Bimanual Finger Tapping: Effects of Frequency and Auditory Information on Timing Consistency and Coordination

The authors' goal in this study was to probe the basis for an earlier, unexpected finding that preferred-frequency finger tapping tends to have higher frequencies and to be less stable for in-phase than for antiphase tasks. In follow-up experiments, 3 protocols were employed: a preferred-frequency replication in both coordination modes, a metronome-driven matching of the preferred frequencies to each of the coordination modes, and a frequency scaling of both modes. The original findings were affirmed for preferred frequency. Tapping to a metronome had a differential effect on in-phase and antiphase: A more stable coupling across frequencies was exhibited during in-phase. Under frequency scaling, the antiphase pattern decomposed at lower frequencies than did in-phase, but no phase transitions were observed. The loss of stable coordination in both modes was attended by sudden increases in frequency differences between fingers and by phase wandering. The emergence of those effects is discussed in light of asymmetric modifications to the Haken-Kelso-Bunz model (H. Haken, J. A. S. Kelso, & H. Bunz, 1985) and the task constraints of tapping.     

Dual-Finger Preferred-Speed Tapping: Effects of Coordination Mode and Anatomical Finger and Limb Pairings

Interlimb and interfinger coordination were examined in a dual-finger tapping paradigm in which 16 subjects performed at preferred frequencies. Three bimanual finger combinations, in random order (2 index; 2 middle; and 1 index and 1 middle), were performed in in-phase and antiphase coordination modes, in addition to 1 unimanual combination (antiphase index-middle). Relative phase means were within 3&percent; accuracy for all conditions. A lower tapping frequency was found in all antiphase vs. in-phase conditions, accompanied by lower phasing variability and lower intrafinger consistency in the antiphase. When frequency was changed from the preferred rate, the 2 coordination modes became more alike in variability and, within the same frequency range, demonstrated no significant differences. The bimanual mixed-fingers tapping tended to have significantly lower phasing values (a small fixed point drift) and higher tapping frequencies than the symmetric conditions. The unimanual task was similar to all other antiphase conditions. Changes in preferred frequency with different coordination modes may be related to differing perceptual informational constraints. Current models addressing natural frequencies of coupled oscillators do not account for the present data.     

Fixed-point drift and hysteresis in frequency-scaled unimanual coordination

ABSTRACT Research on human rhythmic coordination has shown that the in-phase and antiphase coordination modes are typically stable and that the coordination of asymmetric effectors frequently exhibits fixed-point drift. The author extended research on symmetry breaking in coordination dynamics by examining a frequency-scaled unimanual pronation-supination task. The results showed symmetry breaking and fixed-point drift, with the radioulnar joint increasingly more phase advanced than the shoulder with increments in movement frequency. Hysteresis was also observed, as the relative phase patterns produced at 3 of the 4 movement frequencies were lower in the upward frequency scaling direction than in the downward direction. These results showed that the dynamic properties of symmetry breaking and fixed-point drift in unimanual pronation-supination movements were consistent with prior research and modeling. The hysteresis effect was explained as potentially being due to the control structures that organize this redundant coordination task.     

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.     

The metabolic and cognitive energy costs of stabilising a high-energy interlimb coordination task

Kinematic (relative phase error), metabolic (oxygen consumption, heart rate) and attentional (baseline and cycling reaction times) variables were measured while participants practised a high energy-demanding, intrinsically unstable 90 degrees relative phase coordination pattern on independent bicycle ergometers. The variables were found to be strongly inter-correlated, suggesting a link between emerging performance stability with practice and minimal metabolic and attentional cost. The effects of practice of 90 degrees relative phase coordination on the performance of in-phase (0 degrees-phase) and antiphase (180 degrees-phase) coordination were investigated by measuring the relative phase attractor layouts and recording the metabolic and attentional cost of the three coordination patterns before and after practice. The attentional variables did not differ significantly between coordination patterns and did not change with practice. Before practice, the coordination performance was most accurate and stable for in-phase cycling, with antiphase next and 90 degrees-phase the poorest. However, metabolic cost was lower for antiphase than either in-phase or 90 degrees-phase cycling, and the pre-practice attractor layout deviated from that predicted on the basis of dynamic stability as an attractor state, revealing an attraction to antiphase cycling. After practice of 90 degrees-phase cycling, in-phase cycling remained the most accurate and stable, with 90 degrees-phase next and antiphase the poorest, but antiphase retained the lowest metabolic energy cost. The attractor layout had changed, with new attractors formed at the practised 90 degrees-phase pattern and its symmetrical partner of 270 degrees-phase. Considering both the pre- and post-practice results, attractors were formed at either a low metabolic energy cost but less stable (antiphase) pattern or at a more stable but higher metabolic energy cost (90 degrees-phase) pattern, but in neither case at the most stable and accurate (in-phase) pattern. The results suggest that energetic factors affect coordination dynamics and that coordination modes lower in metabolic energy expenditure may compete with dynamically stable modes.     

Diffusive,Synaptic, and Synergetic Coupling: An Evaluation Through In-Phase and Antiphase Rhythmic Movements

The in-phase and antiphase patterns of interlimb l:1 frequency locking were contrasted with respect to models of coordination dynamics in biological movement systems that are based on diffusive coupling, synaptic coupling, and synergetic principles. Predictions were made from each model concerning the stable relative phase phi between the rhythmic units, its standard deviation SDphi and the self-chosen coupled frequency omegasubc;. The experimental task involved human subjects oscillating two handheld pendulums either in-phase or antiphase. The eigenfrequencies of the two hand-pendulum systems were manipulated by varying the length and mass of each pendulum individually. Relative to an eigenfrequency difference of Delta equal to zero, |Deltaomega| > 0 displaced phi from phi = 0 and phi = pi, and amplified SDphi. omegasubc; decreased with |Deltaomega|. Both the displacement of phi and SDphi were greater in the antiphase mode. Additionally, the displacement of phi increased more sharply with |Delta| for antiphase than for in-phase coordination. In contrast, omegasubc; was identical for the two coordination modes. Of the models of interlimb coordination dynamics, the synergetic model was the most successful in addressing the pattern of dependencies of phi and SDphi. The specific forms of the functions relating omegasubc; and phi to Deltaomega pose challenges for all three models, however     

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.     

Phase Transitions and Critical Fluctuations in Rhythmic Coordination of Ipsilateral Hand and Foot

Four subjects performed rhythmic movements of the ankle and the wrist in time with an auditory metronome, in two modes of coordination, antiphase and in-phase. The forearm was placed in either a prone or a supine position. When movements were prepared in the antiphase mode, spontaneous transitions to the in-phase mode, or to phase wandering were observed as metronome frequency was increased. When prepared in the in-phase mode, transitions between in-phase modes or to phase wandering were occasionally observed. Predicted signature features of nonequilbrium phase transitions were noted, including loss of stability and critical fluctuations. The stability of the movement patterns was determined by spatial (dependent upon the direction of movement) rather than anatomical (dependent on the coupling of specific muscle groups) constraints. The position of the forearm had no consistent bearing upon the variability of the phase relations between the limbs, the frequency of phase transitions, or the time of onset of transitions. These results are discussed with reference to the coordination dynamics (e.g., multistability, loss of stability) of multijoint movements.     

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.     

Local stability in coordinated rhythmic movements: fluctuations and relaxation times

An experiment was conducted to examine the stability of the anti-phase and in-phase modes of coordination by means of both fluctuations and relaxation times. Participants (n=6) performed a rhythmic bimanual forearm coordination task that required them to oscillate their forearms in-phase and anti-phase while grasping two manipulanda at fixed frequencies ranging from 0.6 to 1.8 Hz. Relaxation times were measured as the time taken to return to a stable mode following the application of a transient mechanical torque. It was found that relaxation times were not different statistically across participants, frequencies, and coordinative modes. However, fluctuations, as indicated by the mean S.D. of relative phase across individual frequency plateaus, were significantly greater in the anti-phase than in the in-phase mode of coordination, p<0.05. Whilst providing new empirical support for the notion that relaxation times should be of the same order of magnitude at frequencies outside transition regions, the findings suggest that the level of stochastic noise in the anti-phase mode is greater than that of the in-phase mode. Implications are made for the future assessment of local pattern stability.     

Temporal stability of rhythmic tapping “on” and “off the beat”: A developmental study

This study, following a dynamic pattern approach, examines age-related differences in the stability of unimanual rhythmic perception-action patterns. Thirty-six children, aged 7, 9, and 11 years, attempted to synchronize their finger tapping to the beats of an auditory metronome, either “on the beat” (i.e., in-phase coordination), or “off the beat” (i.e., antiphase coordination). The temporal stability of these perception- action patterns was measured by the variability of the relative phase between taps and auditory events and by the critical frequency, that is, the frequency at which a loss of stability was observed when the metronome frequency was increased. Age-related differences in stability were found for both relative phase variability and critical frequency. These findings suggest that the relative phase dynamics underlying perception-action coordination patterns change with age in the direction of an increased temporal stability. Received: 29 June 1998 / Accepted: 15 December 1998     

Intentional switching between patterns of bimanual coordination depends on the intrinsic dynamics of the patterns

Two predictions arising from previous theoretical and empirical work which demonstrated that spontaneous changes of bimanual coordination patterns result from a loss of pattern stability (i.e., a nonequilibrium phase transition) were tested: (a) that the time it takes to intentionally switch from one pattern to another depends on the differential stability of the patterns themselves; and (b) that an intention, defined as an intended behavioral pattern, can change the dynamical characteristics, e.g., the overall stability of the behavioral patterns. Subjects moved both index fingers rhythmically at one of six movement frequencies while performing either an in-phase or antiphase pattern of finger coordination. On cue from an auditory signal, subjects switched from the ongoing pattern to the other pattern. The relative phase of movement between the two fingers was used to characterize the ongoing coordinative pattern. The time taken to switch between patterns, or switching time, and relative phase fluctuations were used to evaluate the modified pattern dynamics resulting from a subject's intention to change patterns. Switching from the in-phase to the antiphase pattern was significantly slower than switching in the opposite direction for all subjects. Both the mean and distribution of switching times in each direction were found to be in agreement with model predictions. movement frequency had little effect on switching time, a finding that is also consistent with the model. Relative phase fluctuations were significantly larger when moving in the antiphase pattern at the highest movement frequencies studied. The results show that, although intentional influences act to modify a coordinative pattern's intrinsic dynamics, the influence of these dynamics on the resulting behavior is always present and is particularly strong at high movement frequencies.     

Metabolic and attentional energy costs of interlimb coordination

The authors investigated metabolic and attentional energy costs as participants (N = 6) practiced in-phase, antiphase, and 90 degrees -phase cycling (order counterbalanced) on independent bicycle ergometers, with resistance (40 W/ergometer) and frequency (40 rpm) held constant. Coordination stabilized and became more accurate for all 3 cycling modes, as shown by measures of relative phase, but that collective variable could not account for other relevant attributes of the multifaceted motor behavior observed across the 3 coordination modes. In-phase and antiphase cycling were similar in stability and accuracy, but antiphase had the lowest metabolic and attentional energy costs. Because both homologous muscle action and perceptually symmetrical oscillations coincided in the in-phase mode, the absence of predominance of the inphase pattern showed that neither of those musculoskeletal and perceptual factors exclusively determined the strongest attractor of the coordination dynamics. Both metabolic and attentional costs declined with practice, consistent with the hypothesis that adaptive motor behavior is guided by sensory information concerning the energy demands of the task. Attentional cost was influenced not only by the information-processing demands of kinematic stability but also by the metabolic energy demands. Metabolic energy cost appeared to be the crucial determinant of the preferred solution for this coordination task.     

Pattern Stability and Error Correction During In-Phase and Antiphase Four-Ball Juggling

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants' high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.     

Pattern stability and error correction during in-phase and antiphase four-ball juggling

The authors studied pattern stability and error correction during in-phase and antiphase 4-ball fountain juggling. To obtain ball trajectories, they made and digitized high-speed film recordings of 4 highly skilled participants juggling at 3 different heights (and thus different frequencies). From those ball trajectories, the authors determined and analyzed critical events (i.e., toss, zenith, catch, and toss onset) in terms of variability of point estimates of relative phase and temporal correlations. Contrary to common findings on basic instances of rhythmic interlimb coordination, in-phase and antiphase patterns were equally variable (i.e., stable). Consistent with previous findings, however, pattern stability decreased with increasing frequency. In contrast to previous results for 3-ball cascade juggling, negative lag-one correlations for catch-catch intervals were absent, but the authors obtained evidence for error corrections between catches and toss onsets. That finding may have reflected participants' high skill level, which yielded smaller errors that allowed for corrections later in the hand cycle.     

Intentional Switching Between Patterns of Bimanual Coordination Depends on the Intrinsic Dynamics of the Patterns

Two predictions arising from previous theoretical and empirical work which demonstrated that spontaneous changes of bimanual coordination patterns result from a loss of pattern stability (i.e., a nonequilibrium phase transition) were tested: (a) that the time it takes to intentionally switch from one pattern to another depends on the differential stability of the patterns themselves; and (b) that an intention, defined as an intended behavioral pattern, can change the dynamical characteristics, e.g., the overall stability of the behavioral patterns. Subjects moved both index fingers rhythmically at one of six movement frequencies while performing either an in-phase or antiphase pattern of finger coordination. On cue from an auditory signal, subjects switched from the ongoing pattern to the other pattern. The relative phase of movement between the two fingers was used to characterize the ongoing coordinative pattern. The time taken to switch between patterns, or switching time, and relative phase fluctuations were used to evaluate the modified pattern dynamics resulting from a subject's intention to change patterns. Switching from the in-phase to the antiphase pattern was significantly slower than switching in the opposite direction for all subjects. Both the mean and distribution of switching times in each direction were found to be in agreement with model predictions. Movement frequency had little effect on switching time, a finding that is also consistent with the model. Relative phase fluctuations were significantly larger when moving in the antiphase pattern at the highest movement frequencies studied. The results show that, although intentional influences act to modify a coordinative pattern's intrinsic dynamics, the influence of these dynamics on the resulting behavior is always present and is particularly strong at high movement frequencies.     

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.     

Age-related differences in the integration of sensory information during the execution of a bimanual coordination task

Young (n = 7) and elderly (n = 7) subjects performed bimanual coordination patterns in the transverse plane according to the in-phase or antiphase mode. Sensory information was manipulated through visual (with or without vision of the limbs) and proprioceptive input (with or without vibratory stimuli on one limb). Movement patterns with vibrations showed higher deviations from the intended relative phase than did those without vibrations. This finding suggests that the proprioceptive information induced by the vibrations and the movement interfered, leading to a disruption of the coordination patterns. In addition, as compared with the elderly, the young subjects performed more stable movements under normal circumstances but were more strongly affected by vibratory stimuli during the performance of in-phase movements. During antiphase movements, both age groups experienced a decrease of pattern stability. Furthermore, the absence or presence of visual feedback influenced the performance of the young subjects more than that of the elderly. The presence of vision led to stable in-phase movements, whereas a decrease of pattern stability was observed for antiphase movements. In general, these results demonstrate that manipulation of feedback sources affects young subjects more than elderly ones, and this can be related to a reduced sensory sensitivity as a function of aging.     

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.     

Effects of correct and transformed visual feedback on rhythmic visuo-motor tracking: tracking performance and visual search behavior

The effects of correct and transformed visual feedback on rhythmic unimanual visuo-motor tracking were examined, focusing on tracking performance (accuracy and stability) and visual search behavior. Twelve participants (reduced to 9 in the analyses) manually tracked an oscillating visual target signal in phase (by moving the hand in the same direction as the target signal) and in antiphase (by moving the hand in the opposite direction), while the frequency of the target signal was gradually increased to probe pattern stability. Besides a control condition without feedback, correct feedback (representing the actual hand movement) or mirrored feedback (representing the hand movement transformed by 180 degrees) were provided during tracking, resulting in either in-phase or antiphase visual motion of the target and feedback signal, depending on the tracking mode performed. The quality (accuracy and stability) of in-phase tracking was hardly affected by the two forms of feedback, whereas antiphase tracking clearly benefited from mirrored feedback but not from correct feedback. This finding extends previous results indicating that the performance of visuo-motor coordination tasks is aided by visual feedback manipulations resulting in coherently grouped (i.e., in-phase) visual motion structures. Further insights into visuo-motor tracking with and without feedback were garnered from the visual search patterns accompanying task performance. Smooth pursuit eye movements only occurred at lower oscillation frequencies and prevailed during in-phase tracking and when target and feedback signal moved in phase. At higher frequencies, point-of-gaze was fixated at a location that depended on the feedback provided and the resulting visual motion structures. During in-phase tracking the mirrored feedback was ignored, which explains why performance was not affected in this condition. Point-of-gaze fixations at one of the end-points were accompanied by reduced motor variability at this location, reflecting a form of visuo-motor anchoring that may support the pick up of discrete information as well as the control of hand movements to a desired location.