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01-09-2006 | Research Article

Dynamical structure of center-of-pressure trajectories in patients recovering from stroke

Authors: M. Roerdink, M. De Haart, A. Daffertshofer, S. F. Donker, A. C. H. Geurts, P. J. Beek

Published in: Experimental Brain Research | Issue 2/2006

Abstract

In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886–895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control.

In the original study of De Haart et al. (2004), each balance assessment consisted of two consecutive test series, incorporating four quiet-standing tasks and one weight-shifting task, presented in a fixed sequence. This sequence was repeated in reverse order to control for time effects. Between the DT and EC condition, participants conducted a trial while looking at a vertical black bar, which served as a visual midline reference. The weight-shifting task was performed twice after (and preceding) the first (second) EC condition. A 1-min rest was given after each balance test, whereas a longer pause was allowed between the two test series. The arithmetic task in the DT condition consisted of a (varying) verbal sequence of eight single-digit additions (e.g., 7+4=11 or 3+5=7) equally timed over the 30-s period. The participants were instructed to verbally indicate the correctness of each summation by good or fault response.

For our data, the first minimum of the mutual information occurred at 11 (mean 11.14, SE 0.15) and 10 (mean 9.91, SE 0.20) data samples for ML and AP sway components of the stroke patients, respectively. These minima did not change with rehabilitation or condition (P>0.05). For the healthy controls, the first minimum of the mutual information occurred at 11 data samples for both ML (mean 11.10, SE 0.27) and AP (mean 10.54, SE 0.21) sway components. Again, no change with condition was found (P>0.05). Note that the choice of the time delay τ was not based on these group averages but was determined independently for each trial.

Correlations between consecutively sampled points can produce spurious indications of low-dimensional structure. With the introduction of the cut-off parameter W>1, it is possible to minimize these correlations (Grassberger 1986; Theiler 1986). Therefore, all pairs of points that are closer together in time than some cut-off W were excluded. W=1 returns the standard Grassberger and Procaccia (1983) formula.

The dimension is often calculated by looking at the slope of the most linear segments of C _m(r), requiring a means of evaluating a score for each plausible linear segment (i.e., based on the length of the segment or the goodness of fit to a line). The ‘optimal’ linear segment is chosen. In this way, these techniques emphasize the possible existence of strange attractors. A drawback of such methods is that the length scale chosen can depend discontinuously on the underlying signal, because a small change in the signal can change the relative ranks of the candidate linear segments and thereby change the calculated dimension substantially (Kaplan et al. 1991). Because the applied dimension analysis in this study did not involve examination of the linear scaling of C _m(r), it would be incorrect to interpret the estimated dimension D ₂ as the dimension of the attractor. Similarly, it would be incorrect to infer from this analysis that an attractor must exist.

In agreement with, e.g., Lake et al. (2002) and Richman and Moorman (2000), time series were normalized to unit variance. Sample entropy software was obtained from PhysioNet (Goldberger et al. 2000).

Notice that a multivariate extension of the detrended fluctuation analysis algorithm yields identical results when applied to the embedded time series (see above) since we assumed stationarity.

To avoid false or spurious conclusions, Hurst exponents were also determined by means of a rescaled range analysis (Hurst 1965; Rangarajan and Ding 2000; Delignières et al. 2003; cf. Wing et al. 2004 for a related power spectral approach), yielding slightly higher estimates of the diffusion process than the DFA. To compare these two methods, the pair-wise two-tailed Pearson correlation coefficient between the scaling exponent based on the rescaled range analysis (H→H _R/S) and the detrended fluctuation analysis (H→H _DFA) was determined for all the trials of the stroke patients (N=990). For both the AP and ML scaling estimates, the correlation analysis showed a good agreement between H _R/S and H _DFA (r=0.918, P<0.01 and r=0.895, P<0.01, respectively).

The significant results reported in Table 3 were all preserved when the averaged post-stroke values were replaced by the earliest post-stroke values.

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Title: Dynamical structure of center-of-pressure trajectories in patients recovering from stroke
Authors: M. Roerdink
M. De Haart
A. Daffertshofer
S. F. Donker
A. C. H. Geurts
P. J. Beek
Publication date: 01-09-2006
Publisher: Springer-Verlag
Published in: Experimental Brain Research / Issue 2/2006
Print ISSN: 0014-4819
Electronic ISSN: 1432-1106
DOI: https://doi.org/10.1007/s00221-006-0441-7

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Dynamical structure of center-of-pressure trajectories in patients recovering from stroke

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