Abstract
Sensory systems often provide ambiguous information. Integration of various sensory cues is required for the CNS to resolve sensory ambiguity and elicit appropriate responses. The vestibular system includes two types of sensors: the semicircular canals, which measure head rotation, and the otolith organs, which measure gravitoinertial force (GIF), the sum of gravitational force and inertial force due to linear acceleration. According to Einstein's equivalence principle, gravitational force is indistinguishable from inertial force due to linear acceleration. As a consequence, otolith measurements must be supplemented with other sensory information for the CNS to distinguish tilt from translation. The GIF resolution hypothesis states that the CNS estimates gravity and linear acceleration, so that the difference between estimates of gravity and linear acceleration matches the measured GIF. Both otolith and semicircular canal cues influence this estimation of gravity and linear acceleration. The GIF resolution hypothesis predicts that inaccurate estimates of both gravity and linear acceleration can occur due to central interactions of sensory cues. The existence of specific patterns of vestibuloocular reflexes (VOR) related to these inaccurate estimates can be used to test the GIF resolution hypothesis. To investigate this hypothesis, we measured eye movements during two different protocols. In one experiment, eight subjects were rotated at a constant velocity about an earthvertical axis and then tilted 90° in darkness to one of eight different evenly spaced final orientations, a socalled “dumping” protocol. Three speeds (200, 100, and 50°/s) and two directions, clockwise (CW) and counterclockwise (CCW), of rotation were tested. In another experiment, four subjects were rotated at a constant velocity (200°/s, CW and CCW) about an earthhorizontal axis and stopped in two different final orientations (noseup and nosedown), a socalled “barbecue” protocol. The GIF resolution hypothesis predicts that postrotatory horizontal VOR eye movements for both protocols should include an “induced” VOR component, compensatory to an interaural estimate of linear acceleration, even though no true interaural linear acceleration is present. The GIF resolution hypothesis accurately predicted VOR and induced VOR dependence on rotation direction, rotation speed, and head orientation. Alternative hypotheses stating that frequency segregation may discriminate tilt from translation or that the postrotatory VOR time constant is dependent on head orientation with respect to the GIF direction did not predict the observed VOR for either experimental protocol.
INTRODUCTION
The vestibular system includes two types of sensors: the semicircular canals and the otolith organs. The semicircular canals behave as integrating angular accelerometers measuring head angular velocity (Wilson and Melvill Jones 1979). The otolith organs behave as linear accelerometers measuring the specific gravitoinertial force (GIF), which is the sum of gravitational force and inertial force due to linear acceleration. Using information from these sensors, the human CNS develops perceptions of spatial orientation and generates VORs that help stabilize gaze in response to head rotation and translation.
A problem arises when the CNS must distinguish head tilt with respect to gravity from linear translation (acceleration) of the head. For example, a compensatory response for tilting the head toward the left shoulder is a torsional eye movement while acceleration toward the right induces a compensatory horizontal eye movement. In both cases, the interaural shear force measured by the otolith organs might be identical, but the compensatory eye responses are quite different. Ideally, having devices that independently measure gravity and linear acceleration could solve the tilttranslation dilemma. However, Einstein's equivalence principle states that no physical device can distinguish gravitational force from inertial force due to linear acceleration. This implies that the CNS is unable to solve the tilttranslation problem using only information from the otolith organs or any other combination of linear accelerometers. Indeed, a given GIF (f) measured by the otolith organs can be produced by an infinite number of combinations of gravity (g), and linear acceleration (a). For example, while in a supine orientation, a linear acceleration of the head to the left down a slight slope (Fig.1 A) can lead to the exact same GIF as a slight yaw tilt (φ) to the right (Fig. 1 B).
In many situations, the eye movements generated in response to head tilts and translations are appropriately compensatory (Angelaki et al. 1999; Merfeld and Young 1995), implying that the CNS is able to somehow distinguish gravity from linear acceleration. At least three hypotheses have been proposed to explain how the CNS makes use of GIF information from the otolith organs to influence eye movements, peripheral processing, frequency segregation, and GIF resolution.
The peripheral processing hypothesis states that some of the separation of the GIF into estimates of gravity and linear acceleration occurs peripherally with the phasic irregular otolith afferent signal interpreted primarily as linear acceleration, while the tonic regular otolith afferent signal might represent gravity (Mayne 1974; Young and Meiry 1967). The frequency segregation hypothesis states that the CNS might resolve the GIF ambiguity using a form of central processing in which lowfrequency cues elicit tilt responses and highfrequency cues elicit translation responses (Mayne 1974; Paige and Tomko 1991). This hypothesis is in accordance with lowfrequency characteristics of tilt perception during centrifugation (Clark and Graybiel 1951; Glasauer 1992). It also matches VOR data during interaural translation, which has both horizontal translationrelated eye movements with highfrequency characteristics and torsional tiltrelated eye movements with lowfrequency characteristics (Paige and Tomko 1991). However, as observed by Angelaki (1998), frequency segregation during interaural translation is affected by the way translation and tilt sensitivities are expressed (Paige and Tomko 1991).
The GIF resolution hypothesis (Merfeld and Young 1995;Merfeld et al. 1993a), an explicit refinement of the “multisensory integration” hypothesis (Guedry 1974;Mayne 1974; Oman 1982; Young 1984), states that additional sensory information is required for the CNS to resolve the GIF ambiguity. Specifically, the CNS systematically separates the otolith GIF measurement (f) into estimates of gravity (ĝ) and linear acceleration (â) using multisensory convergence, so that the difference between these estimates approximately matches the measured GIF (f = ĝ −â). [The specific gravitoinertial force measured by the otolith organs (f) is defined as the sum of gravitational force (g) plus an inertial force per unit mass (−a) acting on the otolith organs and exactly opposing the direction of linear acceleration (a). We choose to adopt the notation of Young (1984) for representing the effect that gravity and linear acceleration have on the otolith organs. Physical variables are mathematically represented by threedimensional vectors, f, g, anda.] The GIF resolution hypothesis appears indistinguishable (other than notational differences) from another recently formulated approach used to explain how the CNS uses semicircular canal cues to distinguish sinusoidal tilt from sinusoidal translation (Angelaki et al. 1999).
When visual cues are absent or cannot be used, the semicircular canal and otolith cues may provide the CNS with conflicting sensory information. Consider the sensory situation experienced by a subject statically positioned in a noseup orientation (Fig.2 A) following a sustained counterclockwise rotation (toward the subject's left) in darkness about an earthhorizontal axis. First, for this experimental protocol, the otolith organs measure a constant GIF due to gravity alone (f = g). In the noseup orientation, this force is aligned with the subject's nasooccipital axis. At the same time, the semicircular canals, because of their dynamics (Wilson and Melvill Jones 1979), have a postrotatory response indicating an ongoing rotation (ω̂) in a clockwise (toward the subject's right) direction even though the subject is actually at rest. Rotational cues are known to influence the perceived orientation of gravity (Stockwell and Guedry 1970), often leading to illusory tilt (Dichgans et al. 1972; Merfeld et al. 1999; von Holst and Grisebach 1951). This evidence suggests that the yaw rotational cue following postrotatory tilt (ω̂) influences the estimated orientation of gravity (ĝ) such that the estimate of gravity (ĝ) rotates in the same direction as if there was an actual rotation. We hypothesize that the CNS computes estimates of gravity (ĝ) and linear acceleration (â) such that their difference matches the measured GIF, which equals gravity in this example (f =g = ĝ − â). Therefore a nonzero estimate of linear acceleration (â= ĝ − g) would be generated whenever the estimate of gravity (ĝ) does not match true gravity (g), as demonstrated in Fig. 2 A. The estimate of interaural linear acceleration (â _{y}) may induce a horizontal VOR component (Fig. 2 B) that should be similar to a horizontal VOR response compensatory to an actual interaural linear acceleration; we refer to this VOR component as an induced VOR. This induced VOR component should combine more or less linearly with the horizontal angular VOR component as previously demonstrated in squirrel monkeys (Sargent and Paige 1991). Since the tilt direction of the estimate of gravity (ĝ) depends on rotation direction, the induced VOR component must depend on rotation direction. Similarly, since the estimate of interaural linear acceleration (â _{y}) depends on subject orientation (θ, Fig. 2 C), the induced VOR component must depend on subject orientation.
To gain insight into how human subjects distinguish tilt from translation, we designed two experiments that created a conflicting sensory situation between semicircular canal and otolith cues, and we measured reflexive slow phase eye movements. In one experiment, subjects were tilted 90° from an upright orientation after they were rotated for 150 s at a constant velocity about an earthvertical axis (“dumping” protocol). In another experiment, subjects were rotated for 150 s at a constant velocity about an earthhorizontal axis and then decelerated to a stop (“barbecue” protocol). For both protocols, we focused on the reflexive eye movements following deceleration to a stop, referred to as the postrotatory responses. Both of these protocols are described in detail in the following section.
Horizontal responses alone have been presented in a previous report for 200°/s dumping protocols (Merfeld et al. 1999). The present report extends this previous study by including VOR responses for 50 and 100°/s dumping protocols to investigate the influence of the magnitude of the rotational stimulus on the GIF resolution. In addition, vertical VOR responses are investigated to identify properties of the axisshift. Moreover responses following barbecuespit rotation are presented to evaluate the dynamic influence of postrotational tilt on the measured responses.
METHODS
Experimental setup and eye movement recording
Informed consent was obtained in accordance with institutional procedures, and subjects were instructed about potential risks, including motion sickness, prior to each testing session.
All protocols were conducted on a twoaxis rotation device. An inner gimbal powered by a 160Nm DC motor (velocity servo control) provided fullcircle rotations about the subject's yaw axis. An outer pitch/roll gimbal powered by a 2,300Nm hydraulic actuator (position servo control) provided rotations about an earthhorizontal axis. Each subject was seated in a kneeling position on a carracetype seat mounted in the device's inner yaw gimbal. The subject's body was restrained using a 5point seatbelt system, lateral shoulder supports, a wide waist belt, and knee restraints. Foam pads were added as needed to ensure maximum stability. During testing the subject gripped a pair of handlebars that provided additional stabilization. The subject's head was secured in an adjustable foamlined head restraint. The subject's interaural axis was aligned with the outer gimbal earthhorizontal axis and the interaural axis midpoint was aligned with the inner gimbal yaw axis.
Binocular eye movements were recorded (Panasonic AGDS850 SVHS VCR) using small video cameras (Machine Vision Hyper CCD Cameras CV36SH) mounted on a bitebar assembly. Infrared lightemitting diodes (LEDs) provided lighting for the video cameras. A mold of each subject's mouth was formed on the bitebar using a dentalimpression compound (3 M Express, 3 M Dental Products, St. Paul, MN). The weight of the camera assembly was supported by elastic bands attached to the yaw gimbal.
An offline application of a custom imageanalysis program provided measurements of the horizontal and vertical coordinates of the pupil center for each field of the video image (59.94 video fields/s). The video system was calibrated by having the subject sequentially direct gaze at 9 horizontal, 9 vertical, and 12 oblique LED target lights. Target viewing evoked horizontal and/or vertical eye movements up to approximately ±20°. Measurements of the threedimensional (3D) locations in space of both the eyes and target LEDs were used to determine the horizontal and vertical angular orientations (Fick coordinates) of the eyes with respect to the head for each gaze orientation. The calibration procedure used these known gaze orientations to determine polynomial equations that related the horizontal and vertical pupil center coordinates to the horizontal and vertical eye orientation angles. These polynomial equations were applied to video data obtained during subsequent test runs to determine horizontal and vertical eye orientation. The overall accuracy of the video measurements is provided by the root mean square error between the absolute eye position prediction from the polynomial fit and the presumed actual eye position. The rms error was less than 0.5° for both horizontal and vertical eye orientations. The repeatability of the video measurements is provided by results of redigitizing and reanalyzing a single video image. This procedure produced a standard deviation of 0.05° for both horizontal and vertical eye position measures. All reported eye movement responses are at least one order of magnitude greater than the videosystem sensitivity. Horizontal and vertical eye position data were digitally filtered and differentiated to yield horizontal and vertical eye velocity, respectively. Torsional eye position was not calculated. Fast phases were automatically removed using a computer algorithm based on peak acceleration detection, with manual editing by experienced personnel, leaving the slow phase eye velocity (SPV).
Experimental protocols
dumping protocol.
Eight healthy subjects age 26–47 (6 males and 2 females) with no history of peripheral or central vestibular disorders volunteered for this study. Clinical testing (including but not limited to rotating chair test battery, Hallpike maneuvers, computerized dynamic posturography, and caloric testing) was performed on seven of the eight subjects and indicated no abnormalities. (The data from the subject not clinically examined were similar to the data from the other subjects.)
The test subjects, with head upright, were accelerated in 2 s to a clockwise (CW) or counterclockwise (CCW) constant yaw angular velocity about an earthvertical axis. (A clockwise rotation is defined as a yaw head rotation toward the subject's right shoulder and a counterclockwise rotation as a yaw head rotation toward the subject's left shoulder.) As a convention, the postrotatory period of a trial is designated by the direction of the preceding rotation. Each subject was tested using three different constant velocities: 50, 100, and 200°/s. The constant velocity rotations were maintained for 150 s and were followed by a 2s angular deceleration to a stop. To control “viewing” distance, a light was turned on, 10 s prior to the stop. During this 5s “lightson” period, the subject was instructed to look straight ahead at a poster fixed to the chair 40 cm in front of the subject's eyes. (Any residual nystagmus was suppressed during this 5s interval, but a small nystagmus returned by the time the subject was brought to a stop.) Immediately after stopping, the subject was tilted 90° about an earthhorizontal axis through the center of the head (at ear level) in 1.5 s. This passive postrotatory tilt positioned the subject in one of eight evenly spaced final orientations: noseup (NU), nosedown (ND), rightdown (RD), leftdown (LD), and each of the four orientations midway between these principal orientations (NURD, NULD, NDRD, NDLD). The trial order was randomized and secret; the direction of rotation (CW or CCW), and the direction of tilt were counterbalanced across eight subjects for each speed. The same testing order was used for each subject for each speed. The order with which the speeds were presented was counterbalanced across six subjects, and the two remaining subjects were tested using two previously tested speed sequences (200, 100, 50 and 200, 50, 100°/s). The speed was always the same within a test session, and at least two nights separated test sessions. For each speed, there were three testing sessions: one session with all NU and ND trials, one session with all LD and RD trials, and one session with all inbetween orientation trials. As controls, each subject was also tested with no tilt following the upright rotation for each velocity (in the 1st 2 sessions). Each subject was also passively tilted 90° to one of eight orientations (in a separate session).
To minimize order effects, lights were turned on for 2 min between trials while the subjects were upright and stationary. During data collection, subjects were instructed to keep their eyes open and to look straight ahead but not to focus on any point, real or imagined, and were challenged with mental arithmetic to maintain alertness.
barbecue spit protocol.
Four healthy male subjects, ages 29–49, with no history of peripheral and central vestibular disorders participated in this portion of the study (2 of the 4 also participated in the dumping protocol). The number of subjects performing this protocol was limited because of severe motion sickness that prevented most subjects from completing the test protocols.
Subjects were initially positioned in a supine orientation and were then accelerated in 2 s to a CW or CCW constant yaw angular velocity of 200°/s about an earthhorizontal axis. The constant velocity rotation was maintained for 150 s before decelerating (2 s) to a stop in either the noseup (NU) or nosedown (ND) orientations. The remainder of the protocol was identical to the dumping protocol. (Ongoing nystagmus was suppressed during the 5s light interval preceding the deceleration but returned to normal by the time the subject was brought to a stop.)
In addition, two subjects who also participated in the dumping study were tested with the barbecue protocol using all eight stop orientations. The trial order for these two subjects was the same as for their dumping tests.
Data analysis
headfixed reference frame.
All vector coordinates (physical variables and internal estimates) were expressed in an orthogonal headfixed frame of reference withx, y, and z axes corresponding to the subject's nasooccipital, interaural, and rostrocaudal axes respectively. The positive axes were directed nasally (x), toward the left ear (y), and toward the top of the skull (z).
fick angles.
To describe eye position and eye angular velocity, we used Fick angles and angular rates defined by the righthand rule with positivex, y, and z coordinates corresponding to CW torsional, downward vertical, and leftward horizontal movements, respectively.
sinusoidal fit.
To characterize the variations of the horizontal induced VOR component, horizontal VOR time constant, and vertical VOR as a function of head orientation, we fit spatial sinusoids to these different data sets for each direction of rotation. For the horizontalinduced VOR component, a sinusoidal variation with head orientation is expected based on the following considerations. The induced VOR component should be proportional to the interaural projection of the estimate of linear acceleration (â _{y}, Fig.2 B). If the estimate of linear acceleration is constant in a spacefixed frame of reference, its interaural projection and the associated compensatory induced VOR component should vary sinusoidally with head orientation in a headfixed frame of reference (Fig. 6). This sinusoidal variation was quantified by measuring the mean horizontal induced VOR component between 3 and 4 s after the tilt and fitting a sine function to these data (Figs. 6 and 8).
Similarly for the vertical VOR, if the VOR axisshift component stays constant in a spacefixed frame of reference, its projection on the vertical axis should vary sinusoidally with head orientation in a headfixed frame of reference. The sinusoidal variation in the vertical VOR with head orientation was quantified by measuring the mean vertical VOR between 10 and 11 s after the tilt (Fig. 10) and fitting a sine function to these data (Fig. 10). We waited 10 s to allow adequate development of the axisshift, which occurs gradually in humans (Fetter et al. 1996; Furman and Koizuka 1994; Harris and Barnes 1987)
For the horizontal VOR time constant, we used a sinusoidal fit based on the apparent sinusoidal variation of the time constant with head orientation (Fig. 4).
For all sinusoidal fits, a leastsquare algorithm was used to fit the data with an analytical function C(θ)
time constants.
To determine time constants, a constrained nonlinear optimization algorithm was used (function const in Matlab 5.2 for Macintosh, The Mathworks). The slow phase velocity was fit with three different analytical functions D(t)
statistics.
Analysis of variance (ANOVA) was used to determine the statistical significance of velocities and time constants of VOR, angular VOR, and induced VOR components as a function of speed of rotation, direction of rotation, and head final orientation. All statistical analyses were performed with Systat 7.0 (SPSS).
Multivariate ANOVA (MANOVA) methods were applied to the statistical analysis of sinusoidal fit results. Each sinusoidal curve, defined by an amplitude M and a phase φ (Eq.1 ), was represented by the complex variableZ = M[cos φ + i sin φ] =X + iY where i ^{2}= −1. To compare mean phase shifts between two groups (φ_{1} and φ_{2}), MANOVA was conducted on the two groups of real pairs [X _{1},Y _{1}] and [X _{2},Y _{2}], where [X, Y] is considered as a pair of related dependent variables in the Hotelling−T ^{2} test (Johnson and Wichern 1982). If the two groups of paired variables [X _{1},Y _{1}] and [X _{2},Y _{2}] were significantly different (MANOVA T ^{2}test) and if the two associated groups of amplitude (M _{1}and M _{2}) were not significantly different (ANOVA ttest), we concluded that the statistically significant difference came from the variations in phase shifts (φ_{1} and φ_{2}). This approach is preferred to ANOVA on the independent parametersM and φ, since separate statistics on M and φ may lead to erroneous results (Calkins 1998).
RESULTS
This report focuses primarily on the responses following deceleration, i.e., slow phase velocity of the postrotatory nystagmus. However, the perrotatory responses to yaw rotations about an earthvertical axis during dumping protocols had average amplitudes and average decay time constants within the normal range (Table1) for all speeds (Hess et al. 1985; Honrubia et al. 1984). The perrotatory horizontal VOR time constants decreased with increasing velocity as previously reported (Baloh et al. 1979; Paige 1989). For barbecue spit trials (Table2), the perrotatory responses showed the usual peak amplitudes and sinusoidal modulations (Wall and Furman 1989).
Postrotatory horizontal eye movements following earthvertical axis rotations (“dumping”)
HORIZONTAL VOR.
The horizontal postrotatory VOR slowphase velocity was determined in eight subjects for three speeds (200, 100, 50°/s), two directions (CW and CCW) of rotation, and eight final tilt orientations. During the first 20 s following the postrotatory tilt, the postrotatory VOR exhibited four very different patterns dependent on rotation direction and head orientations. First, for each of the three speeds tested, the VOR magnitude following a tilt in the NU orientation was greater than the VOR magnitude following a tilt in the ND orientation after identical CCW and CW rotations (Fig. 3,left). We are focusing here on the 20 s following the postrotatory tilt period that begins 3.5 s after the VOR peaked (see graphs to the right of the vertical dashdotted line on each plot in Fig. 3). Second, the VOR magnitude was greater for LD trials than for RD trials following identical CCW rotations, but the VOR magnitude was smaller for LD trials than for RD trials following identical CW rotations for each of the three speeds tested (Fig. 3,2nd column). Third, for NURD and NDLD orientations, little difference was observed following CCW rotation, but the VOR magnitude was greater for NURD trials than for NDLD trials following CW rotation (Fig. 3, 3rd column). Fourth, for NULD and NDRD trials, little difference was observed following CW rotation, but the VOR magnitude was greater for NULD trials than for NDRD trials following CCW rotation (Fig. 3, 4th column). These response patterns were one of our principal findings and were predicted by the GIF resolution hypothesis as discussed later.
For each subject and each trial, a time constant characterizing the postrotatory slow phase VOR was computed (Table3). For the three speeds of rotation (50, 100, and 200°/s), the head orientation effect was significant (P = 0.03, P = 0.0002,P = 0.00001, respectively), but the rotation direction effect was not significant. The mean time constants are plotted (Fig.4) as a function of final head orientation for the three speeds (50, 100, and 200°/s) and two directions (CW and CCW) of rotation. For each speed and direction of rotation, a sinusoidal function was fitted to the mean time constant across subjects.
As a control experiment, we tested all subjects for the three speeds (50, 100, and 200°/s) and two directions (CW and CCW) of rotation without tilting them once stopped. For the three speeds (50, 100, and 200°/s), the mean time constant for all trials with no postrotary tilt (11.2, 11.4, and 9.4 s, respectively) was significantly greater (P < 0.002, P < 0.0005 and P < 0.0005, respectively) than the mean time constant for all trials followed by a postrotatory tilt (5.6, 6.5, and 6.7 s, respectively). These differences illustrate what has been referred to as the dumping effect (Raphan et al. 1981).
ANGULAR AND ORIENTATIONDEPENDENT COMPONENTS OF THE VOR.
We hypothesized that subject orientations separated by 180° (e.g., NU and ND) result in an opposite estimate of interaural linear acceleration (â
_{y}), leading to oppositely directed induced VOR components as well (seediscussion for more details). At the same time, rotational cues from the semicircular canals are identical, consistent with experimental psychophysical reports showing that the duration of rotation sensation following 90° tilts does not depend on subject orientation (Benson and Bodin 1966). Therefore if the VOR slow phase velocities for two head orientations separated by 180° are noted VOR_{1} and VOR_{2}, we calculated, as a simple approximation, an estimate of the angular VOR (AVOR) component as
For each speed and each direction, the mean AVOR response components were computed across the eight subjects for the four orientation pairs separated by 180° (NU and ND, LD and RD, NURD and NDLD, NULD and NDRD). Each computed postrotatory AVOR component was characterized by a time constant, using the same fitting function as for the horizontal VOR (see methods, Eq. 2 ). For the three speeds of rotation (50, 100, and 200°/s), time constants characterizing the postrotatory slow phase AVOR component did not show any significant orientation effect following yaw rotations (P = 0.57, P = 0.78 andP = 0.97, respectively).
Similarly, for each speed and direction, the peak amplitude of the induced VOR component was computed for the four orientation pairs separated by 180°. For all four orientation pairs, the peak amplitude of the induced VOR component decreased with decreasing angular velocity (Fig. 5, the mean across 8 subjects is shown). For each speed and orientation pair, the induced VOR component peaked between 3 and 4 s following the postrotatory tilt. This observation was consistent across all subjects. To rule out the possibility that the induced VOR component was contaminated by the postrotatory tilt, control experiments were performed where the subjects were tilted 90° to the eight different orientations without being previously rotated. For all subjects, there was no apparent nystagmus 3 s after completion of the tilt (not shown). Therefore we concluded that the peak amplitude of the induced VOR component between 3 and 4 s after the postrotatory tilt was not influenced by an artifact due to the tilt alone.
For each rotation direction and speed, the peak amplitude of the induced VOR component calculated between 3 and 4 s after completion of the tilt varied as a function of head orientation for each individual subject (individual data not shown). Individual induced VOR data following CW and CCW rotations varied sinusoidally with head orientation (individual data not shown). For each individual sinusoidal fit, an amplitude M and a phase shift φ were determined. As described in methods, each sinusoidal fit can be represented by a pair of real number [X = M cos φ,X = M sin φ]. For all three speeds (50, 100, and 200°/s), the group of real pairs [X _{1},Y _{1}] for CW rotations were significantly different (P = 0.0004, P= 0.0006, P = 0.0003, respectively, using MANOVA Hotelling−T ^{2}) from the group of real pairs [X _{2},Y _{2}] for the CCW rotations. Since response amplitudes were not significantly different, we concluded that there was a significant phase difference between the results from CW and CCW rotations. The mean phase shift, for the horizontal induced VOR component following CW rotations (157, 153, and 137°, respectively) was significantly different from following CCW rotations (22, 37, and 47°, respectively).
The mean peak amplitude across subjects of the induced VOR component calculated between 3 and 4 s after completion of the tilt also varied as a function of head orientation (Fig.6, left). The CW and CCW mean induced VOR data were well fit by sinusoids shifted with respect to one another. For each stimulus velocity, the induced VOR data supported the GIF resolution hypothesis. Specifically, the sinusoidal fits closely matched the predicted negative of the estimate of interaural linear acceleration (−â _{y}) plotted as a function of head orientation (Fig. 6, right) for different leftward and rightward tilts of the estimate of linear acceleration,â, with earthhorizontal (tilt of âis specified by α̂, see Fig. 2 B). The sensitivity between the negative of the estimate of interaural linear acceleration (−â _{y}) and the sinusoidal fit to the induced VOR data varied between 8.3 and 11° · s^{−1} · g^{−1}. For all three speeds (50, 100, and 200°/s), very good fits were obtained by increasing the tilt of the estimate of linear acceleration with increasing speed (α̂ = 22.5°, α̂ = 30°, andα̂ = 45°, respectively). For each speed, the theoretical angle α̂ (Fig. 2 B) has been chosen as the mean between α̂_{1} = φ_{1}and α̂_{2} = 180° − φ_{2} (for further explanation, see GIF resolution hypothesis in discussion), where φ_{1} and φ_{2} are the phases of the sinusoidal fits to the CCW and CW rotation data respectively: for example, α̂ = (22 + 180 − 157)/2 = 22.5° following 50°/s rotations.
Figure 6, left, presents sinusoidal fits to the data following CW and CCW rotations between 3 and 4 s after the tilt following 50, 100, and 200°/s yaw rotations. Similar plots were made at 1s sequential time increments between 3 and 50 s after completion of the postrotatory tilt. At each 1s increment, a sine fit was made to the CW and CCW mean induced VOR amplitude versus head orientation data to estimate the values of M and φ (Eq. 1 ) at these points in time. These results were combined to form a parametric estimate of the variation of M and φ over time [M(t) and φ(t), respectively]. The induced VOR “experimental trajectories” (Fig.7, left) are defined as a parametric plot X(t) =M(t) cos φ(t) andY(t) = M(t) sin φ(t). The induced VOR experimental trajectories closely matched the estimated linear acceleration (â) theoretical trajectories following CW and CCW rotations (Fig. 7,right). Following 50, 100, and 200°/s yaw rotations, very good matches occurred for maximum tilts of the estimate of linear acceleration with earthhorizontal of ‖α̂‖_{max} = 22.5°, ‖α̂‖_{max} =30°, ‖α̂‖_{max} = 45°, respectively. (The theoretical trajectories of the estimated linear accelerationâ are portions of a circle, the diameter of which is the constant norm of the estimate of gravity ĝ.) The time courses of the tilt of the estimate of linear acceleration with earthhorizontal (α̂) are not shown explicitly. But these time courses are very similar1 to time courses of the induced VOR component (Fig. 5).
Postrotatory horizontal eye movements following an earthhorizontal axis rotation (“barbecue”)
HORIZONTAL EYE MOVEMENTS.
Four subjects completed barbecue rotations with constant yaw angular velocity of 200°/s about an earthhorizontal axis followed by a stop in either the NU or ND orientations. The barbecue postrotatory VOR (Fig. 8 A) and induced VOR (Fig. 8 B) were very similar to the results for 200°/s dumping trials (Figs. 3 and 5). During the 35 s following the tilt, for both CW and CCW rotations, the VOR magnitude following a stop in the NU orientation was greater than following a stop in the ND orientation. For both CW and CCW rotations, the VOR time constant was greater for the NU orientation (12.2 and 12.3 s, respectively) than for the ND orientation (8.7 and 8.9 s, respectively), but due to the small number (n = 4) of subjects tested, the difference was not significant (P = 0.07). These results confirm that the dynamic tilt rotation measured by the semicircular canals in the dumping protocol did not substantially affect or contaminate the horizontal VOR eye movements recorded in the postrotatory period.
To allow a more complete comparison of the dumping and barbecue rotation protocols, two subjects were tested for two directions of rotation and eight orientations at 200°/s for both barbecue and dumping protocols with the same trial order for each protocol. The mean induced VOR amplitudes between 3 and 4 s after the tilt for dumping protocols and after the stop for barbecue protocols are plotted as a function of head orientation (Fig. 8, C andD). The results were very similar for both protocols, again confirming that the dynamic aspect of postrotatory tilt did not substantially contaminate the postrotatory horizontal VOR three or more seconds after the tilt was completed. Therefore head orientation with respect to gravity was the predominant factor influencing postrotatory eye movement responses and not dynamic head tilt per se.
Postrotatory vertical eye movements following earthvertical axis rotations (dumping)
In addition to the postulated induced VOR component discussed previously, previous results in humans (Fetter et al. 1996; Harris and Barnes 1987), rhesus monkeys (Angelaki and Hess 1994), and squirrel monkeys (Merfeld et al. 1993b) demonstrate that a shift in the axis of eye rotation is also observed following postrotatory tilt. This axisshift, which is not specifically predicted (nor precluded) by the GIF resolution hypothesis, indicates the tendency of the VOR rotation axis to align with gravity, as described by any one of several spatial orientation hypotheses (Angelaki and Hess 1994;Cohen et al. 1999; Merfeld et al. 1993b). While both AVOR and induced VOR components should be horizontal eye movements, any axisshift of the VOR rotation axis toward alignment with gravity should induce either vertical or torsional eye movements, depending on the subject's orientation. The axisshift of the VOR rotation axis is not directly related to the induced VOR component, although the induced VOR component would influence the magnitude of the axisshift, since the induced VOR component modifies the horizontal VOR.
We evaluated the spatial reorientation of the postrotatory VOR induced by head movements in the roll plane by plotting postrotatory vertical VOR versus horizontal VOR (Fig. 9) for both LD or RD orientations, for all speeds, and for both directions of rotation. The upward vertical components were on average larger than the downward vertical components. The axisshift was initially small (<10° for all speeds) at the time when the induced VOR component peaked (about 3 s after the postrotatory tilt, Fig. 5), and then increased and peaked at an amplitude of roughly 15–30° between 10 and 20 s after the tilt, depending on the rotation angular velocity. A slow buildup in the axisshift has been previously observed following postrotatory tilt (Fetter et al. 1996) and following offvertical axis rotation in humans (Furman and Koizuka 1994; Harris and Barnes 1987). Figure10 shows plots of the mean vertical VOR between 10 and 11 s after completion of the tilt as a function of head orientation.
For each rotation direction and speed, the peak amplitude of the vertical VOR calculated between 10 and 11 s after completion of the tilt varied sinusoidally as a function of head orientation for each individual subject (not shown). As described in methods, each individual sinusoidal fit can be represented by a pair of real number [X = M cos φ, Y = M sin φ] where M is the amplitude and φ the phase of the sinusoidal fit. For two speeds (100 and 200°/s), the group of real pairs [X _{1},Y _{1}] for CW rotations were significantly different (P = 0.02 and P = 0.03, respectively, for HotellingT ^{2}test) from the group of real pairs [X _{2},Y _{2}] for the CCW rotations. Since response amplitudes were not significantly different, we concluded that there was a significant phase difference between the results from CW and CCW rotations. The mean phase shift for vertical VOR following CW rotations (63 and 66°, respectively) was significantly different from following CCW rotations (−58 and −64°, respectively).
The mean peak amplitude across subjects of the vertical VOR calculated between 10 and 11 s after completion of the tilt also varied as a function of head orientation (Fig. 10). The CW and CCW responses were well fit by sinusoids shifted with respect to one another. The amplitude, the bias, and the phase shift absolute value of the sinusoidal fits to the mean vertical VOR data decreased with decreasing speed for both CW and CCW rotations.
DISCUSSION
For both dumping and barbecue protocols, the postrotatory horizontal VOR demonstrated a clear dependence on both head orientation and direction of the preceding rotation, indicating that interactions between otolith and semicircular canal cues influenced the resulting eye movements. In addition, we have shown that the dynamic tilt of the dumping protocol cannot explain the various asymmetries observed in horizontal eye movements since eye responses following yaw rotation about an earthhorizontal axis demonstrated the same asymmetries (Fig.8). We first compare our results to previous experimental findings and then consider whether any of the existing hypotheses (VOR spatial orientation, frequency segregation, and GIF resolution) that characterize interactions between otolith and semicircular canal cues are consistent with experimentally determined features of dumping and barbecueinduced postrotatory VOR.
Horizontal VOR decay following postrotatory tilts
Previous human studies reported that an eye movement response attenuation (dumping) occurs when graviceptor cues are inconsistent with rotation cues, e.g., after yaw (Benson and Bodin 1966) and roll (Udo de Haes and Schöne 1970) rotation about an earthhorizontal axis and after active (Schrader et al. 1985) and passive (Benson and Bodin 1966) postrotational tilts following yaw rotation about an earthvertical axis. Our data confirm these findings, with the decay time constant of postrotatory VOR significantly smaller for trials with postrotatory tilt than for trials without postrotatory tilt. Previous studies also demonstrated asymmetries in VOR responses for orientations separated by 180° after both passive (Benson and Bodin 1966) and active (Schrader et al. 1985) postrotatory tilts. Other paradigms also appear to induce related orientationdependent asymmetries. For example, human horizontal optokinetic nystagmus and afternystagmus induced by yaw rotation of an optokinetic surround, with subjects and optokinetic surround aligned with earthhorizontal, have been shown to be greater for NU than for ND orientations (Wall et al. 1999). A similar asymmetry has been observed during caloric stimulation of canal plugged squirrel monkeys (Minor and Goldberg 1990; Paige 1985). These extensive sets of data allow for detailed comparisons of predictions of different hypotheses regarding the interactions of otolith and semicircular canal cues on the generation of VOR eye movements.
VOR spatial orientation hypothesis
The VOR spatial orientation hypothesis has been proposed to explain orientation dependent asymmetries in the VOR (Cohen et al. 1999). First, this hypothesis states that the angular VOR time constant (10–20 s) is prolonged when compared with primary semicircular canal afferent (5–6 s) by a velocitystorage mechanism (Raphan et al. 1979). Second, the velocity storage mechanism is dependent on head orientation with respect to the direction of the GIF as demonstrated in rhesus and cynomolgus monkeys (Dai et al. 1991) and humans (Gizzi et al. 1994). Third, a “crosscoupling” in the velocitystorage mechanism occurs from the primary horizontal nystagmus to a secondary vertical nystagmus after a roll tilt or to a secondary torsional component after a pitch tilt (Raphan and Cohen 1988). Because of this crosscoupling, the rotation axis of reflexive eye movements demonstrates a tendency to shift toward alignment with the GIF direction. In several species of monkeys (rhesus, cynomolgus, and squirrel monkeys), this socalled axisshift has been observed for optokinetic nystagmus (OKN) and afternystagmus (OKAN) (Dai et al. 1991), for VOR during centrifugation (Merfeld and Young 1995; Wearne et al. 1999), for VOR following offvertical axis rotation (Raphan et al. 1992), and for VOR following a postrotatory tilt (Angelaki and Hess 1994; Merfeld et al. 1993b). For similar protocols in humans (Fetter et al. 1996; Gizzi et al. 1994; Harris and Barnes 1987; Merfeld et al. 1998), the rotation axis of reflexive eye responses also tends to align with the GIF direction but to a much smaller extent.
According to the VOR spatial orientation hypothesis, a directional gain asymmetry in the secondary nystagmus induced by “crosscoupling” might lead to a time constant asymmetry in the horizontal primary nystagmus (Raphan and Sturm 1991). For example, upward OKN and OKAN are larger than downward OKN and OKAN in rhesus and cynomolgus monkeys (Matsuo et al. 1979). Therefore horizontal OKN and OKAN responses following a roll tilt in either LD or RD orientations demonstrate asymmetries that reverse with the direction of the rotational cues in rhesus and cynomolgus monkeys (Raphan and Cohen 1988). Assuming that a similar upward/downward response asymmetry exists for human VOR responses, the VOR spatial orientation hypothesis might be consistent with our observed LD/RD asymmetries in the horizontal VOR and their dependence on rotation direction.
While upward/downward response asymmetries are consistently observed in rhesus and cynomolgus monkeys, the presence of an upward/downward response asymmetry in humans is rather controversial and is certainly not consistent across subjects. An OKN/OKAN upward/downward asymmetry was reported in humans in some studies (Murasugi and Howard 1989; Wei et al. 1994) but not in other studies where asymmetries were reported for only a minority of human subjects (Baloh et al. 1986; Stiefel 1962). No consistent vertical VOR asymmetry has been reported in humans during pitch rotation about an earthvertical axis (Allum et al. 1988; Baloh et al. 1983) or about an earthhorizontal axis (Baloh and Demer 1991).
It is certainly safe to conclude upward/downward response asymmetries are inconsistent and at best very weak in humans. Furthermore no asymmetries in torsional responses have ever been reported in humans for either optokinetic or vestibular stimulation (Morrow and Sharpe 1993; Peterka 1992; Seidman and Leigh 1989). Therefore the VOR spatial orientation hypothesis cannot explain the observed NU/ND asymmetries in the horizontal VOR. Even if an asymmetry in torsional responses existed, the VOR spatial orientation hypothesis would predict that the NU/ND asymmetry in the postrotatory horizontal VOR should reverse with opposite rotation direction for both dumping and barbecue protocols. This prediction is refuted by our dumping and barbecue protocol data that demonstrate a similar NU/ND asymmetry following both CW and CCW yaw rotations.
Therefore the VOR spatial orientation hypothesis is unable to predict many characteristics found in the measured human responses. This may be because this hypothesis has primarily been developed to explain monkey but not human responses. Furthermore the fact that models of reflexive eye response spatial orientation (Raphan and Sturm 1991;Wearne et al. 1999) do not implement the influence of rotational cues on the estimation of gravity and linear acceleration may explain some of these shortcomings.
Frequency segregation hypothesis
The frequency segregation hypothesis states that the frequency content of the GIF measured by the otolith organs can be used to separate gravity from linear acceleration (Paige and Tomko 1991; Seidman et al. 1998). Specifically, lowfrequency content might contribute to an estimate of gravity while highfrequency content might contribute to an estimate of linear acceleration. Our experimental results are not consistent with this hypothesis.
Rapid tilts yield highfrequency forces measured by the otolith organs. According to the frequency segregation hypothesis, these highfrequency cues should lead to an estimate of linear acceleration in the plane of the postrotatory tilt and therefore should generate a horizontal linear VOR component when the interaural projection of this estimate of linear acceleration is nonzero. First, there should be a horizontal linear VOR component following a dynamic 90° tilt in either LD or RD orientation with no rotation preceding the tilt. These predictions are inconsistent with the absence of horizontal eye movements for both of these passive tilts. Second, there should be no horizontal linear VOR component when the subject is pitched into either a NU or ND orientation. These predictions are inconsistent with the large asymmetry observed between the NU and ND orientations (Fig. 3). In addition, we have shown that the postrotatory tilt alone cannot explain the various asymmetries observed in horizontal VOR eye movements since eye responses following yaw rotation about an earthhorizontal axis demonstrated the same asymmetries (Fig. 8). Some additional central processing, probably involving sensory interactions, must be assumed to explain our data.
GIF resolution hypothesis
The GIF resolution hypothesis predicts that the difference between the estimate of gravity (ĝ) and the estimate of linear acceleration (â) matches the measured GIF (f = ĝ −â). Therefore the GIF resolution hypothesis predicts a nonzero estimate of linear acceleration (â), whenever the measured GIF, in this case gravity (g), and the estimate of gravity (ĝ) do not match. After a postrotatory tilt following a yaw rotation about an earthhorizontal axis, the postrotatory semicircular canal cue induces an illusory tilt (von Holst and Grisebach 1951). Therefore the estimate of gravity (ĝ) does not match gravity (g) and the GIF resolution hypothesis predicts a nonzero estimate of linear acceleration (â, Fig. 2 A). If present, the interaural estimate of linear acceleration should induce a horizontal VOR. This induced VOR component is similar to the VOR evoked by actual linear acceleration (Paige and Tomko 1991;Schwarz and Miles 1991; Schwarz et al. 1989) but is evoked by an estimate of linear acceleration even in the absence of true linear acceleration. The induced VOR component should depend on both rotation direction and head orientation because the rotation direction influences the direction of illusory tilt and therefore the direction of the interaural estimate of linear acceleration and head orientation alters the projection of the estimated linear acceleration on the interaural axis (â _{y}, Fig. 2, B andC). For example, the postrotational response (ω̂) for a CCW rotation is CW. For the NU head orientation, the estimate of gravity (ĝ) tilts toward the subject's right (Fig. 3, 1st column, top). Since the estimate of gravity does not match gravity, a nonzero interaural estimate of linear acceleration (â _{y}) is therefore induced toward the subject's right. The compensatory eye response to this interaural estimate of linear acceleration is a horizontal leftward induced VOR component, which adds to the AVOR component. In contrast, for the ND orientation following a CCW rotation, both the predicted tilt and interaural estimate of linear acceleration are toward the subject's left. This leftward interaural estimate of linear acceleration induces a rightward horizontal induced VOR component, which now deducts from the AVOR component. Consistent with these predictions, in the 20 s following the postrotatory tilt, the magnitude of the VOR following a tilt in the NU orientation was greater than the VOR following a tilt in the ND orientation after identical CCW rotations for each of the three speeds tested (Fig. 3). When the direction of the rotation preceding the postrotatory tilt is CW, the predicted AVOR and induced VOR components both reversed. Again the induced VOR component adds to the AVOR component for the NU orientation but deducts for the ND orientation. Therefore the VOR asymmetry is similar for both rotation directions (Fig. 3).
For the LD orientation, the interaural estimate of linear acceleration (â _{y}) is toward the subject's right for both directions of rotation (Fig. 3, 2nd column), inducing a leftward horizontal induced VOR component. This induced VOR component should add to the AVOR component following CCW rotation and deduct from the angular VOR component following CW rotation. For the RD orientation, both the interaural estimate of linear acceleration and the induced VOR component are inverted. Therefore the induced VOR component should deduct from the AVOR component following CCW rotation and add following CW rotation. Consistent with previous data (Schrader et al. 1985), the LD response magnitude was greater than the RD response magnitude following identical CCW rotations and less than the RD response magnitude following identical CW rotations for each of the three speeds tested (Fig. 3).
For orientations midway between the primary tilt orientations, the observed patterns are also consistent with predictions of the GIF resolution hypothesis. If we assume that the estimate of linear acceleration is tilted approximately 45° to the right of vertical following CCW rotations, the interaural estimate of linear acceleration is nearzero for NURD and NDLD orientations and maximal for NULD and NDRD orientations following CCW rotations (Fig. 3). When the rotation direction is opposite (CW), the estimate of linear acceleration tilts 45° to the left of vertical. Therefore the asymmetry patterns are inverted. Indeed the maximal interaural estimates of acceleration for CW trials occur now for NURD and NDLD orientations (Fig. 3), while nearzero estimates of linear acceleration for CW trials occur for NULD and NDRD orientations (Fig. 3). The dependence of the horizontal VOR time courses on head orientation after a postrotatory tilt (Fig.3) are predicted by previous VOR models that implement the GIF resolution hypothesis (Merfeld et al. 1993a;Zupan 1995). These models include mechanisms that allow the combination of otolith and canal information to contribute to the estimates of both gravity and head angular velocity.
The GIF resolution hypothesis is further supported by sudden increases observed in the horizontal VOR immediately following the postrotatory tilt and by the induced VOR component reversal pattern. First, the VOR actually increases immediately after the postrotatory tilt in some orientations (Fig. 3): this increase is easily noticeable for CW RD, CW NURD, and CCW NULD trials at all speeds. This increase is inconsistent with any type of response attenuation but is consistent with additive influence of an induced VOR component. Second, for 200°/s rotations, the induced VOR component reverses after about 30 s for all orientations except for LD and RD orientations (Fig.5, 3rd row). It is well known that semicircular canal afferents typically show a secondary phase reversal approximately 30 s after deceleration following constant velocity rotation (Goldberg and Fernandez 1971) and a reversal of VOR eye movements consistent with this pattern of afferent discharge is commonly recorded (Correia and Guedry 1966). As the semicircular canal cue diminishes and reverses (Fig.11), the angle between the estimates of gravity (ĝ) and gravity (g) should diminish (t _{2}) and then reverse (t _{3}). Therefore the GIF resolution hypothesis predicts a reversal of the estimate of linear acceleration as well as a reversal of the induced VOR component for most orientations (as illustrated for the NU orientation in Fig.11 B). Such reversals are evident in the horizontal induced VOR component (Fig. 5) following 200°/s yaw rotations. These reversals are also present following 50 and 100°/s yaw rotations but are harder to observe.
However, in the RD and LD positions, the projection of the estimated linear acceleration on the interaural axis is always in a single direction. For example, in the RD orientation (Fig. 11 C), this projection is always toward the subject's left following both CW and CCW rotations. Therefore for the RD and LD orientations, reversal in the estimated tilt does not reverse the interaural estimate of linear acceleration nor does it reverse the induced VOR component even though the VOR for these conditions reverse. Consistent with this prediction, the horizontal induced VOR component does not show a reversal for RD and LD orientations for any of three speeds tested.
According to the GIF resolution hypothesis (Fig. 2), the induced VOR component is proportional to the interaural estimate of linear acceleration (â _{y}) and therefore should vary sinusoidally as a function of head orientation. The induced VOR component should be maximum and positive when the subject's interaural axis is aligned with the estimate of linear acceleration and when this estimate of linear acceleration is toward the right ear. Therefore the amplitude (M) of the sinusoidal fit to induced VOR data (Fig. 6, left) should be proportional to the norm of the estimate of linear acceleration (â). In addition, the phase shift (φ) of the sinusoidal fits should be related to the tilt angle that the estimate of linear acceleration makes with the earth horizontal (α̂, Fig. 2 B). Specifically, the phase shift (φ) should be equal to α̂ for CCW rotations and equal to 180° − α̂ for CW rotations. In agreement with this prediction, the induced VOR component varied sinusoidally with subject orientation at each of the three velocities tested (Fig. 6, left). Moreover, these sinusoidal fits to the 50, 100, and 200°/s data closely matched the variations of the projection of the estimate of linear acceleration (Fig. 6,right) onto the subject's interaural axis (â _{y}) for angles of the estimate of linear acceleration with respect to earthhorizontal (α̂, Fig. 2 B) of 22.5, 32, and 45°, respectively.
In the simple formulation of the GIF resolution hypothesis discussed in this paper, the estimate of gravity (ĝ) has a constant norm [i.e., central processing of canal and graviceptor information leads to an estimate of gravity (ĝ) such that the magnitude of ĝ is always a fixed value, presumably 1g]. Therefore the trajectory of the estimate of linear acceleration (â) is theoretically an arc of a circle with a radius equal to the magnitude of ĝ (Figs. 7,right, and 11). Using simple trigonometry and planar geometry (Fig. 2 B), the theoretical trajectory of the estimate of linear acceleration (Fig. 7, right) is defined by the parametric equations X̂(t) = ∥â(t)∥ cos α̂(t) andŶ(t) = ∥â(t)∥ sin α̂(t). In these equations, t is the time after the postrotatory tilt and α̂ is the tilt of the estimate of linear acceleration with earthhorizontal (Fig. 2 B). The amplitude of the estimate of linear acceleration (∥â∥) is theoretically proportional to the amplitude (M) of the induced VOR sinusoidal fit. In addition, the tilt of the estimate of linear acceleration with earthhorizontal for CCW rotations (α̂, Fig.2 B) and for CW rotations (180° − α̂) is theoretically equal to the phase shift (φ) of the sinusoidal fits to the induced VOR component. Therefore if the GIF resolution hypothesis is valid, the induced VOR experimental trajectories (Fig. 7,left) defined by the parametric equationsX(t) = M(t) cos φ(t) and Y(t) =M(t) sin φ(t) should closely match the theoretical trajectories of the estimate of linear acceleration (Fig. 7, right). Indeed, the experimental trajectories appear consistent with these predictions.
Influence of speed on the GIF resolution hypothesis
Due to semicircular canal dynamics (Wilson and Melvill Jones 1979), the semicircular canal postrotatory cue decreases with decreasing angular velocity. Since the tilt of the estimate of gravity (ĝ) relative to the earthvertical axis is driven by the postrotatory semicircular canal cue, this illusory tilt should decrease with decreasing speed. Therefore both the amplitude of the estimate of linear acceleration (â) and the angle (α̂) of the estimate of linear acceleration with earthhorizontal (i.e., the phase shift) should decrease with decreasing speed (Fig. 6, right).
Using trigonometry and planar geometry (Fig. 2 B), we can calculate that the magnitude of the estimate of linear acceleration (∥â∥) when tilted with respect to earthhorizontal is ∥â∥ = 2∥g∥ sin α̂. This magnitude decreases with decreasing velocity since the tilt angle (α̂) of the estimate of acceleration decreases with decreasing velocity. Since the amplitude (M) of the sinusoidal fits to the induced VOR data are hypothesized to be proportional to the magnitude of the estimate of linear acceleration (â), this amplitude (M) should decrease with decreasing velocity. This expectation is consistent with experimental results showing a decrease in Mwith decreasing velocity (Fig. 6).
The decrease in the magnitude of the induced VOR component could simply be due to the scaling factor of the rotation angular velocity. However, a simple scaling factor explanation cannot explain the phase shift variation between sinusoidal fits to CW and CCW data with speed (Fig.6). In fact, according to the GIF resolution hypothesis, the phase shift (φ) of the sinusoidal fit to the induced VOR data are related to the angle (α̂) of the estimate of linear acceleration (â) with earthhorizontal. Specifically, the orientation angle (θ, see Fig. 2 C) where the induced VOR component is at its positive maximum is equal, by definition, to the phase shift (φ). This angle also corresponds to the orientation where the subject's interaural axis is aligned with the estimate of linear acceleration (â), and this estimate of linear acceleration is directed toward the right ear. As a result, θ =α̂ = φ for CCW rotations and θ = 180° −α̂ = φ for CW rotations. Therefore with decreasing speed, the peak of the sinusoidal fits to the induced VOR data should shift toward 0° for CCW rotations and toward 180° for CW rotations. The experimental results confirm this theoretical prediction (Fig. 6).
Vertical responses
In addition to horizontal responses, vertical eye movements were also evoked following postrotatory tilts (Figs. 9 and 10). These vertical VOR eye movements were not compensatory to either the horizontal postrotatory semicircular canal cues or the postrotatory tilt itself. Therefore these vertical responses must be due to the interaction of these sensory cues.
As previously reported after postrotatory tilts following yaw rotations in rhesus monkeys (Angelaki and Hess 1994) and squirrel monkeys (Merfeld and Young 1992; Merfeld et al. 1993b), the vertical eye movements observed in the dumping protocol illustrate the tendency of the VOR axis of rotation to align with either gravity (g) or an estimate of gravity (ĝ). Consider a subject tilted to the NU orientation following CW or CCW yaw rotations. If the VOR displays a tendency to align its rotation axis with the direction of gravity (g), the axisshift component should be exclusively torsional (Fig.12 A,Ashift_{1} ). Alternatively, if the VOR exhibits a tendency to align its rotation axis with the direction of the estimate of gravity (ĝ), the corresponding axisshift component (Fig. 12 A, Ashift_{2} ) should include a secondary vertical axisshift component in addition to the torsional component. For both CW and CCW directions of rotation, the postrotatory secondary vertical VOR component should be positive (downward) for the NU orientation (Fig. 12 A) and negative (upward) for the ND orientation (Fig. 12 B).
As shown (Fig. 10), the sinusoidal fits to the vertical VOR data for CW and CCW rotations are phase shifted with respect to one another, with a phase shift smaller than 180°. This experimental phase shift is better matched by the predicted phase shift when the VOR rotation axis aligns with the estimate of gravity (ĝ, Fig.12 D) rather than gravity (g, Fig.12 C). In particular, if the VOR rotation axis aligns with gravity (g), no vertical eye movement should be present for NU and ND orientations (Fig. 12 C, orientation angle 0 and 180°, respectively). However, experimental results show that a small vertical VOR is present for both NU and ND orientations, consistent with an axisshift toward alignment with the estimate of gravity (ĝ), as opposed to alignment with gravity.
Conclusion
The GIF resolution hypothesis accurately predicts that postrotatory VOR eye movements recorded during dumping and barbecue protocols include an “induced” VOR component. The induced VOR component is consistent with the idea of a response compensatory to an internally generated neural estimate of linear acceleration even though no physical linear acceleration is present. The GIF resolution hypothesis accurately predicts the VOR and inducedVOR dependency with head orientation, direction, and speed of rotation. Alternative hypotheses, stating that the postrotatory VOR time constant depends on head orientation relative to the GIF or that gravity can be separated from linear acceleration by frequency segregation are not consistent with the various characteristics of the measured postrotatory VOR during dumping and barbecue protocols.
Acknowledgments
We thank S. ClarkDonovan and J. Roth for assistance throughout the data acquisition and analysis, P. Dimitri for advice on statistical analysis, and Dr. R. Lewis for comments on the manuscript.
This work was supported by a grant from the European Space Agency External Fellowship Program to L. H. Zupan, National Institute on Deafness and Other Communication Disorders/National Aeronautics and Space Administration Grant P60DC02072 to R. J. Peterka, and NIDCD Grants R29DC03066 and R01DC04158 to D. M. Merfeld.
Footnotes

Address for reprint requests: L. H. Zupan, Jenks Vestibular Physiology Laboratory, Suite 421, Massachusetts Eye and Ear Infirmary, 243 Charles St., Boston, MA 02114 (Email:lionel_zupan{at}meei.harvard.edu).

↵1 Indeed, the tilt angle (α̂) of the estimate of linear acceleration with respect to earthhorizontal can be approximated as α̂ = arctan (iVOR_{LDRD}/iVOR_{NUND}), where iVOR_{LDRD} is the induced VOR component for the orientation pair LDRD and iVOR_{NUND}is the induced VOR component for the orientation pair NUND for a given rotation direction.

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 Copyright © 2000 The American Physiological Society