John J. Buchanan

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

SummarySubjects 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 (non-homologous 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.

Spontaneous recruitment and annihilation of degrees of freedom in biological coordination

Abstract Whereas bifurcations within an already active set of components are well-known in biological coordination (e.g. gait transitions), less well understood is the process by which previously quiescent degrees of freedom are spontaneously activated. We introduce a simple paradigm to explore how complex, biological systems flexibly recruit and annihilate degrees of freedom according to parametric task requirements. A sequence of transitions within and across planes of motion is observed as a control parameter is varied. Such transitions are invariably preceded by enhancement of fluctuations in trajectory related variables. Our results suggest a theoretical model in which the main qualitative changes observed experimentally are a consequence of two consecutive Hopf bifurcations.

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°), simultaneous coordination of wrist flexion/elbow flexion and wrist extension/elbow extension (termed in-phase); and (2) forearm prone (forearm angle 160°), 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° 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.

Multifunctionality and switching in the coordination dynamics of reaching and grasping

Abstract The coordination dynamics of reaching and grasping an object was studied kinematically. Subjects reached for, grasped and rotated a bar that was positioned at thirty-five different orientations corresponding to positions on a clockface. Object orientation was systematically varied as a control parameter in either a clockwise or counterclockwise direction. Two reaching patterns were defined: (1) forward projection of the hand with supination of the forearm (anti-phase reach); and (2) forward projection of the hand with pronation of the forearm (in-phase reach). The relative timing between wrist forward projection and wrist angular rotation remained quite consistent across conditions. Switching between patterns and hysteresis was observed for a range of object positions. Further, pertubations of the bar across the hysteresis region induced switching between reach patterns. The trajectory of the end effector, whether rectilinear or curvilinear, was dependent on whether the pertubation did or did not induce pattern switching. In the latter case, previously quiescent biomechanical degrees of freedom were spontaneously activated.

Perceptual and attentional influences on continuous 2:1 and 3:2 multi-frequency bimanual coordination.

Two experiments were conducted to determine if multi-frequency (2:1 and 3:2) coordination between the limbs is enhanced when integrated feedback is provided in the form of Lissajous plots, attention demands are reduced, and attempts to consciously coordinate the limbs are not encouraged. To determine the influence of vision of the limbs, covered and uncovered limb groups were provided online Lissajous feedback. To determine the impact of the Lissajous feedback, a control group that was not provided Lissajous feedback was also tested. The data indicated remarkably effective performances after 5 min of practice when limbs were covered and Lissajous feedback was provided. When Lissajous feedback was provided and vision of the limbs was permitted, performance deteriorated. Performance by the group not provided Lissajous feedback was quite poor. The findings suggest that some of the difficulty associated with producing difficult bimanual coordination patterns are due to the less than optimal perceptual information available in various testing situations and the attentional focus imposed by the participant.

Self-organization of trajectory formation. I. Experimental evidence

Abstract. 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, κ. Arcs were displayed on a computer screen in a decreasing and increasing κ 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 κ was systematically increased and decreased, switching between relative phase patterns was observed around critical curvature values, κc. 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 (φ) between the components and the relative joint amplitudes (ρ) are treated as collective variables with arc curvature as a control parameter.

Voluntary control of postural equilibrium patterns

The ability to voluntarily transit from one whole-body movement to another is based on the multisensory integration of visual, vestibular, and somatosensory information. The role of functional sensory ranges and mechanical constraints on the ability to voluntarily transit between whole-body movements was studied by requiring subjects to switch from a head-fixed-to-surface to head-fixed-in-space postural pattern (and vice versa). The head-fixed-to-surface pattern required an erect stance characterized by an in-phase relationship between center of pressure (CoP) and platform motion. The head-fixed-in-space pattern required subjects to fix trunk-head position in-space while producing an anti-phase relationship between CoP and platform motion. The voluntary transition was performed with and without vision while standing on a surface oscillating in the anterior-posterior (A/P) direction. The support surface oscillated at five frequencies (0.2-1Hz) with amplitude fixed at 15cm. The voluntary transition was initiated with an auditory cue. The appropriate CoP-platform phase relationship for the two postural patterns was produced for all frequencies with and without vision. Upper-trunk kinematics revealed that subjects often failed to produce the head-fixed-to-surface pattern for frequencies >/=0.6Hz, while producing the head-fixed-in-space pattern at all frequencies with vision. Without vision, neither pattern was produced consistently based on upper-trunk kinematics. These findings demonstrate separate control processes for upper- and lower-body motion and that functional sensory ranges and mechanical constraints can facilitate or inhibit voluntary production of whole-body movements based on these control processes. The results are discussed in reference to neurological substrates that may be involved in the planning and execution of motor set-switching. The experimental protocol we employ may also have application as a diagnostic tool for the evaluation of postural deficits.

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 pendulums 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.

Systematic scaling of target width: dynamics, planning, and feedback.

The target width of a single target in a two-target reciprocal aiming task was scaled from small (ID = 5.85) to large (ID = 2.85) and large-to-small within individual trials with movement amplitude fixed. Scaling target width produced a transition in the end-effectors dynamics and based on a measure of movement harmonicity, the transition was sensitive to the initial conditions but not to the direction of target width scaling. Hysteresis emerged in a variety of kinematic measures suggesting that the interdependency of planning and feedback control processes was sensitive to initial conditions as well as the direction of target width scaling. Practice increased the efficiency of the reciprocal movements and produced changes in movement time and the measure of harmonic motion that revealed a tuning of the end-effectors dynamics to cyclical motion over as large of range of IDs as possible. The tuning occurred through the modulation of time spent accelerating and decelerating the end-effector for IDs outside the range of 3.85-4.26. The results are discussed with reference to a critical ID boundary that separates regions of parameter space wherein the end-effectors dynamics are more cyclical (limit-cycle) or discrete (fixed-point) in nature.

The spontaneous recruitment and suppression of degrees of freedom in rhythmic hand movements

Abstract In most studies examining pattern switching in biological coordination, emphasis is placed on identifying the mechanisms underlying bifurcations in an already active set of components. Less well understood are the processes by which quiescent degrees of freedom (df) are recruited and active df suppressed. To examine such behavior, we studied four bimanual and two unimanual coordination patterns. Subjects produced the patterns in time with an auditory metronome whose frequency increased from 1.5 to 4.25 Hz in 0.25 Hz steps. Interlimb transitions from asymmetric to symmetric patterns in a motion plane occurred at critical cycling frequencies, f1. Spatial transitions, characterized by recruitment of y-(vertical) and suppression of x-(horizontal) motion, also occurred at critical cycling frequencies, f2. This recruitment-suppression process was either abrupt (2–3 cycles) or gradual (1 to 6 plateaus) where the finger-tips traversed an elliptical orbit in x, y space. Similar spatial transitions were observed in unimanual conditions. The results are discussed in reference to the problem of how task-specific coordination patterns are modified. The Hopf bifurcation is presented as a generic mechanism underlying the recruitment and suppression of df. Similarities between the four component bimanual pattern dynamics and the coordination dynamics of four limb patterns (e.g., in quadrupeds) are discussed.