Exploring the dynamics of balance data — movement variability in terms of drift and diffusion

Gottschall, Julia; Peinke, Joachim; Lippens, Volker; Nagel, Volker

doi:10.1016/j.physleta.2008.12.026

Cited by 19 publications

(8 citation statements)

References 23 publications

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“…Finally, these findings support the hypothesis that the Langevin model has the potential to quantify interesting aspects of postural control, and could be significantly improved by the embedding of the CoM trajectory. Further work is needed to link precisely the parameters of the local recall model to biomechanical components of postural control as well as to investigate if other improvements of the model, such as the addition of nonlinearities [47] or intermittent postural adjustements [24], could lead to a more realistic quantification of postural control.…”

Section: Discussionmentioning

confidence: 99%

A Langevin-Based Model With Moving Posturographic Target to Quantify Postural Control

Nicolaï

Limnios

Trouvé

et al. 2021

IEEE Trans. Neural Syst. Rehabil. Eng.

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Falls are a major concern of public health, particularly for older adults, as the consequences of falls include serious injuries and death. Therefore, the understanding and evaluation of postural control is considered key, as its deterioration is an important risk factor predisposing to falls. In this work we introduce a new Langevin-based model, local recall, that integrates the information from both the center of pressure (CoP) and the center of Mass (CoM) trajectories, and compare its accuracy to a previously proposed model that only uses the CoP. Nine healthy young participants were studied under quiet bipedal standing conditions with eyes either open or closed, while standing on either a rigid surface or a foam. We show that the local recall model produces significantly more accurate prediction than its counterpart, regardless of the eyes and surface conditions, and we replicate these results using another publicly available human dataset. Additionally, we show that parameters estimated using the local recall model are correlated with the quality of postural control, providing a promising method to evaluate static balance. These results suggest that this approach might be interesting to further extend our understanding of the underlying mechanisms of postural control in quiet stance.

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Section: Discussionmentioning

confidence: 99%

A Langevin-Based Model With Moving Posturographic Target to Quantify Postural Control

Nicolaï

Limnios

Trouvé

et al. 2021

IEEE Trans. Neural Syst. Rehabil. Eng.

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“…Discretization is introduced by dividing the range of the X variable (between the minimum and the maximum of the data) into a predefined number of bins. This procedure results in a bin with a constant width (Gottschall et al, 2009;Petelczyc et al, 2009;Petelczyc et al, 2010;Tabar et al, 2006). The conditional histograms needed for Eq.…”

Section: A Brief Summary Of the Kramers-moyal Expansion Methodsmentioning

confidence: 99%

“…II for details). The conditional probabilities are often obtained from histograms through a binning procedure with constant width (Gottschall et al, 2009;Petelczyc et al, 2009;Friedrich et al, 2011). The main advantage of this approach is simplicity; however, it is known that for certain data sets it may lead to artifacts due to poor statistics when the data is sparse (Friedrich et al, 2011;Lamouroux and Lehnertz, 2009;Kleinhans, 2012).…”

Section: Introductionmentioning

confidence: 99%

A fixed mass method for the Kramers-Moyal expansion—Application to time series with outliers

Petelczyc

Żebrowski

Orłowska−Baranowska

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Extraction of stochastic and deterministic components from empirical data-necessary for the reconstruction of the dynamics of the system-is discussed. We determine both components using the Kramers-Moyal expansion. In our earlier papers, we obtained large fluctuations in the magnitude of both terms for rare or extreme valued events in the data. Calculations for such events are burdened by an unsatisfactory quality of the statistics. In general, the method is sensitive to the binning procedure applied for the construction of histograms. Instead of the commonly used constant width of bins, we use here a constant number of counts for each bin. This approach-the fixed mass method-allows to include in the calculation events, which do not yield satisfactory statistics in the fixed bin width method. The method developed is general. To demonstrate its properties, here, we present the modified Kramers-Moyal expansion method and discuss its properties by the application of the fixed mass method to four representative heart rate variability recordings with different numbers of ectopic beats. These beats may be rare events as well as outlying, i.e., very small or very large heart cycle lengths. The properties of ectopic beats are important not only for medical diagnostic purposes but the occurrence of ectopic beats is a general example of the kind of variability that occurs in a signal with outliers. To show that the method is general, we also present results for two examples of data from very different areas of science: daily temperatures at a large European city and recordings of traffics on a highway. Using the fixed mass method, to assess the dynamics leading to the outlying events we studied the occurrence of higher order terms of the Kramers-Moyal expansion in the recordings. We found that the higher order terms of the Kramers-Moyal expansion are negligible for heart rate variability. This finding opens the possibility of the application of the Langevin equation to the whole range of empirical signals containing rare or outlying events. Note, however, that the higher order terms are non-negligible for the other data studied here and for it the Langevin equation is not applicable as a model.

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“…It has been successfully applied to a variety of dynamical problems such as wind power production, 5 in-situ damage detection 7 and balancing data. 2 In this way, the dynamics in the Force F (t) | α can be described by the Langevin equation…”

Section: Iiia Stochastic Analysis Methodsmentioning

confidence: 99%

Stochastic analysis of aerodynamic forces acting on a self-adaptive camber airfoil in turbulent inflow

Kampers¹,

Cordes

Tropea

et al. 2015

33rd AIAA Applied Aerodynamics Conference

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Wind turbines work in turbulent conditions that feature non-Gaussian statistics, which lead to heavy fluctuations in aerodynamic forces and mechanical loads, respectively. Active and passive flow control elements are promising for the reduction of such fluctuations. We present a new experimental testing method for flow control elements under reproducible turbulent inflow conditions. Lift dynamics are studied using a stochastic Langevin approach. This method enables for a quantitative analysis of the dynamical behavior of flow control mechanisms in turbulent conditions.

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Exploring the dynamics of balance data — movement variability in terms of drift and diffusion

Cited by 19 publications

References 23 publications

A Langevin-Based Model With Moving Posturographic Target to Quantify Postural Control

A Langevin-Based Model With Moving Posturographic Target to Quantify Postural Control

A fixed mass method for the Kramers-Moyal expansion—Application to time series with outliers

Stochastic analysis of aerodynamic forces acting on a self-adaptive camber airfoil in turbulent inflow

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