Sofiane Ramdani

On the use of sample entropy to analyze human postural sway data

We analyze the irregularity of human postural sway data during quiet standing using the sample entropy (SampEn) algorithm. By considering recent methodological developments, we show that the SampEn parameter is able to characterize the irregularity of the center of pressure fluctuations through the analysis of the velocity variable. We present a practical method to select the input parameters of the SampEn algorithm. We show that the computed SampEn successfully discriminates two sensory conditions (eyes-open and eyes-closed) in a group of healthy young adults. We also perform surrogate data tests to investigate the nature of the underlying dynamics of our experimental data. Finally, the results of the proposed approach are compared to those obtained with the multiscale entropy algorithm.

Dynamical structure of center of pressure fluctuations in elderly people

This study investigates whether aging has an influence on the dynamics of the fluctuations of the displacement of the center of pressure (COP), during quiet standing. Two groups of healthy subjects were compared (11 young and 12 elderly) for two visual feedback conditions (eyes open and eyes closed). The data were analyzed using (i) classical stabilometric variables (length and surface) and (ii) recurrence quantification analysis (percentage of determinism and entropy), for the dynamical structure of COP signals. The length of the COP displacement was found to be the best discriminating stabilometric variable for both visual and aging effects. Visual feedback influenced recurrence quantification analysis (RQA) variables only for the elderly group. Both RQA outputs in the anterior posterior direction were sufficient to distinguish the young and elderly groups. The entropy estimation computed by RQA was significantly reduced for postural fluctuations in elderly people. We conclude that classical stabilometric variables and RQA outputs provide complementary information for the characterization of ageing effects on postural sway.

Recurrence quantification analysis of surface electromyographic signal: Sensitivity to potentiation and neuromuscular fatigue

This study aimed to assess the capacity of recurrence quantification analysis (RQA) to detect potentiation and to determine the fatigue components to which RQA is sensitive. Fifteen men were divided in two groups [8 endurance-trained athletes (END) and 7 power-trained athletes (POW)]. They performed a 10-min intermittent (5s contraction, 5s rest) knee extension exercise at 50% of their maximal voluntary isometric contraction. Muscular fatigue and potentiation were evaluated with neurostimulation technique. Mechanical (peak torque, Pt) and electrophysiological (M-wave) responses following electrical stimulation of the femoral nerve were measured at rest and every 10s throughout exercise. Vastus lateralis muscle activity (root mean square, RMS) was recorded during each contraction, and RMS was normalized to M-wave area (RMS/M). During contraction, muscle activity was analyzed with RQA to obtain the percentage of determinism (%Det). At the beginning of exercise, a significant Pt increase (+52%, P<0.001) was observed in both groups, indicating potentiation. At this time, %Det remained constant in both groups, indicating that RQA did not detect potentiation. Thereafter, Pt decreased in POW from 5min 30s of exercise (-30%, P<0.001), reflecting impairment in excitation-contraction coupling, and %Det increased from 3min 30s (P<0.01). In END, Pt remained high and %Det was unchanged. These two results indicated that RQA detected the peripheral component of fatigue. Conversely, RQA did not detect central adaptation to fatigue since %Det remained constant when a significant increase in RMS/M (P<0.01) appeared in END.

Influence of noise on the sample entropy algorithm.

We study the effect of static additive noise on the sample entropy (SampEn) algorithm [J. S. Richman and J. R. Moorman, Am. J. Physiol. Heart Circ. Physiol. 278, 2039 (2000); R. B. Govindan et al., Physica A 376, 158 (2007)] for analyzing time series. Using surrogate data tests, we empirically investigate the ability of the SampEn index to detect nonlinearity in simulated time series corrupted by increased amounts of noise. Discrete and continuous chaotic and nonchaotic systems are included in the numerical experiments. Both Gaussian and uniformly distributed noises are considered. The results indicate that the SampEn statistic is a robust index for detecting nonlinearity in time series corrupted by observational noise.

Recurrence Quantification Analysis of Human Postural Fluctuations in Older Fallers and Non-fallers

We investigate postural sway data dynamics in older adult fallers and non-fallers. Center of pressure (COP) signals were recorded during quiet standing in 28 older adults. The subjects were divided in two groups: with and without history of falls. COP time series were analyzed using recurrence quantification analysis (RQA) in both anteroposterior and mediolateral (ML) directions. Classical stabilometric variables (path length and range) were also computed. The results showed that RQA outputs quantifying predictability of COP fluctuations and Shannon entropy of recurrence plot diagonal line length distribution, were significantly higher in fallers, only for ML direction. In addition, the range of ML COP signals was also significantly higher in fallers. This result is in accordance with some findings of the literature and could be interpreted as an increased hip strategy in fallers. The RQA results seem coherent with the theory of loss of complexity with aging and disease. Our results suggest that RQA is a promising approach for the investigation of COP fluctuations in a frail population.

Characterizing the Dynamics of Postural Sway in Humans Using Smoothness and Regularity Measures

We investigate human postural sway velocity time series by computing two dynamical statistics quantifying the smoothness (the central tendency measure or CTM) and the regularity (the sample entropy or SampEn) of their underlying dynamics. The purpose of the study is to investigate the effect of aging and vision on the selected measures and to explore the nature of postural dynamics by performing surrogate data tests. A group of 14 young subjects was compared to a group of 11 older healthy subjects in two visual conditions: with eyes open (EO) and with eyes closed (EC). The results suggest that vision and age do not influence the two statistics of the velocity data in the same way. More specifically, the smoothness statistic is able to detect the aging effect. The regularity measure is sensitive to the visual feedback removal. In contrast with some findings in the literature, the results of the surrogate data tests indicate that the center of pressure velocity dynamics are stochastic and are not produced by a purely determinisitic behavior. Finally, we discuss some potential implications of our results in terms of postural control mechanisms.

A structurally optimal control model for predicting and analyzing human postural coordination

This paper proposes a closed-loop optimal control model predicting changes between in-phase and anti-phase postural coordination during standing and related supra-postural activities. The model allows the evaluation of the influence of body dynamics and balance constraints onto the adoption of postural coordination. This model minimizes the instantaneous norm of the joint torques with a controller in the head space, in contrast with classical linear optimal models used in the postural literature and defined in joint space. The balance constraint is addressed with an adaptive ankle torque saturation. Numerical simulations showed that the model was able to predict changes between in-phase and anti-phase postural coordination modes and other non-linear transient dynamics phenomena.

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.

Physical function decline and degradation of postural sway dynamics in asymptomatic sedentary postmenopausal women

BackgroundPostural control is an important aspect of physical functioning.ObjectiveTo determine whether postural sway complexity could discriminate asymptomatic sedentary postmenopausal women with normal or subnormal physical function from those with lower physical function.DesignCross-sectional study.SettingDepartment of Geriatrics, University Hospital of Montpellier.Participants126 community-dwelling women aged 55 to 76 recruited though public meetings aimed at promoting physical activity in postmenopausal women.MeasurementsWomen were asked to stand still on a force platform, either with eyes open (EO) or eyes closed (EC). Physical function was estimated using the Six-Minute Walking Distance (6MWD) test, expressed as a percentage of the predicted 6MWD (%-pred 6MWD) based on age, gender, body height, and weight. In addition to traditional stabilometric measures, dynamical measures (percentage of determinism of recurrence quantification analysis [DETRQA], sample entropy [SampEn] and complexity index of multiscale entropy [CIMSE]) were used to quantify the complexity of center of pressure (COP) time series (DETRQA: predictability, SampEn: regularity, CIMSE: multiscale regularity).ResultsNone of the traditional stabilometric measures differentiated women with lower (%-pred 6MWD ≤ 85.5%) from those with subnormal or normal (%-pred 6MWD > 85.5%) physical function. Conversely, women with lower physical function showed lower SampEn values in the AP direction in both EO and EC conditions, as well as lower SampEn and higher DETRQA values in the ML direction in EC condition. No significant difference in the CIMSE values was found between the two groups.ConclusionLower physical function was found to be associated with lower postural sway complexity (higher regularity and predictability) in asymptomatic sedentary postmenopausal women, especially in the absence of vision. Future work is needed to determine whether a decrease in postural sway complexity could predict future decline in physical function in these women.

Statistical behavior of edge detectors

In this paper we present a method for estimating the statistical properties of two well-known edge detectors: the non maxima suppression and the zero crossing of the Laplacian algorithms. Assuming the data are corrupted by an additive Gaussian noise we derive the probability density function (pdf) of the detected edge. Thanks to this approach the computed pdf explicitly depends on the parameters of the edge detector. Experimental results on real images and comparisons with Monte Carlo simulations are presented in order to characterize the performance of this method.