Dynamics of 1:2 Coordination: Sources of Symmetry Breaking

Three asymmetries in the dynamics of 1:2 interlimb coordination were examined: the asymmetry in uncoupled frequencies, the asymmetry in coupled frequencies, and the left-right functional asymmetry of the body. In a bimanual 1:2 task, participants (N = 8) oscillated hand-held pendulums whose uncoupled frequencies were adjusted so that the first kind of asymmetry could be manipulated. For any given pendulum pair, the pendulum assuming the faster motion in the 1:2 coordination was oscillated in the right and the left hands. By assigning combinations of uncoupled eigenfrequencies and coupled task-specified frequencies across hands, the authors studied the interaction of all 3 asymmetries. The results confirm the appropriateness of generalized relative phase as a collective variable for 1:2 coordination. Additionally, they suggest that the generalized form of the detuning parameter represents the first asymmetry and that the coupling function expresses the second asymmetry. In 1:2 coordination, the body's functional asymmetry plays a limited role.     

One-to-one and polyrhythmic temporal coordination in bimanual circle tracing

The authors manipulated movement amplitude in a bimanual circle-tracing task to alter the natural tracing frequency of the arms. Participants (N = 14) traced different-diameter circles simultaneously with the two arms in either in-phase (0 degrees) or antiphase (180 degrees) coordination, using the index fingers or plastic styli. Movement amplitude altered the natural tracing frequency of the arms, as demonstrated by the following 2 findings: (a) The larger the difference in circle diameter, the larger was the shift from the fixed-point values of 0 degrees and 180 degrees, and the shift increased as movement frequency increased. Those results are consistent with the manipulation of delta omega in the bimanual pendulum paradigm. (b) Increasing movement frequency induced transitions from 1:1 to non-1:1 coordination, contrary to findings in previous investigations of polyrhythmic coordination. Tactile feedback played a minimal role in stabilizing bimanual coordination in the current tasks.     

Asymmetries in Coupling Dynamics of Perception and Action

The influence of information-based dynamics on coordination dynamics of rhythmic movement was examined with special reference to the expression of asymmetries. In Experiment 1, right-handed subjects performed unimanual, rhythmical movements in coordination with either a discrete or continuous visual display. The right hand-visual display system defined a more stable perception-action collective than the left, particularly when continuous visual information was available. In Experiment 2, the same subjects performed rhythmic bimanual movements in coordination with a continuous visual display. The action collective was inherently more stable than the perception-action collective, although similar patterns were observed at both levels. Importantly, the dynamics of the perception-action collective impinged upon the dynamics of the action collective in terms of stability. Asymmetries remained evident between limbs in the bimanual preparations, with the left hand exhibiting greater limit-cycle variability and also a tendency to more often effect transitions at the action couple. Features of dynamical models that capture characteristics of manual asymmetries are discussed.     

Dynamics of 1:2 Coordination: Temporal Scaling, Latent 1:1, and Bistability

The simplest interlimb multifrequency coordination of 1:2 can be performed at different speeds and in at least two different styles or modes. The effects of speed and mode (in-phase or antiphase) were evaluated in a bimanual 1:2 rhythmic task in which participants (N = 8) oscillated hand-held pendulums with identical or different uncoupled frequencies. A motion equation in relative phase that captures the asymmetries of components and task predicted the 1:2 coordination equilibria resulting from temporal scaling. According to the experimental results, both coordination modes proved to be equally stable. More detailed analyses of individual trials showed signs that the more fundamental 1:1 coordination intruded into the 1:2 coordination.     

Laterally focused attention modulates asymmetric coupling in rhythmic interlimb coordination

Peters (J Motor Behav 21:151-155, 1989; Interlimb coordination: neural, dynamical and cognitive constraints, Academic, Orlando, pp 595-615, 1994) suggested that expressions of handedness in bimanual coordination may be reflections of an inherent attentional bias. Indeed, previous results indicated that focusing attention on one of the limbs affected the relative phasing between the limbs in a manner comparable to the effects of hand dominance. The present study extended the comparison between the effects of attentional focus and handedness by testing their impact on the interactions between the limbs. Both left-handed and right-handed participants performed rhythmic bimanual coordination tasks (in-phase and antiphase coordination), while directing attention to either limb. Using brief mechanical perturbations, the degree to which the limbs were influenced by each other was determined. The results revealed that the non-dominant limb was more strongly affected by the dominant limb than vice versa and that, in line with Peters' proposition, this handedness-related asymmetry in coupling strength was reduced when attention was focused on the non-dominant limb, thereby highlighting the potential relation between inherent (handedness-related) asymmetries and voluntary attentional asymmetries. In contrast to previous findings, the (commonly observed) phase lead of the dominant limb was attenuated (rather than accrued) when attention was focused on this limb. This unexpected result was explained in terms of the observed attention-related difference in amplitude between the limbs.     

Brief bimanual force pulses: correlations between the hands in force and time.

Three experiments assessed coupling phenomena in the coordination of bimanual force pulses. Experiment 1 required symmetric force pulses (equal target forces and rise times for both hands) using the index finger of each hand. As the authors expected, on the basis of bimanual pointing movement results, this experiment revealed positive correlations between both the force rise times and the force amplitudes of the two hands. Experiments 2 and 3 included asymmetric conditions with different target force amplitudes (Experiment 2) or target rise times (Experiment 3). In Experiment 2 force amplitudes but not rise times were fully decoupled in the asymmetric condition. In the asymmetric condition of Experiment 3, however, neither rise times nor force amplitudes were fully decoupled. The results suggest a hierarchical control structure with temporal control dominating nontemporal control of bimanual force coordination.     

Development of Bimanual Skill: The Search for Stable Patterns of Coordination

In 2 experiments, dynamic systems theory predictions concerning intrinsic dynamics and variability of bimanual coordination were examined at different developmental stages. In Experiment 1, ten 4-, 6-, 7-, 8-, and 10-year-old children and adults performed unimanual dominant, unimanual nondominant, and bimanual continuous circle drawing. All tasks were performed at the participants' preferred rate, size, and mode of coordination. The 4-, 6-, and 7-year-old children produced larger circles with longer durations than those of the 8- and 10-year-olds and the adults. That finding demonstrates that younger children display different intrinsic dynamics than older children and adults. The 4-, 6-, and 7-year-old children also displayed more variability in bimanual coordination (more time in less stable patterns of coordination, higher standard deviation in relative phase) and produced more transitions between coordination patterns than the 8- and 10-year-olds and the adults. In Experiment 2, the same participants performed bimanual circles at increasing rates. Consistent with predictions of the HKB model (H. Haken, J. A. S. Kelso, & H. Bunz, 1985), the number of transitions decreased as speed increased. Some support was found for the notion that age-related variables of attention and rate contribute to the increased variability in young children's bimanual coordination.     

Development of bimanual skill: the search for stable patterns of coordination

In 2 experiments, dynamic systems theory predictions concerning intrinsic dynamics and variability of bimanual coordination were examined at different developmental stages. In Experiment 1, ten 4-, 6-, 7-, 8-, and 10-year-old children and adults performed unimanual dominant, unimanual nondominant, and bimanual continuous circle drawing. All tasks were performed at the participants' preferred rate, size, and mode of coordination. The 4-, 6-, and 7-year-old children produced larger circles with longer durations than those of the 8- and 10-year-olds and the adults. That finding demonstrates that younger children display different intrinsic dynamics than older children and adults. The 4-, 6-, and 7-year-old children also displayed more variability in bimanual coordination (more time in less stable patterns of coordination, higher standard deviation in relative phase) and produced more transitions between coordination patterns than the 8- and 10-year-olds and the adults. In Experiment 2, the same participants performed bimanual circles at increasing rates. Consistent with predictions of the HKB model (H. Haken, J. A. S. Kelso, & H. Bunz, 1985), the number of transitions decreased as speed increased. Some support was found for the notion that age-related variables of attention and rate contribute to the increased variability in young children's bimanual coordination.     

To Switch or Not to Switch: Recruitment of Degrees of Freedom Stabilizes Biological Coordination

Recruitment and suppression processes were studied in the swinging-pendulum paradigm (cf. P. N. Kugler & M. T. Turvey, 1987). The authors pursued the hypothesis that active recruitment of previously unmeasured degrees of freedom serves to stabilize an antiphase bimanual coordination pattern and thereby obviates the need for pattern switching from an antiphase to an in-phase coordination pattern, a key prediction of the H. Haken, J. A. S. Kelso, and H. Bunz (1985) model. In Experiment 1, 7 subjects swung single hand-held pendulums in time with an auditory metronome whose frequency increased. Pendulum motion changed from planar (2D) to elliptical (3D), and forearm motion (produced by elbow flexion-extension) was recruited with increasing movement rate for cycling frequencies typically above the pendulum's eigenfrequency. In Experiment 2, 7 subjects swung paired pendulums in either an in-phase or an antiphase coordinative mode as movement rate was increased. With the systematic increase in movement rate, the authors attempted to induce transitions from the antiphase to the in-phase coordinative pattern, with loss of stability the key mechanism of pattern change. Transitions from the antiphase to the in-phase coordinative mode were not observed. Pattern stability, as defined by the variability of the phase relation between the pendulums, was affected only a little by increasing movement rate. As in the single-pendulum case, pendulum motion changed from planar to elliptical, and forearm motion was recruited with increasing cycling frequency. Those results reveal a richer dynamics than previously observed in the pendulum paradigm and support the hypothesis that recruitment processes stabilize coordination in biomechanically redundant systems, thereby reducing the need for pattern switching.     

Goal congruency in bimanual object manipulation

In 3 experiments, the authors investigated the impact of action goals on the production of discrete bimanual responses. Similar to a bartender putting 2 glasses simultaneously on a shelf, participants placed 2 objects into either parallel or opposite orientations by carrying out either mirror-symmetrical or mirror-asymmetrical movements. In Experiment 1, performance was strongly affected by the congruency of the intended object orientations but was essentially unaffected by movement symmetry. Experiment 2 replicated this instrumental goal-congruency effect (and the absence of motor-symmetry effects) when actions were cued in advance. Experiment 3 revealed substantial motor-symmetry effects, provided the movements themselves became the action goal. The authors concluded that performance in bimanual choice reaction tasks is constrained by the creation and maintenance of goal codes rather than by properties inherent in the neuromuscular system that carries out these responses. These goals can relate to either body-intrinsic states or to body-extrinsic states according to the actor's current intentions.     

The effect of volition on the stability of bimanual coordination

The authors investigated how the intention to passively perform a behavior and the intention to persist with a behavior impact upon the spatial and temporal properties of bimanual coordination. Participants (N = 30) were asked to perform a bimanual coordination task that demanded the continuous rhythmic extension-flexion of the wrists. The frequency of movement was scaled by an auditory metronome beat from 1.5 Hz, increasing to 3.25 Hz in.25-Hz increments. The task was further defined by the requirement that the movements be performed initially in a prescribed pattern of coordination (in-phase or antiphase) while the participants assumed one of two different intentional states: stay with the prescribed pattern should it become unstable or do not intervene should the pattern begin to change. Transitions away from the initially prescribed pattern were observed only in trials conducted in the antiphase mode of coordination. The time at which the antiphase pattern of coordination became unstable was not found to be influenced by the intentional state. In addition, the do-not-intervene set led to a switch to an in-phase pattern of coordination whereas the stay set led to phase wandering. Those findings are discussed within the framework of a dynamic account of bimanual coordination.     

Performance of unimanual and bimanual multiphased prehensile movements

By manipulating task action demands in 2 experiments, the author investigated whether the context-dependent effects seen in unimanual multiphase movements are also present in bimanual movements. Participants (N = 14) in Experiment 1 either placed or tossed objects into targets. The results indicated that the intention to perform a subsequent action with an object could influence the performance of an earlier movement in a sequence in both unimanual and bimanual tasks. Furthermore, assimilation effects were found when the subsequent tasks being performed by the 2 hands were incongruent. In Experiment 2, the author investigated in 12 participants whether planning in a multiphase movement includes some representation of the accuracy demands of the subsequent task. The accuracy demands of a subsequent task did not appear to influence initial movement planning. Instead, the present results support the notion that it is the action requirements of the subsequent movement that lead to context-dependent effects.     

Dynamics of 1:2 Coordination: Generalizing Relative Phase to n:m Rhythms

Interlimb rhythmic movements can be modeled as coupled oscillators, with stable performance characterized by the relative phase between the limbs. In the present study, that modeling strategy, verified previously for 1:1 coordination, was generalized to 1:2 coordination with a view to n:m coordination. The generalized model predicted interactions between coordination (specifically, 1:1 vs. 1:2) and the frequency asymmetry between the limbs determining mean relative phase and its variability. The predicted interactions were evaluated with bimanual 1:2 and 1:1 rhythmic tasks in which participants (N = 8) oscillated hand-held pendulums whose uncoupled frequencies could be adjusted so that different interlimb asymmetries were produced. The authors needed new analytic procedures to verify stable 1:2 coordination and to resolve stochastic and deterministic sources of variability in the component oscillations. The major expectations from the generalized model were confirmed, and the implications of additional but unpredicted findings for the modeling of multifrequency behavior are discussed.     

The Dynamics of Bimanual Circle Drawing

A bimanual circle drawing task was employed to elucidate the dynamics of intralimb and interlimb coordination. Right-handed subjects were required to produce circles with both hands in either a symmetrical (mirror) mode (i.e. one hand moving clockwise, the other counter-clockwise) or in an asymmetrical mode (i.e. both hands moving clockwise or counter-clockwise). The frequency of movement was scaled by an auditory metronome from 1.50 Hz to 3.25 Hz in8 (8-sec) steps.In the asymmetrical mode,distortions ofthe movement trajectories, transient departures from the target pattern of coordination, and phase wandering were evident as movement frequency was increased. These features suggested loss of stability. Deviations from circular trajectories were most prominent for movements of the left hand. Transient departures from the required mode of coordination were also largely precipitated by the left hand. The results are discussed with reference to manual asymmetries and mechanisms of interlimb and intersegmental coordination.     

Cognitive activity shifts the attractors of bimanual rhythmic coordination

The attractors of bimanual rhythmic coordination are given as the solutions of a motion equation in relative phase. How are those attractors affected by cognitive activity? In 3 experiments, participants (N = 10 in Experiments 1 and 2; N = 5 in Experiment 3) were required to produce in-phase or antiphase coordination while they either did or did not perform an information-reduction task. The average absolute deviation from in-phase (0 degrees ) and antiphase (180 degrees ) satisfying a particular parameterization of the motion equation was amplified by cognitive activity. That amplification of absolute phase shift was the same for both in-phase and antiphase coordination. Furthermore, the amplification (in degrees) increased linearly with the magnitude of cognitive activity (in bits). Cognitive activity had limited influence on the variability of relative phase and did not affect its average signed deviation. Collectively, the results suggest that cognitive activity produces a shift in the attractors of bimanual coordination dynamics that is directionally nonspecific and is independent of movement speed, detuning, and the in-phase-antiphase distinction.     

Hierarchical organisation of neuro-anatomical constraints in interlimb coordination

Based on the observation that bimanual finger tapping movements tend toward mirror symmetry with respect to the body midline, despite the synchronous activation of non-homologous muscles, F. Mechsner, D. Kerzel, G. Knoblich, and W. Prinz (2001) [Perceptual basis of bimanual coordination. Nature, 414, 69-73] suggested that the basis of rhythmic coordination is purely spatial/perceptual in nature, and independent of the neuro-anatomical constraints of the motor system. To investigate this issue further, we employed a four finger tapping task similar to that used by F. Mechsner and G. Knoblich (2004) [Do muscle matter in bimanual coordination? Journal of Experimental Psychology: Human Perception and Performance, 30, 490-503] in which six male participants were required to alternately tap combinations of adjacent pairs of index (I), middle (M) and ring (R) fingers of each hand in time with an auditory metronome. The metronome pace increased continuously from 1 Hz to 3 Hz over the course of a 30-s trial. Each participant performed three blocks of trials in which finger combination for each hand (IM or MR) and mode of coordination (mirror or parallel) were presented in random order. Within each block, the right hand was placed in one of three orientations; prone, neutral and supine. The order of blocks was counterbalanced across the six participants. The left hand maintained a prone position throughout the experiment. On the basis of discrete relative phase analyses between synchronised taps, the time at which the initial mode of coordination was lost was determined for each trial. When the right hand was prone, transitions occurred only from parallel symmetry to mirror symmetry, regardless of finger combination. In contrast, when the right hand was supine, transitions occurred only from mirror symmetry to parallel but no transitions were observed in the opposite direction. In the right hand neutral condition, mirror and parallel symmetry are insufficient to describe the modes of coordination since the hands are oriented orthogonally. When defined anatomically, however, the results in each of the three right hand orientations are consistent. That is, synchronisation of finger tapping is determined by a hierarchy of control of individual fingers based on their intrinsic neuro-mechanical properties rather than on the basis of their spatial orientation.     

Dynamics of 1:2 Coordination: Temporal Scaling,Latent 1:1, and Bistability

The simplest interlimb multifrequency coordination of 1:2 can be performed at different speeds and in at least two different styles or modes. The effects of speed and mode (in-phase or antiphase) were evaluated in a bimanual 1:2 rhythmic task in which participants (N = 8) oscillated hand-held pendulums with identical or different uncoupled frequencies. A motion equation in relative phase that captures the asymmetries of components and task predicted the 1:2 coordination equilibria resulting from temporal scaling. According to the experimental results, both coordination modes proved to be equally stable. More detailed analyses of individual trials showed signs that the more fundamental 1:1 coordination intruded into the 1:2 coordination.     

Haptic discrimination of bilateral symmetry in 2-dimensional and 3-dimensional unfamiliar displays

In five experiments, we tested the accuracy and sensitivity of the haptic system in detecting bilateral symmetry of raised-line shapes (Experiments 1 and 2) and unfamiliar 3-D objects (Experiments 3–5) under different time constraints and different modes of exploration. Touch was moderately accurate for detecting this property in raised displays. Experiment 1 showed that asymmetric judgments were systematically more accurate than were symmetric judgments with scanning by one finger. Experiment 2 confirmed the results of Experiment 1 but also showed that bimanual exploration facilitated processing of symmetric shapes without improving asymmetric detections. Bimanual exploration of 3-D objects was very accurate and significantly facilitated processing of symmetric objects under different time constraints (Experiment 3). Unimanual exploration did not differ from bimanual exploration (Experiment 4), but restricting hand movements to one enclosure reduced performance significantly (Experiment 5). Spatial reference information, signal detection measures, and hand movements in processing bilateral symmetry by touch are discussed.     

Coordination of complex bimanual multijoint movements under increasing cycling frequencies: The prevalence of mirror-image and translational symmetry

The present study examined the principles underlying inter and intralimb coordination constraints during performance of bimanual elbow–wrist movements at different cycling frequencies (from 0.75 Hz to 2.50 Hz). Participants performed eight coordination tasks that consisted of a combination of in-phase (IN) and/or anti-phase (AN) coordination modes between both elbows and wrists (interlimb), with isodirectional (Iso) or non-isodirectional (NonI) coordination modes within each limb (intralimb). As expected, the principle of muscle homology (in-phase coordination), giving rise to mirror symmetrical movements with respect to the mid-sagittal plane, had a powerful influence on the quality of global coordinative behavior both between and within limbs. When this principle was violated (i.e., when the anti-phase mode was introduced in one or both joint pairs), the non-isodirectional intralimb mode exhibited a (de)stabilizing role in coordination, which became more pronounced at higher cycling frequencies. However, pattern loss with increasing cycling frequency resulted not only in convergence toward the more stable in-phase patterns with the elbows and wrists but also to the anti-phase patterns (which were associated with directional compatibility of within-limb motions). Moreover, participants generally preserved their initial mode of coordination (either in-phase or anti-phase) in the proximal joints (i.e., elbows) while shifting from anti-phase to in-phase (or vice versa) with their distal joint pair (i.e., wrists). Taken together, these findings reflect the impact of two immanent types of symmetry in bimanual coordination: mirror-image and translational symmetry.     

Bimanual coordination dynamics in poststroke hemiparetics

Poststroke hemiparetic individuals (n = 9) and a control group (n = 9) completed a frequency-scaled circle-drawing task in unimanual and bimanual conditions. Measures of intralimb spatial and temporal task accuracy and interlimb coordination parameters were analyzed. Significant reductions in task performance were seen in both limbs of the patients and controls with the introduction of bimanual movement. Spatial performance parameters suggested that the 2 groups focused on different hands during bimanual conditions. In the controls, interlimb coordination variables indicated predictable hand dominance effects, whereas in the patient group, dominance was influenced by the side of impairment and prior handedness of the individual. Therefore, in this particular bimanual task, performance improvements in the hemiplegic side could not be elicited. Intrinsic coupling asymmetries between the hands can be altered by unilateral motor deficits.