scholarly journals Significance of trends in gait dynamics

2019 ◽  
Author(s):  
Klaudia Kozlowska ◽  
Miroslaw Latka ◽  
Bruce J. West
Keyword(s):  
Large Scale ◽  
Stride Length ◽  
Human Gait ◽  
Small Scale ◽  
Strongly Correlated ◽  
Scaling Exponents ◽  
Treadmill Speed ◽  
Gait Parameters ◽  
Instantaneous Values ◽  
Spatio Temporal

AbstractTrends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The group-averaged values of scaling exponents of ST and ST MARS residuals are slightly smaller than 0.5, indicating weak anti-persistence. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. doi:10.1371/journal.pcbi.1000856.Author summaryDuring treadmill walking, the subject’s stride time (ST) and stride length (SL) must yield a stride speed which can fluctuate over a narrow range centered on the treadmill belt’s speed. The fact that both ST and SL are persistent is an intriguing property of human gait. For persistent fluctuations any deviation from the mean value is likely to be followed by a deviation in the same direction. To trace the origin of such persistence, we used a novel approach to determine trends in spatio-temporal gait parameters. We find that the trends of ST and SL of a subject are strongly correlated and are statistically independent of their corresponding residuals. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The persistence of gait parameters stems from superposition of large scale trends and small scale fluctuations.

scholarly journals Significance of trends in gait dynamics

2020 ◽  
Vol 16 (10) ◽  
pp. e1007180
Author(s):  
Klaudia Kozlowska ◽  
Miroslaw Latka ◽  
Bruce J. West
Keyword(s):  
Time Series ◽  
Large Scale ◽  
Fundamental Problem ◽  
Multivariate Adaptive Regression Splines ◽  
Human Gait ◽  
Small Scale ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Treadmill Speed

Trends in time series generated by physiological control systems are ubiquitous. Determining whether trends arise from intrinsic system dynamics or originate outside of the system is a fundamental problem of fractal series analysis. In the latter case, it is necessary to filter out the trends before attempting to quantify correlations in the noise (residuals). For over two decades, detrended fluctuation analysis (DFA) has been used to calculate scaling exponents of stride time (ST), stride length (SL), and stride speed (SS) of human gait. Herein, rather than relying on the very specific form of detrending characteristic of DFA, we adopt Multivariate Adaptive Regression Splines (MARS) to explicitly determine trends in spatio-temporal gait parameters during treadmill walking. Then, we use the madogram estimator to calculate the scaling exponent of the corresponding MARS residuals. The durations of ST and SL trends are determined to be independent of treadmill speed and have distributions with exponential tails. At all speeds considered, the trends of ST and SL are strongly correlated and are statistically independent of their corresponding residuals. The averages of scaling exponents of ST and SL MARS residuals are slightly smaller than 0.5. Thus, contrary to the interpretation prevalent in the literature, the statistical properties of ST and SL time series originate from the superposition of large scale trends and small scale fluctuations. We show that trends serve as the control manifolds about which ST and SL fluctuate. Moreover, the trend speed, defined as the ratio of instantaneous values of SL and ST trends, is tightly controlled about the treadmill speed. The strong coupling between the ST and SL trends ensures that the concomitant changes of their values correspond to movement along the constant speed goal equivalent manifold as postulated by Dingwell et al. 10.1371/journal.pcbi.1000856.

Variability of gait spatio-temporal parameters during treadmill walking

2021 ◽  
Author(s):  
Miroslaw Latka ◽  
Klaudia Kozlowska ◽  
Bruce J. West
Keyword(s):  
Stride Length ◽  
Fundamental Problem ◽  
Treadmill Walking ◽  
Frequency Noise ◽  
Strongly Correlated ◽  
Nonlinear Functions ◽  
Mean Values ◽  
First Case ◽  
Gait Parameters ◽  
Spatio Temporal

Abstract During treadmill walking, the subject’s stride length (SL) and duration (ST) yield a stride speed (SS) which fluctuates over a narrow range centered on the treadmill belt’s speed. We recently demonstrated that ST and SL trends are strongly correlated and serve as control manifolds about which the corresponding gait parameters fluctuate. The fundamental problem, which has not yet been investigated, concerns the contribution of SL and ST fluctuations to SS variability. To investigate this relation, we approximate SS variance by the linear combination of SL variance and ST variance, as well as their covariance. The combination coefficients are nonlinear functions of ST and SL mean values and, consequently, depend on treadmill speed. The approximation applies to constant speed treadmill walking and walking on a treadmill whose belt speed is perturbed by strong, high-frequency noise. In the first case, up to 80% of stride speed variance comes from SL fluctuations. In the presence of perturbations, the SL contribution decreases with increasing speed, but its lowest value is still twice as large as that of either ST variance or SL-ST covariance. The presented evidence supports the hypothesis that stride length adjustments are primarily responsible for speed maintenance during walking. Such a control strategy is evolutionarily advantageous due to the weak speed dependence of the SL contribution to SS variance. The ability to maintain speed close to that of a moving cohort did increase the chance of an individual’s survival throughout most of human evolution.

scholarly journals Persistence and anti-persistence in treadmill walking

2021 ◽  
Author(s):  
Klaudia Kozlowska ◽  
Miroslaw Latka ◽  
Bruce J. West
Keyword(s):  
Large Scale ◽  
Research Question ◽  
Random Noise ◽  
Cauchy Distribution ◽  
Multivariate Adaptive Regression Splines ◽  
Small Scale ◽  
Scaling Exponents ◽  
Belt Speed ◽  
Gait Parameters ◽  
All Speeds

AbstractBackgroundLong-range persistent correlations in stride time (ST) and length (SL) are the fundamental traits of treadmill gait. Our recent work showed that the ST and SL time series’ statistical properties originated from the superposition of large-scale trends and small-scale fluctuations (residuals). Trends served as the control manifolds about which ST and SL fluctuated. The scaling exponents of the residuals were slightly smaller than 0.5.Research questionDo random changes in treadmill belt speed affect the trend properties and scaling exponents of ST/SL residuals?MethodsWe used Multivariate Adaptive Regression Splines (MARS) to determine gait trends during a walk on a treadmill whose belt speed was perturbed by a strong random noise. Then, we calculated the scaling exponents of MARS residuals with the madogram estimator.ResultsExcept for the ST at the lowest treadmill speed v = 0.8 m/s, the normalized trend duration was at least three times greater than that for the unperturbed walk. The Cauchy distribution scale parameter, which served as a measure of the width of SL and ST trend slope distributions, was at v = 1.2 m/s, almost 50% and 25% smaller than the unperturbed values. The differences were even greater at v = 1.6 m/s: 73% and 83%. For all speeds, the ST and SL MARS residuals were strongly anti-persistent. At v = 1.2 m/s, the corresponding scaling exponents were equal to 0.37±0.10 and 0.25±0.09. Apart from ST at v = 0.8 m/s, the ST/SL scaling indices were close to 0.5.SignificancePersistence of gait parameters is closely related to the properties of their trends. Longer trends with a gentle slope and strong anti-persistence of ST/SL residuals are the manifestations or tight control required during the perturbed treadmill walk.

scholarly journals Quantitative assessment of gait parameters in people with Parkinson's disease in laboratory and clinical setting: Are the measures interchangeable?

2018 ◽  
Vol 10 (2) ◽  
Author(s):  
Massimiliano Pau ◽  
Federica Corona ◽  
Roberta Pili ◽  
Carlo Casula ◽  
Marco Guicciardi ◽  
...  
Keyword(s):  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Clinical Setting ◽  
Stride Length ◽  
Experimental Setting ◽  
Optoelectronic System ◽  
Double Support ◽  
Gait Parameters ◽  
Spatio Temporal ◽  
Wearable Accelerometers

This study aimed to investigate possible differences in spatio-temporal gait parameters of people with Parkinson’s Disease (pwPD) when they are tested either in laboratory using 3D Gait Analysis or in a clinical setting using wearable accelerometers. The main spatio-temporal gait parameters (speed, cadence, stride length, stance, swing and double support duration) of 31 pwPD were acquired: i) using a wearable accelerometer in a clinical setting while wearing shoes (ISS); ii) same as condition 1, but barefoot (ISB); iii) using an optoelectronic system (OES) undressed and barefoot. While no significant differences were found for cadence, stance, swing and double support duration, the experimental setting affected speed and stride length that decreased (by 17% and 12% respectively, P<0.005) when passing from the clinical (ISS) to the laboratory (OES) setting. These results suggest that gait assessment should be always performed in the same conditions to avoid errors, which may lead to inaccurate patient’s evaluations.

scholarly journals Solar cycle changes in the geo-effectiveness of small-scale solar wind turbulence measured by Wind and ACE at 1 AU

2007 ◽  
Vol 25 (5) ◽  
pp. 1183-1197 ◽  
Author(s):  
M. L. Parkinson ◽  
R. C. Healey ◽  
P. L. Dyson
Keyword(s):  
Solar Wind ◽  
Solar Cycle ◽  
Solar Minimum ◽  
Large Scale ◽  
Small Scale ◽  
Scaling Exponent ◽  
Mhd Turbulence ◽  
Scaling Exponents ◽  
Solar Wind Turbulence ◽  
Wind Turbulence

Abstract. Multi-scale structure of the solar wind in the ecliptic at 1 AU undergoes significant evolution with the phase of the solar cycle. Wind spacecraft measurements during 1995 to 1998 and ACE spacecraft measurements during 1997 to 2005 were used to characterise the evolution of small-scale (~1 min to 2 h) fluctuations in the solar wind speed vsw, magnetic energy density B2, and solar wind ε parameter, in the context of large-scale (~1 day to years) variations. The large-scale variation in ε most resembled large-scale variations in B2. The probability density of large fluctuations in ε and B2 both had strong minima during 1995, a familiar signature of solar minimum. Generalized Structure Function (GSF) analysis was used to estimate inertial range scaling exponents aGSF and their evolution throughout 1995 to 2005. For the entire data set, the weighted average scaling exponent for small-scale fluctuations in vsw was aGSF=0.284±0.001, a value characteristic of intermittent MHD turbulence (>1/4), whereas the scaling exponents for corresponding fluctuations in B2 and ε were aGSF=0.395±0.001 and 0.334±0.001, respectively. These values are between the range expected for Gaussian fluctuations (1/2) and Kolmogorov turbulence (1/3). However, the scaling exponent for ε changed from a Gaussian-Kolmogorov value of 0.373±0.005 during 1997 (end of solar minimum) to an MHD turbulence value of 0.247±0.004 during 2003 (recurrent fast streams). Changes in the characteristics of solar wind turbulence may be reproducible from one solar cycle to the next.

The effects of salinity, turbidity and flow on fish biomass estimated acoustically in two tidal rivers

2014 ◽  
Vol 65 (3) ◽  
pp. 267 ◽  
Author(s):  
V. F. Matveev ◽  
A. D. L. Steven
Keyword(s):  
Large Scale ◽  
River System ◽  
Fish Abundance ◽  
Practical Significance ◽  
Small Scale ◽  
Fish Biomass ◽  
Strongly Correlated ◽  
Commercial Catch ◽  
Four Seasons ◽  
Annual Means

Establishing drivers of fish abundance in estuaries is an important task of both theoretical and practical significance. Commercial catch data help explain large-scale variation in fish productivity; however, there is insufficient understanding of small-scale changes. We analysed correlations between acoustically estimated fish biomass (FB) and environmental variables, which included indices of primary productivity and physio-chemistry in a coastal river system during four seasons. Spatial series of FB were obtained for the Logan River (main estuary) and the Albert River (tributary) located in South East Queensland, Australia. Most of the year, FB was significantly higher in the Albert River. Annual means for discharge, salinity and pH were significantly lower, whereas phosphorus concentrations were higher in the Albert River. Out of 15 hydrological variables tested, FB was strongly correlated only with salinity, conductivity and turbidity. In the Albert River, where fish were larger, as indicated by greater target strengths, FB was positively correlated with river discharge. Our results suggest that salinity and turbidity can be important seasonal drivers of fish abundance in communities dominated by Mugil spp. and Nematalosa erebi and that the flow-biomass relationship may appear independent of the effects of primary production.

scholarly journals Bobath and traditional approaches in post-stroke gait rehabilitation in adults

2017 ◽  
Vol 9 (1) ◽  
pp. 27-33 ◽  
Author(s):  
Emilia Mikołajewska
Keyword(s):  
Stride Length ◽  
Reference Group ◽  
Traditional Approach ◽  
Gait Velocity ◽  
Treatment Groups ◽  
Post Stroke ◽  
Gait Parameters ◽  
Effective Form ◽  
Spatio Temporal ◽  
Traditional Approaches

Summary Study aim: The aim of this study was to compare the outcomes of a study of post-stroke gait reeducation using the Bobath neuro‑developmental treatment (NDT-Bobath) method and the traditional approach.Material and methods: The study included 30 adult patients after ischemic stroke, aged 32-82. Patients were randomly assigned to one of the treatment groups: the study group (treated with the NDT-Bobath method combined with the traditional approach, ten sessions), and a reference group (treated with the traditional method only, ten sessions). The measurements (spatio-temporal gait parameters based on 10 m walking test: gait velocity, normalized gait velocity, cadence, normalized cadence, stride length, and normalized stride length) were administered twice: on admission (before the therapy) and after the last therapy session.Results: Statistically significant and favorable changes in the gait velocity, cadence and stride length regarding their normalized values were observed. Moderate and high correlations among changes of assessed spatio-temporal gait parameters were observed in both groups.Conclusions: The NDT-Bobath method may be regarded as a more effective form of gait post-stroke rehabilitation in young adults compared to traditional rehabilitation.

scholarly journals Analysis of the spatio-temporal gait parameters of transtibial amputees

2018 ◽  
Vol 1 (2) ◽  
pp. 247-253
Author(s):  
Yuliana Ruiz-Piragauta ◽  
Brigette Paola Torres-Bello ◽  
Esperanza Camargo-Casallas
Keyword(s):  
Lower Limb ◽  
Stride Length ◽  
Inertial Sensors ◽  
Step Length ◽  
Gait Pattern ◽  
Gait Parameters ◽  
Length Step ◽  
Spatio Temporal ◽  
Antipersonnel Mines ◽  
Transtibial Amputees

In this study we analyzed the spatio-temporal parameters (step length, step time, stride length, stride time, speed and rate) of three unilateral transtibial amputees in order to find the best gait pattern and this verify the adaptation of the prosthesis, using inertial sensors of the TECHNAID ® brand in order to make the diagnosis in an objective way; the data were processed using the MARCHA ET software of the DIGITI research group of the Universidad Distrital Francisco José de Caldas. In this study, were analyzed three subjects from the Hospital Militar Central (HMC) the cause of amputation is due to trauma caused by antipersonnel mines. It was found that subjects with unilateral transtibial amputation lean on more time and carry more weight on their healthy lower limb, which leads to an increase in mechanical demand on the knee joint of the amputated leg.

scholarly journals Instantaneous variance scaling of AIRS thermodynamic profiles using a circular area Monte Carlo approach

2018 ◽  
Vol 11 (5) ◽  
pp. 2717-2733
Author(s):  
Jesse Dorrestijn ◽  
Brian H. Kahn ◽  
João Teixeira ◽  
Fredrick W. Irion
Keyword(s):  
Monte Carlo ◽  
Large Scale ◽  
Specific Humidity ◽  
Time Variability ◽  
Small Scale ◽  
Circular Area ◽  
Scaling Exponents ◽  
Cloud Parameterization ◽  
Non Gaussian ◽  
The Tropics

Abstract. Satellite observations are used to obtain vertical profiles of variance scaling of temperature (T) and specific humidity (q) in the atmosphere. A higher spatial resolution nadir retrieval at 13.5 km complements previous Atmospheric Infrared Sounder (AIRS) investigations with 45 km resolution retrievals and enables the derivation of power law scaling exponents to length scales as small as 55 km. We introduce a variable-sized circular-area Monte Carlo methodology to compute exponents instantaneously within the swath of AIRS that yields additional insight into scaling behavior. While this method is approximate and some biases are likely to exist within non-Gaussian portions of the satellite observational swaths of T and q, this method enables the estimation of scale-dependent behavior within instantaneous swaths for individual tropical and extratropical systems of interest. Scaling exponents are shown to fluctuate between β=-1 and −3 at scales ≥500 km, while at scales ≤500 km they are typically near β≈-2, with q slightly lower than T at the smallest scales observed. In the extratropics, the large-scale β is near −3. Within the tropics, however, the large-scale β for T is closer to −1 as small-scale moist convective processes dominate. In the tropics, q exhibits large-scale β between −2 and −3. The values of β are generally consistent with previous works of either time-averaged spatial variance estimates, or aircraft observations that require averaging over numerous flight observational segments. The instantaneous variance scaling methodology is relevant for cloud parameterization development and the assessment of time variability of scaling exponents.

Inertia–gravity waves in a liquid-filled, differentially heated, rotating annulus

2015 ◽  
Vol 782 ◽  
pp. 144-177 ◽  
Author(s):  
Anthony Randriamampianina ◽  
Emilia Crespo del Arco
Keyword(s):  
Prandtl Number ◽  
Gravity Waves ◽  
Large Scale ◽  
Baroclinic Instability ◽  
Zonal Flow ◽  
Small Scale ◽  
Mean Flow ◽  
Baroclinic Waves ◽  
Fluid Properties ◽  
Spatio Temporal

Direct numerical simulations based on high-resolution pseudospectral methods are carried out for detailed investigation into the instabilities arising in a differentially heated, rotating annulus, the baroclinic cavity. Following previous works using air (Randriamampianina et al., J. Fluid Mech., vol. 561, 2006, pp. 359–389), a liquid defined by Prandtl number $Pr=16$ is considered in order to better understand, via the Prandtl number, the effects of fluid properties on the onset of gravity waves. The computations are particularly aimed at identifying and characterizing the spontaneously emitted small-scale fluctuations occurring simultaneously with the baroclinic waves. These features have been observed as soon as the baroclinic instability sets in. A three-term decomposition is introduced to isolate the fluctuation field from the large-scale baroclinic waves and the time-averaged mean flow. Even though these fluctuations are found to propagate as packets, they remain attached to the background baroclinic waves, locally triggering spatio-temporal chaos, a behaviour not observed with the air-filled cavity. The properties of these features are analysed and discussed in the context of linear theory. Based on the Richardson number criterion, the characteristics of the generation mechanism are consistent with a localized instability of the shear zonal flow, invoking resonant over-reflection.

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