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Department of Neurology, University Hospital Zürich, CH-8091 Zurich, Switzerland; and Department of Surgery (Otolaryngology), University of Mississippi Medical Center, Jackson, Mississippi 39216
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Hess, Bernhard J. M. and Dora E. Angelaki. Kinematic principles of primate rotational vestibulo-ocular reflex. I. Spatial organization of fast phase velocity axes. J. Neurophysiol. 78: 2193-2202, 1997. The spatial organization of fast phase velocity vectors of the vestibulo-ocular reflex (VOR) was studied in rhesus monkeys during yaw rotations about an earth-horizontal axis that changed continuously the orientation of the head relative to gravity ("barbecue spit" rotation). In addition to a velocity component parallel to the rotation axis, fast phases also exhibited a velocity component that invariably was oriented along the momentary direction of gravity. As the head rotated through supine and prone positions, torsional components of fast phase velocity axes became prominent. Similarly, as the head rotated through left and right ear-down positions, fast phase velocity axes exhibited prominent vertical components. The larger the speed of head rotation the greater the magnitude of this fast phase component, which was collinear with gravity. The main sequence properties of VOR fast phases were independent of head position. However, peak amplitude as well as peak velocity of fast phases were both modulated as a function of head orientation, exhibiting a minimum in prone position. The results suggest that the fast phases of vestibulo-ocular reflexes not only redirect gaze and reposition the eye in the direction of head motion but also reorient the eye with respect to earth-vertical when the head moves relative to gravity. As further elaborated in the companion paper, the underlying mechanism could be described as a dynamic, gravity-dependent modulation of the coordinates of ocular rotations relative to the head.
To stabilize gaze in space during head movements, the vestibulo-ocular reflex (VOR) transforms head angular velocity into appropriate neural commands to rotate the eye at the same velocity but in opposite direction as the head. Alternating with slow compensatory phases, fast phases rotate the eye rapidly in the direction into which the head is moving and reorient at the same time the gaze line toward targets of potential interest in the visual field.
Eye movement recording
Four juvenile rhesus monkeys (Macaca mulatta) were prepared chronically with a scleral dual-search coil for 3-D eye movement recording and head bolts for restraining the head during the experiment. Details of fabrication, implantation, and calibration of the dual-search coil have been reported elsewhere (Hess 1990 Experimental protocols
During the experiments, animals were seated in a primate chair with their heads restrained in a position of 15° nose-down relative to the stereotaxic horizontal and placed inside the inner frame of a multiaxis turntable with three motor-driven gimbaled axes. The experimental protocols consisted of earth-horizontal axis rotations (in complete darkness) at constant positive or negative speeds of 58, 110, and 184°/s, starting always with the animal in supine position. The order in which the animals were rotated through the four cardinal head positions was: supine, left-ear down, prone, and right-ear down for a positive yaw rotation, and the reverse for a negative yaw rotation. For each VOR record (each of the positive and negative rotational speeds were repeated once or twice in each animal), 5-20 cycles were included in the analysis.
Data analysis
After eye positions had been expressed in the standard head-fixed coordinates (relative to upright primary position), data records were divided for each head revolution into 12 sectors (S1, S2, ··· S12) of 30° width each. These sectors, which were spaced equally throughout each stimulus cycle, were shifted relative to the onset of each cycle by Spatial and dynamic properties
During yaw rotation about an earth-horizontal axis, the fast phase axes of vestibular nystagmus were fanning-out relative to the z axis in a systematic, head position-dependent manner. The basic finding is illustrated in Figs. 1 and 2: Fig. 1 shows a typical record of torsional, vertical, and horizontal eye position during yaw rotation at 184°/s about an earth-horizontal axis. Although the horizontal response component exhibited an almost uniform nystagmus throughout each cycle, there was a large modulation of mean torsional and vertical eye position that was primarily due to alternating positive and negative fast phases (Angelaki and Hess 1996
Effects of eye position on the spatial orientation of fast phase velocity
The exact spatial orientation of the angular velocity vector of a fast phase movement depends on orbital eye position (due to the cross vector product E Influence of head position on main sequence properties of fast phases
To investigate whether not only the spatial orientation but also the metrics of fast phases were modulated by otolith inputs, we computed the amplitude, duration, peak velocity, and time-to-peak velocity of fast phases during ±184°/s rotations as a function of head orientation relative to gravity. As shown in Fig. 5 where these parameters have been plotted for the data set of Fig. 2-4 (negative head rotation), there was little influence of head position on duration or time to peak velocity of fast phases. However, peak fast phase velocity was modulated with head position showing a significant decrease close to prone position (Fig. 5, bottom). This effect was independent of the direction of head rotation. In parallel to peak velocity, fast phase position amplitudes also were modulated as a function of head position relative to gravity. Average amplitude and peak velocity values of pooled fast phases have been plotted separately for positive and negative rotations in Fig. 6, A and B. Even though the minimum of average fast phase amplitude and peak velocity correlated well with prone position, the dependence on head position did not follow a single sinusoidal function (values peaked approximately between right or left ear-down and supine position). This was in contrast to the simple sinusoidal dependence of the spatial orientation of mean fast phase velocity axes on head position (Fig. 3). In fact, peak velocity and amplitude of fast phases were correlated linearly such that there was no resultant effect of gravity on the main sequence of fast phases (Fig. 6C).
Spatial organization of fast phase axes: dependence on rotation speed
These observations demonstrate that there is a profound effect of gravity on the spatial organization of VOR fast phase axes even though there seems to be no change in their dynamic properties. The specific gravity effect on VOR fast phase velocity axes can be described as follows: in addition to a fast phase velocity component along the axis of head rotation, a velocity component is also systematically present along the direction of gravity. This latter component is directed oppositely to gravity such that there is a systematic trend for the velocity axes to be oriented vertically in space.
Gravity-induced dynamic modulation of oculomotor coordinates
In this paper, we have investigated the 3-D organization of fast phase velocity axes of the horizontal vestibulo-ocular reflex. During head movements, vestibular signals determine the angular velocity of slow phases such that the eyes closely match head velocity (with opposite polarity) to compensate for the movement and to stabilize the gaze lines relative to space. Fast phases, on the other hand, do not simply reset the eye in the direction of head rotation: we have shown here that fast phase axes of the vestibulo-ocular reflex exhibit, in addition, a significant component parallel to the direction of gravity. In fact, fast phase axes are tilted systematically away from the axis of head rotation due to a tendency to be maintained vertically oriented in space. The dynamic dependence of fast phase velocity axes on gravity is a function of movement speed (which, in these experiments, is equivalent to the frequency of a sinusoidal modulation of gravity). The faster the head moves in space, i.e., the higher the frequency, the greater is the gravity-dependent tilt of fast phase velocity axes (Fig. 7).
Comparison of the effects due to shifting the oculomotor range versus changing the reference system
To show this, we adopt, for simplicity, a description of fast phases as fixed-axis rotations that carry the eye rapidly from one fixation position, E1, to the next fixation position, E2, i.e., we use the formula: E(t) = E1 +
Neurophysiological substrate of a dynamically changing coordinate system in the generation of fast phases
If gaze control signals in the VOR indeed are coded with respect to space and the direction of gravity, we would assume that the underlying transformations occur at a relatively early stage in processing sensory inputs to motor output. Based on available experimental evidence, we cannot exclude that the superior colliculus plays a role in this process. It recently has been reported that the collicular code of saccade direction depends on head orientation, raising the possibility that this structure receives a gravity-dependent bias signal from sites downstream in the brain stem (Frens et al. 1996b
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
; Ron et al. 1972). Moreover, the same cells in the paramedian pontine reticular formation and in the rostral interstitial nucleus of the medial longitudinal fascicule were found responsible for the generation of saccades and fast phases of nystagmus (Bender and Shanzer 1964; Büttner et al. 1977; Henn et al. 1984; King and Fuchs 1979). Permanent or reversible lesions of these structures affected both fast phases and saccades to the same extent (Crawford and Vilis 1992; Suzuki et al. 1995; Vilis et al. 1989).
; Misslisch et al. 1994). Studies in the monkey have suggested further that VOR fast phases limit deviations of compensatory slow phase movements with respect to these constraints (Crawford andVilis 1991).
). Part of this work has been reported in short communications (Hess and Angelaki 1995, 1997a).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
; Hess et al. 1992). Horizontal, vertical, and torsional eye positions were digitized with 12 bit resolution at a sampling rate of 833 Hz and expressed as rotation vectors, E = tan (
/2) u, where u is a unit vector pointing along the rotation axis of the eye, and is the angle of rotation about u (Haustein 1989). The components of eye position vectors were smoothed and differentiated using quadratic 31-point Skavitzky-Golay filters (Press et al. 1992). The eye angular velocity vector, 
, was computed from the eye position vector, E, and the rate of change in eye position, 
, according to the equation: = 2( + E 
)/(1 + 
E2). This equation captures in simple geometric terms the eye position dependence of eye angular velocity when the monkey looks away from primary position (see also Tweed and Vilis 1987). In contrast to 3-D eye positions that define the (virtual) rotation of the eye relative to a reference position (usually primary position), angular velocity vectors describe the instantaneous orientation of the rotation axis of the eye. The following analysis focuses on these angular velocity vectors.
, scaled by a factor of 2, with the angular velocity, .1 Listing's plane and primary eye position were determined from spontaneous eye movement data in the light with the head upright and stationary. Rotation vectors were expressed relative to a right-handed coordinate system where the x axis was aligned with primary gaze direction (positive x direction is forward) and the y and z axes were lying in Listing's plane (positive y and z directions are leftward and upward, respectively). This standard coordinate system was aligned closely in all four animals with the head roll, pitch. and yaw coordinates (i.e., magnetic field coordinates; for the animal's head posture, see below) being rotated downward by 
6° and leftward or rightward by <2°. According to the right-hand rule, a positive torsional component corresponded to a rotation of the upper pole of the eye toward the right ear, a positive vertical component corresponded to a downward rotation, and a positive horizontal component corresponded to a leftward rotation.
15°. The sectors corresponding to the four cardinal head positions were sector S1, centered around supine (i.e., from 15 to 15°); sector S4, centered around right ear-down (i.e., from 75 to 105°); sector S7, centered around prone (i.e., from 165 to 195°); and sector S10, centered around left ear-down position (i.e., from 255 to 285°). Fast phases of nystagmus were isolated from slow phase segments based on amplitude and time windows that were set for the second derivative of the magnitude of the eye velocity vector and interactively checked by visual inspection of the signals on a graphic screen. This derivative was computed numerically using a quadratic 11-point Savitzky-Golay smoothing filter (Press et al. 1992).
; Press et al. 1992).
11 = (E2 E1 + E1 E2)/(1 + E1·E2) ("°" denotes multiplication of rotation vectors, denotes the cross vector product, and · denotes the scalar product) (see e.g., van Opstal 1993).
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
). In the following, we focus our analyses on the 3-D orientation of the rotational axes of the eye during these fast phases, i.e., on the angular velocity vectors of nystagmus fast phases. Figure 2 illustrates three different views of fast phase eye velocity vectors. The fast phases have been extracted from nystagmus elicited by either positive (i.e., supine 
left ear-down, etc.; from same data record as in Fig. 1) or negative (i.e., supine right ear-down, etc.) head rotations at 184°/s. For clarity, only four groups of fast phases have been displayed according to the respective sectors of nystagmus to which they belonged2: a first group comprises all fast phases from the sectors corresponding to head positions centered around supine position (green trajectories), a second group comprises all fast phases from the sectors around left ear-down position (yellow trajectories), a third group comprises all fast phases from sectors centered around prone position (red trajectories), and finally a fourth group comprised all fast phases collected from the sectors centered around right ear-down position (blue trajectories). Fast phases from both directions of rotation have been superimposed in the side and front views of Fig. 2, A and B. Because a constant slow phase velocity of ~80°/s was generated during constant-velocity yaw rotation at 184°/s, the baselines were shifted by adding 80°/s to positive-going fast phase trajectories (see Fig. 2, A and B, top quadrants) or subtracting 80°/s from negative-going fast phase trajectories (see Fig. 2, A and B, bottom quadrants), to avoid overlap at the coordinate origin. The top view plots illustrate results for positive and negative rotations separately and show that the velocity components in the yaw plane rotated in the same direction as gravity (see curved arrows in Fig. 2C).
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FIG. 1.
Vestibulo-ocular reflex elicited by constant-velocity yaw rotation. Torsional (Etor), vertical (Ever), and horizontal (Ehor) eye position as a function of head orientation relative to gravity during constant-velocity yaw rotation (184°/s) about an earth-horizontal axis (barbecue spit rotation, see inset). H, head position (potentiometer output reset every 360°); pro, prone; red, right ear-down; sup, supine; led, left ear-down position.
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FIG. 2.
Spatial orientation of fast phases of nystagmus elicited by constant-velocity rotation at +184 and 184°/s about an earth-horizontal axis. Fast phase velocities of nystagmus obtained from positive (supine left ear-down) and negative (supine right ear-down) head rotations are displayed in A and B in the same plot and in C in separate plots. All fast phases generated within restricted time windows of 163 ms (=30°/184°/s) around supine position (sup, green trajectories), left ear-down (led, yellow trajectories), prone (prone, red trajectories), and right ear-down position (red, blue trajectories) were pooled. A: side view (z-x plane). Fast phase velocity trajectories with positive z components were tilted forward and backward, respectively, for head positions around supine and prone position. Fast phase trajectories with negative z components were tilted oppositely. There was little tilt of fast phase trajectories in the pitch plane for right and left ear-down head positions. B: front view (z-y plane). Around ear-down positions, fast phases with positive/negative z components were tilted toward the contra-/ipsilateral ear in the roll plane. C: top view (y-x plane). Fast phase velocity components rotated in the yaw plane in the same direction as gravity (curvilinear arrows). Note that gravity rotated in the opposite direction relative to the head as the head rotated relative to space.
); rotation at 184°/s (
)]. As the head rotated, they described two conical surfaces centered around the axis of head rotation (z axis) and oriented in opposite directions. The vertex of each of these cones coincided with the origin of the coordinate system (because offsets due to the slow phase velocity baseline are not shown).
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FIG. 3.
Spatial orientation of fast phase velocity vectors as a function of head orientation. A: side, front, and top view (top to bottom) of average directions of pooled fast phase velocity vectors in each of the 12 sectors. Each dot represents the arrow head of a normalized velocity vector. During positive head rotation, fast phases had a positive velocity component along the z axis ( ) and changed their orientation in the yaw plane (y-x plane) in the clockwise direction (arrow head). Opposite was true for fast phases elicited during a negative head rotation ( and arrow head). B: modulation of normalized fast phase velocity components (i.e., direction cosines) as a function of head position. The kz component showed little variation. The kx and ky components were modulated approximately in phase quadrature as expected from the circular path traced out in the y-x plane. Peaks of modulation coincided approximately with supine/prone (sup/prone) and ear-down (red/led) positions for both directions of rotations (184°/s: ; 184°/s: ). Means ± SD from bootstrap analysis of data plotted in Fig. 1 and 2. For illustration purposes, the normalized velocity vectors have been plotted relative to 0 rather than relative to the respective nonzero slow phase velocity baselines of the nystagmus.
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FIG. 4.
Average orientation of normalized fast phase velocity vectors in the yaw plane. A: comparison of the spatial orientation of fast phase velocity vectors estimated by a straight line fit and the average spatial orientation of peak velocities for each sector. Data points represent the fitted direction cosines of fast phase trajectories ( ) and the average direction cosines of peak velocities () for each of the 12 sectors. B: comparison of spatial orientation of angular velocity and rate of change of fast phase eye position vectors ( and , respectively). Data from positive (left side) and negative (right side) head rotations at 184°/s (as in Fig. 2 and 3).
in the equation of angular eye velocity, ). The effect, being of second order in eye position and velocity (i.e., involving products of the form Eij where Ei < 1 rad), is generally small. To exclude the possibility, however, that the observed dependence was merely due to an eye position effect, we computed the rate of change of eye position, , for fast phase trajectories (see METHODS). Comparison of the estimated spatial orientation of both and (in the x-y plane) demonstrates that modulation of average eye position could not be the major factor in the fanning-out phenomenon of fast phase directions (Fig. 4B).
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FIG. 5.
Duration, time-to-peak velocity, and peak velocity of vestibulo-ocular reflex (VOR) fast phases as a function of head position. Data obtained from 1 animal during constant-velocity yaw rotation at 184°/s (also plotted in Fig. 2-4).
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FIG. 6.
Amplitude and peak velocity of fast phases of nystagmus as a function of head position. A and B; average amplitude (±SD) and average peak velocity (±SD) of VOR fast phases from 3 animals during yaw rotation at ±184°/s were reduced in prone as compared with supine head position for both directions of head rotation. For clarity, data points are shifted along the abscissa. C: correlation between peak velocity and amplitude of nystagmus fast phases elicited by ±184°/s yaw rotation. Same data points as in A and B. 
, straight line fit, y = a + bx, with a = 65°/s and b = 20 s1.
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FIG. 7.
Dependence of spatial orientation of fast phase velocity vectors on speed of head rotation. A: modulation of kz, ky, and kx components of normalized fast phase velocity vectors during positive head rotations (+, supine left ear-down, etc.) at 3 different speeds are plotted as a function of head position. B: modulation of fast phase velocity vectors during negative head rotations (, supine right ear-down, etc.) at 3 different speeds. Degree of modulation of each component increased with the speed of head rotation. Responses were approximately symmetric for the 2 directions of rotation. Means ± SD from 4 animals (for clarity, shown only for the lowest and highest speed.
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FIG. 8.
Tilt of fast phase velocity vectors as a function of frequency (i.e., rotational speed). Average modulation of the kx and ky components of normalized fast phase velocity vectors was obtained by fitting sine waves to the data shown in Fig. 7 separately for each animal. Data shown are means ± SD of these fitted values for all 4 animals. Amplitude of modulation of the direction cosines kx and ky increased linearly with rotational speed. Regression coefficients of the fitted straight line, k = a* 
+ b, were: ax = 0.95 s (slope) and bx = 0.017 (offset) for the x component and ay = 1.13 s (slope), by = 0.002 (offset) for the y component. Note that a rotational speed of 180°/s corresponds to a rotation frequency of 0.5 Hz.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
). Such a gravity-dependent behavior of VOR fast phases seems to be a property that is not limited only to primates. In fact, similar observations regarding spatial control of fast phases of horizontal and vertical nystagmus have been reported recently in rabbits (Pettorossi et al. 1995).
; Meier and Dieringer 1993; MelvillJones 1964). Our results show that fast phases exhibit an additional orienting function. Because the observed gravity-dependent velocity components are perpendicular to the yaw plane, they affect the vertical and torsional orientation of the eye in head. The results reported here suggest that fast phases are organized according to additional functional requirements that correlate with dynamic changes of head orientation relative to gravity. As will be shown in the companion paper (Hess and Angelaki 1997b), fast phase axes are oriented in local displacement planes, which appear to follow a generalized Listing's law and tend to remain space-fixed during head motion.
). Similarly, from static tilt experiments, we know that orbital eye position changes systematically as a function of head position relative to gravity (Crawford and Vilis 1991; Haslwanter et al. 1992). Based on the kinematic dependence of angular velocity on orbital eye position, one could speculate that the observed tilt in the angular velocity vector of fast phases was the result of these eye position changes. However, as demonstrated by the data illustrated in Fig. 4B and as expected based on theoretical grounds, eye position effects per se cannot explain the large tilts of the fast phase angular velocity axes.
), could be interpreted as the result of a vestibular mechanism that adjusts the primary orientation of the eye3 as the head moves in space. Let us hypothesize for the moment that the tilt of fast phase velocity axes reflects a direct effect of gravity on the reference system of ocular rotations, i.e., an effect on primary eye position. Unlike the negligible effects of eye position on angular velocity, a change of the reference system is bound to have an effect of the same order of magnitude on the orientation of angular velocity.
(t)(E2 E1), where (t) is a bell-shaped velocity profile (for details see Hepp 1990; Van Opstal 1993). With this model, it can be shown readily, for example, that a gravity-induced shift of the oculomotor range (in contrast to a reference change) by as much as 30° in downward direction would induce a change in the direction of fast phase velocities by only 15° in the pitch plane (Fig. 9A). The same holds true for a hypothetical shift of the oculomotor range in torsional direction by 30°, which would result in a change of the direction of fast phase velocities in the roll plane by only 15° (Fig. 9B). Thus based on these kinematic relations between eye position and velocity, which have been known since von Helmholtz (1867), and the estimated shifts in the vertical and torsional oculomotor range (±10° on average) (see Angelaki and Hess 1996), we hardly can explain the large tilt angles of fast phase velocities that we have observed (see Figs. 2, 3, 7, and 8).
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FIG. 9.
Effects of eye position and rotation reference on fast phase velocity. A and B: simulated changes in the spatial orientation of fast phase velocity as a function of a gravity-induced shift of the oculomotor range. Rotation reference is 0 (i.e., primary gaze direction is along the x axis). Top: front (z-y plane) and side views (x-z plane) of the same 3 arbitrary fast phase position trajectories after a downward (A) or positive torsional (B) shift of the oculomotor range by 30° (indicated by and ···). Bottom: front and side views of associated fast phase velocity vectors. Shift in eye position induced a change in the tilt of the fast phase velocity vectors in the pitch (A) or roll (B) plane by 15° (···). C and D: changes in spatial orientation of fast phase velocity as a function of a gravity-dependent change in the rotation reference. Top: front and side views of the same fast phases after a downward vertical (C) or positive torsional (D) change in the rotation reference by 30° (). Bottom: front and side views of associated fast phase velocity vectors. Reference change induced a change in the tilt of fast phase positions in the pitch (C) or roll (D) plane by 15° and a tilt of fast phase velocity vectors in the respective planes by 30° (···).
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parallel to the respective rotation axis in Fig. 9, C and D). Even though the primary effect corresponds to a rotation in the indicated directions, there is an additional rotation in an orthogonal direction reflecting the noncommutative algebraic property of 3-D rotations (for this, compare the respective orientations of fast phase trajectories in the top left of Fig. 9, A and C and in the top right of Fig. 9, B and D).4 This issue will be addressed in more detail in the accompanying paper (Hess and Angelaki 1997b), where we provide evidence that passive head motion in space seems indeed to change oculomotor coordinates as defined by a dynamically changing primary eye position.
). Other areas like the cerebellum, which receives input from the motor layers of the superior colliculus through the nucleus reticularis tegmenti pontis and vestibular signals from the vestibular nuclei, might be involved as well (van Opstal et al. 1996). We recently have shown that lesions of the nodulo-uvular lobe lead to persistent oscillations of torsional eye position and abolish dynamic otolith-ocular responses during constant-velocity head rotations (Angelaki and Hess 1994, 1995). These cerebellar lesions did not affect the static otolith-ocular reflexes, suggesting that the neural control of the torsional-vertical oculomotor coordinates is more involved. There is evidence that the midbrain interstitial nucleus of Cajal, which receives strong inputs from the vestibular nuclei (for review, see Brodal 1974), is the site of the torsional-vertical velocity-to-position integrator (Crawford et al. 1991; Fukushima et al. 1990; King et al. 1981). This structure receives inputs from the rostral interstitial nucleus of the medial longitudinal fascicule where short-lead burst neurons are located that generate torsional and vertical eye position signals (King and Fuchs 1979; Vilis et al. 1989). It is a common understanding that these structures are organized in head-fixed coordinates (Büttner et al. 1977; Robinson and Zee 1981; Crawford and Vilis 1992). Based on our behavioral findings, one could speculate that these neurons are in fact organized in a reference system that is modulated by static and dynamic otolith input. Interestingly, lesions of these neuronal populations result not only in oculomotor deficits but also in changes of head posture, indicating that these structures may be involved more generally in gaze control (for a recent review, see Fukushima 1987).
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ACKNOWLEDGEMENTS |
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This work was supported by grants 31-32484.91 from the Swiss National Science Foundation, EY-10851 from the National Eye Institute, NAGW-4377 from the National Aeronautics and Space Administration, F49620 from the Air Force Office of Scientific Research, and 95-25 from the Roche Research Foundation.
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FOOTNOTES |
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1
For a fixed axis rotation E = tan (/2) u, the rate of change of eye position is dE/dt = d/dt(tan /2 u) = (
/2) (1 + E2) u. Therefore, the exact scaling factor is 2/(1 + E2) = 2 cos2 /2 
2 for small . Notice that only the angular velocity vector, , always is oriented along the instantaneous rotation axis of the eye. Its magnitude is equal to angular velocity. The vector of rate of change of eye position, , on the other hand, may deviate from the instantaneous rotation axis of the eye (see Goldstein 1980).
2
Fast phases straddling the sector borders were truncated. Such truncations, however, did not affect appreciably the displacement plane fits.
3
The primary orientation of the eye can be defined when the head is stationary and upright by specifying the orientation of Listing's plane and primary eye position in which the gaze line is orthogonal to Listing's plane. Primary eye position determines the point of zero rotation as well as the orientation of the horizontal, vertical, and torsional rotation axes.
4
This additional rotation is due to the cross-vector product in the formula for multiplication of rotation vectors (see formula in last paragraph of METHODS). If the rotations were expressed as rotation matrices R1(t) and R2(t), it would be proportional to the matrix C = R1R2 R2R1, which is obviously more difficult to interpret in geometric terms.
Address for reprint requests: B.J.M. Hess, Dept. of Neurology, University Hospital Zürich, Frauenklinikstrasse 26, CH-8091, Zurich, Switzerland.
Received 4 February 1997; accepted in final form 18 June 1997.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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This article has been cited by other articles:
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J. D. Crawford, D. B. Tweed, and T. Vilis Static Ocular Counterroll Is Implemented Through the 3-D Neural Integrator J Neurophysiol, October 1, 2003; 90(4): 2777 - 2784. [Abstract] [Full Text] [PDF]
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S. B. Yakushin, T. Raphan, and B. Cohen Gravity-Specific Adaptation of the Angular Vestibuloocular Reflex: Dependence on Head Orientation With Regard to Gravity J Neurophysiol, January 1, 2003; 89(1): 571 - 586. [Abstract] [Full Text] [PDF]
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D. E. Angelaki, S. D. Newlands, and J. D. Dickman Inactivation of Semicircular Canals Causes Adaptive Increases in Otolith-Driven Tilt Responses J Neurophysiol, March 1, 2002; 87(3): 1635 - 1640. [Abstract] [Full Text] [PDF]
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