Statistical Analysis of Gait Maturation in Children Based on Probability Density Functions

Analysis of gait patterns in children is useful for the study of maturation of locomotor control. In this paper, we utilized the Parzen-window method to estimate the probability density functions (PDFs) of the stride interval for 50 children. With the estimated PDFs, the statistical measures, i.e., averaged stride interval (ASI), variation of stride interval (VSI), PDF skewness (SK), and PDF kurtosis (KU), were computed for the gait maturation in three age groups (aged 3-5 years, 6-8 years, and 10-14 years) of young children. The results indicated that the ASI and VSI values are significantly different between the three age groups. The VSI is decreased rapidly until 8 years of age, and then continues to be decreased at a slower rate. The SK values of the PDFs for all of the three age groups are positive, which shows a slight imbalance in the stride interval distribution within each age group. In addition, the decrease of the KU values of the PDFs is age-dependent, which suggests the effects of the musculo-skeletal growth on the gait maturation in young children

Statistical Analysis of Gait Maturation in Children Using Nonparametric Probability Density Function Modeling

Analysis of gait dynamics in children may help understand the development of neuromuscular control and maturation of locomotor function. This paper applied the nonparametric Parzen-window estimation method to establish the probability density function (PDF) models for the stride interval time series of 50 children (25 boys and 25 girls). Four statistical parameters, in terms of averaged stride interval (ASI), variation of stride interval (VSI), PDF skewness (SK), and PDF kurtosis (KU), were computed with the Parzen-window PDFs to study the maturation of stride interval in children. By analyzing the results of the children in three age groups (aged 3–5 years, 6–8 years, and 10–14 years), we summarize the key findings of the present study as follows. (1) The gait cycle duration, in terms of ASI, increases until 14 years of age. On the other hand, the gait variability, in terms of VSI, decreases rapidly until 8 years of age, and then continues to decrease at a slower rate. (2) The SK values of both the histograms and Parzen-window PDFs for all of the three age groups are positive, which indicates an imbalance in the stride interval distribution within an age group. However, such an imbalance would be meliorated when the children grow up. (3) The KU values of both the histograms and Parzen-window PDFs decrease with the body growth in children, which suggests that the musculoskeletal growth enables the children to modulate a gait cadence with ease. (4) The SK and KU results also demonstrate the superiority of the Parzen-window PDF estimation method to the Gaussian distribution modeling, for the study of gait maturation in children.This work was supported by the Fundamental Research Funds for the Central Universities of China (grant no. 2010121061), the Natural Science Foundation of Fujian (grant no. 2011J01371), and the National Natural Science Foundation of China (grant no. 81101115). N. Xiang was supported by Xiamen University Undergraduate Innovation Training Project (grant no. XDDC201210384072). Z. T. Zhong was supported by the Fundamental Research Funds for the Central Universities (grant no. CXB2011023). J. He was supported by the Xiamen University undergraduate student innovative experiment project (grant no. XDDC2011007). The authors acknowledge Hausdorff et al. for providing the data of gait experiments with public access via PhysioNet

Amplitude- and Fluctuation-based Dispersion Entropy

Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel–Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326

Managing variability in the summary and comparison of gait data

Variability in quantitative gait data arises from many potential sources, including natural temporal dynamics of neuromotor control, pathologies of the neurological or musculoskeletal systems, the effects of aging, as well as variations in the external environment, assistive devices, instrumentation or data collection methodologies. In light of this variability, unidimensional, cycle-based gait variables such as stride period should be viewed as random variables and prototypical single-cycle kinematic or kinetic curves ought to be considered as random functions of time. Within this framework, we exemplify some practical solutions to a number of commonly encountered analytical challenges in dealing with gait variability. On the topic of univariate gait variables, robust estimation is proposed as a means of coping with contaminated gait data, and the summary of non-normally distributed gait data is demonstrated by way of empirical examples. On the summary of gait curves, we discuss methods to manage undesirable phase variation and non-robust spread estimates. To overcome the limitations of conventional comparisons among curve landmarks or parameters, we propose as a viable alternative, the combination of curve registration, robust estimation, and formal statistical testing of curves as coherent units. On the basis of these discussions, we provide heuristic guidelines for the summary of gait variables and the comparison of gait curves

Human Development

Human development has different meanings depending on the area we focus on. To the psychologists it is the ontogenetic process of individual development. It considers systematic psychological changes that occur in human beings over the course of their life span. To sociologists and economists, among others, the main consideration is the macro-level of countries or regions and their development conditions related to human needs. Our book has two parts. The first one is entitled "Development in the ontogenesis" and it consists of three chapters whilst the second is "Human development: contextual factors", also including 3 chapters. Together, the two parts give the readers a panoramic view of very complex subjects and complement each other. Researchers of ontogenetic development cannot ignore that contextual factors are the basis of this process. On the other hand, social scientists worried about the macro variables need to remember that they are dealing with people, who are affected one way or another by those variables and whose development is the product of biology and culture

A nonlinear dynamical model of human gait

We present a nonlinear stochastic model of the human gait control system in a variety of gait regimes. The stride interval time series in normal human gait is characterized by slightly multifractal fluctuations. The fractal nature of the fluctuations become more pronounced under both an increase and decrease in the average gait. Moreover, the long-range memory in these fluctuations is lost when the gait is keyed on a metronome. The human locomotion is controlled by a network of neurons capable of producing a correlated syncopated output. The central nervous system is coupled to the motocontrol system, and together they control the locomotion of the gait cycle itself. The metronomic gait is simulated by a forced nonlinear oscillator with a periodic external force associated with the conscious act of walking in a particular way.Comment: 13 pages, 10 figure

Regular and stochastic behavior of Parkinsonian pathological tremor signals

Regular and stochastic behavior in the time series of Parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non-Markov stochastic processes and flicker-noise spectroscopy. We have developed a new method of analyzing and diagnosing Parkinson's disease (PD) by taking into consideration discreteness, fluctuations, long- and short-range correlations, regular and stochastic behavior, Markov and non-Markov effects and dynamic alternation of relaxation modes in the initial time signals. The spectrum of the statistical non-Markovity parameter reflects Markovity and non-Markovity in the initial time series of tremor. The relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states. The local time behavior of the initial time correlation function and the first point of the non-Markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series. The obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a PD patient. Generally, the method allows one to assess the efficacy of the medical treatment for a group of PD patients.Comment: 39 pages, 10 figures, 1 table Physica A, in pres

Sex differences in postural control maturation during childhood andadolescence: a cross-sectional study in children between 4 and 17 years old

Purpose: the aim of this study was to determine the differences between the sexes in the development of postural control during childhood and adolescence. Methods: Three hundred and eighty-nine children were involved in a 30-s trial with eyes open and a 30-s trial with eyes closed. Using a Wii Balance Board, the mean velocity and median frequency in antero-posterior and medio-lateral directions were calculated, as well as the 95% confidence interval ellipse area. Results: The results showed that the youngest boys (4-5 years old) had a greater ellipse area than girls of the same age, while the girls in this age group showed a greater ellipse area ratio, although these differences disappeared until 12-13 years old. At this age, the boys showed greater mean velocity in antero-posterior direction both with eyes open and closed, as well as a greater ellipse area and mean velocity in the medio-lateral direction with eyes open. At 16-17 years old, the boys had lower mean velocity in the medio-lateral direction both with eyes open and eyes closed. Conclusions: In conclusion, the results indicate certain differences in the postural control maturation of girls and boys during childhood and adolescence.Objetivo: el objetivo de este estudio fue determinar las diferencias entre sexos en el desarrollo del control postural durante la infancia y la adolescencia. Material y métodos: Trescientos ochenta y nueve niños participaron en un ensayo de 30s con los ojos abiertos y otro de 30s con los ojos cerrados. Utilizando una Wii Balance Board, se calculó la velocidad media y la frecuencia media en las direcciones anteroposterior y medio-lateral, así como el área de la elipse del intervalo de confianza del 95%. Resultados: Los resultados mostraron que los niños más pequeños (4-5 años) tenían un área de elipse mayor que las niñas de la misma edad, mientras que las niñas de este grupo de edad mostraban una mayor relación de área de elipse, aunque estas diferencias desaparecieron hasta los 12-13 años. A esta edad, los chicos mostraron una mayor velocidad media en dirección anteroposterior tanto con los ojos abiertos como cerrados, así como una mayor área de la elipse y velocidad media en dirección medio-lateral con los ojos abiertos. A los 16-17 años, los chicos presentaban una menor velocidad media en la dirección medio-lateral tanto con los ojos abiertos como cerrados. Conclusiones: los resultados indican ciertas diferencias en la maduración del control postural de chicas y chicos durante la infancia y la adolescencia

The rates of change of the stochastic trajectories of acceleration variability are a good predictor of normal aging and of the stage of Parkinson's disease

The accelerometer data from mobile smart phones provide stochastic trajectories that change over time. This rate of change is unique to each person and can be well-characterized by the continuous two-parameter family of Gamma probability distributions. Accordingly, on the Gamma plane each participant can be uniquely localized by the shape and the scale parameters of the Gamma probability distribution. The scatter of such points contains information that can unambiguously separate the normal controls (NC) from those patients with Parkinson's disease (PD) that are at a later stage of the disease. In general normal aging seems conducive of more predictable patterns of variation in the accelerometer data. Yet this trend breaks down in PD where the statistical signatures seem to be a more relevant predictor of the stage of the disease. Those patients at a later stage of the disease have more random and noisier patterns than those in the earlier stages, whose statistics resemble those of the older NC. Overall the peak rates of change of the stochastic trajectories of the accelerometer are a good predictor of the stage of PD and of the age of a “normally” aging individual