John Peter Scholz

Differences between 12 left-brain (LCVA, 65.4 ± 11.7 years old) and 10 right-brain (RCVA, 61 ± 12.1 years old) chronic stroke survivors and 10 age-matched control adults in coordinating specific joint motions of the arm to stabilize hand path when reaching to a central target were investigated in this study. The importance of coordinating joints to stabilize hand path was tested by comparing results from uncontrolled manifold (UCM) analysis performed on experimental data versus simulated data where the covariation (coordination) between particular joint motions was removed from the original data set. UCM analysis allowed estimation of the joint configuration variance magnitude that led to hand path variability (V _ORT), where the extent of increase in V _ORT after removing a joint’s covariation indicated how well coordinated its motion actually was with those of the other joints. The more strongly coordinated a joint was with other joints, the greater effect removal of its covariance should have on indices of hand path stability. For the paretic arm of stroke survivors, simulated removal of a joint’s covariation, mainly that of shoulder with elbow and wrist, led to less change in the magnitude of V _ORT compared to the same arm of control subjects. These findings confirm a reduced ability of the motion of proximal joint from paretic arm to combine flexibly with motions of the distal joints to stabilize hand path.

The link between visual information and postural control was investigated based on a multi-degree-of-freedom model using the framework of the uncontrolled manifold (UCM) hypothesis. The hypothesis was that because visual information specifies the position of the body in space, it would couple preferentially into those combinations of degrees of freedom (DOFs) that move the body in space and not into combinations of DOFs that do not move the body in space. Subjects stood quietly in a virtual reality cave for 4-min trials with or without a 0.2, 2.0 Hz, or combined 0.2 and 2.0 Hz visual field perturbation that was below perceptual threshold. Motion analysis was used to compute six sagittal plane joint angles. Variance across time of the angular motion was partitioned into (1) variance associated with motion of the body and (2) variance reflecting the use of flexible joint combinations that keep the anterior–posterior positions of the head (HD_POS) and center of mass (CM_POS) invariant. UCM analysis was performed in the frequency domain in order to link the sensory perturbation to each variance component at different frequencies. As predicted, variance related to motion of the body was selectively increased at the 0.2-Hz drive frequency but not at other frequencies of sway for both CM_POS and HD_POS. The dominant effect with the 2.0-Hz visual drive also was limited largely to variance related to motion of the body.

Studies of human upright posture typically have stressed the need to control ankle and hip joints to achieve postural stability. Recent studies, however, suggest that postural stability involves multi degree-of-freedom (DOF) coordination, especially when performing supra-postural tasks. This study investigated kinematic synergies related to control of the body’s position in space (two, four and six DOF models) and changes in the head’s orientation (six DOF model). Subjects either tracked a vertically moving target with a head-mounted laser pointer or fixated a stationary point during 4-min trials. Uncontrolled manifold (UCM) analysis was performed across tracking cycles at each point in time to determine the structure of joint configuration variance related to postural stability or tracking consistency. The effect of simulated removal of covariance among joints on that structure was investigated to further determine the role of multijoint coordination. Results indicated that cervical joint motion was poorly coordinated with other joints to stabilize the position of the body center of mass (CM). However, cervical joints were coordinated in a flexible manner with more caudal joints to achieve consistent changes in head orientation. An understanding of multijoint coordination requires reference to the stability/control of important performance variables. The nature of that coordination differs depending on the reference variable. Stability of upright posture primarily involved multijoint coordination of lower extremity and lower trunk joints. Consistent changes in the orientation of the head, however, required flexible coordination of those joints with motion of the cervical spine. A two-segment model of postural control was unable to account for the observed stability of the CM position during the tracking task, further supporting the need to consider multijoint coordination to understand postural stability.

Motor equivalence expresses the idea that movement components reorganize in the face of perturbations to preserve the value of important performance variables, such as the hand's position in reaching. A formal method is introduced to evaluate this concept quantitatively: changes in joint configuration due to unpredictable elbow perturbation lead to a smaller change in performance variables than expected given the magnitude of joint configuration change. This study investigated whether motor equivalence was present during the entire movement trajectory and how magnitude of motor equivalence was affected by constraints imposed by two different target types. Subjects pointed to spherical and cylindrical targets both with and without an elbow joint perturbation produced by a low- or high-stiffness elastic band. Subjects' view of their arm was blocked in the initial position, and the perturbation condition was randomized to avoid prediction of the perturbation or its magnitude. A modification of the uncontrolled manifold method variance analysis was used to investigate how changes in joint configuration on perturbed vs. nonperturbed trials (joint deviation vector) affected the hand's position or orientation. Evidence for motor equivalence induced by the perturbation was present from the reach onset and increased with the strength of the perturbation after 40% of the reach, becoming more prominent as the reach progressed. Hand orientation was stabilized more strongly by motor equivalent changes in joint configuration than was three-dimensional position regardless of the target condition. Results are consistent with a recent model of neural control that allows for flexible patterns of joint coordination while resisting joint configuration deviations in directions that affect salient performance variables. The observations also fit a general scheme of synergic control with referent configurations defined across different levels of the motor hierarchy.

This study investigated pointing movements in 3D asking two questions: (1) Is goal-directed reaching accompanied by self-motion, a component of the joint velocity vector that leaves the hand’s movement unaffected? (2) Are differences in the terminal joint configurations among different speeds of reaching motor equivalent (i.e., terminal joint configurations differ more in directions of joint space that do not produce different pointer-tip positions than in directions that do) or non-motor equivalent (i.e., terminal joint configurations differ equally or more in directions of joint space that lead to different pointer-tip positions than in directions that do not affect the pointer-tip position). Subjects reached from an identical starting joint configuration and pointer-tip location to targets at slow, moderate, and fast speeds. Ten degrees of freedom of joint motion of the arm were recorded. The relationship between changes in the joint configuration and the three-dimensional pointer-tip position was expressed by a standard kinematic model, and the range- and null subspaces were computed from the associated Jacobian matrix. (1) The joint velocity vector and (2) the difference vector between terminal joint configurations from pairs of speed conditions were projected into the two subspaces. The relative length of the two components was used to quantify the amount of self-motion and the presence of motor equivalence, respectively. Results revealed that reaches were accompanied by a significant amount of self-motion at all reaching speeds. Self-motion scaled with movement speed. In addition, the difference in the terminal joint configuration between pairs of different reaching speeds revealed motor equivalence. The results are consistent with a control system that takes advantage of motor redundancy, allowing for flexibility in the face of perturbations, here induced by different movement speeds.