Characterizing the dynamics of postural sway in humans using smoothness and regularity measures

Nonlinear dynamics of postural control system under visual-vestibular habituation balance practice: evidence from EEG, EMG and center of pressure signals

Human postural control system is inherently complex with nonlinear interaction among multiple subsystems. Accordingly, such postural control system has the flexibility in adaptation to complex environments. Previous studies applied complexity-based methods to analyze center of pressure (COP) to explore nonlinear dynamics of postural sway under changing environments, but direct evidence from central nervous system or muscular system is limited in the existing literature. Therefore, we assessed the fractal dimension of COP, surface electromyographic (sEMG) and electroencephalogram (EEG) signals under visual-vestibular habituation balance practice. We combined a rotating platform and a virtual reality headset to present visual-vestibular congruent or incongruent conditions. We asked participants to undergo repeated exposure to either congruent (n = 14) or incongruent condition (n = 13) five times while maintaining balance. We found repeated practice under both congruent and incongruent conditions increased the complexity of high-frequency (0.5-20 Hz) component of COP data and the complexity of sEMG data from tibialis anterior muscle. In contrast, repeated practice under conflicts decreased the complexity of low-frequency (<0.5 Hz) component of COP data and the complexity of EEG data of parietal and occipital lobes, while repeated practice under congruent environment decreased the complexity of EEG data of parietal and temporal lobes. These results suggested nonlinear dynamics of cortical activity differed after balance practice under congruent and incongruent environments. Also, we found a positive correlation (1) between the complexity of high-frequency component of COP and the complexity of sEMG signals from calf muscles, and (2) between the complexity of low-frequency component of COP and the complexity of EEG signals. These results suggested the low- or high-component of COP might be related to central or muscular adjustment of postural control, respectively.

Multiscale Entropy Algorithms to Analyze Complexity and Variability of Trunk Accelerations Time Series in Subjects with Parkinson's Disease

The aim of this study was to assess the ability of multiscale sample entropy (MSE), refined composite multiscale entropy (RCMSE), and complexity index (CI) to characterize gait complexity through trunk acceleration patterns in subjects with Parkinson's disease (swPD) and healthy subjects, regardless of age or gait speed. The trunk acceleration patterns of 51 swPD and 50 healthy subjects (HS) were acquired using a lumbar-mounted magneto-inertial measurement unit during their walking. MSE, RCMSE, and CI were calculated on 2000 data points, using scale factors (τ) 1-6. Differences between swPD and HS were calculated at each τ, and the area under the receiver operating characteristics, optimal cutoff points, post-test probabilities, and diagnostic odds ratios were calculated. MSE, RCMSE, and CIs showed to differentiate swPD from HS. MSE in the anteroposterior direction at τ4 and τ5, and MSE in the ML direction at τ4 showed to characterize the gait disorders of swPD with the best trade-off between positive and negative posttest probabilities and correlated with the motor disability, pelvic kinematics, and stance phase. Using a time series of 2000 data points, a scale factor of 4 or 5 in the MSE procedure can yield the best trade-off in terms of post-test probabilities when compared to other scale factors for detecting gait variability and complexity in swPD.

Multiscale Fuzzy Entropy Analysis of Balance: Evidences of Scale-Dependent Dynamics on Diabetic Patients With and Without Neuropathy

Postural control is usually assessed by examining the fluctuations of the center of pressure (COP). Balance maintenance is based on sensory feedback and neural interactions, deployed over multiple temporal scales and producing less complex outputs with aging and disease. This paper aims to investigate postural dynamics and complexity on diabetic patients, since diabetic neuropathy (DN) affects the somatosensory system and impairs postural steadiness. A multiscale fuzzy entropy (MSFEn) analysis, over a wide range of temporal scales, was performed on COP timeseries during unperturbed stance in a group of diabetic individuals without neuropathy and two groups of DN patients, with and without symptoms. A parameterization of the MSFEn curve is also proposed. A significant loss of complexity was recognized for the medial-lateral direction in DN groups with respect to non-neuropathic population. For the anterior-posterior direction, symptomatic DN group showed a lowered sway complexity for longer time scales with respect to non neuropathic and asymptomatic patients. The MSFEn approach and the related parameters highlighted that the loss of complexity might be attributed to different factors depending on sway direction, i.e. related to the presence of neuropathy along the medial-lateral axis and to a symptomatic state on the anterior-posterior direction. Results of this study support the use of the MSFEn for gaining insights into balance control mechanisms for diabetic patients, in particular when comparing non neuropathic with neuropathic asymptomatic patients, whose identification by posturographic analysis would be of great value.

The Impact of Hoffmann Reflex on Standing Postural Control Complexity in the Elderly with Impaired Plantar Sensation

In people with peripheral neuropathy (PN), impaired plantar sensation can cause adaptive changes in the central nervous system (CNS), resulting in changes in the standing postural control, which is reflected in the variability of standing output signals. Standard deviation (SD) and entropy are reliable indicators of system variability, especially since entropy is highly sensitive to diseased populations. The relation between SD and entropy, CNS and center of pressure (COP) variability is unclear for people with severe PN. The purpose of this study was to explore the adaptability of the CNS to the severe of PN and its effect on the degree and complexity of COP variability. Here, people with PN were divided into less affected (LA) and more affected (MA) groups based on plantar pressure sensitivity. We studied Hoffmann reflex (H-reflex) and standing balance performance with the control group (n = 8), LA group (n = 10), and MA group (n = 9), recording a 30 s COP time series (30,000 samples) of double-leg standing with eyes open. We observed that the more affected group had less COP complexity than people without PN. There is a significant negative correlation between the SD and sample entropy in people without PN, less affected and more affected. The COP complexity in people without PN was inversely correlated with H-reflex. We concluded that: (1) The complexity of COP variability in patients with severe plantar sensory impairment is changed, which will not affect the degree of COP variability; (2) The independence of the COP entropy in the AP and ML directions decreased, and the interdependence increased in people with PN; (3) Although the CNS of people with PN has a greater contribution to standing balance, its modulation of standing postural control is decreased.

Assessment of the Effectiveness of Rehabilitation after Total Knee Replacement Surgery Using Sample Entropy and Classical Measures of Body Balance

Exercises in virtual reality (VR) have recently become a popular form of rehabilitation and are reported to be more effective than a standard rehabilitation protocol alone. The aim of this study was to assess the efficacy of adjunct VR training in improving postural control in patients after total knee replacement surgery (TKR). Forty-two patients within 7-14 days of TKR were enrolled and divided into a VR group and a control group (C). The C group underwent standard postoperative rehabilitation. The VR group additionally attended twelve 30-min exercise sessions using the Virtual Balance Clinic prototype system. Balance was assessed on the AMTI plate in bipedal standing with and without visual feedback before and after the four-week rehabilitation. Linear measures and sample entropy of CoP data were analyzed. After four weeks of rehabilitation, a significant reduction in parameters in the sagittal plane and ellipse area was noted while the eyes remained open. Regression analysis showed that sample entropy depended on sex, body weight, visual feedback and age. Based on the sample entropy results, it was concluded that the complexity of the body reaction had not improved. The standing-with-eyes-closed test activates automatic balance mechanisms and offers better possibilities as a diagnostic tool.

Nonlinear Measures to Evaluate Upright Postural Stability: A Systematic Review

Conventional biomechanical analyses of human movement have been generally derived from linear mathematics. While these methods can be useful in many situations, they fail to describe the behavior of the human body systems that are predominately nonlinear. For this reason, nonlinear analyses have become more prevalent in recent literature. These analytical techniques are typically investigated using concepts related to variability, stability, complexity, and adaptability. This review aims to investigate the application of nonlinear metrics to assess postural stability. A systematic review was conducted of papers published from 2009 to 2019. Databases searched were PubMed, Google Scholar, Science-Direct and EBSCO. The main inclusion consisted of: Sample entropy, fractal dimension, Lyapunov exponent used as nonlinear measures, and assessment of the variability of the center of pressure during standing using force plate. Following screening, 43 articles out of the initial 1100 were reviewed including 33 articles on sample entropy, 10 articles on fractal dimension, and 4 papers on the Lyapunov exponent. This systematic study shows the reductions in postural regularity related to aging and the disease or injures in the adaptive capabilities of the movement system and how the predictability changes with different task constraints.

Functional Variability in Team-Handball Players during Balance Is Revealed by Non-Linear Measures and Is Related to Age and Expertise Level

Postural control is considered a key variable in team sports, such as handball, which require abilities strongly related to balance. However, postural control and its relationship to the performance of handball skills according to the players’ skill level and age has not been evaluated to date. This study analyzes the relationship between balance ability and team-handball performance according to age and expertise, applying a non-linear approach to balance assessment. Postural control from 114 male team-handball players was analyzed through the center of pressure (COP) during a balance task. Sport performance was measured by the accuracy and speed in throwing. Expert players threw faster, but not more accurately than recreational players. Balance performance was better for 18+ players (older than 18 years old) than those U12 (under 12 years old), but no differences were found according to their skill level. Players who threw with less accuracy showed slower COP velocity during the balance task and their moves were less irregular. Players who threw faster displayed more irregular and less auto-correlated COP movements. In conclusion, experienced team-handball players exhibited better balance performance, and this seems to be related to the maturation of the motor system more than to sport performance level. Nevertheless, non-linear measures of COP excursion revealed an exploratory behavior during balance in expert players, exhibiting more motion adjustments to reduce motor output error. Traditional variables measuring balance performance did not show sensitivity to this motor control process. A non-linear approach to balance assessment revealed functional variability during balance as an intrinsic characteristic of individuals’ motor control according to age and skill level.

Postural Control and Head Impact Exposure in Youth Football Players: Comparison of the Balance Error Scoring System and a Force Plate Protocol

Postural control testing is often used by clinicians and athletic trainers to assess the health of athletes during recovery from a concussion. Characterization of postural control as a clinical tool for use with youth athletes is limited though. The objective of this study was to compare performance on the Balance Error Scoring System (BESS) and a force plate protocol at the beginning and end of a season of football within a cohort of 34 healthy youth football players (average age of 9.9 ± 0.6 y). A secondary aim was to investigate if changes in measures of balance from the postseason to the preseason were correlated with head impact exposure. Players completed testing at the beginning and end of the youth football season. There were no significant differences between BESS scores before the season and after the season (P = .54). Performance on the BESS was not associated with any of the center of pressure metrics considered in this study. No correlation was observed between measures of balance and head impact exposure for the season. Further research is required to determine the viability of postural control testing with this population.

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.

An explorative investigation of functional differences in plantar center of pressure of four foot types using sample entropy method

In the study of biomechanics of different foot types, temporal or spatial parameters derived from plantar pressure are often used. However, there is no comparative study of complexity and regularity of the center of pressure (CoP) during the stance phase among pes valgus, pes cavus, hallux valgus and normal foot. We aim to analyze whether CoP sample entropy characteristics differ among these four foot types. In our experiment participated 40 subjects with normal feet, 40 with pes cavus, 19 with pes valgus and 36 with hallux valgus. A Footscan^® system was used to collect CoP data. We used sample entropy to quantify several parameters of the investigated four foot types. These are the displacement in medial–lateral (M/L) and anterior–posterior (A/P) directions, as well as the vertical ground reaction force of CoP during the stance phase. To fully examine the potential of the sample entropy method for quantification of CoP components, we provide results for two cases: calculating the sample entropy of normalized CoP components, as well as calculating it using the raw data of CoP components. We also explored what are the optimal values of parameters m (the matching length) and r (the tolerance range) when calculating the sample entropy of CoP data obtained during the stance phases. According to statistical results, some factors significantly influenced the sample entropy of CoP components. The sample entropies of non-normalized A/P values for the left foot, as well as for the right foot, were different between the normal foot and pes valgus, and between the normal foot and hallux valgus. The sample entropy of normalized M/L displacement of the right foot was different between the normal foot and pes cavus. The measured variable for A/P and M/L displacements could serve for the study of foot function.

Influence of repeated effort induced by a 6-min walk test on postural response in older sedentary women

According to the latest recommendations, adults should exercise regularly at moderate intensity to improve aerobic fitness and body composition. However, it is unknown whether aerobic exercise at submaximal intensity has detrimental effects on balance in older sedentary adults. We explored the effects of two 6-min walk tests (6MWTs) on the postural responses in 49 sedentary women between 60 and 76 years old. We assumed that an increase in the center of pressure (COP) fluctuations or a loss in the complexity of the COP time series would be a sign of a deleterious effect on balance. We used kinematic stabilometric parameters, recurrence quantification analysis (RQA) and the central tendency measure (CTM). We refer to the measures obtained through RQA and CTM methods by dynamical measures. Repeated-measures analysis of variance showed no significant differences between the three sets of postural kinematic measures (before vs. after the first vs. after the second 6MWT). However, we observed significant differences between the three sets for the CTM measure in the antero-posterior direction (p < 0.002), RQA determinism in the medio-lateral (ML) direction (p < 0.0001), and RQA entropy in the ML direction (F = 5.93; p < 0.004).Our results indicate that the effects of moderate-intensity walking exercise on posture are not revealed by classical postural kinematic measures but only by dynamical measures. The loss of complexity in the COP time series observed after both the first and second 6MWTs may indicate presymptomatic deterioration in the postural adaptive capabilities of sedentary older women.

Parameters Selection for Bivariate Multiscale Entropy Analysis of Postural Fluctuations in Fallers and Non-Fallers Older Adults

Entropy measures are often used to quantify the regularity of postural sway time series. Recent methodological developments provided both multivariate and multiscale approaches allowing the extraction of complexity features from physiological signals; see "Dynamical complexity of human responses: A multivariate data-adaptive framework," in Bulletin of Polish Academy of Science and Technology, vol. 60, p. 433, 2012. The resulting entropy measures are good candidates for the analysis of bivariate postural sway signals exhibiting nonstationarity and multiscale properties. These methods are dependant on several input parameters such as embedding parameters. Using two data sets collected from institutionalized frail older adults, we numerically investigate the behavior of a recent multivariate and multiscale entropy estimator; see "Multivariate multiscale entropy: A tool for complexity analysis of multichannel data," Physics Review E, vol. 84, p. 061918, 2011. We propose criteria for the selection of the input parameters. Using these optimal parameters, we statistically compare the multivariate and multiscale entropy values of postural sway data of non-faller subjects to those of fallers. These two groups are discriminated by the resulting measures over multiple time scales. We also demonstrate that the typical parameter settings proposed in the literature lead to entropy measures that do not distinguish the two groups. This last result confirms the importance of the selection of appropriate input parameters.

A Correlation-Based Framework for Evaluating Postural Control Stochastic Dynamics

The inability to maintain balance during varying postural control conditions can lead to falls, a significant cause of mortality and serious injury among older adults. However, our understanding of the underlying dynamical and stochastic processes in human postural control have not been fully explored. To further our understanding of the underlying dynamical processes, we examine a novel conceptual framework for studying human postural control using the center of pressure (COP) velocity autocorrelation function (COP-VAF) and compare its results to Stabilogram Diffusion Analysis (SDA). Eleven healthy young participants were studied under quiet unipedal or bipedal standing conditions with eyes either opened or closed. COP trajectories were analyzed using both the traditional posturographic measure SDA and the proposed COP-VAF. It is shown that the COP-VAF leads to repeatable, physiologically meaningful measures that distinguish postural control differences in unipedal versus bipedal stance trials with and without vision in healthy individuals. More specifically, both a unipedal stance and lack of visual feedback increased initial values of the COP-VAF, magnitude of the first minimum, and diffusion coefficient, particularly in contrast to bipedal stance trials with open eyes. Use of a stochastic postural control model, based on an Ornstein-Uhlenbeck process that accounts for natural weight-shifts, suggests an increase in spring constant and decreased damping coefficient when fitted to experimental data. This work suggests that we can further extend our understanding of the underlying mechanisms behind postural control in quiet stance under varying stance conditions using the COP-VAF and provides a tool for quantifying future neurorehabilitative interventions.

Sample entropy characteristics of movement for four foot types based on plantar centre of pressure during stance phase

Background

Motion characteristics of CoP (Centre of Pressure, the point of application of the resultant ground reaction force acting on the plate) are useful for foot type characteristics detection. To date, only few studies have investigated the nonlinear characteristics of CoP velocity and acceleration during the stance phase. The aim of this study is to investigate whether CoP regularity is different among four foot types (normal foot, pes valgus, hallux valgus and pes cavus); this might be useful for classification and diagnosis of foot injuries and diseases. To meet this goal, sample entropy, a measure of time-series regularity, was used to quantify the CoP regularity of four foot types.

Methods

One hundred and sixty five subjects that had the same foot type bilaterally (48 subjects with healthy feet, 22 with pes valgus, 47 with hallux valgus, and 48 with pes cavus) were recruited for this study. A Footscan® system was used to collect CoP data when each subject walked at normal and steady speed. The velocity and acceleration in medial-lateral (ML) and anterior-posterior (AP) directions, and resultant velocity and acceleration were derived from CoP. The sample entropy is the negative natural logarithm of the conditional probability that a subseries of length m that matches pointwise within a tolerance r also matches at the next point. This was used to quantify variables of CoP velocity and acceleration of four foot types. The parameters r (the tolerance) and m (the matching length) for sample entropy calculation have been determined by an optimal method.

Results

It has been found that in order to analyze all CoP parameters of velocity and acceleration during the stance phase of walking gait, for each variable there is a different optimal r value. On the contrary, the value m=4 is optimal for all variables.

Sample entropies of both velocity and acceleration in AP direction were highly correlated with their corresponding resultant variables for r>0.91. The sample entropy of the velocity in AP direction was moderately correlated with the one of the acceleration in the same direction (r≥0.673), as well as with the resultant acceleration (r≥0.660). The sample entropy of resultant velocity was moderately correlated with the one of the acceleration in AP direction, as well as with the resultant acceleration (for the both r≥0.689). Moderate correlations were found between variables for the left foot and their corresponding variables for the right foot.

Sample entropies of AP velocity, resultant velocity, AP acceleration, and resultant acceleration of the right foot as well as AP velocity and resultant velocity of the left foot were, respectively, significantly different among the four foot types.

Conclusions

It can be concluded that the sample entropy of AP velocity (or the resultant velocity) of the left foot, ML velocity, resultant velocity, ML acceleration and resultant acceleration could serve for evaluation of foot types or selection of appropriate footwear.

A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

Dynamical and stabilometric measures are complementary for the characterization of postural fluctuations in older women

We investigate the complementarities of several measures extracted from center of pressure (COP) recordings during quiet standing, in older women. The selected variables include classical stabilometric measures (SMs) and several dynamical measures (DMs). The computed DMs quantify various features of the temporal structure of COP signals, including predictability, regularity and smoothness of the trajectories. The postural fluctuations of a group of 101 healthy older women were recorded by means of a force platform. After estimating the SMs and DMs from the COP data, we used principal components analysis (PCA) to quantify the contribution of each measure. The results suggest that SMs and DMs are complementary. In addition, the different DMs are globally not redundant. This finding is a reinforcement argument in favor of the use of DMs as postural signatures.

Fuzzy central tendency measure for time series variability analysis with application to fatigue electromyography signals

A new method, namely fuzzy central tendency measure (fCTM) analysis, that could enable measurement of the variability of a time series, is presented in this study. Tests on simulated data sets show that fCTM is superior to the conventional central tendency measure (CTM) in several respects, including improved relative consistency and robustness to noise. The proposed fCTM method was applied to electromyograph (EMG) signals recorded during sustained isometric contraction for tracking local muscle fatigue. The results showed that the fCTM increased significantly during the development of muscle fatigue, and it was more sensitive to the fatigue phenomenon than mean frequency (MNF), the most commonly-used muscle fatigue indicator.

Contribution of each leg to the control of unperturbed bipedal stance in lower limb amputees: new insights using entropy

The present study was designed to assess the relative contribution of each leg to unperturbed bipedal posture in lower limb amputees. To achieve this goal, eight unilateral traumatic trans-femoral amputees (TFA) were asked to stand as still as possible on a plantar pressure data acquisition system with their eyes closed. Four dependent variables were computed to describe the subject's postural behavior: (1) body weight distribution, (2) amplitude, (3) velocity and (4) regularity of centre of foot pressure (CoP) trajectories under the amputated (A) leg and the non-amputated (NA) leg. Results showed a larger body weight distribution applied to the NA leg than to the A leg and a more regular CoP profiles (lower sample entropy values) with greater amplitude and velocity under the NA leg than under the A leg. Taken together, these findings suggest that the NA leg and the A leg do not equally contribute to the control of unperturbed bipedal posture in TFA. The observation that TFA do actively control unperturbed bipedal posture with their NA leg could be viewed as an adaptive process to the loss of the lower leg afferents and efferents because of the unilateral lower-limb amputation. From a methodological point of view, these results demonstrate the suitability of computing bilateral CoP trajectories regularity for the assessment of lateralized postural control under pathological conditions.