Recurrence dynamics reveals differential control strategies to maintain balance on sloped surfaces

BACKGROUND

Studies on postural control have primarily focused on the maintenance of balance in quiet upright standing on flat horizontal support surfaces that can reveal only a subset of the potential postural stability/instability configurations in everyday contexts.

OBJECTIVES

Here we investigated the nature of dynamical properties of postural coordination in an upright standing task as a function of the systematic scaling of seven support surface angles, +20°, +10° dorsiflexion (+), 0 °Flat, -10°, -20°, -30°, -35° plantarflexion (-), mounted on a force plate.

METHODS

The center of pressure (CoP) and virtual time-to-contact (VTC) were analyzed to examine the spatial and spatio-temporal aspects of postural coordination dynamics, respectively. Recurrence quantification analysis (RQA) was used to characterize the dynamic postural control strategies as a function of slope surface angle.

RESULTS

The recurrence findings showed that on a flat surface the postural CoP dynamic are recurrent with a largely deterministic process and higher Shannon entropy compared to elevated slope angles in dorsiflexion and plantarflexion. There were asymmetrical patterns between similar slope angles for dorsiflexion and plantarflexion postures. The recurrence measures revealed that VTC operates on a higher embedding dimension than that of CoP.

SIGNIFICANCE

VTC showed an enhanced sensitivity to detection of postural instability in relation to the stability boundary that was magnified on the flat surface but progressively reduced over larger surface angles for both the dorsiflexion and plantarflexion postures.

Potential Mediators of Load-Related Changes in Movement Complexity in Young, Healthy Adults

CONTEXT

Movement screening has become increasingly popular among tactical professionals. This popularity has motivated the design of interventions that cater to improving outcomes on the screens themselves, which are often scored in reference to an objective norm. In contrast to the assumptions underlying this approach, dynamical systems theory suggests that movements arise as a function of continuously evolving constraints and that optimal movement strategies may not exist. To date, few data address behavioral complexity in the fundamental movement tasks commonly used in clinical screenings.

OBJECTIVE

To provide evidence of complex variability during movement screens and test the role of modifiable-that is, trainable-constraints in mediating loss of complexity during experimental-task manipulations.

DESIGN

Crossover study.

SETTING

Research laboratory.

PATIENTS OR OTHER PARTICIPANTS

Twenty-five male (age = 23.96 ± 3.74 years, height = 178.82 ± 7.51 cm, mass = 79.66 ± 12.66 kg) and 25 female (age = 22.00 ± 2.02 years, height = 165.40 ± 10.24 cm, mass = 63.98 ± 11.07 kg) recreationally active adults.

INTERVENTION(S)

Participants performed tests of balance, range of motion, and strength. Additionally, they performed cyclical movement tasks under a control (C) condition and while wearing an 18.10-kg weight vest (W).

MAIN OUTCOME MEASURE(S)

Ground reaction forces were sampled at 1000 Hz and used to calculate center of pressure during cyclical movement tests. Multivariate multiscale entropy (MMSE) for the center-of-pressure signal was then calculated. Condition effects (C versus W) were analyzed using paired t tests, and penalized varying-coefficients regression was used to identify models predicting entropy outcomes from balance, range of motion, and strength.

RESULTS

The MMSE decreased during the W condition (MMSEC > MMSEW; t49 range = 3.17-5.21; all P values < .01).

CONCLUSIONS

Moderate evidence supported an association between modifiable constraints and behavioral complexity, but a role in mediating load-related loss of complexity was not demonstrated.

Training history constrains postural sway dynamics: A study of balance in collegiate ice hockey players

BACKGROUND

Balance and postural control are integral to training and sport performance. Demands on posture are contextual and vary in different ways depending on the specific physical activity.

RESEARCH QUESTION

The purpose of this study was to examine the possibility that sustained exposure to environmental constraints, through specific sport participation, might lead to a persistent modification of postural control.

METHODS

Double and single-leg postural sway were compared between ice hockey players, American football players and physically active college students. Data from 30 s trials were analyzed using traditional postural sway measures of range and pathlength of the center of pressure, as well as with Sample Entropy (SEn), in both mediolateral (ML) and anteroposterior (AP) directions.

RESULTS

Each group displayed unique postural sway characteristics. During single-leg stance, ice hockey players show significantly different ML pathlength and ML and AP SEn from the physically active college students (all p < 0.05), and significantly different ML and AP pathlength and AP SEn from the American football players (all p < 0.05). The American football players and the physically active college students differed for all single-legged conditions (all p < 0.05).

SIGNIFICANCE

This suggests that the organization and development of postural sway is not only context dependent but also influenced by training history; supporting the idea that balance training for sport should be designed with regards to sport specific conditions.

The Effects of Aging and Dual Tasking on Human Gait Complexity During Treadmill Walking: A Comparative Study Using Quantized Dynamical Entropy and Sample Entropy

Quantized dynamical entropy (QDE) has recently been proposed as a new measure to quantify the complexity of dynamical systems with the purpose of offering a better computational efficiency. This paper further investigates the viability of this method using five different human gait signals. These signals are recorded while normal walking and while performing secondary tasks among two age groups (young and older age groups). The results are compared with the outcomes of previously established sample entropy (SampEn) measure for the same signals. We also study how analyzing segmented and spatially and temporally normalized signal differs from analyzing whole data. Our findings show that human gait signals become more complex as people age and while they are cognitively loaded. Center of pressure (COP) displacement in mediolateral direction is the best signal for showing the gait changes. Moreover, the results suggest that by segmenting data, more information about intrastride dynamical features are obtained. Most importantly, QDE is shown to be a reliable measure for human gait complexity analysis.

On the effects of signal processing on sample entropy for postural control

Sample entropy, a measure of time series regularity, has become increasingly popular in postural control research. We are developing a virtual reality assessment of sensory integration for postural control in people with vestibular dysfunction and wished to apply sample entropy as an outcome measure. However, despite the common use of sample entropy to quantify postural sway, we found lack of consistency in the literature regarding center-of-pressure signal manipulations prior to the computation of sample entropy. We therefore wished to investigate the effect of parameters choice and signal processing on participants’ sample entropy outcome. For that purpose, we compared center-of-pressure sample entropy data between patients with vestibular dysfunction and age-matched controls. Within our assessment, participants observed virtual reality scenes, while standing on floor or a compliant surface. We then analyzed the effect of: modification of the radius of similarity (r) and the embedding dimension (m); down-sampling or filtering and differencing or detrending. When analyzing the raw center-of-pressure data, we found a significant main effect of surface in medio-lateral and anterior-posterior directions across r’s and m’s. We also found a significant interaction group × surface in the medio-lateral direction when r was 0.05 or 0.1 with a monotonic increase in p value with increasing r in both m’s. These effects were maintained with down-sampling by 2, 3, and 4 and with detrending but not with filtering and differencing. Based on these findings, we suggest that for sample entropy to be compared across postural control studies, there needs to be increased consistency, particularly of signal handling prior to the calculation of sample entropy. Procedures such as filtering, differencing or detrending affect sample entropy values and could artificially alter the time series pattern. Therefore, if such procedures are performed they should be well justified.

The effect of age on balancing behavior: complexity analysis of mediolateral force trajectories

OBJECTIVE

We quantified, via complexity analysis, the postural stability of healthy people from a wide age range.

APPROACH

Thirty-five healthy people aged 18-72 performed three tasks while balancing on one foot on a force plate: standard balancing task, mental task (balancing while answering basic arithmetic questions), and knot-tying task (balancing while tying two knots in a piece of ribbon). Mediolateral force trajectories were analyzed to determine control strategy via Hurst exponents, Lyapunov exponents, Kolmogorov complexity, root mean square, and phase-space plots.

MAIN RESULTS

We found increased pattern repetition in balancing with increased age, as evidenced by the emergence of a double attractor pattern in phase-space plots and the increase of Hurst exponents with age from approximately 0.3 to 0.8.

SIGNIFICANCE

As people age, they tend to develop strong feed-forward control strategies for balancing, and lose the complexity of micro movements intrinsic to young age. There is an open-loop control strategy for balancing that emerges in older adulthood, and there are attractors inherent to balancing which begin to develop in middle age.

Regularity of Center of Pressure Trajectories in Expert Gymnasts during Bipedal Closed-Eyes Quiet Standing

We compared postural control of expert gymnasts (G) to that of non-gymnasts (NG) during bipedal closed-eyes quiet standing using conventional and nonlinear dynamical measures of center of foot pressure (COP) trajectories. Earlier findings based on COP classical variables showed that gymnasts exhibited a better control of postural balance but only in demanding stances. We examined whether the effect of expertise in Gymnastic can be uncovered in less demanding stances, from the analysis of the dynamic patterns of COP trajectories. Three dependent variables were computed to describe the subject's postural behavior: the variability of COP displacements (A_CoP), the variability of the COP velocities (V_CoP) and the sample entropy of COP (SEn_CoP) to quantify COP regularity (i.e., predictability). Conventional analysis of COP trajectories showed that NG and G exhibited similar amount and control of postural sway, as indicated by similar A_CoP and V_CoP values observed in NG and G, respectively. These results suggest that the specialized balance training received by G may not transfer to less challenging balance conditions such as the bipedal eyes-closed stance condition used in the present experiment. Interestingly, nonlinear dynamical analysis of COP trajectories regarding COP regularity showed that G exhibited more irregular COP fluctuations relative to NG, as indicated by the higher SEn_CoP values observed for the G than for the NG. The present results showed that a finer-grained analysis of the dynamic patterns of the COP displacements is required to uncover an effect of gymnastic expertise on postural control in nondemanding postural stance. The present findings shed light on the surplus value in the nonlinear dynamical analysis of COP trajectories to gain further insight into the mechanisms involved in the control of bipedal posture.

Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations

Entropy measures are widely applied to quantify the complexity of dynamical systems in diverse fields. However, the practical application of entropy methods is challenging, due to the variety of entropy measures and estimators and the complexity of real-world time series, including nonstationarities and long-range correlations (LRC). We conduct a systematic study on the performance, bias, and limitations of three basic measures (entropy, conditional entropy, information storage) and three traditionally used estimators (linear, kernel, nearest neighbor). We investigate the dependence of entropy measures on estimator- and process-specific parameters, and we show the effects of three types of nonstationarities due to artifacts (trends, spikes, local variance change) in simulations of stochastic autoregressive processes. We also analyze the impact of LRC on the theoretical and estimated values of entropy measures. Finally, we apply entropy methods on heart rate variability data from subjects in different physiological states and clinical conditions. We find that entropy measures can only differentiate changes of specific types in cardiac dynamics and that appropriate preprocessing is vital for correct estimation and interpretation. Demonstrating the limitations of entropy methods and shedding light on how to mitigate bias and provide correct interpretations of results, this work can serve as a comprehensive reference for the application of entropy methods and the evaluation of existing studies.

Advantages and problems of nonlinear methods applied to analyze physiological time signals: human balance control as an example

Physiological processes are regulated by nonlinear dynamical systems. Various nonlinear measures have frequently been used for characterizing the complexity of fractal time signals to detect system features that cannot be derived from linear analyses. We analysed human balance dynamics ranging from simple standing to balancing on one foot with closed eyes to study the inherent methodological problems when applying fractal dimension analysis to real-world signals. Higuchi dimension was used as an example. Choice of measurement and analysis parameters has a distinct influence on the computed dimension. Noise increases the fractional dimension which may be misinterpreted as a higher complexity of the signal. Publications without specifying the parameter setting, or without analysing the noise-sensitivity are not comparable to findings of others and therefore of limited scientific value.

How players exploit variability and regularity of game actions in female volleyball teams

Variability analysis has been used to understand how competitive constraints shape different behaviours in team sports. In this study, we analysed and compared variability of tactical performance indices in players within complex I at two different competitive levels in volleyball. We also examined whether variability was influenced by set type and period. Eight matches from the 2012 Olympics competition and from the Portuguese national league in the 2014-2015 season were analysed (1496 rallies). Variability of setting conditions, attack zone, attack tempo and block opposition was assessed using Shannon entropy measures. Magnitude-based inferences were used to analyse the practical significance of compared values of selected variables. Results showed differences between elite and national teams for all variables, which were co-adapted to the competitive constraints of set type and set periods. Elite teams exploited system stability in setting conditions and block opposition, but greater unpredictability in zone and tempo of attack. These findings suggest that uncertainty in attacking actions was a key factor that could only be achieved with greater performance stability in other game actions. Data suggested how coaches could help setters develop the capacity to play at faster tempos, diversifying attack zones, especially at critical moments in competition.

Decreased high-frequency center-of-pressure complexity in recently concussed asymptomatic athletes

Two experiments compared multiple methods of estimating postural stability entropy to address: 1) if postural complexity differences exist between concussed and healthy athletes immediately following return-to-play; 2) which methods best detect such differences; and 3) what is an appropriate interpretation of such differences. First, center of pressure (COP) data were collected from six concussed athletes over the six weeks immediately following their concussion and from 24 healthy athletes. Second, 25 healthy non-athletes performed four quiet standing tasks: normal, co-contracting their lower extremity muscles, performing a cognitive arithmetic task, and voluntarily manipulating their sway. Postural complexity was calculated using approximate, sample, multi-variate sample, and multi-variate composite multi-scale (MV-CompMSE) entropy methods for both high-pass filtered and low-pass filtered COP data. MV-CompMSE of the high-pass filtered COP signal identified the most consistent differences between groups, with concussed athletes exhibiting less complexity over the high frequency COP time-series. Among healthy non-athletes, high-pass filtered MV-CompMSE increased only in the co-contraction condition, suggesting the decrease in high frequency MV-CompMSE found in concussed athletes may be due to more relaxed muscles or less complex muscle contractions. This decrease in entropy may associate with reported increases in intra-cortical inhibition. Furthermore, a single-case study suggested high frequency MV-CompMSE may be a useful clinical tool for concussion management.

Associations between Tactile Sensory Threshold and Postural Performance and Effects of Healthy Aging and Subthreshold Vibrotactile Stimulation on Postural Outcomes in a Simple Dual Task

Specific activities that require concurrent processing of postural and cognitive tasks may increase the risk for falls in older adults. We investigated whether peripheral receptor sensitivity was associated with postural performance in a dual-task and whether an intervention in form of subthreshold vibration could affect performance. Ten younger (age: 20–35 years) and ten older adults (70–85 years) performed repeated auditory-verbal 1-back tasks while standing quietly on a force platform. Foot sole vibration was randomly added during several trials. Several postural control and performance measures were assessed and statistically analyzed (significance set to α-levels of .05). There were moderate correlations between peripheral sensitivity and several postural performance and control measures (r = .45 to .59). Several postural performance measures differed significantly between older and younger adults (p < 0.05); addition of vibration did not affect outcome measures. Aging affects healthy older adults' performance in dual-tasks, and peripheral sensitivity may be a contributor to the observed differences. A vibration intervention may only be useful when there are more severe impairments of the sensorimotor system. Hence, future research regarding the efficacy of sensorimotor interventions in the form of vibrotactile stimulation should focus on older adults whose balance is significantly affected.

The relationship between intermittent limit cycles and postural instability associated with Parkinson's disease

BACKGROUND

Many disease-specific factors such as muscular weakness, increased muscle stiffness, varying postural strategies, and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson's disease (PD). Recently, analytical techniques, inspired by the dynamical systems perspective on movement control and coordination, have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD.

METHODS

A wavelet-based technique was used to identify limit cycle oscillations (LCOs) in the anterior-posterior (AP) postural sway of people with mild PD (n = 10) compared to age-matched controls (n = 10). Participants stood on a foam and on a rigid surface while completing a dual task (speaking).

RESULTS

There was no significant difference in the root mean square of center of pressure between groups. Three out of 10 participants with PD demonstrated LCOs on the foam surface, while none in the control group demonstrated LCOs. An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD: time-delay and neuromuscular feedback gain.

CONCLUSION

Overall, the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD. In addition, these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.