1Eye and Ear Research Unit, Department of Neurology, Royal Prince Alfred Hospital, Camperdown, NSW 2050, Sydney, Australia; and 2Institute of Neural and Intelligent Systems, Department of Computer and Information Science, Brooklyn College of City University of New York, Brooklyn, New York 11210
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ABSTRACT |
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Thurtell, Matthew J., Mikhail Kunin, and Theodore Raphan. Role of Muscle Pulleys in Producing Eye Position-Dependence in the Angular Vestibuloocular Reflex: A Model-Based Study. J. Neurophysiol. 84: 639-650, 2000. It is well established that the head and eye velocity axes do not always align during compensatory vestibular slow phases. It has been shown that the eye velocity axis systematically tilts away from the head velocity axis in a manner that is dependent on eye-in-head position. The mechanisms responsible for producing these axis tilts are unclear. In this model-based study, we aimed to determine whether muscle pulleys could be involved in bringing about these phenomena. The model presented incorporates semicircular canals, central vestibular pathways, and an ocular motor plant with pulleys. The pulleys were modeled so that they brought about a rotation of the torque axes of the extraocular muscles that was a fraction of the angle of eye deviation from primary position. The degree to which the pulleys rotated the torque axes was altered by means of a pulley coefficient. Model input was head velocity and initial eye position data from passive and active yaw head impulses with fixation at 0°, 20° up and 20° down, obtained from a previous experiment. The optimal pulley coefficient required to fit the data was determined by calculating the mean square error between data and model predictions of torsional eye velocity. For active head impulses, the optimal pulley coefficient varied considerably between subjects. The median optimal pulley coefficient was found to be 0.5, the pulley coefficient required for producing saccades that perfectly obey Listing's law when using a two-dimensional saccadic pulse signal. The model predicted the direction of the axis tilts observed in response to passive head impulses from 50 ms after onset. During passive head impulses, the median optimal pulley coefficient was found to be 0.21, when roll gain was fixed at 0.7. The model did not accurately predict the alignment of the eye and head velocity axes that was observed early in the response to passive head impulses. We found that this alignment could be well predicted if the roll gain of the angular vestibuloocular reflex was modified during the initial period of the response, while pulley coefficient was maintained at 0.5. Hence a roll gain modification allows stabilization of the retinal image without requiring a change in the pulley effect. Our results therefore indicate that the eye position-dependent velocity axis tilts could arise due to the effects of the pulleys and that a roll gain modification in the central vestibular structures may be responsible for countering the pulley effect.
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INTRODUCTION |
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The angular vestibuloocular reflex (aVOR) has an
important role in minimizing retinal image slip during angular head
rotations. To achieve this minimization, the eye and head velocity axes
must align, and the eye and head velocities must be opposite in
direction but equal in magnitude. That is, the gain of the aVOR must be 1.0 when viewing a target at far distance (more than ~1.0 m) and when
rotating about a head-centered axis. A number of studies have shown
that, during yaw and pitch head rotations, the eye and head velocity
axes do remain approximately aligned and the gain of the aVOR is
approximately equal to 1.0, when the eye is positioned at or near the
center of the ocular motor range at the start of the head rotation
(Aw et al. 1996; Crawford and Vilis 1991
). Interestingly, a number of recent studies have revealed that the eye and head velocity axes do not always align when there is a
requirement to fixate a point away from the primary position. In fact,
during low-frequency sinusoidal oscillations in yaw, pitch, and roll,
the eye velocity axis has been observed to systematically tilt away
from the head velocity axis in a manner that is dependent on
eye-in-head position (Frens et al. 1996
;
Misslisch et al. 1994
). For example, during yaw
oscillations the eye velocity axis tilts back when gaze is directed up
and forward when gaze is directed down. These eye velocity axis tilts
result in mismatches between the roll eye and head velocities, and
hence retinal image slip.
Recently, high acceleration passive (Aw et al. 1996;
Halmagyi et al. 1990
) and active (Foster et al.
1997
) head-on-neck "impulses" have been utilized to study
eye velocity axis tilts in human subjects fixating targets positioned
away from primary position (Thurtell et al. 1999a
). In
response to the passive head impulses, no eye velocity axis tilt was
observed for the first ~50 ms after the onset of the head rotation,
for any eye position. Palla et al. (1999)
have also
observed close alignment of the head and eye velocity axes in the early
part of the response to high velocity passive head impulses.
Thurtell et al. (1999a)
found, however, that the axis
tilts did become apparent after the initial 50 ms of the response, and
were observed to occur in the same direction as seen in previous
studies. The eye velocity axis tilts were also observed in the
responses to active head impulses, but they began within 5 ms of the
onset of the head rotation (Thurtell et al. 1999a
).
The mechanisms responsible for producing the axis tilts are unclear. If
the eye movements obeyed Listing's law, a constraint on ocular
kinematics (von Helmholtz 1866), the angle of eye
velocity axis tilt would be half that of eye deviation away from
primary position (Tweed and Vilis 1990
). However, the
angle of tilt of the velocity axis is less than this (Frens et
al. 1996
; Misslisch et al. 1994
; Solomon
et al. 1997
). Misslisch et al. (1994)
concluded that the tilts arose due to a compromise between no axis tilt (perfect
image stabilization) and the constraints imposed by Listing's law. The
mechanism for achieving the compromise was thought to be neural in
origin. Hence, in response to identical head rotation stimuli, the
signal driving the eye muscles would alter depending on eye position.
Misslisch et al. (1994)
also posited that the goal of
the compromise was to minimize retinal image slip on the fovea, while
allowing retinal image slip to occur on the periphery of the retina.
Recently, it has been shown that the paths of the rectus extraocular
muscle bellies are constrained by orbital tissue, the fibromuscular
pulleys (Clark et al. 1998, 1999
;
Demer et al. 1995
, 1997
; Miller et
al. 1993
). If it is assumed that the pulleys implement a
kinematic rotation of the torque axis that is approximately half the
angle of eye deviation away from primary position, then Listing's law
is obeyed during saccades when the central drive is confined to the
two-dimensional pitch-yaw plane (Raphan 1997
, 1998
). If the pulleys produce such a rotation of the
torque axes, the torque generated by the muscles becomes eye
position-dependent. As a result, the eye velocity axis will tilt as a
function of eye position. Therefore it is no longer clear that eye
position-dependence in the aVOR is neural in origin; it could well
arise as a consequence of the eye plant properties.
The purpose of this study was to investigate the mechanisms by which
the eye position dependence of the aVOR could be generated during
active and passive head rotations, using a model-based approach.
Specifically, we have investigated whether the eye position-dependence of the aVOR can be predicted by a model that incorporates a
semicircular canal system (Yakushin et al. 1998), a
commutative velocity-position integrator in the CNS (Schnabolk
and Raphan 1994
) and a pulley system in the plant
(Raphan 1998
). To evaluate the accuracy of the
predictions, we have compared high-resolution data collected from
normal human subjects (Thurtell et al. 1999a
) with the
predictions of the model. To maximize the validity of the model
predictions, head velocity and initial eye orientation data were used
as input for the model. We have also sought to determine whether and to what extent additional "neural processing" is required to predict the patterns observed in the data. The findings presented in this paper
have previously been presented in abstract form (see Thurtell et
al. 1999b
).
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METHODS |
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Conventions
The head and eye velocities from the data and model simulations were expressed relative to a right-handed head-fixed coordinate system. Positive yaw is a leftward rotation, positive pitch is a downward rotation, and positive roll is a clockwise rotation.
Data collection and analysis
The model simulations presented in this paper were compared
directly with data obtained from a previous study (Thurtell et al. 1999a). The experimental procedures are briefly summarized here. See Thurtell et al. (1999a)
for a complete and
detailed description of the experimental setup and protocols.
Two experiments were conducted: one using high-velocity
passive (manually generated) yaw head rotations, and the
other using high-velocity active (self-generated) yaw head
rotations. Eight normal human subjects were tested in each experiment.
The head rotation stimuli typically had an amplitude of 15-25° (with
peak velocity about 250°/s). The velocity vectors corresponding to the head rotation were approximately aligned with the z-axis
of the head-fixed coordinate system (making the rotation predominantly yaw), although the rotations inevitably had pitch and roll components due to the mechanics of the neck joints and soft tissues. During these
experiments, responses were recorded using the magnetic search coil
technique (Collewijn et al. 1985; Robinson
1963
) with subjects maintaining fixation on different targets
(20° up, 0° and 20° down) located on a tangent screen 94 cm from
the front of the cornea. The search coil signals were digitized at 1 kHz with a 16-bit analog-digital converter. Rotation vectors
corresponding to eye-in-head and head-in-space position, and velocity
vectors corresponding to eye-in-head and head-in-head angular velocity, were calculated from the search coil data (Haslwanter
1995
; Haustein 1989
; Hepp 1990
;
Tweed et al. 1990
). Analysis was restricted to a 100-ms
period, beginning 20 ms before the onset of head rotation, to exclude
the effects of non-VOR systems such as the cervicoocular reflex and
smooth pursuit (Bronstein and Hood 1986
; Carl and
Gellman 1987
; Tychsen and Lisberger 1986
).
In this study, the data and corresponding model predictions will be
presented as time series, and then compared by projecting the predicted
eye velocities onto the pitch (xz) and roll (yz) planes. The model predictions from the 100-ms period will be presented, as for data from Thurtell et al. (1999a). The
predictions for the entire response will be presented in some cases.
Modeling
The model was implemented using the Microsoft Visual C/C++
programming environment. Integration processes in the model were performed using a regular trapezoidal rule algorithm, with temporal update every 0.001 s. Because the dominant time constant of the system
is orders of magnitude larger than this value, the integration technique worked well (Raphan 1998; Yakushin et
al. 1998
).
Since the model assumed that the reference eye position corresponds
with the primary position, we determined primary position from
subjects' Listing's plane data and recomputed the rotation vectors
and velocity vectors relative to primary position. That is, the data
were rotated so that each subject's Listing's plane aligned with the
roll plane of the head-fixed coordinate frame. These computations were
conducted using the methods of Tweed et al. (1990). The
new coordinate frame, which is close to the stereotaxic coordinate
frame, is what we will refer to as being the head-fixed coordinate frame.
The analysis of the model predictions was conducted using MATLAB 5.2 running on an IBM-compatible PC under Windows NT. The figures presented in this paper were generated using Splus running on a DECstation 5000/240 under Ultrix, and Canvas (Version 6.0) running on an IBM-compatible PC under Windows NT.
Model organization and conceptual basis for study
OVERVIEW OF THE aVOR MODEL.
The model of the aVOR is comprised of a number of major components
that, in concert with one another, produce an eye rotation response to
a head rotation stimulus (Fig. 1). While
detailed descriptions are given elsewhere (Raphan 1998;
Yakushin et al. 1998
), a brief description of each of
the model components is included below and in APPENDIXES A AND B.
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MODEL OF SEMICIRCULAR CANALS AND VESTIBULAR AFFERENTS.
The semicircular canal model was based on the canal model presented in
Yakushin et al. (1998). Since each semicircular canal responds to angular acceleration about an axis normal to the canal plane, the canal model must incorporate a kinematic transformation of
the head velocity from head-fixed coordinates into canal coordinates. Thus the head velocity is projected onto each of the canal plane normals, which form a nonorthogonal basis in humans. In the model, the
orientations of the canals were adjusted to agree with those reported
for humans (Blanks et al. 1975
).
MODEL OF THE CENTRAL aVOR PATHWAYS.
The signal from the vestibular nuclei passes to the ocular motor nuclei
via two pathways: a direct ocular motor pathway
(Dp) and one that activates the
velocity-position integrator. The velocity-position integrator was
implemented as a commutative vector integrator, characterized by gain
matrices (Gp and
Cp) and a system matrix (Hp) that determines the integrator's
dynamics (see APPENDIX B for further details). The
parameters of the velocity-position integrator were set as in
Raphan (1998). The matrices were represented with
respect to head-fixed coordinates. The sum of the outputs from the
direct pathway and velocity-position integrator was used to drive the
motoneurons passing to the extraocular muscles.
MODEL OF THE OCULAR MOTOR PLANT.
Torque (m) is generated by the extraocular muscles as a
result of activity in the motoneurons
(mn). Due to the effects of the
fibromuscular pulleys, the torque axis is rotated in a manner depending
on eye position (Fig. 2). For example,
when the eye looks up by an angle , the pulley changes the pulling
direction of the muscle, thereby rotating the torque axis by an angle
. In the model, a muscle matrix M implements the
transformation from motoneuron firing to torque. M is a
rotation matrix that incorporates the action of the pulleys in three
dimensions. The transformation is given by
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(1) |
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(2) |
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OPTIMAL MODEL PARAMETERS.
To determine the optimal pulley coefficient to fit the data in this
study, we calculated the pulley coefficient at which the mean square
error (E2) between roll eye velocities
for data [x(data)] and model prediction [
x(pred)] was a minimum. The pulley
coefficient was varied from 0 to 1, in 0.01 increments. The mean square
error was computed for each pulley coefficient value as
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(3) |
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RESULTS |
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Data-model comparison for active head impulses
Subject 0031m executed active yaw head impulses that
had a large yaw component, and minimal pitch and roll components
throughout the head movement (Fig.
3A). The initial fixation
point of the subject did not affect the starting head position or the
head trajectory (Thurtell et al. 1999a). When the
subject was looking 20° up, the yaw and pitch eye velocities
approximately compensated for the yaw and pitch head velocities,
respectively (Fig. 3A, heavy and dashed shaded lines).
However, the roll eye velocity was inappropriately clockwise, as there
was little roll head velocity. When the subject was fixating a central
target, all components of eye velocity were approximately compensatory
for the head velocity stimulus. When the subject was looking 20°
down, the yaw and pitch eye velocities compensated for the yaw and
pitch head velocities, but the roll component was again inappropriate
(as in the 20° up condition), on this occasion being
counterclockwise. These patterns are consistent with those observed in
data collected from human subjects during low-frequency yaw
oscillations (Misslisch et al. 1994
). A complete
description and analysis of the data for a range of subjects can be
found in Thurtell et al. (1999a)
.
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The head velocity trajectories from the data were used as input for the
model, as were the initial eye position data. The curve representing
mean square error between data and model torsional eye velocities, as a
function of pulley coefficient, was approximately parabolic for both
upward (Fig. 4, - - -) and downward
(Fig. 4, - - - - -) gaze. For the 0° initial fixation position,
the mean square error was not of great magnitude and varied little over the range of pulley coefficients (Fig. 4, · · ·). The curve
representing the mean square error for the average of all gaze
positions had a minimum corresponding to a pulley coefficient of 0.53 (Fig. 4, ). Using this mean value, the yaw, pitch, and roll
components of eye velocity were predicted by the model for all fixation
positions (Fig. 3B).
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Consistent with the finding that a pulley coefficient of 0.53 closely predicted the time course of the torsional component of eye velocity (Fig. 5A, middle), the axis tilt was also predicted at every instant of time during the response (Fig. 5B, middle). When the pulley coefficient was reduced to 0.00, thereby removing the effect of the pulleys, the torsional eye velocity mirrored torsional head velocity (Fig. 5A, bottom), resulting in approximate head and eye velocity axis alignment independent of eye position (Fig. 5B, bottom).
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We also compared the averaged data from eight subjects (Fig. 6A), with model predictions (Fig. 6B). The optimal pulley coefficient value for each subject is given in Table 1. Seven of the subjects had optimal pulley coefficients ranging from 0.27 to 0.58, with only one of the eight subjects having an optimal pulley coefficient <0.25. While the mean square error curves from the subjects demonstrate a single minimum, the gradient of the curve for most subjects was small over a broad range of values close to the optimal pulley coefficient, representing a relative insensitivity in using this method for determining optimal model parameters. However, introducing weights to different parameters would bias our results and would not increase confidence in our findings.
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The optimal pulley coefficient across all subjects occurred when the median of the mean square error over all trials and subjects was minimal; it was found to be 0.5 (Fig. 7A; Table 1). With a pulley coefficient of 0.5, the model predicted the average direction and magnitude of the axis tilts reasonably well (Fig. 6B), although it was more accurate when the individual pulley coefficients were used for each subject (Fig. 5B, middle). For the 20° up condition, the average eye velocity axis was noted to be aligned with the head velocity axis initially, but tilted back for head velocities above about 125°/s (Fig. 6A). The initial alignment occurred in some subjects, affecting the average behavior. In other subjects, there was immediate axis tilt, as predicted by the model (Figs. 5B and 6B). In response to the center condition, the head and eye velocity axes were noted to remain fairly well aligned (Fig. 6A); the model accurately predicted the eye velocity response (Fig. 6B). For the 20° down condition, there was a significant initial and maintained forward axis tilt (Fig. 6A), as predicted by the model (Fig. 6B).
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The axis tilts described above occur predominantly in the pitch plane, and there is little tilt of the eye velocity axis in the roll plane (Fig. 6A). In other words, there is good alignment of head (heavy line) and eye (dashed shaded line) velocity axes in the roll plane at all points in the trajectory. The model predicted no significant axis tilt in the roll plane for any of the subjects, agreeing with the patterns observed in the data (Fig. 6B).
Data-model comparison for passive head impulses
As previously shown (Thurtell et al. 1999a), there
are eye position-dependent velocity axis tilts during passive head
impulses as during active head impulses. The optimal pulley coefficient for passive head impulses was computed in all subjects using a gain
matrix equal to that used for active head impulses; the values of these
pulley coefficients are given in Table 1. Subjects' optimal pulley
coefficients ranged from 0.03 to 0.31. The optimal pulley coefficient
was calculated across all subjects, as for the active head impulses; it
was found to be 0.21 (see Fig. 7B; Table 1).
For subject 0036m, the optimal pulley coefficient was found
to be 0.19 for a roll gain of 0.7. Using this value of pulley coefficient, the model predicted the fundamental features of the axis
tilts (Fig. 8). However, the dynamics of
the axis tilts during passive and active head impulses were distinctly
different, and the model, with a fixed pulley coefficient and aVOR roll
gain, did not predict the dynamics seen during passive impulses (Fig. 8, arrows). The axis tilts described for active head impulses also
occurred during passive impulses, but only after the first 50 ms of the
onset of head rotation. During the first 50 ms of the passive head
impulse, there was close alignment of the head and eye velocity axes
(Thurtell et al. 1999a).
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In subject 0030m, the head velocity stimulus had a large
roll component. Using this subject's data, we first considered whether the close alignment of the axes was due to a dynamic modification of
the pulley effect. Using a roll aVOR gain of 0.7 (Aw et al. 1996) and a pulley coefficient of 0.0, the model predicted
better initial alignment between head and eye velocity axes. But the alignment was not as close as in the data (Fig.
9), suggesting that a change in pulley
coefficient alone was insufficient to bring about the axis alignment.
We next examined the effects of an alteration in the gain of the roll
component of the aVOR (g11 in Fig. 1)
in producing the initial axis alignment. Such a mechanism could
maintain the roll gain at one level during the initial period of the
response and then allow it to revert toward a default value (approximately 0.7) after the 50 ms had elapsed. We tested this hypothesis by adjusting the roll gain to fit the data from
subject 0030m for the first 50 ms of the response, while
keeping the pulley coefficient at a constant value of 0.5 (Fig. 9). For
the center condition, model-data differences were minimized during the
initial period when the roll gain was equal to 1.0 (Fig. 9). For the
20° gaze up condition, the roll gain needed to be equal to 0.7 during this period to maintain axis alignment, while for 20° down, the best
fit to the data occurred when the roll gain was >1.0 (Fig. 9). These
variations in the roll gain as a function of initial eye-in-head
position brought about alignment of the head and eye velocity axes, as
observed in the data (Fig. 9), without requiring a change in pulley
coefficient. We found, however, that there were a number of
combinations of pulley coefficient and roll gain that could produce the
initial axis alignment (see Fig. 10).
It is therefore possible that a combination of dynamic pulley
coefficient and roll gain modification is responsible for producing the
initial axis alignment for each subject.
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DISCUSSION |
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Mechanisms for VOR eye position-dependence
When Misslisch et al. (1994) studied eye
position-dependent eye velocity axis tilts in humans using 0.3-Hz
sinusoidal whole-body rotations, they noted that the tilts were
consistent with a compromise between Listing's law and perfect
compensation for head rotation. After studying the predictions of the
SQUINT model of extraocular muscle geometry (Miller and Robinson
1984
), they concluded that the central signals driving the
extraocular muscles must already encode the appropriate eye velocity
axis tilts, and that orbital mechanics contribute very little to the
production of the tilts. They had not, however, considered the effects
of the rectus fibromuscular pulleys (Clark et al. 1998
,
1999
; Demer et al. 1995
,
1997
; Miller et al. 1993
) in their study.
Preliminary work by Raphan (1997)
indicated that the
pulleys might have an important role in bringing about the tilts. More
recently, however, it has been suggested that even with an ocular motor
plant that incorporates pulleys, no integrator model can predict the
eye position dependence of the aVOR, and consequently a neural
integrator that is quaternion-based and noncommutative is required
(Smith and Crawford 1998
; Tweed 1997
).
However, our model, which incorporates a commutative vector velocity-position integrator, muscle pulleys, and a three-dimensional semicircular canal system, predicts the axis tilts.
The role of the pulley system was first considered in studies concerned
with modeling eye movement trajectories during saccades. In those
studies, it was shown that if the pulleys are correctly positioned and
the command signal is confined to the pitch-yaw plane, kinematically
accurate saccades can be produced by models that incorporate a
commutative vector velocity-position integrator (Quaia and
Optican 1998; Raphan 1997
, 1998
).
The value of the pulley coefficient is critical in the saccadic model,
because it determines the magnitude of the eye velocity axis tilt when the driving signal is in the pitch-yaw plane and, hence, the degree of
adherence to Listing's law (Raphan 1998
). With a
two-dimensional pitch-yaw driving signal, a pulley coefficient of 0.5 gives perfect adherence to Listing's law, since the angle of velocity
axis tilt is exactly half that of eye deviation from primary position.
However, for saccades made between tertiary eye positions, Listing's
law is not perfectly obeyed, as indicated by the presence of
significant torsional transients (Straumann et al. 1995
;
Tweed et al. 1994
). The torsional transients occur
because the eye velocity axis tilt is not always half of the angle of
eye deviation from primary position. Indeed, it has been shown that the
pulley coefficient may vary from 0.39 to 0.6 between individual
subjects, if the torsional transients seen in their saccadic data are
to be predicted using a model that utilizes a two-dimensional driving
signal (Raphan 1998
). Since the pulley system is a
feature of the oculomotor plant, it is reasonable to expect that the
pulleys contribute in the same way during the aVOR as during saccades.
Consequently, it would be expected that if the axis of vestibular
stimulation were confined to the pitch-yaw plane, the velocity axis
tilts would primarily arise as a result of the eye position-dependent changes in the pulling directions of the muscles (Raphan
1998
). The results of this study indicate that the pulley model
accurately predicts axis tilts in accordance with these expectations.
Indeed, the pulley coefficient that gave optimal performance of the
aVOR for active head movements over all subjects was 0.5, the same as
that required for Listing's law to be obeyed during saccadic eye
movement simulations. There were, however, considerable inter-subject differences (see Optimal pulley coefficient
calculations).
Differences between saccadic and aVOR kinematics may be attributed to
the fact that the semicircular canals generate roll control signals,
while the saccadic system probably generates two-dimensional pitch-yaw
signals (Raphan 1998). Since we used actual head impulse
data as input to the model, there was, unavoidably, a roll component to
our stimulus. With the gain of the roll component of the aVOR set to
0.7 during active head impulses, the model accurately predicted, on
average, the variations in tilt as a function of eye position and head
velocity. Thus the model predicts that the axis tilt patterns may
essentially arise as a result of two factors: the pulley
effect and the less-than-unity roll gain. As we have shown, a pulley
coefficient of 0.0 gives approximate eye and head velocity axis
alignment and no eye position dependence (Fig. 5B,
bottom), whereas a pulley coefficient of 0.5 would tilt the
eye velocity axis by half the angle of gaze deviation from primary
position. A pulley coefficient <0.5 gives an eye velocity axis tilt
that is less than half the angle of gaze eccentricity. The
less-than-optimal roll gain of the aVOR (which is ~0.7 during passive
head impulses) would further diminish the relative tilt of the eye
velocity axis if there is a roll component to the head movement.
Variations in the pulley configuration and roll gain between
individuals, in addition to different stimulus and species characteristics, could account for the variations in the amount of tilt
from subject-to-subject and for the differing results reported in
different studies. Thus for active head impulses, there is no need to
postulate an axis tilting mechanism in the central vestibular
structures (Misslisch et al. 1994
) or a complex multiplicative tensor interaction between angular eye velocity and
position with a quaternion integrator (Smith and Crawford 1998
) to bring about this simple result.
Passive-active differences
While the tilt of the eye velocity vector as a function of eye
position was a prominent aspect of the response to active head impulses, there were striking differences when active and passive head
impulses were compared (Thurtell et al. 1999a). For
active head impulses, the tilts became apparent within the first 5 ms of the response and were maintained throughout the trajectory, as
predicted by the model. For passive head impulses, there was little
tilt of the eye velocity axis during the first 50 ms (Thurtell et al. 1999a
). These findings are consistent with data showing negligible axis tilt in the averaged eye velocity vectors during the
first 10° of head movement during passive head impulses (Palla et al. 1999
). The axis of eye velocity was noted to tilt
gradually after the initial 50-ms period (Thurtell et al.
1999a
). Thus passive head impulse axis tilts are not uniform
over time but evolve over the duration of the head trajectory. We found
that the initial alignment of the eye and head velocity axes was
inconsistent with model predictions for a fixed pulley coefficient of
0.5 and a fixed aVOR roll gain of 0.7.
We considered a number of mechanisms that might be responsible
for the temporal evolution of eye velocity axis tilt. Dynamic changes
in pulley effect may arise as a result of the insertion of the orbital
layers of the rectus muscles into the connective tissue of the pulley
structures (Demer et al. 2000). We found that removing the
effect of the pulleys, by adjusting the pulley coefficient to 0.0 and
maintaining the roll gain of the aVOR at 0.7, resulted in closer
initial axis alignment and loss of eye position-dependence. The model
still did not, however, predict the degree of alignment observed in the
data. Thus a dynamic modification in pulley coefficient could not
completely account for the initial axis alignment during passive head
impulses. In addition, such a peripheral mechanism would have to be
specific to the passive aVOR because these dynamic changes in eye
velocity axis tilt were not observed during active head rotations and
have not been observed during the execution of saccades.
We considered whether the axis tilts were due to a neural-based preprogrammed mechanism, which was delayed and therefore responsible for the initial axis alignment. Eye velocity tilting is functionally appropriate for eye positioning mechanisms, such as the saccadic system, which attempt to reduce torsional transients and maintain the eye orientation axis within Listing's plane. Relative tilting of the eye and head velocity axes is functionally counter to the goal of the aVOR, which is to compensate for head velocity both in magnitude and direction, thereby bringing about retinal image stabilization. Thus a preprogrammed mechanism to misalign the eye and head velocity axes would be functionally inappropriate for the aVOR and unlikely to be responsible for generating the axis tilts.
In contrast to preprogrammed axis tilts, we found that the axis
alignment could be predicted well by modifying the roll gain of the
aVOR during the initial 50-ms period while maintaining the pulley
coefficient at a constant value of 0.5. It is important to note that an
almost perfect match to the data could be produced using a number of
combinations of pulley coefficient and aVOR roll gain (Fig. 10).
Therefore either a dynamic roll gain modification or dynamic change in
pulley effect, or a combination of both, could be responsible for
producing the initial axis alignment during passive head rotations. The
roll gain modification would constitute a form of eye
position-dependent processing in central vestibular structures, which
would help counteract the tilting of the eye velocity axis produced by
the pulleys, to bring the eye and head velocity axes into better
alignment. A roll gain modification may be required in the aVOR and not
during saccades because of their essentially different functional
roles. The saccadic system functions to move the eyes from one fixation
point to another. It is, therefore of benefit if the velocity axis
tilts to minimize positional roll transients (Raphan
1998). The aVOR, on the other hand, functions to minimize
retinal slip. It is, therefore inappropriate for the eye velocity axis
to tilt. The roll gain modification that we are proposing is entirely
different from other proposed forms of eye position-dependent central
processing, because it brings about eye and head velocity axis
alignment and increased retinal image stability, rather than the axis
tilt and decreased retinal image stability that would result from the
other mechanisms (Misslisch et al. 1994
).
While it is probable that the pulleys are responsible for producing the
observed axis tilts, as they have been anatomically demonstrated, the
site of the proposed roll gain change is not clear. One possibility is
that the otoliths are involved in the gain modification. During these
yaw head rotations, there would be centripetal acceleration generated
at each macula due to their eccentricity relative to the rotation axis
of the head. During head-on-neck yaw rotations, the head rotates about
the atlantooccipital joint. The distance from this rotation axis to the
maculae is <5 cm (Curthoys et al. 1977). As the
velocity during the initial 50 ms of rotation is <200°/s, the
centripetal acceleration at each macula would be very small (<0.05 g).
In addition, the centripetal accelerations at each macula would be
toward the rotation axis. The effect would be similar to accelerating
forward and would not be expected to generate strong compensatory roll
eye velocity. Indeed, there has been no report of compensatory roll eye
velocity during fore-aft acceleration in squirrel monkeys (Paige
and Tomko 1991
). Furthermore, the latency of compensatory
linear vestibuloocular reflex responses are in the order of 25 ms
(Bronstein and Gresty 1988
), so the effects we are
examining would almost be over by that time. Therefore it is unlikely
that the otoliths significantly contribute to the responses of either
active or passive head impulses in normal human subjects.
The alterations in roll gain may be, in part, related to rapid feedback
from the roll state of the velocity-position integrator to the
secondary vestibular neurons. Such a mechanism would affect the
dynamics of vestibular-evoked eye movements, although its affect on
saccades is probably negligible, since the roll state of the
velocity-position integrator is inactive during saccades in our model
(see Raphan 1998). More fundamental physiological studies are required to determine where such a roll gain change might
occur in the central vestibular structures.
Recent evidence has been presented that neuron responses in the
vestibular nucleus may be attenuated during active head movements (Cullen and Roy 1999; McCrea et al. 1999
)
and may be related to the mechanism that disables a roll gain
modification during active head movements. Cullen and Roy
(1999)
found that some, but not all, neuron responses were
attenuated during the gaze stabilization period of an active head
movement. McCrea et al. (1999)
suggested that reafferent
neck proprioceptive and efference copy signals could be responsible for
the attenuation.
The underlying functional reason for the different dynamic
characteristics of the axis tilts in passive and active head impulses may result from the different goals of the system during these types of
movements. Roll gain modification may not occur during active head
impulses because the goal of the system during normal eye-head
refixations is to shift gaze from one target to another, rather than
maintain fixation on a fixed target. For these refixations, there is
considerable preprogramming but no effort to stabilize the retinal
image initially. Hence there is no reason for the roll gain of the aVOR
to be modified in the initial phase of the response to active head
rotations. In fact, normal aVOR function is probably suppressed during
the initial period of active eye-head refixations (Laurutis and
Robinson 1986), supporting the idea that the proposed
modification of the initial roll gain of the aVOR during passive head
impulses might be suppressed during active head impulses. Passive head
movements may therefore be unmasking an important underlying functional
component of the pure aVOR.
Optimal pulley coefficient calculations
The optimal pulley coefficient varied considerably between
subjects during the active head impulses, ranging from 0.15 to 0.58. Five of the eight subjects had optimal pulley coefficients between 0.39 and 0.6, a range that can be used to predict normal saccade torsional
transients (Raphan 1998). Our data on the range of
pulley coefficients are therefore consistent with the finding that
there are large and reproducible inter-individual differences in both
the magnitude and direction of torsional transients in normal subjects
(Fig. 4d in Straumann et al. 1995
). Our findings on the
range of optimal pulley coefficients are also consistent with the
corresponding range of eye velocity tilt angles that have been reported
when making saccades from secondary to tertiary positions (Table 1 in
Palla et al. 1999
).
The optimal pulley coefficients calculated for the passive head impulse
stimulus also varied considerably between subjects and were, on
average, smaller in magnitude in comparison with the values obtained
for active head impulses. However, as discussed above (see Model
organization and conceptual basis for study), the values of the
optimal pulley coefficient that we have reported do not necessarily
reflect the actual configuration of the pulleys in the plant. Hence we
are unable to determine the actual pulley configuration in subjects'
orbits from the calculated optimal pulley coefficient value. The
trajectories of saccadic eye movements would be more useful for
determining actual pulley configuration, as any eye velocity axis tilt
that occurs during these eye movements presumably arises due to the
effect of the pulleys alone (Raphan 1998). We have
shown, however, that in response to passive head impulses the same eye
velocity data can be closely predicted with a number of different
combinations of pulley coefficient and roll aVOR gain. Indeed, the
pulley coefficient need not be changed from 0.5 to achieve the desired
effect; the data can be predicted just by changing roll aVOR gain.
Therefore it is possible to have a fixed pulley configuration in the
orbit that would not require radical readjustment to execute different
types of eye movements.
In summary, we have presented a model of the aVOR that incorporates the kinematics and dynamics of the semicircular canals, central processing through a modifiable gain matrix, a vector velocity-position integrator, and an ocular motor plant that includes muscle pulleys. With muscle pulleys present, the model predicted the eye position-dependent axis tilts that occur during both active and passive head impulses. Removal of the pulley effect resulted in loss of aVOR eye position- dependence and approximate eye and head velocity axis alignment. It was possible to predict the initial alignment of the eye and head velocity axes, seen in response to passive head impulses, by introducing an eye position-dependent modification in the roll gain of the aVOR. A change in pulley effect alone was insufficient to bring about perfect eye and head velocity axis alignment for those data, but a combination of changing pulley effect and roll gain change was found to be as effective as a roll gain change alone. So, the presence of pulleys takes away the need for the axis tilts to be centrally programmed, and the roll gain modification serves as a means of countering the pulley effect, to produce good axis alignment and retinal image stabilization during high acceleration impulsive head rotations.
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APPENDIX A |
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The model of the three-dimensional semicircular canals (Fig. 1)
was simplified from vector Eqs. 9-18 given in
Yakushin et al. (1998)
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(A1) |
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(A2) |
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(A3) |
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APPENDIX B |
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![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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The velocity-position integrator (Fig. 1) was implemented in the
model as in Raphan (1998)
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![]() |
(B1) |
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(B2) |
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(B3) |
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(B4) |
The matrices in the equations were chosen as
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(B5) |
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A complete derivation of these equations and a description of
how eye orientation is updated based on the Euler-Rodriquez equations
can be found in Raphan (1998).
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ACKNOWLEDGMENTS |
---|
The authors acknowledge R. Black, Dr. I. Curthoys, Dr. B. Cohen, Dr. G. M. Halmagyi, and M. Todd for helpful suggestions.
This work was supported by the Royal Prince Alfred Hospital Department of Neurology Trustees, National Institutes of Health Grants EY-04148 and DC-02384, and a grant from the National Aeronautics and Space Administration through Cooperative Agreement NCC 9-58 with the National Space Biomedical Research Institute.
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FOOTNOTES |
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Address for reprint requests: T. Raphan, Dept. of Computer and Information Science, Brooklyn College, 2900 Bedford Ave., Brooklyn, NY 11210 (E-mail: raphan{at}nsi.brooklyn.cuny.edu).
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 8 December 1999; accepted in final form 22 March 2000.
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REFERENCES |
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