Article Figures & Data
Figures
- Figure 1.
Experimental setup and conditions. A, Subjects used a robotic arm to make planar reaching movements to visual targets that were displayed on an opaque screen that was suspended above the robot handle. The reach target and other visual markers used in the experiment were displayed using an LCD projector held from the ceiling. Direct visual feedback of the hand and arm was prevented by covering the space around the screen using a dark cloth (data not shown). Eye position was measured with an infrared camera attached to a helmet, and a bite bar was used to stabilize the head. B, The reach target, fixation point, and a cursor indicating robot position (beneath screen) were displayed on a 30 × 25 cm screen. The hand starting position was 23 cm away from the subjects’ cyclopean eye position. Angular position can either be expressed relative to the starting location of the hand (reach angle) or expressed relative to the cyclopean eye position (visual angle). C, Conditions in experiment 1 began with the display of a fixation cross (gray crosshair) and hand-cursor (small black circle). The dashed gray lines converging at the fixation point indicate the direction of gaze. The reach target (solid black square) was presented from 500 to 1000 ms. The target was extinguished (dotted black square) at 1000 ms (as well as fixation cross in the control condition only), and a variable memory delay (500, 1500, or 3000 ms in duration) followed in all conditions. In the remapping condition, the fixation cross jumped (black dotted arrow) at 1000 ms, requiring a saccade to the new fixation position. At the end of the memory delay, an auditory tone instructed the subjects to initiate their reach toward the remembered target location. The fixation cross and hand-cursor disappeared before start of the reach. D, Events in conditions of experiment 2 were arranged based on auditory tones delivered at 0, 900, and 1800 ms (gray circles on timelines). These tones corresponded to the following events: appearance of fixation cross, jump in fixation cross requiring saccade (remapping and combined only), and, finally, reach start. Reach target exposure times for each condition are labeled as “Target display” on the timelines. Variable exposure lengths (75, 200, 325, or 450 ms) were used in the static condition and the second target display of the combined condition that could also appear at variable positions of 0, −5, or +5° with respect to the first target display (pre-saccadic). In all conditions, visual markers (fixation cross and hand-cursor) still visible at 1650 ms were extinguished, signaling subjects to begin the reach at 1800 ms with the arrival of the final tone. Remap, Remapping.
- Figure 2.
Performance measure. The error in the reaching movement (solid black line) was quantified by the angle (θ) between the movement and target direction. Movement direction was defined by a line (gray dashed) connecting the start position (gray circle) and the end point of the reach (black dot). The angle (ϕ) between the fixation cross (black cross) and target with respect to the starting hand position was used as a measure of target eccentricity. The equivalent measure of target eccentricity in visual angles is also reported in the Results.
- Figure 3.
Single-subject reach performance in experiment 1. A, Average reach trajectory in the control (dashed line), static (solid line), and remapping (dotted line) conditions, separately for right (circle) and left (square) fixation. The lower box is the starting position. B, Reach end points relative to the target (located at origin) for the control, static, and remapping (Remap) conditions at memory delays of 0.5 and 3 s. For the static and remapping conditions, end points for both left (square) and right (circle) fixations are displayed.
- Figure 4.
Average results of experiment 1. A, Bias of the reach error averaged over fixation (left and right) and subjects. Positive values indicate a bias away from the fixation point. The bias in the control condition for each subject was used as a baseline. B, SD of reach errors as a function of condition and memory interval. Remap, Remapping.
- Figure 5.
Single-subject reach performance in experiment 2. A, Sample eye and hand trajectories of the combined condition (target shift) in the x-direction. Gray circles on the time axis indicate when auditory tones were given. B, Reach end points relative to the target (origin) in the control, remapping (Remap), static, and combined conditions. The end points for both the left (square) and the right (circle) fixation conditions and the 75 and 450 ms exposure levels are shown.
- Figure 6.
Average reach variance in experiment 2. A, SD (st. dev.) in the control, remapping (Remap), static (solid black line; different target exposures), and combined (dotted gray line; different post-saccadic target exposures under no target shift) conditions averaged across fixations and subjects. The mean optimal variance (dashed black line) was calculated individually for each subject based on their static and remapping variability. Motor noise (control condition) was first subtracted from the individual variances (static and remapping) and then added back to the resulting optimal estimate calculated by Equation 6. B, Average optimal weight of the static estimate (dashed black line) calculated (Eq. 5) separately for each subject based on the variability data in A (static and remapping conditions). We also show the actual weight (dotted gray line) found by fitting movement direction data of Figure 7 to Equation 4. These weights were calculated separately for the shift-away and shift-toward trials of the combined condition, and their averages are reported.
- Figure 7.
Average reach direction in experiment 2. A, Mean angular reach direction averaged (over fixation and subject) for the remapping (Remap; black circle) and static (solid black line for all exposures) conditions. The predicted reach direction in the combined condition in which target estimate is based on post-saccadic target exposure [dotted black line both for a post-saccadic target shifted away (square) and shifted toward gaze (triangle)] is also shown. All reach directions are plotted with respect to the pre-saccadic target position of the combined condition (0° grid line). Reach directions are assigned a positive sign if directed away from gaze and a negative sign if directed toward gaze. B, Mean angular reach direction of the combined condition [dotted gray line both for a post-saccadic target shifted away (square) and shifted toward gaze (triangle)] and the predicted optimal reach direction (dashed black line for each shift type). Measures were averaged over subjects and fixations.
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