Departments of Neurology, Physiology, and Biophysics, Mount Sinai School of Medicine, New York, 10029; and Department of Computer and Information Sciences, Brooklyn College, City University of New York, Brooklyn, New York 11210
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ABSTRACT |
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Wearne, Susan,
Theodore Raphan, and
Bernard Cohen.
Effects of tilt of the gravito-inertial acceleration vector on
the angular vestibuloocular reflex during centrifugation.
Interaction of the horizontal linear and angular vestibuloocular
reflexes (lVOR and aVOR) was studied in rhesus and cynomolgus monkeys
during centered rotation and off-center rotation at a constant velocity (centrifugation). During centered rotation, the eye velocity vector was
aligned with the axis of rotation, which was coincident with the
direction of gravity. Facing and back to motion centrifugation tilted
the resultant of gravity and linear acceleration, gravito-inertial acceleration (GIA), inducing cross-coupled vertical components of eye
velocity. These components were upward when facing motion and downward
when back to motion and caused the axis of eye velocity to reorient
from alignment with the body yaw axis toward the tilted GIA. A major
finding was that horizontal time constants were asymmetric in each
monkey, generally being longer when associated with downward than
upward cross coupling. Because of these asymmetries, accurate estimates
of the contribution of the horizontal lVOR could not be obtained by
simply subtracting horizontal eye velocity profiles during facing and
back to motion centrifugation. Instead, it was necessary to consider
the effects of GIA tilts on velocity storage before attempting to
estimate the horizontal lVOR. In each monkey, the horizontal time
constant of optokinetic after-nystagmus (OKAN) was reduced as a
function of increasing head tilt with respect to gravity. When
variations in horizontal time constant as a function of GIA tilt were
included in the aVOR model, the rising and falling phases of horizontal
eye velocity during facing and back to motion centrifugation were
closely predicted, and the estimated contribution of the compensatory
lVOR was negligible. Beating fields of horizontal eye position were
unaffected by the presence or magnitude of linear acceleration during
centrifugation. These conclusions were evaluated in animals in which
the low-frequency aVOR was abolished by canal plugging, isolating the
contribution of the lVOR. Postoperatively, the animals had normal
ocular counterrolling and horizontal eye velocity modulation during
off-vertical axis rotation (OVAR), suggesting that the otoliths were
intact. No measurable horizontal eye velocity was elicited by
centrifugation with angular accelerations 40°/s2 and
angular velocities
400°/s. We conclude that in rhesus and cynomolgus monkeys, differences between horizontal eye velocities recorded during facing and back to motion constant velocity
centrifugation can be explained by orienting effects of the GIA tilt on
the time constants of the horizontal aVOR and not by a superposed lVOR.
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INTRODUCTION |
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Movement in a gravitational environment induces
combined linear and angular accelerations of the head in space,
concurrently activating the linear and angular vestibuloocular reflexes
(lVOR and aVOR). Off-axis rotation, or centrifugation, which induces concomitant centripetal and angular accelerations, has been used extensively to study aVOR and lVOR interaction (Angelaki and
Anderson 1991a,b
; Angelaki et al. 1991
;
Crampton 1966
; Curthoys et al. 1992
;
Lansberg et al. 1965
; Merfeld 1990
, 1995
;
Merfeld and Young 1995
; Merfeld et al. 1991
,
1993
; Sargent and Paige 1991
; Wearne 1993
; Young 1967
). Sargent and Paige
(1991)
tested monkeys with sinusoidal centrifugation to
determine whether the aVOR and lVOR responses superpose. At frequencies
between 1 and 4 Hz, which induced minimal tilts of the gravito-inertial
acceleration (GIA), responses of the horizontal lVOR summed with those
of the horizontal aVOR when the animals were upright. In the supine
position, the aVOR was in the roll direction, but the lVOR was still
horizontal. The horizontal lVOR, estimated by subtracting the aVOR from
the overall response when the animals were upright, was the same as that measured directly when they were supine, supporting the
superposition hypothesis at these frequencies.
In other studies, low-frequency and constant-velocity centrifugation
has been used to extract the lVOR component of eye velocity. We use the
term "constant-velocity centrifugation" to refer to a stimulus
that has a small angular acceleration (10-40°/s2) up to
a constant velocity, which is maintained for a long duration. In these
studies, the horizontal eye velocity trace obtained when subjects had
their backs to the direction of motion was subtracted from that when
they faced the motion (Benson 1974; Merfeld
1990
; Merfeld and Young 1995
; Wearne
1993
; Young 1967
). Because the centripetal
acceleration was identical in both conditions, the subtraction was
assumed to cancel the aVOR responses, while summing the lVOR responses.
One-half of the difference trace then should represent the lVOR
response. Whether superposition holds at low frequencies and large GIA
tilt angles, such as during constant velocity centrifugation, has not
been determined independently. This is primarily because the low gain
of the lVOR at frequencies <0.5 Hz (Paige et al. 1996
;
Paige and Tomko 1991a
,b
; Telford et al.
1997
) makes its contribution to the combined response difficult to evaluate.
Studies of the spatial organization of optokinetic after-nystagmus
(OKAN) in rhesus and cynomolgus monkeys (Dai et al. 1991, 1992
) have shown that eye velocity responses to linear
acceleration due to gravity, and to angular motion of the visual field
do not necessarily superpose but interact through velocity storage.
Specifically, the spatial orientation properties of velocity storage,
reflected in the time constant of horizontal OKAN, vary in monkeys in
side down positions depending on whether the eye velocity is directed toward or away from gravity. The time constant is generally longer during head tilts, which induce downward than upward cross-coupled components (Dai et al. 1991
). Because velocity storage
is common to OKAN and the aVOR (Raphan et al. 1979
), the
orientation changes that are present during OKAN also are present
during postrotatory responses with the head tilted (Angelaki and
Hess 1995
; Harris and Barnes 1987
; Raphan
et al. 1992
). Asymmetries in aVOR time constants also have been
observed for leftward or rightward GIA tilts with respect to the head
during postrotatory nystagmus (Schrader et al. 1985a
,b
)
and during centrifugation in monkeys (Wearne et al.
1994
). Because the angle of GIA tilt increases monotonically during the angular acceleration phase, reaching a maximum tilt angle at
constant angular velocity, any asymmetries in the dependence of the
horizontal time constant on GIA tilt during facing and back to motion
centrifugation will modify the difference trace, invalidating its use
as an index of the compensatory lVOR. If the functional relationship
between the time-varying GIA tilt during centrifugation and the aVOR
time constant were the same as that determined from a series of static
head tilts with respect to the GIA, this could explain the character
and shape of the difference traces observed during facing and back to
motion centrifugation.
The purpose of this study was to investigate the interaction of the horizontal aVOR and lVOR during constant velocity centrifugation. In particular, we determined the relative contributions made by dynamic changes in the aVOR time constants produced by a continuously changing GIA vector, and the compensatory lVOR, to the overall response. We also investigated whether the orientation properties of velocity storage determined from OKAN were sufficient to predict the horizontal eye velocity responses during constant velocity centrifugation.
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METHODS |
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One juvenile rhesus (Macaca mulatta; M9303) and six cynomolgus monkeys (M. fascicularis; M9307, M9306, M9308, M9223, M9351, and M9357) were used in these studies. We have not found differences between rhesus and cynomolgus monkeys in oculomotor or vestibular characteristics in previous studies. In particular, the spatial orientation properties and the dynamic characteristics of the aVOR are very similar for the two species. For this reason, findings from the two species have been used interchangeably in this report. Two of the cynomolgus monkeys (M9308 and M9351) were tested before and after their six semicircular canals were plugged. One cynomolgus monkey (M9357) was tested before and after both lateral canals were plugged. The surgical and experimental procedures conformed to the Principles of Laboratory Animal Care (National Institutes of Health Public 85-23, revised 1985) and were approved by the Institutional Animal Care and Use Committee (IACUC).
Surgical procedures
Animals were prepared at sterile surgery under anesthesia with
two three-turn search coils to record the orientation of one eye in
three dimensions. A frontal coil of 16 mm diam in rhesus monkeys and 14 mm diam in cynomolgus monkeys was sutured to the sclera under the
conjunctiva (Judge et al. 1980). This coil was concentric with the iris, and its normal was aligned with the optic
axis. A second coil of 11 mm diam was wound under the superior rectus
in the horizontal plane of the same eye (Dai et al.
1994
; Robinson 1963
; Yakushin et al.
1995
) such that its normal was approximately orthogonal to that
of the frontal coil. Voltages proportional to the horizontal and
vertical components of eye orientation were transduced by the frontal
coil; voltages proportional to the torsional component of eye
orientation were transduced by the top (roll) coil. Two head bolts were
implanted in dental acrylic on the skull to provide painless head
stabilization in stereotaxic coordinates during experiments. Animals
received analgesics and antibiotics (morphine sulfate 2 mg im;
cephazolin 0.1 g im) after surgery to alleviate pain and counter infection.
At separate surgery, all six semicircular canals were plugged in two
cynomolgus monkeys (M9308 and M9351). The animals
were anesthetized and the middle ear approached posteriorly. The canals were identified under an operating microscope. Plugging was
accomplished by grinding across each canal with a diamond burr until
the membranous canal was interrupted. The region of the canal was
packed with bone and covered with a small piece of muscle (see
Yakushin et al. 1995, for details). Inactivation of the
semicircular canals was verified by the absence of response to 0.2-Hz
sinusoids of angular velocity (peak velocity 60°/s) in any spatial
plane for the six canal plugged animals. The lateral canal plugged
animal had no response when tilted ~40° nose down, so that the
vector sum of the normals to the vertical canals was orthogonal to the rotation axis. Ocular counterrolling was normal in these animals, and
the response to z-axis off-vertical axis rotation (OVAR) was the same as in other canal-plugged animals (Cohen et al.
1983
; Correia and Money 1970
; Yakushin et
al. 1992
), indicating that the otoliths were intact.
Postoperative data reported in this study were obtained 6 and 2 mo
after surgery in M9351 and M9308, respectively.
Stimulation apparatus
The stimulator is shown schematically in Fig.
1A (Neurokinetics, Pittsburgh)
(see also Dai et al. 1994). It was computer controlled and had three gimbaled axes of rotation: an outer horizontal axis (A), a nested yaw axis (B), and a doubly nested
inner pitch-roll axis (C ). The yaw and pitch/roll axes
were enclosed in a light-tight, optokinetic sphere (OKN drum), 109 cm
in diameter, with 10° vertical black and white stripes on the inside.
The axis of the OKN drum (D) was collinear with the yaw axis
(B). When the OKN sphere rotated, driven by the OKN motor
(d ), it produced full-field motion that induced OKN and
OKAN. The horizontal and pitch/roll axes were controlled by position
servos, and the yaw and optokinetic axes by position and velocity
servos. The circular spine, which was the gimbal for the horizontal
axis (A), was driven by the horizontal axis motor
(a). It moved over approximately ±180° with a maximum acceleration of 60°/s2. The nested yaw axis
(B) driven by motor (b) through the yaw axis
gimbal, carried the primate chair and field coils, the centrifuge arm
and the pitch/roll axis motor (c). The maximum acceleration and deceleration of the yaw axis (B) was
200°/s2, and the maximum velocity was 400°/s. The
pitch-roll axis (C ) was driven by motor c, and
moved over ±90° of excursion at a maximum acceleration of
600°/s2.
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Monkeys were seated in a primate chair, shown centered with respect to each rotation axis in the diagram of Fig. 1A. The chair was composed of 1.25 cm lexan, which did not flex during rotation. Velocity steps in yaw about a vertical axis were given in this on-axis position. The chair could be repositioned by 90° along the pitch/roll axis to give the animals velocity steps in pitch or roll about a spatial vertical axis. By tilting the circular spine about the horizontal axis (a) and rotating the animal around the centered yaw axis (b), the animal received OVAR. The chair could be displaced to the end of the centrifuge arms, positioning the monkey's head 25 cm from the center of rotation. The primate chair could be positioned in 90° increments when displaced so that centripetal acceleration was directed along either the interaural or nasooccipital axis during constant velocity yaw axis centrifugation. The terms "centered" and "on-axis" rotation will be used interchangeably as will the terms "centrifugation" and "off-axis" rotation.
Recording and calibration of three-dimensional eye orientation and velocity
Two orthogonal field coils, 33 cm on a side and driven at
frequencies of 24.7 kHz, were fixed to the primate chair. The head bolts were attached to a lexan ring, which fixed the head to the chair
so that the head remained in the same orientation with respect to the
coordinate frame defined by the field coils. With the monkey erect, the
yaw axis was aligned with gravity, and the horizontal stereotaxic plane
was aligned with the gravitational horizontal. Thus the lateral
semicircular canals were tilted up ~30° from the earth horizontal
plane (Blanks et al. 1985; Yakushin et al. 1995
). The search coils were centered with regard to the field coils. Voltages proportional to the projections of the search coils
onto the magnetic fields were recorded with three phase detectors
(Neurodata). If the voltages from the two search coils were not
orthogonal, a portion of the horizontal voltage was fed back and
subtracted from the roll voltage, removing cross talk in the roll
signal when the upright animal was rotated around a spatial vertical
axis. This method electronically orthogonalized the search coil axes so
that the effective normal to the top coil was aligned with an axis from
the bottom to the top pole of the eye. Studies on monkeys have shown
that there is a small nonorthogonal relationship between the maximum
direction for roll and yaw (Crawford and Vilis 1991
),
but the angles are well within the error bounds of the data reported in
the study.
To calibrate yaw, pitch, and roll axis eye movements, animals were
rotated about a spatial vertical axis at 30°/s in the presence of a
lighted, textured visual surround in upright, side down, and prone
positions. It was assumed that horizontal and vertical gains were close
to unity in this condition (Crawford and Vilis 1991;
Raphan et al. 1979
; Robinson 1963
).
Torsional VOR gains during rotation in the light were set to 0.6. Similar roll gains have been obtained for monkeys using other
techniques (Crawford and Vilis 1991
; Dai et al.
1994
; Henn et al. 1992
; Yakushin et al.
1995
; Yue et al. 1994
). The calibration of the
roll coil was checked by rotating a test coil of the same diameter in a
gimbal inside the field coils.
Calibration of eye position after plugging of all semicircular canals was performed in vitro using a replica of the implanted search coils, mounted on a three-axis Fick gimbal. Two three-turn coils of 16 (frontal coil) and 11 mm diam (top coil) were mounted orthogonally on the gimbal, such that the voltages from the frontal coil were minimal when the yaw and pitch axes of the gimbal were aligned with the horizontal and vertical magnetic fields. Voltages were recorded from the two coils for symmetric angular displacements of ±15° in 5° increments, about each of the three gimbal axes in turn. Angular sensitivity of the voltages from each coil was determined using a least-squares fitting procedure (Matlab, The Mathworks). Using this technique, it was determined that the change in voltage produced by a change in eye position was the same after as before plugging.
Details of determination of Euler angles and the eye velocity vector
from the search coil voltages are presented elsewhere (Yakushin
et al. 1995). In brief, eye position and velocity vectors were
referenced to a right-handed, head-fixed coordinate frame (Fig.
1B). Eye orientation is represented as Euler angles in the Fick rotation convention,1
with
,
, and
corresponding to rotations about the
z axis, the rotated x axis, and the doubly
rotated y axis. These angular deviations from the reference
will be referred to as the yaw, pitch, and roll or horizontal,
vertical, and torsional eye positions, respectively. Eye velocities
were determined as vector components along the head-based coordinate
frame (Fig. 1B). Horizontal, vertical, and torsional
components of the eye velocity vector are represented as
(
z,
x,
y), respectively.
The circular arrows correspond to the direction of rotation for a
velocity component along the positive axis, according to a right-hand
rule. Leftward, downward, and counterclockwise rotations (from the
animal's point of view) are represented in the figures by upward
deflections in the eye position and eye velocity traces.
To validate the calibration procedure, we compared Listing's planes
during spontaneous eye movements with those found in the literature. We
assumed that the average coil voltages during spontaneous positions of
fixation while the animal made saccades for 15-30 s in light,
correspond to the straight-ahead eye position with zero roll. This
assumption is consistent with data obtained in trained and calibrated
monkeys for a large range of saccades in light and dark (van
Opstal et al. 1995). These average coil voltages defined the
reference head coordinate frame. With the eye in this orientation, the
visual axis coincides with the roll axis of the head frame. To a good
approximation, this aligns with the stereotaxic coordinate frame of the
head, which we physically aligned with the axes of the horizontal and
vertical field coils. We then used Listing's law to determine the
"displacement plane" (Helmholz 1867
; Tweed
and Vilis 1990
), which approximately contains all axes of
rotation from this reference position during saccades. The unit vector
normal to the displacement plane and its angle with respect to the
reference were determined. We then determined primary position as the
eye position for which the visual axis is normal to the displacement
plane, i.e., Listing's plane. This corresponded to a rotation of twice
the angle between the roll axis and the normal to Listing's plane,
about an axis given by their cross-product (Helmholz
1867
). Computed rotation angles were generally within 15°,
and the rotation axes were confined to a single plane, in accordance
with Listing's law (Crawford and Vilis 1991
;
Haslwanter et al. 1992
). The accuracy of the technique for estimating primary position was determined by comparing
displacement planes and reference positions from the monkey eye
movements with those obtained from a gimbal-mounted search coil system,
the reference system of which could be set arbitrarily. For a given
displacement plane, the reference positions computed from the monkey or
gimbal data were the same.
Experimental protocol
Alertness was maintained by administration of amphetamine
sulfate (0.3 mg/kg) intramuscularly, 30 min before testing. Before data
collection, vestibular and optokinetic time constants were habituated
by repeatedly rotating the animals to each side about all axes
(Cohen et al. 1992), minimizing the effects of further habituation. In consequence, the time constants and initial gains of
OKAN for the upright position did not habituate further during the
period of testing.
Eye movements were induced in three stimulus paradigms. Optokinetic
stimulation was given in the upright position or statically tilted left
ear down (LED) or right ear down (RED) with regard to gravity at angles
of 0, 17, 36, 45, 52, and 90°. Velocity steps of 60 and 90°/s,
lasting 30 s, were used to induce OKAN (Cohen et al.
1977; Raphan et al. 1979
; Waespe et al.
1983
). OVAR was given by tilting the axis of rotation 90°
with respect to gravity and rotating the animal about its yaw axis at
60°/s. Peak interaural linear acceleration was 1 g for
90° tilts.
Combined linear and angular accelerations were delivered by eccentric
rotation on a centrifuge, either facing the direction of motion (Fig.
1C ) or with back to the motion (Fig. 1E ). The direction of gravitational acceleration with respect to the head is
indicated as Ag. The direction of head rotation
during vestibular stimulation also is indicated by a circular arrow and
is denoted HZ. Animals also were rotated about a
centered axis (Fig. 1D). For +z rotation, animals
were right ear out (REO) when facing motion (Fig. 1C ) and
left ear out (LEO) when back to motion (Fig. 1E). For
z rotation, these conventions were reversed. The
centrifuge was accelerated at 40°/s2 to a final angular
velocity of 400°/s. The final stimulus velocity was maintained for
120 s. We term this stimulus constant velocity centrifugation.
During centrifugation with constant angular acceleration, gravitational (Ag) and centripetal (Ac) accelerations sum, producing GIA. At the onset of rotation, the GIA vector rotates in three dimensions, reaching a steady state position in the xz (roll) plane of the head during the period of constant centrifuge velocity. For the angular accelerations used in this study (10 and 40°/s2), a small constant tangential acceleration (<0.02 g) was present throughout the angular acceleration period. Because its magnitude in relation to the centripetal acceleration (1.24 g) was small, its effect on the change in horizontal time constant was neglected. Thus only the effects of GIA tilt in the xz plane on the horizontal time constant were considered.
At a final angular velocity of 400°/s, the GIA was tilted by 52° in
the animal's roll plane. For facing and back to motion centrifugation,
Ac was directed along the interaural axis (Fig. 1, C and E), and the GIA tilted dynamically in
the roll plane of the head, through an angle (R) that
increased with the angular velocity of the centrifuge. Cross-coupled
components of eye velocity appeared when the GIA was tilted with regard
to the head. Changes in eye position and eye velocity were examined
during all of these motions to determine the effects of interaural
linear acceleration on the horizontal component of eye movement.
The respective directions of compensatory linear (black arrows) and
angular (white arrows) VORs during facing and back to motion
centrifugation are indicated in Fig. 1, C and E. Regardless of whether the animal is LEO or REO, the compensatory
horizontal lVOR is always in the centrifugal direction. That is, when
the right ear is out, the direction of the compensatory lVOR should be
rightward (z; Fig. 1C ), and when the left ear
is out, the compensatory lVOR should be leftward (+z; Fig.
1E ).
Data acquisition and processing
Eye position data and photocell voltages, measuring the state of
the light and the passage of stripes, were sampled at a rate of 600 Hz
per channel using the DAOS data acquisition system (Mycon Technology)
running on a 386-based digital computer. Before sampling, eye position
data were prefiltered by an eight-pole Butterworth filter with a corner
frequency of 30 Hz. Slow phase eye velocity was obtained by
transforming the eye velocity vector to head coordinates and removing
saccades with an order statistic filter (Engelken and Stevens
1990, 1991
).
Programs were written using C/C++ and MatLab (MathWorks) to analyze
pitch, roll, and yaw slow phase eye velocities. Eye velocity was
analyzed from the onset of OKAN to the point where the horizontal component decayed to zero. OKAN time constants were estimated by
fitting a single exponential to the decaying portion of eye velocity,
1-2 s after the light was extinguished, indicating offset of the OKN
stimulus. Horizontal VOR time constants were estimated by fitting a sum
of two exponential functions, representing the cupula and velocity
storage modes, following angular velocity steps of 60°/s. The cupula
time constant was constrained to 4 s (Büttner and
Waespe 1981; Fernández and Goldberg 1971
),
and the initial integrator state was constrained to be zero. The time constant of velocity storage was estimated from a constrained fit to
the data with only the integrator time constant allowed to vary. This
technique gives a better estimate of the dynamics of the VOR than if a
single exponential was fitted.
During the angular acceleration at the onset of centrifugation, a
number of processes complicate the estimation of velocity storage time
constants. The input signal driving the aVOR is a ramp of angular
velocity producing a parabolic increase in centripetal acceleration.
This is accompanied by a continuous tilt of the GIA from the spatial
vertical, which induces a corresponding reduction in the horizontal
aVOR velocity storage time constant. In addition, both the cupula
deflection and the induced velocity storage response increase slowly,
producing nonzero initial conditions for the internal states of the
system at the onset of constant angular velocity. Because the states
cannot be measured, they are unconstrained in exponential fits to the
decaying portion of eye velocity. Such unconstrained fits can lead to
widely fluctuating estimates of the system time constants, depending on
the choice of initial states. During centrifugation therefore, aVOR
velocity storage time constants cannot be estimated by fitting a sum of
exponential functions to eye velocity, as they can for steps of head
velocity during centered rotation (Raphan et al. 1979).
The dynamical system representation allowed us to simulate changes in
the time constants as a function of GIA tilt angle, which varied with
time during centrifugation (see section on model implementation and
parameter identification). The aVOR model (Eqs. 1 and 2) was used to estimate system parameters
(hc, h33,
gc0, gs0, and
gs1) for each monkey by fitting the centered
rotation data. The best-fitting parameters then were held constant, and the decline in horizontal time constant as a function of GIA tilt (Eq. 4), derived from OKAN data with the head statically
tilted (Eq. 3), was introduced into the model to predict
facing and back to motion centrifugation traces. A second estimate of
velocity storage time constants during centered rotation and
centrifugation also was obtained by fitting a single exponential
function to the decay of eye velocity, starting 10 s after the onset
of constant angular velocity, to avoid the initial period when both
cupula and velocity storage contribute to eye velocity. Assuming a
cupula time constant of 4 s, the contribution of the cupula mode
will be negligible after 2.5 time constants, and eye velocity should decay with the time constant of velocity storage. Because our method
used only the tail portion of the eye velocity time series, we term it
the "tail-fit time constant." The two methods gave similar
values, and the tail-fit was used as an initial estimate of the
velocity storage time constant when searching for the best-fitting parameters for the model simulations.
Experimental design and statistical analysis
The order of presentation of experimental trials was randomized to avoid systematic order effects. Repeated measures were performed in all experimental conditions: each monkey was tested at least twice in each condition, but not all monkeys were exposed to every experimental paradigm.
Differences in time
constants2 between
experimental conditions were evaluated statistically using planned
contrasts, evaluated with the t-statistic for dependent
samples (Winer et al. 1991). This method minimized the
effects of habituation of time constants on the variance estimate.
Intrasubject variability was assessed both graphically and
analytically. Eye position and desaccaded eye velocity traces from
repeated trials were overlaid, and subject means ±1 SD or ±2 SDs
were computed and graphed using programs written in MATLAB (The
Mathworks). This method provides a clear graphic indication of subject
trends and their variability. Deviations of the model simulations from
the data then could be evaluated graphically.
The time constant of the velocity storage integrator during centrifugation was estimated from optimal first-order fits to data obtained during OKAN. The other parameters were estimated from responses to centered rotation. Simulations were done to assess the model's ability to predict the responses to OKN, OKAN, centered rotation, and centrifugation with a single set of parameters. Because the functions relating eye velocity to the various stimulus components cannot be represented in analytic form in terms of the system parameters to allow their optimization, no figure-of-merit function of individual responses was calculated. Goodness of fit was assessed by determining the extent to which the simulated response fell within 95% confidence intervals of overlayed eye velocity responses.
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RESULTS |
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Effects of combined linear and angular accelerations during centrifugation
Centered rotation about the spatial vertical at an angular
acceleration of 40°/s2 to a constant angular velocity of
400°/s increased horizontal eye velocity (z) during
the period of angular acceleration to a peak value of close to 200°/s
(198°/s, Fig. 2A). The GIA
remained aligned with the animal's z axis for the duration
of rotation. During the constant velocity period, horizontal eye
velocity decayed with a time constant of 12.8 s. Vertical and roll
components of eye velocity (
x and
y) were
close to zero throughout the stimulus. Eccentric rotation on the
centrifuge changed the direction of the GIA vector with respect to the
head and increased its magnitude. When facing the direction of
centrifuge motion (Fig. 2B), horizontal slow phase velocity
(
z) rose approximately exponentially approaching a lower
peak velocity (165°/s) than when centered (198°/s; compare Fig. 2,
A and B). Upward vertical (
x,
arrow B) and counterclockwise roll (+
y) components of
eye velocity appeared during the acceleration period (Fig.
2B). Vertical and roll eye velocities built slowly with the
tilt of the GIA. Their maxima were considerably delayed, relative to
the tilt of the GIA (Fig. 2B). Horizontal eye position (
)
moved into the slow phase direction. Average vertical eye position
(
) remained close to the reference position while the eyes torted
(
) in the direction of GIA rotation (Fig. 2B). During the
constant velocity period, horizontal eye velocity decayed to zero and
was followed by an oppositely directed secondary nystagmus. The
horizontal velocity storage time constant measured by the tail-fit
method (see METHODS) was shorter when facing motion (5.2 s)
than during centered rotation (12.8 s, Fig. 2A). Vertical
eye velocity decayed slowly (arrow B, Fig. 2B), whereas the
roll component decayed more rapidly. Ocular torsion was maintained at
~5° during the constant velocity period while the GIA was tilted
(arrow A, Fig. 2B).
|
When monkeys were oriented with their backs to the motion (Fig.
2C ), horizontal eye velocity rose exponentially during the angular acceleration, reaching a higher peak velocity (175°/s) than
when facing the motion (Fig. 2B). The horizontal time
constant (7.4 s) was shorter than during centered rotation, but was
longer than when facing the motion. Downward vertical and clockwise
roll eye velocity components were generated. Torsional eye position () rotated in a counterclockwise direction, following the tilt of
the GIA, to reach a steady-state value of 7-8° during the period of
steady-state GIA tilt (arrow A, Fig. 2C ).
Differences between horizontal eye velocity profiles during facing and back to motion centrifugation were determined from overlaid traces of desaccaded horizontal eye velocity. In five separate tests in a second monkey (M9307), there was little variability (Fig. 3, A and C ). Horizontal velocity storage time constants, measured by the tail-fit method and averaged over leftward and rightward traces, were smaller when the monkey was rotated off-axis (Fig. 3A, mean facing motion Tc = 5.1 ± 0.6 s; Fig. 3C, mean back to motion Tc = 6.2 ± 0.58 s), than during centered rotation (Fig. 3B, mean centered Tc = 8.5 s).
|
Average horizontal eye position traces during the nystagmus, comprising
both slow and quick phase were plotted for the corresponding leftward
and rightward eye velocities shown in Fig. 3, D-I
(leftward: Fig. 3, D-F; rightward: Fig. 3,
G-I ). The eyes tended to beat across the midline during
rotation regardless of the direction of the GIA vector with a slight
bias toward the quick phase side during the period of angular
acceleration (Chun and Robinson 1978; Hood
1967
). This was followed by a gradual decay toward the slow phase side. The beating fields during centrifugation (Fig. 3, D,
F, G, and I ) were not appreciably different
from those during centered rotation (Fig. 3, E and
H ).
Because the interaural linear acceleration was centripetal, any
compensatory horizontal lVOR should rotate the eyes in the centrifugal
direction whether REO or LEO (Fig. 1, C and E,
black arrows). This produces a compensatory horizontal lVOR and aVOR in
the same direction whenever the animal is facing the motion. Conversely, the lVOR is always opposite to the aVOR when back to motion
(Fig. 1, C and E; compare white arrows with black
arrows). If the aVOR and lVOR superpose (Merfeld and Young
1995; Young 1967
), subtraction of the
back-to-motion response from the facing-motion response (F-B) should
cancel the aVOR and double the lVOR. Division by two then would give an
estimate of the average interaural lVOR. This should be in the
direction of the aVOR eye velocity when facing the motion. That is, for
leftward eye velocities (Fig. 4,
left column), the (F-B)/2 difference traces should be
leftward (+z). For rightward eye velocities (Fig. 4,
right column), the difference traces should be rightward
(
z).
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To assess the aVOR-lVOR superposition hypothesis, difference traces
were computed for each monkey (Fig. 4) and compared with predictions
based on this hypothesis for each monkey. Although each animal's data
were internally consistent, intersubject variability was considerable.
For M9307, the difference trace for leftward aVOR eye
velocities was in the (z) direction (Fig.
4C ), whereas the difference trace for rightward aVOR eye
velocities was in the (+z) direction (Fig. 4D).
These directions are opposite to the prediction of the superposition
hypothesis. The same response pattern was found in two other monkeys
(M9306 and M9308, Fig. 4, E-H ).
Patterns were inconsistent in the last two monkeys (M9223 and M9303, Fig. 4, I-L). M9303
showed little difference between facing and back to motion responses
for leftward eye velocities (Fig. 4K ) but had a
(
z) difference response, opposite to the trend in the
other four animals, for rightward eye velocities (Fig. 4L).
M9223 had a significant (+z) response for both
leftward and rightward eye velocities (Fig. 4, I and
J ). Thus the prediction of the superposition hypothesis,
that the (F
B)/2 difference traces should
be leftward for rightward eye velocities and rightward for leftward eye
velocities, was not supported by the data in general and directly
contradicted by the data of three monkeys.
Our alternative hypothesis was that linear acceleration affects the orientation properties of the velocity storage system, differentially modifying its time constants according to the direction of GIA tilt. According to this hypothesis, the difference between facing and back to motion eye velocities represents a difference between two waveforms with different time constants at each instant of time. To test this hypothesis, we compared each monkey's responses to OKAN, centrifugation, and centered rotation with simulations using our one-dimensional system model of lVOR-aVOR interaction (Fig. 5), with a single set of parameters for each monkey in all three paradigms.
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Model-data comparisons
The one-dimensional model of lVOR/aVOR interaction includes
cascaded dynamical subsystems. These generate the velocity command from
the angular VOR, the effects of GIA on velocity storage, the
velocity-position transformation that drives the motoneurons, and the
contribution of the compensatory linear VOR (lVOR). The block labeled
"otolith afferent processing" comprises subblocks of otolith
sensory afferent neurons with discharge regularities range from regular
(REG) through intermediate (INT) to irregular (IRREG) and with
corresponding ranges of response dynamics (Fernández and
Goldberg 1976). These afferents are activated by linear
acceleration of the head in space, which is an inertial frame. This
acceleration is converted into the head frame because the afferents are
fixed to the head. This implicit transformation is represented by the box "space-head transf." The afferents combine to generate the compensatory lVOR response ("compensatory lVOR system"). Another system ("orienting lVOR system"), the output of which is denoted by a heavy line (Fig. 5) is responsible for modifying the spatial orientation properties of velocity storage and the subsequent orientation and time constants of the eye velocity vector. The system
implementing the aVOR, incorporating velocity storage has been adapted
from previous work (Raphan and Sturm 1991
; Raphan et al. 1979
). The output of velocity storage and the direct
aVOR pathway, ysz sums with the output of the
compensatory lVOR system, ycz. The summed signal
is input to the velocity position integrator and its direct path to
drive the oculomotor plant.
The effect of the orienting system on the aVOR was modeled as a
parametric modification of the velocity storage time constant, 1/h33, shown by the heavy arrow through
"nodulus/uvula" to h33. The time constant
was varied as a function of GIA tilt relative to the head in accordance
with data obtained from OKAN with monkeys in tilted positions
(Dai et al. 1991). The model then was implemented as
a dynamical system, using the regression fits obtained from the
OKAN data. The model simulations during centered, and facing and
back to motion centrifugation were compared with the actual data (see
METHODS).
MODEL IMPLEMENTATION AND PARAMETER IDENTIFICATION.
The state equations describing the one-dimensional angular acceleration
transduction performed by the semicircular canals were approximated as
a first-order system (Fig. 5, Hc) and implemented as follows:
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(1) |
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(2) |
IMPLEMENTATION OF EFFECT OF GIA TILT ON HORIZONTAL TIME CONSTANT:
OKAN TIME CONSTANTS AS A FUNCTION OF STATIC HEAD TILT.
The function relating the horizontal time constant to the angle of GIA
tilt with respect to the head z axis was estimated for each
monkey during OKAN with the head statically tilted in roll, either LED
or RED, through angles ranging from 17 to 90°. An example is shown
for M9307 (Fig. 6). For the
upright condition, the time constant of leftward horizontal eye
velocity (+Z) was 7.1 s (Fig. 6A). For a
90° tilt left ear down (LED), an upward eye velocity
(
X) was induced, and the horizontal time constant fell
to 1.8 s (Fig. 6B). The rate of decrease of the
horizontal time constant during OKAN with the head tilted LED, as a
function of tilt angle, shown by open circle in Fig.
7A, 1 and
2, could be approximated by a straight line with negative
slope. The GIA tilt induced under this condition was analogous to tilt
experienced during centrifugation while facing motion with the left ear
out (Fig. 2A). In each case, the GIA tilted toward the right
ear, and an upward cross-coupled component of eye velocity was induced.
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|
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(3) |
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(4) |
|
CENTRIFUGATION AFTER INACTIVATION OF THE SEMICIRCULAR CANALS.
The foregoing results indicate that the contribution of the
compensatory lVOR to horizontal eye velocity during constant velocity centrifugation is small. To support this conclusion, we compared responses to centrifugation before and after inactivation of the aVOR.
We reasoned that any nystagmus after the canals were inactivated could
be attributed to the intact lVOR. Canal plugging was performed in three
animals, two of which had all six canals plugged (M9308 and
M9357) and a third in which the lateral canals were plugged (M9351). The lateral canal plugged monkey was tilted forward
40° during testing so that the vertical canals were not activated by
the rotation around a spatial vertical axis (Yakushin et al. 1995). In this position, this monkey's responses were
equivalent to those of the six-canal plugged animals.
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DISCUSSION |
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This study shows that during constant velocity centrifugation the effect of spatial orientation on the dominant time constants of the aVOR is the primary factor in determining horizontal eye velocity in rhesus and cynomolgus monkeys. The compensatory lVOR contributes little to the response. This was demonstrated by the finding that the differences between horizontal eye velocity when facing and back to motion were in the direction opposite to that predicted by the superposition hypothesis in three monkeys. Data were inconsistent in the other two monkeys, being in the direction predicted by the hypothesis for eye velocity in one direction and opposite to it the other direction. This conclusion was verified by a model-based technique in which eye velocity data obtained during centrifugation were fit by simulations using data from the same monkeys obtained during OKAN with head tilts and on-center rotation. Simulations using the same set of parameters predicted the responses at low and high values of angular acceleration. Confirmation of this conclusion was obtained in canal-plugged animals.
This conclusion is consistent with studies describing the frequency
characteristics of the lVOR (Telford et al. 1997) but contradicts conclusions drawn previously from studies of lVOR-aVOR interaction using constant velocity centrifugation in which it was
assumed that the lVOR and aVOR superposed (Wearne 1993
;
Young 1967
). Characteristics of the lVOR in squirrel
monkeys have been inferred from difference traces during constant
velocity centrifugation (Merfeld 1990
; Merfeld
and Young 1995
; Merfeld et al. 1993
), using a
three-dimensional model (Merfeld 1995
). Again, it was
assumed that differences between facing and back to motion
centrifugation are due solely to a superposition of the compensatory
lVOR and aVOR. Two inputs to a system are considered to superpose if
the sum of the individual responses to each is equal to the response when both inputs are applied together. In the context of
centrifugation, this means that the sum of the eye velocity responses
to centered rotation and to constant linear acceleration on a sled
should equal the response during constant velocity centrifugation. When the orientation effects on velocity storage are negligible, such as
during high-frequency sinusoidal centrifugation when the GIA tilt is
minimal, near-superposition of aVOR and lVOR holds. There also may be a
contribution during OVAR where there is a sinusoidally varying
compensatory lVOR, generated by the interaural projection of the
rotating GIA vector. This study shows, however, that a tilted GIA
during constant velocity centrifugation induces orientation effects
that shorten the time constant of the aVOR. Thus superposition as
defined earlier cannot hold.
Central to modeling eye velocities during constant velocity centrifugation was the ability to describe dynamic changes in the horizontal time constant when the direction of the GIA was continuously changing. At the onset of rotation, there is a small centripetal acceleration and a larger tangential acceleration. The tangential acceleration dies rapidly as the centripetal acceleration builds. At every instant, the centripetal and tangential linear accelerations are combined with the gravitational acceleration. Thus there is a complex changing linear acceleration vector during the initial stages of rotation until the subject reaches a constant angular acceleration.
Despite this dynamically changing linear acceleration stimulus,
the direction and approximate magnitude of the difference traces could
be predicted for each animal from asymmetric reductions in the
horizontal OKAN time constant as a function of head tilt. In both
M9306 and M9307, the horizontal time constant was
shorter at 52° GIA tilt during upward than downward cross-coupling,
corresponding to a shorter horizontal time constant during facing than
back to motion centrifugation. In accordance with the data, this OKAN time constant asymmetry predicted that the (F B)/2 difference trace would be negative during leftward
(+z) eye velocities (Fig. 4, C and
E ) and positive during rightward (
z) eye
velocities (Fig. 4, D and F ). Importantly, the
temporal pattern of the difference traces was opposite to that
predicted by the lVOR superposition hypothesis. Although the pattern of
OKAN time constant asymmetries in M9303 differed from the
other two monkeys, its centrifugation data were nonetheless predictable
from its corresponding OKAN time constants. For leftward eye velocity
during OKAN, no up-down related asymmetry was present. Accordingly, the
difference traces for leftward eye velocities in this monkey were close
to zero (Fig. 4K ). For rightward eye velocity during OKAN,
the horizontal time constant was longer for upward than downward
cross-coupling, opposite to the trends in the other two monkeys. The
difference traces for rightward eye velocity were correspondingly
negative-going, opposite to those of the other four monkeys (Fig.
4L).
The shape of the difference traces provides further evidence that
they are not produced by the compensatory lVOR in the monkeys that were
tested. In all cases, the difference traces rose slowly to a peak value
then decayed to zero with a time constant of ~6 s (Fig. 4). These
dynamics are characteristic of a difference between two exponential
modes with different time constants. They would not be produced by the
low-frequency characteristics of the compensatory lVOR (Paige
and Tomko 1991a,b
; Paige et al. 1996
; Raphan et al. 1996
; Telford et al. 1997
).
The dynamic changes in time constant adequately describe the
differences between horizontal eye velocities during centrifugation
when facing and back to motion. Moreover, in contrast with the large
variations observed in humans (Wearne 1993
), the beating
field of horizontal eye position was not appreciably affected by the
presence or magnitude of linear acceleration during centrifugation
(Fig. 3). Finally, the absence of any measurable lVOR during
centrifugation after inactivation of the semicircular canals by canal
plugging, in the presence of a robust otolith counterrolling response,
argues strongly that the observed facing-back differences are generated
by the canals and not the otoliths. We conclude that it is not possible
to estimate the lVOR during constant velocity centrifugation simply by
subtracting the responses during facing and back to motion. Rather in
rhesus and cynomolgus monkeys, these difference traces are dominated by
asymmetries in dynamic modification of the horizontal time constant,
which depend on the direction of vertical cross-coupled components
induced by the tilted GIA.
We considered whether the squirrel monkey might have a
characteristically different lVOR response from that of the rhesus or
cynomolgus, which could explain the different conclusions. This seems
unlikely because constant velocity centrifugation with low initial
angular acceleration (Merfeld 1995; Merfeld and
Young 1995
) is a low-frequency stimulus. The sensitivity of the
lVOR at these low frequencies is <0.05° · cm
1 · m
1 (Telford et al.
1997
). The facing-back to motion difference traces, which were
attributed to the lVOR, contained large transients (Merfeld
1995
; Merfeld and Young 1995
) the amplitude and
temporal characteristics of which are not consistent with the lVOR at
these frequencies. Whether time constant asymmetries might be
responsible for generating difference responses attributed to the lVOR
during facing and back to motion centrifugation in the squirrel monkey is not known because the time constants of OKAN were not measured as a
function of head tilt.
Another difference between this study and those done in squirrel
monkeys is that the radius arm of our centrifuge was smaller. We
considered whether this could explain differences between our data and
those of previous studies where the acceleration gradient was smaller
(Lansberg et al. 1965; Merfeld and Young
1995
). If it is assumed that there is a 5-cm difference between
the two otoliths, a radius of 25 cm and off-center rotation at 400°/s to produce a centripetal acceleration of 1 g, the short arm
centrifugation used in this study creates a gradient of linear
acceleration between the two ears of
0.25 g. This
gradient is ~25% of the centripetal acceleration and would cause the
tilt of the GIA to be slightly different between the two ears. At the
center of the head, the tilt of the GIA would be
52°. On the
inboard side, the tilt would be 48°, and on the outboard side it
would be 53°. Changes in time constant over these angles are small
and would fall within the resolution of our time constant measurements
for the aVOR and for OKAN (Fig. 7). The centripetal acceleration
gradient was the same whether animals were moving forward or back and
also could not have been responsible for the time constant asymmetries
that were observed in this study. Moreover, the asymmetries in
horizontal time constant as measured during OKAN, where there is no
acceleration gradient between the two ears, adequately explained the
centrifugation data for both 10 and 40°/s2 (Fig. 8).
Therefore the linear acceleration gradient across the two ears could
not have been responsible for the differences between our conclusions
and those reported in earlier studies.
The lVOR gain is reduced as fixation distance increases, and in this,
as in the previous studies that used constant velocity centrifugation,
viewing distance was not controlled (Merfeld and Young
1995; Young 1967
). Considering the low gain of
the lVOR during stimulation at constant velocity (zero frequency),
it is unlikely that the viewing distance could have been close enough to generate a significant lVOR in any study where it was not
controlled. As Paige et al. (1996)
have shown, it is not possible to
maintain near fixation in darkness for even short periods (30 s to 1 min) while viewing an imagined target.
The minimal contribution of the compensatory lVOR during constant
velocity centrifugation in rhesus and cynomolgus monkeys contrasts with
that found in humans. Humans generate stronger compensatory responses
to the centripetal acceleration and correspondingly stronger shifts in
the beating field (Wearne 1993; Wearne et al. 1994
). These shifts appear to affect eye velocity by clamping the response during facing motion and enhancing the response during back to motion centrifugation (Raphan et al. 1996
). This
may, however, be an ancillary effect of a mechanism that causes a
change in the beating field rather than a difference in the way the
aVOR and lVOR combine to generate the velocity command to the
oculomotor system (Raphan et al. 1996
). Different
frequency characteristics during sinusoidal linear acceleration and
different weightings given to sensory context (Paige
1996
) also could explain the more prominent role for the
compensatory lVOR during centrifugation in humans (Raphan et al.
1996
). Because OKAN is weak in humans, it will be difficult to
assess the effect of a tilted GIA on the horizontal time constant using
this technique. Such information is critical, however, for assessing
the contribution of the lVOR to constant velocity centrifugation.
In summary, the results are consistent with the hypothesis that the compensatory lVOR contributes minimally during constant velocity centrifugation in rhesus and cynomolgus monkeys. The dominant effects of the lVOR are the orientation changes manifest as ocular counterrolling, shifts of the axis of eye velocity, and changes in the time constants of the aVOR. The orientation-induced changes during centrifugation, OKN and OKAN, can be related quantitatively to spatial orientation properties of velocity storage. Thus while quantitative aspects of low-frequency lVOR behavior remain speculative, the proposed model of aVOR-lVOR interaction captures the salient features of the lVOR-aVOR interaction at low frequencies in rhesus and cynomolgus monkeys and provides a basis for comparison with the human response.
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APPENDIX |
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The asymptotic behavior of the aVOR eye velocity in response to
a constant angular acceleration can be computed from the state equations for the cupula (Eq. 1) and velocity storage
(Eq. 2) systems, when the states are no longer changing,
i.e., when c = 0 and
sz = 0. Under these conditions
![]() |
(A1) |
![]() |
(A2) |
![]() |
(A3) |
![]() |
(A4) |
Substituting Eqs. A1-A3 into Eq. A4 gives
the neural eye velocity command, ysz(ss) in
terms of the angular acceleration
![]() |
(A5) |
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ACKNOWLEDGMENTS |
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We thank V. Rodriguez for preparing the figures.
This work was supported by National Institutes of Health Research Grants EY-04148, EY-11812, EY-01867, and NS-00294.
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FOOTNOTES |
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Address for reprint requests: T. Raphan, Institute of Neural and Intelligent Systems, Dept. of Computer and Information Science, Brooklyn College, 2900 Bedford Ave., Brooklyn, NY 11210.
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.
1 The Fick rotation convention parameterizes any three dimensional rotation as three sequential rotations about three nonorthogonal axes, z, the rotated y, and the final x (optic axis), in that order.
2 The time constants and peak eye velocity value quoted in Figs. 1 and 2 were measured from the traces in these figures. Variability within animals was small and is indicated by plotting means ± SD for desaccaded eye velocity traces in Figs. 3, 4, and 7.
Received 10 August 1998; accepted in final form 12 January 1999.
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REFERENCES |
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