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Unraveling Interlimb Interactions Underlying Bimanual Coordination

Institute for Fundamental and Clinical Human Movement Sciences, Faculty of Human Movement Sciences, Vrije Universiteit, Amsterdam, The Netherlands

Submitted 13 October 2004; accepted in final form 26 June 2005

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Three sources of interlimb interactions have been postulated to underlie the stability characteristics of bimanual coordination but have never been evaluated in conjunction: integrated timing of feedforward control signals, phase entrainment by contralateral afference, and timing corrections based on the perceived error of relative phase. In this study, the relative contributions of these interactions were discerned through systematic comparisons of five tasks involving rhythmic flexion–extension movements about the wrist, performed bimanually (in-phase and antiphase coordination) or unimanually with or without comparable passive movements of the contralateral hand. The main findings were the following. 1) Contralateral passive movements during unimanual active movements induced phase entrainment to interlimb phasing of either 0° (in-phase) or 180° (antiphase). 2) Entrainment strength increased with the passive movements' amplitude, but was similar for in-phase and antiphase movements. 3) Coordination of unimanual active movements with passive movements of the contralateral hand (kinesthetic tracking) was characterized by similar bilateral EMG activity as observed in active bimanual coordination. 4) During kinesthetic tracking the timing of the movements of the active hand was modulated by afference-based error corrections, which were more pronounced during in-phase coordination. 5) Indications of in-phase coordination being more stable than antiphase coordination were most prominent during active bimanual coordination and marginal during kinesthetic tracking. Together the results indicated that phase entrainment by contralateral afference contributed equally to the stability of in-phase and antiphase coordination, and that differential stability of these patterns depended predominantly on integrated timing of feedforward signals, with only a minor role for afference-based error corrections.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Rhythmic interlimb coordination is governed by interactions between the limbs (e.g., Peper et al. 1995; Schmidt et al. 1993; Swinnen 2002; Von Holst 1937/1973) arising from a variety of constraints at different levels of the motor system (Carson and Kelso 2004). Behavioral studies of rhythmic interlimb coordination in isofrequency tasks focused on the stability of the phase relation between the limbs (relative phase ) in relation to various experimental manipulations, pertaining to movement frequency (e.g., Kelso 1984), loading (e.g., Baldissera et al. 1991), eigenfrequency differences (e.g., Jeka and Kelso 1995), movement amplitude (e.g., Peper and Beek 1998), movement direction (e.g., Swinnen et al. 2003), mechanical perturbations (e.g., Kay et al. 1991), and sensory feedback (e.g., Kelso et al. 2001; Mechsner et al. 2001). A common finding in all these studies was that only two bimanual patterns could be stably performed without training, and the one (in-phase, = 0°) more so than the other (antiphase, = 180°). At higher movement frequencies the stability difference between these patterns increases, eventually resulting in large fluctuations of during antiphase coordination indexing a loss of stability (Schöner et al. 1986), often followed by an involuntary transition to the in-phase pattern (Kelso 1984).

Although the stability characteristics of rhythmic interlimb coordination are well documented, considerably less is known about their neurophysiological underpinnings (Carson and Kelso 2004; Peper et al. 2004; Swinnen 2002). In the literature, three sources of interlimb interaction have been postulated to account for the stability differences between in-phase and antiphase coordination, which may be labeled 1) integrated timing, 2) corrections of relative phasing errors, and 3) phase entrainment. Integrated timing constitutes an interaction between the feedforward timing of the movements of both hands, i.e., without adjustments made on the basis of afferent feedback. Functionally, integrated timing can be regarded as the specification of a bimanual pattern by means of interactions between two internal timekeepers or clocks underlying the temporal control of the individual limb movements, and empirical findings have been reported that are consistent with the existence of such "open loop" timing mechanisms (Helmuth and Ivry 1996; Jagacinski et al. 1988; Semjen and Ivry 2001).

In addition, neurophysiological modeling studies have shown that salient stability-related phenomena in interlimb coordination (e.g., in-phase being more stable than antiphase; frequency-induced transitions between movement patterns) can arise in a system of two coupled neural oscillators in the absence of afferent feedback, yielding a dynamical account of integrated timing (Asai et al. 2003; Grossberg et al. 1997). However, afference-based interlimb interactions have also been demonstrated, e.g., in the form of effects of passive limb movements on the stability of rhythmic interlimb coordination (Serrien et al. 2001; Stinear and Byblow 2001; Swinnen et al. 1995). Specifically, two afference-based sources of interlimb interaction have been put forward (Baldissera et al. 1991, 1998; Carson and Riek 1998). First, a relatively rigid low-gain mechanism based on peripheral reflexes has been proposed to bring about phase entrainment by afferent input from the opposite limb. Second, a more flexible error correction mechanism has been posited that stabilizes intended phase relations between the limbs by means of supraspinal processes for detecting and repairing errors in the relative phase through monitoring and adjusting the timing of the individual limb movements. Figure 1C schematically depicts the relations between the three sources of interlimb interaction that are allegedly involved in active bimanual coordination.

View larger version (54K): [in this window] [in a new window]   FIG. 1. Three diagrams of the proposed sources of interlimb interaction in terms of relations between movement timing (MT), the monitoring of errors (ME), motor output (MO), and the afferent signals elicited by the hand movements (Hd, dominant hand; Hn, nondominant hand). PECA, phase entrainment by contralateral afference; ECRP, correction of relative phasing errors; ITFF, integrated timing of feedforward signals. A: unimanual tasks (UN/UNm). Solid lines indicate factors involved in both tasks; dashed lines specify additional factors resulting from the distractor (passive movement) in UNm. Interlimb interaction is solely attributed to phase entrainment induced by the contralateral afference in UNm. B: kinesthetic tracking tasks (KT/KTa). Solid lines indicate factors involved in both tasks; dashed lines specify additional factors resulting from the distractor (metronome pacing) in KTa. Interlimb interactions result from phase entrainment as well as corrections based on the monitoring of errors in the intended relative phase as determined from kinesthetic afference. C: bimanual task (AB) involving all sources of interlimb interaction: phase entrainment, corrections of relative phasing errors, and the integrated timing of feedforward signals. In addition to the interlimb interactions, external factors are also shown: metronome pacing in AB, KTa, UNm, and UN; intended relative phase (int) in AB, KT, and KTa; and the motor driving the nondominant hand in KT, KTa, and UNm (indicated by the gear).

Rationale for experiment

To anticipate the experimental design in the METHODS section, the relative contributions of the three postulated sources of interlimb interaction were identified by comparison of five different unimanual and bimanual wrist cycling tasks that were performed without visual feedback. At the two extremes, all sources of interaction are supposedly involved during active bimanual coordination of both hands (AB), whereas no interaction occurs during performance of a unimanual (UN) task. Between these extremes, the active use of afferent feedback was assessed in a kinesthetic tracking (KT) task, which required coordination of the active movements of the dominant hand and the passive movements of the nondominant hand in the absence of an auditory pacing signal. Two additional coordinative tasks were created based on UN and KT using a secondary signal (distractor). The task UNm was identical to UN (unimanual movement paced by an auditory metronome) except that passive movement of the contralateral hand was used as distractor. The task KTa was identical to KT (kinesthetic tracking of the contralateral passive movement) but, in this case, the auditory metronome was added as distractor. AB, KT, and KTa were considered bimanual tasks because the task objective was defined in terms of the relative phasing between the hands. In contrast, UN and UNm constituted unimanual tasks. The timing of the movement of the dominant hand was specified by an auditory metronome in AB, UNm, and UN, and by the passive movement of the nondominant hand in KTa and KT. To examine the effects of the distractors (passive movement in UNm and the auditory metronome in KTa), their presentation was shifted by –30, 0, and +30° with respect to the reference signals (auditory metronome in UNm and passive movement in KTa).

In terms of the proposed sources of interaction, the hypothetical control processes underlying coordinative tasks AB, KT, KTa, UNm, and UN are displayed in Fig. 1. Obviously, no interlimb interactions occur in the unimanual task UN. However, in the other unimanual task, UNm, interactions arise as a result of the passive movement of the contralateral limb, which is expected to induce phase entrainment of the actively moving limb by contralateral afference (see Fig. 1A). Because contralateral afference is present in all bimanual tasks, the resulting phase entrainment affects the behavior in tasks KT, KTa, and AB as well. In addition, the task requirements of kinesthetic tracking (KT) entail an intentional control of the relative phase between the hands by means of correction of relative phasing errors, and thereby invoke an additional source of interlimb interaction (see Fig. 1B). The same two sources of interlimb interaction are involved in KTa because the distracting auditory pacing signal does not constitute an additional source of interaction between the limbs. During active bimanual coordination (AB) both afference-based sources of interaction affect the behavior because contralateral afference is present and a specific relative phase between the hands is required. However, in AB the open-loop bimanual control signal may contribute to the behavioral stability as well, since AB also involves interlimb interactions in terms of integrated timing (see Fig. 1C). The resultant hypothetical mapping between coordinative tasks and sources of interlimb interactions (see Table 1) allows for the assessment of the relative contribution of each source of interlimb interaction to the stability of rhythmic bimanual coordination by means of the following four explicit comparisons between pairs of coordinative tasks.

Because this study focused primarily on the relative contributions of the sources of interlimb interaction to the differential stability of the two bimanual patterns (in-phase and antiphase), pattern-related effects were assessed in all aforementioned comparisons. In the unimanual task of UNm, pattern-related influences were discerned by presenting the (distracting) passive movement at different phase relations with the (reference) metronome pacing, resulting in an interlimb phasing close to 0° (in-phase) or 180° (antiphase). In the first two comparisons (AB vs. KT; KTa vs. UNm) the circular SD of the relative phase (SD) was adopted as a measure of the stability of performance (cf. Schöner et al. 1986). In contrast, the last two comparisons focused on the effects of the (phase-shifted) distractor on the mean relative phase (KTa vs. KT) and on the mean phasing with respect to the metronome (UNm vs. UN) to examine the correction of relative phasing errors and phase entrainment, respectively. In addition to these measures, correlations between temporal variables were calculated to gain more insight into specific interactions. First, it was expected that the contribution of integrated timing would also be manifested in terms of correlations between the cycle durations of the hands during simultaneously performed cycles. Second, corrections of relative phasing errors were expected to result in negative correlations between the discrete error in relative phase (i.e., the timing error of the dominant hand at the moment of peak flexion or extension, relative to movement of the nondominant hand) and the duration of the subsequent cycle of the dominant hand. In addition to these kinematic measures, EMGs were analyzed to support the neurophysiological interpretation of the results.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Subjects

Eleven healthy subjects (six males, five females; aged 18–30 yr) participated in the experiment. Nine subjects were right-handed and two were left-handed, as determined by an inventory (Oldfield 1971). The subjects had no previous experience with the task. The experiment was approved by the ethics committee of the Faculty of Human Movement Sciences, and before participation all subjects gave their written informed consent.

Apparatus

Subjects were seated comfortably in a height-adjustable chair with their elbows slightly flexed and their feet supported. On two racks, positioned on both sides of the chair, manipulanda were mounted that were used to either register (active) or control (passive) movements of the wrist in the horizontal plane. The forearms were placed in the apparatus in a neutral position (thumbs up and palms facing inward), and their position was restrained by the support surface on the medial and ventral side, by two vertical foam-coated supports on the dorsal side, and by one horizontal foam-coated support on the lateral side. Both hands were fixated against the flat manipulanda using two Velcro straps, with all fingers extended. A white opaque screen was used to eliminate visual feedback of the hand movements. To register joint angles during active movement the manipulandum was mounted coaxially with a potentiometer (Sakae, type FCP40A-5k, linearity 0.1%). The potentiometer's output voltage was digitized by a 12-bit ADC (Labmaster DMA) and stored on a microcomputer at a sampling frequency of 200 Hz. The active movements were recorded with a precision of about 0.1°.

A custom-made metronome generated the auditory pacing signal, consisting of a sequence of alternating high-pitched (400-Hz) and low-pitched (200-Hz) beeps, which were presented to the subject through earphones (Sony, type MDR-ED21LP). Commercially available ear protectors (Peltor, type H7A) and a moderate level of "white" background noise eliminated any auditory feedback of the motion of the motor. The passive movements were generated using a DC brush motor (PARVEX, type RS440GR) that was controlled by a PC-mounted servocontroller (ACS-Tech80, type SB214). The maximum torque of the motor was such that subjects were unable to alter the trajectory of the applied movements, and the maximum error in the trajectory of the passive movements was 0.26°.

Surface electromyograms (EMGs) were obtained from M. flexor carpi radialis (FCR), M. flexor digitorum superficialis (FDS), M. extensor carpi radialis (ECR), and M. extensor digitorum communis (EDC) of both forearms. A bipolar arrangement of disposable electrodes (Medicotest, Ag/AgCl electrodes, square 5 x 5-mm pick-up area) was attached with a center-to-center distance of 2 cm after cleansing and abrasion of the skin. The electrodes were positioned on the center of the muscle belly on the line from origin to insertion as determined by palpation. EMG signals were sampled at 1,000 Hz (TMS International, type Porti5-16/ASD; 22 bits ADC) after band-pass filtering (0.5–400 Hz), and stored on a microcomputer.

Passive movement and metronome pacing

To allow comparison between tasks, the passive movements in KT, KTa, and UNm were identical to the kinematics of the nondominant hand as recorded during active bimanual coordination (AB). Thus the variability in amplitude and cycle duration of the passive movements were the same as those during active movements of the nondominant hand. Passive movements of reduced amplitude were used to manipulate the strength of the movement-elicited afference: the amplitude of the passive movements was either equal to the amplitude in AB (normal amplitude) or scaled by a factor 0.5 (reduced amplitude). In UNm and KTa, the phasing between the passive movements and the metronome pacing was varied systematically, using the same six phase relations between the distractor and the reference signal for both coordinative tasks (three centered around in-phase movement of the hands; three centered around antiphase movement of the hands). In KTa, the phasing of the metronome signal (distractor) was shifted by –30, 0, or +30° relative to the phasing of the passive movements (reference). These shifts were applied during in-phase as well as antiphase coordination to study effects related to these coordination patterns. In UNm the passive movements (distractor) were either (relatively) in-phase or in antiphase with respect to the required movements of the dominant hand (as paced by the metronome), with additional phase shifts of –30, 0, or +30°.

If antiphase (in-phase) coordination was required in KT and KTa, and if the phase relation between the passive movements and the pacing signal was about 180° (0°) in UNm, the passive movements were based on those obtained for the nondominant hand in the antiphase (in-phase) trials performed in the AB task (i.e., one trajectory for each repetition; cf. Procedure). To obtain these trajectories, the kinematics of the nondominant hand in the AB trials were low-pass filtered using a second-order bidirectional (zero-lag) Butterworth filter with a cutoff frequency of 8 Hz. To avoid transient effects at the start of the trials the last 35 s were used, and this time series was multiplied with a windowing function to ensure a smooth increase and decrease of the amplitude of the passive movement during the first and last 5 s, respectively. For UNm, phase-shifted passive movements were prepared by cubic spline interpolation at the start of the trial to virtually slow down or speed up the movement to arrive at the desired phase relation of +30 or –30° after 5 s. Similarly, for KTa the intervals between the metronome beeps were lengthened or shortened during the first 5 s of a trial to achieve phase shifts of +30 and –30°, respectively. In the familiarization trials before the experimental trials (see Procedure) subjects chose which of the beeps in the auditory pacing signal (high-pitched or low-pitched) indicated maximum flexion or maximum extension of the dominant hand. This preference was used and verified throughout the remainder of the experiment to ensure that proper phase relations between the hands could be applied in KTa and UNm, where accurate relative phasing of the auditory metronome and passive movement was essential. A brief interview with the subjects after the experiment indicated that the additional phase shifts between passive movement and metronome were not consciously detected.

Procedure

For the purpose of normalization of the EMG all subjects performed maximum voluntary contractions by generating an isometric flexion or extension torque with each arm. While resting on a table the subject's forearm was restrained by the experimenter (supinated and palm up for flexion, and pronated and palm down for extension). The root mean square of the EMG was obtained from the plateau of the maximum voluntary contraction for the muscles involved (flexion: FCR and FDS; extension: ECR and EDC). Each maximum voluntary contraction was performed twice and the higher of the two values was used in the normalization of the EMG.

Subjects performed a total of 97 experimental trials in five coordinative tasks. Task-specific instructions were given in relation to the timing of the peak excursions of the wrists. For the bimanual tasks (AB, KT, KTa), subjects were instructed to reach peak flexion and peak extension of both wrists simultaneously (in-phase pattern), or to let peak flexion of one hand coincide with peak extension of the other hand (antiphase pattern). In addition, subjects were instructed to let peak flexion and extension of the wrist of the dominant hand coincide with the beeps of the pacing signal in the bimanual task AB, and in the unimanual tasks UN and UNm. Note that beeps were not present in condition KT, and that the instructions in condition KTa did not involve reference to the beeps. In all tasks subjects were told specifically to generate fluent oscillatory movements, to adhere to the required pattern, and to correct their movements if the pattern was lost.

Before the experiment subjects familiarized themselves with the AB task and the apparatus by actively performing the in-phase and antiphase patterns at 1.0 Hz (two to four trials, depending on the subject). Next, a relatively high movement frequency was selected for each individual subject to facilitate the detection of stability-related effects. This frequency was defined as the frequency at which the subject was able to perform both bimanual coordination patterns accurately (mean relative phase within 20° of the intended relative phase) and stably (fluctuations of the phasing of the individual limbs <30°, in correspondence with the phase shift of the distractor in KTa and UNm). This latter requirement implied that all absolute deviations in cycle duration were <8.33% (30/360) during an epoch of 25 s. Subjects performed one trial in each coordination pattern at a specified movement frequency, starting at 1.0 Hz. For each following pair of trials, the frequency was increased in 0.2-Hz steps until the subject failed to meet the performance criteria in either coordination pattern. In every subsequent pair of trials, the movement frequency was decreased in 0.1-Hz steps until the criteria were met again for both patterns. To avoid possible effects of muscle fatigue, the maximum movement frequency was set at 1.6 Hz. This procedure yielded the following movement frequencies: 1.6 Hz (five subjects), 1.5 Hz (one subject), 1.4 Hz (three subjects), and 1.2 Hz (two subjects). All tasks were performed at this individually determined movement frequency.

Because the passive movements were based on movements obtained for the nondominant hand in AB, all subjects started with this condition. For each bimanual coordination pattern (in-phase and antiphase), the order of which was counterbalanced across subjects, five trials were performed. For each subject, the three trials with the smallest variability of the cycle durations of the nondominant hand were retained for the generation of the passive movements and the data analysis.

Task KT was performed for both bimanual patterns and with two amplitudes of passive movements, resulting in 2 (Bimanual pattern) x 2 (Amplitude) x 3 repetitions = 12 trials. For KTa the additional phase shifts between metronome and passive movement yielded 2 (Bimanual pattern) x 2 (Amplitude) x 3 (Phase shift) x 3 repetitions = 36 trials. These trials were grouped together in two blocks of 24 trials according to the instruction given to the subjects (one block for in-phase coordination and one block for antiphase coordination), with the trials being presented in random order within each block. Likewise, the UNm and UN trials were randomly divided over two blocks (one block of 19 trials and one block of 20 trials). The instruction for these 39 trials was the same (i.e., let peak flexion and extension of the wrist of the dominant hand coincide with the beeps of the pacing signal). UNm involved 2 (Bimanual pattern) x 2 (Amplitude) x 3 (Phase shift) x 3 repetitions = 36 trials, whereas UN involved only three trials (i.e., three repetitions of the unimanual task without passive movement of the nondominant hand). The order of the four blocks (two blocks UN and UNm, and two blocks KT and KTa) was counterbalanced across subjects. The three repetitions conducted for each condition involving passive movements were based on the three selected reference trajectories (see above), applied in random order.

The duration of the trials varied over the tasks in view of the requirements for the generation of the passive movement trajectories (see above). Trial duration was 40 s in AB, 35 s in tasks with passive movement (KT, KTa, UNm), and 25 s in UN. For the first three subjects the durations of the trials were slightly longer (50 s for condition AB and 40 s for the other tasks conditions). For the next subjects, trial durations were adapted to ensure that the total duration of the experiment did not exceed 4 h, while still leaving 20 s per trial available for analysis.

Analyses of kinematics

After removal of transients at the beginning of each trial a period of 20 s was selected for analysis, ensuring that the movements of the nondominant hand were identical in AB, KT, KTa, and UNm. Before the analyses, kinematic data were low-pass filtered using a second-order bidirectional (zero-lag) Butterworth filter with a cutoff frequency of 8 Hz. Because the task requirements were defined in relation to the timing of discrete events in the movement cycle (i.e., the moments of peak flexion and extension), these events formed the basis for the analyses of the kinematics. All analyses were performed for flexion and extension separately.

In the bimanual tasks (AB, KT, KTa), the relative phase between the hands was calculated for each cycle as _i = 2(t_y,i – t_x,i)/(t_x, i + 1 – t_x,i), where t_y,i and t_x,i indicate the time of the ith peak flexion (extension) of the dominant hand and the nondominant hand, respectively (for a similar method see, e.g., Carson et al. 1995). Similarly, in the unimanual tasks (UN, UNm), the phase was determined relative to the metronome for each cycle as _i = 2(t_y,i – t_x,i)/(t_x, i + 1 – t_x,i), where t_y,i indicates the time of the ith peak flexion (extension) of the dominant hand and t_x,i corresponds to the moment of the ith metronome beep that specified peak flexion (extension). For both and , a positive relative phase meant that the dominant hand (y) was lagging the reference signal (x).

Nonstationarity (Chatfield 1984) of the relative phase was occasionally observed as a consequence of a difference between the durations of several consecutive cycles of the dominant hand and the reference signal. Episodes of nonstationary behavior were identified in 22 trials (2.6%) by visual inspection and removed from the trial, including potential transient effects in three cycles before and after this episode. Only epochs of at least ten consecutive cycles of stationary behavior were retained for the subsequent analyses. Circular statistics (Mardia 1972) was used to calculate the mean and the circular SD of the relative phase for each trial, for flexion and extension separately. Before the statistical analyses, the values obtained for flexion and extension were averaged per condition.

Correlations between temporal variables were calculated for the tasks that involved two moving hands (AB, KT, KTa, and UNm). To this end, the beginning and end of a cycle were defined by peak flexion (F-cycle) or by peak extension (E-cycle). Two correlations were determined: the correlation between the durations of simultaneously performed cycles (R_CD), and the correlation between the error in the discrete relative phase and the duration of the following cycle of the dominant hand (R_EC). R_CD was defined as the correlation between the durations of F(E)-cycles of the preferred hand and the durations of the simultaneous F(E)-cycles of the nonpreferred hand if the hands moved in the in-phase pattern, and as the correlation between the durations of F(E)-cycles of one hand and the duration of the simultaneous E(F)-cycles in the other hand for the antiphase pattern. For analysis of cycle-by-cycle error correction (R_EC), the timing error was defined as the interval between the moment at which the ith peak flexion (extension) occurred in the two hands (for in-phase), or between the moment of the ith peak flexion (extension) in the dominant hand and the moment of ith peak extension (flexion) of the nondominant hand (for antiphase). R_EC was defined as the correlation between these relative timing errors and the duration of the subsequent F(E)-cycle of the dominant hand. For statistical analysis R_CD and R_EC were transformed into normally distributed variables using the Fisher transform. For clarity, the inverse of the Fisher transformation (bounded on the interval [0, 1]) was used to present the average correlations.

EMG analyses

EMG analyses were performed on the stationary epochs as identified in the analyses of the kinematics. Before the analyses, EMG records were band-pass filtered (10–500 Hz) using a second-order bidirectional (zero-lag) Butterworth filter (Merletti et al. 1999). To visualize the average muscle activity within a cycle, eight bins were defined in relation to the continuous phase of the movement = arctan [(dX/dt)/(2fX)], where X and (dX/dt) are joint angle and joint angular velocity, respectively, and f is the movement frequency. Thus each bin represented an equal part of the phase of the hand oscillation. The first bin was centered around = 0° (i.e., full extension) and the fifth bin was centered around = 180° (i.e., full flexion). The root mean square of the EMG was calculated for the samples that corresponded to each bin, and normalized to that obtained for maximum voluntary contraction. The average normalized root mean square values per condition were used to visualize the global activation patterns of the muscles.

For the coherence analysis EMG records were full-wave rectified, and the weighted coherence (C_W; cf. Porges et al. 1980) of the full-wave–rectified EMG of homologous muscles was defined as

where f defines a bandwidth around the movement frequency f (f = 0.1 Hz). P_yy is the power spectrum of the rectified EMG of the dominant hand and C_xy is the coherence of the signals x and y, which are the rectified EMGs of the homologous muscles in the nondominant and the dominant hand, respectively. The coherence C_xy is equal to P_xy(P_xxP_yy)^–1, where P_xy is the cross-spectrum of the rectified EMGs of the dominant and the nondominant hand and P_xx is the power spectrum of the rectified EMG of the nondominant hand. The power spectra and the cross-spectrum were estimated with Welch's modified periodogram method (Oppenheim and Schafer 1975) using a Hamming window of six cycles. For statistical analysis, the weighted coherence of each muscle pair on each trial was transformed using the Fisher transformation (Rosenberg et al. 1989). Per subject, the transformed values were averaged to obtain weighted coherence measures for each condition. For clarity, the inverse of the Fisher transformation (bounded on the interval [0, 1]) was used to present average values of the weighted coherence.

Statistical analyses

Because the number of experimental manipulations differed between the coordinative tasks (see Procedure), it was not possible to compare the tasks directly using a repeated-measures ANOVA with Task as factor. Because our primary interest focused on examining the differential stability of in-phase and antiphase coordination, planned comparisons were performed separately for each task that involved two moving hands (AB, KT, KTa, and UNm) to evaluate pattern-related differences in the variability of the relative phase between the hands. In addition, two different methods of analysis were used for comparison between tasks as outlined in the following.

The first method consisted of two steps and was applied in the four strategic comparisons of different pairs of tasks (cf. Table 1) in terms of mean and SD of the (relative) phasing of the limb(s) ( and ). First, the differences between the results obtained for the two tasks (whenever possible matched for common factors in both tasks) were calculated per subject and tested with two-tailed t-tests to determine which of these differences was significant (i.e., nonzero). Second, these differences between two tasks were also subjected to repeated-measures ANOVA to examine the additional effect(s) of the experimental manipulation(s) of interest. These manipulations included the factors Bimanual pattern (in-phase vs. antiphase), Amplitude (of the passive movements), and Phase shift (of the distractor).

In contrast to the (relative) phase measures, no effects of the experimental manipulations related to the passive movements (Amplitude and Phase shift) were expected a priori for the correlations and coherence (R_EC, R_CD, and C_W). By excluding the factors Amplitude and Phase shift from the initial analyses, we directly compared multiple tasks in terms of these variables (as second method). For the correlations (R_EC and R_CD) a repeated-measures ANOVA was used to examine the effects of Task and Bimanual pattern for all tasks that involved two moving hands (AB, KT, KTa, UNm). Note that UN was not included in these analyses given that R_CD and R_EC could not be calculated for UN because, in this task, the nondominant hand was not moving (and was restrained by the apparatus). Similarly, for the coherence C_W a repeated-measures ANOVA examining the effects of Task, Bimanual pattern, and Muscle was applied to the same four tasks. Although C_W was calculated for UN, this task was excluded from the initial analysis because it did not involve Bimanual pattern as a factor. The results of these ANOVAs on R_EC, R_CD, and C_W were used as a departure point for subsequent, more detailed analysis, which are motivated and presented in RESULTS.

In the RESULTS section significant effects (P < 0.05) as well as tendencies (0.05 < P < 0.1) are reported. To facilitate the interpretation of significant results obtained with the ANOVAs, paired-sample t-tests were used for post hoc analysis (P < 0.05), and effect sizes (f) were calculated in terms of partial ² (Cohen 1988). Conventionally, small-, medium-, and large-effect sizes are indicated by 0.1, 0.25, and 0.4, respectively (Cohen 1988).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

 
Before presenting the results of the comparisons of the tasks for each dependent variable, it is useful to mention a number of additional properties of the data set. Data of two subjects were discarded for different reasons. One subject was unable to perform the unimanual task in the UNm condition, resulting in nonstationary behavior in 11 of the 36 trials, which prohibited analysis of these data in terms of means and SDs of relative phase. For another subject the passive movement trajectories as prepared for the antiphase conditions exhibited a significantly greater variability than those used for the in-phase conditions, which would confound the intended comparisons of in-phase and antiphase coordination based on tasks KT and KTa. For the remaining nine subjects, the relevant characteristics of the passive movement trajectories were examined with regard to differences between in-phase and antiphase coordination. One-way repeated-measures ANOVAs with the factor Bimanual pattern on the SD of the cycle duration [F(1,8) = 0.04; P = 0.846], the average range of motion [F(1,8) = 0.95; P = 0.347], and the mean joint angle [F(1,8) = 0.49; P = 0.502] indicated that the passive movements used for the in-phase and antiphase patterns were practically equivalent.

At the individually determined movement frequencies, the subjects adequately performed both bimanual patterns in AB [mean values of : 171.8° (antiphase), –6.8° (in-phase); between-subjects SD: 6.6° (antiphase), 5.8° (in-phase)]. The planned comparison of in-phase and antiphase coordination in terms of the circular SD of (SD) revealed that, for AB, SD was significantly higher in antiphase coordination (SD = 8.32°) than in in-phase coordination (SD = 7.53°), indicating that the antiphase pattern was less stable [F(1,8) = 4.14; P = 0.047; f = 0.83]. In contrast, planned comparisons of in-phase and antiphase coordination in terms of SD revealed no significant effects of Bimanual pattern for any of the other tasks that involved two moving hands (KT, KTa, and UNm).

SD of the relative phase between the hands (SD)

The contribution of integrated timing to the stability of bimanual coordination was examined in terms of the variability of the relative phase between the hands (SD) by comparing AB to KT (see INTRODUCTION and Table 1). For each subject, the values of SD for the four conditions of KT were subtracted from the corresponding (i.e., matched qua Bimanual pattern) values obtained for AB. Two-tailed t-tests indicated that these differences were nonzero for both bimanual patterns and amplitudes of passive movement in KT. Thus SD was significantly higher in KT than in AB (Fig. 2), implying a significant contribution of integrated timing to the stability of both bimanual patterns. The 2 (Bimanual pattern) x 2 (Amplitude) repeated-measures ANOVA on these differences between KT and AB revealed no significant effects, indicating that the contribution of integrated timing was not modulated by the associated manipulations.

View larger version (18K): [in this window] [in a new window]   FIG. 2. Mean circular SD of the relative phase between the hands (SD) during active bimanual coordination (AB) and during kinesthetic tracking (KT) of passive movements with reduced amplitude (RA) or normal amplitude (NA). Significant differences as determined by paired-samples t-test are also indicated (**P < 0.01; ***P < 0.001). Error bars represent the SE. Note that the difference between in-phase and antiphase was significant only for task AB (P = 0.043; not indicated in the figure).

View this table: [in this window] [in a new window]   TABLE 2. Comparison of SD in tasks UNm and KTa

Mean relative phase between the hands (M)

The correction of relative phasing errors was also evaluated with respect to its susceptibility to a distracting metronome signal in terms of the mean relative phase between the hands (M) by comparison of KT and KTa (see INTRODUCTION and Table 1). For each subject, M for the four conditions of KT was subtracted from the corresponding values (i.e., matched qua Amplitude and Bimanual pattern) for all 2 (Bimanual pattern) x 2 (Amplitude) x 3 (Phase shift) = 12 variations of KTa. Two-tailed t-tests revealed significant (i.e., nonzero) differences between these tasks, mainly if the metronome pacing was delayed (+30°) relative to the passive movement (Table 3). In addition, the difference between KT and KTa in terms of M was analyzed using a 2 (Bimanual pattern) x 2 (Amplitude) x 3 (Phase shift) repeated-measures ANOVA, which revealed a significant main effect of Phase shift [F(2,16) = 12.46; P = 0.004; f = 1.25], a significant interaction between Phase shift and Bimanual pattern [F(2,16) = 6.07; P = 0.023; f = 0.84], and a significant three-way interaction between Phase shift, Bimanual pattern, and Amplitude [F(2,16) = 5.44; P = 0.036; f = 0.78]. These results indicated a significant influence of the distractor (effect of Phase shift; compare the three bottom rows of Table 3). The dependency of M on the phase shift indicated that the dominant hand was relatively lagging (leading) the nondominant hand (relative to KT) if metronome pacing was delayed (advanced) relative to the passive movement (cf. Fig. 3), indicating that the phasing of the dominant hand was attracted toward synchronization with the (distracting) metronome signal. Post hoc t-tests indicated significant differences between all phase shifts for antiphase, whereas for in-phase only the difference between –30 and +30° was significant. The interaction between Phase shift and Bimanual pattern reflected a stronger attraction of the active hand by the metronome for antiphase coordination, resulting in larger shifts in (relative to KT) than for in-phase coordination (see Fig. 3). During antiphase coordination the effect of the distractor was greater at small amplitudes than at normal amplitudes, whereas the reverse was the case during in-phase coordination, resulting in the three-way interaction.

View this table: [in this window] [in a new window]   TABLE 3. Comparison of M in tasks KT and KTa

View larger version (35K): [in this window] [in a new window]   FIG. 3. Effects induced by the distracting metronome signal on kinesthetic tracking in task KTa. Changes in the relative phase between the hands are presented relative to the values obtained without the auditory metronome (KTa – KT) as a function of the additional phase shift between the passive movement and the metronome. Negative and positive values of the phase shifts (horizontal axis) indicate that the distracting metronome signal was relatively advanced or delayed with respect to the passive movement, respectively. Left panel: results for the 2 bimanual coordination patterns (IP, in-phase; AP, antiphase) and 2 amplitude levels of passive movement (RA, reduced amplitude; NA, normal amplitude). Right panels: mean results for each bimanual pattern (top) and amplitude condition (bottom).

Mean phase of dominant hand relative to metronome (M)

The phasing of the dominant hand relative to the metronome () indicated that the dominant hand was, on average, lagging the metronome in the unimanual task UN (mean: 19.7°; between-subject SD: 19.0°). The effects of phase entrainment by contralateral afference were analyzed in terms of the mean value of (M) in relation to the phase-shifted passive movement of the nondominant hand in UNm. For each subject, M for UN was subtracted from the corresponding values obtained for the 2 (Bimanual pattern) x 2 (Amplitude) x 3 (Phase shift) = 12 conditions of UNm. Two-tailed t-tests revealed that these differences were significant (i.e., nonzero) if the passive movement was advanced (–30°) relative to the metronome pacing (Table 4). The differences in M were subjected to a 2 (Bimanual pattern) x 2 (Amplitude) x 3 (Phase shift) repeated-measures ANOVA, which revealed a significant effect of Phase shift [F(2,16) = 18.78; P < 0.001; f = 1.53], a significant interaction between Phase shift and Amplitude [F(2,16) = 3.86; P = 0.043; f = 0.70], and a nonsignificant tendency for the interaction between Bimanual pattern and Amplitude [F(1,8) = 3.58; P = 0.096; f = 0.67]. The dependency of M on the Phase shift pointed out that the dominant hand was lagging (leading) the metronome if the passive movement of the nondominant hand was delayed (advanced) relative to the reference condition (cf. Fig. 4). Post hoc t-tests indicated significant differences between all phase shifts for the normal amplitude of passive movement, and significant differences between –30 and 0° and between –30 and +30° for the reduced amplitude. Thus as a consequence of phase entrainment the phasing of the active movement of the dominant hand was attracted toward a bimanual pattern, in which the hands moved either in-phase or in antiphase. The absence of significant effects of Bimanual pattern and of an interaction between Bimanual pattern and Phase shift (cf. Fig. 4) indicated that the attraction ascribed to phase entrainment was equally prominent for the in-phase and the antiphase pattern. The significant interaction between Phase shift and Amplitude indicated that the effect of phase entrainment was stronger if the amplitude of the passive movement was larger (cf. Fig. 4). The nonsignificant interaction tendency between Bimanual pattern and Amplitude resulted from a larger difference between UNm and UN for the normal amplitude than for the reduced amplitude if the hands moved approximately in antiphase (4.3 vs. 2.6°, averaged over phase shifts), whereas the reverse was true if the hands moved in-phase (3.9 vs. 2.3°, averaged over phase shifts).

View this table: [in this window] [in a new window]   TABLE 4. Comparison of M in tasks UNm and UN

View larger version (36K): [in this window] [in a new window]   FIG. 4. Phase entrainment effects induced by the passive movement of the nondominant hand in task UNm. Changes in the phasing of the dominant hand with respect to the metronome are presented relative to the values obtained without passive movement (UNm – UN) as a function of the additional phase shift between passive movement and metronome. Negative and positive values of the phase shifts (horizontal axis) indicate that the distracting passive movement was relatively advanced or delayed with respect to the reference signal (auditory metronome), respectively. Left panel: results for 2 amplitude levels of passive movement (RA, reduced amplitude; NA, normal amplitude) and the 2 bimanual patterns (IP, hands moving relatively in-phase; AP, hands moving relatively antiphase). Right panels: mean results for each bimanual pattern (top) and amplitude condition (bottom). Note that the tasks UN and UNm did not require coordination between the hands.

The correlations between the cycle durations of both limbs (R_CD) were determined for the four tasks that involved two moving hands (AB, KT, KTa, UNm). To allow for comparison with AB, only results obtained in trials with passive movement of normal amplitude (KT, KTa, UNm) and zero phase shift between passive movement and metronome (KTa and UNm) were subjected to a 4 (Task) x 2 (Bimanual pattern) repeated-measures ANOVA. The analysis revealed a significant main effect of Task [F(3,24) = 22.22; P < 0.001; f = 1.67], and a tendency of interaction between Task and Bimanual pattern [F(3,24) = 2.44; P = 0.089; f = 0.55]. Post hoc analysis indicated a significant difference between AB and the other three conditions, but no significant differences between KT, KTa, and UNm (Fig. 5). One-sided t-tests revealed that only in AB R_CD was significantly larger than zero, during both in-phase coordination [t(8) = 5.93; P < 0.001] and antiphase coordination [t(8) = 3.46; P = 0.009]. This motivated a one-way repeated-measures ANOVA with the factor Bimanual pattern conducted for AB, which indicated that the difference between in-phase and antiphase coordination in AB tended toward significance [F(1,8) = 4.53; P = 0.066; f = 0.75; possibly related to the abovementioned tendency of interaction between Task and Bimanual pattern]. This trend suggested that, for AB, the correlations were larger during in-phase than during antiphase coordination. Because integrated timing of the feedforward signals was expected to induce positive values of R_CD for AB, these results underscored the contribution of this source of interlimb interaction to active bimanual coordination and to the corresponding differential stability of the coordinative patterns.

View larger version (18K): [in this window] [in a new window]   FIG. 5. Average correlations between the durations of movement cycles of the 2 hands that were performed simultaneously. These correlations were not significantly different from zero if the nondominant hand was moved passively (KT, KTa, UNm). Only trials with passive movements of normal amplitude (KT, KTa, UNm) and without additional phase shifts (KTa, UNm) were included. Significant differences between the tasks as determined by paired-samples t-test are also indicated (*P < 0.05; **P < 0.01; ***P < 0.001). Error bars represent the SE.

The four tasks that involved two moving hands (AB, KT, KTa, UNm) were also compared with respect to the cycle-by-cycle error corrections, i.e., the correlations between timing errors and the durations of subsequent cycles (R_EC). To allow for comparison with AB, only results obtained in trials with passive movement of normal amplitude (KT, KTa, UNm) and zero phase shift between passive movement and metronome (KTa, UNm) were included in the analysis. The 4 (Task) x 2 (Bimanual pattern) repeated-measures ANOVA revealed a significant effect of Task [F(3,24) = 30.78; P < 0.001]. The post hoc analysis indicated that the values of R_EC were significantly more negative for KT and KTa than for AB and UNm, but no differences between either KT and KTa or AB and UNm were found (Fig. 6). In terms of the proposed sources of interlimb interaction, this result suggested that corrections of relative phasing errors were prominent in the kinesthetic tracking tasks (KT and KTa), but not in active bimanual coordination (AB).

View larger version (23K): [in this window] [in a new window]   FIG. 6. Average correlations between the timing errors and the duration of the consecutive cycles as obtained for the tasks that involved 2 moving hands. Only trials with passive movements of normal amplitude (KT, KTa, UNm) and without additional phase shifts (KTa, UNm) were included in the analysis. Significant differences between conditions as determined by paired-samples t-test are also indicated (**P < 0.01; ***P < 0.001). Error bars represent the SE.

EMG

The normalized EMG amplitude of the muscles in the nondominant arm revealed a striking difference between unimanual (UN, UNm) and bimanual tasks (AB, KT, KTa). The curves in Fig. 7, A and B exhibit the typical phase-dependent activation patterns of muscles during active rhythmic movements. This phase-dependent EMG was absent in the nondominant hand in the two conditions that involved a unimanual task (Fig. 7, C and D), irrespective of the absence (UN) or presence (UNm) of a passive movement. In contrast, a clearly phase dependent EMG pattern was observed in the muscles of the nondominant hand for all conditions that involved a bimanual task, even when this hand was moved passively as in conditions KT and KTa. This phenomenon was also observed for trials with passive movements of small amplitude and was present for both coordination patterns (not shown).

View larger version (39K): [in this window] [in a new window]   FIG. 7. Average muscle activation patterns for both arms in the 5 tasks as obtained from averaged normalized root mean square values of EMG of all subjects (results are given as a percentage of the root mean square value obtained for maximum voluntary contraction). Results of 2 muscles (ECR and FCR) are presented for 8 phases of the movement cycle. A and B: activation patterns of the dominant (actively moving) hand. C and D: activation patterns of the nondominant hand, which was actively moving (AB), being moved passively (KT, KTa, UNm), or motionless (UN). Patterns observed for FDS and EDC (not shown) were almost identical to those of FCR and ECR, respectively. Only data obtained in trials with normal amplitude (KT, KTa, UNm) and zero phase shift (KTa, UNm) were included in the averages.

View larger version (31K): [in this window] [in a new window]   FIG. 8. Mean weighted coherence (CW) of the rectified EMG of homologous muscles in all 5 coordinative tasks. Only trials with passive movements of normal amplitude (KT, KTa, UNm) and without additional phase shifts (KTa, UNm) were included in the analysis. Post hoc tests indicated that for each muscle all differences between the tasks were significant, except the difference between KT and KTa. For clarity, only the nonsignificant (ns) difference is indicated in the figure. Error bars represent the SE.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION GRANTS ACKNOWLEDGMENTS REFERENCES

Phase entrainment by contralateral afference

Comparison of the performance of the unimanual task with (UNm) and without (UN) passive movement of the contralateral hand clearly indicated that the passive movement entrained the movement of the active hand toward in-phase or antiphase. The absence of a difference in entrainment strength toward in-phase and antiphase contradicted the hypothesis that lower stability of antiphase results from afference-based entrainment toward in-phase (Baldissera et al. 1991; Carson and Riek 1998). In contrast, phase entrainment effects appeared to contribute equally to the stability of both bimanual patterns. The strength of the effect depended on the amplitude of the passive movement, which is taken to imply a reflexlike influence of the afferent signals generated by the passive movement on the phasing of the movement of the contralateral limb.

Correction of relative phasing errors

Several results revealed that perceived errors in the relative phase were corrected during bimanual coordination, particularly during kinesthetic tracking tasks (KT and KTa), and that this error correction was more efficient during in-phase than during antiphase coordination. The contribution of this source of interlimb interaction to bimanual coordination was examined in three different ways. First, the correlations between timing errors and the duration of the subsequent cycle were calculated (R_EC). Second, the variability of the relative phase between the hands (SD) was compared between KTa and UNm, which differed only with respect to the instructions to subjects, i.e., in KTa coordination between the hands was required, whereas in UNm subjects had to follow the auditory metronome. Third, a distracting (phase-shifted) auditory metronome signal was presented during the kinethestic tracking task of KTa to evaluate the efficacy of the corrections of relative phasing errors in counteracting this disturbance, in terms of the induced shifts in the mean relative phase between the hands (M).

Direct evidence for (afference-based) correction of relative phasing errors was provided by the values of R_EC that were significantly more negative in kinesthetic tracking tasks (KT and KTa) than in UNm and AB (see Fig. 6). The amplitude dependency of R_EC for the unimanual task UNm (which presumably did not involve correction of relative phasing errors; cf. Table 1) indicated that the value obtained for UNm may well be attributable to the effects of phase entrainment. Because phase entrainment by contralateral afference is regarded as a reflexlike phenomenon, the strength of which depends only on the intensity of the afferent signals, the value of R_EC found for UNm can thus be regarded as a baseline. The fact that AB and UNm did not yield significantly different values of R_EC may therefore indicate that also for AB the obtained R_EC was largely a result of phase entrainment effects, suggesting that the error correction mechanism was not, or only marginally, involved in active bimanual coordination.

Several observations, pertaining to stability (SD), accuracy (deviations in M), and the values of R_EC, indicated that the correction of relative phasing errors was more effective during in-phase coordination than during antiphase coordination. Significantly smaller values for SD were found in KTa compared with UNm in two of the four conditions (Table 3), which underscored the contribution of these error corrections to the behavioral stability, and a nonsignificant trend in the data suggested that this contribution was stronger for in-phase coordination than for antiphase coordination. In addition, comparison of KT and KTa showed that the distractor (auditory metronome) induced larger shifts in M during antiphase than in-phase coordination (Fig. 3). Further support for a pattern-related difference in the corrections of relative phasing errors was provided by the analysis of R_EC for KTa, which revealed that the values of R_EC were more negative for in-phase than for antiphase, signifying a more effective correction of errors in the relative phase during in-phase coordination. Although these results indicated that corrections of relative phasing errors may contribute to the greater stability of in-phase coordination compared with antiphase coordination, the absence of similar effects in KT suggested that these results primarily stemmed from the susceptibility of these error corrections to an external disturbance (i.e., the distracting metronome signal in KTa), possibly because the underlying processes require strong attentive effort (Baldissera et al. 1991).

Integrated timing of feedforward signals

The results indicated marked contributions of integrated timing to the stability of interlimb coordination. A striking result in this regard was that the archetypal difference in the variability of the relative phase (SD) between in-phase and antiphase (with in-phase being more stable and, thus less variable; e.g., Baldissera et al. 1991; Kelso 1984; Swinnen 2002) was observed only if integrated timing contributed to the behavioral stability, i.e., in active bimanual coordination (AB). However, the intended comparison of AB and kinesthetic tracking (KT) to single out the contribution of integrated timing (cf. Table 1) was complicated by two factors. First, it is possible that the metronome pacing in AB induced an "anchoring effect" (Beek 1989; Byblow et al. 1994), enhancing the stability of bimanual coordination (Fink et al. 2000). Second, the analysis of R_EC discussed in the previous paragraph indicated that the contribution of correction of relative phasing errors to pattern stability was marginal in