1Department of Psychology, Seoul National University, Seoul 151-742, Korea; 2Department of Neurology, Johns Hopkins University, Baltimore, Maryland 21287; and 3Department of Neurology, Zurich University Hospital, CH-8091 Zurich, Switzerland
![]() |
ABSTRACT |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Lee, Choongkil, David S. Zee, and Dominik Straumann. Saccades From Torsional Offset Positions Back to Listing's Plane. J. Neurophysiol. 83: 3241-3253, 2000. Rapid eye movements include saccades and quick phases of nystagmus and may have components around all three axes of ocular rotation: horizontal, vertical, and torsional. In this study, we recorded horizontal, vertical, and torsional eye movements in normal subjects with their heads upright and stationary. We asked how the eyes are brought back to Listing's plane after they are displaced from it. We found that torsional offsets, induced with a rotating optokinetic disk oriented perpendicular to the subject's straight ahead, were corrected during both horizontal and vertical voluntary saccades. Thus three-dimensional errors are synchronously reduced during saccades. The speed of the torsional correction was much faster than could be accounted for by passive mechanical forces. During vertical saccades, the peak torsional velocity decreased and the time of peak torsional velocity was delayed, as the amplitude of vertical saccades increased. In contrast, there was no consistent reduction of torsional velocity or change in time of peak torsional velocity with an increase in the amplitude of horizontal saccades. These findings suggest that 1) the correction of stimulus-induced torsion is neurally commanded and 2) there is cross-coupling between the torsional and vertical but not between the torsional and horizontal saccade generating systems. This latter dichotomy may reflect the fact that vertical and torsional rapid eye movements are generated by common premotor circuits located in the rostral interstitial nucleus of the medial longitudinal fasciculus (riMLF). When horizontal or vertical saccade duration was relatively short, the torsional offset was not completely corrected during the primary saccade, indicating that although the saccade itself is three-dimensional, saccade duration is determined by the error in the horizontal or the vertical, but not by the error in the torsional component.
![]() |
INTRODUCTION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
The brain stem saccade generators produce rapid
eye movements, including quick phases, that rotate the globe around all
three axes: horizontal, vertical, and torsional. The paramedian
reticular formation in the pons (PPRF) encodes signals for the
horizontal component of saccades, and the rostral interstitial nucleus
of the medial longitudinal fasciculus (riMLF) in the midbrain encodes signals for the vertical and torsional components of saccades. Voluntary control of torsional rapid eye movements is limited, however;
torsional quick phases do occur during vestibular stimulation but only
a rare subject can make voluntary torsional saccades (Balliet
and Nakayama 1978). Nevertheless, several investigators have
suggested that the oculomotor system takes three-dimensional eye
orientation into account when generating voluntary saccades (Klier and Crawford 1998
; Tweed et al.
1998
). Van Opstal et al. (1996)
also suggested
that there is active neural control of torsion associated with
saccades; electrical stimulation in the nucleus reticularis tegmenti
pontis (NRTP) perturbed the torsional orientation of the eye, which was
corrected in association with the next horizontal or vertical saccade.
Lesions in this same area interfered with corrections of torsional offsets.
Although three-dimensional eye orientation appears to be neurally
commanded, any torsional movement during horizontal or vertical saccades with head stationary is normally minimized as dictated by
Listing's law, except for a small torsional transient, or "blip", up to 1-2° (Bruno and Van den Berg 1997;
Straumann et al. 1995
, 1996
; Tweed
et al. 1994
). Listing's law states that the three-dimensional orientation of all rotation axes that bring the eyes from the reference
position to an eccentric position lie in a single plane that is roughly
perpendicular to the straight ahead eye position (Helmholtz
1867
). Listing's law is a specification of Donders' law,
which states that for every eccentric eye position there is a specific
torsional orientation of the eye (Donders 1848
). It is
Listing's law that formulates the mathematical relation between the
torsional orientation of the eye and the horizontal-vertical direction
of gaze and quantitatively specifies "desired" torsional orientation. The rationale of Listing's or Donders' laws is not firmly established; no single motor or sensory hypotheses is completely satisfactory (Hepp et al. 1997
; Melis and van
Gisbergen 1995
; Tweed et al. 1998
).
In this study, we used roll optokinetic stimulation, around the line of sight of subjects with their heads upright and stationary, to produce torsional errors that drove the eyes out of Listing's plane. We asked how such torsional errors were corrected during subsequent horizontal and vertical saccades. We specifically investigated the dynamic properties of the movements that corrected such torsional errors (and brought the eyes back to Listing's plane) and how the torsional corrections interacted with the horizontal and vertical components of voluntary saccades.
![]() |
METHODS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Subjects
Four normal male subjects (CL, DZ, MH, and NH, 21-52 yr of age) participated in this study. The nature and possible consequences of the experiments were explained to each subject, and informed consent, approved by The Johns Hopkins University Committee on Clinical Investigation, was obtained. The subjects had no prior history of ocular motility disorders and were taking no medications.
Optokinetic stimulus
A rotating circular flat disk (Fig. 1) was used for optokinetic stimulation and so induced torsional errors. The disk was positioned in front of the subjects, 0.52 m from their eyes with the center of the disk at eye level. At this distance the radius of the disk was 40°. The surface of the disk was equally divided into 30 radial segments with an alternating black and white pattern. White circular strips were concentrically pasted on the surface at eccentricities of 5, 10, 15, and 20° to prevent intensity modulation of laser targets during the disk rotation. Two lasers were used to elicit horizontal and vertical saccades. The light from one laser was projected to the center of the disk and from the other projected to one of eight loci spaced 5° apart rightward or upward from the center as shown in Fig. 1. A motor rotated the disk clockwise or counterclockwise at a constant velocity of either 10 or 30°/s.
|
Eye movement recording
Movements of both eyes about all three rotation axes were
simultaneously recorded using dual search coils (Skalar, Netherlands). The description of the coil system and its calibration can be found in
Straumann et al. (1995). In brief, three pairs of field coils were wound in a cubic frame (Remmel 1984
), with
the length of each side 1.02 m. Voltage offsets were nullified
with the scleral annuli placed in a metallic tube. For a calibration,
the maximal voltages induced in each of the two detection coils by the
three magnetic fields were determined by aligning the sensitivity
vector of the detection coils with the three orthogonal field coil
axes, using a gimbal system located at the center of the field coil frame. Signals from the annuli were phase-detected (field frequencies of 55.5, 83.3, and 42.6 kHz), and the analog signals from the corresponding 12 channels were sampled at a rate of 500 Hz with a
resolution of <0.1° (peak-to-peak noise level). These signals were
then normalized to the maximal voltage vectors, and the sensitivity vectors of the direction and torsion coils were orthogonalized. Rotation vectors were calculated to describe the three-dimensional orientation of the scleral annuli (Haustein 1989
). We
shall describe the three components of rotation vectors in angular
degrees whereby x, y, and z describe the
torsional, vertical, and horizontal directions, respectively. According
to the right-hand rule, leftward, downward, and extorsion of the right
eye and intorsion of the left eye are positive.
Experimental procedures
Subjects were seated inside the coil frame so that the center of the interpupillary line was aligned with the center of the frame. After the conjunctiva was anesthetized with a few drops of 0.5% proparacaine hydrochloride, the dual search coils were mounted on the eyes. The head was held still with a bite bar and dental impression material. The optokinetic disk (Fig. 1) was placed in front of the subject at the opening of the coil frame. Featureless black cardboard and black curtains covered the top and side openings of the coil frame. Each subject participated in two recording sessions: one for a horizontal and the other for a vertical series of saccades. In each session, subjects participated in the three paradigms explained below with both eyes viewing.
PARADIGM I. This was the main experimental paradigm, and its purpose was to compare torsional components of saccades made with and without the torsional offset induced with the optokinetic disk (Fig. 2). Subjects made saccades between two laser targets: one at the center of the disk and the other at one of four eccentricities, 5, 10, 15, and 20°, to the right (horizontal series), or up (vertical series). Brief tones (arrows in Fig. 2) signaled when subjects were to make a saccade to the eccentric target and a pair of brief tones signaled when to make saccades back to the center target. A trial started with subjects fixing on the laser target at the center of the disk. Fifty percent of the centrifugal saccades toward eccentric laser targets were made in an otherwise completely dark room without any torsional offset. These saccades will be referred to as D-saccades. Before the remaining 50% of the centrifugal saccades, the rotating optokinetic disk was made visible for a few seconds so that the torsional position of the eye was driven out of the resting position, i.e., away from Listing's plane. The single tone then sounded to signal the time to make the centrifugal saccades. The overhead light went off when the eye position broke a 2° electronic window around the center target, i.e., just after the saccade began. These saccades will be referred to as L-saccades. For each saccade eccentricity, four conditions were used: two disk speeds (10 or 30°/s) and two directions of disk rotation [clockwise (CW) or counterclockwise (CCW)], relative to the experimental subject. The location of the eccentric laser target was changed between blocks by a computer-driven mirror galvanometer. Within a session (horizontal or vertical), there were 20 blocks (5 amplitudes × 2 directions × 2 speeds), each consisting of four continuous repetitions of the trial shown in Fig. 2. Thus from a single successful block four D-saccades and four L-saccades were collected.
|
PARADIGM II. In this paradigm, subjects fixed on the center target while the disk was rotating, and no saccades were made. While subjects were fixing on the central target, the overhead light went on and off. The purpose of this paradigm was to examine the time course of passive recovery in torsional eye positions, and to obtain data on the dynamic properties of pure torsional quick phases.
PARADIGM III. This paradigm was the same as paradigm I, except that the overhead light stayed on during centrifugal saccades. The purpose of this paradigm was to evaluate the effect of extinguishing the light during saccades on the corrective torsional movements. Four blocks of data were collected using this paradigm for each session: two speeds × two directions of disk rotation × one saccade amplitude of 10°.
Before and after each experimental session, data for fitting Listing's plane were collected while subjects fixed on six small dots marked on the resting optokinetic disk, equally spaced apart at 12.5° of eccentricity.Data analysis
Rotation vectors describing three-dimensional eye position were
calculated every 4 ms with [0,0,0] taken as the first sample of the
session during fixation of the central target. To determine the amount
of torsion specifically associated with saccades, called the
"dynamic" torsion, we corrected for changes in static torsion that
simply depended on static horizontal and vertical positions of the eye
by subtracting the "false" torsion that depends on the choice of
the reference position, so-called reference-position-dependent torsion
(Suzuki et al. 1994). This procedure, described
elsewhere (Straumann et al. 1995
), is equivalent to
analyzing the trajectories after rotating the eye position data such
that Listing's plane is perpendicular to the head-fixed coordinate
system. For each block of paradigm I, the torsional
components of rotation vectors before, and 2 s after the onset of
the saccade made to the eccentric target, were obtained to be used for
the correction for any change in static torsion. Any dynamic torsion
then was defined as the deviation from this estimate of static
torsional position.
A displacement vector, d, was calculated to describe the
magnitude of the three-dimensional change of eye position from
r1 to r2
positions as follows (Van Opstal 1993)
![]() |
![]() |
![]() |
RESULTS |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
Torsional correction
Figure 3 shows representative data
obtained from one block of four trials. Saccades to a laser target at
20° to the right, without (left panels) and with
(right panels) torsional offsets are illustrated. The
torsional offset was introduced by the optokinetic disk rotating
counterclockwise (CCW) at 30°/s, thus intorting the right eye
(pulling T position negatively). The torsional (T, top
panels) and horizontal (H, bottom panels) components
are each superimposed. The saccades made in the dark (without the
torsional offset, D-saccades) show a torsional component (top
left panel), the so-called blip, which transiently moves the eye
out of Listing's plane during saccades (Straumann et al.
1995). For L-saccades, shown in the right panels,
the "torsional error" is defined as an offset from the zero torsion
value indicated by a horizontal line. This zero torsion value was
virtually identical to the torsional component of the primary eye
position based on the orientation of Listing's plane (also see the
legend to Fig. 3). One can see that the torsional error was minimized
while the saccade was being made. This torsional movement reflects the
sum of both the torsional blip associated with the saccade itself and
the reduction of the torsional offset that had been induced by the
optokinetic disk. In this condition (CCW rotation) these two components
work in the same direction to rotate the eye back toward zero torsion.
|
Figure 4 illustrates the torsional
components associated with rightward saccades of varying amplitudes.
The four panels in the left column show the torsional
components of horizontal D-saccades toward targets at
various rightward eccentricities (5, 10, 15, and 20°). The torsional
blip increased as horizontal saccade amplitude increased, as previously
described by Straumann et al. (1995). Here, the blips
extort the right eye during the saccades. The right panels
show the torsional components of L-saccades that were made after
torsional offsets were induced with the optokinetic disk rotating at
30°/s CCW. During horizontal saccades (short horizontal bars at
bottom of each panel), the torsional offset (approximately
3°) was reduced by a corrective torsional movement that was in the
same direction (positive) as the torsional blip. For small horizontal
saccades, e.g., 5°, the torsional offset (i.e., error from zero
torsion) was not fully corrected, and the residual torsional error was
slowly corrected after the saccade while fixing on the eccentric
target.
|
To reveal the corrective torsional movement in the L-saccades, the mean
trace of the torsional blip from the D-saccades was obtained and
subtracted from that of the torsional component of L-saccades (Fig.
5). Due to the torsional blip of
D-saccades, which first extorted the eye (Fig. 5, top
panels), the torsional component of L-saccades appeared asymmetric
between the clockwise (CW) and CCW conditions (Fig. 5, middle
panels). After the effect of the torsional blip was removed,
however, the asymmetry in the magnitude of the torsion was greatly
reduced (Fig. 5, bottom panels). The blip-subtracted torsion
(b a), thus reflects corrective torsional
movements; intorting in CW and extorting in CCW disk rotation
conditions.
|
The blip-subtracted torsional movements during saccades (bottom
panels, b a, of Fig. 5) were fast;
their time constants were 19 ms in CW and 25 ms in the CCW conditions.
Thus recovery from extorsion was slightly faster in this condition, but
in other conditions, when different target amplitudes and disk speeds
were used, recovery from intorsion could be slightly faster. For
example, in the condition when saccades were made toward 10° to the
right with the OKN disk rotating at 10°/s (in the same subject,
CL), the time constants of the blip-subtracted torsional
corrections were 28 ms in the CW and 17 ms in the CCW conditions. There
was inter- and within-subject variability in these time constants; subject MH showed the fastest torsional movement and in the
same condition as Fig. 5, the time constants of b
a were 7.5 ms in CW and 9 ms in CCW conditions. Time
constants for subject DZ were 12 and 27, and for
subject NH were 20 and 24 ms for CW and CCW conditions,
respectively. The overall mean time constant was 18 ± 7.4 (SD) ms. The time constants of the blip-subtracted torsional correction were comparable for vertical saccades (mean, 24 ± 14 ms).
To determine whether the blip-subtracted torsional correction has the
dynamic characteristics as saccades, the main sequence of the
blip-subtracted torsion was examined. On Fig.
6, the main sequence relationships (peak
velocity as a function of amplitude) of blip-subtracted torsional
movements during L-saccades (in paradigm I) and torsional
movements during torsional quick phases (in paradigm II) are
compared for all four subjects. In all cases, the OKN disk was rotating
at 30°/s. The peak torsional velocity of torsional quick phase
(circles) was comparable to the blip-subtracted torsion during
L-saccades toward horizontal targets (asterisks), matched for torsional
amplitude. In each panel, a best-fit line was drawn through the
asterisk points. The mean of the slopes was 24.3 (deg/s)/deg. A similar
pattern of relationship between the peak torsional velocity and
torsional displacement was found for quick phases in response to the
10°/s optokinetic stimulus alone; there were no differences between
the slope and intercept of the best-fit line through this quick phase
data and the torsional data from paradigm I (asterisks). The
peak torsional velocities obtained in this study were similar to those
reported for torsional saccades by Collewijn et al.
(1985).
|
Effects of the speed of disk rotation
For L-saccades, we pooled all the data from all subjects and stimulus conditions for the disk rotating at 10°/s (229 L-saccades) and 30°/s (232 L-saccades), and calculated the mean torsional component at saccade onset. This value was subtracted from the mean torsional eye position at the onset of D-saccades to obtain a measure of the stimulus-induced torsional deviation prior to L-saccades. Similarly, the mean of the torsional component during the D-saccades was subtracted from the torsional component of the displacement vector defined by rotation vectors at the onset and offset times of horizontal or vertical L-saccade to obtain the stimulus-induced torsional movement. The initial torsional deviation and the magnitude of the torsional component of blip-subtracted L-saccades are presented in Table 1. The effect of the OKN disk on initial torsional deviation was variable among subjects (F3,453 = 157.25, P < 0.001 for right eye and F3,453 = 124.57, P < 0.001 for left eye). The mean initial torsional deviation of blip-subtracted L-saccades made for the right eye in the 10°/s disk rotation condition was 1.11 ± 0.68° and in the 30°/s condition, 1.46 ± 1.05°. For the left eye, the value for 10°/s disk rotation was 0.96 ± 0.63° and for the 30°/s, 1.21 ± 0.96°. This difference in initial torsional deviation between the two disk speeds was statistically significant (F1,453 = 38.26, P < 0.001 for the right eye, F1,453 = 20.37, P < 0.001 for the left eye). In contrast to the other three subjects, for subject NH there was little effect of disk speed.
|
Initial torsional offset and magnitude of torsional correction
To determine whether the magnitude of torsional correction is
related to the initial torsional offset, the blip-subtracted torsional
displacement of L-saccades was plotted as a function of the initial
torsional position (Fig. 7). For both
eyes making both horizontal and vertical saccades, if the initial
torsional deviation was larger, then the torsional movement during the
saccade was larger. Note that both the initial torsional position and torsional magnitude were normalized with respect to D-saccades, and
thus the initial torsional position reflects the stimulus-induced torsional offset, and the torsional magnitude reflects the amount of
correction of torsional error that was induced by the stimulus. The
correction was not perfect (Table 1, Fig. 7); the slope relating the
torsional magnitude to initial torsional position was approximately 0.5, indicating that ~50% of the initial torsional offset was corrected during the primary saccade in our experimental paradigm. The
torsional correction was 8% larger for vertical saccades than for
horizontal saccades, as estimated by the difference in the slope given
in the legend to Fig. 7.
|
The ratio of torsional magnitude to initial torsional offset (T correction ratio) was related to saccade duration and amplitude (Fig. 8). The slope relating this ratio to saccade duration was higher for horizontal than for vertical saccades (Fig. 8A), but this could be due to the fact that saccade duration was considerably lower for horizontal than for vertical saccades as can be seen in Fig. 8A. When the same ratio was plotted as a function of saccade amplitude, the slopes became closer (Fig. 8B). The linear regression equation relating the ratio of torsional correction to saccade amplitude for horizontal saccades, combining all subjects was y = 0.0387x + 0.1537, and that for vertical saccades was y = 0.0283x + 0.3658. The slopes of the linear regression equations for combined horizontal and vertical saccades for each subject were 0.0321 (CL), 0.0341 (DZ), 0.0375 (MH), and 0.0379 (NH), and that combined for horizontal and vertical saccades for all subjects was y = 0.0318x + 0.2829. This suggests that approximately 3.18% of the torsional deviation is corrected per degree of horizontal or vertical saccade. Thus in addition to the initial torsional deviation, saccade amplitude appears to be a major predictor of the amount of intrasaccadic torsional correction. Furthermore, the fact that the ratio is higher for vertical than for horizontal saccades (Figs. 7 and 8B) suggests that saccade duration is also related to the amount of torsional correction, and that a saccade provides a temporal window within which the initial torsional offset is corrected.
|
Torsional velocity
Figure 9 shows the trajectory of the torsional component of the angular velocity vectors for rightward saccades of subject CL. Saccades were made to a target 15° to the right. In the top left panel, torsional blip velocity is shown for horizontal D-saccades. Due to the asymmetry in torsional blip velocity (CW early, CCW late), the torsional velocity traces of L-saccades are different between the CW and CCW torsional offset conditions (middle and bottom, left panels). In the right panels, the torsional velocities of L-saccades in the CW and CCW conditions are shown after the effect of the torsional blip was subtracted. With this subtraction, the absolute values of peak torsional velocity can be compared between the L-saccades in the CW and the CCW conditions.
|
The peak torsional velocity, after subtracting the blip torsion, increased with the speed of rotation of the disk; the peak torsional velocity of blip-subtracted L-saccades combined for horizontal and vertical series for all subjects was 13.5°/s for the 10°/s OKN disk speed, and 18.1°/s for the 30°/s disk speed. This difference in peak torsional velocity was probably related to the difference in the initial torsional deviation described above. Thus peak torsional velocity, corrected for the blip, reflects the parameters of stimulation, in much the same way as the magnitude of the blip-subtracted torsion increased with the speed of the OKN disk. Accordingly, we can divide the saccade-related torsion into two components: blip torsion and stimulus-induced torsion. The peak torsional velocity of blip-subtracted L-saccades increased with horizontal or vertical saccade amplitude, and this is related to the fact that the intrasaccadic torsional change increased with saccade amplitude (Fig. 8).
Control experiments
Since a major question about our results is whether or not the movements that correct for torsional offset during saccades simply reflect passive recovery due to muscle mechanics, we did two control experiments. First, we examined the return of torsion to its baseline value in the absence of saccades using paradigm II, in which the optokinetic disk was alternately visible and invisible while the eyes maintained fixation on the central target (Fig. 10). The periods immediately after the light OFF, and free of saccades or quick phases, were isolated and the time constants of return of torsional position to baseline were calculated by fitting an exponential function (see legend to Fig. 5). Twenty-three traces from three subjects [data from one subject (NH) showed too many quick phases to be included] were analyzed for this purpose. The mean time constant for the right eye across all subjects was 740 ± 325 ms, and that of the left eye was 766 ± 566 ms. This difference was not statistically significant. There were also no statistically significant differences in the time constants between the CW and CCW conditions (P > 0.64 for the right eye and P > 0.37 for the left eye).
|
In paradigm III, the effects of illumination of the background on torsional movements were examined. The overhead light stayed on during saccades, and the torsional component of these saccades was compared with that obtained in paradigm I, in which case the light went out when the saccade began. Regardless of the visibility of the optokinetic disk, the associated torsion during and immediately after the saccade followed the same stereotypical trajectory to approximately 240 ms after the onset of the saccade (Fig. 11) for both disk speeds.
|
Conjugacy of torsional movements
Torsional movements of D-saccades were asymmetric; blip torsion
was bigger in the right eye during rightward saccades and bigger in the
left eye for leftward saccades (not shown); thus there was a transient
blip-associated cyclovergence as reported by Straumann et al.
(1995). During L-saccades, torsional movements actively
corrected the OKN-induced torsional error as described above, and these
movements were conjugate. In this condition, the magnitude of the
torsional component was different between the right and left eyes (Fig.
12), but after the blip torsion was removed, the torsional movements were approximately the same in both
eyes. Figure 13 illustrates this for a
representative subject CL. Saccades were made to targets at
four different eccentricities to the right. Torsion in the right eye
(
) was approximately the same as that in the left eye (- - -),
after correcting for the blip torsion. In the CCW condition, the
torsion in the right eye was slightly bigger than that in the left eye
in this subject, but this pattern was not consistently observed and in
fact, reversed in one subject (NH). The overall mean value
for the cyclovergence component of the torsional correction across all
subjects was only 0.15 ± 0.17° for horizontal saccades.
Similarly, intrasaccadic torsional corrective movements were largely
conjugate for vertical saccades; after correcting for the blip-torsion
in all subjects, the mean cyclovergence across all subjects was only
0.17 ± 0.14°. The amount of cyclovergence was not significantly
different between horizontal and vertical saccades.
|
|
Coupling of torsion to vertical but not to horizontal saccades
When oblique saccades are made in which the horizontal or vertical
component is larger, there is often "stretching" of the smaller of
the two components (be it vertical or horizontal) with a corresponding
increase in duration and decrease in peak velocity. We wondered whether
a similar phenomenon could be observed with the torsional component of
horizontal and of vertical L-saccades. The relationship of the peak
velocity of the blip-subtracted intrasaccadic torsion to saccade
amplitude appeared to be different for horizontal and for vertical
saccades, although there was intersubject variability (Fig.
14). For horizontal saccades, peak
torsional velocity of blip-subtracted L-saccades tended to increase
with the amplitude of horizontal saccades. On the other hand, for
vertical saccades, either the peak torsional velocity tended to
decrease with the amplitude of vertical saccades, or there was little
relationship between peak torsional velocity and saccade amplitude
(Fig. 14 and Table 2). The difference in
the slopes of the regression lines relating the peak torsional velocity
to saccade amplitude for horizontal and vertical saccades was prominent
in the CW stimulus condition, and observed in both eyes. For example,
the overall slope for horizontal saccades in the CW condition was
1.22, indicating that the peak torsional velocity increases with
horizontal target amplitude (the corrective torsional movement is
negative in the CW condition). The slope for vertical saccades was
0.17, suggesting that the peak torsional velocity tended to decrease,
if anything. For CCW conditions, the slopes did not actually reverse
sign, but the slope was nonetheless less for vertical saccades (0.41 vs. 0.68).
|
|
To further determine whether the torsional component was coupled to the vertical, but not to the horizontal component, the torsional velocity of blip-subtracted L-saccades was plotted against the horizontal or vertical component of angular velocity. In all four subjects, the time that peak torsional velocity was reached occurred later as vertical saccade amplitude increased and thus the ratio of torsional velocity to vertical velocity at the time of the peak torsional velocity ("T/V ratio") systematically decreased (Fig. 15A). This result is compatible with the idea that torsion is coupled to the vertical system. No such systematic relationship was found between the torsional and horizontal components of angular velocity (Fig. 15B). We emphasize, however, that although the duration of vertical saccades was greater than those of horizontal saccades of matching amplitudes, there were no consistent increases in duration for either horizontal or vertical L-saccades compared with D-saccades.
|
Horizontal L-saccades were often dysmetric, missing the visual target
because of a directional error in saccade accuracy. Figure
16 shows trajectories of primary
saccades made toward a target 15° to the right, taken from a
representative subject (CL). When a CCW torsional offset was
induced, the endpoints of the primary saccades contained an error with
an unwanted upward component. This error in vertical direction was
reduced with subsequent corrective saccades (arrows in Fig.
17). Figure
18 shows a quantitative summary of
saccade error for both horizontal and vertical saccades for all
subjects. To summarize the size and direction of saccade error, median
endpoints of D-saccades and L-saccades (asterisks in Fig. 16) were
calculated. H and V errors were defined as the difference between these
two median points in the horizontal and vertical dimensions,
respectively. Saccade errors were greater with larger amplitude
saccades, and accordingly in Fig. 18, saccades toward targets at 15 and
20° to the right (Horizontal) were combined, and likewise for 15 and
20° up (Vertical). As shown in Fig. 16, horizontal saccades with the
CCW torsional offset condition ended higher than D-saccades, thus
containing positive V errors (filled symbols of Fig. 18, Horizontal).
Similarly horizontal saccades with the CW torsional offset ended lower
than D-saccades, thus containing negative V errors (open symbols of
Fig. 18, Horizontal). For vertical saccades, however, no consistent
error in saccade end position with respect to D-saccades was found
(Fig. 18, Vertical). Person's 2 test was
performed to determine whether the polarity of saccade error and the
direction of torsional offset (CW or CCW) were statistically independent. For horizontal saccades, they were not statistically independent (
2 = 21.13, P < 0.001), whereas for vertical saccades, they were independent
(
2 = 3.77, P > 0.05). Thus
the accuracy of horizontal and vertical saccades is differentially
affected when a torsional error is introduced.
|
|
|
![]() |
DISCUSSION |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|
A fundamental question in ocular motor physiology is how Donders'
and Listing's laws are maintained. Current hypotheses include both
peripheral (mechanical) explanations (Demer et al. 1997, 2000
; Quaia and Optican 1998
;
Raphan 1998
; Schnabolk and Raphan 1994
)
and central (neurally encoded) explanations (Crawford and Guitton 1997
; Klier and Crawford 1998
;
Tweed et al. 1998
; Van Opstal et al.
1996
). Here we addressed a specific aspect of this issue by
examining how visually induced torsional offsets, which temporarily
take the eyes out of Listing's plane, are corrected. The main
conclusion is that a neurally encoded central command is responsible
for correcting such torsional errors, and that the correction takes
place in association with the occurrence of horizontal or vertical
saccades, implying three-dimensional control of saccades. We will first
discuss potential confounding factors that might argue against this interpretation.
Torsional "blips"
Torsional blips, which transiently take the eye out of Listing's plane during normal horizontal and vertical saccades, must be considered to make an accurate interpretation of the nature of any torsional corrective movements during saccades. We believe our corrections for such blips were accurate since subtraction of the saccade-induced blip torsion from the total intrasaccadic torsion of L-saccades (saccades with induced torsional offset) produced symmetrical torsional corrections. Furthermore the corrections were equally accurate whether the direction of the torsional offset was the same or opposite to the blip torsion.
Active versus passive control of torsion
A second key question is whether or not the intrasaccadic
torsional corrections are simply generated passively by the mechanical characteristics of the ocular motor plant. Seidman et al.
(1995), based on the course of return of the eye to the resting
position after mechanical displacements into extorsion and intorsion,
reported that the return of the torsional position of the eye was
asymmetric; the time constant of return from extorsion was 83 ms,
whereas that from intorsion was 210 ms. In contrast, in our study the correction of the torsional offsets, after subtracting the torsional blip, was much faster than the return of the eye after a mechanical displacement. The time constant of the correction for the
stimulus-induced torsion was approximately 20 ms (Fig. 5), and we found
no asymmetry in the time course of these corrective torsional
movements. This is strong evidence that the torsional error, i.e., the
offset from the Listing's plane, is corrected by an active, neural, mechanism.
In a control experiment, we examined the return of the eye toward the Listing's plane following optokinetic stimulation. The time course of the return was >380 ms, and much larger than the average values for the passive return from the mechanically displaced torsion. One might conclude that in this paradigm the slow "passive" return in the absence of a saccade during the control paradigm reflects the properties of the torsional optokinetic system, or of the torsional velocity-to-position gaze-holding integrator. In either case, the slow decay of torsion would reflect the dissipation of "stored" activity, which had outlasted the time course of the passive orbital forces.
Finally, and perhaps most importantly, the main-sequence relationship between peak velocity and amplitude for the torsional corrections was comparable to that for the pure torsional quick phases that were elicited during roll optokinetic stimulation. This finding also argues strongly for a central mechanism underlying the correction of torsional errors during saccades.
Three-dimensional control of saccades and quick phases
Based on the dependence of the torsional displacement during
spontaneous saccadic eye movements on the initial torsional position, Van Opstal et al. (1996) concluded that errors in
torsional position are monitored and corrected during the subsequent
saccade, and that the correction is driven by a central
three-dimensional command. Crawford and Guitton (1997)
developed a model for the three-dimensional control of saccades and
predicted one of the main results of our experiments: the active
correction of torsion toward Listing's plane during horizontal and
vertical saccades. Thus our results also support the idea that
torsional error is monitored and actively corrected by a central
three-dimensional neural control mechanism, rather than by a passive
plant property. Put in another way, central saccade circuits can encode
three-dimensional eye movement commands when there is a need to restore
eye positions back to Listing's plane. This will ensure correct
torsional eye orientation during fixation. Our findings and this
interpretation are consonant with what has been reported in monkeys
when their eyes were artificially moved out of Listing's plane by
electrical stimulation in the caudal aspect of the nucleus reticularis
tegmenti pointis (cNRTP) (Van Opstal et al. 1996
). As in
our experiments, the torsional error was corrected in association with
the next saccade. One important caveat should be kept in mind, however.
Both our results and those of Van Opstal et al. (1996)
do not exclude a role for orbital muscle pulleys in the mediation of
centrally generated command in the control of eye torsion, since
orbital muscle pulleys seem to have a neural innervation (Demer
et al. 2000
).
Anatomic substrate for the control of ocular torsion
One important question is which structures within the brain
mediate these three-dimensional control mechanisms. Since lesions in
the cNRTP impair this torsional correction mechanism (Van Opstal et al. 1996), it may be that the cerebellum, which receives
projections from the cNRTP, plays a role in correcting torsional
deviations from Listing's plane, and that cerebellar lesions might
lead to a torsional dysmetria in which the eyes are not properly
brought to Listing's plane in association with horizontal or vertical saccades. The abnormality of saccade-associated torsion described by
Helmchen et al. (1997)
and by Morrow and Sharpe
(1988)
in patients with lesions in the dorsal lateral medulla
and cerebellum support this idea. There is additional evidence for a
role for the cerebellum in the control of torsional eye position and
Listing's plane. Patients with diffuse cerebellar degenerations also
show abnormalities of the control of torsional eye position; they have
abnormal torsional drift that changes with orbital position
(Straumann et al. 2000
).
Coupling of torsional corrections and vertical saccades
Another important result in our study is the apparent difference in the coupling between torsional and vertical, and between torsional and horizontal saccades. Whereas for horizontal saccades, peak torsional velocity increased with the amplitude of horizontal saccades, this was not the case for peak torsional velocity and the amplitude of vertical saccades. Furthermore, the time when peak torsional velocity was reached was delayed as the amplitude of vertical saccades increased but there was no such relationship between torsional peak velocity and the amplitude of horizontal saccades. Thus the patterns of coupling between the dynamic properties of torsional saccades and of horizontal or vertical saccades were different.
Systematic errors in saccade accuracy were also seen when
torsional corrections were coupled with horizontal but not with vertical saccades. Currently no saccade model accounts for this differential effect. Crawford and Guitton (1997)
considered saccade accuracy to test properties of their
three-dimensional models for generating kinematically correct saccades
and pointed out that errors in saccade accuracy might occur with
torsional offsets unless there were specific adjustments in premotor
commands for saccades depending on three-dimensional eye position.
Furthermore, the adjustments in their model had to be at a specific
location ("upstream") relative to a "Listing's law operator."
They did not, however, predict a different pattern of dysmetria
depending on whether the saccade was vertical or horizontal nor was one found when Klier and Crawford (1998)
looked for
directional errors in normal subjects with a torsional offset
(counterroll) induced by head tilt. They did find, however, small
directional errors but with a general trend for the errors to be in the
opposite direction as the counterroll of the eyes, which is the
opposite to our findings for horizontal saccades. For example, with CCW torsional offset, more of a down component was observed for rightward saccades (Figs. 10B and 11C of Klier and
Crawford 1998
), whereas in our study more of an up component
was found (Figs. 16 and 18). In their paradigm the torsional offset of
the eyes was produced by a head tilt, and saccades were made while the
head tilt was maintained, and thus were basically two-dimensional and
within Listing's plane. Thus in their paradigm, although an initial
torsional offset existed when saccades started, the torsional offset
was not and did not have to be corrected. In our paradigm, in contrast, the torsional offset occurred without any actual rotation of the head
in space, and in that sense did not serve the same purpose as a natural
counterroll. Hence subsequent saccades incorporated a torsional
correction to bring the eyes back toward Listing's plane.
To epitomize, our results suggest the presence of coupling between the torsional and vertical, but not between the torsional and horizontal systems, both with respect to saccade accuracy as well as to saccade dynamic properties. The errors in saccade accuracy associated with horizontal but not vertical saccades suggest that the vertical-torsional saccade-generating circuits in the rostral interstitial nucleus of medial longitudinal fasciculus (riMLF) may receive a desired eye orientation signal that takes into account the torsional error, while the horizontal saccade-generating circuits in the pons do not. The correction of torsional offsets, however, takes place with saccades of either direction, implying a separate mechanism for programming a correction to keep the eyes in Listing's plane. With respect to the dynamic aspects of coupling of torsion during saccades, it seems possible that the selective coupling for vertical saccades reflects the common neural substrate in the riMLF for generating premotor saccade commands for both torsional and vertical rapid eye movements. Finally, some coupling of torsion to vertical motion might also occur in the ocular motor periphery because of sharing of muscles for torsion and vertical rotations of the globe. But the active, centrally commanded nature of the torsional correction is still suggested by the time course of the torsional correction, which was quite rapid during horizontal as well as vertical saccades. It should be pointed out, however, that the coupling between torsional and vertical components is not exactly like the one between horizontal and vertical components showing so-called component stretching, since there was no consistent increase in duration of horizontal or vertical L-saccades compared with D-saccades.
Implications for three-dimensional saccade generation models
The torsional error was corrected synchronously with the
horizontal or vertical error, but its correction during the primary saccade was incomplete, leaving a residual torsional error to be
corrected by other mechanisms with longer time constants (Fig. 8A, and also see for an individual example, the 1st and 2nd
figures in the right panel of Fig. 4). The ratio of
corrected torsion to the initial torsional offset was linearly related
to horizontal or vertical saccade amplitude (Fig. 8B),
indicating that the torsional correction is yoked to the horizontal or
vertical correction. Thus although the saccade itself is
three-dimensional, saccade duration is determined by the error in the
horizontal or vertical, but not in the torsional component.
Robinson (1975) was the first to propose the local
feedback hypothesis controlling saccade generation, and numerous
modifications of the original model (Gancarz and Grossberg
1998
; Jürgens et al. 1981
; Quaia
and Optican 1998
; Scudder 1988
, to list only a
few) have appeared. In these models, saccade amplitude and duration are
determined by signals of desired and current eye position, orientation,
or displacement provided by local feedback. The yoked torsional
correction suggests that the local feedback loops that control saccade
amplitude and duration are two-dimensional in
nature, i.e., feedback for horizontal and vertical orientations only,
and that Donder's and Listing's laws are implemented downstream from
local feedback loops.
![]() |
ACKNOWLEDGMENTS |
---|
We thank A. Lasker for providing technical expertise in building and operating the stimuli and D. Roberts for computer programming and help with data collection.
This research was supported by the Korea Research Foundation (98-001-C01153), the Korea Ministry of Science and Technology under the Brain Science Research Program, National Eye Institute Grant RO1-EY01849, the Swiss National Science Foundation (3231-051938.97/3200-052187.97), and the Betty and David Koetser Foundation for Brain Research.
![]() |
FOOTNOTES |
---|
Address for reprint requests: C. Lee, Dept. of Psychology, Seoul National University, Kwanak, Seoul 151-742, Korea.
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 2 August 1999; accepted in final form 8 February 2000.
![]() |
REFERENCES |
---|
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
---|