Figure 2 (subject S1) shows a representative example of the torsional component of eye rotation (dark traces) with the original
(Fig. 2A) and the modified
(Fig. 2C) coil during the first four repetitions of the horizontal saccade paradigm (paradigm 1, see the Methods section). In the left eye (
Fig 2A ; original coil) the torsional component varied slightly with the 20° up and the 20° down gaze of this eye (note the undulation of the torsional trace over time), but not so in the right eye (
Fig 2C ; modified coil). Both coils, however, showed a small clockwise (CW) rotation with right gaze and a small counterclockwise (CCW) rotation with left gaze (
Figs 2B , original coil, and 2D, modified coil). The open arrows indicate that sometimes there were changes in dynamic torsion during and just at the end of saccades. This intra- and immediately post-saccadic “blip” torsion could be greater (e.g.,
Fig 2B , top open arrow; 2D, bottom open arrow) or less (e.g.,
Fig 2B , bottom open arrow, or
Fig 2D , top open arrow) than that expected from any change in static torsion associated with the change in eye position from the saccade itself. The blip torsion promptly decayed to a steady value at fixation.
To characterize the orientation of Listing’s plane for each eye in each paradigm, we calculated primary position. The amount by which primary position differed from the reference (straight ahead) position is reflected in the changes in torsion that are associated with different vertical and horizontal eye positions.
Figure 3 summarizes the primary positions of both eyes based on fixations immediately preceding vertical and horizontal saccades in all three subjects, using the original and the modified coils. The amount by which Listing’s plane was rotated temporally varied considerably in the four conditions. With the modified coil, Listing’s primary position was similar for horizontal saccades (mean temporal distance from zero: 2.9°,
Fig. 3A ) and vertical (3.3°,
Fig. 3C ) saccades. With the original coil, primary position was more temporal after horizontal (12.3°,
Fig. 3B ) than after vertical (6.1°,
Fig. 3D ) saccades. Vertical primary position, however, was similarly located with both coils (modified: 16.6°,
Fig. 3A and 11.5°,
Fig. 3C ; original: 14.2°,
Fig. 3B and 8.41°,
Fig. 3D ). The intersession difference of primary position was lower with the modified coil than the original coil, as depicted with the line lengths on top of the location of primary position. Most of the difference occurred with the original coils during horizontal saccades (see longest line between the two sessions in
Fig. 3B ), with the next largest difference being with original coils during vertical saccades. When using the modified coils, there were smaller differences in primary position between the two sessions.
We next asked how well our data could be fit to a single plane in each testing condition. The thickness of Listing’s plane, as reflected in the standard deviation of torsion from the plane, was calculated at each session separately and then summarized for all six eyes after the average was calculated from the two repetitions
(Fig. 4) . Listing’s plane was thinner with the modified coil after both horizontal (standard deviation of torsion from plane of 0.71° vs. 1.31°;
P = 0.002) and vertical (0.84° vs. 1.67°;
P = 0.02) saccades. We also asked whether there was any curvature of the plane using the “twist” factor. There was no statistically significant difference between the two types of coil with either horizontal or vertical saccades, but the curvature of Listing’s plane was significantly greater with vertical than horizontal saccades with either type of coil (modified coil: 0.38 vs. 0.20;
P = 0.014; original coil: 0.48 vs. 0.14;
P = 0.001, see
Fig. 4B ). The twist factor was always positive, indicating that the fitted surface showed the same type of curvature, not the inverse shape.
Next, Donders’ law was investigated from the same data set as just described, at 12 gaze directions for horizontal and for vertical saccades
(Fig. 5) . Donders’ law was better obeyed at gaze positions with the modified coil—less so with horizontal (
Fig. 5A versus 5B) than with vertical (
Fig. 5C versus 5D) saccades.
Figure 6 demonstrates the variability of the recordings on two different days from the modified and the original coils (right eye of subject S3, same coil). The inset depicts the start and the end position of the 40° saccades. Qualitatively, the torsional component measured on the two different days with the modified coil seemed more consistent in direction and amplitude than that recorded with the original coil (median torsional tracings of up to 10 repetitions). A slow drift after saccades was less common with the modified coil, as shown qualitatively in
Figures 6E and 6F . Considering all subjects, however, there were no statistically significant differences between the torsion measured in the two sessions with either the modified or the original coil.
Figure 7 shows the torsional component of eye movements analyzed in different gaze regions. Horizontal saccades of 10°, 20°, and 40° amplitudes
(Figs. 7A 7B) were analyzed separately at 20° elevation, 20° depression, and straight-ahead gaze. Regardless of which type of coil was used, there was approximately 6° torsion with 40° saccades, 3° torsion with 20° saccades, and 1.5° torsion with 10° horizontal saccades in elevation. In depression, the torsion was less, 4° torsion with 40° saccades, 2° torsion with 20° saccades, and 1° torsion with 10° horizontal saccades, respectively. Because Listing’s plane was predominantly rotated upward in the subjects
(Fig. 3) , there was more of a torsional change with horizontal saccades
(Figs. 3A 3B) , which is reflected in the vertical component of primary position, than with vertical
(Figs. 3C 3D) saccades, which is reflected in the horizontal component of primary position.
With vertical saccades, the pattern of torsion between the modified and original coils differed considerably
(Figs. 7C 7D) . With the original coil, more torsion change occurred when saccades were made in the nasal than in the temporal field of gaze. This increase of torsion toward the nose, implying cyclovergence, was seen with the original coil, but only with vertical saccades. With the modified coil, however, there was slightly more torsion at the right than the left gaze. In contrast, no cyclovergence was noted when comparing the torsion of the left and right eyes
(Fig 7C) . Again, note that the torsion change shown after horizontal saccades
(Figs. 7A 7B) can only be used to infer the vertical component of primary position, and the torsion change shown after vertical saccades
(Figs. 7C 7D) can only be used to infer the horizontal component of primary position.
We also investigated changes in intrasaccadic torsion, looking at the 40° saccade trials. For all three subjects,
Figure 8A summarizes the torsion (all dashed lines) associated with 40° horizontal saccades (solid line) along the horizontal meridian. The median traces show that only subject S1 (see closed arrows) had a clear blip—that is, a dynamic change in torsion during the saccade that was out of the range from that expected from the change in static torsion associated with the change in eye position produced by the saccade itself (
Fig. 8A , open arrows). The extent of blips was not influenced by the degree of elevation. There was also little difference in overall blip torsion between using the modified and the original search coil with horizontal saccades.
Figure 8B shows that for vertical saccades, too, there was little difference in blip torsion between the original and the modified search coil. However, as shown earlier, the change in static torsion with the different fixation positions was greater with the original coil than with the modified coil (closed arrows) and accounts for the differences in the location of primary position (see also
Fig. 3 ).