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Open Access 01-07-2007 | Research Article

Regularity of center-of-pressure trajectories depends on the amount of attention invested in postural control

Authors: Stella F. Donker, Melvyn Roerdink, An J. Greven, Peter J. Beek

Published in: Experimental Brain Research | Issue 1/2007

Abstract

The influence of attention on the dynamical structure of postural sway was examined in 30 healthy young adults by manipulating the focus of attention. In line with the proposed direct relation between the amount of attention invested in postural control and regularity of center-of-pressure (COP) time series, we hypothesized that: (1) increasing cognitive involvement in postural control (i.e., creating an internal focus by increasing task difficulty through visual deprivation) increases COP regularity, and (2) withdrawing attention from postural control (i.e., creating an external focus by performing a cognitive dual task) decreases COP regularity. We quantified COP dynamics in terms of sample entropy (regularity), standard deviation (variability), sway-path length of the normalized posturogram (curviness), largest Lyapunov exponent (local stability), correlation dimension (dimensionality) and scaling exponent (scaling behavior). Consistent with hypothesis 1, standing with eyes closed significantly increased COP regularity. Furthermore, variability increased and local stability decreased, implying ineffective postural control. Conversely, and in line with hypothesis 2, performing a cognitive dual task while standing with eyes closed led to greater irregularity and smaller variability, suggesting an increase in the “efficiency, or “automaticity” of postural control”. In conclusion, these findings not only indicate that regularity of COP trajectories is positively related to the amount of attention invested in postural control, but also substantiate that in certain situations an increased internal focus may in fact be detrimental to postural control.

The measuring range of the amplifier was −10 V to +10 V, and the signals from the amplifiers were digitized into a 12-bit signal by an AD converter (NI PCi 60405, National Instruments, Austin, TX, USA). The resolution was 0.28 N/bit. Calibration tests performed on the custom-made force plate showed a maximal systematic error of 3 mm along both x and y axis and a resonance frequency along the z axis of 30 Hz. In addition, experimental noise introduced variations that were less than 0.08 kg in magnitude in the measured test mass (i.e., 25 kg recorded for 5 s on eight different days). The random error was smaller than 0.3 mm along both x and y axis, as determined by calculating and averaging the standard deviation of all recordings of each participant after high-pass filtering (cut-off frequency of 12.5 Hz).

Though filtering may affect subtle nuances of a nonlinear structure, an area of concern that is in general lacking throughout the literature, it must be emphasized that the potential effect of filtering will be limited given that 95% of the power of COP time-series is located well below 5 Hz (e.g., Dozza et al. 2005; Maurer and Peterka 2005; Rocchi et al. 2002).

We selected window length M to be 3 (Pincus and Goldberger 1994). An optimal value for r was calculated according to a procedure described by Lake et al. (2002). In line with, e.g., Lake et al. (2002), the time-series were first normalized to unit variance. We performed these calculations using software from PhysioNet (Goldberger et al. 2000).

The largest Lyapunov exponent λ_max was defined as the average exponential divergence d(t) at time t of initially close state-space trajectories, \( d(t) \propto C{\text{e}}^{{\lambda _{{\max }} t}} , \) where C is a constant that normalizes the initial separation (e.g., Rosenstein et al. 1993). To calculate the largest Lyapunov exponent, the embedding dimension m, as determined for the calculation of D ₂ (i.e., m > 2d _m + 1) was used. Distances between neighboring trajectories in state space were calculated as a function of time, i.e., j × Δt = 3 s, and then averaged over all original pairs of nearest neighbors i. Finally, using a least-squares fit to the “average” line defined by \( y(j) = \frac{1} {{\Delta t}}\frac{1} {N}{\sum\limits_{i = 1}^N {\ln d_{i} (j)} } \) (where Δt is the sampling period, and d _i(j) is the distance between the i-th pair of nearest neighbors after j discrete time steps, i.e., j × Δt = 3 s), λ_max was estimated from its slope after fitting a range from j × Δt = 0 to 0.75 s (Rosenstein et al. 1993).

Note that after plotting the modified correlation sum against r (i.e., a distance on a log scale) on a logarithmic scale, its linear slopes d _mwere estimated over a certain interval covering the most linear segments of the logarithmic plot of the modified correlation sum (i.e., between the distance r capturing 0.5% of the pairs of points and the distance r capturing 75% of the pairs of points). Moreover, the dimension D ₂ was estimated when the slopes d _m saturated with increasing embedding dimension m, satisfying the condition m > 2d _m + 1. If this condition was fulfilled, then D ₂ was considered a reliable estimate for a given embedding dimension. See also Roerdink et al. (2006).

For the calculation of the scaling exponent α we followed the procedure described in Roerdink et al. (2006) without transforming the calculated α values to Hurst exponents H_DFA. Note that in Roerdink et al. (2006) this transformation was based on an incorrect transformation rule. Fortunately, however, as the applied transformation was linear, it only affected the mean values of the reported scaling exponents and not the statistical results over experimental conditions.

Note that for the dependent variable sway path-length the within-subject factor plane was redundant and, accordingly, left out of the design.

To determine the largest Lyapunov exponent, the embedding dimension m, as determined for the calculation of D ₂ was required. However, the constraint m > 2d _m + 1 was never met in the time-randomized surrogate data due to the high-dimensional noise.

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Title: Regularity of center-of-pressure trajectories depends on the amount of attention invested in postural control
Authors: Stella F. Donker
Melvyn Roerdink
An J. Greven
Peter J. Beek
Publication date: 01-07-2007
Publisher: Springer-Verlag
Published in: Experimental Brain Research / Issue 1/2007
Print ISSN: 0014-4819
Electronic ISSN: 1432-1106
DOI: https://doi.org/10.1007/s00221-007-0905-4

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Regularity of center-of-pressure trajectories depends on the amount of attention invested in postural control

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