Download Vestibular Contributions to Gaze Stability During Transient Forward

J Neurophysiol 90: 1996 –2004, 2003.
First published May 28, 2003; 10.1152/jn.00302.2003.
Vestibular Contributions to Gaze Stability During Transient Forward and
Backward Motion
Bernhard J. M. Hess and Dora E. Angelaki
Department of Neurology, University Hospital Zurich, CH-8091 Zurich, Switzerland; and Department of Neurobiology,
Washington University School of Medicine, St. Louis, Missouri 63130
Submitted 28 March 2003; accepted in final form 13 May 2003
Translational disturbances of the head and body elicit shortlatency vestibuloocular reflexes that help to stabilize gaze in
space, known as the translational (or linear) vestibuloocular
reflex (TVOR) (Angelaki and McHenry 1999; Busettini et al.
1994; Gianna et al. 1997; McHenry and Angelaki 2000; Paige
and Tomko 1991a,b; Schwarz and Miles 1991; Schwarz et al.
1989; Telford et al. 1997). Because no single eye movement
could generally result in stabilization of the whole visual field,
the TVOR is organized such that it cares to stabilize images on
the fovea (Angelaki and Hess 2001; Angelaki et al. 2003). In
addition, motion parallax dictates that the amplitude of the eye
movement required to maintain fixation should be inversely
proportional to viewing distance during translation. Thus sim-
ple geometrical calculations dictate that eye movements during
translation should be scaled by a signal related to a neural
estimate of the inverse of target distance as well as a signal
proportional to a sinusoidal function of monocular eye position. Behavioral studies have indeed shown that vestibularly
evoked eye movements are organized to reflect these geometrical requirements, not only during lateral and fore-aft motion
(McHenry and Angelaki 2000; Paige and Tomko 1991b; Seidman et al. 1999) but also along in-between heading directions
(Angelaki and Hess 2001; Tomko and Paige 1992).
Even though the TVOR has been shown to depend on
viewing distance, this scaling is less than optimal (Schwarz and
Miles 1991; Schwarz et al. 1989; Telford et al. 1997). As a
result, gains are typically lower than unity and eye velocity is
undercompensatory during near target viewing (Angelaki et al.
2000; Paige and Tomko 1991a,b; Schwarz and Miles 1991;
Schwarz et al. 1989; Telford et al. 1997). These conclusions
were typically drawn based on an analysis of velocity gains,
that is, through a comparison of the instantaneous velocity of
the eye relative to ideal velocity that would keep images stable
on the retina. In addition, almost all previous studies have
concentrated on small sinusoidal perturbations, requiring small
eye movements to keep images stable on the fovea. Using such
velocity analysis during high-frequency sinusoidal movements,
it was found that although version (i.e., conjugate) velocity
gains are strongly undercompensatory, vergence velocity was
compensatory with gains near unity (Angelaki and Hess 2001;
McHenry and Angelaki 2000). These results were interpreted
to suggest that the TVOR’s goal is to minimize binocular
disparities and optimize binocular coordination during movements along forward/backward headings. However, how these
velocity gains relate to the limits of monocular visual acuity
and binocular fusion during natural motions consisting of transient motion profiles and whether these suboptimal TVOR
behaviors are still consistent with an efficient and effective
visual acuity and stereoacuity remain unknown. Finally, the
role of the TVOR and the quality of gaze stability during
transient forward motions, which are the most commonly experienced head and body movements in everyday life, have
remained uncharacterized. It is possible, for example, that,
through a selective evolutionary process, the visual consequences of forward movements are better anticipated and com-
Address for reprint requests: B.J.M. Hess, Neurology Dept, University
Hospital Zurich, Frauenklinikstrasse 26, CH-8091 Zurich (E-mail:
[email protected]).
The costs of publication of this article were defrayed in part by the payment
of page charges. The article must therefore be hereby marked ‘‘advertisement’’
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
INTRODUCTION
1996
0022-3077/03 $5.00 Copyright © 2003 The American Physiological Society
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Hess, Bernhard J. M. and Dora E. Angelaki. Vestibular contributions to gaze stability during transient forward and backward motion.
May 28, 2003J Neurophysiol 90: 1996 –2004, 2003. First published
May 28, 2003; 10.1152/jn.00302.2003. The accuracy with which the
vestibular system anticipates and compensates for the visual consequences of translation during forward and backward movements was
investigated with transient motion profiles in rhesus monkeys trained
to fixate targets on an isovergence screen. Early during motion when
visuomotor reflexes remain relatively ineffective and vestibulardriven mechanisms have an important role for controlling the movement of the eyes, a large asymmetry was observed for forward and
backward heading directions. During forward motion, ocular velocity
gains increased steeply and reached near unity gains as early as 40 –50
ms after motion onset. In addition, instantaneous directional errors
also remained ⬍10° for forward headings. In contrast, backward
motion was characterized by smaller vestibular gains and larger
directional errors during the first 70 ms of the movement. To evaluate
the accumulated retinal slip and vergence errors during the early
epochs of motion when vestibular-driven mechanisms dominate gaze
stability, the movement of a virtual fixation point defined by the
intersection of the two gaze lines was quantitatively compared with
the respective movement of the extinguished target in head coordinates. Both conjugate retinal slip and vergence errors were ⬍0.2°
during the first 70 ms of the movement, with forward motion conjugate errors typically being smaller as compared with backward motion
directions. Thus vestibularly driven gaze stabilization mechanisms
can effectively minimize conjugate retinal slip errors as well as keep
binocular disparity errors low during the open loop interval of head
movement.
EYE MOVEMENTS DURING FORWARD/BACKWARD MOTION
pensated for by the TVOR. Because only small amplitude,
high-frequency sinusoidal stimuli have been used so far, the
role of vestibular signals in gaze stabilization for forward
versus backward movements has remained uncharacterized.
The present study aimed to investigate the vestibular contribution to binocular gaze stability during forward and backward movements using transient movement profiles. In particular, data analyses focused on the first 100 ms of motion during
which translational visuomotor reflexes remain relatively ineffective (Busettini et al. 1996b, 1997; Miles 1993, 1998;
Schwarz et al. 1989; Yang et al. 1999). To provide a quantitative assessment for the efficacy of the TVOR to compensate
for the visual consequences of translation, we used not only an
instantaneous velocity analysis but also a fixation position
analysis that would allow us to calculate the accumulated error
in retinal slip and disparity during the early epochs of motion
when vestibular-driven mechanisms dominate gaze stability.
Animal preparation and training
Three juvenile rhesus monkeys were implanted with a lightweight
delrin head ring that was anchored to the skull by stainless steel
screws and dual eye coils (Hess 1990) in each eye. Binocular threedimensional eye movements were recorded inside a fiberglass cubic
magnetic field frame of 16-in side length (CNC Engineering). Eye
movements were calibrated using both daily fixation routines as well
as preimplantation calibration values (Angelaki 1998; Hess et al.
1992). All animals were trained with juice rewards to fixate randomly
presented red light-emitting diode (LED) targets. Specifically animals
were trained to fixate targets paired with an auditory cue for variable
time periods (300 –1,000 ms), then to maintain fixation after the target
was turned off for as long as the auditory target was present (ⱖ250
ms). Adequate fixation was determined on-line by comparing binocular horizontal and vertical eye positions with ideal target position
windows of ⫾1–2°. The monkey was assumed to be fixating the target
binocularly when the right and left eyes fell within separate behavioral
windows whose center was computed based on the geometrical relationship between target distance, interocular distance (2.8 –3.2 cm),
and target eccentricity (see APPENDIX). Animals were usually trained 5
days/wk with free access to water on the weekend. All animal surgeries and experimental protocols were in accordance to Institutional
and National Institutes of Health guidelines.
Experimental setup and protocols
During vestibular testing, animals were rigidly secured to the inner
axis of a three-dimensional rotator mounted on a linear sled (Acutronics). Animals were secured with lap and shoulder belts to a
primate chair with their limbs loosely bound. In all experiments, the
head was statically pitched 18° nose-down from the horizontal stereotaxic plane. Special care was taken to rigidly couple the animal’s
head to the fiberglass inner gimbal of the motion delivery system, and
a head coil was used to ascertain that there was no head movement
signal during the motion (Angelaki et al. 2000). All presented targets
(13 total) were on a 20-cm isovergence array that was specifically
constructed with LEDs at 2.5° intervals (⬃⫾16° relative to a cyclopean eye). With an interocular distance of 3 cm, the 20-cm isovergence array would correspond to a vergence angle of 8.4°. Average
vergence angles, computed from right and left eye position for the last
10 ms of virtual fixation of the 13 targets (i.e., just before motion
onset) was 7.4 ⫾ 0.2°, 8.5 ⫾ 0.4°, and 8.9 ⫾ 0.8° in the three animals.
In all experiments, gaze elevation was less than ⫾1° of the horizontal
meridian.
J Neurophysiol • VOL
Translational stimuli consisted of step-like linear acceleration profiles, followed by a short period of constant velocity (peak linear
acceleration: 0.2 g; steady-state velocity 12 cm/s). These stimuli were
delivered along five different headings, including straight ahead, as
well as 15 and 30° to the left and to the right (30°L, 15°L, 0°, 15°R,
30°R). Each trial was initiated under computer control when the
animal had satisfactorily fixated a target on the 20 cm isovergence
screen for a random period of ⬃300 –1,000 ms. During all fixations,
the room was illuminated (through small red lights) such that the
animals could easily establish relative distance estimates of the targets. The target and background lights were extinguished immediately
before the onset of acceleration and remained off for the entire
motion. Within a random time of 2–20 ms after the target was turned
off, the stimulus profile commenced. Throughout the first ⬃250 ms of
movement, the auditory tone remained on to provide guidance for the
trained animals regarding the duration of the required fixation. Animals received a juice reward after completion of the movement. This
reward was contingent on the initial fixation of the target, and no
performance requirements were reinforced either during the movement or after the sled came to a stop. Intermingled runs where animals
were required to fixate, but no sled movement occurred were also
routinely used. In all experimental protocols, the direction of sled
motion (positive, negative, and no motion) and the target illuminated
were presented in a pseudorandom fashion. Intermingled between
days of experimental sessions were additional training sessions that
were identical to the pretraining sessions (with animals stationary)
such that animals continued to be trained to fixate and maintain
fixation under the auditory tone guidance for a minimum of 1 s after
the target light was turned off.
Demodulated eye coil signals and the outputs of a three-axis accelerometer (rigidly attached to the fiberglass members to which the
magnetic field coil assembly and the animal’s head were firmly
attached) were anti-alias filtered (200 Hz, 6-pole low-pass Bessel).
The signals were digitized at 833.3 Hz (Cambridge Electronics Design, model 1401 plus, 16-bit resolution) and stored for off-line
analysis.
Data analyses
Binocular, three-dimensional (3-D) eye position was computed as
rotation vectors (Haustein 1989) with straight ahead as the reference
position. All three components of the calibrated eye position vectors
were smoothed and differentiated with a Savitzky-Golay quadratic
polynomial filter (Press et al. 1988; Savitzky and Golay 1964). Angular eye velocity was computed accordingly (Hepp 1990) and expressed as vector components in a head-fixed, right-handed coordinate
system, as defined in the 18° nose-down position (typical position of
all animals during experiments). Torsional, vertical, and horizontal
eye position and velocity were the components of the eye position and
eye velocity vectors along the naso-occipital, interaural and vertical
head axes, respectively. Positive directions were clockwise (as viewed
from the animal, i.e., rotation of the upper pole of the eye toward the
right ear), downward, and leftward for the torsional, vertical, and
horizontal components, respectively.
An automated analysis routine displayed each experimental run
sequentially and allowed the experimenter to select only saccade-free
runs to be included for grand averages constructed in each animal for
each heading direction and each target on the isovergence screen.
Horizontal left and right eye position and velocity at different times
after motion onset was then calculated from these grand-averages (5
heading directions, backward/forward motion and 13 different targets
positioned at 2.5° intervals along the horizontal isovergence screen)
and used for subsequent analyses. In this study, the analyses focused
on horizontal eye position (␪r, ␪l) and velocity (␪˙r, ␪˙l) because the
fixation targets were all in the horizontal plane, i.e., vertical eye
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METHODS
1997
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B.J.M. HESS AND D. E. ANGELAKI
position during fixation of these targets was close to zero. Head
velocity and position was computed by integrating the output of a 3-D
linear accelerometer that was mounted close to the animal’s head
using the trapezoidal rule. Positive linear acceleration and velocity
was defined to be rightward and backward for the y and x components
of the linear accelerometer output, respectively.
The instantaneous velocity gain analysis was similar to that previously performed for
sinusoidal motion stimuli (Angelaki and Hess 2001). As presented in
detail in the APPENDIX, the time-varying horizontal eye velocity of each
eye [␪˙(t) or ␪˙(t)] can be computed as a function of head velocity, ␯F,
the respective eye-to-target distance [dRF(t): right eye to fixation point
distance; dLF(t): left eye to fixation point distance] and the sine of the
difference between the gaze angle (␪r or ␪l) and heading direction
(␣F), as follows (Fig. 1A)
INSTANTANEOUS EYE VELOCITY ANALYSIS.
␯F
␪˙ r ⫽
sin共␪r ⫺ ␣F兲 and
dRF
␯F
␪˙l ⫽
sin共␪l ⫺ ␣F兲
dLF
(1)
RESULTS
Geometrical dependence of horizontal eye velocity on gaze
and heading directions
FIG. 1. Geometrical relations between head motion and gaze during stable
fixation of a target, F, in the horizontal plane as a subject was moving along
direction ␣ with velocity v ⫽ vhead, with components ẋhead and ẏhead. A: the
coordinates (xF, yF) of target F, defined by the Fick angles of the right (␪r) and
left eye (␪l), change relative to the right eye as indicated. B: the spatial
deviation of the virtual fixation point (F) from the target (T) was estimated
3
from the fixation-to-target point error vector, FT, that subtended the angles ␦R
and ␦L, as viewed from the right and left eye, respectively. At the initiation of
the movement, T ⫽ F, both lying on the same plane of fixation (PF) at t ⫽ 0.
At any given time during the motion, the intersection of the two gaze lines at
F correspond to a plane of fixation PF(t) that is in general different from that
of the target. ⌬, interocular distance; RT, right-eye-to-target distance; RF,
right-eye-to-fixation point distance.
J Neurophysiol • VOL
Stabilization of a target on the fovea during translational
disturbances of the head depends on both the direction of linear
motion and the relative location of the target. The influence of
these two parameters on the TVOR is illustrated in Fig. 2 for
three different fixation targets and five different headings of
forward translation. To keep the effect of vergence on the VOR
constant, all targets were arranged on an isovergence screen
such that fixations subtended a constant vergence angle of
⬃8 –9° (see METHODS). When the animal was translated in a
direction that was nearly parallel to gaze direction, only a small
eye movement needed to be elicited to keep gaze on the
previously lit target during motion. For example, during
straight-ahead (0°) motion, the smallest eye velocity was observed for the central (green) target. In contrast, during forward
motion along a heading 15° to the left of straight-ahead (15°L),
the smallest eye velocity was observed for the leftward (red)
target. Similarly, during forward motion along a heading 15° to
the right of straight-ahead (15°R), the smallest eye velocity
was observed for the rightward (blue) target.
The more eccentric the gaze direction was relative to head-
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Using the nonlinear least-squares algorithm of Levenberg-Marquard
(Mathlab, MathWorks), Eq. 1 was fitted to the right and left eyevelocity data, sampled at different times after motion onset, and
plotted as a function of instantaneous eye position (␪r, ␪l). Thus
parameters ␯F and ␣F, representing the amplitude and heading direction of a virtual fixation point reconstructed from the motions of both
eyes, were computed at different times during the motion profile,
separately for each heading direction (but simultaneously for all 13
targets). Instantaneous velocity gain was then calculated as the ratio of
the computed value of ␯F over the actual instantaneous velocity of the
head. Similarly, the directional error of instantaneous velocity was
calculated as the absolute difference between the computed value for
␣F and the actual heading direction.
BINOCULAR EYE-POSITION ANALYSIS. The second set of analyses
was based on the actual displacement of the virtual fixation point as a
function of time during motion. Thus as explained in detail in the
APPENDIX, we computed the time-dependent path of the virtual fixation
point [xF(t), yF(t)] for each of the 13 fixations and each of the 5 ⫻ 2
heading directions (⫽ 130 different stimulus configurations). Similar
to the eye-velocity analyses, these computations were done on average
response profiles that were obtained from five or more single trials in
each stimulus configuration. We assumed that at time 0, the target and
fixation point coincided (T ⫽ F at t ⫽ 0; Fig. 1B), but that the virtual
fixation point defined by the intersection of the two gaze lines traced
a path, F(t), that in general differed from the relative target motion,
T(t). We then computed the angular position error of each eye (␦R, ␦L;
Fig. 1B) as the difference between actual and ideal eye position. From
these values, we also computed the conjugate (version) and disconjugate (vergence) position errors as (␦R ⫹ ␦L)/2 and ␦R ⫺ ␦L,
respectively. We also calculated the conjugate and vergence velocity
errors by taking the time derivatives using Savitzky-Golay quadratic
polynomial filters with a seven-point wide moving smoothing window. The reported conjugate position and velocity errors were calculated as the absolute value of (␦R ⫹ ␦L)/2 and (␦˙R ⫹ ␦˙L)/2. Vergence
position and velocity errors were positive, if the fixation point, F(t),
moved closer to the animal than the extinguished target, T(t). Accordingly, during forward motion, positive position errors would correspond to larger than expected increases in vergence angle. In contrast,
during backward motion, positive position errors corresponded to
smaller than expected decreases in vergence angle. These parameters
were used as a direct measure of the ability of the vestibular system
to anticipate the visual consequences of translation as a function of
time throughout the first 100 ms of motion.
All statistical comparisons were based on analyses of variance with
repeated measures.
EYE MOVEMENTS DURING FORWARD/BACKWARD MOTION
1999
ing direction, the larger was the elicited eye movement. For
example, forward motion along the 30°L heading elicited a
rightward (negative) rotation of both eyes with angular velocities that increased for the rightward-located targets (Fig. 2).
The opposite was true for heading directions to the right of
straight ahead, where the largest eye movement was seen for
leftward-located targets. To study these dependencies of eye
velocity on gaze and heading directions, we “sampled” the
instantaneous eye velocity at different times (e.g., 30, 50, and
70 ms shown in Fig. 2) after motion onset. We then computed
at those sampled times how well (in terms of both instantaneous velocity and displacement) the movement of a virtual
fixation point defined by the intersection of the two gaze lines
in the horizontal plane anticipated and followed the relative
motion of the extinguished target during translation. In the
presentation that follows, we will first present the results based
on the instantaneous velocity analysis, followed by those when
the actual fixation point trajectories were considered.
Instantaneous velocity gains and directional errors
The dependence of horizontal eye velocity on gaze and
heading directions is illustrated in Fig. 3, by plotting eye
J Neurophysiol • VOL
velocity 50 ms after motion onset for each of the 13 fixation
targets as a function of the corresponding eye position for the
five different heading directions (30°L, 15°L, 0°, 15°R, 30°R).
The graphs show that ocular velocity systematically increased
as a function of horizontal eye position for each eye. Furthermore, there was a horizontal equilibrium position for each eye,
i.e., a position for which head translation induced no eye
movement (i.e., zero velocity). This equilibrium position depended in a systematic way on heading direction. For example,
for heading straight ahead the equilibrium position was close to
straight-ahead for each eye (Fig. 3, short vertical dotted lines
for 0° heading). In contrast, during leftward heading, the equilibrium positions shifted leftward (positive eye position values). Similarly, during heading to the right, the equilibrium
positions shifted rightward (negative) eye positions. Such a
dependence on heading direction is a direct consequence of
Eq. 1.
To quantify the efficacy of the vestibular-driven instantaneous eye velocity in anticipating the visual consequences of
relative target motion as a function of time during the imposed
transient motion profiles, we computed the velocity amplitude
(␯F) and direction (␣F) of the movement of a virtual fixation
point defined by the intersection of the two gaze directions in
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FIG. 2. Eye- and head-movement profiles during forward motion along 5 different heading directions. Panels from left to right
show averages of horizontal eye and head velocity traces during heading 30° to the left (30°L), 15° to the left (15°L), straight ahead
(0°), 15° to the right (15°R), and 30° to the right (30°R) while fixating 1 of 3 targets ⬃15° to the left (red traces), straight ahead
(green traces), or 15° to the right (blue traces). Center: the 5 different heading directions and the three fixation targets schematically.
Data represent averages over 5 or more trials. Solid/dashed color traces denote right/left horizontal eye velocity, respectively. Black
traces illustrate head velocity (vel) and head acceleration (acc). Dashed vertical lines indicate 30, 50, and 70 ms after motion onset.
2000
B.J.M. HESS AND D. E. ANGELAKI
the horizontal plane (see METHODS and APPENDIX). Accordingly,
parameters ␯F and ␣F were calculated by fitting Eq. 1 to the
eye-velocity data simultaneously for all 13 fixation points but
separately for each of the 5 ⫻ 2 heading directions. This
analysis was performed at different times after motion onset
and separately for right and left eye velocity (Fig. 3, gray and
black solid lines, respectively). Ideally, if the animal maintained binocular fixation on the extinguished target during
motion, parameters ␯F and ␣F would be identical to the velocity
and heading direction of the imposed head motion. Thus an
instantaneous velocity gain was defined as the ratio of the
computed versus actual velocity. Similarly, a velocity directional error was defined as the absolute value of the difference
between the computed heading direction of the virtual fixation
point and the actual heading direction of the animal. Average
(⫾SD) values of the instantaneous velocity gains and directional errors measured at three different times (30, 50, and 70
ms) after motion onset have been plotted in Fig. 4 (F, 䡲, and
Œ, respectively). As parameters were independent on whether
right or left eye-velocity data were used for the computation
[␯F : F(1,40) ⫽ 0.2; ␣F : F(1,40) ⫽ 3.1, P ⬎ 0.05], values have
been averaged together.
Forward directions of motion were characterized by larger
instantaneous velocity gains than backward movements [␯F :
F(1,50) ⫽ 70.8, P ⬍ 0.05]. Backward motions were also
typically characterized by larger directional errors than forward
motions, particularly so early into the motion and for oblique
headings [␣F : F(1,50) ⫽ 10.8, P ⬍ 0.05]. Only at 70 ms after
motion onset were the directional errors for backward motions
as small as those during forward movements (⬃5°). The time
dependence of instantaneous velocity gain and directional errors is better illustrated in Fig. 5, A–C, which plots average
gains and directional errors for all heading directions in each
animal as a function of time after stimulus onset. A consistent
and significant asymmetry in velocity gains during forward and
backward motions was observed early into the motion
J Neurophysiol • VOL
FIG. 4. Instantaneous velocity gains and directional errors as a function of
heading direction at different times after motion onset during forward motion
(A) and backward motion (B). F, Œ, ■: 30, 50, and 70 ms after motion onset.
Error bars represent SDs. Data represent averages from all 3 animals.
[F(4,200) ⫽ 83.2, P ⬍ 0.05]. In all animals, velocity gains for
backward motion were small during the first tens of milliseconds after movement onset. In contrast, velocity gains for
forward motion increased sharply to a peak that was observed
⬃40 –50 ms after motion onset, reaching values as high as
FIG. 5. Instantaneous velocity gains and directional errors as a function of
time after motion onset. Data (means ⫾ SD) have been plotted separately for
each animal (A–C). F, U: forward/backward motion, respectively.
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FIG. 3. Dependence of instantaneous eye velocity on horizontal gaze direction. Right and left eye velocity (black and gray dots) 50 ms after motion
onset for each of the 13 targets has been plotted as a function of the respective
eye position separately for heading directions 30° to the left (30°L), 15° to the
left (15°L), straight ahead (0°), 15° to the right (15°R), and 30° to the right
(30°R). Positive numbers correspond to leftward eye positions. The black and
gray lines show the respective fits of Eq. 1. The long vertical line marks zero
eye position (0°); the short black and gray vertical lines mark the 0 crossing of
right and left eye velocity, respectively. The monkey head sketch (top view)
and arrows illustrate schematically the five heading directions.
EYE MOVEMENTS DURING FORWARD/BACKWARD MOTION
0.7–1. Velocity gains decreased slightly thereafter during forward headings, although they continued to increase for backward heading directions. Forward and backward gains were
similar beyond 80 ms into the movement. Directional errors
tended to be variable during the first tens of milliseconds after
movement onset but were generally similar for the two motion
directions thereafter.
Trajectories of fixation point and position error analyses
a function of time in Fig. 7, A and B. The corresponding
velocity errors have been illustrated in Fig. 7, C and D. Conjugate position errors 70 ms after motion onset averaged
0.10 ⫾ 0.06 and 0.14 ⫾ 0.08° for forward and backward
motion, respectively. Corresponding velocity errors were
3.2 ⫾ 1.9 and 4.3 ⫾ 2.4°/s. Both position and velocity errors
were larger during backward than forward motions [F(1,4) ⫽
18 and 27, P ⬍ 0.01].
Vergence errors were negative for forward motion and positive for backward motion. Thus during forward motion, vergence angle increased less than that required for binocular gaze
stability. During backward motion, vergence angle did not
decrease quickly enough for optimal binocular fixation on the
target. Vergence position errors 70 ms after motion onset
averaged ⫺0.09 ⫾ 0.07 and 0.07 ⫾ 0.04° for forward and
backward motions, respectively. Vergence velocity errors 70
ms after motion onset averaged ⫺1.9 ⫾ 1.9 and 2.3 ⫾ 1.6°/s
for forward and backward motions, respectively. The magnitude of vergence position and velocity errors were not significantly different for forward and backward directions
[F(1,4) ⫽ 0.4 and 0.01, P ⬎ 0.05].
DISCUSSION
The effectiveness of the VOR system to anticipate and
compensate for the visual consequences of translation during
forward and backward movements was for the first time investigated here using transient movement profiles in rhesus monkeys trained to fixate near targets. The present analyses, in
particular, focused on the first 100 ms of motion during which
visuomotor reflexes remain relatively ineffective and vestibular-driven mechanisms have an important role for controlling
the movement of the eyes. We used both an instantaneous
velocity gain and a fixation trajectory analyses that allow
calculation of the accumulated error in retinal slip and disparity. Results can be summarized as follows: first, the retinal slip
and vergence position errors that were accumulated during the
open-loop portion of the movement were small, in the range of
⬃0.1° (position) and ⬃2– 4°/s (velocity) 70 ms after motion
onset. Second, there was an initial gain asymmetry during
forward and backward headings. Specifically, instantaneous
velocity gains during forward motion increased steeply and
reached near unity gain values as early as 40 –50 ms after
motion onset. Instantaneous directional errors also remained
⬍10° for forward headings. In contrast, vestibular gains during
FIG. 6. Summary of fixation point spatial trajectories in
1 animal (same data as those of Fig. 1 and 2) during forward
motion (A) and backward motion (B). Colored traces illustrate average fixation point trajectories (0 –70 ms) for each
of the 13 targets and the five heading directions (as indicated by the monkey sketches and arrows). For easier
comparison across different targets, all 13 target trajectories
were aligned at time ⫽ 0 ms for each heading direction. The
color scale from blue to red symbolizes targets from right to
left. Solid gray lines and circles, the respective trajectories
of the target motion relative to the head; black lines and
circles, the mean fixation point trajectory for all 13 targets.
J Neurophysiol • VOL
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The instantaneous eye velocity analyses, as typically used in
VOR studies, are important to compute the instantaneous performance of the reflex. We were in addition interested in
characterizing the position and velocity errors that accumulate
as a function of time during motion. Thus for each heading
direction and target position, we calculated the trajectory followed by the virtual fixation point (defined by the intersection
of the 2 gaze lines) during the first 100 ms of motion. The
two-dimensional (2-D) spatial trajectories for all 13 targets
(aligned at the beginning of motion and plotted only for the
first 70 ms) have been summarized for the five heading directions separately for forward and backward headings in Fig. 6,
A and B, respectively. Typically, the fixation point underestimated the equivalent target trajectory as illustrated by comparing the mean fixation point trajectory with that of the target for
each heading (Fig. 6, compare thick black with gray lines and
circles). As expected from the lower velocity gains reported in
the instantaneous velocity analyses, this underestimation was
largest for backward movements (Fig. 6B). In addition, early
into the motion there was often a small movement of the
fixation point in the opposite direction from that of the target.
During backward 30°R motion, for example, an initial curvature in the trajectory was observed, as the virtual fixation point
first moved in the opposite direction from that expected based
on the relative target motion. In two of the three animals, this
initial movement in the wrong direction was typically small
and was quickly compensated by an eye movement, and thus a
fixation point trajectory, in the correct, compensatory direction.
The third animal, however, exhibited large initial anticompensatory movements.
From these trajectories we computed the absolute magnitude
of the conjugate retinal slip (version position and velocity
error) as well as the corresponding disconjugate (vergence
position and velocity) error at different times during the first
100 ms of motion. Average error values have been presented as
2001
2002
B.J.M. HESS AND D. E. ANGELAKI
during translation, visual stabilization mechanisms arise from
relatively low-level preattentive cortical processing that sense
the observer’s motion by decoding either the pattern of optic
flow (Busettini et al. 1997; Miles 1993, 1998; Miles and
Busettini 1992; Miles et al. 1991; Schwarz et al. 1989; Yang et
al. 1999) or depth and binocular disparity cues (Busettini et al.
1994, 1996a,b). However, these visually driven gaze stabilization mechanisms have latencies in the range of 50 – 80 ms,
leaving the vestibular system as the sole sensory information
source for gaze stabilization in the first ⬍70 ms of motion.
Conjugate and vergence errors during transient
forward/backward motions
backward motion were smaller and only approached near unity
gains 80 –100 ms into the motion.
Relationship to previous studies
Only a few studies have characterized the vestibular contribution to binocular gaze stability during forward and backward
translations. Most studies used high-frequency sinusoidal oscillations, stimuli that typically result in small eye excursions
(Angelaki and Hess 2001; McHenry and Angelaki 2000; Paige
and Tomko 1991b; Seidman et al. 1999). To our knowledge
only one study to date utilized more natural, transient forward
and backward motion stimuli, although analyses focused
mainly on response latencies (Angelaki and McHenry 1999).
In contrast to the relatively paucity of work addressing ocular
stabilization during forward/backward motions, several studies
have studied binocular eye movements during left/right motion
stimuli using both sinusoidal and transient profiles. During
lateral motion stimuli, numerous investigations have shown
that TVOR gains are strongly undercompensatory during near
target viewing (Angelaki and McHenry 1999; Angelaki 2002;
Busettini et al. 1994; Crane et al. 2003; Gianna et al. 1997;
McHenry and Angelaki 2000; Paige and Tomko 1991b; Ramat
and Zee 2002; Ramat et al. 2001; Schwarz and Miles 1991;
Schwarz et al. 1989; Telford et al. 1997; Zhou et al. 2002). In
contrast, high-frequency sinusoidal responses during different
heading directions exhibited vergence velocity gains that were
typically higher than the corresponding version velocity gains
(Angelaki and Hess 2001; McHenry and Angelaki 2000).
Transient VOR analysis presents several advantages over the
more commonly used sinusoidal stimuli. For example, transient movement profiles allow the quantification of the adequacy of gaze stabilization during the open-loop interval when
visual stabilization mechanisms are ineffective. Specifically
J Neurophysiol • VOL
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FIG. 7. Mean (solid lines) and associated SD (dotted lines) of vergence and
version position (A and B) and velocity (C and D) errors. These parameters
illustrate the effectiveness of vestibular-driven ocular compensation as a function of time during translation. Positive vergence errors illustrate larger vergence increases than expected during forward (solid black lines) motion and
less vergence decreases than expected during backward (solid gray lines)
motion. Data illustrated represent averages for all targets and heading directions (3 animals).
The main goal of the present study was to measure the
accuracy of the vestibularly-driven gaze stability during large
transient displacements in an attempt to determine if the less
than optimal TVOR gains would introduce errors that would
compromise visual acuity and binocular fusion. For this purpose, we quantified responses during the first 100 ms of motion
in complete darkness in animals trained to maintain vergence
on near isovergence targets. We found that 70 ms into the
motion, position errors remain ⬍0.2° and velocity errors ⬍4 –
5°/s, values that would be close to the range required for
maintaining good visual acuity. Specifically, Ludvigh (1949)
and Brown (1972) reported that good acuity is maintained with
a position error of 2–2.5°, values larger than the maximum
conjugate position errors present during the large transient
stimuli used here. Other studies have demonstrated that retinal
slip velocities lower than ⬃2–3°/s do not degrade visual acuity
(Demer and Amjadi 1993; Demer et al. 1994; Murphy 1978;
Steinman et al. 1973, 1982; Westheimer and McKee 1975).
Whereas monocular and conjugate retinal slip would be
within the limits of dynamic visual acuity, the vergence errors
observed seem to be incompatible with the very low threshold
observed in stereoacuity tests. Stereoacuity in standard stereoscopic tests is based on judgements of a set of relative distances
and have been reported to yield sensitivities typically in the
order of 10 s of arc (Ogle 1967; Sarmiento 1975). In our
experiments, we measured binocular position errors that would
be more analogous to the absolute disparity of a single imaginary target T (if it was visible). Disparity values observed
under such conditions cannot be compared with those obtained
in usual tests of stereoacuity because such tests rely on stimulus configurations that contain relative disparities. Stereoacuity thresholds for simultaneously presented line pair stereograms raise by about an order of magnitude if the lines are
presented successively at different absolute disparities (Foley
1976; Westheimer 1979). Steinman and Collewijn (1980) have
also shown that relative binocular image motion can be on the
order of 2°/s and still maintain clear and stable visual perception during natural head movements. Further studies of the
effects of instabilities of gaze and vergence have shown that
stereofusion and stereoacuity is preserved in the presence of
fast and large changes in vergence (Patterson and Fox 1984;
Steinman et al. 1985; see Collewijn et al. 1991 for a review).
Thus the vergence position and velocity errors reported here
suggest that vestibular mechanisms are capable to keep absolute disparities to a minimum, thus allowing for the slower
visual mechanisms to take over and to fine tune convergence
EYE MOVEMENTS DURING FORWARD/BACKWARD MOTION
2003
(during forward motion) or divergence (during backward motion) of the eyes.
Equation A3 can be expressed as functions of eye position (␪r, ␪l) and
the interocular distance (⌬) using Eq. A2.
Asymmetries between forward and backward motions
Estimation of heading velocity and direction from fixations
The significant difference in instantaneous velocity gains
between forward and backward motion might be related to a
functional adaptation of the vestibular system to the most
commonly experienced forward movements. This asymmetry
shows mostly in the mococular and conjugate response gains
but not in vergence position or velocity errors. To our knowledge, such a difference in gain during forward and backward
headings has never been reported previously. Largely asymmetric responses to different motion directions have been reported in the majority of translation-sensitive vestibular nuclei
neurons (Musallam and Tomlinson 2002). How and why these
asymmetries are introduced remains unknown. It is clear that
forward motion has a quite different biological meaning than
backward motion. Under normal visual conditions, during
translational motion it is most important to avoid blur of the
retinal image to facilitate evaluation of predictive information
about the distance to a target or object. During backward
motion, this information is less relevant because there is no
visible threat to bump into an object. This difference could
explain why the initial gain is larger during forward than
during backward motion. Despite these asymmetries and a
nonideal TVOR gain, the present results demonstrate that both
monocular and conjugate vestibular-driven mechanisms exist
that help to stabilize the eyes during the open-loop interval of
natural head movements and facilitate further stabilization by
slower visual mechanisms.
As the subject starts moving with heading velocity (␯) and direction
(␣), the motion of the target in head coordinates can be expressed as
In this section, we briefly summarize the steps necessary to compute the movement parameters of the virtual fixation point defined by
the intersection of the gaze directions of the two eyes as a function of
horizontal eye position (␪r, ␪l), the interocular distance, ⌬, as well as
the velocity (␯ ⫽ ␯head) and direction (␣) of the animal’s displacement. Equations will be presented in an orthogonal Cartesian coordinate system, with the x axis straight ahead relative to the right eye and
the y axis passing through the rotation centers of the right and the left
eye (Fig. 1).
Computing the fixation point coordinates from binocular
eye movements
Let xF and yF be the x-y coordinates of the fixation point (F) before
motion onset, as the animal fixated a target on a isovergence screen.
The tangent of eye position can thus be expressed as a function of xF
and yF, as follows (Fig. 1A)
tan ␪r ⫽
yF
xF
tan ␪l ⫽
and
yF ⫺ ⌬
xF
(A1)
Using these relations, the coordinates of the fixation point (xF, yF) can
be expressed as
xF ⫽
⌬
tan ␪r ⫺ tan ␪l
and
yF ⫽
⌬ tan ␪r
tan ␪r ⫺ tan ␪l
冑xF2 ⫹ yF2
and
dLF ⫽
冑xF2 ⫹ 共yF ⫺ ⌬兲2
yT共t兲 ⫽ yF ⫹ ␯ cos 共␣兲
(A4)
At motion onset we have: xT (t ⫽ 0) ⫽ xF, yT(t ⫽ 0) ⫽ yF, and ẋT(t ⫽
0) ⫽ v sin(␣), ẏT(t ⫽ 0) ⫽ v cos(␣). To derive a relationship for the
changes in horizontal eye movements that are required to maintain
fixation, we calculate first the time derivative of horizontal eye position, d/dt(␪T) ⫽ d/dt[tan⫺1 (yF/xF)], as a function of the (premotion)
fixation point using the relations (Eq. A1). Specifically, for the right
eye we obtain from the right-eye-to-target distance, dRF (Eq. A3), and
the relations sin ␪T ⫽ yF/dRF and cos ␪T ⫽ xF/dRF
ẏ F xF ⫹ ẋFyF ẏF cos 共␪r兲 ⫹ ẋF sin 共␪r兲
␪˙ r ⫽
⫽
2
d RF
dRF
(A5)
When the animal tries to keep fixation (i.e., T ⫽ F), the instantaneous
velocity and direction of the fixation point at motion onset is: ␯F ⫽
␯T ⫽ 冑ẋT2 ⫹ ẏT2 and ␣F ⫽ ␣T ⫽ tan⫺1(ẏT/ẋT). Introducing these relations into Eq. A5, we obtain (␪˙l can be derived analogously to ␪˙r)
␯F
␯F
␪˙ r ⫽
sin 共␪r ⫺ ␣F兲, ␪˙l ⫽
sin 共␪l ⫺ ␣F兲
dRF
dLF
(A6)
Equations A2–A6 describe implicitly the velocity (␯F) and direction
(␣F) of the fixation point as a function of right and left eye position (␪r,
␪l) and either the right or left eye velocity (␪˙r, ␪˙l) at motion onset.
Later into motion, they describe the motion of the virtual fixation
point in space and can be used to compute the animal’s estimate of
heading velocity and direction under the assumption that the animal
tried to maintain fixation during motion.
Error analysis of the virtual fixation point during translation
The spatial deviation of the virtual fixation point from the target
3
was estimated from the fixation-to-target point error vector, FT, that
subtended the angles ␦R and ␦L as viewed from the right and left eye
3
(Fig. 1B). Based on this vector FT, two errors, corresponding to
version and vergence, were computed. For this, we define the sign of
the angle ␦R (␦L) as positive if the cross product of the radius vectors
3
from the center of the right (left) eye to the virtual fixation point (RF,
3
3 3
LF) on the one hand and to the target (RT, LT,) on the other hand is
positive (Fig. 1B). The version error is defined as ␦vers ⫽ (␦R ⫹ ␦L)/2
whereas the vergence error was calculated as ␦verg ⫽ c| (␦R ⫺ ␦L) |/2
with c ⫽ ⫾1. The sign (c) of this error was chosen to be positive when
the plane of the virtual fixation point was closer to the animal than the
target plane (Fig. 1B). Thus during both forward and backward motion
a positive vergence error corresponded to a relative excess in vergence.
DISCLOSURES
This work was supported by grants from the National Institutes of Health
Grants EY-12814 and DC-04160, the Swiss National Science Foundation
(31-57086.99), and the Betty and David Koetser Foundation for Brain Research.
(A2)
From the coordinates of the fixation point we computed the right- and
left-eye-to-target distance (dRF, dLF) as follows
d RF ⫽
and
(A3)
J Neurophysiol • VOL
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APPENDIX
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