A Re-Appraisal of the Effect of Amplitude on the Stability of Interlimb Coordination Based on Tightened Normalization Procedures

Abstract

The stability of rhythmic interlimb coordination is governed by the coupling between limb movements. While it is amply documented how coordinative performance depends on movement frequency, theoretical considerations and recent empirical findings suggest that interlimb coupling (and hence coordinative stability) is actually mediated more by movement amplitude. Here, we present the results of a reanalysis of the data of Post, Peper, and Beek (2000), which were collected in an experiment aimed at teasing apart the effects of frequency and amplitude on coordinative stability of both steady-state and perturbed in-phase and antiphase interlimb coordination. The dataset in question was selected because we found indications that the according results were prone to artifacts, which may have obscured the potential effects of amplitude on the post-perturbation stability of interlimb coordination. We therefore redid the same analysis based on movement signals that were normalized each half-cycle for variations in oscillation center and movement frequency. With this refined analysis we found that (1) stability of both steady-state and perturbed coordination indeed seemed to depend more on amplitude than on movement frequency per se, and that (2) whereas steady-state antiphase coordination became less stable with increasing frequency for prescribed amplitudes, in-phase coordination became more stable at higher frequencies. Such effects may have been obscured in previous studies due to (1) unnoticed changes in performed amplitudes, and/or (2) artifacts related to inappropriate data normalization. The results of the present reanalysis therefore give cause for reconsidering the relation between the frequency, amplitude, and stability of interlimb coordination.

Keywords: bimanual interaction; coordination dynamics; dynamical systems; entrainment; perturbations; relative phase; rhythmic movement; synchronization.

Figure A1

Upper panel: Generated oscillatory signal $x=Asin\omega \left(t\right)+d$, in which a perfect sinusoid was added to a linear trend in oscillation center d. Lower panel: The corresponding instantaneous phase without (red line) and with prior detrending (black line).

Figure A2

Upper panel: Generated oscillatory signal $x=Asin\omega \left(t\right)+d$, in which each half cycle is perfectly sinusoidal while d and A change every half cycle. Lower panel: The corresponding instantaneous phase without (red line) and with prior half-cycle normalization (black line).

Figure 1

(a–e). A typical example of data directly after perturbation release: (a) Angular position data of both arms (blue = left arm, red = right arm) and the corresponding phase portraits as (b) determined in the original paper, and (c) after half-cycle normalization was applied; straight lines exemplify the calculated phase angle at t = 1.2 s; (d) depicts the corresponding phase angles ${\theta }_{\mathrm{return}}$ for the original data (upper panel) and after half-cycle normalization (lower panel); and (e) shows the resultant relative-phase signal ${\phi }_{\mathrm{return}}$ as determined by Post et al. [21] (grey line) and after half-cycle normalization (black line). Green line = fitted decay function. The trial condition was in-phase, the frequency = 2.25 Hz, and the prescribed amplitude = 0.2 rad. See main text for further explanation.

Figure 2

Performed movement amplitudes averaged over participants, as a function of frequency and amplitude conditions, for (a) in-phase and (b) antiphase coordination; free = unprescribed amplitude condition. Error bars depict between-subjects standard errors.

Figure 3

Stability of steady-state coordination ($SD\phi$, with lower values indicating superior stability) for in-phase and antiphase coordination as a function of frequency conditions, for (a) prescribed amplitude and (b) free amplitude conditions. Error bars depict between-subjects standard errors.

Figure 4

Post-perturbation coordinative stability ($\lambda ,$ with higher values indicating superior stability) for in-phase and antiphase coordination as a function of frequency conditions, for (a) prescribed amplitude and (b) free amplitude conditions. Error bars depict between-subjects standard errors.