Symmetry, broken symmetry, and handedness in bimanual coordination dynamics

Abstract

The symmetrical dynamics of 1:1 rhythmic bimanual coordination may be specified by an order parameter equation involving the relative phase between rhythmic components, and an interlimb coupling which determines the relative attractiveness of in-phase and anti-phase patterns. Symmetry breaking of these dynamics can occur via the difference in the natural frequencies, delta omega, of the left and right rhythmic components, or by the intrinsic asymmetrical dynamics of the body. The latter is captured by additional terms that render the symmetrical coupling slightly anisotropic. A major prediction resulting from this step is that although delta omega = 0, as the frequency of coordination is increased, the asymmetrical coupling will increase and the symmetrical coupling will decrease. This results in a greater left-limb bias in left-handers and right-limb bias in right-handers. This "increased handedness" prediction was confirmed in an experiment in which 20 left-handed and 20 right-handed individuals performed 1:1 coordination with hand-held rigid pendulums. Manipulations of left and right pendulum lengths controlled delta omega, and the coupled frequency was determined by a metronome. Also confirmed was the prediction that the small shift in equilibria from in-phase and anti-phase due to the intrinsic asymmetry should be amplified in left-handers when delta omega > 0 and in right-handers when delta omega < 0. Further, the bias in left-handers was more consistent than the bias in right-handers, and a subgroup of right-handers was identified who performed similarly to left-handers. The coordination dynamics of functional asymmetry provides insights into the elementary synergy between the limbs, the dynamical mechanism that modulates it, and the nature of the asymmetry in left-handed and right-handed individuals.

Laterally focused attention modulates asymmetric coupling in rhythmic interlimb coordination

“…De Poel et al, in press;Treffner & Turvey, 1995) and increased with movement frequency (cf. De Poel et al, in press;Stucchi & Viviani, 1993;Treffner & Turvey, 1996), although the latter effect was only significant for RH participants.…”

Are frequency-induced transitions in rhythmic coordination mediated by a drop in amplitude?

“…Whereas in many instances the dynamics of relative phase has been demonstrated to adhere to the HKB model or one of its more recent extensions (e.g., Kelso et al 1990;Trener and Turvey 1996), the current results, as well as those of Peper and Beek (1998) and Molenaar and Newell (1997), suggest that the HKB potential function, the validity of which has been well corroborated, is not yet accompanied by an equally wellvalidated system of coupled dierential equations. Although the proposed versions of the coupled oscillator model result in the required order parameter dynamics and as such are consistent with the HKB potential function, the predicted relations between pattern stability and movement kinematics have not been fully corroborated.…”

Bilateral motor unit synchronization is functionally organized

“…During bilateral movements the participating limbs do not move independently but inXuence each other (e.g., TreVner and Turvey 1996). Such mutual inXuences have been extensively investigated in bimanual rhythmic tasks involving Wnger oscillations and manual circle drawing (see, e.g., Kelso 1995 for an overview).…”

“…To examine the interactions and processes underlying bimanual coordination, bilateral coupling has been probed by manipulating various parameters, including movement tempo and amplitude (Peper et al 1995;Post et al 2000a, b), amount of torque applied (Peper and Carson 1999), handedness (TreVner and Turvey 1996), attention (Swinnen et al 1996;Amazeen et al 1997), and more. Remarkably, muscle fatigue has hardly been investigated in this context, even though it appears a particularly expedient vehicle to gain insight T. W. Boonstra (&) · A. DaVertshofer · E. van As · S. van der Vlugt · P. J. Beek Institute for Fundamental and Clinical Human Movement Sciences, Faculty of Human Movement Sciences, Vrije Universiteit, Van der Boechorststraat 9, 1081BT Amsterdam, The Netherlands e-mail: t.boonstra@fbw.vu.nl into the interactions governing interlimb coordination.…”