Distinguishing between the effects of frequency and amplitude on interlimb coupling in tapping a 2:3 polyrhythm

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.