Cerebellar reaching ataxia is exacerbated by timing demands and assistive interaction torques

Abstract

Individuals with cerebellar ataxia face significant challenges in controlling reaching, especially when multi-joint movements are involved. This study investigated the effects of kinematic and dynamic demands on reaching using a home-based virtual reality task. Participants with and without cerebellar ataxia reached to target locations designed to elicit a range of coordination strategies between shoulder and elbow joint movements. Compared with control subjects, cerebellar subjects presented greater initial reaching direction errors, larger hand trajectory curvatures, and more variability. Kinematic simulations indicated that early hand movement errors were sensitive to the required onset times and rates of joint movements and were most impaired when opposite direction joint movements were required (e.g., elbow extension with shoulder flexion). Dynamic analysis revealed that cerebellar participants' movements were more impaired in reaching directions where interaction torques would normally assist the desired elbow and shoulder movements. These reach directions were also those that required joint movements in opposite directions. Overall, our data suggest that reaching deficits in cerebellar ataxia result from (1) the early-phase motion planning deficits that are exacerbated by stringent timing coordination requirements and (2) the inability to compensate for interaction torques, particularly when they assist the intended movement.

Keywords: Ataxia; Cerebellum; Coordination; Dynamics; Kinematics; Reaching.

Fig. 1

Task diagram. (A) Initial position: The shoulder joint is angled at 40 degrees from the ground direction, and the elbow joint is at 90 degrees, positioning the hand at the height of the right shoulder. The positive direction for the joint angles is counterclockwise when viewed from the right. (B) Target Locations: The starting point and all the targets are located on a sagittal plane that aligns with the right shoulder. The hand paths leading to four single-joint targets are illustrated in red, whereas those leading to four two-joint targets are indicated in blue.

Fig. 2

Hand paths. (A) Mean hand path trajectories of all control subjects (left: sagittal view from the right; right: front view). (B) Mean hand path trajectories of all cerebellar ataxia subjects (left: sagittal view from the right; right: front view). Individual lines represent the mean curves of each subject, and the thick black lines denote the mean trajectories of each subject group. The blue and red lines correspond to hand paths to single-joint and two-joint targets respectively. The hand trajectories of the different subjects were scaled to the average target distances of all the subjects. Axes display directions: the Y-axis (up-down) and X-axis (anterior–posterior for the sagittal view, medial–lateral for the front view). Units are in meters.

Fig. 3

Kinematic measures of the hand path. Box plots showing the median (line), upper and lower quartiles (box), extremes (whisker) and outliers (individual points). (A) Maximum deviation ratio. (B) Path ratio. (C) 2D initial angle. The sign of hand movement and initial direction was defined as relative to the target direction connecting the starting point and the target, with counterclockwise considered positive when viewed from the right side of the participants. *p < 0.05, **p < 0.001. (D) Mean hand path trajectories of representative control and cerebellar ataxia subjects. The Y-axis represents the upward (positive) and downward (negative) directions, and the X-axis represents the anterior (positive) and posterior (negative) directions, measured in meters. The blue and red lines represent hand trajectories to single-joint and two-joint targets, respectively.

Fig. 4

(A) Acceleration, deceleration, and total reaching times (sec) for the control and cerebellar ataxia groups. (B) Box plots for peak hand velocity (m/sec) of the controls and cerebellar groups for each target.

Fig. 5

Joint angle trajectories and inter-subject variations. (A) Joint angle trajectories for eight target locations, presented in the normalized time. The first and second columns display the individual mean and group mean trajectories for the control and cerebellar groups, respectively. The third column shows only group mean trajectories for both groups. (B) Joint angle variation (in degrees) measured by the standard deviation of individual joint angles at 50% of the reaching time.

Fig. 6

Simulated hand paths resulting from variations in shoulder and elbow joint movements. (A) Baseline template of typical joint motions (average joint motion of the control group). (B) Simulated changes in shoulder joint onset times. Shoulder joint angle trajectories with onset times 100 ms earlier or later than those of the elbow joint are shown in green and purple, respectively. (C) Simulated changes in the shoulder joint angle rates. The red and blue shoulder angle trajectories represent cases where the relative rate ratios between the shoulder and elbow are 1.3 and 0.7, respectively. (D,E) Joint angle trajectories over time for each condition. The black dots indicate the points where the hand reaches 25% of the distance from the starting position in the direction of the target. At these points, the hand’s deviation angle from the target line was calculated.

Fig. 7

Kinematic simulations of the hand deviation from the target directions for two-joint targets: (A) target T5 , (B) T6, (C) T7, and (D) T8. The X-axis shows the onset time difference between the shoulder and elbow joints, where a gray vertical line represents the average onset time difference in controls. The Y-axis indicates the ratio of joint change rates between the shoulder and elbow joints, with a gray horizontal line representing the average rate ratio for the control group. Each subject’s joint onset time and joint change rate are marked individually, enabling a comparison between the predicted hand deviation from the simulation and the measured hand deviation from the experiment. Confidence ellipses (80%) are shown for controls (black) and the cerebellar group (white).

Fig. 8

Group mean joint torque for two-joint targets: (A) target T5 (shoulder flexion and elbow flexion, (B) target T6 (shoulder flexion and elbow extension, (C) target T7 (shoulder extension and elbow flexion, and (D) target T8 (shoulder extension and elbow extension. Subpanel a: shoulder joint torques in the control group. subpanel b: elbow joint torques in the control group. subpanel c: shoulder joint torques in the cerebellar ataxia group. subpanel d: elbow joint torques in the cerebellar ataxia group.

Fig. 9

Box plots showing zero-lag cross-correlation between dynamic muscle torque and interaction torque in the shoulder and elbow joints for two-joint targets (*: p < 0.05).

Fig. 10

Box plots illustrating the contribution index. (*p < 0.05, **p < 0.01, and ***p < 0.001).