DFA as a window into postural dynamics supporting task performance: does choice of step size matter?

Introduction: Detrended Fluctuation Analysis (DFA) has been used to investigate self-similarity in center of pressure (CoP) time series. For fractional gaussian noise (fGn) signals, the analysis returns a scaling exponent, DFA-α, whose value characterizes the temporal correlations as persistent, random, or anti-persistent. In the study of postural control, DFA has revealed two time scaling regions, one at the short-term and one at the long-term scaling regions in the diffusion plots, suggesting different types of postural dynamics. Much attention has been given to the selection of minimum and maximum scales, but the choice of spacing (step size) between the window sizes at which the fluctuation function is evaluated may also affect the estimates of scaling exponents. The aim of this study is twofold. First, to determine whether DFA can reveal postural adjustments supporting performance of an upper limb task under variable demands. Second, to compare evenly-spaced DFA with two different step sizes, 0.5 and 1.0 in log2 units, applied to CoP time series. Methods: We analyzed time series of anterior-posterior (AP) and medial-lateral (ML) CoP displacement from healthy participants performing a sequential upper limb task under variable demand. Results: DFA diffusion plots revealed two scaling regions in the AP and ML CoP time series. The short-term scaling region generally showed hyper-diffusive dynamics and long-term scaling revealed mildly persistent dynamics in the ML direction and random-like dynamics in the AP direction. There was a systematic tendency for higher estimates of DFA-α and lower estimates for crossover points for the 0.5-unit step size vs. 1.0-unit size. Discussion: Results provide evidence that DFA-α captures task-related differences between postural adjustments in the AP and ML directions. Results also showed that DFA-α estimates and crossover points are sensitive to step size. A step size of 0.5 led to less variable DFA-α for the long-term scaling region, higher estimation for the short-term scaling region, lower estimate for crossover points, and revealed anomalous estimates at the very short range that had implications for choice of minimum window size. We, therefore, recommend the use of 0.5 step size in evenly spaced DFAs for CoP time series similar to ours.

Effects of Task Constraint on Action Dynamics.

The actualization of action possibilities (i.e., affordances) can often be accomplished in numerous ways. For instance, an individual could walk over to a rubbish bin to drop an item in or throw the piece of rubbish into the bin from some distance away. The aim of the current study was to investigate the action dynamics that emerge from such under-constrained task or action spaces using an object transportation task. Participants were instructed to transport balls between a starting location and a large wooden box located 9 meters away. The temporal interval between the sequential presentation of balls was manipulated as a control parameter and was expected to influence the distance participants moved prior to throwing or dropping the ball into the target box. A two-parameter state space derived from the Cusp Catastrophe Model was employed to illustrate how behavioral variability emerged as a consequence of the under-constrained task context. Two follow-up experiments demonstrated direct correspondence between model predictions and observed action dynamics as a function of increasing task constraints. Implications for modelling, the theory of affordances, and empirical studies more generally are discussed.