The Journal of Neurophysiology Vol. 80 No. 6 December 1998, pp. 3077-3099
Copyright ©1998 by the American Physiological Society

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

Abstract Introduction Methods Results Discussion References

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.

	INTRODUCTION

Abstract Introduction Methods Results Discussion References

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

Abstract Introduction Methods Results Discussion References

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).

View larger version (120K): [in this window] [in a new window]   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.

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.

View larger version (36K): [in this window] [in a new window]   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.

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 g_c is the coupling relating canal output to angular acceleration input d/dt(_c) (Raphan and Cohen 1981). The parameter, T_c, is the dominant time constant of the canal dynamics, and r_v is the canal afferent output. We will refer to T_c 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, g_d, referenced to an equivalent composite canal activation, r_veq. Therefore eye velocity about a particular axis, _e, can be given by

(2)

where g_ceq is the coupling from head acceleration to r_req. The gain of the reflex, g_VOR, then can be given by the equation

(3)

Using Eqs. 2 and 3, the gain, g_VOR, can be measured in a number of ways dependent on the magnitude of the dominant time constant. In the normal monkey, T_c 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, g_VOR, 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 T_c, 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(r_veq) (Eq. 2) is close to zero. In these instances, the gain, g_VOR, 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 (T_c) 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 (e_X) along an interaural axis from the left ear. The roll axis (e_Y) lies along the naso-occipital axis and points out the back of the head, and the yaw axis (e_Z) 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 e_X (roll), e_Y (pitch), and e_Z (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 (e_a), posterior canal (e_p), and lateral canal (e_l), corresponding to the X_c, Y_c, and Z_c axes. These basis vectors do not form an orthonormal set.

View larger version (19K): [in this window] [in a new window]   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.

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.

View larger version (30K): [in this window] [in a new window]   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).

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.

View larger version (43K): [in this window] [in a new window]   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°).

	RESULTS

Abstract Introduction Methods Results Discussion References

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*10⁸ 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.

View larger version (34K): [in this window] [in a new window]   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 valuetilt forward; negative valuetilt 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).

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.

View larger version (33K): [in this window] [in a new window]   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).

View larger version (24K): [in this window] [in a new window]   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).

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).

View larger version (30K): [in this window] [in a new window]   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.

View larger version (35K): [in this window] [in a new window]   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.

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 (T_c) 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, g_VOR, [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 T_c 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).

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.

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).

View larger version (107K): [in this window] [in a new window]   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.

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,  = (e_X, e_Y, e_Z) into an associated set of canal-based basis vectors, ' = (e_a, e_p, e_l) (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 e_X unit vector and are _a, _a, and _a. Those associated with the posterior canal correspond to a rotation of the e_Y unit vector and are given by _p, _p, and