Cerebellar ataxia impairs modulation of arm stiffness during postural maintenance

Abstract

Impedance control enables humans to effectively interact with their environment during postural and movement tasks, adjusting the mechanical behavior of their limbs to account for instability. Previous work has shown that people are able to selectively modulate the end-point stiffness of their arms, adjusting for varying directions of environmental disturbances. Behavioral studies also suggest that separate controllers are used for impedance modulation versus joint torque coordination. Here we tested whether people with cerebellar damage have deficits in impedance control. It is known that these individuals have poor motor coordination, which has typically been attributed to deficits in joint torque control. Subjects performed a static postural maintenance task with two different types of directional force perturbations. On average, patients with cerebellar ataxia modified stiffness differentially for the two perturbation conditions, although significantly less than age-matched control subjects. Thus cerebellar damage may impair the ability to modulate arm impedance. Surprisingly, the patients' intact ability to generally alter their limb stiffness during the postural task (albeit less than age-matched control subjects) improved their movement performance in a subsequent tracing task. The transfer of stiffness control from the static to the movement task may be a strategy that can be used by patients to compensate for their motor deficits.

Keywords: arm stiffness; cerebellar ataxia; impedance control.

Fig. 1.

Experimental protocol. A: subjects first performed a Familiarization session to acquaint themselves with tracing the parallelogram template (B, 1st column). In the 6 Baseline Pre blocks, baseline arm impedance was estimated with trapezoidal position displacements in 8 directions (representative hand trajectories shown in black). Only data from the first 300 ms were used for impedance estimates (B, 2nd column). Next, subjects performed 6 blocks of a postural maintenance task in the Clockwise (CW) Perturbation session. Sinusoidal force perturbations were applied to the hand along an axis rotated 45° clockwise to the major axis of each subject's baseline stiffness ellipse. Subjects attempted to stay within the target and resist the perturbations (representative hand trajectories shown in red) (B, 3rd column). Subjects then performed the same postural maintenance task in the Isotropic Perturbation session. Perturbations were applied in 8 directions distributed evenly around a circle, with a direction-dependent magnitude (representative hand trajectories shown in blue) (B, 4th column). During the CW and Isotropic blocks, hand movement was constrained to the perturbation axis via a force channel. Position displacements were pseudorandomly presented during the perturbation blocks to measure changes in arm impedance. Finally, 3 Baseline Post blocks were performed to again measure baseline arm impedance. The trace task was performed at the end of every block to compare performance between the different sessions.

Fig. 2.

Kinematics of postural maintenance task. A: representative perturbation kinematics (mean ± SD) of a control subject and a patient in response to CW (top) and Isotropic (bottom) perturbations. Position trajectories were collapsed over all directions, where a positive value represents displacement in the direction of the force perturbation. The perturbation was applied between the dotted lines. The shaded gray region represents the area in which the hand cursor was completely within the target. B: group data for the time spent outside the target (mean ± SE). The timer started upon initiation of the force perturbation and ended when the subject's hand was inside the target and held there for 1 s. C: overshoot of the target (mean ± SE), after the force perturbation, in control subjects (C) and patients (P). Overshoot was measured as the maximum negative displacement (in the direction opposite the applied perturbation). Data were averaged over the last 20 trials of each block, over all 6 blocks. *P < 0.05.

Fig. 3.

Changes in stiffness between CW and Isotropic conditions. A: various changes to subjects' stiffness were observed during the postural maintenance task in the presence of force perturbations (mean ± SE). Stiffness modulation between the CW and Isotropic conditions was quantified by changes in the hand stiffness ellipse orientation (1st plot; positive value represents counterclockwise rotation), aspect ratio (2nd plot; negative value represents rounder shape), and size (3rd plot; positive value represents larger size). Changes were also observed in the joint stiffness ratio (4th plot), which represents the relative contribution of shoulder and elbow stiffness. The ratio is between the R_ss and R_ee components of the joint stiffness matrix. Dots represent outliers (>2 SD from mean of all subjects). B: size of the hand stiffness ellipse during the Baseline (Pre and Post combined), CW, and Isotropic sessions (mean ± SE). *P < 0.05.

Fig. 4.

Hand stiffness ellipses. Estimated stiffness ellipses from the CW and Isotropic conditions are shown for all control subjects (top) and patients (bottom). Stiffness ellipses were estimated using impedance measurements from all 6 blocks of the respective perturbation sessions. The major axes are extended to highlight changes in orientation. Probability density functions P[θ] for the ellipse orientation in degrees θ, as determined by a bootstrapping procedure, are plotted for each subject. *P < 0.05.

Fig. 5.

Trace performance. A: traces from a representative patient during the Baseline Pre, CW, Isotropic, and Baseline Post sessions. Trace area error between the template (blue) and patient's hand path (black) is shown in gray. B: the size of the hand stiffness ellipse (mean ± SE) was greater in the Perturbation sessions (CW and Isotropic measurements averaged) than in the Baseline sessions (Pre and Post measurements averaged) for both control subjects and patients. However, only the patients showed an improvement in trace area error between the Baseline and Perturbation sessions. Statistics represent the results of 1-way paired t-tests (*P < 0.05). C: time to perform the tracing task did not differ between groups or conditions.