Dynamics and Kinematics of the Angular Vestibulo-Ocular Reflex in Monkey: Effects of Canal Plugging
Sergei B. Yakushin1,
Theodore Raphan2,
Jun-Ichi Suzuki3,
Yasuko Arai4, and
Bernard Cohen1
1 Departments of Neurology and Physiology and Biophysics, Mount Sinai School of Medicine, New York, New York 10029; 2 Department of Computer and Information Science, Brooklyn College of the City University of New York, Brooklyn, New York 11210; 3 Department of Otolaryngology, Teikyo University and 4 Tokyo Women's Medical College, Tokyo 117-0003, Japan
 |
ABSTRACT |
Yakushin, Sergei B., Theodore Raphan, Jun-Ichi Suzuki, Yasuko Arai, and Bernard Cohen. Dynamics and kinematics of the angular vestibulo-ocular reflex in monkey: effects of canal plugging. J. Neurophysiol. 80: 3077-3099, 1998. Horizontal and roll components of the angular vestibulo-ocular reflex (aVOR) were elicited by sinusoidal rotation at frequencies from 0.2 Hz (60°/s) to 4.0 Hz (
6°/s) in cynomolgus monkeys. Animals had both lateral canals plugged (VC, vertical canals intact), both lateral canals and one pair of the vertical canals plugged (RALP, right anterior and left posterior canals intact; LARP, left anterior and right posterior canal intact), or all six semicircular canal plugged (NC, no canals). In normal animals, horizontal and roll eye velocity was in phase with head velocity and peak horizontal and roll gains were
0.8 and 0.6 in upright and 90° pitch, respectively. NC animals had small aVOR gains at 0.2 Hz, and the temporal phases were shifted
90° toward acceleration. As the frequency increased to 4 Hz, aVOR temporal gains and phases tended to normalize. Findings were similar for the LARP, RALP, and VC animals when they were rotated in the planes of the plugged canals. That is, they tended to normalize at higher frequencies. A model was developed incorporating the geometric organization of the canals and first order canal-endolymph dynamics. Canal plugging was modeled as an alteration in the low frequency 3-db roll-off and corresponding dominant time constant. The shift in the low-frequency 3-dB roll-off was seen in the temporal responses as a phase lead of the aVOR toward acceleration at higher frequencies. The phase shifted toward stimulus velocity as the frequency increased toward 4.0 Hz. By incorporating a dynamic model of the canals into the three-dimensional canal system, the spatial responses were predicted at all frequencies. Animals were also stimulated with steps of velocity in planes parallel to the plugged lateral canals. This induced a response with a short time constant and low peak velocity in each monkey. Gains were normalized for step rotation with respect to time constant as (steady state eye velocity)/(stimulus acceleration × time constant). Using this procedure, the gains were the same in canal plugged as in normal animals and corresponded to gains obtained in the frequency analysis. The study suggests that canal plugging does not block the afferent response to rotation, it merely shifts the dynamic response to higher frequencies.
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INTRODUCTION |
The semicircular canal system, which comprises three pairs of complementary canals, forms the sensory basis for the angular vestibulo-ocular reflex (aVOR). The two lateral semicircular canals can be approximated by a single plane, as can one anterior and the contralateral posterior canal. This results in three push-pull pairs, right and left lateral (RLLL), right anterior and left posterior (RALP), and left anterior and right posterior (LARP), that code all angular head movements. The precise angles of the individual semicircular canals have been estimated in several studies, which indicate that the canal planes form a nonorthogonal basis for sensing head acceleration (Blanks et al. 1985
; Curthoys et al. 1977
; Dickman 1996
; Reisine et al. 1985
, 1988
). The precise contribution of the canal pairs has been evaluated using the technique of canal plugging (Ewald 1892
; Money and Scott 1962
). After plugging, bone completely obliterates the canal space for several millimeters. It generally is assumed that there is no flow of endolymph when the canals are plugged adequately. The implication is that a plugged canal can be modeled as having no cupula deflection and no afferent modulation when the head is rotated. Using canal plugging, it was shown that the semicircular canal pairs contribute to the aVOR gain according to the geometric relationship between the canals and stereotaxic head coordinate frame in which eye movements are measured (Angelaki and Hess 1996
; Angelaki et al. 1996
; Baker et al. 1987
; Böhmer et al. 1985
; Yakushin et al. 1995
). From the nonorthogonal geometry of the canals and from parameters identified with data from normal monkeys, a model of the aVOR was constructed that predicted the responses to 0.2-Hz sinusoidal rotation after canal plugging simply by setting the response from plugged canals to zero (Yakushin et al. 1995
). This demonstrated the contribution of the individual reciprocal canal pairs quantitatively. It also indicated that when a specific canal pair is plugged, no adaptation takes place in the spatial eye velocity response generated by the remaining semicircular canals at a midband frequency of 0.2 Hz (Yakushin et al. 1995
).
The conclusion that there was no adaptation after canal plugging has been challenged. The gains and phases of the aVOR after lateral canal plugging were closer to those of the normal animal when tested with a higher frequency (1.1 Hz) (Angelaki and Hess 1996
; Angelaki et al. 1996
). This was explained as an adaptive response or spatial "recalibration" of the central vestibular system. That is, by producing a stronger horizontal response from the vertical canals, the response plane of the vertical canals effectively would be rotated. Such recalibrations in response plane of the intact canal system have been observed after "cross-axis adaptation." Schultheis and Robinson (1981)
demonstrated that cats could be adapted with continued sinusoidal pitching while an optokinetic surround sinusoidally oscillated in a horizontal plane. When animals were later tested in darkness with a pitching stimulus, eye velocity was oblique with a horizontal component. The magnitude of the eye velocity also could be adaptively reduced or increased, depending on the phase relationship between the adapting vestibular and optokinetic stimuli, and cross-axis adaptation was greater when the otolith organs were reoriented relative to a spatial vertical during head rotation. Other types of cross-axis adaptation also have been described (Baker et al. 1986
, 1987
; Harrison et al. 1986
; Peng et al. 1994
; Peterson et al. 1991
).
That there might be adaptation after canal plugging also could be inferred from the classic studies of Ewald (1892)
. After single canals were plugged in pigeons, the birds still could fly to the ceiling of their cage on recovery from anesthesia. These results were different from the behavior of pigeons after unilateral labyrinthectomy. These animals were unable to fly. In addition, they had sustained torsion of the head and held abnormal postures for prolonged periods (Ewald 1892
). It is striking, that even after extensive canal plugging in the monkey, animals regain relative postural stability and the ability to move rapidly in space after a period of several weeks (Yakushin et al. 1995
). The basis for this adaptation is unknown. One obvious difference between the canal-plugged and labyrinthectomized animals is that the spontaneous discharge of the primary afferents is maintained after canal plugging (Goldberg and Fernandez 1975
), whereas the spontaneous input is lost after labyrinthectomy.
In preliminary studies, we have found that there was a measurable aVOR response when monkeys were rotated in the plane of plugged canals. This also was present in an animal with all semicircular canals plugged (Yakushin et al. 1997
), ruling out the possibility that there was reorganization of vertical canal input to support yaw eye movements. The purpose of this study was to clarify the etiology of the responses to high-frequency sinusoids and steps of velocity in animals with plugged canals. Our aim was to develop a three-dimensional dynamic and kinematic model of the semicircular canals that predicted the quantitative responses before and after plugging to low- and high-frequency rotations and to steps of constant velocity.
 |
METHODS |
Experiments were performed on six cynomolgus monkeys. In five animals, one or more reciprocal semicircular canal pairs were plugged. One other animal was used to obtain control data. Partial data also were obtained from five other canal-plugged animals. The experiments conformed to the Guide for the Care and Use of Laboratory Animals (National Research Council 1996
) and were approved by the Institutional Animal Care and Use Committee.
Surgical procedures
The surgical procedures used in these experiments have been described in detail (Yakushin et al. 1995
). Briefly, head bolts were implanted on the skull in dental acrylic cement under general anesthesia in sterile surgical conditions. This provided painless fixation of the head in stereotaxic coordinates during testing. When the animals were upright during testing, the normal to the horizontal stereotaxic plane was along the spatial vertical. Eye movements were recorded with scleral search coils. Two coils were implanted on the left eye. One coil was used to measure horizontal and vertical eye position (Judge et al. 1980
). A second coil was placed approximately orthogonal to the frontal coil to measure roll eye position (Cohen et al. 1992a
; Dai et al. 1994
; Yakushin et al. 1995
). Both coils were sutured to the sclera at the time of surgery. Postmortem, the coils were embedded firmly in connective tissue that was attached to the sclera. From this, we assume that there was no movement of the coils relative to the globe during eye movement.
About 1 mo after coil implantation, the semicircular canals were plugged by grinding across the bony and membranous canals and packing the orifices with bone dust (Cohen et al. 1964
, 1965
; Money and Scott 1962
; Suzuki and Cohen 1966
; Suzuki et al. 1964
; Yakushin et al. 1995
). The plugging was performed on the side opposite to the ampulla. This left the hair cells of the canals and otoliths intact. After recovery, the bone fused to provide an impenetrable block to the flow of endolymph (Fig. 10).

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| FIG. 10.
Anatomic verification of semicircular canal plugging in a LARP animal (M9356). A-C, left: sections of the temporal bones with plugged semicircular canals. Right: detail of the plugged right anterior (D), right lateral (E), left lateral (F), and left posterior (G) canals. Triangles in D-G are marking to the borders of the plugged semicircular canals. RAC, right anterior canal; RLC, right lateral canal; LLC, left lateral canal; LPC, left posterior canal.
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Two animals had all six semicircular canal plugged (no canal animals, NC: M9308 and M9357). One animal had both lateral canal plugged (vertical canals intact, VC: M9354) and two animals had only one reciprocal vertical canal pair intact: right anterior and left posterior canals intact (RALP: M9355) or left anterior and right posterior canals intact (LARP: M9306). Partial data on step responses and time constants also were obtained from five other animals with canal plugging (LC, M9008; VC, M9003; LARP, M9006 and M9356; RALP, M9223). Data presented in this study were obtained from 2 wk to 2 yr after canal plugging. Deficits in postural control and uncoordinated head movements in the plane of the plugged canals that were observed in the first weeks after surgery had largely disappeared by the time of testing. Thus the results that will be reported were from animals that had recovered from the acute effects of operation.
Canal plugging was verified anatomically in several animals and physiologically in others by the characteristic alteration in the response to sinusoidal rotation at 0.2-Hz, 60°/s peak velocity around an axis perpendicular to the average plane of the plugged canals (Yakushin et al. 1995
).
Data collection and processing
During testing, the monkey's head was fixed in a rigid 15 cm frame made of 12.2-mm Plexiglas. The frame held two sets of 13-cm field coils that generated orthogonal oscillating magnetic fields at a frequency of 24 kHz. The axes of the field coils were along the interaural and dorsoventral axes of the head, establishing a head fixed reference frame for measuring the orientation of the search coils in front and on top of the left eye. The head was fixed relative to the field coils with the left eye centered in the magnetic fields. Eye velocities were calibrated by rotating the animals in light at 30°/s about the pitch, roll, and yaw axis. It was assumed that horizontal and vertical gains were unity in this condition (Crawford and Vilis 1991
; Dai et al. 1991
; Raphan et al. 1979
; Robinson 1963
). Roll gains were assumed to be 0.6 when rotation was around a naso-occipital axis aligned with the spatial vertical (Crawford and Vilis 1991
; Henn et al. 1992
; Yakushin et al. 1995
). This agrees with roll gains determined for monkeys using other techniques (Dai et al. 1994
; Telford et al. 1996
; Yue et al. 1994
). In this paper, we use the terms "horizontal" and "yaw" interchangeably. Eye velocities to the left, down, and counterclockwise (from the animal's point of view) are represented by downward deflections in the velocity traces in the figures. Data were recorded with amplifiers having a band-pass of DC to 40 Hz. The equipment was controlled and data were acquired with a computer. Voltages were digitized at 600 Hz/channel with 12 bit resolution and stored on optical disk. Eye position voltages were smoothed and digitally differentiated by finding the slope of the least squares linear fit, corresponding to a filter with a 3-dB cutoff >40 Hz, the cutoff frequency of the filters used for data acquisition. Saccades were eliminated using an order statistic filter (Engelken and Stevens 1990
; Engelken et al. 1996
).
During testing animals sat in a primate chair in a multiaxis vestibular stimulator (Neurokinetics) that has been described previously (Dai et al. 1991
; Reisine and Raphan 1992
). In brief, the stimulator is composed of three gimbaled axes for rotation, a horizontal axis parallel to the earth horizontal, a nested yaw axis, and a doubly nested inner pitch/roll axis. The yaw and pitch/roll axes are enclosed in a light-tight optokinetic cylinder, 91 cm in diameter with 10° black and white stripes. The axis of the OKN cylinder also is controlled independently and is collinear with the yaw axis. Each axis went through the center of rotation of the head and was computer controlled. The pitch/roll and horizontal axes were controlled by position servos and the yaw and OKN axes by velocity servos. The peak acceleration of the primate axis was 270°/s2. Monkeys sat in the primate chair with their heads fixed to a box that held the field coils. When animals were rotated in light, they had full field optokinetic stimulation. When the monkeys were upright, the lateral semicircular plane formed an angle of 15-22° with earth horizontal (Blanks et al. 1985
; Reisine et al. 1988
). In these experiments, the animals sat so that the interaural axis was aligned with the pitch/roll axis. They were upright or were tilted to a fixed pitch position and rotated about a spatial vertical axis. This paradigm is similar to that used in previous studies of horizontal eye movements induced after semicircular canal plugging (Angelaki and Hess 1996
; Angelaki et al. 1996
; Baker and Peterson 1991
; Baker et al. 1982
, 1986
; Böhmer et al. 1985
; Minor and Goldberg 1990
; Yakushin et al. 1995
).
Sinusoidal analysis
Testing was performed with animals upright (0°) and statically tilted forward (nose down, +) or backward (nose up,
) in 10° increments up to ±90°. Animals were rotated sinusoidally about a spatial vertical axis in darkness. This stimulus induced yaw eye movements when animals were upright and both yaw and roll eye movements when the animals were pitched forward or back (Yakushin et al. 1995
). Animals with normal semicircular canals were used as controls, and their data were compared with data obtained from canal-plugged animals. At least 10 cycles were collected for each of the 19 test positions. Two normal and the five canal-plugged animals were tested during sinusoidal rotation at a variety of frequencies (0.2 and 0.5 Hz at peak velocity 60°/s, 1.0 Hz at
33°/s, 2.0 Hz at
16°/s, and 4.0 Hz at
6°/s). Desaccaded eye velocities were fit with a sinusoid at the frequency of oscillation using a least mean square algorithm. From this, the average value of peak eye velocity and the phase relative to the stimulus (temporal phase) were determined. The maximum and minimum values of the data for each individual cycle of eye velocity were obtained at the times of the peaks of the fitted curves. Temporal gains of the aVOR were determined for each cycle as (peak-to-peak eye velocity)/(peak-to-peak stimulus velocity). Mean gain and standard deviations were obtained over all peak values.
We evaluated whether there was an artifactual component in the eye velocity as a result of deformation of the Plexiglas box in which the field coils were embedded. An eye coil of the same diameter and number of turns as that placed on the eye of the monkey was mounted on a Plexiglas plate and fixed to the coil box in the center of the field. No modulation in voltage was induced by applied frequencies of oscillation
4 Hz or by steps of velocity. We also tested whether there was movement of the animal's head relative to the coil box, using animals with the Sirota head implantation technique (Sirota et al. 1988
). In this technique, the lateral stability of the head was not different from that used in the other monkeys in this series. Tape was placed around the head over the eyes at the level of the forehead to reduce possible skin movement, and a coil was attached to the tape. No modulation in voltage was induced by applied frequencies of oscillation
4 Hz or by steps of velocity. We conclude that there was neither deformation of the coil box nor slip of the monkey's head relative to the coil field during rotation at high frequency or during steps.
Step response analysis
Animals were tested with approximate ramps of velocity. Rotation began with an approximate step of angular acceleration from 0 to 270°/s2 (Fig. 9B). Peak acceleration was reached after 33 ms and was maintained for 195 ms, after which the animals were decelerated with the same slope to 0°/s2. This generated a ramp of velocity over 260 ms up to a peak of 60°/s (Fig. 9A). To measure the horizontal aVOR gain, rotation was held for 5 s in darkness. Rotation was stopped with the animal in light for
5 s to damp any postrotatory response (Raphan et al. 1979
). Alternate rotations to the left and right were repeated 10 times.

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| FIG. 9.
Horizontal (C and D) eye velocity during constant velocity rotation to the right (left) and to the left (right) when animal (M9308) was tested in 30° tilt forward position before (C) and after plugging all 6 canal (D). Each graph represents the superposition of several eye velocity responses. A represent velocities and B represent acceleration of the head rotation.
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The interest in this paper was in the canal dynamics. This includes the contributions of the endolymph flow, the elastic and viscous properties of the canal structure, and the spike encoding process that transduces the mechanical motion to nerve impulses along the eighth nerve (Fernandez and Goldberg 1971
; Highstein et al. 1996
; Landolt and Correia 1980
). The canal dynamics can be described as a first-order model given by
|
(1)
|
where gc is the coupling relating canal output to angular acceleration input d/dt(
c) (Raphan and Cohen 1981
). The parameter, Tc, is the dominant time constant of the canal dynamics, and rv is the canal afferent output. We will refer to Tc as the canal time constant. Because the acceleration lasted for only 260 ms, only the canal dynamics and direct pathway would be activated during the period of acceleration. Eye velocity was assumed to be proportional to the afferent output of the canals about the axis of rotation. It was assumed further that there was no contribution of velocity storage. This can be approximated by an equivalent direct pathway gain, gd, referenced to an equivalent composite canal activation, rveq. Therefore eye velocity about a particular axis,
e, can be given by
|
(2)
|
where gceq is the coupling from head acceleration to rreq. The gain of the reflex, gVOR, then can be given by the equation
|
(3)
|
Using Eqs. 2 and 3, the gain, gVOR, can be measured in a number of ways dependent on the magnitude of the dominant time constant. In the normal monkey, Tc was assumed equal to 4 s (3-6 s) (Büttner and Waespe 1981
; Correia et al. 1992
; Goldberg and Fernandez 1971
; Reisine and Henn 1984
). During the 260 ms of acceleration, using Eqs. 1-3, eye velocity about a given axis can be related to head velocity and will be approximately linear with
|
(4)
|
Therefore, using Eq. 4, the gain, gVOR, could be computed as a ratio of eye acceleration to head acceleration or as a ratio of the peak eye velocity to stimulus velocity (
h).
For canal time constants Tc, which were much less than 4 s, and for which eye velocity responses reached a steady-state value within the 200 ms from onset of acceleration (Fig. 9D), d/dt(rveq) (Eq. 2) is close to zero. In these instances, the gain, gVOR, could be computed from
|
(5)
|
as the ratio of the steady-state eye velocity to (time constant multiplied by stimulus acceleration, d/dt(
h)). For normal animals, gains computed from the steady-state and acceleration periods are equivalent; measurements were made from slow phase velocity during the steady state. In the canal-plugged animals, the gains were determined from the calculation shown in Eq. 5. (For a more complete description of the computation, see section on Modeling the three-dimensional kinematics and dynamics of the semicircular canals: effects of plugging below).
The gain and canal time constant (Tc) for plugged lateral canal was obtained from responses to rotation when the head was tilted 30-40° forward, which approximately eliminated the contribution of the vertical canals. Desaccaded eye velocities in response to steps of rotation at 60°/s were synchronized to the beginning of rotation. The average value of eye velocity divided by average stimulus velocity over the first 20 ms that contained no saccades after the ramp of velocity had stabilized was taken as the gain of the individual response. Individual gains were averaged over 10 responses to obtain the average gain and standard deviation of the step response. Time constants were computed by fitting individual response curves with a single exponential rising to the "steady-state" value and finding their average value and standard deviation.
Both per- and postrotatory responses produced by constant velocity rotation in darkness were used to measure the central or velocity storage time constant of the horizontal aVOR. After the initial 260-ms period of acceleration, the velocity of rotation was held constant for a prolonged period with the animal in darkness until the slow phase velocity had decayed to zero. A similar acceleration profile was used to stop rotation, generating a postrotatory response. The velocity storage time constant for the normal monkeys was calculated from a double exponential technique previously described (Raphan et al. 1979
), assuming a 4-s canal time constant. The time constant of velocity storage also was obtained from optokinetic after-nystagmus (OKAN) by fitting the declining velocity with a single exponential (Cohen et al. 1977).
Coordinate notation
In previous studies from our laboratory, we used the coordinate notation originally used by Fernandez and Goldberg (1976)
. This reference frame has the pitch axis (eX) along an interaural axis from the left ear. The roll axis (eY) lies along the naso-occipital axis and points out the back of the head, and the yaw axis (eZ) is out the top of the head. This frame was utilized in Yakushin et al. (1995)
in which three-dimensional eye responses from canal-plugged monkeys were studied at 0.2 Hz (Yakushin et al. 1995
), and in Wearne et al. (1996
-1998)
, which referenced much of the previous work. In the current study, we have used a different reference frame, one that is rotated 90° relative to that used previously (Fig. 1). This frame has been used in psychophysical studies of the vestibular system (Guedry 1974
), and recently has become a general standard in vestibular studies. It is also commonly used in aerospace engineering. The major differences are that the basis vectors for the head coordinate frame are eX (roll), eY (pitch), and eZ (yaw), corresponding to the X, Y, and Z axes, respectively. The canal basis unit vectors are defined as before (Yakushin et al. 1995
). These are the normals to the anterior canal (ea), posterior canal (ep), and lateral canal (el), corresponding to the Xc, Yc, and Zc axes. These basis vectors do not form an orthonormal set.

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| FIG. 1.
A: position of the left labyrinth of a monkey. Coordinate frame of the head, taken as the stereotaxic frame, is the coordinate frame in which roll (torsion), pitch (vertical), and yaw (horizontal) eye movements were measured. X represents the roll axis, Y the pitch axis, and Z the yaw axis. B: representation of the relative orientation of the coordinate axes of the stereotaxic frame (X-Z) and the coordinate axes determined by the normals to the semicircular canal planes. Positive directions of these normals were determined by using a right hand rule for the rotation direction, which excited an individual canal. Xc represents the positive direction for the anterior canal, Yc the posterior canal, and Zc the lateral canal. l is the angle between stereotaxic vertical axis (Z) and the average direction of the lateral canal axis (Zc). The Xc axis is obtained by rotating the X axis about the Y axis through an angle  a and then about the intermediate Z axis through an angle a. The Yc axis is obtained by rotating the Y axis about the Y axis through an angle  p (this corresponds to no rotation of the vector but only orients the intermediate Z axis) and then about the intermediate Z axis through an angle p. Each canal axis is therefore characterized by 2 generalized coordinates that determine its orientation.
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Each canal basis vector can be given as a rotation of one of the head basis vectors and can be defined by two Euler angles. In this
way, the most general transformation between the two basis sets can be given by six angles that define how the canal afferents code the head acceleration or velocity signals (see modeling section for a complete derivation).
Convention of temporal gain and phase representation
Because of the vector nature of the head and eye velocities, the projections of the stimulus velocity, which is along the spatial vertical, is related by a cosine of the angle between the stimulus axis and the axis of measurement. The positive Z axis always maintains an angle
90° relative to the positive stimulus axis for head tilts between ±90° (Fig. 2, A and B). Therefore the projection of the stimulus onto the yaw axis of the head is always positive. The positive X axis has an angle >90° when tilted forward and <90° when tilted back (Fig. 2, A and B) and the projection changes sign. Therefore references for gains and phases of eye velocity were defined independently to be consistent with the spatial gain curves represented in our previous work on canal plugging at 0.2 Hz (Yakushin et al. 1995
). For perfect compensation, phases were defined as
180° for yaw under all conditions and for roll when tilted back (Fig. 2, E, F, and H). For roll in the tilted forward condition, the phase for perfect compensation was defined as 0° (Fig. 2G). After canal plugging, there were increases in phase shifts at higher frequencies.

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| FIG. 2.
Conventions for describing eye velocity in the head. A and B: positive directions associated with the vector components of head and eye movements referenced to a head-based coordinate frame. A positive value along the reference directions corresponds to a rotation according to a right hand rule. Thus a positive value for Z corresponds to a leftward movement and a positive value for X corresponds to a clockwise rotation from the animal's viewpoint. Reference sinusoid for computing gains was along the spatial vertical (C and D). E and G: for the tilted-forward condition, the components of head velocity along the yaw (Z) and roll (X) axes are positive, and the corresponding compensatory eye velocity components were taken as 180° out of phase (E) or in phase (0°) (G) with reference sinusoid. This has been taken as a positive gain. F and H: with the head tilted backward, the component of head velocity along the yaw axis is positive and the component along the roll axis is negative. This corresponds to yaw (F) and roll (H) eye velocities, which have phases of 180° with the reference sinusoid. Gain of the yaw component therefore was taken as positive, whereas the gain of the roll component was taken as negative. Peak temporal phases were varied from optimal in or out of phase position (arrow, E-H) after canal plugging when tested at different frequencies. Phase was considered to be positive or negative if it did not deviate more than ±90° from corresponding optimal phase (shadow area, E-H).
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Gain (the ratio of eye velocity in head to stimulus velocity in space) was defined as positive or negative depending on the positive direction for the unit vector of the head coordinate relative to stimulus velocity (X, Z, Fig. 2, A and B) (Yakushin et al. 1995
). When the animal was tilted <90° forward or backward, yaw eye velocity was considered to have a positive gain when it was in the shaded region around the phase of
180° relative to stimulus velocity (compare Fig. 2, C and D, and E and F). For roll, gain was considered positive when tilted forward (Fig. 2G) and negative when tilted back (Fig. 2H).
Data analysis
The spatial gains and phases of the horizontal and roll aVOR were the variables of interest of this study. An equal number of individual gain values was obtained for each tilt position. The gain values as a function of tilt angle were fit, using a minimum mean square error criteria, with a sinusoid y = A* cos(x + B), where x is the tilt angle. The peak value (A, spatial gain) and its phase relative to the upright (B, spatial phase) were obtained from the fit.
Changes in eye position as a function of tilt angle can introduce errors in the measurement of eye velocity (Yakushin et al. 1995
). To determine the approximate size of the errors, we evaluated the effect of static head pitch on horizontal, vertical, and roll components of eye position in the two normal and four canal-plugged animals used in this study. Head tilt had no effect on horizontal eye position in the normal animals (M9357 and M9358) when they were tested at different frequencies from 0.2 to 4.0 Hz (0 ± 2°). The vertical component of eye position varied as a function of tilt angle. The eyes were minimally deviated in the upright and ±90° tilt positions and maximally deviated for ±45° tilts (M9358, 7°; M9357, 4°). The torsional component of eye position was not affected by forward tilts in either normal animal. It increased as a function of backward tilt in M9358, being maximal (up to
20°) when the animal was tilted
50°. In the canal-plugged animals, horizontal and roll eye position did not vary as a function of head tilt. The vertical component deviated up to ±10° for the RALP and LARP animals. The eye deviation was up with forward tilts and down with backward tilts. Thus in agreement with our previous findings (Yakushin et al. 1995
), eye deviations within ±15° did not introduce significant errors between eye velocities and those computed as a derivative of coil voltages.
Statistical analysis of data
A standard unpaired t-test was used to compare two groups of data. For more than two groups of data, an analysis of variance (ANOVA) was used. If the general ANOVA showed significant differences between data sets, then each between-group degree of freedom was analyzed separately by developing orthogonal contrasts. In this case, results of the test were adjusted with a Scheffe approach (Keppel 1991
). In the statistical analyses for goodness of fit, the null hypothesis was that the mean gain of the data for each tilt angle is equal to the value obtained from the optimal fit to the data over all angles of tilt. Hypotheses were tested by examining the ratio of the variance of the data relative to the mean and the variance relative to the fitted value. Because each measurement of gain at each tilt angle was done independently, the ratio follows an F distribution (Keppel 1991
; Yakushin et al. 1995
). Data in this paper are described by means ± SD.

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| FIG. 3.
Horizontal (left column) and roll (right column) eye velocity of one of the animals in which all 6 canals were plugged (NC, M9308) tested at 0.2 (A), 1.0 (B), 2.0 (C), and 4.0 Hz (D). Monkey was upright when the horizontal eye velocities were recorded (left) and tilted forward 90° when the roll eye velocities were recorded (right). ···, sinusoidal line on each graph represents head velocity with reversed polarity to facilitate comparison. E: when stimulus frequency increased, the temporal phases of yaw and roll shifted from being approximately in phase with stimulus acceleration to being in phase with stimulus velocity (from 90 to 180°).
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RESULTS |
Sinusoidal analyses
TEMPORAL CHARACTERISTICS OF THE aVOR BEFORE AND AFTER CANAL PLUGGING.
In response to sinusoidal oscillation at 0.2 Hz, the gain of the aVOR is negligible for rotation in a plane orthogonal to the average plane of the remaining canals (Yakushin et al. 1995
). The effects of frequency on the gain of the responses were striking. In two animals with all six semicircular canals plugged (NC animals; M9308 and M9357), aVOR gains during rotation at 0.2 Hz about any axis was close to zero (Fig. 3A). As stimulus frequency increased, the gain of both the horizontal and roll components increased concurrently. In M9308, the peak gains of the horizontal component, tested in the upright position, rose from 0.05 ± 0.04 at 0.2 Hz to 0.52 ± 0.10 at 4.0 Hz (Fig. 3, A-D, left). In M9357, the peak horizontal gain at a frequency of 0.2 Hz was significantly different from the gain at a frequency of 4.0 Hz (0.02 ± 0.03 and 0.37 ± 0.17, respectively, P < 0.6*10
8 using 2-tailed t-test). The roll responses rose from 0.03 ± 0.03 at 0.2 Hz to 0.47 ± 0.14 at 4.0 Hz in M9308 when tested in the 90° tilt forward condition (Fig. 3, A-D, right) and from 0.02 ± 0.04 to 0.28 ± 0.16 when M9357 was tilted 90° forward (P < 0.0008). It should be noted that the peak velocity of the stimulus was different for sinusoids at different frequencies. Peak stimulus acceleration was maintained at 200°/s2 across the frequency spectrum, which kept the system in the linear range for the normal animal. We assumed that linearity also was maintained for the canal-plugged animals.
As the gains rose, the temporal phases of the horizontal sinusoids and roll sinusoids shifted from being in phase with head acceleration <1.0 Hz (Fig. 3, B and E) toward being in phase with head velocity at 4 Hz (Fig. 3, C-E). Thus the gains and phases of the responses tended to normalize when tested at higher frequencies. Baker et al. (1982)
also reported canal responses in two cats with all six semicircular canal plugged. Their animals had small, but consistent aVOR gains (0.07 and 0.08) when they were tested at 2.5 Hz. The temporal responses had a phase lead of
90° relative to head acceleration (Baker et al. 1982
), consistent with findings in this study.
Because the peak stimulus velocity at 4.0 Hz was low (
6°/s), other frequency components of the stimulus or noise could have distorted the results. We evaluated the spectral composition of the stimulus and the response both before and after canal plugging. The stimulus had an approximate Gaussian spectral density distribution with a mean at 4 ± 0.2 Hz. Eye velocity responses before and after plugging had the same spectral distribution. Both had large peaks in their spectra at 4 Hz with a standard deviation approximately equal to that of the stimulus. The spectral distribution, both before and after plugging was close to zero, 4 SD from where the spectrum of the stimulus was at a peak at 4 Hz. Therefore contributions of frequencies other than 4 Hz to the stimulus and response were not significant. Because the amplitude of the responses and the signal to noise ratio was lowest at 4 Hz, this conclusion can be extended to the lower frequencies, as well.
The responses of the NC animal were compared with the horizontal and roll temporal phases of two normal animals as a function of head tilt about the interaural (pitch) axis at various frequencies. For the normal animals, the horizontal component of the aVOR was compensatory, being
180° out of phase with stimulus velocity at each frequency from 0.2 to 4.0 Hz for tilts in the range of ±90° (Fig. 4A). The temporal phases of the roll components were also compensatory, being about
180° relative to stimulus velocity when the normal animals were tilted backward and 0° when tilted forward (Fig. 4D; also see phase convention, Fig. 2). There was a range of uncertainty approximately equal to ±10° around the upright position for the roll temporal phases. This is a region of head tilt where the gain is close to zero and the phase is uncertain. This was largely due to the small gains that were elicited in these head orientations. At each frequency, the temporal phases of the horizontal and roll components were not significantly different from being compensatory at any tilt angle (P > 0.20, ANOVA). Therefore, data at a given frequency were pooled for all tilt angles, and an ANOVA was performed to determine whether there was variation of temporal phase as a function of stimulus frequency. Variations in temporal phase of the horizontal and roll components were small and insignificant for both animals (ANOVA, Scheffe post hoc adjustment; P > 0.05). Thus temporal phases were not significantly different from being compensatory at any tilt angle or frequency in the normal animals.

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| FIG. 4.
Temporal phase shifts between horizontal (A-C) or roll (D-F) components of slow phase eye velocity and stimulus velocity at different frequencies (see inset in A) as a function of head tilt (abscissa, positive value tilt forward; negative value tilt backward). Negative values on ordinate correspond to the condition when eye velocity led stimulus velocity. Insets below D-F: animal's head position at that angle of tilt. A and D: in the normal animal, the horizontal component was 180° out of phase with stimulus velocity (A). Roll component was 180° out of phase when the head was tilted forward and in phase with stimulus velocity when head was tilted backward (D). Roll temporal phases reversed about the upright (0°) position. Response at 4 Hz is emboldened to facilitate comparison. B and E: horizontal component of the NC animal was shifted ~90° in all head positions when tested at 0.2 Hz (B); the temporal phase shift tended to normalize at higher frequencies of rotation. E: roll temporal phases also were shifted 90° for the normal animal in any head orientation and tended to normalize at higher frequencies. C and F: temporal phase of the horizontal component of the VC animal (C) had the normal characteristics when the head was tilted back (rotation in plane of intact canals) and characteristics similar to the NC animal when the animal was tilted forward (rotation in plugged canal plane).
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When the NC animals were tested in different head orientations, the temporal phases tended to be relatively invariant over the range of tilt angles for all frequencies, with the exception of the uncertainty region (Fig. 4, B and E). The temporal responses of the horizontal and roll eye velocity led the normal response by 90° when tested at 0.2 Hz. This is demonstrated in Fig. 4 for M9308 (compare thin lines, Fig. 4, A and B,
92 ± 21° for horizontal and Fig. 4, D and E,
72 ± 21° for roll phases). As the frequency increased, the average temporal phase shifted toward
180°, which was closer to being compensatory for head velocity, as in the normal animal (Figs. 3E and 4, 1 Hz:
119 ± 26° for horizontal and
107 ± 9° for roll; 4 Hz:
148 ± 34° for horizontal and
162 ± 7° for roll). The change in temporal phase as a function of frequency was similar for M9357 (Fig. 3E).
In the VC animal, the intact vertical canals would dominate the response when the animal was tilted back and rotated (Yakushin et al. 1995
). In this position, the temporal phases of the horizontal component of the aVOR were similar to those of the normal animals (negative values on abscissa, Fig. 4, C and F). When the VC animal was tilted forward so that the vertical canals were orthogonal to the rotation plane, they would not contribute to the response. In this condition, the plugged lateral canals were close to the plane of stimulation. The horizontal components of the response (positive values on abscissa, Fig. 4C) were similar to those of the NC animal (Fig. 4B). The roll temporal phases had a large region of uncertainty but were similar to those of the normal animal (Fig. 4F). The temporal phases obtained from LARP (M9306) and RALP (M9355) animals were similar to those described for the VC animal (not shown). Böhmer et al. (1982)
also reported a significant phase lead of the horizontal aVOR for a VC animal, tested in the plane of the plugged lateral canals 7 mo after operation. When the animal was tested at 0.2 Hz, the temporal phase lead was ~50°, but it normalized at 4 Hz (Fig. 2 in Böhmer et al. 1982
).
SPATIAL CHARACTERISTICS OF THE aVOR BEFORE AND AFTER CANAL PLUGGING.
When normal animals were rotated in darkness, the gain of the horizontal component was maximum in the upright position and decreased when the animals were statically tilted forward or backward regardless of frequency of oscillation [Fig. 5, A-D,
(Yakushin et al. 1995
)]. The gain of the roll component was zero with monkeys in an upright position and gradually increased with static tilt forward or backward (Fig. 5, E-H). The vertical components of eye velocity were negligible in any head orientation in pitch, and there was minimal spontaneous vertical nystagmus, which was not affected by the stimulus (not shown). The spatial gains and phases as a function of frequency are summarized for the two normal animals in Fig. 6, A-D. There was no consistent trend in spatial peak gain as a function of frequency in either of the normal animals. The spatial gain of the horizontal component varied from 0.78 to 0.89 in M9357 and from 0.66 to 0.80 in M9358 (Fig. 6A, Table 1). The spatial phases of the horizontal components were invariant for M9357 but decreased at 1 Hz and above for M9358 (Fig. 6B; Table 1). The peak gain of the roll component ranged from 0.66 to 0.70 in M9357 and from 0.43 to 0.58 in M9358. There was no systematic effect of frequency on the roll gain (Fig. 6C), and the roll phases were invariant (approximately
90°) for both animals (Fig. 6D). Thus in agreement with Telford et al. (1996)
, the spatial gains and phases of the horizontal and roll components of the aVOR were relatively constant across frequencies from 0.2 to 4.0 Hz.

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| FIG. 5.
Spatial gain responses of the NC animal (M9357) tested at different frequencies of sinusoidal rotation before ( and ) and after plugging. Spatial gain curves were composed of temporal responses to rotation at 0.2 Hz, 60°/s (A and E); 1.0 Hz, 30°/s (B and F); 2.0 Hz, 15°/s (C and G); and 4.0 Hz, 5°/s (D and H). Spatial gain curves before surgery were the same at any frequency. , best sinusoidal fit to the horizontal and roll gains at the test frequency. Insets (bottom): animal's head position at that angle of tilt. and , gains obtained after surgery. Horizontal and roll gains were close to 0 when the animal was tested as 2.0 Hz (A and E) but tended to normalize at higher frequencies (B-D and F-H).
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| FIG. 6.
Spatial gains and phases of the normal (A-D) and NC animals (E-H) tested at different frequencies. A-D: spatial gains (A and C) and phases (B and D) of the horizontal (A and B) and roll (C and D) components of the angular vestibulo-ocular reflex (aVOR) of 2 normal monkey ( , M9357; , M9358) tested in darkness at different frequencies. E-H: spatial gains (E and G) and phases (F and H) of the horizontal (E and F) and roll (G and H) components of the aVOR of the NC animals (M9308 and M9357) tested in darkness at frequencies of 0.2-4.0 Hz. - - -, correspond to 0° in B and F and 90° in D and H, the normal values for the horizontal and roll components. In general, gains and phases were stable across the different stimulus frequencies. Spatial phases at 0.2 Hz (F and H) were omitted because gains were close to 0 and, therefore, phases were not meaningful (see Table 1).
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Before semicircular canal plugging in M9357, the spatial gain of the horizontal component of the aVOR at 0.2 Hz was 0.89 at 2° tilt forward (Fig. 5A,
). The gain of the roll component was 0.66 at
88° tilt (backward) (Fig. 5E,
; 0 crossing at 2°). There was no significant gain of the vertical component of the aVOR at any tilt position (not shown). Therefore before canal plugging this animal was similar to other normal animals (Yakushin et al. 1995
). Two weeks after all six semicircular canals had been plugged, the spatial gain in the NC animal, M9357, when tested at 0.2 Hz had a peak horizontal component of 0.03, occurring at
16° tilt (backward) (Fig. 5A). The spatial gain of the roll component was 0.01, occurring at
87° tilt (Fig. 5E). Both the horizontal and roll spatial curves were not significantly different from a straight line of zero slope and intercept (horizontal: P = 0.1, roll: P = 0.14).
As the frequency of stimulation increased, the spatial gain of both the horizontal and roll components increased. At 1.0 Hz, the spatial horizontal gain was 0.13 occurring at
3° tilt (Fig. 5B). When the animal was tested at 2 and 4 Hz, the peak horizontal spatial gain increased further (2 Hz: gain 0.24 at
6°, Fig. 5C; 4 Hz: gain 0.42 at 0° tilt, Fig. 5D; Table 1). At each frequency >0.2 Hz, the horizontal curve was significantly different from a line of zero slope and intercept (P < 0.05). The same was true for the roll component. Roll gains increased at 1.0 Hz (0.05 at
90° tilt; P < 0.05; Fig. 5F), 2 Hz (0.17), and 4 Hz (0.34). The spatial phases were unaffected (Fig. 5, F-H). Vertical gains were zero or insignificant (P = 0.20) at any frequency of rotation. Similar gain changes were observed in M9308 when the animal was tested 2 yr after canal plugging (Table 1).
The data from both NC animals are summarized in Fig. 6, E-H. Spatial horizontal and roll gains increased monotonically with frequency, approaching normal gains at 4 Hz (Fig. 6, E and G). The spatial phases of the horizontal and roll components remained invariant with frequency (Fig. 6, F and H; Table 1). The horizontal spatial phases were close to normal >0.2 Hz for both animals (Fig. 6F). The roll component was close to normal in M9357 but was shifted ~45° over the same frequency range in M9308 (Fig. 6H, Table 1). Thus spatial gain and phases obtained from the NC animals tended to normalize at high frequencies for horizontal and roll.
When the NC animal, M9308, was tested in light at 0.2 Hz, the spatial gains and phases of the horizontal and roll eye velocity components were close to preoperative values. After surgery, the difference between the spatial gains of the responses in light and darkness decreased as the frequency of rotation was increased to 1 Hz due to a reduction in the gain of the responses in light and an increase in the gain of the responses in darkness. At
2 Hz, there was no significant difference between the two data sets. Similar results were obtained from M9357. Thus spatial gain of the aVOR tested in light decreased at frequencies >1.0 Hz, consistent with results of Tabak and Collewijn (1995)
.
As shown in Yakushin et al. (1995)
, the animal with both lateral canals plugged (VC animal, M9354) had a horizontal spatial gain of 0.21 at
51° tilt backward for a frequency of 0.2 Hz (Fig. 7A). The peak roll gain of 0.50 occurred at
66° tilt back (Fig. 7D; Table 1). This was due to the contribution of the intact vertical canals. At higher frequencies, the spatial gains increased as a function of frequency, and the spatial phase were shifted toward normal (Figs. 7, B, C, E, and F, and 8, A and E). Two other animals (LARP and RALP) had the same spatial phases but lower spatial gains when tested at 0.2 Hz (Yakushin et al. 1995
). At higher frequencies, the spatial gains increased (Fig. 8A), and the spatial phases of the horizontal component normalized (Fig. 8B). The spatial phase of the roll component normalized only in the VC animal, however (Fig. 8F,
). A vertical component was present in the response of both animals with only one vertical canal pair intact (Fig. 8, C and D). Presumably, as predicted by the model (Yakushin et al. 1995
), it was due to the projection of only one vertical canal pair onto the pitch plane that was not cancelled by its complementary canal pair. The vertical gains and phases did not vary as a function of stimulus frequency (Fig. 8, C and D; Table 1).

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| FIG. 7.
Spatial responses of the monkey with both lateral canals plugged (VC animal) tested at different frequency of sinusoidal rotation. Average gains of the yaw (A-C) and roll (D-F) components, tested at 0.2 Hz and 60°/s (A and D), at 1.0 Hz and 33°/s (B and E), and at 4.0 Hz, 7°/s (C and F). , minimum mean square error fit to the horizontal and torsional gains at the tested frequencies. Insets (bottom): animal's head position at that angle of tilt. When this animal was tested after surgery, the responses (gains and spatial phases) tended to normalize as the testing frequency increased.
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| FIG. 8.
Spatial gains (A, C, and E) and phases (B, D, and F) of the horizontal (A and B), vertical (C and D), and roll (E and F) components of the aVOR of the VC (M9354, ), left anterior and right posterior canal intact (LARP; M9306, ), and right anterior and left posterior canals intact (RALP; M9355, ) animals, tested in darkness from 0.2 to 4 Hz. Horizontal and roll gains and horizontal spatial phases tended to normalize with increases in frequency. Vertical gains and phases for the LARP and RALP animals were not dependent on stimulus frequency.
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Responses to steps of acceleration
As noted in METHODS, the aVOR gain of normal animals could be obtained as a ratio of peak eye velocity to peak stimulus velocity or as a ratio of eye acceleration to stimulus acceleration using a velocity ramp stimulus with a high acceleration (Fig. 9, A and C). This is because eye velocity essentially follows stimulus velocity during the ramp. After the semicircular canals were plugged, the eye velocity response did not follow stimulus velocity during acceleration. Stimulus velocity rose linearly, but eye velocity had an exponential increase which reached a steady-state value when stimulus velocity was still increasing (Fig. 9, A and D). The time constant (Tc) of the exponential increase in animal M9308 was 69 ± 13 ms for slow phase eye velocity to the left and 78 ± 15 ms for slow phase eye velocity to the right (P = 0.37) when the animal was rotated in the plane of the plugged lateral canal (30° tilt forward). Steady-state eye velocity of this exponential increase was symmetrical, and there was no significant difference between the response to either side (left: 14.7 ± 3.3°/s, right 14.6 ± 3.3°/s; P < 0.05). For one NC animal, M9308, aVOR gain, gVOR, [eye velocity/(stimulus acceleration * time constant)] was 0.81 ± 0.15 to the left and 0.72 ± 0.15 to the right (P = 0.33). Both were not significantly different from normal (P = 0.480 and P = 0.479 for rotation to the left and to the right, respectively; Table 2). In the other NC animal, M9357, the values of Tc and steady-state eye velocities were similar (Table 2), and computed gains were 0.76 ± 0.21 for rotation to the left and 0.81 ± 0.30 for rotation to the right. Similar results were obtained for one VC, two LARP, and two RALP animals (Table 2). That is, the canal-plugged gains were close to preoperative values. The results indicate that canal plugging shortens the canal time constant by almost two orders of magnitude but does not affect its gain. Thus the response of the unplugged canals to a ramp of velocity over 260 ms was close to the velocity of the stimulus (Fig. 9, A and C). For the plugged canals, the time constant was much shorter, and the response to the same ramp of velocity was exponential and was closer to the acceleration of the stimulus (Fig. 9, B and D).
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|
TABLE 2.
aVOR gain in response to rotation with a ramp of acceleration before and after semicircular canal plugging
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Canal plugging also was associated with a reduction in the dominant time constant of the aVOR and of OKAN. The average central aVOR and OKAN (velocity storage) time constants before operation varied between 40 and 50 s. After plugging, OKAN time constants on average were ~10 s (Table 3). The reduction of the integrator time constant would raise the low-frequency 3-dB cutoff to ~0.02 Hz, which is still well below the frequency range considered in this study. This justified neglecting the contribution of the velocity storage integrator.
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|
TABLE 3.
Dominant time constant of the velocity storage integrator measured before and after semicircular canal plugging
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Morphological and physiological verification of canal plugging
Morphology was available for several of the animals the data of which are presented in this study. An example from a LARP animal (M9356) is shown in Figs. 10 and 11. Both lateral canals and the right anterior and left posterior canals were blocked (Fig. 10, D-G). The length of the plugged area was estimated as 2-3 mm. The ampullae of the six canals, including the hair cells and crista and the four maculae of the otolith organs, as well as the organ of Corti were intact (Fig. 11). In another LARP animal (M9006), both horizontal, and the right anterior and left posterior canals were completely plugged, and the left anterior and right posterior canals were patent (not shown). The hair cells of the six ampullae and the four maculae and the organ of Corti appeared intact in this animal. The nerves and ganglion cells, and the dark cell area were normal. The otolith membranes were not smooth, but the sensory cells looked intact. Plugging was also complete in M9003 (VC animal) and M9008 (LC animal). Similar results using the same techniques for canal plugging in the monkey (Suzuki et al. 1991
) previously have been reported by Angelaki et al. (1996)
.

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| FIG. 11.
Anatomic verification of the hair cells condition of plugged and not plugged semicircular canal in a LARP animal (M9356). , pointing to intact hair cell areas in the cupula of left (A) and right (B) anterior, left (C) and right (D) lateral, left (E) and right (F) posterior semicircular canals, and left (G) and right (H) saccule and utricle. Right anterior (B), both lateral (C and D), and left posterior (E) canals were plugged. LAC and RAC, left and right anterior canals; LLC and RLC, left and right lateral canals; LPC and RPC, left and right posterior canals; L Sac and R Sac, left and right saccules; L Utr and R Utr, left and right utricles.
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Morphological data for other animals are not available. However, the reduction of the time constants during step rotation in the plane of the plugged lateral canals, obtained from animals with morphologically proved plugging, was similar to the reductions obtained from the other canal-plugged animals used in this study. Before plugging, the time constants of the animals, tested with steps of velocity at 60°/s while upright, ranged from 20 to 70 s, and peak velocities were ~57-60°/s. After surgery, when the animals were rotated in the plane of the plugged canals with steps of velocity, there was a weak transient response with a short time constant (
70 ms, Table 2). The time constant of the step responses after surgery was similar in all of the tested animals, including those in which canal plugging was morphologically verified.
Modeling the three-dimensional kinematics and dynamics of the semicircular canals: effects of plugging
Each semicircular canal is an inertial mechanism that responds to angular acceleration along the normal to the canal plane. A coordinate frame whose basis vectors are the canal plane normals (Canal Frame), although nonorthogonal, is a convenient frame of reference to describe the activation of the canals due to head rotation. Head rotations, however, are best described in a coordinate frame defined by the roll, pitch, and yaw axes of the head (Head Frame). To understand the contribution of canal pairs to eye movements, which are measured in a Head Frame, a general kinematic transformation was made between the Head and the Canal Frames. In addition, each semicircular canal has afferent output that is temporally related to the input angular acceleration, and this was represented by a dynamical system. The model that was developed combines these two approaches.
Generalized kinematics of three-dimensional head to canal transfer function
The most general kinematic transformation between the head and canal coordinate transformation is obtained by rotating each of the head-based basis vectors,
= (eX, eY, eZ) into an associated set of canal-based basis vectors,
' = (ea, ep, el) (Fig. 1, A and B). A generalized rotation in terms of Euler angles is as follows
Where
,
, and
are the Euler angles representing rotations about the head yaw (Z) axis, the rotated Y axis (line of nodes), and the rotated yaw axis (Z'). Each normal unit vector has its own set of Euler angles. The Euler angles associated with the anterior canal normal correspond to a rotation of the eX unit vector and are
a,
a, and
a. Those associated with the posterior canal correspond to a rotation of the eY unit vector and are given by
p,
p, and
p. Those associated with the lateral canal normal is a rotation of the eZ vector given by the angles
l,
l, and
l. The canal basis vectors can then be given in terms of the head basis vectors by the following
|
(7)
|
Because each basis vector in the canal basis is a rotation of a unit vector in the head basis, only two generalized coordinates are necessary to define the rotation of one unit vector into another. Therefore without loss of generality, the transformation between basis vector can be reduced to the following by setting
a =
p =
l = 0
|
(8)
|
The relationship described by Eq. 8 defines the matrix of the transformation, Tcan, that project vectors given in head coordinates along the normals of the canals, which represent the canal coordinate frame. The matrix Tcan is given as follows
|
(9)
|
The inverse of the above matrix, describes how the basis vectors eX, eY, and eZ can be given in terms of ea, ep, and el, and is given by
|
(10)
|
where T
1can is given by
|
(11)
|
Using the inverse matrix, a projection mapping from canal coordinates back to head coordinates, Thead can be obtained as
|
(12)
|
The g parameters represent the percentage the canal activation along a coordinate axis of the head. We now consider how the kinematic transformation is incorporated into the state equations that govern the dynamics of the semicircular canals in three dimensions.
Three-dimensional aspects of semicircular canal dynamics
Each semicircular canal can be approximately described by a first-order linear differential equation (Eq. 1). Put into standard state form, it is given by
|
(13)
|
where rv is the eighth nerve output,
c is the projection of the input angular head velocity along a canal normal, Tc is the canal time constant, and gc is the high-frequency gain of the semicircular canal system function and xcan is the state of the canal (the sum of the eighth nerve output and the component of angular velocity along the normal to its plane). Applying Eq. 13 to each canal, the three-dimensional state equations are given by
|
(14)
|
|
(15)
|
|
(16)
|
where
|
(17)
|
and Tcan and Thead are the projection mappings from head-to-canal and canal-to-head coordinates, respectively. The vectors rh, rv, xcup, and
e are the head velocities, VIII nerve activation, and cupula state given by
|
(18)
|
It should be noted that matrices Tc and Gc represent the time constant of individual canals and their coupling from angular acceleration along their normals, respectively. These matrices are diagonal because it is assumed that there is no cross coupling between canals at the peripheral level.
The three-dimensional transfer function H(j
) can be obtained by substituting j
for the derivative operator in Eq. 16 and solving for the Fourier transform of We in terms of the Fourier transform of Rh
|
(19)
|
Therefore the transfer function H(j
) can be given in a simplified form as
|
(20)
|
Thus Eqs. 16 and 20 model how three-dimensional eye velocity is generated over the direct pathway of the aVOR in the time and frequency domains.
Comparison of model simulation with experimental data
For simulation purposes, the parameters of the model were chosen as follows: Tc(Normal) = 4 s, corresponding to the measured time constant of vestibular nerve afferents (Büttner and Waespe 1981
; Correia et al. 1992
; Goldberg and Fernandez 1971
; Reisine and Henn 1984
). The average canal time constant, measured at 30° tilt forward for all canal-plugged animals tested in this study, was 0.074 ± 0.011 s and ranged from 0.056 to 0.089 s (Table 2). For modeling purposes, we chose a canal time constant (Tc Plugged) of 0.070 s.
a=
p =
40°,
a =
p = 135°, g00 = g01 = g02 = 0.52, g10 = g11 = 0.83, g12 = 0, g20 = g21 = g22 = 0.87 represent the kinematics of the canal orientation in the head and the specific gains associated with projections of velocities represented in canal coordinates back to head coordinates (Yakushin et al. 1995
). Model simulations were first obtained for ramps of acceleration analogous to those that produced the data (Fig. 12). The normal response rises approximately linearly over the duration of acceleration (Fig. 12A, Normal). For the NC condition, the response rises exponentially approximately reaching its steady-state value within 300 ms. The initial slope of the eye velocity response is the same as in the normal condition because the gain of the canal is the same after as before plugging. The differences between the curves are due to the differences in time constant.

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| FIG. 12.
Model prediction of the horizontal eye velocity (A) for the normal (canal time constant of 4 s) and NC (canal time constant 0.070 s) animals to the ramp of stimulus acceleration (B).
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The frequency domain responses were also consistent with the data. For the normal animal, the model predicted that the temporal phase of the yaw component would be approximately
168° relative to stimulus velocity over tilt angles of ±90° at a frequency of 0.2 Hz (Fig. 13A). As the frequency increased to 4.0 Hz, the temporal phase shifted toward
180°, the perfect compensatory phase. The modeled roll temporal phases also shifted over 12° as the frequency of rotation increased from 0.2 to 4 Hz. At 4 Hz, roll temporal phases were
180° for tilt backward and 0° for forward tilt (Fig. 13E). For the NC animal, the yaw phases were approximately
90° at 0.2 Hz, 90° phase advanced from velocity and in phase with acceleration (Fig. 13B). As frequency increased toward 4 Hz, the phase shifted toward
180°, which is the ideal compensatory phase. The roll phases were
90° at 0.2 Hz. This was 90° lagged from the normal compensatory response. The lag decreased with increases in frequency reaching 30° lag at 4.0 Hz. The simulation of temporal phase as a function of frequency for the NC condition was close to the data obtained from the NC animals (Figs. 3E and 4, B and E; 0.2 Hz, yaw =
88 ± 21°; roll =
68 ± 21°; 4 Hz, yaw =
148 ± 34°, roll =
162 ± 7°; for M9357 at 0.5 Hz, yaw =
98 ± 11° and roll =
85 ± 12°; at 4 Hz, yaw =
135 ± 10° and roll =
137 ± 31°). Model simulations of the temporal phases were similar for the VC and LARP/RALP conditions (Fig. 13, C, D, G, and H) and fit the data from the VC animal (Fig. 4, C and F). For both the curves could be considered a combination of the responses of the normal and the NC animal. At 40° tilt forward, the intact vertical canals are not activated during rotation for the VC, LARP, and RALP animals. Therefore their responses should have the same variation of temporal phases as a function of frequency as the NC animal. This can be seen by examining the temporal phases for the different frequencies along the dotted lines in Fig. 13, B-D and F-H). When the animals were tilted backward so that one or both pairs of reciprocal intact vertical canals were close to the plane of rotation, the temporal phases of the VC and LARP animals converged to be approximately equal to
180°, close to values predicted for animals with normal labyrinths. Thus changing the dominant time constant of the canal from 4.0 s (normal) to 0.070 s (canal-plugged condition) could explain the observed phase variations for the canal-plugged animals used in this study at all applied frequencies.

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| FIG. 13.
Model prediction of the temporal phase shifts between horizontal (A-D) and roll (E-H) components of slow phase eye velocity and stimulus velocity at different frequencies (see inset in A) as a function of head tilt (abscissa, positive value tilt forward; negative value tilt backward). Negative values correspond to the condition when eye velocity led stimulus velocity. A and E: in the normal animal, the horizontal component was predicted to be ~180° out of phase with stimulus velocity (A). Roll component was predicted to be in phase with stimulus when the head was tilted forward and ~180° out of phase with stimulus velocity when head was tilted backward (E). Roll temporal phases reversed about the upright (0°) position. Response at 4.0 Hz is emboldened to facilitate comparison. B and F: temporal phase of the horizontal component of NC animal was predicted to lead by ~90° in all head positions when tested at 0.2 Hz (B); the lead normalizes at higher frequencies of rotation. F: roll temporal phases were also predicted lead 90° more than for the normal animal in any head orientation and the lead was predicted to normalize at higher frequencies. C and H: temporal phase of the horizontal component of the VC (C) and LARP (D) animals were predicted to be close to normal when the head was tilted back (rotation in plane of intact canals). When animal were tilted forward, temporal phases were predicted to be similar to the NC animal (rotation in plugged canal plane).
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The model predicted that the temporal gains for the yaw and roll components would vary sinusoidally as a function of tilt for the normal animal and that the spatial phase for yaw would be 0° and roll would be 90° tilt forward at all frequencies (Fig. 14, open symbols; Table 4). The spatial gains rose slightly from 0.85 at 0.2 Hz (Fig. 14A) to 0.87 at
0.5 Hz (Fig. 14, B-D) for yaw eye movements and from 0.51 at 0.2 Hz (Fig. 14E) to 0.52 at
0.5 Hz (
, Fig. 14, F-H) for roll eye movements. This prediction is in agreement with data obtained from two normal animals (Table 1).

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| FIG. 14.
Model prediction of the horizontal (A-D) and roll (E-H) spatial gains for the normal ( and ) and NC ( and ) animals tested at 0.2 Hz (A and E), 1.0 Hz (B and F), 2.0 Hz (C and G), and 4.0 Hz (D and H). Compare with Figs. 6 and 8.
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Spatial gains of the yaw response of the NC animals were predicted to be 0.08 at 0.2 Hz and increased as a function of frequency of rotation to 0.76 at 4 Hz (
, Fig. 14, A-D). This was close to data obtained from the NC animals, which varied from 0.03 to 0.05 at 0.2 Hz and 0.42 to 0.55 at 4 Hz (Table 1). The spatial gains of the roll response were predicted to be 0.05 at 0.2 Hz, rising to 0.45 at 4 Hz (
, Fig. 14, E-H). These spatial gains were close to those recorded in the NC animal, which were 0.01-0.04 rising to 0.34-0.58 at the same frequencies (Table 1). The spatial phases of the yaw and roll gains were predicted to be the same at each frequency for the NC animals, as in the normal animals. The spatial phases of the yaw and roll components in M9357 were ~10° (Fig. 6, F and H, Table 1) and ~10° for yaw and 40° for roll in M9308. Thus the simulations generally conformed to the experimental data. These data demonstrate that a reduction in the canal time constant to 0.07 s would decrease the yaw and roll spatial gains at low frequencies but that at higher frequencies the gains would tend to normalize.
The model predicted that when the VC animal was tested at 0.2 Hz, the spatial gain for yaw would occur at
48° and the roll spatial gains was predicted to be at
51° tilt backward at 0.2 Hz (
, Fig. 15, A and E; Table 4). This is approximately the position that aligns the rotation plane with the intact canals. As the stimulus frequency increased, the spatial phases of both yaw and roll normalized (
, Fig. 15, B-D and F-H; Table 4). These values were close to those measured in the VC animals (Table 1).

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| FIG. 15.
Model prediction of the horizontal (A-D) and roll (E-H) spatial gains for the normal ( ), VC ( ), and RALP ( ) animals tested at 0.2 Hz (A and E), 1.0 Hz (B and F), 2.0 Hz (C and G), and 4.0 Hz (D and H). Compare with Fig. 10.
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It should be noted that despite the general concurrence of model and experimental data, none of the observed or predicted data for the canal-plugged animals reached preoperative value in the frequencies range 0.2 to 4.0 Hz. The model predicted that activation of the plugged semicircular canal at these frequencies would be different from the normal. To obtain responses similar to the response of the intact canal, higher frequencies should be applied. Figure 16 shows the model predictions for canal-plugged animals for frequencies
20 Hz. The spatial phases were close to the normal responses at the frequency of
4 Hz (Fig. 16, B and D). Nevertheless, complete spatial gain compensation would occur only at ~10 Hz (Fig. 16, A and C). Similar observations have been made by R. Rabbitt et al. (personal communication), using a different paradigm in the toadfish.

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| FIG. 16.
Model prediction for the spatial gains (A and C) and phases (B and D) as a function of stimulus frequency for the normal animals and after different canal plugging (see inset in A).
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DISCUSSION |
This study demonstrates that the gains and phases of the aVOR of canal-plugged monkeys approach normal values when the animals are stimulated at high frequencies. When animals were rotated about axes normal to the plane of the plugged canals at 0.2 Hz, the gains of the induced responses were small, and the phases were close to head acceleration (Angelaki and Hess 1996
; Angelaki et al. 1996
; Baker et al. 1982
; Böhmer and Henn 1983
; Böhmer et al. 1982
, 1985
; Yakushin et al. 1995
). As the frequency was increased to 4 Hz, both the gains and phases tended to normalize for all types of plugged conditions. This result was found in each of the canal-plugged animals, and the data were internally consistent.
Due to equipment limitations, it was not possible to rotate the animals at the same peak velocity at every frequency, and the peak velocities at 1, 2, and 4 Hz were different from those than at 0.2 and 0.5 Hz. The vestibular system is approximately linear in normal animals over the range of angular velocities at which the animals were tested (5-60°/s) (Telford et al. 1996
). After canal plugging it is not known whether the same linearity still applies. Morphological study has shown the membranous and bony canals, the ampullae, and the vestibular nerves are normal at the light microscopic level (Fig. 11) (also Angelaki and Hess 1996
; Angelaki et al. 1996
), although a recent study has questioned whether the cupula is still attached after canal plugging (R. Rabbitt, personal communication). However, the resting frequency of canal afferents is the same in plugged as in normal animals (Goldberg and Fernandez 1975
), and the central vestibular system is intact in these animals. Velocity storage is intact, and they can generate nystagmus during off-vertical axis rotation (Cohen et al. 1983
; Correia and Money 1970
) and optokinetic nystagmus and after-nystagmus (Cohen et al. 1983
). More significant, a linear model was sufficient to predict the amplitudes and phase responses despite the fact that different frequencies and velocities were used. From this, we conclude that the vestibular system remained approximately linear in the canal-plugged animals.
There are actually two time constants associated with the responses, a dominant time constant of 4 s and a short time constant estimated to be ~3 ms (Steinhausen 1933
). The dominant time constant is proportional to the viscosity of the endolymph and inversely proportional to the moment of inertia. The short time constant is proportional to the viscosity and inversely proportional to the elasticity of the cupula membrane. Either an increase in viscosity or a decrease in the moment of inertia could decrease the canal time constant after plugging. An increase in the viscosity would cause the dominant time constant to decrease but would cause the small time constant to increase. This would produce a lower gain at higher frequencies. However, our results show a monotonic increase in gain with frequency corresponding to a 50-fold reduction in dominant time constant. An equivalent 50-fold increase in the small time constant would cause a gain reduction at 1 Hz, which was not observed. Therefore, it is unlikely that the short time constant of the canals was changed. This suggests that the viscosity of the endolymph was unaltered before and after plugging.
There are two techniques that have been described for plugging the canals. Ewald's original technique was to open the perilymphatic space and compress the membranous canal with gutta percha, a clay-like material. The Money/Scott/Suzuki technique, which was used in these experiments (Money and Scott 1962
; Suzuki et al. 1991
) entails drilling across the bony and membranous canals and filling the opening with bone chips and soft tissue. Initially after surgery there probably is mixing of endolymph and perilymph with this plugging technique. The cupula also may be disconnected from the roof of the ampulla (R. Rabbitt, personal communication), which may account for the decreased responses seen immediately after surgery (Angelaki and Hess 1996
; Angelaki et al. 1996
). However, in the long term, it is likely that the endolymph and perilymph compartments are separated and that the cupula reattaches. Moreover, a mixture of endolymph and perilymph would have a decreased not an increased viscosity, which would produce a longer not a shorter time constant. It is more likely that the canal plug had reduced the effective moment of inertia in response to angular acceleration of the head, although the exact nature of the mechanism is not clear.
There has been controversy as to whether there is spatial adaptation of the response of the remaining canals after canal plugging. Yakushin et al. (1995)
tested animals at 0.2 Hz and concluded that such adaptation did not occur. Angelaki and Hess (1996a) reported similar changes in phase when animals were tested between 0.05 and 1.1 Hz but concluded that spatial adaptation had occurred in the planes of the intact canals to account for the frequency-dependent responses in the planes of the plugged canals (Angelaki and Hess 1996
; Angelaki et al. 1996
). The responses of the NC animals were critical in resolving this question. Independent of head orientation to the axis of rotation, the temporal and spatial gains and phases of the horizontal and roll eye velocity components tended to normalize at higher frequencies in the NC animals. At 4 Hz, the responses were close to being 180° out of phase or in phase with head velocity (Figs. 3, 4, and 6). The induced eye movements could not have arisen from spatial adaptation in the NC animals because there were no intact canals left to adapt. The responses in the NC animals were similar to those of the other animals when rotated around axes orthogonal to the plugged canals. Because the frequency response of the eye movements induced at 2-4 Hz is above the peak frequency of eye movements produced by activation of neck muscles in plugged canal animals (0.5 Hz) (Böhmer and Henn 1983
), the most likely alternate hypothesis is that the responses arose from the plugged canals.
In support of this alternative hypothesis, the responses of each of the animals with various combinations of canal plugging formed a consistent set of data over a range of frequencies from 0.2 to 4.0 Hz. In every case, when the animals were rotated sinusoidally in the plane of the plugged canals at lower frequencies, the response was in phase with head acceleration. As the frequency of rotation increased, it moved toward being in phase with head velocity. Consequently, when the animals were rotated sinusoidally in the plane of the plugged canals at lower frequencies, the gain was close to zero, but it approached the normal response gain and phase as the frequency of rotation increased. General support for this alternative hypothesis came from the finding that the spatial gains and phases for the horizontal component could be predicted by combining responses of the plugged and the normal canals. This was simply done using a model, in which the gain of the aVOR was held constant, but the time constant of the canal was reduced due to changes in the canal dynamics after plugging. One problem, which arose in one of the NC animals (M9308), was that the spatial phase of the roll component remained at
45° (Fig. 6H) and did not approach the
90° spatial phase of the normal for the frequency range
4 Hz (Fig. 6D). The reason for this is not apparent. The roll component was consistent with model predictions in the other NC animal (M9357).
We considered the possibility that activity responsible for eye movements in the planes of the plugged canals may have arisen in the otolith organs. Goldberg and Fernandez (1975)
demonstrated during centered or on-axis rotation that "otolith neurons do not respond to even intense angular accelerations." From this, it is unlikely that the activity responsible for the eye velocities recorded in the canal plugged animals came from the otolith organs. Recently it has been suggested that movement of the endolymph on the utricular side of the cupula could provide a source for fluid movement even in the presence of plugging (R. Rabbitt, personal communication). Our study, which suggests that plugging does not inactivate the response of a canal but merely changes its dynamics so that the lower end of the pass-band is moved to a higher frequency, are in agreement with this suggestion.
It was especially striking that both the sinusoidal and step response to short ramps of angular acceleration could be predicted for canal-plugged and normal animals by modifying a single parameter, the time constant of the afferent output of the semicircular canals. Normal canals were associated with an afferent time constant of
4 s, while plugged canals were associated with a time constant of 70 ms. The reduced time constant would lead to a shift of the low-frequency cutoff, i.e., the frequency at which the gain is down to 0.707 (the 3-dB cutoff), from 0.039 to 2.270 Hz. As a result, canal plugging essentially has the effect of blocking the output of the canals at lower frequencies (
0.2 Hz) while sustaining a normal response at higher frequencies (
4 Hz). The shortened time constant also would lead to the prediction of a reduced steady-state gain for steps of rotation lasting longer than three time constants (
200 ms). These conclusions are consistent with studies that demonstrate reduced eye velocities in response to step rotation in canal plugged animals (Backous et al. 1996
; Böhmer et al. 1982
). Our interpretation of these results is that it was not the gain that was reduced, but rather the time constant that had been modified.
For normal animals, the semicircular canal afferents have a linear rise over the whole period of constant acceleration. Thus the time constant can be neglected in calculations of the gain (Raphan and Cohen 1981
, 1986
). In contrast, as a result of the short time constant in the canal-plugged animal, the increase in eye velocity during constant angular acceleration has an exponential rise, which reaches a close-to-steady-state level within the first 200-300 ms. Thus the canal time constant is a critical factor in aVOR gain calculations (Raphan and Cohen 1986
). As shown in this paper, if the time constant is considered, the gain of the aVOR response to a step of velocity is not different in the canal-plugged animals from those of normal monkeys or from those of sinusoidal rotation at high frequencies.
High-frequency head rotation is of considerable clinical value in detecting abnormalities due to vestibular denervation (Aw et al. 1996a
,b
; Halmagyi and Curthoys 1988
). Peak eye velocities are lower and compensation is less when the head is rotated toward a denervated labyrinth in accordance with Ewald's Second Law (1892). A similar result was obtained from plugged canals, although there was a significant difference between the canal-plugged and nerve-cut subjects (Aw et al. 1996b
). Aw et al. used accelerations of
4,000°/s2, which last for
50 ms and then reverse for
100 ms, with decelerations being smaller than accelerations. This gives peak head velocities during the acceleration phase of 200-250°/s. If the time constant of the plugged canal was the same as that we found in the monkey after canal plugging (0.07 s), the model would give a gain close to 1. This is because the time constant is larger than the time of stimulation. However, if the time constant were only 30 ms in the canal-plugged condition, which is smaller than the period of stimulation, the model would give a peak response of <120°/s. This would be consistent with the
120°/s that Aw et al. found in the plugged individuals. Correspondingly, the frequency characteristics would be different. The cut-in frequency would be
6 Hz, as opposed to the 2- to 3-Hz cut-in frequency we found in the monkey (100/0.03 * 2
). Thus the data of Aw et al. (1996a
,b
) may imply that in humans, the canal time constant after posterior canal plugging is shorter and the cut-in frequency is higher than in the monkey. The practical implication is that the type of canal plugging used by Aw et al. (1996a
,b
) on humans rendered the canal ineffective even at frequencies close to 20-30 Hz.
The model predicted that there would be no changes in spatial gain and phase of the yaw and roll components as a function of frequency in the normal animal. It also predicted that there would be an 11° temporal phase shift from perfect compensation. These predictions were based on the assumption that there was a 4-s time constant of the canals and that the contribution of velocity storage was negligible. The response was limited solely to the direct vestibular pathway, which is predominantly active during frequencies of sinusoidal rotation between 0.1 and 8 Hz. The gain predictions were realized in the two normal monkeys used in this study but none of the normal responses had the 11° phase shift at the lower frequencies. If the contribution of velocity storage was included, the difference between model predictions and experimental data would have been reduced significantly. This suggests that velocity storage not only contributes to the aVOR in the low-frequency range (between 0.001 and 0.1), but it also makes an important contribution to the response at midband frequencies (0.2-0.5 Hz) by producing phase lags that reduce the phase leads coming from the canals. At low frequencies, there would be cross-coupling of velocity storage in tilted positions (Dai et al. 1991
; Raphan and Sturm 1991
; Raphan et al. 1992
). This would superpose the spatial organization of velocity storage with the spatial organization of the semicircular canals, thereby altering the overall spatial response of the system.
It is of interest to speculate why the general motor behavior of the animals with plugged canals recovered, even in the NC animals. These monkeys could jump in their cages and maintain balance. Their only obvious behavioral abnormality was a tendency for the head to overshoot briefly during gaze shifts in the planes of the plugged canals. Similar findings were reported by Ewald (1892)
. He noted that pigeons with plugged canals could fly to the roof of the cage on the same day after plugging as soon as they had recovered from anesthesia. Normally, there is dual compensation for head movement by both vision and vestibular input in the range of 0.1-1 Hz. This redundancy provides a robustness of compensation, which protects against individual variability and effects of lesions. Plugging narrows this range of overlap, and the canals are essentially ineffective in the range of 0.1-1 Hz. As we have previously shown, vision substitutes for the aVOR during head movements at
0.2 Hz in canal-plugged animals (Yakushin et al. 1995
). This study demonstrates that vision also can contribute significantly to normalization of the aVOR in animals with plugged canals up to ~1 Hz. It is at this critical frequency and above that, the aVOR becomes significantly active. Therefore with a mixture of vision and input from the plugged canals, the animals could generate compensatory eye velocity against head velocity over a full range of head movements despite the canal plugging.
The reduction in the dominant time constant of the aVOR and OKAN after canal plugging has not been noted before. Presumably, it represents habituation of velocity storage after canal plugging (Cohen et al. 1992b
). This habituation could account for the
50% drop in steady state eye velocity noted during off-vertical axis rotation (OVAR) after canal plugging (Cohen et al. 1983
; Correia and Money 1968). The reason for this habituation is not known.
In summary, the data support the hypothesis that plugging at a point distant from the cupula may alter but it does not block the response of the semicircular canals. Rather it alters the dynamic response so that the canals contribute differently at different frequencies. The data support the hypothesis that the individual canal pairs contribute eye velocity components according to their vector projection onto the individual canals, even after the canals are plugged. They suggest that despite considerable plasticity in the aVOR, the innate coordinate frame with regard to the head is not altered in adult animals by partial inactivation of the individual canals over a wide range of frequencies.
 |
ACKNOWLEDGEMENTS |
We thank Dr. Minjia Dai for help in data collection and for the use of data acquisition programs, Dr. Evgeny Buharin for writing the programs for data analysis, M. Kunin for implementing the equations for the model dynamics, and V. Rodriguez for technical assistance.
This work was supported by National Institutes of Health Grants NS-00294, EY-11812, EY-04148, EY-01867, and DC-03787.
 |
FOOTNOTES |
Address for reprint requests: S. B. Yakushin, Dept. of Neurology, Box 1135, Mount Sinai School of Medicine, 1 E. 100th St., New York, NY 10029.
Received 17 December 1997; accepted in final form 13 July 1998.
 |
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