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  • 1
    Electronic Resource
    Electronic Resource
    Distinguishing between the effects of frequency and amplitude on interlimb coupling in tapping a 2:3 polyrhythm (1998)
    Springer
    Experimental brain research 118 (1998), S. 78-92 
    Details
    ISSN: 1432-1106
    Keywords: Key words Bimanual rhythmic movement ; Interlimb coordination ; Coordination dynamics ; Polyrhythmic tapping ; Nonlinear oscillators ; Human
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract  Rhythmic interlimb coordination is characterized by attraction to stable phase and frequency relations. Sudden, unintended transitions between such coordination patterns have been observed in iso- and multifrequency tasks when movement frequency was gradually increased. These transitions have been accounted for by modeling the two limbs as nonlinearly coupled oscillators. The prevailing form of the coupling function is based on time derivatives, but an alternative formulation can be derived by incorporating time delays. These time delays may be related to the neurophysiological delays associated with the use of kinesthetic afferences. The two ways of deriving coupling functions for interlimb coordination allow for different predictions with respect to the effects of movement frequency and amplitude on the strength of interaction between the limbs. In the current experiment, the effects of amplitude and frequency were dissociated experimentally, so as to arrive at an empirically motivated choice between the two ways of formalizing interlimb coupling. Subjects tapped the polyrhythm 2:3 at five different frequencies under three amplitude conditions. Whereas no effects of amplitude were observed, the strength of interaction between the hands decreased with increasing movement frequency. These results support the time-delay version of the model, in which differential (loss of) stability of coordination modes results from differential dependence on movement amplitude, but overall coupling strength is related reciprocally to movement frequency squared. This version of the model was related tentatively to three proposed aspects of interlimb coordination: (1) neurophysiological delays associated with the use of kinesthetic afferences; (2) rate-dependent decrease in pattern stability; and (3) differential entrainment influences of kinesthetic signals.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002210050257
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  • 2
    Electronic Resource
    Electronic Resource
    Bimanual coordination between isometric contractions and rhythmic movements: an asymmetric coupling (1999)
    Springer
    Experimental brain research 129 (1999), S. 417-432 
    Details
    ISSN: 1432-1106
    Keywords: Key words Rhythmic movements ; Coordination dynamics ; Stability ; Electromyography ; Isometric
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract  Interactions between rhythmically moving limbs typically result in attraction to a limited number of coordination modes, which are distinguished in terms of their stability. In addition, the stability of coordination typically decreases with elevations in movement frequency. To gain more insight into the neurophysiological mechanisms underlying these stability characteristics, the effects of phasic voluntary muscle activation onto the movement pattern of the contralateral limb as well as onto the stability of interlimb coordination were examined. This was done in circumstances in which a minimal degree of movement-elicited afferent information was available to mediate the coupling influences. The task involved rhythmic application of isometric torque by one hand, while the other hand was moving rhythmically with unconstrained amplitude. The effects of two levels of applied torque, two coordination patterns (inphase and antiphase), and two movement frequencies were determined, both at the behavioural level (movement kinematics and kinetics) and the neuromuscular level (EMG). The isometric applications of torque clearly influenced the muscle-activation profile and movement pattern of the other limb, affecting both temporal variability and amplitude. Surprisingly, there were no differences between the two coordination patterns or between the tempo conditions. As such, the results did not conform to the Haken-Kelso-Bunz model for rhythmic movement coordination. These data suggest that the archetypal differences in stability of rhythmic bimanual coordination are contingent upon a correspondence between the limbs in terms of their respective tasks. This interpretation is elaborated in terms of the role of sensory feedback and the functional specificity of motor unit recruitment in rhythmic interlimb coordination.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002210050909
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  • 3
    Electronic Resource
    Electronic Resource
    Relative phase dynamics in perturbed interlimb coordination: the effects of frequency and amplitude (2000)
    Springer
    Biological cybernetics 83 (2000), S. 529-542 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract. Schöner [Schöner G (1995) Ecol Psychol 7: 291–314] argued that the relative phase dynamics of rhythmic interlimb coordination may be attributed to the timing level in that the stability properties of the relative phase are largely independent of dynamical principles operating at the goal level, such as those related to the maintenance of a particular amplitude or target position. Yet, according to the coupling functions in the coupled oscillator model proposed by Haken et al. [Haken H, Kelso JAS, Bunz H (1985) Biol Cybern 51: 347–356], the effect of frequency on the stability properties of relative phase is either wholly or partially mediated by frequency-induced changes in amplitude, implying that the relative phase dynamics strongly depends on spatial factors. In order to distinguish between these contrasting interpretations of the organizational principles underwriting the phase dynamics of interlimb coordination, an experiment was conducted in which the effects of frequency and amplitude on the stability of relative phase were separated. Six subjects performed both in-phase and anti-phase coordination patterns at seven different frequencies and three different amplitudes. Two measures of pattern stability were used, the standard deviation of relative phase and the exponent of the relaxation process following phasic perturbations of relative phase. According to both measures, pattern stability decreased with increasing frequency, whereas the amplitude manipulation only had a significant effect on the standard deviation of relative phase. This result was interpreted to imply that the organizational principles at the (relative) timing level are affected only moderately by task constraints pertaining to the goal level, and that models of interlimb coordination in which amplitude coupling plays a partial or subordinate role should be preferred above models relying solely on amplitude coupling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220000185
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  • 4
    Electronic Resource
    Electronic Resource
    Relative phase dynamics in perturbed interlimb coordination: stability and stochasticity (2000)
    Springer
    Biological cybernetics 83 (2000), S. 443-459 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract.  Various stability features of bimanual rhythmic coordination, including phase transitions, have been modeled successfully by means of a one-dimensional equation of motion for relative phase obeying a gradient dynamics, the Haken-Kelso-Bunz model. The present study aimed at assessing pattern stability for stationary performance and estimating the model parameters (a, b, and Q) for the stochastic extension of this model. Estimates of a and b allowed for reconstruction of the potential defining the gradient dynamics. Two coordination patterns between the forearms (in-phase, anti-phase) were performed at seven different frequencies. Model parameters were estimated on the basis of an exponential decay parameter describing the relaxation behavior of continuous relative phase following a mechanical perturbation. Variability of relative phase and relaxation time provided measures of pattern stability. Although the predicted inverse relation between pattern stability and movement frequency was observed for the lower tempo conditions, it was absent for the higher tempos, reflecting the influence of task constraints. No statistically significant differences in stability were observed between the two coordination modes, indicating the influence of intention. The reconstructed potential reflected the observed stability features, underscoring the adequacy of the parameter estimations. The relaxation process could not be captured adequately by means of a simple exponential decay function but required an additional oscillatory term. In accordance with previous assumptions, noise strength Q did not vary as a function of movement frequency. However, systematic differences in Q were observed between the two coordination modes. The advantages and (potential) pitfalls of using stationary performance of single patterns to examine the stability features of a bistable potential were discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004220000177
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    Paper (German National Licenses)
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