Artificial neural networks for analyzing inter-limb coordination: the golf chip shot

Motor control research relies on theories, such as coordination dynamics, adapted from physical sciences to explain the emergence of coordinated movement in biological systems. Historically, many studies of coordination have involved inter-limb coordination of relatively few degrees of freedom. This study looked at the high-dimensional inter-limb coordination used to perform the golf chip shot toward six different target distances. This study also introduces a visualization of high-dimensional coordination relevant within the coordination dynamics theoretical framework. A specific type of Artificial Neural Network (ANN), the Self-Organizing Map (SOM), was used for the analysis. In this study, the trajectory of consecutive best-matching nodes on the output map was used as a collective variable and subsequently fed into a second SOM which was used to create visualization of coordination stability. The SOM trajectories showed changes in coordination between movement patterns used for short chip shots and movement patterns used for long chip shots. The attractor diagrams showed non-linear phase transitions for three out of four players. The methods used in this study may offer a solution for researchers from a coordination dynamics perspective who intend to use data obtained from discrete high-dimensional movements.     

Dynamics of human postural transitions

In the present study, the authors examined transitions between postural coordination modes involved in human stance. The analysis was motivated by dynamical theories of pattern formation, in which coordination modes and transitions between modes are emergent, self-organized properties of the dynamics of animal-environment systems. In 2 experiments, standing participants tracked a moving target with the head. Results are consistent with the hypothesis that changes in body coordination follow typical nonequilibrium phase transitions, exhibiting multistability, bifurcation, critical fluctuations, hysteresis, and critical slowing down. The findings suggest that posture may be organized in terms of dynamical principles and favor the existence of general and common principles governing pattern formation and flexibility in complex systems.     

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.     

Learning as change of coordination dynamics: theory and experiment

Learning of coordination patterns was investigated theoretically from the point of view of a dynamic theory of biological coordination and with reference to recent experiments on the learning of relative timing patterns. The theory is based on theoretical and experimental work showing that coordinated movement is characterized not only by the actually performed pattern of coordination but by an entire dynamics of coordination. Theoretically, such dynamics are captured as equations of motion of relevant collective variables. Experimentally, signatures of these underlying dynamics can be found in the temporal stability of coordination patterns, which can be assessed through various stability measures as well as through processes of pattern change. We argue that not only intrinsic coordination tendencies, but also specific behavioral requirements, be they perceived, memorized, or intended, must be expressed in terms of such dynamics. The concept of behavioral information captures such requirements as part of the coordination dynamics. We expound two hypotheses on the nature of learning in this framework. First, we assume that at each point during the learning process the system is governed by a well-defined coordination dynamics. This equation of motion evolves with learning so as to acquire an attractor solution near the to-be-learned pattern. Second, we hypothesize that this change of the coordination dynamics, captured by the time course of memorized behavioral information, can itself be ascribed to an additional layer of dynamics, the slower learning dynamics. Testable consequences of these views are discussed in the light of recent experimental findings on the learning of a relative phase in rhythmic movement: (a) Learning affects dynamic properties of performed coordination patterns, in particular, their stability; (b) the change of the coordination dynamics due to learning leads to specific changes of behavior also under conditions other than the learned condition, namely, to systematic deviation toward the learned patterns; (c) learning may lead to instabilities in the coordination behavior if initial and learned performance differ sufficiently; and (d) the dynamic properties of the performed coordination patterns are distinct on the two time scales of learning and of performance.     

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.     

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.     

The interplay of attention and bimanual coordination dynamics

Despite their common origin, studies on motor coordination and on attentional load have developed into separate fields of investigation, bringing out findings, methods, and theories which are diverse if not mutually exclusive. Sitting at the intersection of these two fields, this article addresses the issue of behavioral flexibility by investigating how intention modifies the stability of existing patterns of coordination between moving limbs. It addresses the issue, largely ignored until now, of the attentional cost incurred by the central nervous system (CNS) in maintaining a coordination pattern at a given level of stability, in particular under different attentional priority requirements. The experimental paradigm adopted in these studies provides an original mix of a classical measure of attentional load, namely, reaction time, and of a dynamic approach to coordination, most suitable for characterizing the dynamic properties of coordinated behavior and behavioral change. Findings showed that central cost and pattern stability covary, suggesting that bimanual coordination and the attentional activity of the CNS involved in maintaining such a coordination bear on the same underlying dynamics. Such a conclusion provides a strong support to a unified approach to coordination encompassing a conceptualization in terms of information processing and another, more recent framework rooted in self-organization theories and dynamical systems models     

Modeling rhythmic interlimb coordination: The roles of movement amplitude and time delays

Rhythmic interlimb coordination is characterized by attraction to stable phase and frequency relations. Sudden transitions between the resulting coordination patterns, which are observed when movement frequency is gradually increased, have been modeled at two formally related levels: a potential function and a system of coupled oscillators. At the latter level of the model, two alternative derivations resulted in different predictions with respect to the way in which movement frequency and amplitude affect pattern stability. Our recent results contradicted the prevailing version of the model, which predicts that the influence of movement frequency is fully mediated by the associated changes in amplitude. Although the results could be reconciled with the alternative derivation of the model in which time delays (possibly related to neurophysiological delays) were incorporated, the absence of amplitude-mediated effects on pattern stability challenges both versions of the model. It is argued that by studying coordination dynamics at the level of the potential function as well as at the level of coupled oscillators, new insights into the way in which control parameters influence pattern dynamics may be obtained. This may open up ways to link the coordination dynamics to specific characteristics of the movements of the limbs and the way in which they interact.PsycINFO classification: 2300; 2330     

Visual cues two-steps ahead are adequate to grasp an object while walking without compromising stability

In our prior studies, participants walked and grasped a dowel using an anticipatory mode of control. However, it is unknown how this combined task would change in a less predictable environment. We investigated the online control aspects involved in the combined task of walking and grasping under different coordination patterns between upper- and lower-limbs in young adults. Fifteen young adults walked and grasped a dowel under several experimental conditions combining the instant of visual cue appearance and coordination pattern of upper and lower limbs used to grasp the dowel. Visual cues provided two steps ahead or earlier were enough for executing the combined task of walking and prehension appropriately. Visual cues provided within this window impacted both walking stability and the execution of the prehension movement. Although an ipsilateral arm-leg coordination pattern increased mediolateral stability, a contralateral pattern significantly decreased mediolateral center of mass stability when the visual cue appeared one-step before grasping the object. These results imply that acquiring information to plan the combined task of walking and reaching for an object two steps ahead allows the maintenance of the general movement characteristics present when the decision to reach out for the object is defined two or more steps ahead. These results indicate that the prehension movement is initiated well before heel contact on that side when given sufficient planning time, but that a disruption of the natural arm-leg coordination dynamics emerges to accomplish the task when the cue is provided one step before the object.     

Evolution of behavioral attractors with learning: nonequilibrium phase transitions.

Learning a bimanual coordination task (synchronization to a visually specified phasing relation) was studied as a dynamical process over 5 days of practicing a required phasing pattern. Systematic probes of the attractor layout of the 5 Ss' coordination dynamics (expressed through a collective variable, relative phase) were conducted before, during, and after practice. Depending on the relationship between the initial coordination dynamics (so-called intrinsic dynamics) and the pattern to be learned (termed behavioral information, which acts as an attractor of the coordination dynamics toward the required phasing), qualitative changes in the phase diagram occurred with learning, accompanied by quantitative evidence for loss of stability (phase transitions). Such effects persisted beyond 1 week. The nature of change due to learning (e.g., abrupt vs. gradual) is shown to arise from the cooperative or competitive interplay between behavioral information and the intrinsic dynamics.     

The acquisition of bimanual coordination is mediated by anisotropic coupling between the hands

The present study was designed to test two predictions from the coupled oscillator model of multifrequency coordination. First, it was predicted that multifrequency tasks that match the inherent manual asymmetry (i.e., the preferred hand assigned to the faster tempo) would be easier to learn than tasks that do not match the inherent dynamics (i.e., the non-preferred hand assigned to the faster tempo). Second, in the latter case acquisition of the multifrequency coordination would involve a reorganisation of the coupling dynamics such that the faster hand would exert a greater influence on the slower hand than vice versa. Sixteen right-handed volunteers received extensive training on a 2:1 coordination pattern involving a bimanual forearm pronation-supination task. Participants were randomly assigned to one of two groups: 1L:2R in which the preferred right hand performed the higher frequency, or 2L:1R in which the non-preferred left hand performed the higher frequency. The dynamic stability of the patterns was assessed by the ability of participants to maintain the coordination pattern as movement frequency was increased. Changes in the directional coupling between the hands was assessed by transition pathways and lead-lag relationship evident in a 1:1 anti-phase frequency-scaled coordination task performed prior to and following three practice sessions of the 2:1 task. The predicted differential stability between the multifrequency patterns was evident in the initial acquisition sessions but by the end of training the two patterns evidenced equivalent stability. Unexpectedly, for both groups the fast hand displayed greater variability in amplitude and movement frequency than the slow hand perhaps reflecting anchoring afforded to the slow hand by synchronising movement endpoints with the auditory pacing metronome. Analysis of pre- to post-training changes to the coupling dynamics in the 1:1 anti-phase task support the hypothesis that acquisition of the 2L:1R pattern involved reorganisation of the inherent dynamics.     

The acquisition of movement skills: practice enhances the dynamic stability of bimanual coordination.

During bimanual movements, two relatively stable "inherent" patterns of coordination (in-phase and anti-phase) are displayed (e.g., Kelso, Am. J. Physiol. 246 (1984) R1000). Recent research has shown that new patterns of coordination can be learned. For example, following practice a 90 degrees out-of-phase pattern can emerge as an additional, relatively stable, state (e.g., Zanone & Kelso, J. Exp. Psychol.: Human Performance and Perception 18 (1992) 403). On this basis, it has been concluded that practice leads to the evolution and stabilisation of the newly learned pattern and that this process of learning changes the entire attractor layout of the dynamic system. A general feature of such research has been to observe the changes of the targeted pattern's stability characteristics during training at a single movement frequency. The present study was designed to examine how practice affects the maintenance of a coordinated pattern as the movement frequency is scaled. Eleven volunteers were asked to perform a bimanual forearm pronation-supination task. Time to transition onset was used as an index of the subjects' ability to maintain two symmetrically opposite coordinated patterns (target task - 90 degrees out-of-phase - transfer task - 270 degrees out-of-phase). Their ability to maintain the target task and the transfer task were examined again after five practice sessions each consisting of 15 trials of only the 90 degrees out-of-phase pattern. Concurrent performance feedback (a Lissajous figure) was available to the participants during each practice trial. A comparison of the time to transition onset showed that the target task was more stable after practice (p=0.025). These changes were still observed one week (p=0.05) and two months (p=0.075) after the practice period. Changes in the stability of the transfer task were not observed until two months after practice (p=0.025). Notably, following practice, transitions from the 90 degrees pattern were generally to the anti-phase (180 degrees ) pattern, whereas, transitions from the 270 degrees pattern were to the 90 degrees pattern. These results suggest that practice does improve the stability of a 90 degrees pattern, and that such improvements are transferable to the performance of the unpractised 270 degrees pattern. In addition, the anti-phase pattern remained more stable than the practised 90 degrees pattern throughout.     

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     

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.     

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.     

Amplitude scaling in a bimanual circle-drawing task: pattern switching and end-effector variability

The authors manipulated movement amplitude in a bimanual circle-tracing task performed by 11 participants. With pacing frequency fixed, the systematic increase and decrease of circle diameter within a trial induced phase transitions from the asymmetric (33% of trials) to the symmetric bimanual circle-tracing pattern; the transitions resulted from a loss of stability in the asymmetric pattern. Tracing frequency varied inversely with circle diameter so that end-effector variability was minimized in a set of self-paced trials in which the circle diameter in a trial was fixed. In the amplitude-scaling trials, end-effector variability varied directly with circle diameter, a consistent speed-accuracy tradeoff. The results support the conclusion that movement amplitude is a nonspecific control parameter. The findings are discussed with reference to several factors, e.g., tactile feedback, the recruitment and suppression of biomechanical degrees of freedom, and the role those factors may play in stabilizing bimanual coordination patterns     

The influence of augmented feedback and prior learning on the acquisition of a new bimanual coordination pattern

The present research examined two variables regarding the acquisition of a new bimanual coordination pattern: the role of previous experience and the nature of augmented feedback. Two groups of participants acquired a new coordination pattern (135 degrees relative phase) following two sessions of practice of another novel pattern (90 degrees relative phase). Transfer of learning in these groups was compared to two groups that had not previously learned a new pattern, but were nevertheless influenced by coordination patterns that are intrinsic to the task of bimanual relative timing (in-phase, 0 degrees, and anti-phase, 180 degrees). The findings revealed that new learning overshadowed the influence of the intrinsic patterns. Learning was also greatly affected by augmented feedback: dynamic, on-line pursuit tracking information was more effective in transfer than static, terminal feedback. Implications of these findings regarding theoretical constructs in motor learning are discussed.