Patterns of Human Interlimb Coordination Emerge from the Properties of Non-Linear,Limit Cycle Oscillatory Processes

The present article represents an initial attempt to offer a principled solution to a fundamental problem of movement identified by Bernstein (1967), namely, how the degrees of freedom of the motor system are regulated. Conventional views of movement control focus on motor programs or closed-loop devices and have little or nothing to say on this matter. As an appropriate conceptual framework we offer Iberall and his colleagues’ physical theory of homeokinetics first elaborated for movement by Kugler, Kelso, and Turvey (1980). Homeokinetic theory characterizes biological systems as ensembles of non-linear, limit cycle oscillatory processes coupled and mutually entrained at all levels of organization. Patterns of interlimb coordination may be predicted from the properties of non-linear, limit cycle oscillators. In a set of experiments and formal demonstrations we show that cyclical, two-handed movements maintain fixed amplitude and frequency (a stable limit cycle organization) under the following conditions: (a) when brief and constantly applied load perturbations are imposed on one hand or the other, (b) regardless of the presence or absence of fixed mechanical constraints, and (c) in the face of a range of external driving frequencies from a visual source. In addition, we observe a tight phasic relationship between the hands before and after perturbations (quantified by cross-correlation techniques), a tendency of one limb to entrain the other (mutual entrainment) and that limbs cycling at different frequencies reveal non-arbitrary, sub-harmonic relationships (small integer, subharmonic entrainment). In short, all the above patterns of interlimb coordination fall out of a non-linear oscillatory design. Discussion focuses on the compatibility of these results with past and present neurobiological work, and the theoretical insights into problems of movement offered by homeokinetic physics. Among these are, we think, the beginnings of a principled solution to the degrees of freedom problem, and the tentative claim that coordination and control are emergent consequences of dynamical interactions among non-linear, limit cycle oscillatory processes.     

Attentional loads associated with interlimb interactions underlying rhythmic bimanual coordination

Studies of rhythmic bimanual coordination under dual-task conditions revealed (1) a dependence of secondary task performance on the stability of coordinative tasks, in that secondary task performance was better during in-phase than antiphase coordination, and (2) a shift in the mean relative phasing between the limbs compared to single-task conditions. The present study aimed to account for these phenomena by dissociating three qualitatively different interactions between the limbs that govern this motor behavior, related to movement planning, error correction, and interlimb reflex activity. The experiment probed the cognitive demands associated with each interlimb interaction by examining the attentional load under dual-task conditions, indexed by reaction times of the secondary task and kinematic changes in the coordinative tasks relative to single-task conditions. First, only in the condition that involved interlimb interactions at the level of movement planning reaction times were shorter for in-phase than for antiphase coordination, highlighting an intimate relation between movement planning and attentional processes. Second, under dual-task conditions a shift in the mean relative phase was observed relative to single-task conditions, but only for the interlimb interactions that depend directly on sensory feedback (error correction and interlimb reflex activity). These observations qualified the effects of attentional load reported in previous studies. Third, reaction times varied systematically over the movement cycle. These variations revealed a dynamical signature of the attentional load that differed between the three interlimb interactions.     

Interlimb coordination following stroke

Studies investigating whether simultaneous bilateral movements can facilitate performance of the impaired limb(s) of stroke patients have returned mixed results. In the present study we compared unilateral limb performance (amplitude, cycle duration) with performance during an interlimb coordination task involving both homologous (both arms, both legs) and non-homologous (one arm, one leg) limbs in stroke participants (n=7) and healthy age-matched controls (n=7). In addition, the effect of on-line augmented visual feedback on interlimb coordination was investigated. Participants performed cyclical flexion-extension movements of the arms and legs in the sagittal plane paced by an auditory metronome (1 Hz). Movement amplitudes were larger and cycle durations shorter during homologous limb coordination than non-homologous coordination. Compared with unilateral movements both groups had reduced movement amplitudes and the stroke group increased cycle duration when interlimb coordination tasks were performed. These effects were most evident during non-homologous (arm and leg) coordination. No evidence of facilitation of the impaired limb(s) was found in any of the interlimb coordination conditions. Augmented visual feedback had minimal effect on the movements of control participants but lead to an increase of cycle duration for stroke participants.     

Effector dynamics of rhythmic wrist activity and its implications for (modeling) bimanual coordination

To examine the role of the effector dynamics of the wrist in the production of rhythmic motor activity, we estimated the phase shifts between the EMG and the task-related output for a rhythmic isometric torque production task and an oscillatory movement, and found a substantial difference (45-52 degrees) between the two. For both tasks, the relation between EMG and task-related output (torque or displacement) was adequately reproduced with a physiologically motivated musculoskeletal model. The model simulations demonstrated the importance of the contribution of passive structures to the overall dynamics and provided an account for the observed phase shifts in the dynamic task. Additional simulations of the musculoskeletal model with added load suggested that particular changes in the phase relation between EMG and movement may follow largely from the intrinsic muscle dynamics, rather than being the result of adaptations in the neural control of joint stiffness. The implications of these results are discussed in relation to (models of) interlimb coordination in rhythmic tasks.     

Interlimb Coordination During Step-to-Step Transition and Gait Performance

Most energy spent in walking is due to step-to-step transitions. During this phase, the interlimb coordination assumes a crucial role to meet the demands of postural and movement control. The authors review studies that have been carried out regarding the interlimb coordination during gait, as well as the basic biomechanical and neurophysiological principles of interlimb coordination. The knowledge gathered from these studies is useful for understanding step-to-step transition during gait from a motor control perspective and for interpreting walking impairments and inefficiency related to pathologies, such as stroke. This review shows that unimpaired walking is characterized by a consistent and reciprocal interlimb influence that is supported by biomechanical models, and spinal and supraspinal mechanisms. This interlimb coordination is perturbed in subjects with stroke.     

Roles of Visual Information for Control of Reaching Movements in Children

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.     

What Does Computer-Mediated Control of a Thermal-Hydraulic System Have to Do With Moving Your Jaw to Speak? Evidence for Synergies in Process Control

Coordination phenomena can take many diverse forms, but ecological psychologists have focused primarily on understanding human motor control. In this article we report an experiment on human-machine coordination that was designed to replicate and extend an early experiment on human jaw movement during speech production that provided initial evidence of synergies. Participants controlled a thermal-hydraulic process simulation for about 1 hr per weekday for approximately 1 month. Half of the participants used a human-computer interface that presented predominantly lower level physical (P) information, whereas the other half used an interface that presented higher level functional (P+F) information as well. During the last block of trials, local perturbations were introduced by increasing the time constant of a particular component per trial by a factor of 20. The component perturbations had less impact on the performance of the P+F participants than the P, and this effect was mostly localized to components that had alternative degrees of freedom for control. Most important, the P+F participants exhibited more evidence of higher level control than the P, providing some initial evidence for synergies in process control. These findings suggest that it may be possible to develop a general unified theory of coordination that subsumes motor control and human-machine interaction as special cases.     

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.     

Effects of attentional prioritisation on the temporal and spatial components of an interlimb circle-drawing task

This study aimed to examine the effects of directing attention to the spatial dimension of the circle-drawing task on interlimb coordination patterns across limbs. Eighteen participants performed a circle-drawing task involving in-phase and antiphase coordination modes under upper limb, contralateral and ipsilateral limb combinations. Results indicated that (a) coordination pattern stability co-varied with central cost when attentional focus was directed to the spatial dimensions of the interlimb circle-drawing task; (b) attentional focus on the spatial components modified the inherent performance asymmetries between the limbs; (c) finally, attention to the spatial components of the interlimb circle-drawing task modulated movement trajectories and at the same time the stability of temporal coordination.     

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.     

Interleg coordination in quiet standing: influence of age and visual environment on noise and stability

The authors reexamined reported effects of age, illumination, and stationary visible structure on the net center of pressure (COP) derived from dual, side-by-side force plates (J. Kinsella-Shaw, S. Harrison, C. Colon-Semenza, & M. Turvey, 2006 ) from the perspective of axial postural control. They questioned how left and right COP(x)(t), COP(y)(t), and vertically oriented ground reactive force, GRF(z)(t), coordinated during quiet standing. The Cross-recurrence Quantification (CRQ) revealed that coordination was primarily between fluctuations of similar direction, with coordination of left and right COP(y) (t) (anteroposterior fluctuations) dominant. CRQ also revealed that (a) illumination and structure affected the interlimb dynamics of older (M age = 72.2 ± 4.90 years) participants more than their younger (M age = 22.8 ± 0.83 years) counterparts, and (b) older participants exhibited greater interlimb entrainment (dynamical stability) in the presence of greater interlimb noise.     

THREE-MONTH-OLD INFANTS CAN LEARN TASK-SPECIFIC PATTERNS OF INTERLIMB COORDINATION

Three-month-old infants cannot yet coordinate and control their limbs for functional tasks like reaching or locomoting This study demonstrates that given an appropriate, novel task, infants can transform their seemingly spontaneous kicking movements into new and efficient patterns of interlimb coordination even at this early age Three-month-old infants were allowed to control the movement of an overhead mobile by means of a string attached to their left ankles In addition, some groups had their two legs yoked together at the ankle with a soft elastic The elastic permitted kicks to be coordinated in any pattern—alternating, single, or simultaneous—but simultaneous kicks provided the most vigorous activation of the mobile All infants kicked more and faster when their kicks were reinforced by mobile movement than when their kicks did not activate the mobile However, only the yoked infants increasingly moved their legs in a simultaneous, or in-phase, pattern The study suggests that learning processes are in place at 3 months for infants to discover a match between their interlimb coordination patterns and a specific task, and that these learning processes, rather than autonomous brain "maturation," may underlie the acquisition of motor skills     

Oscillator mechanisms in the human motor system: investigating their properties using the aftercontraction effect

It is proposed that the human motor system is organized to use hardware and/or software non-linear oscillator mechanisms, the output of these oscillators being responsible for driving the limbs via signals to muscle groups. Following earlier theoretical development, it is argued that these muscle groupings act as a unit and themselves are likely to behave as a non-linear system. The attributes of non-linear oscillators are many, and they are potentially significant for the explanation of motor behavior. This paper reviews and presents recent experiments that investigated the properties of muscular aftercontraction. The basic finding shows that subsequent to a period of moderate strain against a fixed surface the treated limb exhibits prolonged involuntary molar oscillations in the plane of the treatment. These results provide for the presence of driving oscillator mechanisms in the human motor apparatus. The mechanisms show generality of action in that directed attention can lead to oscillation of untreated limbs. Overall, the experiments showed that the movements exhibited the mutual interaction, synchronization, and preservation of phase relationships that are fundamental properties of non-linear oscillators. the picture that emerges is that these mechanisms can drive involuntary movements that are richly patterned: like slow versions of voluntary movements. The aftercontraction phenomenon proves to be an excellent tool for research on the oscillatory substrate of human motor organization.     

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.     

A developmental study of the interlimb coordination in running and galloping

Using a dynamical systems perspective on motor behavior, it was predicted that interlimb coordination of running and galloping would behave like coupled, nonlinear, limit-cycle oscillators, which show the properties of phase locking, entrainment, and structural stability. Female subjects ranging in age from 2.5 years to adult were filmed while running and galloping with and without a weight perturbation. Analysis of both temporal- and amplitude-phasing measures revealed that both gaits demonstrated oscillatory properties. Differences between gaits and across age were primarily a matter of degree. In general, children 4 years of age and below had slightly less table phasing patterns, and all age groups showed slightly less ability in the gallop, particularly with amplitude phasing.     

An Exchange on Franz,Rowse, and Ballantine (2002)

Using a dynamical systems perspective on motor behavior, it was predicted that interlimb coordination of running and galloping would behave like coupled, nonlinear, limit-cycle oscillators, which show the properties of phase locking, entrainment, and structural stability. Female subjects ranging in age from 2.5 years to adult were filmed while running and galloping with and without a weight perturbation. Analysis of both temporal- and amplitude-phasing measures revealed that both gaits demonstrated oscillatory properties. Differences between gaits and across age were primarily a matter of degree. In general, children 4 years of age and below had slightly less stable phasing patterns, and all age groups showed slightly less stability in the gallop, particularly with amplitude phasing.     

Coping with systematic bias during bilateral movement

The present studies examined the nature of kinematic interlimb interference during bilateral elbow movements of 1:1, 2:1 and 3:1 frequency ratios and the manner in which subjects cope with coordination bias. Analysis of movement trajectories in the first experiment indicated progressively greater angular velocity assimilation across 2:1 and 3:1 conditions. The desired temporal relationship was maintained by slowing or pausing the low-frequency movement at peak extension while the high-frequency arm produced intervening cycles. An increase in amplitude was also evident for concurrent, homologous cycles. Movement smoothness was emphasized and additional practice was provided in a second experiment. This resulted in dissociated peak angular velocity between limbs and eliminated hesitations and amplitude effects. Bias was still evident, however, as an intermittent approach toward a 1:1 ratio within each cycle. This systematic tendency was somewhat greater at the lower of two absolute frequency combinations but was not influenced by the role of each arm in producing the higher or lower frequency movement. The findings from the first experiment suggest that subjects initially accommodate interlimb kinematic assimilation, while producing the intended timing ratio, by intermittently slowing or pausing the lower-frequency movement. This attenuates the need for bilaterally-disparate movement parameters and provides additional time for organizing residual kinematic differences, perhaps reducing transient coupling. Evidence from the second experiment indicates that subtle relative motion preferences are still evident following sufficient practice to perform the movements smoothly. The within-cycle locations of the points of greatest interlimb bias for the 2:1 rhythms were positively displaced from those previously observed for 1:1 oscillations. The persistent coordination tendencies noted in both experiments perhaps reflect an assimilation/compensation cycle and constitute one potential source of the systematic error that often emerges during the acquisition of complex skills.     

Dissociation of muscular and spatial constraints on patterns of interlimb coordination

Interlimb coordination is subject to constraints. One major constraint has been described as a tendency for homologous muscle groups to be activated simultaneously. Another has been described as a biasing of limb segments to movement in the same direction. In 2 experiments, the 2 constraints were placed in opposition: In-phase or antiphase contraction of homologous muscles of contralateral limbs produced movement that was spatially antiphase or in-phase, respectively. Probability distributions of relative phase were obtained under manipulations of phase detuning and movement speed. They revealed that the equilibrium and stability of coordination were related, respectively, to spatial relative phase and muscular relative phase. Previously observed spatial and muscular constraints reflect a (possibly very general) factorization of attractor location and attractor strength in the dynamics of interlimb coordination.