Department of Neurology, University of Zurich, CH-8091 Zurich, Switzerland
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ABSTRACT |
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Misslisch, Hubert and Bernhard J. M. Hess. Three-Dimensional Vestibuloocular Reflex of the Monkey: Optimal Retinal Image Stabilization Versus Listing's Law. J. Neurophysiol. 83: 3264-3276, 2000. If the rotational vestibuloocular reflex (VOR) were to achieve optimal retinal image stabilization during head rotations in three-dimensional space, it must turn the eye around the same axis as the head, with equal velocity but in the opposite direction. This optimal VOR strategy implies that the position of the eye in the orbit must not affect the VOR. However, if the VOR were to follow Listing's law, then the slow-phase eye rotation axis should tilt as a function of current eye position. We trained animals to fixate visual targets placed straight ahead or 20° up, down, left or right while being oscillated in yaw, pitch, and roll at 0.5-4 Hz, either with or without a full-field visual background. Our main result was that the visually assisted VOR of normal monkeys invariantly rotated the eye around the same axis as the head during yaw, pitch, and roll (optimal VOR). In the absence of a visual background, eccentric eye positions evoked small axis tilts of slow phases in normal animals. Under the same visual condition, a prominent effect of eye position was found during roll but not during pitch or yaw in animals with low torsional and vertical gains following plugging of the vertical semicircular canals. This result was in accordance with a model incorporating a specific compromise between an optimal VOR and a VOR that perfectly obeys Listing's law. We conclude that the visually assisted VOR of the normal monkey optimally stabilizes foveal as well as peripheral retinal images. The finding of optimal VOR performance challenges a dominant role of plant mechanics and supports the notion of noncommutative operations in the oculomotor control system.
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INTRODUCTION |
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Stabilization of the entire retinal image requires
that the three-dimensional (3D) rotational vestibuloocular reflex (VOR) spins the eye around the same axis as the head and in the opposite direction, independent of eye position (optimal VOR
strategy). To determine whether the VOR actually follows this strategy,
the effect of eye position on VOR slow phases has been studied in humans during active or passive rotations in yaw, pitch, and roll with
various frequencies and illuminations (Misslisch 1995;
Misslisch et al. 1994
, 1996
;
Solomon et al. 1997
; Thurtell et al.
1999
; Tweed et al. 1994
). The findings showed
that the eye rotation axis tilted with the gaze line during
yaw or pitch and opposite to the gaze line during roll. This
pattern has been interpreted as a specific compromise between perfect
retinal image stabilization and perfect compliance with Listing's law
(partial Listing VOR strategy).
Listing's law is a kinematic constraint that holds during
saccades and fixations (e.g., Ferman et al. 1987;
Minken et al. 1993
; Tweed and Vilis
1990
), smooth pursuit (Haslwanter et al. 1991
;
Tweed et al. 1992
), and, more generally, during VOR fast phases (Hess and Angelaki 1997
). Listing's law implies
a particular relation between eye position and eye velocity that is
relevant for understanding its possible role in the VOR: when the eye
is in a given position, then the eye velocity vector must lie in a
head-fixed plane, the velocity plane associated with that
position. The velocity planes for different eye positions differ by
half the change in gaze direction (half-angle rule). The
unique eye position for which the gaze line is orthogonal to its
associated velocity plane is called primary position, its
velocity plane Listing's plane (Tweed and Vilis
1990
; Von Helmholtz 1863
, 1867
).
Figure 1 illustrates the theoretical
predictions of optimal VOR and partial Listing VOR strategies during
pitch (top panel) and roll (bottom panel) head
rotation for a 20° left gaze direction. Velocity vectors are plotted
in Listing's coordinates, i.e., Listing's plane (LP) aligns with the
y-axis and primary gaze direction (gaze line when the eye is
in primary position) with the x-axis of the coordinate
system. A VOR that perfectly follows Listing's law predicts eye
velocity vectors to lie in the velocity plane (VP) which, according to
the half-angle rule, is tilted by (20/2)° in the direction of gaze.
The optimal VOR strategy requires an eye velocity that is equal and
opposite to head velocity and independent of gaze direction, i.e.,
completely violates Listing's law (see opt
and
head in Fig. 1). The parallel
projection Listing VOR model yields a velocity vector that
stabilizes the foveal image and is found by projecting the optimal VOR
vector parallel to the gaze line onto VP. Any vector with its tip along
the dotted lines (and its origin in the center of the coordinate
system) represents such a VOR response, each with a particular degree of compliance with Listing's law as quantified by a Listing
factor (LL): the unique velocity vector that lies in VP (LL = 1) corresponds to a Listing factor of one (full compliance). The
optimal VOR velocity vector (LL = 0) corresponds to a Listing
factor of zero (no compliance). All vectors in between (along the
dotted line) represent Listing factors ranging from 1 to 0, depending
on the distance of their tips from VP. For example, a half-Listing VOR (LL = 0.5) lies halfway in between the responses denoted by
LL = 1 and LL = 0. Previous studies have shown that the human
VOR follows this parallel projection half-Listing strategy
(Misslisch 1995
; Misslisch et al. 1996
).
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Another possible compromise between optimal VOR and Listing VOR is the orthogonal projection model, where the velocity vector is found by projecting the optimal vector on VP and orthogonal to it. Any vector with its tip along the dashed lines represents such a VOR response. Again, the degree of compliance with Listing's law (eye position-dependent tilt of the VOR response) can be characterized by a Listing factor. As will be shown in this study, the orthogonal projection model accounts for the direction of VOR responses in monkeys with low torsional gains (due to plugging of their vertical semicircular canals; see Figs. 4 and 6). Note that both Listing's law models predict VOR responses that tilt in the direction of gaze during pitch (and yaw, not shown) and opposite to gaze during roll head rotations. The functional significance of the two compromise strategies will be considered in the DISCUSSION (see also APPENDIX).
The performance of the VOR and its possible dependence on eye position
has implications for two general problems in oculomotor control. First,
the recent discovery of soft rectus muscle pulleys that
restrict the path of extraocular muscles (Demer et al.
1995, 1997
; Miller and Demer
1997
; Miller et al. 1993
) has revived the long
standing debate on whether or not Listing's law can be attributed to
mechanical properties of the oculomotor plant rather than to neural
control systems. As a recent example, Thurtell et al.
(1999)
studied high acceleration active and passive yaw head
rotations in humans and found eye position-dependent VOR responses in
directions predicted by Listing's law. The authors concluded that the
eye position dependence is probably due to the effect of fibromuscular pulleys on the paths of the rectus muscles. This supports the earlier
proposal of Raphan (1997)
, who claimed that a
commutative VOR model, when implementing the action of extraocular
muscle pulleys, can account for the half-Listing behavior described in humans (Misslisch et al. 1994
).
Second, in a comprehensive modeling work, Smith and Crawford
(1998) demonstrated the necessity of noncommutative
operations in the brain circuits underlying the VOR. Their computer
simulations demonstrated that any commutative VOR model
predicts nonoptimal VOR responses with slow phase rotation axes that
deviate from the axis of head rotation, a behavior that results in a
severe degradation of vision. Moreover, this finding was independent of
the mechanical properties of the oculomotor plant, i.e., whether the
effect of fibromuscular pulleys was incorporated in the model or not.
Smith and Crawford concluded that an internal multiplicative processing
of eye position and head velocity signals was required to account for
the noncommutative properties of 3D rotations and to produce optimal
VOR responses that allow a stable image on the entire retina.
Additional evidence for noncommutative operations in the brain was
reported by Tweed et al. (1999)
, who found the predicted
(noncommutative) VOR responses after two sequences of head rotations
around the same axes but in reversed order.
A detailed quantitative study on the influence of eye position on the
monkey rotational VOR has not been performed so far. Observations made
in nontrained monkeys suggested no systematic effect (Crawford
and Vilis 1991). The aim of this study was to characterize the
monkey VOR in a condition where the animals were trained to fixate
eccentric targets, with or without a visual background, while being
oscillated at various frequencies in yaw, pitch, and roll. We found
that when full-field vision was present, monkeys showed optimal VOR
behavior in all three dimensions. When visual and/or vestibular inputs
were reduced, eye position-dependent VOR responses in accordance with
the orthogonal projection model were found during roll but not during
pitch or yaw. Preliminary results have been published in abstract form
(Misslisch and Hess 1998
).
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METHODS |
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Animal preparation
Five juvenile rhesus monkeys (Macaca mulatta;
abbreviated JU, SU, RO, JE, and TW) were
chronically prepared with skull bolts for head restraint. Dual search
coils were implanted on one eye under the conjunctiva at about 4 mm
from the limbus corneae (Hess 1990). In two animals
(JE and TW), all anterior and posterior semicircular canals were plugged about 1 yr before participating in
this study. All surgical procedures were performed under sterile conditions, with the monkeys in deep anesthesia. After surgery, animals
were treated with antibiotics and analgesics. All procedures were in
accordance with the National Institutes of Health Guide for the Care
and Use of Laboratory Animals, and the Veterinary Office of the Canton
of Zürich approved the protocol.
Recording, calibration, and representation of 3D eye position and velocity
3D eye positions were measured with the magnetic search coil
technique (Robinson 1963) using an Eye Position Meter
3000 (Skalar, Delft, The Netherlands). A coil mounted on a cubic frame
of 0.3-m side length generated a horizontal and vertical magnetic field (20 kHz, phase and space quadrature). The output of the dual search coil corresponded to the horizontal and vertical angular orientation of
two sensitivity vectors, one pointing roughly in the direction of the
visual axis and the other approximately perpendicular to that. The four
coil voltages, as well as the head position and velocity signals and a
signal from a photodiode indicating illumination inside the sphere,
were digitized at a rate of 833 Hz (Cambridge Electronic Design, model
1401plus) and stored on the hard disk of a microcomputer for off-line analysis.
3D eye position was calibrated as described in detail elsewhere
(Hess et al. 1992). In short, the magnitude of the two
coil sensitivity vectors as well as the angle between them was computed in an in vitro procedure. On each experimental day, the monkeys repeatedly fixated three light-emitting diodes (LEDs) placed at straight ahead and 20° up or 20° down. The measured voltages were used in combination with the parameters determined in vitro to compute
the 3D orientation of the search coil on the eye. As a control of the
quality of eye position recording, monkeys were made to fixate visual
targets in the laboratory for about 90 s before each experiment.
Then, a Listing's plane was computed for the complete data set
including saccadic and fixation intervals as described elsewhere
(Hess et al. 1992
).
Three-dimensional eye positions were expressed as rotation vectors,
where the eye's orientation when looking straight ahead was chosen as
reference position (Haustein 1989; Hess et al.
1992
). The eye angular velocity vector
was
computed as described in Hepp (1990)
. Eye position and
eye velocity vectors were expressed using a head-fixed, right-handed
coordinate system with the x-, y-, and
z-axes pointing along the nasooccipital, interaural, and longitudinal head axis, respectively. Positive directions of the coordinate axes represented clockwise, downward and leftward components (as seen from the subject's point of view) of eye position and eye velocity.
Training, experimental setup, and protocols
The monkeys were seated in a primate chair and secured with shoulder and lap belts. The head was restrained in an upright position (lateral semicircular canals elevated by about 15° anteriorly). The primate chair was then secured inside the inner frame of a vestibular rotator with three motor-driven axes (Acutronic, Jona, Switzerland). The rotator was surrounded by a lightproof sphere of 0.8-m radius to guarantee experiments with or without a full-field visual background. The profile and onset of sinusoidal chair rotation (frequency, amplitude) was chosen and controlled via computer.
All animals were pretrained to fixate LEDs using water rewards. The quality of fixation was controlled with behavioral windows. Animals were usually trained 3 or 4 days per week with free water access during the other days.
The effect of eye position on the monkey VOR was tested for different frequencies of sinusoidal yaw, pitch, and roll chair rotation (0.5, 1, 2, and 4 Hz; amplitude ±18, 5, 1.5, and 0.5°; peak velocity: 56.6, 31.4, 18.9, and 12.6°/s). Due to technical constraints, animals with plugged vertical semicircular canals were tested only at 0.5 Hz (TW) and 1.0 Hz (TW and JE). The target LEDs were on during the whole 4-s test period. The illumination inside the sphere was either on (SU and JU) or not (all animals) so that the numerous, randomly placed and different-sized (between 2 and 17 cm diam at 0.9 m distance, corresponding to a visual angle covered by the disks between 1.3 and 10.8°) black disks against a white background were either visible or not. An experiment started with the selection of a type of chair rotation (yaw, pitch, or roll). A computer program then randomly picked the first target, located either straight ahead or 20° eccentric (for yaw: up, center, down; for pitch: left, center, right; for roll: up, down, center, left, right). The current combination (head rotation, target) was signaled to a second computer, which set and controlled the behavioral reward window on-line. After the main computer initiated data recording, the vestibular rotator started moving if the monkey had kept proper fixation for 500-800 ms. The monkey was required to keep its gaze on the earth-stationary target while being rotated for 4 s. The animals were rewarded with water after the rotator had come to a stop. Trials were aborted when the monkey's eye position exceeded the behavioral window. The computer program selected each combination of chair rotation and target location until 10 successful repetitions were obtained. For a given frequency and illumination condition, the total number of trials was 110 (3 times 10 during yaw, 3 times 10 during pitch, and 5 times 10 during roll).
Data analysis
Digitized 3D eye velocity and eye position data were desaccaded
with a semi-automatic computer program using thresholds for the second
derivative of 3D eye velocity (jerk). Falsely placed or missing markers
were identified and corrected interactively. Data were then cut such
that the first (last) sample corresponded to the onset (offset) of
vestibular stimulation. A sinusoidal function was fitted (in the
least-squares sense) to the chair velocity, yielding an estimate of
frequency and amplitude of 3D head rotation. These head velocity data,
Head, were combined with the data
representing 3D eye position, E, to model slow-phase eye
velocity,
, following a multivariable function fitting
approach as used in a previous study (Misslisch et al. 1994
; Press et al. 1988
). To quantify how eye
position E influences the VOR responses for a given head
velocity
Head, we assumed that angular
eye velocity
was not only a linear function of head
velocity but also depended linearly on eye position as follows
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(1) |
where s is ocular drift velocity,
[G] is a 3 × 3 gain matrix, and [B] is
a 3 × 3 × 3 array representing the influence of eye
position for a given head velocity (for more details see APPENDIX of Misslisch et al. 1994
). In
practice, we rearranged the three input vectors
s,
Head,
and E in this linear equation by defining a 3 × 13 generalized gain matrix [C], which is applied
to the following 13 × 1 input vector Q (written in
transposed form for convenience)
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(2) |
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Concepts of optimal VOR and eye position dependence
Unfortunately, different notions of gaze dependence have been
used in previous VOR studies due to the fact that researchers did not
always carefully distinguish between angular velocity and coordinate velocity v. Here,
we define the VOR as optimal if it achieves a perfectly stable image of
the visual world on the entire retina, with VOR angular velocity being equal in magnitude and opposite in direction to angular head velocity (independent of current eye position). The concept of angular velocity
is a kinematic property describing rigid body motion independent of the
particular coordinates used (Goldstein 1980
). Accordingly, eye angular velocity represents the motion of the eye from
one position to another where its axis coincides with the axis of
rotation and its length represents the speed of rotation. Thus if one
aims to examine the effect of eye position on VOR slow phases, one has
to analyze angular eye velocity with the eye in various positions. This
issue cannot be addressed by representing eye velocity as coordinate
velocity, for example as time derivative of the Fick angles, since this
time derivative will depend on eye position for elementary kinematic
reasons leading to results whose physiological interpretation is
dubious (for the mathematical concepts involved in 3D kinematics see,
e.g., Haslwanter 1995
; Tweed 1997
;
Tweed and Vilis 1987
, 1990
).
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RESULTS |
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The main observations of this study can be summarized as follows. First, when testing normal animals under "natural" conditions, i.e., with the animal fixating a target against a structured background, the visually assisted VOR optimally compensated for the head rotation: the eyes were driven in the opposite direction as the head, at the same speed and around the same axis. The fact that the slow phase rotation axis was not affected by the current position of the eye was invariably found in both animals tested in this condition. Second, when normal monkeys were tested while fixating a target in an otherwise dark environment, small eye position-dependent tilts of the slow-phase axis were observed in directions predicted by Listing's law. Third, in monkeys with low vertical and torsional VOR gains after plugging of the vertical semicircular canals, prominent eye position-dependent tilts were observed during roll, but not during pitch and yaw head rotations.
Optimal VOR responses in the presence of full-field vision
Figure 2 illustrates that the visually assisted VOR in normal monkeys was not influenced by eye position. Representative eye angular velocity vectors (gray dots) are plotted during four cycles of sinusoidal whole-body rotations at 1 Hz (± 5°; peak velocity 31°/s) in yaw (Fig. 2A), pitch (Fig. 2B), and roll (Fig. 2, C and D). In these examples, the (normal) animal was fixating visual targets placed either at 20° up, center and 20° down (Fig. 2, A and C) or 20° left, center and 20° right (Fig. 2, B and D). A structured background was visible throughout the experiment. The tips of the eye velocity vectors are seen from the subject's right side so that horizontal velocity is plotted versus torsional velocity in magnetic field coordinates (Fig. 2, A and C), or from above the subject, i.e., vertical velocity is plotted versus torsional velocity (Fig. 2, B and D; see cartoon monkey heads). Slow-phase responses derived from the computed generalized gain matrices (heavy black lines, see METHODS) are plotted on top of the data (gray lines). Dashed arrows denote the direction of the gaze line, dashed planes indicate the velocity planes, i.e., the planes that would contain the slow-phase velocity vectors if the VOR would perfectly follow Listing's law.
When the monkey was rotated in yaw while fixating the center target (middle panel in Fig. 2A), the slow-phase velocity vectors perfectly aligned with the axis of rotation (ordinate), i.e., the eye rotation axis was parallel to the head rotation axis (according to the right-hand rule, vectors lying along the positive/negative ordinate denote leftward/rightward eye rotation). Thus when looking straight ahead the orientation of the slow-phase axes was consistent with the optimal VOR strategy. More interestingly, the direction of yaw VOR responses remained optimal for eccentric gaze directions. For example, if gaze was 20° up (left panel in Fig. 2A) or 20° down (right panel in Fig. 2A) VOR velocity vectors were still aligned with the head rotation axis. Recall that the half-angle rule (Listing's law) predicts that the axis of eye rotation must tilt by half the angle of gaze eccentricity, i.e., by 10° (dashed plane tilted backward/forward when gaze is 20° up/20° down), a prediction not matched by the data. Thus eye position does not influence the axis of eye rotation during yaw head rotation.
Analogous results were obtained when the animal was rotated in pitch and roll (Fig. 2, B-D). In all cases, the velocity vectors were aligned with the axis of head rotation (ordinate in Fig. 2B, abscissa in Fig. 2, C and D), i.e., the eye rotation axis was completely independent of eye position.
Minor deviations from optimal VOR responses in the absence of full-field vision
When peripheral vision was eliminated, the axis of slow phases showed minor eye position-dependent deviations from the optimal VOR responses. Figure 3 shows examples of VOR velocity vectors (gray dots) for the same animal, the same rotational stimuli (plotted in the same format) as in Fig. 2, but this time collected in a condition without a visible structured background. In the yaw case and when looking straight ahead, the axis of the best-fit VOR response (solid black line) tilted slightly back from perfect alignment with the head rotation axis (ordinate). When looking 20° up (dashed arrow in Fig. 3A, left panel), the VOR's rotation axis tilted further back (by 1.6°) and when looking 20° down (Fig. 3A, right panel) the axis tilted slightly forward (by 1.6°). Thus VOR responses tilted slightly in the directions predicted by Listing's law (dashed planes).
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Minor eye position-dependent tilts of the slow-phase rotation axis were also observed during pitch head rotations (Fig. 3B), but in this example the axis tilted slightly opposite to the direction of gaze (to the right by 2.1° when gaze is 20° left and to the left by 1.8° when gaze is 20° right). In other words, the VOR rotation axis tilted slightly in directions violating the predictions of Listing's law.
The tilt of the VOR rotation axis was generally larger during roll head rotations and in directions that were opposite to the change in gaze, in agreement with the predictions of Listing's law. In this example, when gaze changed in elevation (Fig. 3C) the best-fit VOR rotation axis tilted by 4.3° down (gaze 20° up) and by 4.4° up (gaze 20° down). When gaze changed in azimuth the rotation axis tilted by 6.7° right (gaze 20° left) and 6.8° left (gaze 20° right).
Large deviations from optimal roll VOR responses in animals with low torsional gain
Animals whose vertical semicircular canals have been plugged showed low vertical and even lower torsional gains in combination with eye position-dependent tilts of the eye rotation axis during roll but not during pitch head rotations. Figure 4 illustrates an example of prominent tilts of slow-phase axes during four cycles of sinusoidal roll (1 Hz, ± 5°, peak velocity 31°/s, no visual background). In Fig. 4A, the animal was fixating targets located either at straight ahead (middle panels) or at 20° up (left panel) or 20° down (right panel). The cartoon heads indicate that slow-phase velocity vectors are viewed from the subject's right side (top panels) and from above the subject (bottom panels). Thus the top panels plot the horizontal component of eye angular velocity versus the torsional component. As in Figs. 2 and 3, VOR responses determined from the best-fit generalized gain matrices (black lines) are plotted on top of the velocity vectors (gray dots). When gaze was straight ahead, the velocity vectors were tilted slightly down (due to the fact that in this animal the Listing's plane was tilted slightly up with respect to the magnetic field coordinates). Relative to this orientation, the vectors tilt much further down when gaze was 20° up (left panel) and further up when gaze was 20° down (right panel). That is, VOR responses showed substantial tilts in directions predicted by Listing's law (dashed lines). Plotting the vertical component of slow-phase velocity against the torsional component revealed that the direction of VOR responses was limited to the plane of gaze changes and did not change in the x-y plane, i.e., did not tilt left- or rightward (bottom panels, Fig. 4A).
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Similar results were obtained when the monkey fixated targets at 20° left or 20° right (Fig. 4B). Here, the angular velocity vector tilted prominently to the right (relative to its orientation at center gaze) when gaze was 20° left and to the left when gaze was 20° right (Fig. 4B, top panels). In this case, the orientation of the eye rotation axis in the x-z plane was not affected by the change in gaze direction (Fig. 4B, bottom panels).
Influence of frequency of head rotation and visual background
The effect of eye position on individual slow phases was quantified as described in METHODS, ultimately yielding the tilt angles of the VOR rotation axis, relative to their orientation during center gaze, for each stimulus combination (yaw with gaze 20° up/down, pitch with gaze 20° left/right, roll with gaze 20° up/down and roll with gaze 20° left/right). Each combination of vestibular stimulation and gaze direction was repeated 10 times. Because the eye velocity vectors for a given head rotation (e.g., yaw) showed symmetrical tilt angles for the two gaze directions (e.g., yaw: 20° up/down; see Figs. 2 and 3), the relative tilt angles of the 20 corresponding values were averaged.
Figure 5 summarizes the means ± SD
of the tilt angles collected in normal animals during yaw (), pitch
(
), and roll (left- and rightward pointing triangle for 20°
up/down and 20° left/right gaze directions) as a function of head
rotational frequency. Figure 5, A and B, shows
data obtained with (JU and SU) and without
(JU, SU, and RO) a visual background, i.e., with
or without full-field vision. Positive tilt angles were defined to
indicate a tilt of the eye rotation axis in the direction predicted by
a VOR, which qualitatively obeys Listing's law, i.e., in
the direction of gaze during yaw and pitch and opposite to
the direction of gaze during roll (Fig. 1, Misslisch et al.
1994
; Tweed et al. 1994
).
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The optimal VOR strategy predicts that eye angular velocity is
always parallel to head angular velocity despite changes in gaze
direction so that the computed tilt angles should be zero in all
examined conditions. If the VOR would fully obey Listing's law, tilt angles of 10.0° would be expected during yaw or pitch and
tilt angles of 80.0° during roll (20° eccentric gaze). Smaller angles would be predicted if Listing's law was only
partially followed (see Figs. 1 and
68).
For example, if the monkey VOR would show the same eye
position-dependent pattern of axis tilts as found in humans, i.e.,
half-follow Listing's law, one would expect tilt angles of about
5.0° during yaw or pitch and tilt angles of 9.4° (orthogonal
projection model) and 17.9° (parallel projection model) during roll
(Fig. 1).
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Two main observations can be made from inspecting Fig. 5. First, when normal animals were tested against a full-field visual background (Fig. 5A), tilt angles were close to zero for all rotational frequencies. This indicates that the responses of the visually assisted VOR agree with the predictions of the optimal VOR strategy. Second, when normal animals were tested without visual background (Fig. 5B), a weak dependence of the direction of VOR responses on eye position was found. In this condition, slow phases were somewhat more influenced by eccentric gaze direction during roll as compared with yaw or pitch, especially at higher frequencies of head rotation. Note that the tilt angles obtained during roll were always positive, i.e., the eye rotation axis invariantly tilted in the direction predicted by Listing's law (opposite to gaze). During yaw and pitch, the small tilt angles were usually largest at the lowest frequency of 0.5 Hz and generally decreased to values close to zero at higher frequencies.
Thus VOR responses in normal monkeys were not influenced by the direction of gaze when tested in a relatively natural condition, i.e., during head rotations while viewing a target of interest against a structured visual background. When information from the retinal periphery was eliminated, VOR responses showed small deviations from perfect alignment with the head rotation axis. As shown in Fig. 4, even larger misalignments were seen in animals with plugged vertical semicircular canals during roll. In what follows, we shall describe that the tilt of slow-phase axes, and therefore the adherence to one of the competing predictions of the optimal VOR versus the partial Listing VOR strategies, was related to the strength of the VOR response (gain) during roll, but not during pitch or yaw head rotations.
Orientation of roll VOR axis as a function of torsional gain
Figure 6 shows the mean relative tilt angles of the slow phase rotation axis (±SD) during roll head rotation as a function of torsional gain. As mentioned before, tilt angles for 20° eccentric eye positions are computed relative to their orientation during center gaze. Each symbol denotes the average of 40 measurements obtained at one frequency of torsional head rotation, i.e., 10 repeated measurements of slow-phase tilt for each of the four eccentric gaze directions (20° up, down, right, left). Positive tilt angles denote that the slow-phase axis during roll head rotation tilts in the direction predicted by Listing's law, i.e., opposite to gaze. In this and the subsequent two figures, the following data are shown: for two normal animals (SU and JU), data were obtained at all frequencies and for both visual conditions: without visual background (filled symbols in Figs. 6-8) or with visual background (empty symbols in Figs. 6-8). In the remaining animals, data were collected without a visual background: in the third normal monkey (RO) at all frequencies and in the monkeys with plugged vertical semicircular canals (stars) at 1.0 Hz (JE) or at 0.5 and 1.0 Hz (TW), respectively.
For comparison, the predictions of different VOR strategies are plotted: optimal VOR (black solid line), parallel projection model (black dotted line), and orthogonal projection model (black dashed line). The ordinate on the right side represents the Listing factor associated with the computed tilt angles as predicted by the orthogonal projection model (the one that actually fits the roll data under conditions with reduced visual and vestibular inputs). This factor denotes which tilt angle had to be expected for a 20° eccentric gaze if the VOR would follow Listing's law by the degree shown on the scale. If the Listing factor is zero, the eye rotation axis during roll should tilt by zero degrees, corresponding to the optimal VOR strategy. This factor of Listing's law adherence is linked with torsional VOR gain by a nonlinear relation, i.e., it increases with decreasing torsional gain (APPENDIX, Fig. A1). Note that a torsional gain of unity (optimal VOR) goes along with a Listing factor of zero.
Figure 6A compares VOR responses obtained in normal animals with or without a visible structured background. In the presence of full-field vision (empty symbols) the tilt angles of the eye rotation axis clustered around zero; i.e., under this condition the VOR rotates the eye around the same axis as the head (cf. Figs. 2 and 5A). The corresponding torsional gains were close to unity, indicating that the visually assisted roll VOR counterrotates the eye with about the same speed as the head. The combination of these two findings implies that the visually assisted VOR during roll head rotations optimally stabilizes the retinal image in normal animals. When tested without a visual background (filled symbols), normal animals (SU, JU, and RO) showed torsional gains between about 0.7 and 0.85 and tilt angles of a few degrees. Note, however, that on average the eye rotation axis invariantly tilted in the direction consistent with Listing's law (positive angles).
Figure 6B illustrates that in animals with plugged
semicircular canals (JE and TW) torsional gains
were very low, ranging from 0.2 to 0.5, and the corresponding tilt
angles were quite large, ranging between about 12 and 32° (note the
different scales for abscissa and ordinates: gray shaded area in Fig.
6B corresponds to the range used in Fig. 6A).
Interestingly, the tilt angles from normal and plugged canal animals
collected without visual background lay close to the curve predicted by
the orthogonal projection model (black dashed curve). To quantify the
relation between data and model prediction, we computed a Listing's
law function that best fitted the entire data set, characterizing the
tilt angle as a function of the torsional gain and the projection angle (for details see APPENDIX, Fig. A1). Note that the
fitted curve (solid gray line) lay very close to the orthogonal
projection function (dashed black line) and clearly deviated from the
parallel projection function (dotted black line). For example, if one
sets the Listing's factor to 0.5, corresponding to a VOR that half follows Listing's law, then the following tilt angles
are derived from the data and the two model predictions: data fit, 10.2°; orthogonal projection model, 9.4°; parallel projection model, 17.9°. Very similar results were obtained for the data fits when restricting the fit on separate data sets: all data for normal animals
only equal 11.0°; data for plugged animals without visual background:
= 10.1°; data for normal animals without visual background
equal 11.0°. Thus the orthogonal projection model adequately described the eye position-dependent VOR axis tilts that emerged when
torsional gain decreased due to a reduction of visual and/or vestibular inputs.
Orientation of pitch and yaw VOR axis as a function of vertical and horizontal gain
Figure 7 shows the average relative tilt angles of the VOR rotation axis (±SD) during pitch head rotations with eccentric gaze as a function of vertical gain. To illustrate the theoretical predictions, the same line style conventions were used as in Fig. 6: optimal VOR strategy (black solid line), orthogonal projection model (dashed line), and parallel projection model (dotted line). Again, the ordinate on the right side represents the Listing factor associated with the orthogonal projection model. A Listing factor of one indicates full compliance with Listing's law and predicts that when gaze was 20° left or right the eye rotation axis should tilt by 10° (half-angle rule), and in the direction of gaze.
As in the roll case, tilt angles determined for the condition where full-field vision was present were very close to zero (open symbols), and vertical gains were close to unity, indicating optimal performance of the visually assisted VOR during pitch head rotations.
When no structured background was present, the vertical gain of normal animals was still larger than 0.9, and the tilt angles (filled symbols) clustered around zero, with minor positive (in the direction of gaze) and negative (opposite to the direction of gaze) values. Animals with their vertical canals plugged (stars) showed even lower vertical gains, ranging from about 0.5 to 0.8 and tilt angles near zero. That is, despite the low response gains, slow-phase axes in these animals were well aligned with the pitch axis, in accordance with the optimal VOR strategy.
A regression analysis performed on the pooled data (normal animals for both visual conditions and plugged animals for the no-background condition; gray line in Fig. 7) verified that tilt angles and vertical gain were not correlated (r = 0.1023, n = 23, P = 0.05, 2-sided). No significant correlation between tilt of the eye rotation axis and vertical gain was found when applying the regression analysis on separate data sets (normal monkeys, pooled for both visual conditions; normal monkeys, one visual condition; plugged monkeys).
Figure 8 summarizes the relation between averaged relative tilt angles of the VOR rotation axis (±SD) during yaw head rotations with eccentric gaze as a function of horizontal gain. Data were denoted by the same symbols as in Figs. 6 and 7, and the same line style conventions were used to plot the predictions of the different VOR models. As in the pitch case, the optimal VOR predicts tilt angles of 0°, whereas a pure Listing VOR predicts relative tilt angles of 10° (gaze 20° up/down).
Horizontal head rotation evoked optimal VOR responses in the presence of full-field vision. That is, horizontal gain was close to unity, and the averaged tilt angles of the slow-phase eye rotation axis were near zero. As in the pitch case, when the VOR was tested by presenting a target without a visible background, slightly smaller gain values were observed, but the tilt angles were still close to zero. Animals with plugged vertical canals, tested without visual background, showed horizontal gains that did not differ from those obtained in the normal animals for the same condition. With one exception, mean tilt angles were very small and scattered around zero. The regression line fitted on the pooled data (gray solid line) as a function of horizontal gain showed no significant correlation between relative tilt angles and horizontal gain (r = 0.3279, n = 23, P = 0.05, 2-sided). Further, no correlation between axis tilts and horizontal gain was observed when applying the regression analysis on separate data sets.
It is important to note that the absence of eye rotation axis tilts during yaw and pitch head rotations while animals fixated an eccentric point target cannot be attributed to the contribution of the smooth pursuit system. On the contrary, because smooth pursuit obeys Listing's law, one would expect that the eye rotation axis tilts half as far as the gaze line, i.e., by 10°. In contrast, our data show tilt angles near zero, indicating that smooth pursuit did not contribute to the measured eye rotation.
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DISCUSSION |
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The main result of this study is that the visually assisted VOR in the rhesus monkey invariantly rotates the eye around the same axis as the head (i.e., optimally stabilizes the entire retinal image), independent of the current position of the eye. Deviations from this optimal VOR behavior were found during roll head rotations when the visual and vestibular inputs were reduced, being most prominent for vestibular-deficient animals with low torsional gains. In the following we will consider the implications of these results for the role of vision in human and nonhuman primates, for oculomotor control models, and for the intrinsic coordinate system of the monkey VOR.
Role of vision on monkey and human VOR strategies
Crawford and Vilis (1991) reported that monkey
slow-phase velocity axes did not consistently depend on eye position
when tested during head rotations at 0.5 Hz in a lighted visual
environment. We found that VOR eye rotation axes during yaw and pitch
(at 0.5 Hz) and during roll (at all frequencies) without a
visual background did show small but consistent tilts in directions
predicted by Listing's law (Figs. 3 and 5B). However, this
effect became negligible when animals were tested with a
structured visual background (Figs. 2 and 5A, empty symbols
in Figs. 6-8) corroborating Crawford and Vilis's
(1991)
observations. The finding that the visibility of a
structured background cancels the weak influence of eye position on
normal monkey VOR disagrees with findings in human studies (Misslisch 1995
; Misslisch et al. 1994
,
1996
; Solomon et al. 1997
; Tweed
et al. 1994
). Regardless of whether humans imagined targets in
complete darkness or fixated visible targets on a structured visual
background, the eye position-dependent VOR rotation axis tilts were
almost indistinguishable (Misslisch 1995
). Why does full-field vision apparently alter the VOR strategy in monkeys but not
in humans?
One possibility is that the different VOR strategies reflect a
difference in the relative importance of central and peripheral vision
in human and nonhuman primates. In fact, earlier studies found cortical
magnification factor curves, which indicated that human visual areas
have a greater emphasis on foveal vision than observed in macaques
(Sereno et al. 1995; Tolhurst and Ling
1988
). More recent studies, however, seem to challenge this
notion (Horton and Hocking 1997
; Sereno
1998
). Yet, the functional differences between monkey
and human VOR favor the earlier reports of differences in nonfoveal
versus foveal vision. Namely, our monkey data showed that the
stimulation of the retinal periphery reduced the small deviations from
optimal VOR performance observed when there were no peripheral stimuli,
indicating that stabilization of peripheral retinal images is an
important task of the monkey VOR. In comparison, humans showed the
parallel projection version of a half-Listing VOR (Fig. 1), which
reduced the optical flow over the fovea at the expense of an increased
image slip over more peripheral retinal parts (Misslisch
1995
; Tweed et al. 1994
) (see also below, Fig. A2). Remarkably, this behavior was found even in darkness when there
was no optical flow (Misslisch 1995
; Misslisch et
al. 1994
). Because the observed VOR responses could not be
explained by the effect of ocular plant mechanics (Misslisch et
al. 1994
), it has been suggested that the brain combines
information on head rotation (vestibular organs) with eye position
signals (efference copy and/or proprioception) to compute the direction
of VOR responses that would reduce the optical flow over the fovea in a
lighted environment (Tweed et al. 1994
) (see also
arguments on noncommutative operations below).
Optimal VOR strategy and current models of oculomotor control
The finding of optimal VOR performance in monkeys is significant for clarifying two controversial problems in 3D oculomotor control, i.e., the existence of noncommutative neural operations and the consequences of oculomotor plant mechanics.
To account for the fundamental noncommutative properties of 3D
rotations in the saccadic system, Tweed and Vilis (1987)
proposed a multiplicative interaction between 3D eye position and eye
velocity signals upstream from the neural integrator. Recent work
claimed that this noncommutative multiplicative step may not be needed in the brain stem circuits generating saccades and possibly VOR slow
phases (Quaia and Optican 1998
; Raphan
1997
, 1998
) if one assumes an oculomotor plant
equipped with the recently discovered fibromuscular pulleys
(Demer et al. 1995
, 1997
; Miller
and Demer 1997
; Miller et al. 1993
). In
contrast, Smith and Crawford (1998)
concluded from their
simulation studies that an optimal VOR strategy is incompatible with
any commutative VOR models (Raphan 1997
) and that this
result was independent of the mechanical properties of the plant (i.e.,
whether the effects of fibromuscular pulleys were included in the
simulation of the plant or not). The role of muscle pulleys has also
been discussed in a recent investigation on the human yaw VOR, which
confirmed that slow-phase axes tilt when varying vertical eye position
(Thurtell et al. 1999
).
Along with the results of the Smith and Crawford study (Smith
and Crawford 1998), the simplest interpretation of our data are
to assume neuronal control mechanisms rather than mechanical plant
properties to account for the different VOR strategies that accomplish
the different visual needs in humans and monkeys. One problem with the
argument that the plant mechanics provide Listing's law during
saccadic and smooth pursuit eye movements (Miller and Demer
1997
) is that the deviations of VOR eye movements from the Listing's law behavior would have to be interpreted as an incomplete neural compensation of the mechanically set default behavior. This kind
of reasoning, however, could not explain the differential effects of
eye position on VOR responses during roll (large axis tilts) and pitch
(minor axis tilts) when visual and vestibular inputs are impaired (cf.
data of plugged animals denoted by stars in Figs. 6 and 7).
Listing's law and coordinate system of the VOR
The main finding of this study is that the visually assisted VOR
in normal monkeys functions in head-fixed coordinates and is
independent of the current gaze direction (optimal VOR strategy). Previous investigations have shown that the orientation of the semicircular canals in the head represents the sensory coordinate system for rotational vestibular information processing (Blanks et al. 1985; Reisine et al. 1988
). Moreover, the
pulling directions of the extraocular muscles as well as the
on-directions of their motoneurons align approximately with those of
the semicircular canals (Miller and Robins 1987
;
Suzuki et al. 1999
). Neurons in the rostral interstitial
nucleus of the medial longitudinal fasciculus showed directional coding
in the head-fixed coordinates defined by Listing's law
(Crawford and Vilis 1992
; Hepp et al.
1994
; Vilis et al. 1989
). And finally, the
vertical-torsional integrator in the interstitial nucleus of Cajal also
seems to operate in Listing's coordinates (Crawford
1994
). Taken together, this suggests that both sensory and
motor brain structures in the monkey use head-fixed coordinate systems
that may simplify sensorimotor transformations and facilitate accurate
VOR eye movements at short latency.
When rotating normal monkeys during roll without a visual background,
we found that torsional gain decreased and slow-phase axes tilted
slightly in the directions predicted by the Listing models (Figs. 3 and
5B). Monkeys with reduced torsional and vertical gains
following plugging of the vertical semicircular canals showed large eye
position-dependent tilts of the axis of slow-phase velocity during
roll but not during pitch head rotations (Figs. 4, 6, and 7). The
relative importance of optimal VOR versus partial Listing's law
strategies during roll appeared to depend on the torsional gain: if
torsional gain decreased, a dependence of the VOR rotation axis on eye
position emergedin a manner that was remarkably consistent with the
orthogonal projection model. The functional significance of this
strategy could be to reduce deviations from visuomotor constraints
imposed by Listing's law, i.e., to restrict torsional eye velocity.
The fact that VOR in normal monkeys completely ignores Listing's law
makes this explanation improbable, however. A more likely reason
relates to the geometric fact that during roll head rotation the
optical flow over the fovea strongly depends on the gaze direction
(Tweed et al. 1994
). For example, a counterclockwise head rotation with the subject looking straight ahead induces a
clockwise optical flow, with a stable foveal center and increasing clockwise flow velocities in the eccentric retinal regions. If the
subject looks 20° left (see bottom panel in Fig. 1),
targets around the fovea have a predominantly upward motion component relative to the head (purely upward at the center of the fovea). Thus
efficient tracking of targets in that condition demands that the eye
rotates upward in addition to the compensatory counterclockwise rotation. In other words, the VOR rotation axis should move rightward, a requirement matched by the data (Fig. 4B). Even though
this strategy of tilting the eye rotation axis as predicted by the orthogonal projection model cannot perfectly stabilize the retinal image it improves foveal and perifoveal image stabilization. Perfect stabilization of the fovea, at the expense of the retinal periphery, is
achieved by tilting the eye rotation axis according to the parallel
projection strategy. This strategy was found in normal human subjects
and requires much larger axis tilts than the orthogonal projection
strategy (e.g., Misslisch 1995
; Misslisch et al.
1994
; Tweed et al. 1994
). The moderate axis
tilts found in plugged-canal monkeys were consistent with the
orthogonal projection model. It can be shown that this strategy
considerably reduces the optical flow over foveal and off-foveal
regions, compared with a low-gain roll VOR with a nontilting rotation
axis (for details see APPENDIX, Fig. A2).
Conclusions
Under natural visual conditions, normal monkeys choose the unique VOR angular velocity vector that provides a stable image on the entire retina: opposite in direction (and of equal size) than head velocity. When visual and/or vestibular inputs are reduced, eye position-dependent responses in directions predicted by Listing's law appear during roll but not pitch or yaw head rotations. The finding of optimal yaw, pitch, and roll VOR behavior in normal monkeys may be related to the greater significance of peripheral relative to central vision in nonhuman as compared with human primates. The demonstration of optimal VOR behavior in the monkey also supports the notion of noncommutative operations in the oculomotor system and questions a dominant role of plant mechanics.
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APPENDIX |
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Tilt angles, Listing factor, and VOR models
To compare the experimentally determined tilt angles of VOR
responses, we fitted an angle to the data describing the tilt of
eye velocity (angle
) as a function of torsional gain (k, see Fig. A1)
![]() |
(A1) |
|
To quantify the degree of compliance with the orthogonal projection
model (Listing factor LL), we measured the length P of the
vector difference between the normalized optimal VOR eye velocity vector (opt) and the normalized measured
eye velocity vector (
exp) as a function
of the torsional gain (k; i.e., the projection of the vector
exp onto the x-axis). In the
orthogonal projection model (
=
/2), full compliance with Listing's law (half-angle rule) would yield a maximal, gaze-dependent torsional gain of kL = sin2(
/2) (Fig. A1). Any further increase in
torsional gain k would decrease the Listing's law factor
(LL = p*) as follows
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(A2) |
Retinal image stabilization and VOR models
The consequences of the partial Listing VOR models for gaze
stabilization during roll head rotations can be quantified by the
foveal gain, Gfovea,
defined as the ratio of image velocity over the fovea (when gaze
deviates from the head's roll axis) and VOR-induced velocity of the
gaze line. The foveal gain depends on gaze eccentricity as follows
![]() |
(A3) |
|
Figure A2 (left panel) shows that if the VOR follows the
projection model (filled symbols) the foveal gain is considerably enhanced over a range of gaze eccentricities. For example, a tilt of
the rotation axis of = 8.3°/17.2° would increase foveal
gain from 0.38/0.38 (average torsional gain in 3 monkeys with plugged vertical semicircular canals for an axis tilt
= 0, open
symbols in Fig. A2, cf. stars in Fig. 6) to 0.69/0.67 when gaze is
10°/20° eccentric. Thus a comparable foveal gaze enhancement
requires increasingly larger axis tilts when gaze becomes more
eccentric. Note that
exp/
opt = 0.38 is
kept constant, reflecting the assumption that the vestibular signals
are constant and independent of the gaze direction. Figure A2
(right panel) shows the result of using Eq.
A2 to compute the change in meridional gain,
Gmerid, defined as the gain at
different eccentricities along a meridian through the fovea. In the
simulation shown, gaze direction is 20° left. For the parallel
projection model (stars), Gmerid is
ideal at the fovea and increases or decreases in the retinal periphery, producing additional retinal image slip off the fovea. For the orthogonal projection model (filled symbols),
Gmerid is ideal 10° right from the
fovea and also shows an increase or decrease at other retinal eccentricities.
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ACKNOWLEDGMENTS |
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We thank B. Disler and A. Züger for excellent technical assistance.
This work was supported by Swiss National Science Foundation Grant 31-47 287.96.
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FOOTNOTES |
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Address for reprint requests: H. Misslisch, Dept. of Neurology, University of Zurich, Frauenklinikstr. 26, CH-8091 Zurich, Switzerland.
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 14 December 1999; accepted in final form 16 February 2000.
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REFERENCES |
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