Motor Control & Sensory Integration

The Dynamics of Bimanual Circling 247 Specifically, it is suggested that in addition to properly timed muscle activation, to maintain an anti-phase relation between the limbs requires the prevention of kinesthetic signals from automatically entraining the in-phase coupling. This inhibitory control is possible because the afferent feedback during in-phase coupling is weak and is processed \"by a low-gain, automatic feedback mechanism, which operates on the efferent pathways, perhaps at the spinal level\" (Baldissera, Cavallari & Tesio, 1994, p. 240). Anti-phase coupling, in contrast, relies on the conscious monitoring of the phase relationship between the hands at a certain point in the movement cycle. Teasdale et al (1994), however, suggest that dual- task interference arises at the level of movement organisation or planning. They examined dual-task performance in a deafferented patient suffering total loss of sensation in the four limbs but with the peripheral motor system intact. Dual-task interference was more pronounced in the patient than in normal subjects indicating that the interference was located at a higher cognitive level rather than in the monitoring of afferent signals from the limbs. Interestingly, when the patient was asked to draw circles with the two hands she had to \"think about it\" before initiating the movements and then shift her attention from one hand to the other quickly resulting in a temporal desynchronisation of the hands. This suggests that although dual- task interference may occur at the central level, in normal subjects afferent information from the moving limbs is important in sustaining interlimb coordination. Semjen, Summers and Cattaert (in press) have also argued that the coupling between the hands depends on movement derived kinesthetic feedback and that the evaluation of these signals depends on the spatial organisation of the movements. In symmetrical circling movements because both hands are moving either toward or away from the frontal plane (Y axis) and either toward or away from the body midline (X axis) the feedback signals from the two hands match. In asymmetrical circling movements, however, while the hands are in- phase on the Y axis, on the X axis one hand is moving toward and the other away from the body midline. It seems likely that the monitoring of feedback signals in the latter condition may be more difficult and requiting of constant attention. Furthermore, when movement frequency is scaled up under the asymmetrical mode of coordination the nondominant hand tended to lag behind the dominant hand making the precise detection of the spatial positions reached by the two hands even more difficult. It is possible that under such conditions the discrepancy in the feedback signals from the two limbs may be interpreted as indicating a deviation from symmetrical coordination (the preferred coordination) rather

248 J.J. Summers et al. than a deviation from asymmetrical coordination (the harder to maintain coordination) and a movement reversal may occur. In summary, the trajectory distortions, movement reversals, and corrections observed when frequency was scaled up and the system became unstable may be interpreted as reflecting competition between an intrinsically stable state and the intentionally selected current state (Schoner & Kelso, 1988). 5.2 Manual Asymmetries Previously, it was suggested that the manual asymmetries observed during bimanual tasks may not reflect differences in constituent intrinsic frequencies but differences in coupling influence which is stronger in the direction of the fight hand on the left hand than vice versa. Recent analysis of movement related neuro-magnetic and neuro-electric fields suggests that there are bilateral 'generators' for both unilateral and bilateral movements. Of particular interest, however, is the finding that the pattern of activity preceding movements of the left hand alone is similar to the pattern of activity preceding bimanual movements (Kristeva, Cheyne & Deecke, 1991). Large negative DC shifts in cortical potentials have also been observed for movements of the left hand (Lang, Zilch, Koska, Lindinger, & Deecke, 1989). Thus, it appears that left hand movements produce greater ipsilateral activation than fight hand movements (Carson, 1994). It is interesting to speculate that, at least in fight handers, one source of the erratic behaviour of the left hand during maximum rate asymmetrical circling may be interference within the left motor cortex between contralateral control of fight arm movements and ipsilateral control of left arm movements. 6. CONCLUSION In this chapter we have examined the control of bimanual movements within a task requiring multijoint intralimb and interlimb coordination. The task involved tracing circles with both hands simultaneously in either a symmetrical or asymmetrical coordination mode. The results across two studies and involving both fight and left hand dominant subjects have been straightforward and consistent. Symmetrical movements were produced with greater temporal and spatial accuracy and less variability than asymmetrical movements. When the rate at which asymmetrical movements are executed was increased large manual asymmetries emerged. Specifically, the nondominant hand exhibited a loss of temporal and

The Dynamics of Bimanual Circling 249 spatial control and spontaneous and sometimes dramatic distortions in movement trajectories, including movement reversals, were observed. These effects were restricted to the nondominant hand in both right- and left-handed subjects. The fact that a movement reversal during asymmetrical circling was invariably followed, almost immediately, by a return to the required coordination mode suggests that the circling task may provide some important insights into the interaction between intentionality, attention and dynamics. While many of the observed effects were consistent with recent work describing manual asymmetries in a variety of bimanual tasks and the well researched transitions from anti- phase to in-phase coordination, the circling task provides a paradigm through which the interaction between the temporal and spatial components of movement can be studied. ACKNOWLEDGEMENTS The second experiment reported in this chapter was supported by Australian Research Council Small Grant No. 179112. Some analyses (Experiment 2) were conducted using programs made available by the Human Motor Systems Laboratory, Simon Fraser University. REFERENCES Baldissera, F., Cavallari, P., & Tesio, L. (1994). Coordination of cyclic coupled movements of hand and foot in normal patients and on the healthy side of hemiplegic patients. In S.P. Swinnen, H. Heuer, J. Massion, & P. Casaer (Eds.), lnterlimb coordination: Neural dynamical, and cognitive constraints (pp.229-242). San Diego: Academic Press. Baldissera, F., Cavallari, P., Marini, G., & Tassone, G. (1991). Differential control of in- phase and anti-phase coupling of rhythmic movements of ipsilateralhand and foot. Experimental Brain Research, 83, 375-380. Bfinkman, J., & Kuypers, H.G.J.M. (1972). Splitbrain monkeys: cerebral control of ipsilateral and contralateral arm, hand, and finger movements. Science, 176, 53-538. Bfinkman, J., & Kuypers, H.G.J.M. (1973). Cerebral control of contralateral and ipsilateral arm, hand, and finger movements in the split-brain rhesus monkey. Brain, 96, 653-674. Byblow, W.D., Carson, R.G., & Goodman, D. (1994). Expressions of asymmetries and anchoring in bimanual coordination. Human Movement Science, 13, 3-28. Carson, R.G. (1993). Manual asymmetries: Old problems and new directions. Human Movement Science, 12, 479-506.

250 J.J. Summers et al. Carson, R.G. (in press). The dynamics of isometric bimanual coordination. Experimental Brain Research. Carson, R.G., Byblow, W.D., & Goodman, D. (1994). The dynamical substructure of bimanual coordination. In S.P. Swinnen, H. Heuer., J. Massion., & P. Casaer (Eds.). Interlimb coordination: Neural dynamical and cognitive constraints (pp.319-337). San Diego: Academic Press. Carson, R.G., Goodman, D., Kelso, J.A.S., & Elliott, D. (in press). Phase transitions and critical fluctuations in rhythmic coordination of ipsilateral hand and foot. Journal of Motor Behavior. Cohen, L. (1971). Synchronous bimanual movements performed by homologous and non- homologous muscles. Perceptual and Motor Skills, 32, 639-644. Franz, E.A., Zelaznik, H.N., & McCabe, G. (1991). Spatial topological constraints in a bimanual task. Acta Psychologica, 77, 137-151. Haken, H., Kelso, J.A.S., & Bunz, H. (1985). A theoretical model of phase transitions in human hand movements. Biological Cybernetics, 51,347-356. Ibbotson, N.R. & Morton, J. (1981). Rhythm and dominance. Cognition, 9, 125-135. Jardin, K., Swinnen, S., & Meulenbroek, R. (1994). Unimanual and bimanual two dimensional drawing movements. Journal of Sport & Exercise Psychology, 16 (SuppL ), $69. Kelso, J.A.S., & Jeka, J.J. (1992). Symmetry breaking dynamics of human multilimb coordination. Journal of Experimental Psychology: Human Perception and Performance, 18, 645-668. Kelso, J.A.S., Buchanan, J.J., & Wallace, S.A. (1991). Order parameters for the neural organization of single, multijoint limb movement patterns. Experimental Brain Research, 85, 432-444. Kelso, J.A.S., DelColle, J.D., & Schoner, G. (1990). Action-perception as a pattern formation process. In M.Jeannerod (Ed.), Attention and Performance XIII, (pp. 139- 169). Hillsdale, NJ: Erlbaum. Kelso, J.A.S., Holt, K.G., Rubin, P., & Kugler, P.N. (1981). Patterns of human interlimb coordination emerge from the properties of non-linear, limit-cycle oscillatory processes: Theory and data. Journal of Motor Behavior, 13, 22-21.

The Dynamicsof Bimanual Circling 251 Kristeva, R., Cheyne, D., & Deecke, L. (1991). Neuromagnetic fields accompanying unilateral and bilateral voluntary movements. Topography and analysis of cortical sources. Electroencephalography and Clinical Neurophysiology, 81,284-298. Lang, W., Zilch, O., Koska, C., Lindberger, G., & Deecke, L. (1989). Negative cortical DC shifts preceding and accompanying simple and complex sequential movements. Experimental Brain Research, 74, 99-104. MacKenzie, C.L. & Patla, A.E. (1983). Breakdown in rapid bimanual finger tapping as a function of orientation and phasing. Neuroscience Abstracts, 297:12, 1033. Peters, M. (1981). Attentional asymmetries duringconcurrent bimanual performance. Quarterly Journal of Experimental Psychology, 33, 95-103. Peters, M. (1985). Constraints in the coordination of bimanual movements and their expression in skilled and unskilled subjects. Quarterly Journal of Experimental Psychology, 37A, 171-196. Peters, M. (1990). Interaction of vocal and manual movements. In G.E. Hammond (Ed.), Cerebral control of speech and limb movements (pp. 535-574). Amsterdam: North- Holland. Peters, M. (1994a). Does handedness play a role in the coordination of bimanual movement? In S.P. Swinnen, H.Heuer, J. Massion, & P. Casaer (Eds.), lnterlimb coordination: Neural dynamical and cognitive constraints (pp. 595-615). San Diego: Academic Press. Peters, M. (1994b). When can attention not be divided? Journal of Motor Behavior, 26, 19-199. Peters, M., & Schwartz, S. (1989). Coordination of the two hands and effects of attentional manipulation in the production of a bimanual 2:3 polyrhythm. Australian Journal of Psychology, 41,215-224. Scholz, J.P., & Kelso, J.A.S. (1989). A quantitative approach to understanding the formation and change of coordinated movement patterns. Journal of Motor Behavior, 21,122-144. Schoner, G., & Kelso, J.A.S. (1988). A synergetic theory of environmentally-specified and learned patterns of movement coordination. I. Relative phase dynamics. Biological Cybernetics, 58, 71-80. Semjen, A., Summers, J.J., & Cattaert, D. (in press). Hand coordination in bimanual circle drawing. Journal of Experimental Psychology: Human Perception and Performance.

252 J.J. Summers et al. Stucchi, N., & Viviani, P. (1993). Cerebral dominance and asynchrony between bimanual two-dimensional movements. Journal of Experimental Psychology: Human Perception and Performance, 19, 1200-1220. Summers, J.J., & Kennedy, T. (1992). Strategies in the_production of a 5:3 polyrhythm. Human Movement Science, 11, 101-112. Summers, J.J., & Pressing, J. (1994). Coordinating the two hands in polyrhythmic tapping. In S.P. Swinnen, H. Heuer, J. Massion., & P. Casaer (Eds.), Interlimb coordination: Neural dynamical and cognitive constraints (pp. 571-593). San Diego: Academic Press. Swinnen, S.P., & Walter, C.B. (1988). Constraints in coordinating movements. In A.M. Coney, & J.R. Beech (Eds.), Cognition and action in skilled behavior (pp. 127-143). Amsterdam: North-Holland. Swinnen, S.P., Walter, C.B., & Shapiro, D.C. (1988). The coordination of limb movements with different kinematic pattems. Brain and Cognition, 8, 326-347. Swinnen, S.P., Walter, C.B., Beinrinckx, M.B. & Meugens, P.F. (1991). Dissociating the structural and metrical specifications of bimanual movements. Journal of Motor Behavior, 23, 263-279. Swinnen, S.P., Heuer, H., Massion. J., & Casaer, P. (Eds.) (1994). Interlimb coordination: Neural, dynamical, and cognitive constraints. San Diego: Academic Press. Teasdale, N., Bard, C., Fleury, M., Paillard, J., Forget, R., & Lamarre, Y. (1994). Bimanual interference in a deafferented patient and control subjects. In S.P. Swinnen., H. Heuer., J. Massion., P. Casaer (Eds.), Interlimb coordination: Neural, dynamical, and cognitive constraints (pp. 243-258). San Diego: Academic Press. Treffner, P.J., & Turvey, M.T. (in press). Handedness and the asymmetric dynamics of bimanual rhythmic coordination. Journal of Experimental Psychology: Human Perception and Performance. Tuller, B., & Kelso, J.A.S. (1989). Environmentally-specified patterns of movement coordination in normal and split-brain subjects. Experimental Brain Research, 75, 306- 316. Walter, C.B., & Swinnen, S.P. (1994). The formation and dissolution of \"bad habits\" during the acquisition of coordination skills. In S.P. Swinnen, H. Heuer, J. Massion., & P. Casaer (Eds.), Interlimb coordination: Neural, dynamical, and cognitive constraints, (pp. 491-513). San Diego: Academic Press.

The Dynamics of Bimanual Circling 253 Waiters, M.R., & Carson, R.G. (1994). A method for calculating the circularity of movement trajectories. Journal of Sport & Exercise Psychology, 16 (Suppl.), S12.

Motor Control and Sensory Motor Integration: Issues and Directions 255 D.J. Gleneross and J.P. Piek (Editors) 9 1995Elsevier Science B.V. All rights reserved. Chapter 10 ASYMMETRIES IN THE DYNAMICS OF INTERLIMB COORDINATION R.G. Carson* School of Kinesiology, Simon Fraser University D. Goodman, School of Kinesiology, Simon Fraser University D. Elliott Department of Kinesiology, McMaster University J.A.S. Kelso Centerfor Complex @stems, Florida Atlantic University Two experiments were conducted to examine whether asymmetries in cortical organization with respect to timing functions are expressed in the dynamics of self paced, and externally paced, rhythmic coordination tasks. Four subjects performed movements of the ankle and the wrist, in two modes of coordination, anti-phase and in-phase. In Experiment 1, subjects conducted these movements at their preferred frequencies. In Experiment 2 their movements were paced by an auditory metronome at I Hz and 2 Hz. Coordination dynamics were examined at both the kinematic (Experiments I & 2) and the neuromuscular (Experiment 1) levels of observation. When self-paced, movements of the left side were more variable with respect to oscillation frequency than movements of the right side. Uniformity of the order parameter, relative phase, was also greater for movements of the right side. These differences were eliminated when movements were externally paced. 1. INTRODUCTION Contemporary \"dynamical\" approaches to the study of coordination have emphasised the self-organizing, autonomous nature of systems comprising multiple degrees of freeAom representing neural, muscular and metabolic components (e.g., Bingham, Schmidt, Turvey, & Rosenblum, 1991; Kelso, Sch6ner, Scholz, & Haken, 1987). *The first author is presently at the Department of Human Movement Studies, University of Queensland, Brisbane, Queensland, 4072, Australia, where this work was completed. The analysis routines were implementedby CliffStorlund. Somepreliminary analysisprocedures were conducted usingprogramsprovidedbyRon Marteniukand ChristineMackenzie.

256 R. G. Carson et al. These elements act cooperatively to enable a relatively small number of complex behavioural patterns exhibiting low-dimensional dynamics (Kelso, 1988). The dynamics may be elucidated by examining situations in which there is a qualitative change of pattern or \"phase transition\". As such change, by definition, permits one pattern to be distinguished from another, the pre and post transition behaviour delineates the essential dimensions of the patterns, termed the \"collective variables\" or \"order parameters\" (Haken, Kelso, & Bunz, 1985; Kelso, 1990). Since the order parameter expresses the most salient features of a system engaged in task specific coordination (Haken et al., 1985, Kelso & SchiSner, 1988; Schtiner & Kelso, 1988a; Turvey, 1990), analysis conducted in terms of the dynamics of order parameters represents a reduction of the degrees of freedom which describe the system from the potential to the essential (Carson, 1993a). The study of phase transitions also allows consideration of control parameters, such as oscillation frequency, changes in which induce the acquisition of new patterns of behaviour. Coordination dynamics may also be explicated in regions of state space in which phase transitions are atypical. In this regard, advances have been made by investigators using analytic techniques derived from the bimanual paradigm introduced by Kugler and Turvey (1987) (e.g., Bingham et al., 1991; Kugler, Turvey, Schmidt, & Rosenblum, 1990; Rosenblum & Turvey, 1988; Schmidt, Beek, Treffner, & Turvey, 1991; Schmidt, Treffner, Shaw, & Turvey, 1992). The essence of biological coordination is the assembly of special purpose solutions to the challenges created by environmental contingencies (Turvey, 1990). Stationary states, corresponding to attractors of the order parameter dynamics, express organizing principles or constraints which are specific to particular movement tasks. In throwing and kicking, the generation of maximal velocities in distal limb segments is contingent upon a generation of torques which proceeds in a proximal to distal fashion. It can be argued that this sequence is desirable because of both the linked segmental nature of the limbs, and the \"stretch-shortening\" characteristics of the muscles themselves (e.g., Chapman & Sanderson, 1990). While the proximal to distal pattern expresses an organizing principle for these tasks, optimization of performance requires precise variations on this basic temporal pattern, in response to circumstantial demands. Calvin (1983) has argued that the launching of projectiles, and in particular the precision in timing required to maintain accuracy with increases in target distance, has exerted strong evolutionary pressure on the organization of hominid brains. The

Asymmetries in the Dynamics of Interlimb Coordination 257 assembly of large numbers of intrinsically \"noisy\" individual neurons into collectives which possess a stability sufficient to mediate the precise recruitment of muscles, appears to have been localized to a greater degree in the left cerebral hemisphere1. Indeed, a large body of theoretical work has been based explicitly upon the assumption that the left hemisphere assumes some privileged role in the execution of timing functions (e.g., Bradshaw & Nettleton, 1981; Ojemann, 1984; Tzeng & Wang, 1984). There is a great deal of evidence documenting asymmetries in the timing of movements. The fingers of the fight hand tap more rapidly than those of the left hand (e.g., Peters, 1977, 1987, 1990; Truman & Hammond, 1990) and are consistently less variable at maximal rates of responding (e.g., Hammond, Bolton, Plant & Manning, 1988; Peters, 1980; Peters & Durding 1978, 1979a; Todor & Kyprie, 1980; Todor & Smiley-Oyen, 1987; Truman & Hammond, 1990). These findings have been reproduced for movements of more proximal upper limb segments (e.g., Harrison, 1991; Rouselle & Wolff, 1991; Todor, Kyprie, & Price, 1982) and of the foot (Augustyn & Peters, 1986; Peters & Durding, 1979b). In bimanual tasks requiring absolute coordination, the fight hand is often characterized by a smaller degree of variability in frequency (Carson, Byblow, & Goodman, 1994a; Kay, Kelso, Saltzman, & Sch~ner, 1987; Riek, Carson, & Byblow, 1992). It has been suggested that motor timing functions are largely mediated by subcortical mechanisms (e.g., Grillner, 1981; Ivry & Keele, 1989), yet there is little evidence to suggest the presence of asymmetries at subcortical levels (Trevarthen, 1984). This contrariety may be resolved if it is noted that the bulk of experimental work countenancing the role of subcortical structures in timing has been concerned with human and animal locomotion. Control processes mediating cycling of the limbs in locomotion may be assembled to optimize energy consumption through exploitation of the pendular properties of the limbs (Keele & Ivry, 1987; Turvey, Schmidt, Rosenblum, & Kugler, 1988; cf., Bach, Chapman, & Calvert, 1983). Indeed, it has been contended that the maximum rate of reciprocation in running can be accounted for largely in terms of inertial properties of the limbs (Heglund, Taylor, & McMahon, 1974). However, rhythmical movements of other effectors are thought to be less sensitive to energetic considerations and may be modulated by combinations of \"control modules\" which are 1In thispaperany referenceto lateralityand handednessis withrespectto righthanders.

258 R. G. Carson et al. different from those involved in locomotion (Keele & Ivry, 1987; cf., Guiard, 1993). It is these movements which are likely to provide a window upon cortical organization visa vis timing functions. Carson (1993a) has proposed that asymmetries in coordination dynamics, and their relation to timing functions, may be elucidated through consideration of features such as the relative stability of stationary states, and the variability with which control parameter regimes are instantiated. In the present paper, consideration is given to two experiments, conducted to determine whether putative asymmetries in cortical organization with respect to timing functions are expressed in the dynamics of self paced, and externally paced, rhythmic coordinated movements. The specific aim of these studies was to ascertain whether the greater variability of movement frequency exhibited by a variety of effectors on the left side of the body at maximal rates of response, is reproduced at sub-maximal frequencies in a task requiring the coordination of two limb segments. In Experiment 1, flexion and extension movements of the wrist and plantar- and dorsi-flexion of the ankle were examined both when these joints were moving singly and when coupled, following the paradigm introduced by Baldissera, CavaUari, and Civaschi (1982). In addition, the dynamics of coupled movements were assessed to determine whether asymmetries are expressed in terms of the collective variables which encapsulate stable coordinative states. Previous work had demonstrated that the relative phase relation between the ankle and the wrist joints represents a suitable collective variable for this task (Carson, Goodman, Kelso, & Elliott, in press). These features were examined at both the kinematic and the neuromuscular levels of observation. In Experiment 2, the dynamics were assessed when coupled movements were paced by an auditory metronome. 2. EXPERIMENT 1 2.1 Methods Subjects Three normal adult females (24-27 years) and one normal adult male (24 years) from the university population were employed in these experiments. All were right-handed (Oldfield 1971) and were paid for their participation.

Asymmetries in the Dynamics of Interlimb Coordination 259 Apparatus =_ Subjects were positioned in a padded wooden seat. Custom built manipulanda were used to monitor the flexion and extension of the wrist, and the plantar-flexion and dorsi- flexion of the foot. Linear potendometers (Bourns Instruments, Model # 3540, 0.25%) located coaxially with the centre of rotation of each manipulandum allowed for the continuous transduction of angular displacement. Wrist manipulanda were mounted on a frame in front of the subject, and could be moved in the transverse plane such that they were located a comfortable distance from the subject's midline. The height of the frame was adjustable so that subjects could passively rest their forearms, on semi-rigid foam blocks, in a fully pronated or fully supinated position. Subjects' hands were attached to the manipulandum by means of two rubber loops passing over the second and third, and fourth and fifth fingers at about the metacarpal phalangeal joint. These loops ensured that it was not necessary for subjects to \"grip\" the manipulandum. The manipulanda were adjusted for each subject to ensure that the axis of rotation was coaxial with the wrist joint. Subjects' forearms were secured with a wide velcro belt, ensuring that movements were restricted to flexion/extension of the wrist. Foot manipulanda comprised freely rotating, neoprene padded foot plates. Subjects' feet were placed on these plates and secured by a heel support and five velcro straps applied over the upper surface of the foot. The length of the shafts from which the foot plates were suspended could be adjusted such that the axes of rotation of the manipulanda were coaxial with subjects' ankle joints. The manipulanda were positioned on a sliding trackway mounted in front of the subject. When seated, subjects' thighs were in a horizontal position with knees flexed at approximately 45 ~. Fine, \"comfort\", adjustments could be performed by moving the manipulanda along the trackway either towards or away from the subject. Auditory signals providing pacing for movements (Experiment 2) or indicating either the initiation or termination of data collection were presented via a loudspeaker mounted on the floor directly in front of subjects. These signals (50 ms square waves (500 Hz)) were output through a Scientific Solutions Inc. LABMASTER board mounted in a microcomputer. EMG signals (Experiment 1) and the voltage signals from each potendometer and metronome pulses were sampled at 500 Hz by a 12 bit WATSCOPE (Northern Digital) A/D converter and stored to disk upon completion of each triM. Electromyographic recordings (Experiment 1) of the wrist flexor (flexor carpi radialis) and extensor (extensor carpi radialis) and foot plantar flexor (medial head

260 R.G. Carson et al. gastrocnemius) and dorsi flexor (tibialis anterior) were obtained using a multichannel electromyographic system (Strawbridge Technologies, Waterloo, Ontario). Using standard skin preparation procedures, silver/silver chloride electrodes were mounted on the surface of the subject's forearm and lower leg over the muscles of interest (Delagi, Perotto, Iazzetti, and Morrison, 1975). EMG signals were monitored on oscilloscopes and input gains adjusted when necessary. Following preamplification, all EMG signals were passed through a 4th order butterworth f'flter (20 - 500 Hz) prior to digital sampling. 2.2 Procedure Movements consisting of the rhythmic flexion and extension of the wrist and/or the plantar-flexion and dorsi-flexion of the foot, were performed with the forearm either in a supine or a prone position. Emphasis was placed upon the adoption of a comfortable frequency and amplitude such that the movements \"could be performed all day\" if necessary. Upon achieving their preferred frequency, subjects made a verbal signal to the experimenter. Data collection was then initiated. After 500 msec an auditory tone was presented to subjects signalling commencement of the trial. Following a further 30 sec, a second auditory tone signalled termination of the trial. Single Limb. Subjects first performed trials consisting of movements of a single limb in the following order, wrist alone (forearm supinated), foot alone, wrist alone (forearm pronated). Six trials, preceded by a practice trial, were conducted in each condition. The side on which trials commenced (left or fight) was counterbalanced across subjects. Coupled. Following single limb trials, subjects performed movements of both limbs in two modes of coordination, in-phase and anti-phase. In the in-phase (forearm supinated) mode, flexion (extension) of the wrist was required to be coincident with dorsi-flexion (plantar-flexion) of the ipsilateral foot. In the anti-phase (forearm supinated) mode, flexion (extension) of the wrist was required to be coincident with plantar-flexion (dorsi- flexion) of the foot. When the forearm was in a pronated position, in the in-phase mode, flexion (extension) of the wrist was required to be coincident with plantar-flexion (dorsi- flexion) of the foot and in the anti-phase mode, flexion (extension) of the wrist was required to be coincident with dorsi-flexion (plantar-flexion)of the foot.

Asymmetries in the Dynamics of lnterlimb Coordination 261 In each forearm position, trials alternated between in-phase and anti-phase. For each side (left or fight) six trials were performed for each combination of coordination mode and forearm position, for a total of 24 trials. In each condition, subjects were permitted one practice trial. The side on which trials commenced was counterbalanced across subjects. 2.3 Data Reduction 2.3.1 Kinematic Data Fast fourier transforms of angular displacement data indicated that the power of the signal was predominantly distributed over harmonics below 5 Hz. Displacement data were then low pass filtered using a 2nd order Butterworth dual pass filter with a cut off frequency of 10 Hz. The maximum and minimum angular displacements for each movement cycle were delineated using a custom \"peak peaking\" algorithm. Discrete estimates of oscillation frequency were thus obtained. For all coupled trials, discrete estimates of relative phase were derived following Carson (1993b) (see also Byblow, Carson & Goodman, 1994; Carson et al., in press). Mean relative phase was calculated as outlined by Mardia (1972) (see also Batschelet, 1981 and Burgess-Limerick, Abernethy, & Neal, 1991). Measures of circular variance (uniformity) were calculated and transformed to the range 0 to ~, following Mardia (1972). 2.3.2 EMG Data EMG data for coupled trials were treated by first removing DC bias and rectifying. Having ascertained that frequencies of oscillation were below 1.5 Hz, EMG profiles were then enveloped through the application of a low pass (digital) filter (dual pass 2nd order Butterworth, cutoff 2 Hz). These data were differentiated using a two-point central difference algorithm. A custom \"peak peaking\" algorithm was applied to the resulting \"velocity\" profiles in order to delineate points corresponding the maximum rate of increase of activity for each EMG burst2. Discrete (cycle to cycle) estimates of oscillation frequency and relative phase were based upon these events. 2 It was assumedthatfor a given frequencyof oscillation,the intensitiesof the excitationpulses, and thereforethe initial slopesof EMG remainconstant(seeGottlieb,Corcos, & Agarwal, 1989;Heuer, 1989).

262 R. G. Carson et al. 2.4 Results As the details of movement dynamics differ markedly between individuals (e.g., Kelso, 1984), data from each subject were analysed separately. Thus, each subject can be considered an experiment, providing in effect four replications. Examples of time series obtained from representative coupled trials are presented in Figures 1 and 2. It is evident that the phase relation of the modulated muscular activity closely parallels that of the limbs, in both the anti-phase (Figure 1) and in-phase (Figure 2) conditions. Figure 1. Experiment 1. Sampletime seriesof a movementpreparedin the anti- phase modewith the forearmin a supinatedposition (subjectI) 2.4.1 Single Joint Movements Frequency Independent analyses of variance for mean preferred frequency and coefficient of variation (CV) were performed for each subject using a 2 side (left, fight) by 3 joint condition (wrist-forearm pronated, wrist-forearm supinated, ankle) design. There was little evidence to suggest the consistent expression of asymmetries in preferred frequencies of oscillation. Subject II exhibited higher preferred frequencies for movements of the left side (0.92 Hz) than for movements of the fight side (0.74 Hz) (F(1, 30) = 293.69, p < 0.01). Whereas, for subject IV this trend was reversed.

Asymmetries in the Dynamics of Interlimb Coordination 263 Frequencies were higher for movements made by the right side (2.32 Hz) than by me left side (1.93 Hz) (F(1, 30) = 67.44, p < 0.01). Figure 2. Experiment 1. Sample time series of a movement prepared in the in-phase mode with the forearm in a supinated position (subject I) In two of the four subjects (I and IV), larger coefficients of variation were associated with movements of joints on the left side than on the right side (F(1, 30) = 13.31 (I), & 14.86 (IV), p < 0.01) 3. 2.4.2 Coupled Movements Frequency Independent analyses of variance for mean preferred frequency and coefficient of variation (CV) were performed for each subject using a 2 side (left, fight) by 2 mode (anti-phase, in-phase) by 2 forearm position (pronated, supinated) by 2 joint (wrist, ankle) design. 3 There were a small number of unremarkable effects pertaining to joint condition. As these do not represent a focus of this study, they will not be treated further.

264 R.G. Carson et al. Subjects I (left = 0.84 Hz, fight = 0.90 Hz) and IV (left = 1.30 Hz, fight = 1.46 Hz) presented preferred frequencies which were higher for movements of the fight side F(1, 40) = 132.67 (I), & 37.84 (IV), p < 0.01). Subjects II (left = 1.11 Hz, fight = 0.91 Hz) and HI (left = 0.94 Hz, fight = 0.89 Hz) exhibited the reverse trend (F(1, 40) = 183.66 (II) & 57.69 (III), p < 0.01). Generally, preferred frequencies were lower in the anti-phase mode than in the in- phase mode (F(1, 40) = 47.04 (I), 23.79 (III), & 247.10 (IV), p < 0.01, 3.97 (II) p = 0.053). In a single subject (IV), an interaction of side and mode (F(1, 40) = 12.28, p < 0.01) indicated that mean frequencies in the fight in-phase condition were higher than in all other conditions, and that in the left in-phase condition frequencies were higher than in both anti-phase conditions (Tukey HSD, p < 0.01)4. Subjects II (left = 8.12, fight = 6.05, F(1, 40) = 18.01, p < 0.01), III (left = 6.47, fight = 5.20, F(1, 40) = 12.19, p < 0.01) and IV (left = 11.94, fight = 8.90, F(1, 40) = 9.45, p < 0.01) exhibited larger coefficients of variation for movements of the left side. For subject I, a trend in this direction did not attain conventional levels of statistical significance (left = 4.18, fight = 3.82, F(1, 40) = 3.46, p = 0.07). Movements of the left side when the forearm was supinated, made by subject II were more variable than movements of the fight side both when the forearm was supinated and pronated (p < 0.05, Tukey HSD). Movements of the left side when the forearm was pronated were more variable than movements of the fight side when the forearm was supinated (p < 0.05, Tukey, HSD). These effects were accentuated in the anti-phase mode. For two subjects, coefficients of variation were larger in the anti-phase mode than in the in-phase mode (F(1, 40) = 25.76 (II), & 56.24 (IV), p < 0.01). For subject I, a trend in this direction failed to attain conventional levels of statistical significance (F(1, 40) = 3.46, p = 0.07). An interaction of side and mode (F(1, 40) = 8.38, p < 0.01) for subject III, indicated that movements of the left side in the anti-phase mode exhibited greater variability than all other combinations of side and mode, which were equivalent (Tukey HSD, p < 0.01). 4 While higher frequencies were often exhibited when the forearm was placed in a pronated position (I, II, & W), for subject III the reverse was true. Interactions involving side and forearm position were inconsistently expressed across subjects, and as not of theoretical significance, they will not be dealt with further.

Asymmetries in the Dynamics of Interlimb Coordination 265 Relative Phase The relative phase values obtained for each trial were tested for uniformity using the Rayleigh test (Mardia, 1972). This test indicates whether directional data are sufficiently uniform to derive measures of central tendency and dispersion. It was confirmed for each subject that for all trials the hypothesis of uniformity was accepted (p < 0.01) indicating that in every case there existed a dominant direction of relative phase. Test statistics for mean relative phase were calculated separately for anti-phase and in-phase trials. In the first instance, in order to compare left side to fight side conditions, data were collapsed over forearm position. In the second instance, in order to compare forearm pronated to forearm supinated conditions, data were collapsed over side. In order to control for the potential inflation of Type I errors resulting from multiple comparisons, alpha was assigned as 0.01. Mean relative phase values were also assessed with respect to the target relative phase value for each mode of coordination. Analyses of variance for transformed uniformity measures were performed for each subject using a 2 side (left, fight) by 2 mode (anti-phase, in-phase) by 2 forearm position (pronated, supinated) design. When instructed to maintain an anti-phase mode of coordination, in three subjects (I, II, and III), the ankle lagged the wrist to a greater degree than was prescribed (p < 0.01). When required to produce an in-phase mode of coordination, three subjects (I, II, & IV) exhibited relative phase values which deviated slightly from the target value. However, the pattern of deviation was not consistent across individuals. There were no consistent effects attributable to side or to forearm position. In three of four subjects (II, III and IV), uniformity of relative phase was lower for movements of the left side than for movements of the fight side (F(1, 40) = 29.00 (II) & 27.95 (III), p < 0.01, 5.81 (IV), p < 0.05). For subjects III and IV, this effect was most clearly expressed when these movements were conducted in the anti-phase mode (F(1, 40) = 4.70 (III), & 5.61 (IV), p < 0.05)). For subject II, the effect of side was mediated by the position of the forearm (F(1, 40) = 8.01, p < 0.01). Movements of the left side when the forearm was supinated were less uniform than movements in all other conditions (p < 0.05, Tukey HSD). Movements made by the left side when the forearm was pronated were less consistent than movements made by the fight side when the

266 R.G. Carson et al. forearm was supinated (p < 0.05, Tukey HSD). Uniformity values were lower in the anti- phase mode than in the in-phase mode for subject II only (F(1, 40) = 14.27, p < 0.01). 2.4.3 EMG Measures (coupled movements) Due to occasional inconsistencies in the EMG activity of muscles which had lines of action coincident with the force of gravity, analyses were restricted to muscles which acted predominantly in opposition to gravity. Thus, in conditions in which the forearm was supine, the activity of flexor carpi radialis and tibialis anterior was examined. When the forearm was prone, the activity of extensor carpi radialis and tibialis anterior was examined. Frequency (EMG) Independent analyses of variance for coefficients of variation (CV) were performed for each subject5 using a 2 side (left, fight) by 2 mode (anti-phase, in-phase) by 2 forearm position (pronated, supinated) by 2 joint (wrist, ankle) design. Planned orthogonal comparisons of means were performed to highlight a limited number of preselected contrasts. Two of three subjects (I and II) exhibited higher coefficients of variation for movements of the left side than for movements of the fight side (F(1, 40) = 5.48 (I), p < 0.05, 48.18 (II), p < 0.01). For subject I this difference existed primarily in the anti-phase mode. In three subjects (I, II, & IV), variability of frequency was greater for movements prepared anti-phase than those prepared in-phase (F(1, 40) = 5.50 (I), p < 0.05, 9.26 (II) & 33.66 (IV), p < 0.01). Relative Phase (EMG) Analyses of variance for transformed uniformity scores were performed for each subject using a 2 side (left, fight) by 2 mode (anti-phase, in-phase) by 2 forearm position (pronated, supinated) design. Planned orthogonal comparisons of means were performed to highlight a limited number of preselected contrasts. In two of three subjects (I and II), uniformity values were lower for movements of the left side than of the fight side (F(1, 40) = 21.41 (I) & 26.14 (II), p < 0.01). These 5 Due to technicalproblems which wereundetectedat the timeof data collection, it was not possible to deriveEMG measuresfor movementsof the left sidemadeby subjectIV.

Asymmetries in the Dynamics of Interlimb Coordination 267 effects were expressed for movements prepared in the in-phase and anti-phase modes of coordination. Movements produced by subjects II and IV in the anti-phase mode, exhibited a lesser degree of uniformity than movements made in the in-phase mode (F(1, 40) = 4.45 (II), p < 0.05, & F(1, 20) = 44.66 (IV), p < 0.01). 2.5 Discussion Differences in preferred frequencies of oscillation between movements of the left side and those of the right side, were expressed in two subjects in the single joint trials, and in all subjects in the coupled conditions. In both conditions, subjects were evenly divided between those who exhibited higher frequencies for movements of the left side and those who exhibited higher frequencies for movements of the right side. In single joint conditions, greater consistency in movement frequency was present for movements of the fight side in two subjects. In coupled conditions, all subjects exhibited higher coefficients of variation for movements of the left side. Furthermore, in all of the subjects in whom differences were expressed, intervals between EMG bursts varied to a greater degree when movements were performed by the left side. Instances in which the periods of movements made by the fight side were more variable than those made by the left side were never observed. In coupled conditions, in which subjects were required to coordinate movements of the two joints, the variability of the collective variable was also sensitive to the side on which movements were performed. In three of four subjects, the uniformity of relative phase was greater for movements of the fight side. In two subjects this effect was further mediated by the mode of coordination in which the system was prepared. Differences were most clearly expressed when movements were conducted in the anti-phase mode. When the collective variable was defined at the level of EMG activity, uniformity of relative phase was smaller for movements of the left side in two of three subjects. One subject evidenced a smaller degree of uniformity for movements made in the anti-phase mode. The spatial position of the forearm had essentially no bearing on these measures (cf. Baldissera et al., 1982). One of the most consistent findings to emerge from previous research has been that higher and less variable rates of response are elicited for movements of limb segments on the fight side of the body. This feature is present both in unimanual tasks, such as tapping, and in bimanual tasks. In the present experiment, when measures of frequency

268 R.G. Carson et al. variability distinguished movements made by the left and right sides, the left side was in every instance more variable. It is especially notable that these differences were present in the absence of a requirement for maximal rates of response (cf. Hammond et al., 1988). Differences which were unevenly expressed for movements of single joints, were consistently displayed in conditions requiring the coordinated movement of the wrist and the ankle joints. However, there was no evidence of a \"trade-off\" between oscillation frequency and variability. While oscillation frequencies were always more variable for movements of the left side, the number of subjects exhibiting higher frequencies for movements of the left side was equal to the number showing higher frequencies for movements of the fight side. Similarly, differences between movements of the left and fight side, in terms of the uniformity of relative phase, could not be ascribed to trade-offs between maintainence of an appropriate phase relation and the variability of relative phase. 3. EXPERIMENT 2 3.1 Introduction Behavioural data suggest that when coordinative systems are \"driven\" in some fashion, the pattern of successive response intervals or cycle durations exhibits a free structure which is contingent upon both the nature of the movement response and of the driving signal. For example, the degree of compliance with predictions of negative lag 1 autocorrelations of response intervals (Wing & Kristofferson, 1973), and the means by which changes in response interval durations are effected, are dependent upon whether movements are conducted in the induction or continuation phase of the protocol (Wrisberg & Liemohn, 1990). Recent neurophysiological evidence supports the view that the provision of external pacing leads to a fundamental reorganization of the neural activity mediating the regulation, of movement. Kelso, Bressler, Buchanan, DeGuzman, Ding, Fuchs, & Holroyd (1992) examined neuromagnetic field patterns in a task in which subjects were required to syncopate flexion movements of the index f'mger of the fight hand with an auditory metronome. Temporal and spatial coherence in the brain's electromagnetic field, distributed over large areas of the cortex, was observed when a meaningful mode of

Asymmetries in the Dynamics of Interlimb Coordination 269 coordination commenced, particularly in the pre-frontal and the premotor cortex. Increases in the frequency of pacing resulted in transitions from syncopation to synchronization, which were mirrored by shifts in the relative phasing of activity in various parts of the cortex. During self-paced movements, conducted without the metronome, neural activity was largely confined to the motor cortex, and auditory evoked potentials (from the metronome alone) were primarily located in the auditory cortex. Thus the patterns of activation observed in paced movements did not simply arise from a superposition of auditory and motor potentials. Rather, the provision of an external pacing signal, and the patterns of coordination to which this gave rise, realised a distribution of cortical activity which was qualitatively different from that subserving self-paced movement. In Experiment 1 it was demonstrated that there exist differences between movements of the left and fight sides in terms of the variability of spontaneously elicited oscillation frequencies. These differences were particularly pronounced in coupled movements requiring the spatial and temporal coordination of the wrist and ankle. In these movements, asymmetries were also expressed in terms of the variability of the order parameter relative phase. The present experiment was conducted to determine whether the asymmetries revealed by the use of a self-paced protocol in Experiment 1 would be reproduced when subjects were required to follow an external pacing signal. Pacing was provided by an auditory metronome at two frequencies, at 1 Hz which approximated the preferred frequencies of oscillation observed in coupled conditions in Experiment 1, and also at 2 Hz. 3.2 Methods Subjects Subjects were those individuals who participated in Experiment 1. ADDaratus In all respects the apparatus was identical to that utilized in the previous experiment. Although electromyographic data were recorded, they were not analysed.

270 R. G. Carson et al. Procedure Subjects performed paced oscillatory motions of the wrist and foot commencing in two modes of coordination, in-phase and anti-phase. Pacing was provided by means of an auditory metronome at two frequencies, 1 Hz and 2 Hz. These movements were performed with the forearm either in a supine or a prone position. In each forearm position, trials alternated between in-phase and anti-phase trials. Blocks of trials at 1 Hz preceded those at 2 Hz. Thus, for each side (left or fight), four blocks of trials were performed, one for each combination of forearm position and oscillation frequency. Eight trials were performed in each block (four in each coordination mode) for a grand total of 64 trials. Subjects were permitted one practice trial in each condition. Two subjects fu'st performed all trials for the left side followed by all trials for the fight side. For the other two subjects, the order was reversed. Subjects were instructed to maintain a 1:1 frequency relation with the auditory metronome. They were also made aware that, should the pattern of coordination begin to change, they were to attempt to maintain it. Subjects were given no direction concerning the temporal locus of the metronome pulse with respect to the movement cycle. The duration of a trial was 30 seconds. Trials commenced with 2 seconds of \"lead- in\" metronome pulses before data collection was initiated. To obviate anticipation of the end of the trial, two seconds of pulses terminated the trial. 3.3 Results Examples of time series obtained from representative coupled trials, in both the in- phase and anti-phase modes of coordination are presented in Figures 3 and 4. 3.3.1 Metronome Limb Relations As a preliminary means of estimating the extent to which subjects maintained the required frequency relation, Pearson product-moment correlations were calculated between individual limb frequencies and metronome frequencies. Data from each joint and from trials in each forearm position were pooled for the purposes of these analyses.

Asymmetries in the Dynamics of lnterlimb Coordination 271 Met. /- wrist exlenslo dorst- flexion ankle plantar- flexion 180 - R.P. (deg.) 0- -180 - Figure 3. Experiment 2. Sample time series of a movement prepared in the in-phase mode and paced at a frequency of 1 Hz with the forearm in a supinated position (subject IV) lMet. R.___YL_ rl R__[1 E__/q __.1-1 17 [1 E__YI___,q__J r __l']~rl flexion ................................. 540720__~-. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . aeOlao~.p. ..... (deg.) 0- Figure 4. Experiment 2. Sample time series of a movement prepared in the anti-phase mode and paced at a frequency of 2 Hz with the forearm in a supinated position (subject IV).

272 R. G. Carson et al. Thus measures of association were available for each side in each mode of coordination and at each metronome frequency. It was noted that, for all subjects in all conditions, the degree of correlation exceeded 0.99. Although these data indicate that there was a high degree of consistency within conditions, inspection of the mean frequencies suggested that there existed systematic differences in the degree of deviation from the metronome frequency. In order to examine these tendencies in greater detail, a frequency deviation score was calculated for each trial. This score reflected the difference between the mean frequency for that trial and the metronome frequency, expressed as a ratio of the metronome frequency. The resulting percentage deviation scores were treated to promote homogeneity of variance using an arc sine transformation (Myers, 1979) and analysed using a 2 side (left, fight) by 2 mode (anti-phase, in-phase) by 2 frequency (1 Hz, 2 Hz) by 2 forearm position (pronated, supinated) by 2 joint (wrist, ankle) design. Planned orthogonal comparisons of means were performed to highlight a limited number of preselected contrasts. In three of the four subjects (II, III & IV), the degree of deviation from the metronome frequency was markedly greater when the pacing frequency was 2 Hz compared to when 1 Hz (F(1, 48) = 91.58 (II), 207.63 (III), & 139.34 (IV), p < 0.01). In all subjects, movements of the left hand prepared in the anti-phase mode and paced at 2 Hz deviated from the metronome to a greater degree than those paced at 1 Hz (F(1, 48) = 14.59 (I), 36.81 (II), 266.82 (III), & 25.23 (IV), p < 0.01). For all subjects other than I, this was also the case for anti-phase movements of the fight hand (F(1, 48) = 84.55 (I), 217.64 (II), & 59.23 (IV), p < 0.01). Deviations from the metronome frequency, for in-phase movements paced at 2 Hz, were larger than for movements paced at 1 Hz in two subjects when conducted on the left side (F(1, 48) = 6.67 (II), p < 0.05, & 17.89 (IV), p < 0.01), and for a single subject when performed on the fight side (F(1, 48) = 44.34 (IV), p < 0.01). 3.3.2 Frequency Independent analyses of variance for coefficients of variation (CV) of frequency were performed for each subject using a 2 side (left, right) by 2 mode (anti-phase, in-phase) by 2 frequency (1 Hz, 2 Hz) by 2 forearm position (pronated, supinated) by 2 joint (wrist, ankle) design. Planned orthogonal comparisons of means were performed to highlight a limited number of preselected contrasts.

Asymmetries in the Dynamics of lnterlimb Coordination 273 In a single subject (I), coefficients of variation were larger for movements of the left side than the fight side (F(1, 48) = 5.28, p < 0.01). However, as is apparent from inspection of Figure 5 (panel A), these differences were present only when movements were prepared in the anti-phase mode, and when paced at 2 Hz (F(1, 48) = 18.65, p < 0.01). Figure 5. Experiment 2. Coefficients of variation of frequency for subjects I (A), II (B),III (C), and IV (D) shown as a function of side, mode and pacing frequency. For subject II, when movements were conducted in the anti-phase mode, those of the right side exhibited larger coefficients of variation than those of the left side, especially when paced at 2 Hz (F(1, 48) = 28.32, p < 0.01) (Figure 5, panel B). However, movements in the in-phase mode which were paced at 2 Hz exhibited a difference in the reverse direction (F(1, 48) = 6.09, p < 0.05). When movements were paced at 1 Hz there were no differences in variability between the left and right side (F < 1). In contrast,

274 R. G. Carson et al. when movements were paced at 2 Hz, greater variability was exhibited by movements of the right side than by those of the left side (F(1, 48) = 4.07, p < 0.05). Movements of the left and the fight side, executed by subject III (Figure 5, panel C), were not distinguished overall in terms of frequency variability. When conducted in the anti-phase mode of coordination and paced at 2 Hz, fight side movements were more variable than those of the left side (F(1, 48) = 5.81, p < 0.05). Movements of the left and the fight side completed by subject IV were equivalent in all conditions. Coefficients of variation were always larger for movements prepared in the anti- phase than for those prepared in the in-phase mode of coordination (F(1, 48) = 10.41 (I), 67.88 (II), 147.33 (III), & 30.59 (IV), p < 0.01). In all subjects, movements paced at a frequency of 2 Hz were more variable than those paced at 1 Hz (F(1, 48) = 252.90 (II), 56.72 (III), & 34.87 (IV), p < 0.01, & 4.61 (I), p < 0.05). These differences were always expressed in the anti-phase mode, whereas, with the exception of subject II they were not expressed in the in-phase mode (Figure 5). Figure 6. Experiment 2. Proportionof trials on which phase wandering was observed for subjects I (A), II (B), III (D) shown as a function of side, mode and pacing frequency.

Asymmetries in the Dynamics of Interlimb Coordination 275 3.3.3 Relative Phase Preliminary inspection of relative phase time series suggested that on some trials subjects had been unable to maintain the required relative phase relation (e.g., Figure 4). Therefore, as a precursor to the derivation of test statistics for relative phase, a number of measures were employed to appraise stationarity. The relative phase values obtained for each trial were tested for uniformity using the Rayleigh test (Mardia, 1972). All trials performed by subjects I and III satisfied the criterion of uniformity in all conditions. In contrast, 75 percent of left side trials, and 22.5 percent of fight side trials, executed by subject II in the anti-phase mode and paced at 2 Hz, failed to satisfy the criterion. A small proportion (22.5%) of left side trials performed by Subject IV in the anti-phase mode and paced at 2 Hz, failed to demonstrate uniformity. Each trial was also classified on the basis of whether phase wandering had occurred. Phase wandering was defined as a deviation of more than 180~ from the target relative phase value (Figure 6). Figure 7. Experiment 2. Subject: I, Proportion of total time accounted for by transformed relative phase values in the ranges 0.00 - 0.17, 0.17 - 0.33, and 0.33 - 0.50, 1 Hz (anti-phase) (A), 2 Hz (anti-phase) (B), 1 Hz (in-phase) (C), 2 Hz (in-phase) (D).

276 R. G. Carson et al. In addition a quasi-continuous measure of relative phase was obtained by performing a linear interpolation between the discrete relative phase values at the original sampling frequency. These data were transformed such that values expressed the \"distance\" from the in-phase and the anti-phase mode in the range 0 to _+0.5. A value of 0 expressed perfect in-phase coordination, whereas a value of _-+0.5 expressed perfect anti-phase coordination. These values were rectified and histograms constructed of the proportion of the total trial time accounted for by values of the transformed relative phase series in the ranges 0.00 - 0.17, 0.17 - 0.33, and 0.33 - 0.50. These data are represented independently for each subject in figures 7 to 10. Figure 8. Experiment 2. Subject: II, proportion of total time accounted for by transformed relative phase values in the ranges 0.0 - 0.17, 0.17 - 0.33, and 0.33 - 0.50, 1 Hz (anti phase) (A), 2 Hz (anti-phase) (B), 1 Hz (in-phase) (C), 2 Hz (in-phase) (D).

Asymmetries in the Dynamics of lnterlimb Coordination 277 Figure 9. Experiment 2. Subject: III,proportion of total time accounted for by transformed relative phase values in the ranges 0.00 - 0.17, 0.17 - 0.33, and 0.33 - 0.50, 1 Hz (anti-phase) (A), 2 Hz (anti-phase) (B), 1 Hz (in-phase) (C), 2 Hz (in-phase) (O). In light of the observation that in three subjects, non-stationarity was present in the majority of trials prepared in the anti-phase mode and paced at 2 Hz, it was concluded that no meaningful analysis of phase relations could be performed for trials conducted at this frequency. However, analyses of the uniformity of relative phase were performed for movements paced at 1 Hz, as all trials satisfied the criterion of uniformity. Analyses of variance for transformed uniformity scores were performed for each subject using a 2 side (left, fight) by 2 mode (anti-phase, in-phase) by 2 forearm position (pronated, supinated) design. Planned orthogonal comparisons of means were performed to highlight a limited number of preselected contrasts. In two subjects (I & IV), movements of the left and fight side were equivalent in terms of uniformity of relative phase. Subject II exhibited uniformity values which were

278 R. G. Carson et al. larger overall for movements of the left side than for movements of the right side (F(1, 48) = 4.68, p < 0.05). This effect was accounted for entirely by movements conducted in the in-phase mode (F(1, 48) = 7.54, p < 0.01). In contrast, for subject III, movements of the fight side were more uniform than those of the left side (F(1, 48) = 39.98, p < 0.01). This effect was expressed in both the in-phase (F(1, 48) = 18.87, p < 0.01) and anti- phase (F(1, 48) = 20.53, p < 0.01) modes of coordination. Figure 10. Experiment2. Subject : IV, proportion of total time accounted for by transformed relative phase values in the ranges 0.00 - 0.17, 0.17 - 0.33, and 0.33 - 0.50, 1 Hz (anti-phase) (A), 2 Hz (anti-phase) (B), 1 Hz (in-phase) (C), 2 Hz (in-phase) (D). 3.4 Discussion The objective of this experiment was to examine the influence of external pacing upon asymmetries of the coordination dynamics. Analyses of alterations in the dynamics resulting from changes in frequency are contingent upon subjects' adherence to the pacing regime. It is customary (e.g., Jeka, 1992; Scholz & Kelso, 1990) to evaluate

Asymmetries in the Dynamics of Interlimb Coordination 279 concurrence of limb and metronome frequencies through measures of correlation. However it can be demonstrated that two samples which exhibit large differences in absolute values may be highly correlated. In the present experiment, the degree of correlation between individual limb frequencies and metronome frequencies was close to unity (greater than 0.99), suggesting that subjects adhered closely to the metronome frequency. However the deviation of the limb frequency from the metronome frequency (cf., Scholz & Kelso, 1989) was in fact highly dependent upon the pacing frequency. While emphasis was placed upon the maintainence of a 1:1 frequency relation with the metronome, subjects compromised this requirement, particularly when paced at 2 Hz in the anti-phase mode, perhaps in attempting to maintain the prescribed, though unstable, mode of coordination. Such a strategy may be conceived of as the superposition of an intentional dynamic upon the intrinsic dynamics (e.g., Sch~3ner & Kelso, 1988b). If the intrinsic dynamics pertaining at 2 Hz were such as to virtually preclude the maintainence of the anti-phase mode, it is likely that attempts to achieve the prescribed mode required almost continuous intentional intervention. In previous work (Carson et al., in press) employing a similar paradigm, and a \"do not intervene\" protocol, spontaneous transitions from the anti-phase to the in-phase mode of coordination were demonstrated as oscillation frequency was stepped from 1.25 Hz to 2.75 Hz. Signature features of nonequilibrium phase transitions, such as loss of stability and critical fluctuations were exhibited. In the present experiment, inspection of relative phase time series demonstrated that, when paced at 2 Hz, most subjects were unable to sustain the anti-phase mode of coordination. If uniformity of relative phase is to be interpreted as an index of stability, it must reflect dispersion about a mean value corresponding to a stationary (attractor) state. Failure to observe stationarity reflects loss of stability, and suggests that the system is no longer confined to the region of state space defining an attractor. In the absence of stationary solutions, the system may exhibit loss of entrainment, expressed as running solutions in which relative phase is ever increasing or decreasing. These running solutions do however possess a \"fine structure\" whereby the system is more often ensconced at relative phase values at which the rate of change of the order parameter is minimal, even though stability has been lost (Kelso, DeGuzman, & Holroyd, 1991; Kelso, DelColle, & Schtiner, 1990). The distributions of relative phase values

280 R.G. Carson et al. represented in Figures 7-10 illustrate the fine structure of the dynamics, including the relative stability of regions of state space corresponding to the remnants of attractors. Three measures were employed to evaluate the stationarity of relative phase, the Rayleigh test of uniformity, classification of deviations from the target value of relative phase, and relative phase distribution histograms. While, the Rayleigh test provides an objective criterion against which stationarity may be evaluated, it is not definitive. If phase wandering occurs during a limited portion of a trial, uniformity values satisfying the criterion of stationarity may still be obtained. In the present experiment, all measures were consistent in indicating that, in three subjects, stationarity was not present when movements were initially prepared in the anti-phase mode of coordination and paced at 2 Hz. These observations suggest that in these subjects the attractor at 180~ which was evident when movements were paced at 1 Hz, was no longer present when movements were paced at 2 Hz. Remnants of the attractor previously located at 180~ were sometimes evident. Subject III demonstrated continued attraction to the anti-phase mode (Figure 9, panel B), whereas for subject IV, the in-phase mode dominated at a pacing frequency of 2 Hz regardless of initial preparation (Figure 10, panel B). The greater variability of frequency for movements of the left side, which was consistently evident in Experiment 1, was not present in this experiment. Only subject I demonstrated coefficients of variation for discrete frequency which were larger for movements of the left side, and this difference was accounted for entirely by movements which were prepared in the anti-phase mode and paced at 2 Hz. Subject II exhibited coefficients of variation which were larger for movements of the fight side which were prepared in the anti-phase mode. Differences in this direction were not observed in Experiment 1. Uniformity of relative phase was greater for movements of the fight side in a single subject III, and greater for movements of the left side in subject II. In experiment 1, in every instance in which differences were present, movements of the fight side were more uniform than those of the left side. These data strongly suggest that, in this task, asymmetries in the variability of oscillation frequency, and in the variability of the collective variable relative phase, were eliminated through the imposition of external pacing.

Asymmetries in the Dynamics of Interlimb Coordination 281 4. GENERAL DISCUSSION When self-paced rhythmic movements of the ankle and the wrist, were produced either singly, or coupled in anti-phase or in-phase modes of coordination (Experiment 1), movements of the left side exhibited greater variability of oscillation frequency than movements of the fight side. Furthermore, in coupled conditions, in which target relative phase relations imposed additional timing demands, asymmetries were accentuated relative to single joint conditions. In coupled movements, the uniformity of relative phase was lower for movements of the left side. However, when movements were externally paced in Experiment 2 these asymmetries were eliminated (cf., Truman & Hammond, 1990). It is conceivable that the elimination of the asymmetries was confounded with practice. However, there is extensive evidence to suggest that handedness effects are robust in the face of extensive practice (Annett, Hudson, & Turner, 1974; Peters, 1981; Todor & Smiley, 1985). There is additional evidence to suggest that the provision of external pacing has a profound influence upon the movement dynamics. The duration of intentional transitions between modes of coordination, is strongly influenced by the frequency of external pacing. Individuals organize their movements such that pacing signals anchor the onsets and offsets of changes in coordinative pattern (Carson, Goodman, Kelso, & Elliott, 1994b). The temporal locus of a discrete pacing signal with respect to the movement cycle also exerts a potent influence upon both individual limb and collective variable dynamics (Kelso et al., 1990). In bimanual coordination these factors are sufficient to govern the selection of specific transition pathways (Byblow et al., 1994; Carson et al., 1994a). Moreover, the relative continuity of pacing information exerts a strong influence upon the coordination dynamics (Byblow, Chua, & Goodman, in press). Recent studies of oscillatory responses in the visual cortex have demonstrated phase- and frequency-locking in spatially separate neurons both within (Gray, K/3nig, Engel, & Singer, 1989) and between hemispheres (Engel, Ktinig, Kreiter, & Singer, 1991). It is suspected that deficits arising from cerebral palsy may be attenuated when movements are made in time with a rhythmic beat (Hari & Tillemans, 1984), and it is widely known that the performance of stutterers is enhanced through the provision of an external rhythm. One may speculate that the provision of an external time base, such as through

282 R.G. Carson et al. auditory pacing, results in phasic activity which is distributed over a larger area of cortex, and involves greater numbers of neural structures and individual neurons than that occuring during self-paced movements (Kelso, et al., 1992). Such distributed activity may provide a basis for more precise sequential recruitment of muscles, and ultimately limb segments. For unimanual movements of the non-dominant hand, temporal precision is likely to be further enhanced by usurping areas of the left cerebral cortex, a tendency which is evident to some degree in self-paced movements (Kristeva, Cheyne, & Deecke, 1991; Lang, Obrig, Lindberger, Cheyne, & Deecke, 1990). REFERENCES Annett, M., Hudson, P.T.W., & Turner, A. (1974). The reliability of differences between the hands in motor skill. Neuropsychologia, 12, 527-531. Augustyn, C., & Peters, M. (1986). On the relation between footedness and handedness. Perceptual and Motor Skills, 63, 1115-1118. Bach, T.M., Chapman, A.E., & Calvert, T.W. (1983). Mechanical resonance of the human body during voluntary oscillations about the ankle joint. Journal of Biomechanics, 16, 85-90. Baldissera, F., Cavallari, P., & Civaschi, P. (1982). Preferential coupling between voluntary movements of ipsilateral limbs. Neuroscience Letters, 34, 95-100. Batschelet, E. (1981). Circular statistics in biology. London: Academic Press. Bingham, G.P., Schmidt, R.C., Turvey, M.T., & Rosenblum, L.D. (1991). Task dynamics and resource dynamics in the assembly of a coordinated rhythmic activity. Journal of Experimental Psychology: Human Perception and Performance, 17, 359- 381. Bradshaw, J.L., & Nettleton, N.C. (1981). The nature of hemispheric specialization in man. The Behavioral and Brain Sciences, 4, 51-91. Burgess-Limerick, R., Abemethy, B., & Neal, R.J. (1991). Note: A statistical problem in testing invariance of movement using the phase plane model. Journal of Motor Behavior, 23, 301-303. Byblow, W.D., Carson, R.G., & Goodman, D. (1994). Expressions of asymmetries and anchoring in bimanual coordination. Human Movement Science, 13, 3-28. Byblow, W.D. Chua, R., & Goodman, D. (in press). Asymmetries in coupling dynamics of perception and action. Journal of Motor Behavior.

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Motor Control and Sensory Motor Integration: Issues and Directions 289 D.J. Glencross and J.P. Pier (Editors) 9 1995 Elsevier Science B.V. All fights reserved. Chapter 11 LEARNING A DYNAMIC LIMB SYNERGY Nicholas O'Dwyer Peter Neilson Cerebral Palsy Research Unit, Institute of Neurological Sciences, The Prince Henry Hospital and School of Electrical Engineering, University of New South Wales, Sydney, Australia Dynamic and non-dynamic bimanual synergies were studied during pursuit tracking of a common visual target by both hands. Subjects were required to track a target with two response cursors simultaneously. The target moved in the centre of a computer screen, while the response cursors were located at either side of the target and controlled via a joystick with either hand. The target moved irregularly in amplitude and speed, with a frequency bandwidth up to 2Hz. The tracking system was contrived in two ways so as to produce either dynamic or non-dynamic synergies between the hands. Six subjects practised tracking where the joystick-cursor relation was a straighO~orward, non-dynamic, scalar relation, identical for the left and right joysticks. This meant that, in order to track the target, the left and right hands simply had to be moved in synergy in an identical fashion, with only one virtual degree of freedom of movement. This was a scalar, non-dynamic synergy. Another six subjects practised a novel task where the right joystick input was first linearly filtered (first-order, low-pass) before driving the response cursor. This meant that, in order to track the target together, the left and right hands had to be moved with different amplitudes and out of phase with each other, but still in synergy. The relative amplitude and timing of the limbs in this synergy were required to vary with the frequency of the movement, so that this was a dynamic synergy. The results showed that the subjects accomplished both non-dynamic and dynamic inter-limb synergies. In the former case, the hands were coupled as expected in a simple, one-to-one relation. In the latter case, the hands were coupled in a dynamic, linear relation, although the specific characteristics of this relation deviated from those required for full compensation for the effect of the filter on the joystick. The degree of inter-limb coupling did not differ between the non-dynamic and dynamic synergies and was high (87-91%)for both, indicating little independent activity between the limbs in either case. Furthermore, the demands of forming the inter-limb synergies, either non-dynamic or dynamic, interfered only minimally with tracking performance, since only minor differences were observed between single-handed and bimanual tracking. 1. INTRODUCTION Studies of bimanual coordination may be divided into three broad categories on the basis of the dependence or independence of the amplitude and timing of the movements in the limbs. The first category includes tasks where the limbs execute movements with independent timing,

290 N. O'Dwyer & P. Neilson such as in piano playing or tapping different rhythms with each hand. A primary focus of studies in this category has been the constraints on achieving independence between the limbs, owing to the tendency for the limbs to interfere or become synchronised (e.g., Kelso & DeGuzman, 1992; Klapp, 1979; Peters, 1985; Shaffer, 1981; Swinnen, Walter, Beirinckx and Meugens, 1991). The second category includes tasks where the limbs execute movements with the same timing (though the limbs may be either 'in phase' or 'out of phase') and amplitude (e.g., Kelso, 1984; Schmidt, Zelaznik, Hawkins, Frank & Quinn, 1979; Turvey, Schmidt & Beek, 1993). These studies have focused on the nature of the inter-limb dependence when the limbs move with similar amplitude and timing, such as moving opposite wrists or fingers rhythmically together. The third category includes tasks where the limbs execute movements with independent amplitude but where independent timing has not been critical to successful task performance (e.g., Kelso, Southard & Goodman, 1979; Marteniuk, MacKenzie & Baba, 1984; Sherwood, 1989). This has been the case, for example, in two- handed aiming to targets at different distances. In the first category, the movements in different limbs were, or strove to be, independent or mathematically uncorrelated. Rhythmical movements of different frequencies are, by def'mition, uncorrelated. For the movements to be uncorrelated, their temporo-spatial trajectories must be quite different. Everyday examples in this category include the cooperative limb movements in doing up buttons or using a knife and fork. In such movements the two hands perform different actions but in order to work cooperatively, their timing must coincide at crucial moments. Movements in this category exemplify the suggestion of Kelso and DeGuzman (1992) that \"coordination holds only at some points in the signal \"trajectories\" of the individual components: in between, trajectories may vary spatially (e.g., characteristic amplitudes) and temporally (e.g., characteristic periods and frequency content)\". Similar considerations apply to the coordination between respiratory, laryngeal, pharyngeal, velar and articulatory movements during speech. In both the second and third categories, the movements were dependent or mathematically correlated. This means that the trajectories of the movements must be quite similar. Everyday examples here include clapping the hands together, catching a ball in both hands and turning the steering wheel of a car. It is precisely by virtue of the correlation between the movements in different limbs that these actions can be said to involve synergies between the limbs.

Learning a Dynamic Limb Synergy 291 The correlation or dependency between limbs or limb segments reduces the effective degrees of fw.exlom to be controlled. In studies of synergies to date, however, despite differences in amplitude between the limbs, the inter- II limb relation invariably has been a scalar one, without dynamics in the relation per Figure 1. Illustration of signals related in a linear, dynamicway. se. (this is not to deny dynamics in the movements of the limbs themselves, but only in the relation between the limbs). A non-dynamic synergy is one where the limbs have a constant phase relation. This may be 'in phase' or 'out of phase', but the important point is that the phase relation is constant. Furthermore, the gain or relative amplitude between the limbs is also constant in the same way. A dynamic relation, on the other hand, is one where both the gain and phase between the limbs vary as a continuous function of the frequency. (Frequency is directly related to speed as long as the amplitude remains constant). In other words, both the spatial and temporal aspects of the limb trajectories vary. A specific example is illustrated in Figure 1. It can be seen that the signals differ both in amplitude and timing, with the thick trace being both smaller and smoother than the thin trace and lagging it in time. In spite of these spatial and temporal differences, the signals are in fact perfectly linearly correlated - the thin trace represents the input and the thick trace the output of a first-order, low-pass digital f'llter. However, a linear regression analysis of the signals (actually 1 minute in duration, of which only 4.4 seconds are shown here) shows a coefficient of variation (r ~) of only 0.57. On the other hand, a cross-correlational and spectral analysis (Bendat & Piersol, 1966; McRuer & Krendel, 1959; Neilson, 1972), which computes the best-fit linear dynamic relation between the signals, accounts for 98% of their variance. The importance of dynamic relations cannot be overemphasised because they are ubiquitous in movement control. One of the most obvious examples is the relation between muscle tensions and joint movements, where the inertial load of the limbs on muscles introduces important dynamics. The relation between the firing of a motor neuron pool and the resulting muscle tension is also a dynamic relation, akin to a low-pass filter (Partridge, 1965). In our interactions with the external environment, examples abound of diverse dynamic

292 N. O ' D ~ e r & P. NeUson relations. Consider the relations between rotation of the steering wheel of a car or a ship and the resultant changes in direction of motion; or the change in load on the ann in using a teaspoon compared with a serving spoon; or the effect of one hand holding an object which is manipulated by the free hand. This latter is an example of bimanual coordination where the relation between the limbs involves dynamics due to the additional inertial load on one limb. Since dynamic relations occur so commonly in controlling and coordinating movement, it follows that the human central nervous system (CNS) must be able to learn to cope with new dynamic relations. It is with such learning that this chapter is concerned. We describe two experiments on bimanual coordination, one involving a non-dynamic and one a dynamic relation between the limbs. The first experiment involves movements that are identical in amplitude and timing in each hand, whereas the second involves movements that are dissimilar in amplitude and timing in each hand. However, in both studies the hand movements are required to remain linearly correlated (dependent). The former involves a simple, non- dynamic (zero-order) relation between the limbs, while the latter involves a dynamic (first- order), though still linear, relation. The particular dynamic relation to be studied here means that the hands move in phase and with equal amplitude for very slow movements and move out of phase and with differing amplitudes for faster movements - this in a task that involves a mixture of slow and fast movements. Our main aim is to observe how our subjects adapt to this unfamiliar inter-limb relation. An additional feature of the experiments to be described here is that they involve arrhythmic movements, whereas many studies in this area have involved rhythmic movements. We examine continuous, irregular movements during pursuit tracking of a visual target. In this task, the characteristics of the movements required of the subject are determined by the characteristics of the target signal. These can be controlled in advance by the experimenter. By using irregular movements, the predictability of the task is greatly reduced and the complexity of the movement waveforms is increased. These features are characteristic of many everyday tasks such as visually fixating irregularly moving objects or maintaining upright posture in a moving vehicle. Additionally, tracking is an externally-paced task, so that the time to respond is limited and this imposes a greater processing load on the subject. Again, this feature applies to many everyday tasks such as driving a car or catching a ball

Learning a Dynamic Limb Synergy 293 2. TRACKING SETUP The tracking setup is illustrated in Figure 2. The target cursor is the bar in the middle of the screen. There are two response cursors, one on either side. The target moves irregularly in the vertical plane only. The left and fight response cursors are controlled by the joysticks shown on the left and fight, respectively. Forward rotation of the joystick sends the response cursor up the screen and backward rotation brings it down. The subjects were required to keep both response cursors aligned with the target cursor. This meant that they had to move both joysticks (and both hands) together. Figure 2. Schematic diagram of tracking setup for both experiments. The target (hatched bar) was red and both response cursors (solid bars) were blue. The screen background colour was pale green. The angular excursion of thejoysticks was approximately + 30~ We were interested in the coordination between the two hands in this tracking task, but we also needed to compare two-handed tracking with single-handed tracking. Therefore, the general procedure was that subjects performed an initial series of two-handed and one-handed (both left and fight) tests, then practised on the two-handed test only and finally repeated the initial series of two-handed and one-handed tests. All tests were continuous pursuit tracking of one-minute duration. Practice consisted of 10 one-minute tests per day for 13 days, performed over a period of two months, giving a total of 130 minutes of distributed practice. Two experirnents were carded out - the first with a simple relation between the hands and the second with a dynamic relation between the hands.

294 N. O'Dwyer & P. Neilson The movement of the target was driven by signals generated in advance by the experimenters. Computer-generated pseudo-random numbers were filtered (2*d-order, Butterworth) at 1Hz to produce signals that were irregular and contained a mixture of slow and fast changes. Two 'test' target signals and one 'practice' target signal were produced in this way. The frequency spectra of the targets showed substantial power up to almost 2Hz and low-level power up to about 3Hz (see Figure 8). The sampling and display rate of the target and response cursors was 40Is. 3. EXPERIMENT 1 3.1 Subjects Six adult volunteers aged 22-33 years (mean=26.5) participated. There were three males and three females and all were right-handed. All were university students or graduates and had no musculoskeletal or uncorrected visual problems or any known neurological disease. All subjects were fully informed of the procedures before data collection was undertaken. 3.2 Procedure The purpose of this first experiment was primarily to provide baseline performance against which the results of Experiment 2 could be assessed. On the first day the subjects performed three types of tracking test: (i) two-handed tracking (L+R), (ii) single-handed tracking with the right hand (R), ('tii) single-handed tracking with the left hand (L). For the two-handed tests, the response cursors were independent, so that rotation of the left joystick moved only the left cursor and rotation of the right joystick moved only the right cursor. For the single-handed tests, the response cursors were linked together so that rotation of one joystick moved both the left and right cursors. In this way the visual display was as similar as possible for the two-handed and single-handed tests. Following an initial one-minute familiarisation test (L+R) using the 'practice' target, the subjects performed each of the three tests - L+R, R and L - using the two 'test' targets, to give a total of six tests. The order of the tests was counterbalanced across the group in order to minimise possible sequence effects. On the subsequent 13 days (spread over two months)

Learning a DynamicLimb Synergy 295 they practised only the two-handed (L+R) test using the 'practice' target. On the final day, each subject repeated the test sequence that they had performed on the first day. 3.3 Analysis of TracdkingPerformance Five sets of analysis were required. The relation between the target and response signals was analysed for each of the single-handed tests. Similarly, the relation between the target and the left response and the target and the right response was analysed for the two-handed tests. In addition, for the two-handed tests, the relation between the left and right response was analysed. Thus, the two-handed tests required three sets of analysis. Table 1 illustrates the analysis sets and the notation employed (in parentheses). Since neither the target nor response signals contained frequency power above about 4Hz, the sampling rate was reduced to 10Hz (ie, still greater than twice the maximum frequency in the signals) for these analyses. Table 1. Trackinganalyses Two-Handed (L+R) Single -Handed Target-Left (L) (R) (L/L+R) Target-Left Target-Right (L) (R/L+R) Target-Right Left-Right (R) (L-R) An overall measure of tracking performance was provided by the root mean square (RMS) value of the error between the target and response signals (McRuer and Krendel, 1959). In addition, cross-correlational and spectral analysis was carded out on the five signal-pairs indicated in Table 1. This analysis illuminates aspects of tracking performance that cannot be assessed via conventional measures of error alone. It is based on the waveform similarity between the target and response and therefore it measures both amplitude and timing aspects of performance. The degree of waveform similarity (ie, correlation) between the target and response is quantified by the coherence for each frequency, the magnitude of the correlated response relative to the target is quantified by the gain for each frequency and the time lag of the correlated response behind the target is quantified by the phase for each frequency. It

296 N. O'Dwyer & P. NeUson should be noted that the coherence measures the variance of the response that is correlated with the target at each frequency as a proportion of the subject's total response at that frequency. The overall coherence quantifies the degree of correlation between target and response over all frequencies and is analogous to the coefficient of determination (r 2) in a regression analysis. For ideal tracking, the response waveform would be an exact replica of the target waveform; hence, for all frequencies, the coherence would be 100%, the gain would be unity and the phase lag zero. In actual tracking, of course, the response never exactly matches the target, but instead lags behind and reproduces the target waveform only in a 'noisy' fashion. Repeated measures analyses of variance were subsequently applied to all of the above measures in order to test for significant differences (i) before and after practice, (ii) between one-handed and two-handed tracking and (iii) between the left and right hand. In addition, using frequency as a fourth factor in the analyses of variance, we tested the pattern of variation across frequency of the coherence, gain and phase measures. 3.4 Results The results will be presented in two sections: (i) left- right coordination and (ii) left and right hand performance in tracking the target. 3.4.1 Left-Right Coordination The degree of coupling between the left and right hand in two-handed tracking is quantified by the coherence versus frequency, shown in Figure 3. Also shown for comparison is the coherence of either hand with the target. It can be seen that following practice there was an overall increase in left-fight, target-left and target-fight coherence (F[1,5]=7.16, p<0.05), as well as a change in the variation of coherence with frequency (F[5,25]=2.64, p<0.05), the latter due to a greater increase in coherence at the higher frequencies. The increase in coherence of each hand with the target shows that the subjects were tracking the target better after practice than before, while the increase in left-right coherence shows that the two hands were more tightly coupled after practice. In fact the coupling between the hands after practice accounted for 91% of the variance of their movements. Moreover, the coherence between the hands was signifcanfly greater than the coherence of either hand with the target (F[2,10]=20.69, p<0.001). Furthermore, as reflected in a significant interaction between the three coherences and frequency (F[10,50]=7.47, p<0.001), the coherence

Learning a Dynamic Limb Synergy 297 between the hands was maintained for higher frequencies than was the coherence of either hand with the target. 100 .....,~ ..... '~ . . . . . . . . 90 / ] ,,cl~ - ,.1~ A / ( @ z 9-o-- T-L eo - 80 Before Practice 9,,o.,,, L-R Lr .1 .3 .5 .7 .9 1.1 Hz t- After Practice oO 70 60 Figure 3. Coherenceversus frequency of target and left hand (r-L), target and right hand (r-R) and left and right hand (L-R), during two-handed tracking. Hz: cycles per second. 1.1 - o - Before , no~ \"'O 20 Practice ,,\" m El\" .~ 10 ..o.- After E Practice ~) 0.9 t(,I.). E l . . . . .O. . . . . ._= ~) 0 t0 v (3 I1. 0.8 -20 .1. . .3 . .5. ..7 . .9 1.1 Hz .1 .3 .5 .7 .9 1.1 Hz Frequency Frequency Figure 4. Left hand-right hand gain and phase versus frequency,beforeand after practice, during two-handed tracking. Of equal importance to the degree of coupling between the hands is the nature of their coupling, that is, their relative amplitude and timing. This is quantified by their gain and phase relations, respectively (Figure 4). The changes with practice were not significant here (F[1,5]<2.74, p_>0.16). The average left-fight gain approached unity, indicating that the fight and left hand movements were very similar in amplitude. Similarly, the average left-fight phase approached zero, indicating that the fight and left hand movements were very closely locked in phase with each other. Furthermore, with the exception of the left-fight gain at 0.1Hz only, the gain (F[4,20]=0.46, p--0.77) and phase (F[5,25]--0.11, p--0.99) values did not