INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Movement in a gravitational environment induces combined linear and angular accelerations of the head in space, concurrently activating the linear and angular vestibuloocular reflexes (lVOR and aVOR). Off-axis rotation, or centrifugation, which induces concomitant centripetal and angular accelerations, has been used extensively to study aVOR and lVOR interaction (Angelaki and Anderson 1991a,b; Angelaki et al. 1991; Crampton 1966; Curthoys et al. 1992; Lansberg et al. 1965; Merfeld 1990, 1995; Merfeld and Young 1995; Merfeld et al. 1991, 1993; Sargent and Paige 1991; Wearne 1993; Young 1967). Sargent and Paige (1991) tested monkeys with sinusoidal centrifugation to determine whether the aVOR and lVOR responses superpose. At frequencies between 1 and 4 Hz, which induced minimal tilts of the gravito-inertial acceleration (GIA), responses of the horizontal lVOR summed with those of the horizontal aVOR when the animals were upright. In the supine position, the aVOR was in the roll direction, but the lVOR was still horizontal. The horizontal lVOR, estimated by subtracting the aVOR from the overall response when the animals were upright, was the same as that measured directly when they were supine, supporting the superposition hypothesis at these frequencies.

In other studies, low-frequency and constant-velocity centrifugation has been used to extract the lVOR component of eye velocity. We use the term "constant-velocity centrifugation" to refer to a stimulus that has a small angular acceleration (10-40°/s²) up to a constant velocity, which is maintained for a long duration. In these studies, the horizontal eye velocity trace obtained when subjects had their backs to the direction of motion was subtracted from that when they faced the motion (Benson 1974; Merfeld 1990; Merfeld and Young 1995; Wearne 1993; Young 1967). Because the centripetal acceleration was identical in both conditions, the subtraction was assumed to cancel the aVOR responses, while summing the lVOR responses. One-half of the difference trace then should represent the lVOR response. Whether superposition holds at low frequencies and large GIA tilt angles, such as during constant velocity centrifugation, has not been determined independently. This is primarily because the low gain of the lVOR at frequencies <0.5 Hz (Paige et al. 1996; Paige and Tomko 1991a,b; Telford et al. 1997) makes its contribution to the combined response difficult to evaluate.

Studies of the spatial organization of optokinetic after-nystagmus (OKAN) in rhesus and cynomolgus monkeys (Dai et al. 1991, 1992) have shown that eye velocity responses to linear acceleration due to gravity, and to angular motion of the visual field do not necessarily superpose but interact through velocity storage. Specifically, the spatial orientation properties of velocity storage, reflected in the time constant of horizontal OKAN, vary in monkeys in side down positions depending on whether the eye velocity is directed toward or away from gravity. The time constant is generally longer during head tilts, which induce downward than upward cross-coupled components (Dai et al. 1991). Because velocity storage is common to OKAN and the aVOR (Raphan et al. 1979), the orientation changes that are present during OKAN also are present during postrotatory responses with the head tilted (Angelaki and Hess 1995; Harris and Barnes 1987; Raphan et al. 1992). Asymmetries in aVOR time constants also have been observed for leftward or rightward GIA tilts with respect to the head during postrotatory nystagmus (Schrader et al. 1985a,b) and during centrifugation in monkeys (Wearne et al. 1994). Because the angle of GIA tilt increases monotonically during the angular acceleration phase, reaching a maximum tilt angle at constant angular velocity, any asymmetries in the dependence of the horizontal time constant on GIA tilt during facing and back to motion centrifugation will modify the difference trace, invalidating its use as an index of the compensatory lVOR. If the functional relationship between the time-varying GIA tilt during centrifugation and the aVOR time constant were the same as that determined from a series of static head tilts with respect to the GIA, this could explain the character and shape of the difference traces observed during facing and back to motion centrifugation.

The purpose of this study was to investigate the interaction of the horizontal aVOR and lVOR during constant velocity centrifugation. In particular, we determined the relative contributions made by dynamic changes in the aVOR time constants produced by a continuously changing GIA vector, and the compensatory lVOR, to the overall response. We also investigated whether the orientation properties of velocity storage determined from OKAN were sufficient to predict the horizontal eye velocity responses during constant velocity centrifugation.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

One juvenile rhesus (Macaca mulatta; M9303) and six cynomolgus monkeys (M. fascicularis; M9307, M9306, M9308, M9223, M9351, and M9357) were used in these studies. We have not found differences between rhesus and cynomolgus monkeys in oculomotor or vestibular characteristics in previous studies. In particular, the spatial orientation properties and the dynamic characteristics of the aVOR are very similar for the two species. For this reason, findings from the two species have been used interchangeably in this report. Two of the cynomolgus monkeys (M9308 and M9351) were tested before and after their six semicircular canals were plugged. One cynomolgus monkey (M9357) was tested before and after both lateral canals were plugged. The surgical and experimental procedures conformed to the Principles of Laboratory Animal Care (National Institutes of Health Public 85-23, revised 1985) and were approved by the Institutional Animal Care and Use Committee (IACUC).

Surgical procedures

Animals were prepared at sterile surgery under anesthesia with two three-turn search coils to record the orientation of one eye in three dimensions. A frontal coil of 16 mm diam in rhesus monkeys and 14 mm diam in cynomolgus monkeys was sutured to the sclera under the conjunctiva (Judge et al. 1980). This coil was concentric with the iris, and its normal was aligned with the optic axis. A second coil of 11 mm diam was wound under the superior rectus in the horizontal plane of the same eye (Dai et al. 1994; Robinson 1963; Yakushin et al. 1995) such that its normal was approximately orthogonal to that of the frontal coil. Voltages proportional to the horizontal and vertical components of eye orientation were transduced by the frontal coil; voltages proportional to the torsional component of eye orientation were transduced by the top (roll) coil. Two head bolts were implanted in dental acrylic on the skull to provide painless head stabilization in stereotaxic coordinates during experiments. Animals received analgesics and antibiotics (morphine sulfate 2 mg im; cephazolin 0.1 g im) after surgery to alleviate pain and counter infection.

At separate surgery, all six semicircular canals were plugged in two cynomolgus monkeys (M9308 and M9351). The animals were anesthetized and the middle ear approached posteriorly. The canals were identified under an operating microscope. Plugging was accomplished by grinding across each canal with a diamond burr until the membranous canal was interrupted. The region of the canal was packed with bone and covered with a small piece of muscle (see Yakushin et al. 1995, for details). Inactivation of the semicircular canals was verified by the absence of response to 0.2-Hz sinusoids of angular velocity (peak velocity 60°/s) in any spatial plane for the six canal plugged animals. The lateral canal plugged animal had no response when tilted ~40° nose down, so that the vector sum of the normals to the vertical canals was orthogonal to the rotation axis. Ocular counterrolling was normal in these animals, and the response to z-axis off-vertical axis rotation (OVAR) was the same as in other canal-plugged animals (Cohen et al. 1983; Correia and Money 1970; Yakushin et al. 1992), indicating that the otoliths were intact. Postoperative data reported in this study were obtained 6 and 2 mo after surgery in M9351 and M9308, respectively.

Stimulation apparatus

The stimulator is shown schematically in Fig. 1A (Neurokinetics, Pittsburgh) (see also Dai et al. 1994). It was computer controlled and had three gimbaled axes of rotation: an outer horizontal axis (A), a nested yaw axis (B), and a doubly nested inner pitch-roll axis (C ). The yaw and pitch/roll axes were enclosed in a light-tight, optokinetic sphere (OKN drum), 109 cm in diameter, with 10° vertical black and white stripes on the inside. The axis of the OKN drum (D) was collinear with the yaw axis (B). When the OKN sphere rotated, driven by the OKN motor (d ), it produced full-field motion that induced OKN and OKAN. The horizontal and pitch/roll axes were controlled by position servos, and the yaw and optokinetic axes by position and velocity servos. The circular spine, which was the gimbal for the horizontal axis (A), was driven by the horizontal axis motor (a). It moved over approximately ±180° with a maximum acceleration of 60°/s². The nested yaw axis (B) driven by motor (b) through the yaw axis gimbal, carried the primate chair and field coils, the centrifuge arm and the pitch/roll axis motor (c). The maximum acceleration and deceleration of the yaw axis (B) was 200°/s², and the maximum velocity was 400°/s. The pitch-roll axis (C ) was driven by motor c, and moved over ±90° of excursion at a maximum acceleration of 600°/s².

View larger version (33K): [in this window] [in a new window]   Fig. 1. A: 4-axis vestibular and optokinetic stimulator. B: right-handed coordinate system referenced to the head. Positive x axis (pitch) points out of the left ear, the positive y axis (roll) out of the back of the head, and the positive z axis (yaw) out of the top of the head. Positive directions of angular eye velocity vectors, x, y, and z, are aligned with these axes. The positive directions of rotation are in accordance with the right hand rule and are indicated by the circular arrows. C-E: centrifugation facing the motion (C ), centered (D), and back to motion (E ). Centripetal acceleration is indicated as Ac. Ag is the equivalent acceleration due to gravity. Vector sum of Ag and Ac is the gravito-inertial acceleration (GIA) vector. Angle between Ag and the GIA in the roll plane is given as R. Filled arrows at the base of each figure indicate the direction of the compensatory linear vestibuloocular reflexes (lVOR); open arrows indicate the direction of the compensatory angular vestibuloocular reflexes (aVOR) during +HZ or HZ rotation. For +HZ rotation, the animal was oriented right ear out when facing motion and left ear out when back to motion. An analogous stimulus paradigm was given for HZ rotation, with left ear out when facing motion and right ear out when back to motion.

Monkeys were seated in a primate chair, shown centered with respect to each rotation axis in the diagram of Fig. 1A. The chair was composed of 1.25 cm lexan, which did not flex during rotation. Velocity steps in yaw about a vertical axis were given in this on-axis position. The chair could be repositioned by 90° along the pitch/roll axis to give the animals velocity steps in pitch or roll about a spatial vertical axis. By tilting the circular spine about the horizontal axis (a) and rotating the animal around the centered yaw axis (b), the animal received OVAR. The chair could be displaced to the end of the centrifuge arms, positioning the monkey's head 25 cm from the center of rotation. The primate chair could be positioned in 90° increments when displaced so that centripetal acceleration was directed along either the interaural or nasooccipital axis during constant velocity yaw axis centrifugation. The terms "centered" and "on-axis" rotation will be used interchangeably as will the terms "centrifugation" and "off-axis" rotation.

Recording and calibration of three-dimensional eye orientation and velocity

Two orthogonal field coils, 33 cm on a side and driven at frequencies of 24.7 kHz, were fixed to the primate chair. The head bolts were attached to a lexan ring, which fixed the head to the chair so that the head remained in the same orientation with respect to the coordinate frame defined by the field coils. With the monkey erect, the yaw axis was aligned with gravity, and the horizontal stereotaxic plane was aligned with the gravitational horizontal. Thus the lateral semicircular canals were tilted up ~30° from the earth horizontal plane (Blanks et al. 1985; Yakushin et al. 1995). The search coils were centered with regard to the field coils. Voltages proportional to the projections of the search coils onto the magnetic fields were recorded with three phase detectors (Neurodata). If the voltages from the two search coils were not orthogonal, a portion of the horizontal voltage was fed back and subtracted from the roll voltage, removing cross talk in the roll signal when the upright animal was rotated around a spatial vertical axis. This method electronically orthogonalized the search coil axes so that the effective normal to the top coil was aligned with an axis from the bottom to the top pole of the eye. Studies on monkeys have shown that there is a small nonorthogonal relationship between the maximum direction for roll and yaw (Crawford and Vilis 1991), but the angles are well within the error bounds of the data reported in the study.

To calibrate yaw, pitch, and roll axis eye movements, animals were rotated about a spatial vertical axis at 30°/s in the presence of a lighted, textured visual surround in upright, side down, and prone positions. It was assumed that horizontal and vertical gains were close to unity in this condition (Crawford and Vilis 1991; Raphan et al. 1979; Robinson 1963). Torsional VOR gains during rotation in the light were set to 0.6. Similar roll gains have been obtained for monkeys using other techniques (Crawford and Vilis 1991; Dai et al. 1994; Henn et al. 1992; Yakushin et al. 1995; Yue et al. 1994). The calibration of the roll coil was checked by rotating a test coil of the same diameter in a gimbal inside the field coils.

Calibration of eye position after plugging of all semicircular canals was performed in vitro using a replica of the implanted search coils, mounted on a three-axis Fick gimbal. Two three-turn coils of 16 (frontal coil) and 11 mm diam (top coil) were mounted orthogonally on the gimbal, such that the voltages from the frontal coil were minimal when the yaw and pitch axes of the gimbal were aligned with the horizontal and vertical magnetic fields. Voltages were recorded from the two coils for symmetric angular displacements of ±15° in 5° increments, about each of the three gimbal axes in turn. Angular sensitivity of the voltages from each coil was determined using a least-squares fitting procedure (Matlab, The Mathworks). Using this technique, it was determined that the change in voltage produced by a change in eye position was the same after as before plugging.

Details of determination of Euler angles and the eye velocity vector from the search coil voltages are presented elsewhere (Yakushin et al. 1995). In brief, eye position and velocity vectors were referenced to a right-handed, head-fixed coordinate frame (Fig. 1B). Eye orientation is represented as Euler angles in the Fick rotation convention,¹ with , , and  corresponding to rotations about the z axis, the rotated x axis, and the doubly rotated y axis. These angular deviations from the reference will be referred to as the yaw, pitch, and roll or horizontal, vertical, and torsional eye positions, respectively. Eye velocities were determined as vector components along the head-based coordinate frame (Fig. 1B). Horizontal, vertical, and torsional components of the eye velocity vector are represented as (_z, _x, _y), respectively. The circular arrows correspond to the direction of rotation for a velocity component along the positive axis, according to a right-hand rule. Leftward, downward, and counterclockwise rotations (from the animal's point of view) are represented in the figures by upward deflections in the eye position and eye velocity traces.

To validate the calibration procedure, we compared Listing's planes during spontaneous eye movements with those found in the literature. We assumed that the average coil voltages during spontaneous positions of fixation while the animal made saccades for 15-30 s in light, correspond to the straight-ahead eye position with zero roll. This assumption is consistent with data obtained in trained and calibrated monkeys for a large range of saccades in light and dark (van Opstal et al. 1995). These average coil voltages defined the reference head coordinate frame. With the eye in this orientation, the visual axis coincides with the roll axis of the head frame. To a good approximation, this aligns with the stereotaxic coordinate frame of the head, which we physically aligned with the axes of the horizontal and vertical field coils. We then used Listing's law to determine the "displacement plane" (Helmholz 1867; Tweed and Vilis 1990), which approximately contains all axes of rotation from this reference position during saccades. The unit vector normal to the displacement plane and its angle with respect to the reference were determined. We then determined primary position as the eye position for which the visual axis is normal to the displacement plane, i.e., Listing's plane. This corresponded to a rotation of twice the angle between the roll axis and the normal to Listing's plane, about an axis given by their cross-product (Helmholz 1867). Computed rotation angles were generally within 15°, and the rotation axes were confined to a single plane, in accordance with Listing's law (Crawford and Vilis 1991; Haslwanter et al. 1992). The accuracy of the technique for estimating primary position was determined by comparing displacement planes and reference positions from the monkey eye movements with those obtained from a gimbal-mounted search coil system, the reference system of which could be set arbitrarily. For a given displacement plane, the reference positions computed from the monkey or gimbal data were the same.

Experimental protocol

Alertness was maintained by administration of amphetamine sulfate (0.3 mg/kg) intramuscularly, 30 min before testing. Before data collection, vestibular and optokinetic time constants were habituated by repeatedly rotating the animals to each side about all axes (Cohen et al. 1992), minimizing the effects of further habituation. In consequence, the time constants and initial gains of OKAN for the upright position did not habituate further during the period of testing.

Eye movements were induced in three stimulus paradigms. Optokinetic stimulation was given in the upright position or statically tilted left ear down (LED) or right ear down (RED) with regard to gravity at angles of 0, 17, 36, 45, 52, and 90°. Velocity steps of 60 and 90°/s, lasting 30 s, were used to induce OKAN (Cohen et al. 1977; Raphan et al. 1979; Waespe et al. 1983). OVAR was given by tilting the axis of rotation 90° with respect to gravity and rotating the animal about its yaw axis at 60°/s. Peak interaural linear acceleration was 1 g for 90° tilts.

Combined linear and angular accelerations were delivered by eccentric rotation on a centrifuge, either facing the direction of motion (Fig. 1C ) or with back to the motion (Fig. 1E ). The direction of gravitational acceleration with respect to the head is indicated as A_g. The direction of head rotation during vestibular stimulation also is indicated by a circular arrow and is denoted _HZ. Animals also were rotated about a centered axis (Fig. 1D). For +z rotation, animals were right ear out (REO) when facing motion (Fig. 1C ) and left ear out (LEO) when back to motion (Fig. 1E). For z rotation, these conventions were reversed. The centrifuge was accelerated at 40°/s² to a final angular velocity of 400°/s. The final stimulus velocity was maintained for 120 s. We term this stimulus constant velocity centrifugation.

During centrifugation with constant angular acceleration, gravitational (A_g) and centripetal (A_c) accelerations sum, producing GIA. At the onset of rotation, the GIA vector rotates in three dimensions, reaching a steady state position in the xz (roll) plane of the head during the period of constant centrifuge velocity. For the angular accelerations used in this study (10 and 40°/s²), a small constant tangential acceleration (<0.02 g) was present throughout the angular acceleration period. Because its magnitude in relation to the centripetal acceleration (1.24 g) was small, its effect on the change in horizontal time constant was neglected. Thus only the effects of GIA tilt in the xz plane on the horizontal time constant were considered.

At a final angular velocity of 400°/s, the GIA was tilted by 52° in the animal's roll plane. For facing and back to motion centrifugation, A_c was directed along the interaural axis (Fig. 1, C and E), and the GIA tilted dynamically in the roll plane of the head, through an angle (_R) that increased with the angular velocity of the centrifuge. Cross-coupled components of eye velocity appeared when the GIA was tilted with regard to the head. Changes in eye position and eye velocity were examined during all of these motions to determine the effects of interaural linear acceleration on the horizontal component of eye movement.

The respective directions of compensatory linear (black arrows) and angular (white arrows) VORs during facing and back to motion centrifugation are indicated in Fig. 1, C and E. Regardless of whether the animal is LEO or REO, the compensatory horizontal lVOR is always in the centrifugal direction. That is, when the right ear is out, the direction of the compensatory lVOR should be rightward (z; Fig. 1C ), and when the left ear is out, the compensatory lVOR should be leftward (+z; Fig. 1E ).

Data acquisition and processing

Eye position data and photocell voltages, measuring the state of the light and the passage of stripes, were sampled at a rate of 600 Hz per channel using the DAOS data acquisition system (Mycon Technology) running on a 386-based digital computer. Before sampling, eye position data were prefiltered by an eight-pole Butterworth filter with a corner frequency of 30 Hz. Slow phase eye velocity was obtained by transforming the eye velocity vector to head coordinates and removing saccades with an order statistic filter (Engelken and Stevens 1990, 1991).

Programs were written using C/C++ and MatLab (MathWorks) to analyze pitch, roll, and yaw slow phase eye velocities. Eye velocity was analyzed from the onset of OKAN to the point where the horizontal component decayed to zero. OKAN time constants were estimated by fitting a single exponential to the decaying portion of eye velocity, 1-2 s after the light was extinguished, indicating offset of the OKN stimulus. Horizontal VOR time constants were estimated by fitting a sum of two exponential functions, representing the cupula and velocity storage modes, following angular velocity steps of 60°/s. The cupula time constant was constrained to 4 s (Büttner and Waespe 1981; Fernández and Goldberg 1971), and the initial integrator state was constrained to be zero. The time constant of velocity storage was estimated from a constrained fit to the data with only the integrator time constant allowed to vary. This technique gives a better estimate of the dynamics of the VOR than if a single exponential was fitted.

During the angular acceleration at the onset of centrifugation, a number of processes complicate the estimation of velocity storage time constants. The input signal driving the aVOR is a ramp of angular velocity producing a parabolic increase in centripetal acceleration. This is accompanied by a continuous tilt of the GIA from the spatial vertical, which induces a corresponding reduction in the horizontal aVOR velocity storage time constant. In addition, both the cupula deflection and the induced velocity storage response increase slowly, producing nonzero initial conditions for the internal states of the system at the onset of constant angular velocity. Because the states cannot be measured, they are unconstrained in exponential fits to the decaying portion of eye velocity. Such unconstrained fits can lead to widely fluctuating estimates of the system time constants, depending on the choice of initial states. During centrifugation therefore, aVOR velocity storage time constants cannot be estimated by fitting a sum of exponential functions to eye velocity, as they can for steps of head velocity during centered rotation (Raphan et al. 1979).

The dynamical system representation allowed us to simulate changes in the time constants as a function of GIA tilt angle, which varied with time during centrifugation (see section on model implementation and parameter identification). The aVOR model (Eqs. 1 and 2) was used to estimate system parameters (h_c, h₃₃, g_c0, g_s0, and g_s1) for each monkey by fitting the centered rotation data. The best-fitting parameters then were held constant, and the decline in horizontal time constant as a function of GIA tilt (Eq. 4), derived from OKAN data with the head statically tilted (Eq. 3), was introduced into the model to predict facing and back to motion centrifugation traces. A second estimate of velocity storage time constants during centered rotation and centrifugation also was obtained by fitting a single exponential function to the decay of eye velocity, starting 10 s after the onset of constant angular velocity, to avoid the initial period when both cupula and velocity storage contribute to eye velocity. Assuming a cupula time constant of 4 s, the contribution of the cupula mode will be negligible after 2.5 time constants, and eye velocity should decay with the time constant of velocity storage. Because our method used only the tail portion of the eye velocity time series, we term it the "tail-fit time constant." The two methods gave similar values, and the tail-fit was used as an initial estimate of the velocity storage time constant when searching for the best-fitting parameters for the model simulations.

Experimental design and statistical analysis

The order of presentation of experimental trials was randomized to avoid systematic order effects. Repeated measures were performed in all experimental conditions: each monkey was tested at least twice in each condition, but not all monkeys were exposed to every experimental paradigm.

Differences in time constants² between experimental conditions were evaluated statistically using planned contrasts, evaluated with the t-statistic for dependent samples (Winer et al. 1991). This method minimized the effects of habituation of time constants on the variance estimate. Intrasubject variability was assessed both graphically and analytically. Eye position and desaccaded eye velocity traces from repeated trials were overlaid, and subject means ±1 SD or ±2 SDs were computed and graphed using programs written in MATLAB (The Mathworks). This method provides a clear graphic indication of subject trends and their variability. Deviations of the model simulations from the data then could be evaluated graphically.

The time constant of the velocity storage integrator during centrifugation was estimated from optimal first-order fits to data obtained during OKAN. The other parameters were estimated from responses to centered rotation. Simulations were done to assess the model's ability to predict the responses to OKN, OKAN, centered rotation, and centrifugation with a single set of parameters. Because the functions relating eye velocity to the various stimulus components cannot be represented in analytic form in terms of the system parameters to allow their optimization, no figure-of-merit function of individual responses was calculated. Goodness of fit was assessed by determining the extent to which the simulated response fell within 95% confidence intervals of overlayed eye velocity responses.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Effects of combined linear and angular accelerations during centrifugation

Centered rotation about the spatial vertical at an angular acceleration of 40°/s² to a constant angular velocity of 400°/s increased horizontal eye velocity (_z) during the period of angular acceleration to a peak value of close to 200°/s (198°/s, Fig. 2A). The GIA remained aligned with the animal's z axis for the duration of rotation. During the constant velocity period, horizontal eye velocity decayed with a time constant of 12.8 s. Vertical and roll components of eye velocity (_x and _y) were close to zero throughout the stimulus. Eccentric rotation on the centrifuge changed the direction of the GIA vector with respect to the head and increased its magnitude. When facing the direction of centrifuge motion (Fig. 2B), horizontal slow phase velocity (_z) rose approximately exponentially approaching a lower peak velocity (165°/s) than when centered (198°/s; compare Fig. 2, A and B). Upward vertical (_x, arrow B) and counterclockwise roll (+_y) components of eye velocity appeared during the acceleration period (Fig. 2B). Vertical and roll eye velocities built slowly with the tilt of the GIA. Their maxima were considerably delayed, relative to the tilt of the GIA (Fig. 2B). Horizontal eye position () moved into the slow phase direction. Average vertical eye position () remained close to the reference position while the eyes torted () in the direction of GIA rotation (Fig. 2B). During the constant velocity period, horizontal eye velocity decayed to zero and was followed by an oppositely directed secondary nystagmus. The horizontal velocity storage time constant measured by the tail-fit method (see METHODS) was shorter when facing motion (5.2 s) than during centered rotation (12.8 s, Fig. 2A). Vertical eye velocity decayed slowly (arrow B, Fig. 2B), whereas the roll component decayed more rapidly. Ocular torsion was maintained at ~5° during the constant velocity period while the GIA was tilted (arrow A, Fig. 2B).

View larger version (35K): [in this window] [in a new window]   Fig. 2. Eye position and eye velocity responses to yaw axis centered rotation and centrifugation. Duration of angular acceleration is indicated (black bar) under the horizontal eye velocity trace (z) in A-C. A: eye position and eye velocity responses during centered rotation in yaw. Angular acceleration was 40°/s2 up to a peak angular velocity of 400°/s. Three-dimensional eye position is represented using Euler angles in the Fick rotation convention, with (, , ) designating rotations about the yaw axis, the rotated pitch axis, and the optic (roll) axis in that order. Pitch (x), roll (y), and yaw (z) components of the eye velocity vector are displayed in head coordinates. Top: angular and linear stimulus profiles over time: the angular velocity of the centrifuge (ANG VEL) is indicated with a light line and ranges from 0 to 400°/s; the corresponding tilt angle of the GIA is indicated with a heavier line. For centered rotation, the GIA tilt remains at 0°. Horizontal time constant, estimated by the tail-fit technique (see METHODS), was 12.8 s. B: facing motion with left ear out. Time constant of horizontal eye velocity (z), estimated by the tail-fit method, was shorter when facing motion (5.2 s) than when centered (12.8 s, A). An upward vertical cross-coupled component of eye velocity (x) appeared when facing motion (arrow B). Torsional eye position (), remained close to 0 when centered (A) but rotated in the direction of the GIA during facing motion centrifugation (arrow A), reaching a steady-state level of about 5° torsion. C: back to motion centrifugation with right ear out. Horizontal time constant was shorter when back to motion (7.4 s) than when centered (A) but longer than when facing motion. Downward cross-coupled vertical component appeared (arrow B; trace x). Torsional eye position () followed the tilt of the GIA, reaching ~7-8° counterclockwise torsion at 52° GIA tilt (arrow A).

When monkeys were oriented with their backs to the motion (Fig. 2C ), horizontal eye velocity rose exponentially during the angular acceleration, reaching a higher peak velocity (175°/s) than when facing the motion (Fig. 2B). The horizontal time constant (7.4 s) was shorter than during centered rotation, but was longer than when facing the motion. Downward vertical and clockwise roll eye velocity components were generated. Torsional eye position () rotated in a counterclockwise direction, following the tilt of the GIA, to reach a steady-state value of 7-8° during the period of steady-state GIA tilt (arrow A, Fig. 2C ).

Differences between horizontal eye velocity profiles during facing and back to motion centrifugation were determined from overlaid traces of desaccaded horizontal eye velocity. In five separate tests in a second monkey (M9307), there was little variability (Fig. 3, A and C ). Horizontal velocity storage time constants, measured by the tail-fit method and averaged over leftward and rightward traces, were smaller when the monkey was rotated off-axis (Fig. 3A, mean facing motion Tc = 5.1 ± 0.6 s; Fig. 3C, mean back to motion Tc = 6.2 ± 0.58 s), than during centered rotation (Fig. 3B, mean centered Tc = 8.5 s).

View larger version (40K): [in this window] [in a new window]   Fig. 3. A-I: overlaid eye velocity (A-C ) and eye position (D-I ) traces from 1 monkey (M9307) tested on 5 occasions when facing and back to motion and on 2 occasions when centered. Duration of angular acceleration is indicated by black bar under traces A and G. Desaccaded eye velocity traces for both directions of rotation (left ear out, LEO and right ear out, REO) are superimposed to emphasize any left/right asymmetries. Horizontal time constant was consistently shorter when facing motion (A) than when centered (B) or back to motion (C ). D-F: mean horizontal eye position ± SE (shaded area) during z rotations; G-I: horizontal eye position ± SE during +z rotations. During centered rotation (E and H ), mean horizontal eye position moved into the quick phase direction during the period of angular acceleration and slowly drifted back toward the slow phase side during the constant velocity period. Addition of linear acceleration (D, F, G, and I ) did not significantly alter this trend.

Average horizontal eye position traces during the nystagmus, comprising both slow and quick phase were plotted for the corresponding leftward and rightward eye velocities shown in Fig. 3, D-I (leftward: Fig. 3, D-F; rightward: Fig. 3, G-I ). The eyes tended to beat across the midline during rotation regardless of the direction of the GIA vector with a slight bias toward the quick phase side during the period of angular acceleration (Chun and Robinson 1978; Hood 1967). This was followed by a gradual decay toward the slow phase side. The beating fields during centrifugation (Fig. 3, D, F, G, and I ) were not appreciably different from those during centered rotation (Fig. 3, E and H ).

Because the interaural linear acceleration was centripetal, any compensatory horizontal lVOR should rotate the eyes in the centrifugal direction whether REO or LEO (Fig. 1, C and E, black arrows). This produces a compensatory horizontal lVOR and aVOR in the same direction whenever the animal is facing the motion. Conversely, the lVOR is always opposite to the aVOR when back to motion (Fig. 1, C and E; compare white arrows with black arrows). If the aVOR and lVOR superpose (Merfeld and Young 1995; Young 1967), subtraction of the back-to-motion response from the facing-motion response (F-B) should cancel the aVOR and double the lVOR. Division by two then would give an estimate of the average interaural lVOR. This should be in the direction of the aVOR eye velocity when facing the motion. That is, for leftward eye velocities (Fig. 4, left column), the (F-B)/2 difference traces should be leftward (+z). For rightward eye velocities (Fig. 4, right column), the difference traces should be rightward (z).

View larger version (34K): [in this window] [in a new window]   Fig. 4. Computed difference traces (facing-back)/2 for each of the 5 monkeys for repeated trials (ranging from 2 to 5 repetitions) on each monkey. Left: difference traces for leftward eye velocities (z rotations) (A, C, E, G, I, and K ). Right: difference traces for rightward eye velocities (+z rotations) (B, D, F, G, J, and L). Monkey number and the number of repeated measures in the average traces are indicated on the right side of each row. A and B: 5 overlaid (F  B)/2 difference traces for M9307. C and D: means ± SD (shaded region) for the data of A and B. E-L: means ± SD for the difference traces of the remaining 4 monkeys. With the exception of traces I, K, and L, the difference traces consistently were in the opposite direction to the prediction of the compensatory lVOR superposition hypothesis. Individual subtracted traces for M9307 shown in A and B were overlaid, and means ± SD computed. Standard deviations for M9307 and the other monkeys are indicated by shaded regions C-L; the superimposed solid trace is the mean.

To assess the aVOR-lVOR superposition hypothesis, difference traces were computed for each monkey (Fig. 4) and compared with predictions based on this hypothesis for each monkey. Although each animal's data were internally consistent, intersubject variability was considerable. For M9307, the difference trace for leftward aVOR eye velocities was in the (z) direction (Fig. 4C ), whereas the difference trace for rightward aVOR eye velocities was in the (+z) direction (Fig. 4D). These directions are opposite to the prediction of the superposition hypothesis. The same response pattern was found in two other monkeys (M9306 and M9308, Fig. 4, E-H ). Patterns were inconsistent in the last two monkeys (M9223 and M9303, Fig. 4, I-L). M9303 showed little difference between facing and back to motion responses for leftward eye velocities (Fig. 4K ) but had a (z) difference response, opposite to the trend in the other four animals, for rightward eye velocities (Fig. 4L). M9223 had a significant (+z) response for both leftward and rightward eye velocities (Fig. 4, I and J ). Thus the prediction of the superposition hypothesis, that the (F  B)/2 difference traces should be leftward for rightward eye velocities and rightward for leftward eye velocities, was not supported by the data in general and directly contradicted by the data of three monkeys.

Our alternative hypothesis was that linear acceleration affects the orientation properties of the velocity storage system, differentially modifying its time constants according to the direction of GIA tilt. According to this hypothesis, the difference between facing and back to motion eye velocities represents a difference between two waveforms with different time constants at each instant of time. To test this hypothesis, we compared each monkey's responses to OKAN, centrifugation, and centered rotation with simulations using our one-dimensional system model of lVOR-aVOR interaction (Fig. 5), with a single set of parameters for each monkey in all three paradigms.

View larger version (39K): [in this window] [in a new window]   Fig. 5. Composite model of horizontal lVOR-aVOR interaction. Model comprises previously estimated cascaded dynamical systems representing otolith afferents, central otolith processing, central angular acceleration processing, including velocity storage and its control by the nodulus and uvula, velocity-position integration, motor neurons and the oculomotor plant. Specific parameters of the model for this one-dimensional case have been identified to best fit the data.

Model-data comparisons

The one-dimensional model of lVOR/aVOR interaction includes cascaded dynamical subsystems. These generate the velocity command from the angular VOR, the effects of GIA on velocity storage, the velocity-position transformation that drives the motoneurons, and the contribution of the compensatory linear VOR (lVOR). The block labeled "otolith afferent processing" comprises subblocks of otolith sensory afferent neurons with discharge regularities range from regular (REG) through intermediate (INT) to irregular (IRREG) and with corresponding ranges of response dynamics (Fernández and Goldberg 1976). These afferents are activated by linear acceleration of the head in space, which is an inertial frame. This acceleration is converted into the head frame because the afferents are fixed to the head. This implicit transformation is represented by the box "space-head transf." The afferents combine to generate the compensatory lVOR response ("compensatory lVOR system"). Another system ("orienting lVOR system"), the output of which is denoted by a heavy line (Fig. 5) is responsible for modifying the spatial orientation properties of velocity storage and the subsequent orientation and time constants of the eye velocity vector. The system implementing the aVOR, incorporating velocity storage has been adapted from previous work (Raphan and Sturm 1991; Raphan et al. 1979). The output of velocity storage and the direct aVOR pathway, y_sz sums with the output of the compensatory lVOR system, y_cz. The summed signal is input to the velocity position integrator and its direct path to drive the oculomotor plant.

The effect of the orienting system on the aVOR was modeled as a parametric modification of the velocity storage time constant, 1/h₃₃, shown by the heavy arrow through "nodulus/uvula" to h₃₃. The time constant was varied as a function of GIA tilt relative to the head in accordance with data obtained from OKAN with monkeys in tilted positions (Dai et al. 1991). The model then was implemented as a dynamical system, using the regression fits obtained from the OKAN data. The model simulations during centered, and facing and back to motion centrifugation were compared with the actual data (see METHODS).

MODEL IMPLEMENTATION AND PARAMETER IDENTIFICATION. The state equations describing the one-dimensional angular acceleration transduction performed by the semicircular canals were approximated as a first-order system (Fig. 5, H_c) and implemented as follows:

(1)

The variable _z represents yaw axis angular acceleration, x_cz represents the horizontal state of the cupula, h_c is the yaw axis eigenvalue of the cupula dynamics, equivalent to the negative reciprocal of the dominant cupula time constant (4 s). The parameter g_c0 is the coupling gain from angular acceleration to the cupula state. The signal r_vz is the neural signal carried by primary canal afferents, which drives the velocity storage integrator and direct pathway during yaw axis angular acceleration.

(2)

IMPLEMENTATION OF EFFECT OF GIA TILT ON HORIZONTAL TIME CONSTANT: OKAN TIME CONSTANTS AS A FUNCTION OF STATIC HEAD TILT. The function relating the horizontal time constant to the angle of GIA tilt with respect to the head z axis was estimated for each monkey during OKAN with the head statically tilted in roll, either LED or RED, through angles ranging from 17 to 90°. An example is shown for M9307 (Fig. 6). For the upright condition, the time constant of leftward horizontal eye velocity (+_Z) was 7.1 s (Fig. 6A). For a 90° tilt left ear down (LED), an upward eye velocity (_X) was induced, and the horizontal time constant fell to 1.8 s (Fig. 6B). The rate of decrease of the horizontal time constant during OKAN with the head tilted LED, as a function of tilt angle, shown by open circle in Fig. 7A, 1 and 2, could be approximated by a straight line with negative slope. The GIA tilt induced under this condition was analogous to tilt experienced during centrifugation while facing motion with the left ear out (Fig. 2A). In each case, the GIA tilted toward the right ear, and an upward cross-coupled component of eye velocity was induced.

View larger version (47K): [in this window] [in a new window]   Fig. 6. A: horizontal and vertical eye velocity responses to leftward (+z) optokinetic (OKN) with the head upright for M9307. Horizontal OKN was present when the light was on () and optokinetic after-nystagmus (OKAN) decayed in darkness with a time constant of 7.1 s. No vertical component was present during either OKN or OKAN. B: tilting the head 90° left ear down induced a large upward-coupled vertical component and the horizontal time constant decayed rapidly with a time constant of 1.8 s. C: tilting the head right ear down induced a small downward-coupled vertical component, and the horizontal time constant decayed more slowly, with a time constant of 4.2 s.

View larger version (37K): [in this window] [in a new window]   Fig. 7. A: linear regression fits to OKAN time constants and simulations of horizontal eye velocities during centrifugation for M9307. 1: computed horizontal time constants during +z (leftward) optokinetic stimulation, for head tilts ranging from 0 to 90° left or right ear down. Each data point is an average of 2 measurements of the horizontal time constant during OKAN at a particular head tilt angle. Open circles, horizontal time constants associated with upward vertical cross-coupling. Filled triangles, horizontal time constants associated with downward vertical cross-coupling. First-order linear regressions were fitted separately to LED and RED data, and the slopes of the best-fitting equations are shown on the graphs. Horizontal time constants were shorter, and declined more rapidly with tilt angle, for tilts that induce upward-coupled components (open circles; slope = 0.06) than for downward-coupled components (filled triangles; slope = 0.04). 2: computed horizontal time constants during z (rightward) optokinetic stimulation. As in 1, horizontal time constants were shorter and reduced more rapidly with tilt angle for head tilts that induced upward coupled components (open circles) than downward coupled components (filled triangles). 3: model simulations for M9307 during facing motion centrifugation. Rate of decline in the horizontal time constant as a function of GIA tilt angle for OKAN was incorporated into the model to generate predicted changes in horizontal eye velocity during centrifugation (solid line). Equations used to simulate this decline for each condition (Eqs. 3 and 4) are printed above (leftward eye velocities) or below (rightward eye velocities) the peak eye velocity. Slope parameters were derived from the regression curves for horizontal time constants during upward cross-coupling and represent the reduction in horizontal time constant per degree of GIA tilt. Offset parameter was constrained from the upright time constant (T33UD), estimated during centered rotation. 4: model simulations during centered rotation. Centered horizontal time constant was estimated as 7.8 s for leftward and 9.1 s for rightward eye velocities. 5: simulations during back to motion centrifugation, using OKAN slope parameters obtained during downward cross-coupling conditions. Slope was lower for leftward eye velocity (0.04 s/deg) than for rightward eye velocity (0.07 s/deg). B: linear regression fits to OKAN time constants and simulations of horizontal eye velocities during centrifugation for M9303. 1: computed horizontal time constants during +z (leftward) optokinetic stimulation for head tilts ranging from 0° to 90° left or right ear down. 2: computed horizontal time constants during z (rightward) optokinetic stimulation. Symbols are as for A. See text for details. 3: model simulations for M9303, superimposed on 95% confidence intervals during facing motion centrifugation (3), centered rotation (4), and back to motion centrifugation (5). C: linear regression fits to OKAN time constants and simulations of horizontal eye velocities during centrifugation for M9306. 1: computed horizontal time constants during +z (leftward) optokinetic stimulation for head tilts ranging from 0 to 90° left or right ear down. 2: computed horizontal time constants during z (rightward) optokinetic stimulation. Symbols are as for A. 1-5: model simulations superimposed on the 95% confidence interval during during facing motion centrifugation (3), centered rotation (4), and back to motion centrifugation (5) for M9306. Linear regression fits to OKAN time constants as a function of tilt angle were used for the simulations for each condition.

(3)

(4)

View larger version (35K): [in this window] [in a new window]   Fig. 8. Horizontal slow phase eye velocity from M9307 (A) and simulated eye velocity (B) during angular accelerations of 10°/s2 (heavy lines) and 40°/s2 (lighter lines). Heavy bar below the facing motion traces indicates the duration of the 10°/s2 angular acceleration (40 s); lighter bar indicates the duration of the 40°/s2 angular acceleration (10 s). A: desaccaded horizontal eye velocities for M9307. During centered rotation (middle), the response to angular acceleration of 10°/s2 reaches an asymptote at ~80°/s (arrow A). For an angular acceleration of 40°/s2, slow phase velocity rises more steeply to a higher peak of ~200°/s. When facing motion (left), the response at 10°/s2 asymptotes earlier, at ~50°/s2, then decreases to a lower value (arrow B) as the GIA tilt increases and the horizontal time constant is reduced. B: model simulations at 10°/s2 (heavy trace) and 40°/s2 (light traces). Simulations at 10°/s2 were performed using the same parameters as for the fits to data at 40°/s2. Simulations closely approximated the data at both angular accelerations.

CENTRIFUGATION AFTER INACTIVATION OF THE SEMICIRCULAR CANALS. The foregoing results indicate that the contribution of the compensatory lVOR to horizontal eye velocity during constant velocity centrifugation is small. To support this conclusion, we compared responses to centrifugation before and after inactivation of the aVOR. We reasoned that any nystagmus after the canals were inactivated could be attributed to the intact lVOR. Canal plugging was performed in three animals, two of which had all six canals plugged (M9308 and M9357