Perceptual influences on Fitts' law.

The linear relationship between movement time (MT) and index of difficulty (ID) for Fitts' type tasks has proven ubiquitous over the last 50+ years. A reciprocal aiming task (IDs 3, 4.5, 6) was used to determine if an enlarged visual display (visual angle 5.1 degrees , 7.4 degrees , or 13.3 degrees) would alter this relationship. With ID = 6, a condition typically associated with discrete action control, the largest visual display (13.3 degrees) allowed the motor system to exploit features of cyclical action control, e.g., shorter dwell times, more harmonic motion, less time decelerating the limb. The large visual display resulted in a quadratic relationship between MT and ID. For the IDs of 3 and 4.5, the visual displays did not alter the underlying control processes. The results are discussed in terms of the preference of the motor system to assemble movements from harmonic basis functions when salient visual information is provided.

Compensatory postural adaptations during continuous, variable amplitude perturbations reveal generalized rather than sequence-specific learning.

We examined changes in the motor organization of postural control in response to continuous, variable amplitude oscillations evoked by a translating platform and explored whether these changes reflected implicit sequence learning. The platform underwent random amplitude (maximum +/- 15 cm) and constant frequency (0.5 Hz) oscillations. Each trial was composed of three 15-s segments containing seemingly random oscillations. Unbeknownst to participants, the middle segment was repeated in each of 42 trials on the first day of testing and in an additional seven trials completed approximately 24 h later. Kinematic data were used to determine spatial and temporal components of total body centre of mass (COM) and joint segment coordination. Results showed that with repeated trials, participants reduced their magnitude of COM displacement, shifted from a COM phase lag to a phase lead relative to platform motion and increased correlations between ankle/platform motion and hip/platform motion as they shifted from an ankle strategy to a multi-segment control strategy involving the ankle and hip. Maintenance of these changes across days provided evidence for learning. Similar improvements for the random and repeated segments, indicated that participants did not exploit the sequence of perturbations to improve balance control. Rather, the central nervous system may have been tuning into more general features of platform motion. These findings provide important insight into the generalizabilty of improved compensatory balance control with training.

Learning and transfer of a relative phase pattern and a joint amplitude ratio in a rhythmic multijoint arm movement.

According to the coordination dynamics perspective, one can characterize the learning of novel relative phase patterns as the formation of a stable attractor in the coordination landscape of the order parameter relative phase. The authors examined 18 participants' learning and transfer of a 90 degrees relative phase pattern and a 0.6-joint-amplitude ratio between the elbow and wrist. Variability in the relative phasing and the joint amplitude ratio between the elbow and wrist decreased with practice. Positive transfer of the 90 degrees relative phase pattern was not dependent on the learning arm (dominant or nondominant). Positive transfer of the joint amplitude ratio was dependent on the learning arm and the direction of transfer. The results demonstrated that relative phase is an order parameter that characterizes the coordination dynamics of learning and transferring multijoint arm movements, and they provide preliminary evidence that joint amplitude ratios act as order parameters in the learning and transfer of multijoint arm movements.

Vestibular loss disrupts control of head and trunk on a sinusoidally moving platform.

Twelve subjects, 6 bilateral vestibular-loss (3 well compensated and 3 poorly compensated) and 6 controls, attempted to maintain balance during anterior-posterior sinusoidal surface translation at 6 different frequencies. For frequencies or= 0.75 Hz, these subjects fixed their head/upper-trunk in space. Poorly compensated vestibular subjects showed large head and center of mass variability and were unable to balance at frequencies requiring a head fixed in space pattern. All vestibular subjects were less stable with vision than the controls. Without vision, vestibular subjects experienced more falls than the controls at all frequencies, with falls observed in 61% of the vestibular subjects trials and 16% of the control subjects trials. Vestibular information is important in stabilizing head and upper-trunk motion in space. Visual and somatosensory information can compensate, in part, for vestibular-loss. The results are discussed in light of models that characterize postural control in a vestibular/visual top-down and somatosensory bottom-up manner.

Posturally induced transitions in rhythmic multijoint limb movements.

The coordination dynamics (e.g., stability, loss of stability, switching) of multijoint arm movements are studied as a function of forearm rotation. Rhythmical coordination of flexion and extension of the right elbow and wrist was examined under the following conditions: (1) forearm supine (forearm angle 0 degrees), simultaneous coordination of wrist flexion/elbow flexion and wrist extension/elbow extension (termed in-phase); and (2) forearm prone (forearm angle 160 degrees), simultaneous coordination of wrist flexion/elbow extension and wrist extension/elbow flexion (termed anti-phase). Starting in either pattern, subjects rotated the forearm in nine 20 degrees steps, producing 15 cycles of motion per step at a frequency of 1.25 Hz. Spontaneous transitions from pattern 1 to pattern 2 and from pattern 2 to pattern 1 were observed at a critical forearm angle. The critical angle depended on the direction of forearm rotational change, thus revealing the hysteretic nature of the switching process. En route to the transition, regardless of direction of forearm rotation, enhancement of phase fluctuations and an increase in perturbation response times (critical slowing down) were observed in the relative phasing between the joints. Such observations support loss of stability as a central, self-organizing process underlying coordinative change. Neurophysiological mechanisms supporting multijoint coordinative dynamics are discussed.

Emergence of postural patterns as a function of vision and translation frequency.

Emergence of postural patterns as a function of vision and translation frequency. We examined the frequency characteristics of human postural coordination and the role of visual information in this coordination. Eight healthy adults maintained balance in stance during sinusoidal support surface translations (12 cm peak to peak) in the anterior-posterior direction at six different frequencies. Changes in kinematic and dynamic measures revealed that both sensory and biomechanical constraints limit postural coordination patterns as a function of translation frequency. At slow frequencies (0.1 and 0.25 Hz), subjects ride the platform (with the eyes open or closed). For fast frequencies (1.0 and 1.25 Hz) with the eyes open, subjects fix their head and upper trunk in space. With the eyes closed, large-amplitude, slow-sway motion of the head and trunk occurred for fast frequencies above 0.5 Hz. Visual information stabilized posture by reducing the variability of the head's position in space and the position of the center of mass (CoM) within the support surface defined by the feet for all but the slowest translation frequencies. When subjects rode the platform, there was little oscillatory joint motion, with muscle activity limited mostly to the ankles. To support the head fixed in space and slow-sway postural patterns, subjects produced stable interjoint hip and ankle joint coordination patterns. This increase in joint motion of the lower body dissipated the energy input by fast translation frequencies and facilitated the control of upper body motion. CoM amplitude decreased with increasing translation frequency, whereas the center of pressure amplitude increased with increasing translation frequency. Our results suggest that visual information was important to maintaining a fixed position of the head and trunk in space, whereas proprioceptive information was sufficient to produce stable coordinative patterns between the support surface and legs. The CNS organizes postural patterns in this balance task as a function of available sensory information, biomechanical constraints, and translation frequency.

Transitions in a postural task: do the recruitment and suppression of degrees of freedom stabilize posture?

In this study, we examined flexibility in postural coordination by inducing transitions between postural patterns. Previous work demonstrated that the postural control system produces two task-specific postural patterns as a function of the frequency of support surface translation. For slow translation frequencies (<0.5 Hz), subjects ride on the platform reminiscent of upright stance (ride pattern), and for fast frequencies (> or =0.75 Hz) subjects actively fixed the head and trunk in space (head fixed pattern) during anterior-posterior platform motion. To study the adaptation of the postural control system, we had subjects stand on a support surface undergoing increases (from 0.2 to 1.0 Hz in 0.1-Hz steps) and decreases (from 1.0 to 0.2 Hz in 0.1-Hz steps) in translation frequency with the eyes open and closed. Kinematic measures of sagittal plane body motion revealed a gradual transition between these two postural patterns as a function of frequency scaling. In both the increasing and decreasing frequency conditions with visual input, center of mass displacements gradually decreased and increased, respectively, whereas upper-trunk (and head) displacement decreased gradually within the ride pattern until a head fixed pattern was observed without any significant changes in displacement for translation frequencies at and above 0.6 Hz. Without visual input, the scaling of the ride pattern was similar except the transition to the head fixed pattern never emerged with increasing frequency; instead, a less stable pattern exhibiting slow drift in head-trunk anterior-posterior motion (drift pattern) was observed at and above 0.5 Hz oscillations. The stability of the head fixed pattern at fast frequencies was clearly dependent on visual input suggesting that vision was more critical for trunk and head control in space at high than low translation frequencies. Head velocity was kept constant, and lower with vision, as translation frequency (and velocity) changed suggesting a head velocity threshold constraint across postural patterns. The gradual transition from the ride to the head fixed pattern was made possible by the recruitment of available degrees of freedom in the form of ankle, then knee, and then hip joint motion. In turn, the transition from the head fixed or drift pattern was made possible by the gradual suppression of available degrees of freedom in the form of reducing hip, then knee, and then ankle motion. The gradual change in postural kinematics without instabilities and hysteresis suggests that the ability to recruit and suppress biomechanical degrees of freedom allows the postural control system to gradually change postural strategies without suffering a loss of stability. The results are discussed in light of possible self-organizing mechanisms in the multisensory control of posture.

Order parameters for the neural organization of single, multijoint limb movement patterns.

Subjects performed two patterns of coordination between the elbow and wrist joints of the right arm: 1) wrist flexion synchronized with elbow flexion and wrist extension with elbow extension (homologous muscle groups); and 2) wrist extension synchronized with elbow flexion and wrist flexion with elbow extension (nonhomologous muscle groups). As a parameter, cycling frequency, was increased, an abrupt switch in the phase relation between the elbow and wrist joints occurred. Similar effects were observed in underlying neuromuscular (EMG) timing patterns. Observed transitions depended on whether the forearm was prone or supine, not simply on the muscle pairing across the joints. With the forearm supine, transitions were from pattern (2) to pattern (1) above, and with the forearm prone the transitions were from pattern (1) to pattern (2). When subjects were initially prepared in pattern (1) with the forearm supine or in pattern (2) with the forearm prone, switching did not occur. En route to transitions, enhanced fluctuations in the phase relation occurred, indicating that loss of stability is at the origin of pattern change. Accompanying such changes in coordination were characteristic effects on end effector trajectories and velocity profiles. Possible neurophysiological mechanisms for context dependence in multijoint coordination are discussed.

Coordination dynamics of trajectory formation.

The present study aims to understand the neurally based coordination dynamics (multistability, loss of stability, transitions, etc.) of trajectory formation in a simple task. Six subjects produced two spatial patterns of coordination in the xy plane by alternating the abduction-adduction and flexion-extension motions of their right index finger. Each pattern was characterized by a unique temporal ratio between the x and y directions of motion: (1) a figure zero, a 1:1 temporal pattern; and (2) a figure eight, a 2:1 temporal pattern. The patterns were produced rhythmically and movement frequency was scaled across ten frequency plateaus, with ten cycles of motion per step. As movement frequency increased, switching from a figure eight to a figure zero was observed at critical cycling frequencies. The switch from pattern (2) to pattern (1) was identified in the spatial trajectory and power spectra of x(t) and y(t). En route to the transition, enhancement of fluctuations was observed in the Fourier amplitudes of x(t) and y(t), specifically at f0 (the metronome frequency) and 2f0 (the first harmonic of f0). Interestingly, there was no difference in the spatial variability of the two patterns. Overall, the data demonstrate that spatial patterns of coordination can be characterized in terms of the temporal relationship between the spatial components of the trajectory itself. We discuss the experimental findings in relation to other end-point planning and multijoint control strategies, as well as the much more general problem of temporal synchronization in many interlimb and intralimb coordination tasks.

To Switch or Not to Switch: Recruitment of Degrees of Freedom Stabilizes Biological Coordination.

Recruitment and suppression processes were studied in the swinging-pendulum paradigm (cf. P. N. Kugler & M. T. Turvey, 1987). The authors pursued the hypothesis that active recruitment of previously unmeasured degrees of freedom serves to stabilize an antiphase bimanual coordination pattern and thereby obviates the need for pattern switching from an antiphase to an in-phase coordination pattern, a key prediction of the H. Haken, J. A. S. Kelso, and H. Bunz (1985) model. In Experiment 1, 7 subjects swung single hand-held pendulums in time with an auditory metronome whose frequency increased. Pendulum motion changed from planar (2D) to elliptical (3D), and forearm motion (produced by elbow flexion-extension) was recruited with increasing movement rate for cycling frequencies typically above the pendulum's eigenfrequency. In Experiment 2, 7 subjects swung paired pendulums in either an in-phase or an antiphase coordinative mode as movement rate was increased. With the systematic increase in movement rate, the authors attempted to induce transitions from the antiphase to the in-phase coordinative pattern, with loss of stability the key mechanism of pattern change. Transitions from the antiphase to the in-phase coordinative mode were not observed. Pattern stability, as defined by the variability of the phase relation between the pendulums, was affected only a little by increasing movement rate. As in the single-pendulum case, pendulum motion changed from planar to elliptical, and forearm motion was recruited with increasing cycling frequency. Those results reveal a richer dynamics than previously observed in the pendulum paradigm and support the hypothesis that recruitment processes stabilize coordination in biomechanically redundant systems, thereby reducing the need for pattern switching.

Self-organization of trajectory formation. I. Experimental evidence.

Most studies examining the stability and change of patterns in biological coordination have focused on identifying generic bifurcation mechanisms in an already active set of components (see Kelso 1994). A less well understood phenomenon is the process by which previously quiescent degrees of freedom (df) are spontaneously recruited and active df suppressed. To examine such behavior, in part I we study a single limb system composed of three joints (wrist, elbow, and shoulder) performing the kinematically redundant task of tracing a sequence of two-dimensional arcs of monotonically varying curvature, kappa. Arcs were displayed on a computer screen in a decreasing and increasing kappa sequence, and subjects rhythmically traced the arcs with the right hand in the sagittal plane at a fixed frequency (1.0 Hz), with motion restricted to flexion-extension of the wrist, elbow, and shoulder. Only a few coordinative patterns among the three joints were stably produced, e.g., in-phase (flexion-extension of one joint coordinated with flexion-extension of another joint) and antiphase (flexion-extension coordinated with extension-flexion). As kappa was systematically increased and decreased, switching between relative phase patterns was observed around critical curvature values, kappa c. A serendipitous finding was a strong 2:1 frequency ratio between the shoulder and elbow that occurred across all curvature values for some subjects, regardless of the wrist-elbow relative phase pattern. Transitions from 1:1 to 2:1 frequency entrainment and vice versa were also observed. The results indicate that both amplitude modulation and relative phase change are utilized to stabilize the end-effector trajectory. In part II, a theoretical model is derived from three coupled nonlinear oscillators, in which the relative phases (phi) between the components and the relative joint amplitudes (rho) are treated as collective variables with arc curvature as a control parameter.

Self-organization of trajectory formation. II. Theoretical model.

Most studies of movement coordination deal with temporal patterns of synchronization between components, often without regard to the actual amplitudes the components make. When such a system is required to produce a composite action that is spatially constrained, coordination persists, but its stability is modulated by spatial requirements effected, we hypothesize, through the component amplitudes. As shown experimentally in part I, when a redundant three-joint system (wrist, elbow, and shoulder) is required to trace a specified arc in space, the joint angles may be frequency- and phased-locked even as the curvature of the trajectory is manipulated. Transitions between joint coordination patterns occur at a critical curvature, accompanied by a significant reduction in wrist amplitude. Such amplitude reduction is viewed as destabilizing the existing coordinative pattern under current task constraints, thereby forcing the joints into a more stable phase relationship. This paper presents a theoretical analysis of these multijoint patterns and proposes an amplitude mechanism for the transition process. Our model uses three linearly coupled, nonlinear oscillators for the joint angles and reproduces both the observed interjoint coordination and component amplitude effects as well as the resulting trajectories of the end effector.