Amplitude Scaling in a Bimanual Circle-Drawing Task: Pattern Switching and End-Effector Variability

Spontaneity competes with intention to influence the coordination dynamics of interpersonal performance tendencies

Research has shown that spontaneous visual coupling supports frequency entrainment, phase attraction, and intermittent interpersonal coordination when co-actors are switched from a no-vision (NV) to vision (V) context. In two experiments, co-actors started in a NV context while producing the same or different amplitude movements. The same amplitude resulted in similar self-paced frequencies, while different amplitudes resulted in disparate frequencies. In experiment 1, co-actors were instructed to maintain amplitude while receiving no instructions to coordinate their actions. Frequency and phase entrainment was limited in the V context even when co-actors started the NV context with the same amplitude. In experiment 2, co-actors were instructed to maintain amplitude and intentionally coordinate together, but not at a specific pattern. Significant frequency modulations occurred to maintain amplitude as the co-actors sought to coordinate their actions. With the open-ended instructions, co-actors produced in-phase and anti-phase coordination along with intermittent performance exhibited by shifts between a variety of stable relative phase patterns. The proposed hypotheses and findings are discussed within the context of a shared manifold representation for joint action contexts, with the coordination dynamics expressed by the HKB model of relative phase serving to conceptualization the representations in the shared manifold.

The Effect of Crank Resistance on Arm Configuration and Muscle Activation Variances in Arm Cycling Movements

Arm cycling on an ergometer is common in sports training and rehabilitation protocols. The hand movement is constrained along a circular path, and the user is working against a resistance, maintaining a cadence. Even if the desired hand trajectory is given, there is the flexibility to choose patterns of joint coordination and muscle activation, given the kinematic redundancy of the upper limb. With changing external load, motor noise and changing joint stiffness may affect the pose of the arm even though the endpoint trajectory is unchanged. The objective of this study was to examine how the crank resistance influences the variances of joint configuration and muscle activation. Fifteen healthy participants performed arm cranking on an arm-cycle ergometer both unimanually and bimanually with a cadence of 60 rpm against three crank resistances. Joint configuration was represented in a 3-dimensional joint space defined by inter-segmental joint angles, while muscle activation in a 4-dimensional "muscle activation space" defined by EMGs of 4 arm muscles. Joint configuration variance in the course of arm cranking was not affected by crank resistance, whereas muscle activation variance was proportional to the square of muscle activation. The shape of the variance time profiles for both joint configuration and muscle activation was not affected by crank resistance. Contrary to the prevailing assumption that an increased motor noise would affect the variance of auxiliary movements, the influence of noise doesn't appear at the joint configuration level even when the system is redundant. Our results suggest the separation of kinematic- and force-control, via mechanisms that are compensating for dynamic nonlinearities. Arm cranking may be suitable when the aim is to perform training under different load conditions, preserving stable and secure control of joint movements and muscle activations.

A Re-Appraisal of the Effect of Amplitude on the Stability of Interlimb Coordination Based on Tightened Normalization Procedures

The stability of rhythmic interlimb coordination is governed by the coupling between limb movements. While it is amply documented how coordinative performance depends on movement frequency, theoretical considerations and recent empirical findings suggest that interlimb coupling (and hence coordinative stability) is actually mediated more by movement amplitude. Here, we present the results of a reanalysis of the data of Post, Peper, and Beek (2000), which were collected in an experiment aimed at teasing apart the effects of frequency and amplitude on coordinative stability of both steady-state and perturbed in-phase and antiphase interlimb coordination. The dataset in question was selected because we found indications that the according results were prone to artifacts, which may have obscured the potential effects of amplitude on the post-perturbation stability of interlimb coordination. We therefore redid the same analysis based on movement signals that were normalized each half-cycle for variations in oscillation center and movement frequency. With this refined analysis we found that (1) stability of both steady-state and perturbed coordination indeed seemed to depend more on amplitude than on movement frequency per se, and that (2) whereas steady-state antiphase coordination became less stable with increasing frequency for prescribed amplitudes, in-phase coordination became more stable at higher frequencies. Such effects may have been obscured in previous studies due to (1) unnoticed changes in performed amplitudes, and/or (2) artifacts related to inappropriate data normalization. The results of the present reanalysis therefore give cause for reconsidering the relation between the frequency, amplitude, and stability of interlimb coordination.

The Development of Bimanual Coordination Across Toddlerhood

As one of the hallmarks of human activity and cultural achievement, bimanual coordination has been the focus of research efforts in multiple fields of inquiry. Since the seminal work of Cohen (1971) and Kelso and colleagues (Haken, Kelso, & Bunz, 1985; Kelso, Southard, & Goodman, 1979), bimanual action has served as a model system used to investigate the role of cortical, perceptual, cognitive, and situational underpinnings of coordinated movement sequences (e.g., Bingham, 2004; Oliveira & Ivry, 2008). This work has been guided primarily by dynamical systems theory in general, and by the formal Haken-Kelso-Bunz (HKB; 1985) model of bimanual coordination, in particular. The HKB model describes the self-organizing relationship between a coordinated movement pattern and the underlying parameters that support that pattern, and can also be used to conceptualize and test predictions of how changes in coordination occur. Much of the work investigating bimanual control under the HKB model has been conducted with adults who are acting over time periods of a few seconds to a few days. However, there are also changes in bimanual control that occur over far longer time spans, including those that emerge across childhood and into adolescence (e.g., Wolff, Kotwica, & Obregon, 1998). Using the formal HKB model as a starting point, we analyzed the ontogenetic emergence of a particular pattern of bimanual coordination, specifically, the anti-phase (or inverse oscillatory motion) coordination pattern between the upper limbs in toddlers who are performing a drumming task (see Brakke, Fragaszy, Simpson, Hoy, & Cummins-Sebree, 2007). This study represents a first attempt to document the emergence of the anti-phase pattern by examining both microgenetic and ontogenetic patterns of change in bimanual activity. We report the results of a longitudinal study in which seven toddlers engaged monthly in a bimanual drumming task from 15 to 27 months of age. On some trials, an adult modeled in-phase or anti-phase action; on other trials, no action was modeled. We documented the motion dynamics accompanying the emergence of the anti-phase bimanual coordination pattern by assessing bout-to-bout and month-to-month changes in several movement parameters-oscillation frequency, amplitude ratio of the drumsticks, initial position of the limbs to begin bouts, and primary arm-joint involvement. These parameters provided a good starting point to understand how toddlers explore movement space in order to achieve greater stability in performing the anti-phase coordination pattern. Trained research assistants used Motus software to isolate each bout of drumming and to digitize the movement of the two drumstick heads relative to the stationary drum surface. Because we were primarily interested in the vertical movement of the drumsticks that were held in the child's hands, we relied on two-dimensional analyses and analyzed data that were tracked by a single camera. We used linear mixed effects analyses as well as qualitative analyses for each participant to help elucidate the emergence and stability of the child's use of anti-phase coordination. This approach facilitated descriptions of individual pathways of behavior that are possible only with longitudinal designs such as the one used here. Our analyses indicated that toddlers who were learning to produce anti-phase motion in this context employed a variety of strategies to adjust the topography of their action. Specifically, as we hypothesized, toddlers differentially exploited oscillation frequency and movement amplitude to support change to anti-phase action, which briefly appeared as early as 15 months of age but did not become relatively stable until approximately 20 months of age. We found evidence that many toddlers reduced oscillation frequency before transitioning from in-phase to anti-phase drumming. Toddlers also used different means of momentarily modulating the amplitude ratio between limbs to allow a change in coordination from in-phase to anti-phase. Nevertheless, these oscillation-frequency and amplitude-ratio strategies were interspersed by periods of nonsystematic exploration both within and between bouts of practice. We also observed that toddlers sometimes changed their initial limb positions to start a bout or altered which primary arm joints they used when drumming. When they enacted these changes, the toddlers increased performance of the anti-phase coordination pattern in their drumming. However, we found no evidence of systematic exploration with these changes in limb position and joint employment, suggesting that the toddlers did not intentionally employ these strategies to improve their performance on the task. Although bimanual drumming represents a highly specific behavior, our examination of the mechanisms underlying emergence of the anti-phase coordination pattern in this context is one of the missing pieces needed to understand the development of motor coordination more broadly. Our results document that the anti-phase coordination pattern emerges and stabilizes through modulation of the dynamics of the movement and change of the attractor landscape (i.e., the motor repertoire). Consistent with literatures in motor control, motor learning, and skill development, our results suggest that the acquisition of movements in ontogenetic development can be thought of as exploration of the emergent dynamics of perception and action. This conclusion is commensurate with a systemic approach to motor development in which functional dynamics, rather than specific structures, provide the basis for understanding developmental changes in skill. Based on our results as well as the relevant previous empirical literature, we present a conceptual model that incorporates developmental dynamics into the HKB model. This conceptual model calls for new investigations using a dynamical systems approach that allows direct control of movement parameters, and that builds on the methods and phenomena that we have described in the current work.

On the One Hand or on the Other: Trade-Off in Timing Precision in Bimanual Musical Scale Playing

Music performance requires simultaneously producing challenging movement sequences with the left and right hand. A key question in bimanual motor control research is whether bimanual movements are produced by combining unimanual controllers or through a dedicated bimanual controller. Here, 34 expert pianists performed musical scale playing movements with the left or right hand alone and with both hands simultaneously. We found that for the left hand, scale playing was more variable when playing with both hands simultaneously rather than with one hand at a time, but for the right hand, performance was identical. This indicates that when task constraints are high, musicians prioritize timing accuracy in the right hand at the cost of detriment of performance in the left hand. We also found that individual differences in timing substantially overlap between the unimanual and bimanual condition, suggesting control policies are similar but not identical when playing with two hands or one. In the bimanual condition, the left-hand keystrokes tended to occur before right-hand ones, and more so when the hands were further apart. Performance of the two hands was furthermore coupled so that they tended to be early and late together, especially in the beginning and end of each scale. This suggests that experts are able to achieve tightly coupled timing of scale playing movements between the hands. Taken together, these findings show evidence for partially overlapping and partially separate controllers for bimanual and unimanual movements in piano playing.

The Interaction of Tactile Information and Movement Amplitude in a Multijoint Bimanual Circle-Tracing Task: Phase Transitions and Loss of Stability

Adaptive behaviour in bimanual coordination was examined with the use of a bimanual circle-tracing task. Circle diameter and tactile information were manipulated to form four tracing conditions: tracing a pair of 3-cm diameter circles with the tips of the index fingers (3F) or hand-held styli (3S) and tracing a pair of 10-cm diameter circles with the tips of the index fingers (10F) or hand-held styli (10S). Movement frequency was increased in all conditions. In the 3F, 3S, and 10S tracing conditions, an abrupt transition from asymmetric to symmetric coordination was the main adaptive response, while in the 10F tracing condition, phase wandering was the main adaptive response. Enhancement of fluctuations in relative phase, a signature of loss of stability, occurred before the transition from asymmetric to symmetric coordination. Movement frequency and movement amplitude interact as control parameters in this task. The results are discussed with reference to tactile surface contact and joint motion as sources of sensory information that can be used to stabilize bimanual coordination patterns. The presence or absence of tactile information is directly linked to the specific form of adaptive behaviour (phase transition or phase wandering) that emerges as a function of required movement amplitude and required pacing frequency.

Unintentional force changes in cyclical tasks performed by an abundant system: Empirical observations and a dynamical model

The study explored unintentional force changes elicited by removing visual feedback during cyclical, two-finger isometric force production tasks. Subjects performed two types of tasks at 1Hz, paced by an auditory metronome. One - Force task - required cyclical changes in total force while maintaining the sharing, defined as relative contribution of a finger to total force. The other task - Share task - required cyclical changes in sharing while keeping total force unchanged. Each trial started under full visual feedback on both force and sharing; subsequently, feedback on the variable that was instructed to stay constant was frozen, and finally feedback on the other variable was also removed. In both tasks, turning off visual feedback on total force elicited a drop in the mid-point of the force cycle and an increase in the peak-to-peak force amplitude. Turning off visual feedback on sharing led to a drift of mean share toward 50:50 across both tasks. Without visual feedback there was consistent deviation of the two force time series from the in-phase pattern (typical of the Force task) and from the out-of-phase pattern (typical of the Share task). This finding is in contrast to most earlier studies that demonstrated only two stable patterns, in-phase and out-of-phase. We interpret the results as consequences of drifts of parameters in a dynamical system leading in particular to drifts in the referent finger coordinates toward their actual coordinates. The relative phase desynchronization is caused by the right-left differences in the hypothesized drift processes, consistent with the dynamic dominance hypothesis.

The organization of intralimb and interlimb synergies in response to different joint dynamics

We sought to understand differences in joint coordination between the dominant and nondominant arms when performing repetitive tasks. The uncontrolled manifold approach was used to decompose the variability of joint motions into components that reflect the use of motor redundancy or movement error. First, we hypothesized that coordination of the dominant arm would demonstrate greater use of motor redundancy to compensate for interaction forces than would coordination of the nondominant arm. Secondly, we hypothesized that when interjoint dynamics were more complex, control of the interlimb relationship would remain stable despite differences in control of individual hand paths. Healthy adults performed bimanual tracing of two orientations of ellipses that resulted in different magnitudes of elbow interaction forces. For the dominant arm, joint variance leading to hand path error was the same for both ellipsis orientations, whereas joint variance reflecting the use of motor redundancy increased when interaction moment was highest. For the nondominant arm, more joint error variance was found when interaction moment was highest, whereas motor redundancy did not differ across orientations. There was no apparent difference in interjoint dynamics between the two arms. Thus, greater skill exhibited by the dominant arm may be related to its ability to utilize motor redundancy to compensate for the effect of interaction forces. However, despite the greater error associated with control of the nondominant hand, control of the interlimb relationship remained stable when the interaction moment increased. This suggests separate levels of control for inter- versus intra-limb coordination in this bimanual task.

Torso Movement Constraint in Stability of Bimanual Coordination

This study investigated the relation between postural movement and upper-limb coordination stability. Adults produced bimanual circles using in-phase and anti-phase coordination patterns in time to an increasing rate metronome (i.e., movement-time instruction) in the horizontal (e.g., tabletop) and vertical (e.g., “wall” perpendicular to body) planes. All participants produced the instructed in- and anti-phase patterns. Coordination stability (i.e., SD of relative phase) was larger for anti-phase than in-phase patterns in both planes; however, anti-phase coordination stability was lower in the vertical plane than in the horizontal plane. Torso movement was larger during anti-phase coordination patterns in the horizontal plane, whereas it was larger during in-phase coordination patterns in the vertical plane. These results indicate that different orientations of the same task can produce different results for stability of coordination. This information may be important for performing and learning complex motor-coordination movements (e.g., playing musical instruments).

Action and perception at the level of synergies

Meeting the challenge of assembling coherent organizations of very many muscles characterizes a functional level of biological movement systems referred to as the level of muscular-articular links or synergies. The present article examines the issues confronting the forming, regulating, and ordering of synergies and the hypothesized principles, both classical and contemporary, which resolve them. A primary goal of the article is to highlight the abstractness of the concepts and tools required to understand the level's action-perception competence. Coverage is given to symmetry groups, task space, order parameters, metastability, biotensegrity, allometric scaling, and impredicative definitions.

One-to-one and polyrhythmic temporal coordination in bimanual circle tracing

The authors manipulated movement amplitude in a bimanual circle-tracing task to alter the natural tracing frequency of the arms. Participants (N = 14) traced different-diameter circles simultaneously with the two arms in either in-phase (0 degrees) or antiphase (180 degrees) coordination, using the index fingers or plastic styli. Movement amplitude altered the natural tracing frequency of the arms, as demonstrated by the following 2 findings: (a) The larger the difference in circle diameter, the larger was the shift from the fixed-point values of 0 degrees and 180 degrees, and the shift increased as movement frequency increased. Those results are consistent with the manipulation of delta omega in the bimanual pendulum paradigm. (b) Increasing movement frequency induced transitions from 1:1 to non-1:1 coordination, contrary to findings in previous investigations of polyrhythmic coordination. Tactile feedback played a minimal role in stabilizing bimanual coordination in the current tasks.

Effects of movement frequency and joint kinetics on the joint coordination underlying bimanual circle drawing

Ten healthy participants performed bimanual symmetric and asymmetric circle drawing at 4 frequencies. The authors partitioned the variance of the joint configuration across repetitions into 1 component representing equivalent joint configurations with respect to achieving stability of the mean hand path (i.e., goal-equivalent variance, GEV) and 1 component leading to a variable hand path (non-goal-equivalent variance, NGEV) across cycles. Higher frequencies led to increased NGEV related to control of the nondominant hand and to the relative position and orientation between the hands during asymmetric drawing. The results were related to differences in muscle and interaction moments between the arms, and they suggest a possible relationship between the ability to use intersegmental forces and the stability of interlimb synergy.

Target width scaling in a repetitive aiming task: switching between cyclical and discrete units of action

An aiming task was used to identify the processes whereby the motor system adapted a repetitive aiming action to systematic changes in ID (ID = log(2 )(2A/W), Fitts in J Exp Psychol 47:381-391, 1954) within a single trial. Task ID was scaled in a trial by moving the outside edge of two stationary targets to produce nine different target IDs in a trail. The ID within a trial was scaled in one of two directions: (1) an increasing ID condition, starting with an ID = 3.07 and ending with an ID = 5.91; and (2) a decreasing ID condition, starting with an ID = 5.91 and ending with an ID = 3.07. An index of movement harmonicity (Guiard in Acta Psychol 82:139-159, 1993) revealed that the repetitive aiming action was harmonic in nature when task ID was 3.07, and consisted of a series of discrete segments when task ID was 5.91. This finding provides evidence for the existence of discrete and cyclical units of action that are irreducible and that may be employed independently to assemble longer continuous actions. The scaling of ID within a trial promoted a transition in repetitive aiming motions assembled from discrete and cyclical units of action. A variety of kinematic measures (e.g., movement harmonicity, time spent accelerating the limb) revealed a critical ID (ID(c)) region (4.01-4.91) separating aiming motions governed by the different units of action. Enhancement of fluctuations before the transition were found in the movement harmonicity data and in the distance traveled to peak velocity data, with variability in these measures highest in the ID(c) region. The enhancement of fluctuations indicates that loss of stability in the limb's motion acted as a key mechanism underlying the transition between units of action. The loss of stability was associated with the transition from cyclical to discrete actions and with the transition from discrete to cyclical actions. The transition between units of action may be conceptualized as a transition from a limit cycle attractor (cyclical unit of action) to a shift between two fixed-point attractors (discrete unit of action) when ID was increased, with the transition occurring in the opposite direction when ID was decreased.