1Centre for Vision Research and Departments of Psychology and Biology, York University, Toronto, Ontario M3J 1P3; and 2Montreal Neurological Institute and Department of Neurology and Neurosurgery, McGill University, Montreal, Quebec H3A 2B4, Canada
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ABSTRACT |
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Crawford, J. Douglas, Melike Z. Ceylan, Eliana M. Klier, and Daniel Guitton. Three-dimensional eye-head coordination during gaze saccades in the primate. The purpose of this investigation was to describe the neural constraints on three-dimensional (3-D) orientations of the eye in space (Es), head in space (Hs), and eye in head (Eh) during visual fixations in the monkey and the control strategies used to implement these constraints during head-free gaze saccades. Dual scleral search coil signals were used to compute 3-D orientation quaternions, two-dimensional (2-D) direction vectors, and 3-D angular velocity vectors for both the eye and head in three monkeys during the following visual tasks: radial to/from center, repetitive horizontal, nonrepetitive oblique, random (wide 2-D range), and random with pin-hole goggles. Although 2-D gaze direction (of Es) was controlled more tightly than the contributing 2-D Hs and Eh components, the torsional standard deviation of Es was greater (mean 3.55°) than Hs (3.10°), which in turn was greater than Eh (1.87°) during random fixations. Thus the 3-D Es range appeared to be the byproduct of Hs and Eh constraints, resulting in a pseudoplanar Es range that was twisted (in orthogonal coordinates) like the zero torsion range of Fick coordinates. The Hs fixation range was similarly Fick-like, whereas the Eh fixation range was quasiplanar. The latter Eh range was maintained through exquisite saccade/slow phase coordination, i.e., during each head movement, multiple anticipatory saccades drove the eye torsionally out of the planar range such that subsequent slow phases drove the eye back toward the fixation range. The Fick-like Hs constraint was maintained by the following strategies: first, during purely vertical/horizontal movements, the head rotated about constantly oriented axes that closely resembled physical Fick gimbals, i.e., about head-fixed horizontal axes and space-fixed vertical axes, respectively (although in 1 animal, the latter constraint was relaxed during repetitive horizontal movements, allowing for trajectory optimization). However, during large oblique movements, head orientation made transient but dramatic departures from the zero-torsion Fick surface, taking the shortest path between two torsionally eccentric fixation points on the surface. Moreover, in the pin-hole goggle task, the head-orientation range flattened significantly, suggesting a task-dependent default strategy similar to Listing's law. These and previous observations suggest two quasi-independent brain stem circuits: an oculomotor 2-D to 3-D transformation that coordinates anticipatory saccades with slow phases to uphold Listing's law, and a flexible "Fick operator" that selects head motor error; both nested within a dynamic gaze feedback loop.
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INTRODUCTION |
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This study deals with the coordinated movements of
the eye and head during large gaze shifts, i.e., head-free gaze
saccades. This topic has been studied with increasing frequency
during the last decade, both for its intrinsic importance and as a
possible general model for coordination and control. Initial studies
focused on one-dimensional (1-D), i.e., horizontal, aspects of eye-head coordination (e.g., Bizzi et al. 1971; Dichgans
et al. 1973
; Fuller 1996
; Guitton
1992
; Guitton and Volle 1987
; Laurutis
and Robinson 1986
Tomlinson 1990
) but recently
have been extended to two dimensions (Freedman and Sparks
1997
; Goossens and Van Opstal 1997
). Moreover, the three-dimensional (3-D) kinematics of human gaze shifts,
i.e., the trajectories of eye and head orientation in space,
now have been described in some detail (Glenn and Vilis
1992
; Misslisch et al. 1998
; Radau et al.
1994
; Tweed et al. 1995
). The latter investigations largely focused on behavioral constraints that reduce
the redundant degrees of freedom of the eye-in-space (Es), head-in-space (Hs), and eye-in-head (Eh) during visual fixation. However, it is unclear how the brain organizes 3-D Hs trajectories and
coordinates 3-D Eh saccades with vestibuloocular reflex (VOR) slow
phases to implement these final fixation constraints. Furthermore, it
remains unclear whether these constraints exist to optimize anatomy- or
task-related variables (Radau et al. 1994
). Finally, an
animal model is required to investigate the physiological mechanisms of
these behaviors. The purpose of the current investigation was to
develop such a model by describing the 3-D kinematic constraints on
eye-head coordination during visual fixation in the monkey, to determine how the trajectories of the eye and head are controlled to
achieve these constraints, and to determine if these constraints optimize anatomic or behavioral requirements.
If the primary purpose of the head-free saccade generator is to
redirect gaze direction (i.e., the visual axis in space), then its
secondary purpose is probably to determine the 3-D orientation of the
eye about this axis. This orientation is important because it
determines the geometric correspondence of lines in space with the eye
and thus the pattern of retinal stimulation (Crawford and
Guitton 1997a; Glenn and Vilis 1992
;
Haustein and Mittelstaedt 1990
; von Helmholtz
1925
; Klier and Crawford 1998
). In
general, Donders' law predicts that the eye will achieve the same
orientation for each gaze direction, irrespective of the preceding
trajectory (Donders 1848
). When the head is mechanically
fixed or at rest, a specific form of Donders' law called
Listing's law is obeyed (Ferman et al.
1987a
; von Helmholtz 1925
; Tweed and
Vilis 1990
). Listing's law states that 3-D eye position
vectors (defined in the following text) align within a plane such that
rotations about a head-fixed torsional axis are minimized. The question
thus arises, does Listing's law continue to hold for Es when the head
is free to move?
It appears that when the human head is free to move,
Donders' law of Es still is obeyed, at least approximately
(Straumann et al. 1991). However, the orientations of Es
do not form a Listing's plane but rather a twisted 2-D surface
(Glenn and Vilis 1992
; Radau et al.
1994
). The observed twist is more consistent with the
orientations produced by a Fick gimbal (e.g., like a telescope mount),
where ideally, horizontal movements are achieved through rotations
about a body or space-fixed vertical axis, but vertical rotations occur
about an eye-fixed horizontal axis. This provides the observed form of
Donders' law, where rotations about the third, eye-fixed torsional
axis are minimized. This strategy has different perceptual consequences
than Listing's law; for example, it tends to better preserve
horizontal lines on the retina (Glenn and Vilis 1992
).
However, it was initially unclear whether this apparent constraint on
Es results from a deliberate control strategy or whether it follows
trivially from more fundamental mechanical or neural constraints on Hs
and Eh.
Like Es, Hs and Eh each pose a degrees-of-freedom problem for their
respective control systems because these segments are mechanically (and
behaviorally in some circumstances) capable of rotating in the
redundant torsional dimension (Collewijn et al. 1985;
Crawford and Vilis 1991
, 1995
; Hess and Angelaki
1997
; Misslisch et al. 1994a
). When the
orientation vectors of Eh are quantified during a range of human
head-free gaze fixations, they appear to form (or at least
are indistinguishable from) a plane similar to the head-fixed
Listing's plane (Radau et al. 1994
). The human head
also appears to follow Donders' law during head-free visual fixations
(Straumann et al. 1991
; Tweed and Vilis
1992
), but in this case it is more consistent with the Fick
gimbal strategy described earlier for Es (Glenn and Vilis
1992
; Melis 1996
; Theeuwen et al.
1993
). This means that all three possible measures (Es, Hs, and
Eh) obey Donders' law at least in approximation, but geometrically only two of these rules need to be enforced and the third will simply
fall out: but which one is this? Radau et al. (1994)
attempted to answer this by quantifying the variance of torsion in each of these segments and found that of the three, static Eh torsion was
controlled most tightly and Es torsion was controlled least tightly. They concluded that the brain was actually controlling Hs and
Eh orientation and that, at least in terms of control, the Fick-like
nature of Es orientation was the trivial fall-out of these more
fundamental rules. Our first goal was to similarly evaluate the
head-free orientation ranges of Es, Hs, and Eh during visual gaze
fixations in monkeys.
Knowing the orientations of the eye and head during gaze fixations does
not tell us how these segments rotate to achieve these positions.
Because of the noncommutativity of rotations, Donders' law can never
be achieved by consistently rotating a given segment about the shortest
path axis orthogonal to current and desired pointing direction. With
Listing's law, there is a kinematic rule that selects a single ideal
axis of rotation for any one saccade that will preserve eye position in
Listing's plane throughout the trajectory (Tweed and Vilis
1990). However, during head-free gaze shifts, this is
problematic for both the eye and the head.
First, the eye cannot use a simple kinematic strategy to maintain
Listing's law during head free gaze saccades because of the VOR. Each
gaze shift typically is accompanied by an initial Eh saccade that is
followed by a VOR slow phase, which stabilizes desired eye orientation
in space once the visual target is acquired to prevent overshoot while
the head continues to move (Bizzi et al. 1971; reviewed
in Guitton 1992
). The VOR is known to not
obey Donders' law but rather rotates the eye about the same or nearly the same axis as the head (Crawford and Vilis 1991
;
Haslwanter et al. 1995
; Hess and Angelaki
1997
; Misslisch et al. 1994a
), resulting in
accumulation of Eh torsion (Smith and Crawford 1998
). Recent gaze saccade experiments have suggested that the 2-D components of Eh saccades anticipate subsequent VOR slow phases to bring the eye
toward a final desired position in the head (Crawford and
Guitton 1997b
; Tweed et al. 1995
). This concurs
with the earlier observation that during passive head rotations,
saccade-like quick phases drive the eye out of Listing's plane in an
anticipatory fashion such that vestibular driven slow phases end up
bringing the eye back toward Listing's plane (Collewijn et al.
1985
; Crawford and Vilis 1991
; Crawford
et al. 1989
).
Here we consider whether Eh saccades during head-free gaze shifts would
similarly drive eye position out of Listing's plane in an anticipatory
fashion such that VOR slow phases would end up bringing the eye back
into Listing's plane at fixation. This would require very precise
control over all the torsional components of the saccade burst
generator (Crawford et al. 1997; Henn et al.
1989
) during goal-directed gaze shifts. If so, this would be
difficult to reconcile with the view that Listing's law emerges from a
simple projection of visual vectors onto a saccade command aligned in
Listing's plane (Raphan 1997
, 1998
). Furthermore, this would have important general implications for understanding the organization of eye-head coordination downstream from the common gaze
error command (Freedman et al. 1996
; Munoz et al.
1992
; Robinson and Zee 1981
).
Finally, it is not yet clear how the trajectories of head motion
subserve the Fick gimbal strategy observed during fixation. In
particular, it is not known if Donders' law of the head is maintained
during movements or if it is only obeyed between movements. It has been
observed that during repetitive back-and-forth head movements, humans
transiently violate the Fick gimbal strategy in favor of a "minimum
rotation" strategy, where the head simply rotates about the axis
orthogonal to the plane of its initial and final facing directions
(Tweed and Vilis 1992). However, it is not yet clear
what happens during normal, nonrepetitive movements. Presumably the
head-control system might achieve purely vertical or horizontal
rotations about constant axes very similar to those seen in the
telescope-like physical implementation of a Fick gimbal. In other
words, it might maintain Donders' law throughout the course
of each movement by rotating the head about a constant, space-fixed vertical axis during horizontal movements and a
constant head-fixed horizontal axis during vertical
movements. If so, then the head would behave both statically and
dynamically like Fick gimbals.
However, by corollary, because these horizontal and vertical axes of Fick coordinates are fixed thus in different segments, in some situations mechanically rigged Fick gimbals must rotate the controlled object about nonconstant axes, i.e., axes that do not have a constant orientation in space. In particular, during large oblique head movements, the head-fixed horizontal axis would have to rotate along with the head around the space-fixed vertical axis during the movement to maintain head orientation at zero torsion in Fick coordinates. In other words, a mechanically rigged Fick gimbal with torsion fixed at zero rotates about nonconstant, torsionally looping axes during oblique movements. Alternatively, without this dynamic constraint, any final Fick orientation can be reached from any initial Fick orientation by a constant axis of rotation that transiently violates the Fick form of Donders' law during the movement. It is currently unknown if the head-control system optimizes head axes in this fashion during oblique head movements or maintains Donders' law during movements according to the previous alternative.
The latter question is important, because it may reveal whether the
Fick gimbal strategy of the head is mechanical or neural in origin, and
if neural, whether it is implemented in a feed-forward fashion while
planning the movement or within an internal feedback loop during the
movement. Moreover, if this strategy is neural in origin, then it might
show some capacity for plasticity or task-dependence (Tweed
1997), which could in turn reveal the normal functional
significance of the Fick gimbal strategy of the head. For example, even
if the Fick strategy is neural in origin, it still may function to
optimize either anatomic (Radau et al. 1994
; Theeuwen et al. 1993
), perceptual (Glenn and
Vilis 1992
), or task-related requirements. We set about to test
among these options both in normal gaze shifts and also in a pin-hole
goggle paradigm where several task constraints (that might normally
encourage or enforce the Fick strategy) were removed (Crawford
and Guitton 1997b
). Some of these experiments have been
described briefly in abstract form (Crawford and Guitton
1995
; Guitton and Crawford 1994
; Klier et
al. 1998
).
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METHODS |
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Surgery and equipment
Three monkeys (Macaca fascicularis), henceforth
designated animals M1, M2, and M3, underwent
aseptic surgery under general anesthesia (isoflurane, 0.8-1.2%)
during which they were fitted with an acrylic skull-cap. Two 5-mm-diam
scleral search coils also were implanted in the right eye of each
animal for 3-D recordings, using a method described previously
(Crawford and Vilis 1991; Tweed et al.
1990
). Animals were given analgesic medication and prophylactic
antibiotic treatment during the postsurgical period. Experiments
commenced after 2 wk of postoperative care. All animal care and
experimental procedures were approved by the McGill and/or York Animal
Care Committees and were in accordance with the Canadian Council on
Animal Care policy on the use of laboratory animals.
Before experimentation, animals were placed in a Crist Instruments
primate chair, with the top plate modified to reduce encumbrances to
head movement. Specifically, for the first two animals (M1 and M2), the top plate was integrated to fit flanges on
custom-made plastic monkey collars, such that the collar slid in,
leaving a 1-cm-thick, 7.5-cm-diam ring of rigid plastic around the neck (Crawford and Guitton 1997b). A recessed hollow also was
built into the front of this plate so that it did not interfere with the animal's chin on looking down. Other than gaze directions >50°
downward (which we did not explore), rotational head movements and the
visual range were left unobstructed by this apparatus. However, the
rigid structure of the materials surrounding the neck restricted
translational movements of the head and forced the animal to sit
upright without slouching. To test whether these mechanical constraints
might interact or interfere with the neural constraints on head
orientation, a different chair was used with the third animal
(M3). In the latter chair, the rigid structures surrounding
the neck were replaced altogether by a reenforced cloth that was
buckled snugly at the animals back during experiments, similar to the
system used by Freedman and Sparks (1997)
. This arrangement allowed animal M3 to obtain its accustomed
slouching posture and make unobstructed head translations over a
reasonably wide range.
During experiments, the primate chair was placed such that the head was
at the center of three mutually orthogonal magnetic fields (1.5 m diam,
giving uniform quaternion measurements within ±15 cm of center).
Signals were low-pass filtered at 125 Hz, 12 dB/octave and digitized at
100 Hz from the eye coils and from two orthogonal 1-cm "head"
coils embedded in plastic. For head-free experiments, the head coils
and wire leads for the eye coils were secured with nylon screws to the
skull-cap. These preparatory procedures were performed with the head
fixed via a bolt screwed to a frontally placed cylindrical implant,
which could be detached using a quick release mechanism, and the
head-restraint assembly swung backward on the primate chair for
relatively unencumbered head-free recordings. Because chest orientation
was not measured, head orientation relative to the chest could not be
precisely computed. However, given that the chest was nearly stationary during experiments, our measures of Es and Hs were roughly equivalent to eye and head relative to the chest. Some translational movement was
observed qualitatively during experiments with M3 but was not quantified. Therefore this study could not directly address the
stability of rotational axes in translational space (Melis 1996) or the contributions of head translations to gaze control but rather focused on measurements of behavioral constraints on 3-D orientation.
Visual tasks and training
All training was performed with the head unrestrained. Animals
initially were trained to sit upright and face forward in the primate
chair. Animals were next trained to fixate "primate treats" held
at a 80 to 100 cm distance throughout a large range of the visual field
(Crawford and Guitton 1997b). These targets were held at
the end of forceps and moved very rapidly from location to location to
avoid pursuit movements. If the animal faithfully followed the visual
target, it (the treat) was fed manually to the animal. This procedure
was continued until the animal would follow the target with discrete
gaze saccades for ~3 min before acquiring the reward. Other than this
requirement, no time constraints were added, i.e., animals were always
allowed make self-paced gaze shifts between targets using an eye-head
coordination strategy of their own choosing. This paradigm, where the
visual target was the reward, was designed to emulate a biologically
natural pattern of motivated gaze shifts. It resembled the food/barrier paradigm used extensively to investigate head-free gaze shifts in the
cat (e.g., Guitton et al. 1990
) except that a rich
amount of visual motion information was available during repositioning of the target.
During control experiments, four standard paradigms were used. First, the radial task: animals oriented toward the target with gaze saccades toward and away from center, following a roughly even distribution of directions. A reproducible center point was maintained by fixing a pair of nylon strings orthogonally across the front of the Helmholtz coils forming a cross-hair directly ahead of the right eye in magnetic field coordinates. Among other things, this task was used to determine a reference point with a behaviorally natural combination of eye and head positions (see following text). Second, the repetitive task: using visual aids that could be repositioned at the front of the Helmholtz coils as a guide, targets were repositioned back and forth to induce repetitive horizontal/vertical gaze shifts at various vertical/horizontal levels. Third, the hour-glass paradigm (illustrated graphically in RESULTS): similar to the last, but inducing horizontal, vertical, and oblique movements in a reproducible but nonrepetitive fashion. Finally, the random task: the target was repositioned throughout the visual range in a nonrepetitive 200-s sequence that covered the range in as random an order as possible. Targets were held as eccentrically as possible without inducing whole body rotations (as determined through trial and error): approximately ±60-80°. These measurements were repeated on subsequent days for a total of 10 control experiments in animal M1 and 19 in M2. Nine further random-task experiments were obtained in animal M3, but this last animal could not be induced to comply with the task requirements of the more demanding paradigms.
When initial training was completed and control data were gathered,
animals also were fitted with a pair of opaque plastic goggles that
attached (via wing nuts) to screws implanted in the skull-cap. These
goggles were shaped to the contour of the monkeys' faces with
additional soft flanges at the edge so as to completely occlude vision
in both eyes. A single round aperture then was added such that the
right eye was given a useful visual range of ±4°. Details of this
procedure have been described elsewhere (Crawford and Guitton
1997b). Forty-five minute per day training sessions with the
goggles then commenced. Initially, animals were trained to visually
follow slow movements, and then as the speed of their gaze movements
increased, targets were displaced rapidly over a wide range until they
easily made rapid searching head movements to visually acquire the
target. Invariably animals mastered horizontal gaze shifts first, then
vertical gaze shifts, and finally oblique gaze shifts. Between training
periods, the goggles were removed, and the animals were returned to
their normal housing area. As judged subjectively, the total training
time required for rapid, accurate, and discrete movements in all
directions and throughout the entire range required ~4 wk in
animal M1, and ~10 days in animal M2. After
this training period, the radial and random tasks were repeated both
without and then with the goggles, for a total of five experiments in
animal M1 and 9 in M2. (Further behavioral
experiments done with these animals/preparations were reported
elsewhere) (Crawford and Guitton 1997b
.)
Data analysis
The analysis of 3-D movements evokes several challenging
computational problems, such as nontrivial coordinate system problems, degrees-of-freedom problems, and the noncommutativity of rotations (Haslwanter 1995; Tweed 1997
). Thus a
very rigorous and clearly defined quantification of the data was
required. A computer was used to convert coil signals into eye position
quaternions using a method described previously (Tweed et al.
1990
). Quaternions were used because, unlike raw coil signals,
they provide an accurate and convenient measure of 3-D eye position
over a 360° range. Quaternions represent each eye position as a
fixed-axis rotation from some specified reference position
(Westheimer 1957
). Quaternions are composed of a scalar
part q0, and a vector part q. It is
the vector part that is used for representation of data. To interpret
the data, one need only understand that q is parallel with
the axis of eye rotation, and its length is proportional to the
magnitude of this rotation. To be specific, a quaternion is related to
the axis and magnitude of a rotation as follows
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(1) |
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(2) |
The choice of reference positions for the eye and head is potentially
somewhat arbitrary in the head-free preparation because an infinite
number of eye-head combinations could subserve a single gaze direction,
and there may not be a rigorously definable "primary position"
for Es (Glenn and Vilis 1992). To choose a convenient and behaviorally meaningful set of reference positions for each experiment, we scrutinized the spread of eye and head coil signals during fixation of the central target in the head-free radial task and
then selected a point where both the 2-D pointing directions of the eye
and head were near the center of their somewhat variable ranges (see
Fig. 2). This resulted in a reference position for Es orientation
defined in magnetic field coordinates, where gaze was directed straight
ahead along the forward pointing field; a behaviorally central
reference orientation for Hs orientation defined similarly in field
coordinates; and a behaviorally central reference orientation for Eh,
defined in head coordinates, which were themselves defined by the
intersection of the magnetic fields with the head when it was at its
reference position.
The position of Eh then had to be computed from both the eye coil
signals (which directly gave eye position in space) and the head coil
signals. In one dimension, this would be done by subtracting head
position from gaze position. In three dimension, this was done by
dividing the Es quaternion by the Hs quaternion (Glenn and Vilis
1992) as follows
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(3) |
2-D "pointing vectors" were computed from quaternions as
described previously (Tweed et al. 1990). These unit
vectors typically were projected onto the frontal plane to indicate
where the eye or head was pointing. For the eye, these vectors align
with the visual axis in either space coordinates, i.e., gaze, or head
coordinates. For the head, they can be thought of as the aiming
direction of the nose. Finally, instantaneous angular velocity vectors
were computed from position quaternions using the method described previously (Crawford and Vilis 1991
). These were vectors
aligned with the instantaneous axis of rotation of length equal to the instantaneous angular speed of rotation. Like the quaternion vectors, the angular velocity vectors were expressed according to the right-hand rule, as described further in the following text. Because translations could not be measured, "axis constancy" in the
RESULTS refers to the orientation of the
velocity vector during movements.
To quantify the orientation ranges of Es, Hs, and Eh, first-, second-,
and third-order fits were made to Es, Hs, and Eh quaternions using the
previously described procedure (Glenn and Vilis 1992; Radau et al. 1994
; Tweed et al. 1990
).
The following formula provides the equation for a second-order fit for
a generic position quaternion (q)
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(4) |
An additional measure of the 3-D range, called the "gimbal score"
also was applied to the head-orientation data (Glenn and Vilis
1992). For this test, the head quaternion data first were rotated into alignment with the pitch-yaw axes plane using the parameters derived from Eq. 5 and then fit to the following
equation to provide the single term s
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(5) |
The preceding measures of fit and variance were applied to several subranges of the data selected on the basis of various velocity criteria. For example, the "fixation" range was defined to be those positions where the velocity (more correctly the 1-D magnitude of 3-D velocity) of both Es and Eh were <10°/s. Other, more complex criteria were used to select the position ranges at peak head velocities, at the starts of Eh saccades, at the ends of Eh saccades, at the starts of slow phases, and at the ends of slow phases. Simple but robust algorithms for selection of these subranges (provided in the APPENDIX) were developed on a trial-and-error basis from the recorded 3-D data.
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RESULTS |
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Figure 1 reveals most of the issues
and challenges of describing eye- and head-orientation trajectories in
3-D space. These data were selected from a sequence of large,
pseudorandom-gaze shifts between widely dispersed peripheral targets
(i.e., the random task) in M1. The primary object of
control, 2-D gaze direction in space, is shown in Fig. 1A;
show the trajectories of gaze while it was moving, whereas
indicate points of fixation between these movements (where both the eye
and head were stationary). Note that these data portray gaze as the tip
of a unit vector, projected onto the page as if from behind the subject
(the perspective is indicated by the head caricatures in the figures).
When similar representations are used below, they will be referred to
as "gaze vectors" (for Es) or "direction vectors" (for Hs).
This particular set of data (Fig. 1) was selected to show a sequence of
very large pseudorandom gaze shifts between eccentric targets, roughly
corresponding to the limit of the obtainable range in our preparation.
Clearly, the animal could acquire a large range of visual targets in
all directions (with the downward visual range somewhat limited because it was obscured by the primate chair).
|
The remainder of Fig. 1 (B-E) uses a different convention
to portray 3-D orientations from the same subset of data as
Fig. 1A. Again, both 3-D trajectories during movements ()
and orientations during eye/head fixations (
) are shown. However,
these data now represent 3-D position vectors. For example, if one
chooses any one fixation point or any one point on a trajectory, it is
actually the tip of a vector emanating from the origin. Each vector is aligned with the axis of rotation that would take the eye or head from
the reference position (defined in METHODS) and is
stretched to a length proportionate to the angle of this relative
rotation. Furthermore these vectors are oriented according to the
right-hand rule, such that a vector pointing upward (thumb of right
hand) represents a position rotated to the left (curl of fingers on right hand). Note that these data are portrayed in orthogonal coordinates, where the torsional, horizontal, and vertical coordinate axes are all fixed either in space or in the head. The head caricatures in Fig. 1, B-E, indicate that these coordinates and 3-D
position vectors are viewed from the right of the subject throughout
the figure, such that they show the horizontal and torsional components of eye and head orientations (head + torso symbols designate space coordinates, whereas head only symbols designate head coordinates).
Figure 1B shows the orientations of Es that correspond to
the gaze directions in A. It is important to remember that
in these and all further illustrations, Fick coordinates are not used
to represent the data, and thus torsion is not rotation
about the visual axis. In this case, the torsional coordinate is an
axis fixed in space. With these coordinates and data, it is evident that the range of eye torsion in space is relatively compact compared with the horizontal range but still shows considerable variability (~40° peak to peak), both during and between fixations. Thus a flat
Listing's plane was not evident in such plots, but at this point it
was not clear whether Es torsion obeyed some other nonplanar constraint, was simply much sloppier than head-restrained eye torsion
(Tweed et al. 1990), or both.
The remainder of the figure shows the head and Eh orientations that
contributed to the Es orientations shown in Fig. 1B. Figure 1C shows similar vector representations of head orientation
in the same space-fixed, orthogonal coordinate system. The head range seems slightly more compressed torsionally and more aligned with the
vertical but is otherwise similar to the Es range. However, there is
still considerable variability (~30° peak to peak) in torsional
head positions during gaze fixations ().
Finally, Fig. 1, D and E, shows orientations
ranges of Eh, plotted in the same scale as the preceding data. The
fixation points () are the same in both D and
E, showing Eh orientations at the end of multiple-step gaze
shifts, where both the eye and head were stationary. However, the
position trajectories (underlying continuous lines) have been
subdivided to show saccade trajectories (when head was also moving) in
D, and VOR slow phase trajectories in
E. Compared with the head and Es, which showed considerable variability in torsion both during movement and head/gaze fixation (
), the Eh fixation range (
) formed a relatively compact range. This range was clearly most compact along the dimension indicated (- - -). However, the Eh trajectories during movements (
) were less
restricted, extending outward from the fixation ranges both during
saccades (D) and slow phases (E).
Although Fig. 1 provides an overview and some clues to the kinematics
of eye-head coordination, it also shows the somewhat daunting
complexity of deriving simple rules from this complex data. To derive
such rules, we had to analyze the data in a more reductive fashion. The
subsequent sections will adhere to the following course of analysis,
noting first that Es orientation during fixations is most
directly relevant to vision (the biological task of this system).
Second, the head and Eh orientations observed during these fixations
thus presumably will be the goals of the eye- and head-control systems.
Therefore we will begin by considering the ranges of Es orientation
during stable gaze fixations, and the ranges of head and Eh orientation
that contribute to these positions ( in Fig. 1). After establishing
the rules that govern these ranges, we then will consider the movement
trajectories used to obtain these ranges.
3-D fixation ranges of Es, Hs, and Eh
Figure 2 introduces the subject by
showing the ranges used to fixate a single target. These data were
selected from a series of gaze fixations toward a central,
straight-ahead target, reached by a radial pattern of centripetal gaze
shifts (not shown) from a wide distribution of peripheral targets (the
radial task). Figure 2, top (A-C), shows the
horizontal and vertical components of 2-D direction vectors. The gaze
vectors for Es (A) form a tight group around the zero point,
showing that the target was foveated accurately after each centripetal
gaze shift. In contrast, the vertical and horizontal components of the
head (B) and the Eh (C) vectors show considerable
variability during the same fixations. This is possible because an
infinite number of combinations of head (B) and eye
(C) position can give rise to the same gaze direction in
space (A). Considering only gaze fixations within ±1° of
the central fixation point, the range of horizontal head position (quantified as 4 SD, i.e., ~98% of the data) was 14.5° in
animal M1 and 10.0° in M2, averaged across all
radial task experiments. The average vertical head range was also
14.5° in animal M1 but lower at 5.2° in M2.
(Note that, as follows trivially, Eh showed almost identical
variations). Such 2-D variations have been described before (e.g.,
Freedman and Sparks 1997; Radau et al.
1994
) and will not be examined further here. The point to be
taken is that from this 2-D perspective, the system appeared to control
gaze direction much more tightly than the precise combinations of eye and head position that contributed to gaze.
|
The 3-D orientations of the same eye and head data revealed a somewhat
different picture. The remainder of Fig. 2 shows the torsional
orientations of the eye and head plotted against horizontal position
(middle) and vertical position (bottom). In the
case of Es (left), the torsional orientation is considerably
more variable than either horizontal (D) or vertical
(G) position. In this particular task, the space-fixed
torsional coordinate happens to align with the visual axis. Most
interestingly, whereas horizontal and vertical position were controlled
tightly to land gaze on target (A), the torsional
orientation of Es around the line of gaze varied by 20°
for this same single target direction (Fig. 2, D and
G). Using the 4 SD definition from the preceding paragraph,
the average torsional range of Es was 9.3° in animal M1
and 13.7° in M2, considerably larger than the ±1° gaze
window used to compute these values. (Animal M3 refused to
fixate the central target over enough repetitions to perform this
measurement but showed qualitatively similar results).
In contrast, Eh torsion formed a very compact range much smaller than
the horizontal (F) or vertical (I) range of Eh
positions used for this one target. Indeed, even for a single target
these ranges give the appearance of a tilted Listing's plane,
suggesting that eye orientation was only allowed to vary within a
quasiplanar range. Because torsional variance previously has been
quantified using the single standard deviation (e.g., Glenn and
Vilis 1992; Radau et al. 1994
), we henceforth
will follow the same convention. The average (across experiments)
torsional SD of Eh was only 0.99° in M1 and 0.72° in
M2 in this task (where gaze was within ±1° of center),
considerably less than those of Es (2.32 and 3.43°, respectively).
The distribution of head orientations (Fig. 2, E and
H) was intermediate between these extremes, showing roughly equal ranges of torsion, vertical, and horizontal variance (2.99, 2.46, and 3.07° SD, respectively; averaged across experiments and then
between animals).
Thus from this data, it would appear that the 2-D contributions of the eye and head to gaze direction were controlled rather loosely compared with gaze in space (top) but that Eh torsion was controlled much more tightly than Es torsion (middle and bottom). However, the rule governing head position is not yet clear from Fig. 2. To more completely characterize these rules, we next examined orientations over a much wider distribution of gaze fixations toward multiple target directions.
The first two columns of Fig.
3 show 3-D orientation vectors during
fixations toward a wide range of target directions, as best seen in
A. (The data range in the previous Fig. 2 corresponds roughly to a small subset of the data near the coordinate origins in
Fig. 3.) In Fig. 3, Es (top), Hs (middle), and Eh
(bottom) orientations are viewed from the behind perspective
(1st column), i.e., vertical versus horizontal, and side
perspective (2nd column), i.e., torsion versus horizontal.
From the behind perspective, it is evident that the Hs fixation range
(B) was elongated in the horizontal dimension, whereas the
Eh range (C) was elongated in the vertical dimension.
Because the Es range (A) roughly corresponds to the sum of
the latter two ranges, the head thus contributed relatively more to the
horizontal Es fixation range, whereas Eh contributed relatively more to
the vertical Es range. This was typical in our animals and matched
previous reports of head-free primate behavior (Freedman and
Sparks 1997; Glenn and Vilis 1992
) but was not
further quantified. From the side perspective, it is evident that for a
large range of fixation directions, torsional Es (D), Hs
(E), and Eh (F) ranges were somewhat restricted,
but the precise nature of this restriction remains incomplete in these plots.
|
To reveal the 3-D shape of these flattened position ranges, we employed
the same methods used in similar human studies (Glenn and Vilis
1992; Melis 1996
; Radau et al.
1994
), applying second order "surface" fits (Eq. 5). The remaining rightward columns of Fig. 3
graphically depict the surfaces fit to the data shown in the
first two leftward columns. These plots show the dependence of torsional position on the other components of position, where each
grid mark indicates 10° of horizontal/vertical excursion. The
third column of Fig. 3 shows the side view corresponding to the second column, whereas the rightmost column
of Fig. 3 depicts the "below" view, showing the dependence of
torsional orientations on vertical positions in a way that orients
upward position upward on the page. (Imagine that the plots in the
3rd column were rotated 90° about the torsional axis,
bringing their bottom parts out of the page, to obtain the
"below" perspective in the 4th row). The rectangular
corners of these fits, which usually extended beyond the more rounded
range of the actual data, are labeled according to the corresponding
2-D pointing directions (DL, UL, UR, DR) to facilitate interpretation.
The fits to the Es and Hs data show the same striking feature: the ranges are twisted into a flattened 2-D bow-tie-like shape. This is most evident from the side views (note that the apparently greater "fanning out" of the Es bow-tie compared with the head bow-tie is largely due to the wider distribution of vertical gaze positions rather than a greater twist to the bow-tie). The same bow-tie like twist is evident in the below views of this data as well (right column), but the vertex of the twist was shifted upward on the graph (i.e., toward an upward position). The latter is simply a perspective effect: because the bow tie is tilted backward (i.e., upward about the horizontal axis) from the side perspective, its vertex automatically looks shifted from the "below" view. In concrete terms, this bow-tie shape signifies that Es/Hs assumes relatively (compared with its neighboring corner on the illustrated plot) counterclockwise orientations in down-left (DL) and up-right (UR) positions and assumes relatively clockwise orientations in up-left (UL) and down-right (DR) positions. (Note that this description is only meaningful in the current orthogonal, space-fixed coordinate system).
To be consistent, we also have plotted the second-order surfaces fit to
the Eh data (bottom). These also show a similar bow-tie twist in this particular example but were highly variable. For example,
the "twist score" (described in more detail in the following text) of the Eh range across experiments was 3.3 times as variable as
the Es twist score [quantified as the average ratio of the standard
deviations of parameter a5 (Eq. 5)
across all random-task experiments, further averaged across all 3 animals]. This variability may have been exaggerated because the Eh
ranges were too small (Fig. 3E) for this method to provide a
highly meaningful fit (as pointed out by Radau et al.
1994). Therefore we did not further investigate the subtleties
of the shape of the Eh fixation range but rather focused on its
torsional "thickness."
Quantifying the torsional thickness of the fixation ranges
In quantifying the 3-D ranges of eye and head orientation in
humans, two measures have proven useful: the parameters used to form
the fits illustrated in Fig. 3, and the standard deviation of torsional
eye position (in the actual data) from these ideal 2-D fits
(Glenn and Vilis 1992; Radau et al.
1994
). We employed the same approach to quantitatively address
two questions: which of the three segments (Es, Hs, and Eh) are
constrained most tightly by Donders' law, and what form does this law
take in each of these segments?
Figure 4 shows torsional standard
deviations from first-, second-, and third-order fits to all three
segments, computed from random-task fixation data such as those
illustrated in Fig. 3. Data from all three animals are plotted
separately in A-C, whereas each bar represents a value
averaged across all random-task measurements in one particular animal.
In each case, the bars are grouped according to the order of the fit
used to compute the relative torsional standard deviation. The first
point to be taken from this figure is that as the order of the fit
increased, the torsional variance from this fit decreased. For example,
note how the average torsional SD for Es () dropped dramatically
between the first- and second-order fits and dropped further at the
third-order fit. However, note (in Fig. 4) that the jump from first- to
second-order fits produced the greatest effect in Es and Hs variance
(compared with the 2nd-3rd interval), whereas the torsional SD of Eh
showed a steady, less dramatic decline toward higher orders of fit
(perhaps due to the problems in fitting the head-free Eh range
mentioned earlier). Nevertheless, statistically significant
(P < 0.001) decreases in variance occurred across both
intervals (i.e., 1st-2nd and 2nd-3rd) for each and every case for Es,
Hs, and Eh, in all three animals. In summary, although each increase in
the order of fit decreased the torsional variance of Es, Hs, and Eh in
the statistical sense, visual inspection of the data (Fig. 4, see
particularly animal M3) suggested that the jump from first
to second order gave the most important improvement in the Es and Hs
fits, whereas second- and third-order terms appeared to have little
effect on the Eh fit.
|
The second point to be gleaned from Fig. 4 is that there were
consistent differences between the torsional variance of Es, Hs, and
Es, regardless of which order of fit was used. First, the torsional SD
of the Es range was always greater than the torsional variance of the
Hs range. This was true in all animals, no matter how complex were the
parameters of the fit (1st, 2nd, or 3rd order). In each and every
individual case, this difference was statistically significant (range
of P 0.0005-0.007 in M1 and M2,
P
0.04 in M3). Similarly, in each and
every case in all animals, for all levels of fit, the torsional SD of
the Hs range was significantly larger than the torsional SD of the Eh
range (P
0.0005). Thus even at a third-order fit the
torsional SD of Es (mean across animals: 3.55°) was greater than the
torsional variance of Hs (mean 3.10°), which in turn was greater than
that of Eh (mean 1.87°). This relative ranking agrees with the
qualitative descriptions provided above (Figs. 1-3), as well as
observations in humans (Radau et al. 1994
). According to
the arguments employed by Radau et al. (1994)
, this
suggests that Donders' law was only enforced by the
individual control systems of Hs and Eh, whereas the Donders' law for
Es was simply a geometric byproduct of the other two laws.
From the preceding, data we draw three interim conclusions necessary
for the further development of our analysis: first, the motor
implementation of Donders' law in Es during head-free gaze fixations can be attributed to relatively tight
3-D control of Hs and Eh. Second, the rule governing head orientation
during fixation gives rise to a decidedly nonplanar, twisted range.
Third, Eh orientation vectors were restricted to a relatively thin
quasiplanar (or indeterminately twisted) range. These observations are
in close agreement with the human data (Glenn and Vilis
1992; Radau et al. 1994
). On the basis of these
observations, we then analyzed the segmental trajectories
that give rise to these fixation constraints.
3-D eye-in-head trajectories
On the basis of head-fixed data (Ferman et al.
1987b; Straumann et al. 1995
; Tweed and
Vilis 1990
; Tweed et al. 1994
), it might seem
reasonable to hypothesize that Eh would obey Donders' law (i.e.,
remain in Listing's plane) at all times throughout a head-free gaze
shift, with only minor and pseudorandom "torsional transients."
However, this hypothesis is problematic because head-free gaze shifts
include substantial periods where gaze is stabilized by VOR slow
phases. Slow phases are known to violate Listing's law in that they
tend to rotate the eye about almost the same axis as the head
(Crawford and Vilis 1991
; Misslisch et al.
1994a
). Thus if the head rotation axis does not align with
Listing's plane, a slow phase will tend to drive eye torsion out of
Listing's plane. Moreover, even if the head axis does align with
Listing's plane, the complex kinematics of eye rotation will cause the
eye to deviate torsionally as a function of eye position
(Crawford and Vilis 1991
). How does the head-free gaze
control system deal with this problem?
Figure 5 provides several clues to
the solution to this problem. Figure 5, left, shows the
familiar 2-D plot of Eh direction trajectories, where up is up and left
is left, etc., whereas Fig. 5, right, shows the right-side
view of Eh quaternion vectors. The latter have been rotated into a
coordinate system that aligns with the first-order fit to the
associated fixation range. From this data it is evident that the
primary position at the origin (where the 2-D Eh direction vector is
orthogonal to the fixation range) did not necessarily correspond to the
center of the head-free Eh range. Figure 5, top, shows Eh
saccade trajectories (where indicate saccade endpoints) during
random head-free gaze shifts, whereas bottom shows similar
2- and 3-D views of the slow phase eye movements from the
same data set, and their endpoints (
). Note that, as shown more
explicitly in the next figure, most head movements were associated with
several Eh saccades and slow phases. Each and all of these sequential
eye movements have been included in Fig. 5.
|
Focusing first on 2-D direction (Fig. 5, A and
B), it is evident that during the random task, Eh saccades
(A) were directed in a pseudorandom pattern that tended to
land final horizontal and vertical eye position over a roughly
homogenous range including relatively eccentric positions (). In
contrast, slow phases (B) tended to center eye position,
driving it more exclusively toward less eccentric final positions
(
). This is not surprising, given the known kinematics of head-free
gaze control (Bizzi et al. 1971
). However, how should
one expect torsional eye position to behave? From the known kinematics
of saccades and the VOR, one might expect the latter to drive the eye
out of Listing's plane, whereas each saccade might correct any
accumulated deviation from Listing's plane. In fact, the opposite
pattern appeared to occur: Eh saccades (C) tended to drive
final torsional eye position (
) away from the fixation plane
(centered on the vertical axis), whereas VOR slow phases (D)
tended to land final torsional eye position (
) closer to the center
of the fixation plane. Thus the same rule applied to all
three dimensions of Eh: saccades tended to drive the eye
eccentrically, whereas slow phases tended to center the eye.
The detailed kinematics of this behavior are more clear in Fig.
6, which plots the three components of
eye position relative to the head as a function of time during a
typical large gaze shift, selected from data recorded during the random
paradigm. For reference, the components of head position also are
plotted, rotated to align with the vertical axis of the Fick range,
such that the horizontal dotted line corresponds approximately to zero torsion in Fick coordinates. As described in the METHODS,
the animals were not constrained by time or reward to use any
particular strategy to obtain visual targets, and they invariably chose
to implement large multiple-step gaze shifts (i.e., with several interim saccades and fixations). This is evident in Fig. 6 where the
animal made four consecutively smaller vertical/horizontal Eh saccades
() during the single head movement, roughly in the same direction as
the single smoother head movement profile. Between these saccades, the
VOR evidently was engaged, producing slow phases (
) that rotated the
eye counter to the head and thus briefly stabilized gaze whenever
possible during the gaze shift. Considered from the perspective of 1-or
2-D gaze control, the temporal coordination of this pattern seemed
relatively trivial, i.e., saccades shifted gaze toward the target, and
then the VOR trivially caused the eye to roll back toward a central
position.
|
From a 3-D perspective, the temporal coordination of this pattern was
much more complex. A similar nystagmus-like pattern also occurred in
the torsional component of Eh position ({). Note that this Eh data
has been rotated into Listing's coordinates, such that - - -
represents zero torsion in Listing's plane. The slow phases thus had a
considerable torsional component relative to Listing's plane even
though the head did not rotate torsionally. As explained in more detail
elsewhere (Crawford and Vilis 1991; Smith and
Crawford 1998
), this accumulation of torsion was primarily a
kinematic consequence of rotating the eye about the same axis as the
head independent of eye position. In this case, slow phase rotation of
Eh in the rightward direction, from an upward eye position, caused
torsional eye position to deviate in the counterclockwise direction, as
predicted from the laws of rotational kinematics (Smith and
Crawford 1998
). However, these slow phases did not take the eye
away from Listing's plane but rather toward it. This resembled a
similar effect described for torsional slow phases during passive head
rotation (Crawford and Vilis 1991
) except that passively
induced slow phases tended to overshoot Listing's plane, whereas these
slow phases appeared to land the eye quite accurately within the
fixation range (as quantified in the next figure).
The latter effect occurred because each preceding saccade also had a
torsional component, but in the opposite direction, such that the
overall torsional excursion was negated by the subsequent slow phase.
Indeed without such torsional saccades the eye would presumably
accumulate a huge Eh torsion, as extrapolated on Fig. 6. Furthermore
because the torsional components of these quick phases did not
contribute to shifting gaze toward the target and because the torsional
direction of the subsequent slow phase could only be predicted by
taking both head velocity and eye position into account
(Crawford and Vilis 1991), the temporal coordination of
this 3-D pattern did not appear to arise accidentally. Instead, it
appeared that the system produced specific torsional components in Eh
saccades to anticipate subsequent vestibular-driven
torsional movements, such that ocular torsion always returned to
Listing's plane at the end of each slow phase.
To quantify these observations, it was necessary to further subdivide and analyze the Eh position range during multiple-step gaze shifts. Figure 7A shows examples of each of these subranges, derived from a single random-task measurement with the use of the algorithms described in the APPENDIX. The 3-D data are viewed from the side (i.e., torsional position vs. horizontal position) in coordinates rotated to align with the head-free Eh fixation range. The first example (Fig. 7A, left) shows the latter fixation range explicitly, revealing a torsionally compact group of Eh positions. The remaining examples show Eh positions at various start/endpoints of the saccades and slow phases from the same data set. The rest of Fig. 7 (B-D) shows the SDs of torsion from each of these ranges, relative to a second-order fit made to the fixation range at gaze shift ends. The individual bars show average values across all head-free random paradigm measurements (with error bars showing SEs across measurements) in animals M1 (B), M2 (C), and M3 (D). These bars have been aligned in vertical columns with the example ranges in Fig. 7A, to facilitate comparison between these columns, where the fixation data (column 1) establishes the baseline (- - -) for such comparisons.
|
Figure 7, second column, shows eye positions at the
initial points of Eh saccades (labeled as quick phases)
sampled throughout the multiple-step gaze shift. Compared with the
baseline, this range was only slightly, but significantly, expanded
(P 0.001, all animals). However, at the ends of
these saccades (column 3), the torsional variance was
increased further (P
0.001, all animals) and by a
larger step. If the function of these saccades components is to
anticipate subsequent torsional components in slow phases, as
hypothesized above, one might expect saccades during high head velocities (which tend to produce larger violations of Listing's law
in the typical intersaccadic interval) to push torsion even more
eccentrically. As shown in the fourth column, the subset of
saccade ends where current head velocity was >150°/s did tend to
land the eye at positions even more eccentric to the zero torsion zone
(P
0.003, all animals). However, after the
subsequent slow phases (column 5), the eye was brought back
to a torsional range almost as tight as the fixation range. Not
surprisingly, the slow phase end range was very similar to the saccade
start range because the two overlapped considerably during
multiple-step gaze shifts (although final fixation points
with the head motionless were included only in the former and starting
points of the 1st Eh saccade with the head moving were only
included in the latter). More importantly, the torsional variance at
the end of slow phases was reduced (highly significantly) compared with
saccade ends in all three animals (P < 2 × 10
4 in M1, P < 5 × 10
9 in M2, P < 6 × 10
6 in M3). Thus unlike the head-fixed
Listing's law, Donders' law of Eh was not obeyed
throughout the overall gaze shift but only held during
steady fixation (column 1) and transiently approximated toward the ends of interim slow phases (column 5).
3-D head trajectories
Figures 3 and 4 suggested that during steady fixations, the head-orientation range formed a pseudoplanar, twisted surface that required at least a second-order fit for adequate quantification. The latter is provided explicitly in Fig. 8, which shows the average parameters of second-order fits to the head-fixation range (averaged ± SD across all random-task measurements) for animals M1 (A), M2 (B), and M3 (C).
|
Each parameter provides the dependence of Hs torsion on various
combinations of horizontal and vertical position. The first parameter
(a1) measures the torsional shift of the range
from the reference position, which was (not surprisingly) small (0.025, averaged across animals). The second parameter
(a2) indicates the dependence of torsion on
vertical eye position, which was also small (0.022, averaged across
animals) and rather inconsistent. In comparison, the third parameter
(a3) was relatively large (
0.274, averaged
across animals) and consistent both within and between animals. This
term was significantly less than zero in all animals (P < 3 × 10
8 in M1, P < 2 × 10
14 in M2, P < 10
6 in M3). This value represents the
dependence of torsional head position on horizontal head position, and
the illustrated negative value describes the upward (backward) tilt
observable in the side view of the head fixation range illustrated in
Fig. 3 (E and H), such that rightward positions
tended to be more clockwise compared with leftward positions. The
fourth parameter (a4) was also negative on
average. This negative value describes a curvature in the position vector range and signifies a tendency for the head to tilt
counterclockwise when looking up or down (this is difficult to see in
Fig. 3 because other terms are more dominant). Although
a4 was statistically significant in two of the
three animals (M1 and M2, P < 0.05), its mean value was relatively small (
0.301, mean across animals) compared with its standard deviation between experiments (0.526, SD
averaged across animals). The a6 term,
signifying curvature of torsion with horizontal eye position, was
smaller again (
0.095, averaged across animals) and was only
statistically significant in one animal (P < 0.001 in
M1, P
0.257 in M2, P
0.371 in M3). Clearly, the most prominent term in the
second-order head fits was the remaining a5
parameter, the so-called "twist score" (Glen and Vilis
1992
), which captures the bow-tie like twist illustrated in
Fig. 3, H and K. As expected, this score was
always negative (
1.104, averaged across animals), and was
statistically significant across experiments in all animals
(P < 8 × 10
6 in M1,
P < 2 × 10
15 in M2,
P < 2 × 10
5 in M3),
confirming that the characteristic twist described above was consistent
with the general trend.
Glenn and Vilis (1992) were the first to describe
such negative twist scores in the human Hs range and to point out that
this is the type of range that would be produced by a system acting like a set of Fick gimbals, i.e., a head-fixed horizontal axis (for
vertical rotation) nested within a body- or space-fixed vertical axis
(for horizontal rotation). They used a range-independent gimbal score
(Eq. 6) to further quantify this twist, where
1.0 corresponds to zero torsion in a perfect Fick coordinate system, 0 corresponds to Listing's law, and 1.0 corresponds to zero torsion in a
perfect Helmholtz coordinate system. The gimbal scores for our animals
were
0.653 ± 0.136 (M1),
0.830 ± 0.086 (M2), and
0.567 ± 0.096 (M3) (mean ± SE across random-task experiments). This suggested a constraint on
static head orientation during fixations that was intermediate between
Listing's law and a perfect Fick system but somewhat closer to the latter.
However, because an infinite number of rotational axes can take
the head between any two fixation points (Tweed and Vilis 1990), it was not clear from this data, or the previously
published human fixation data (Glenn and Vilis 1992
;
Radau et al. 1994
), whether the head actually rotates
like Fick gimbals during movements. To answer this question, it was
necessary to directly examine the instantaneous axes of head rotation
during gaze shifts. To begin at a relatively simple level, purely
vertical or horizontal head movements first were examined. Figure
9 illustrates the typically observed
behavior, showing the instantaneous axes of rotation (angular
velocities) used for various vertical (A) and horizontal (B) head movements from various initial head orientations.
Figure 9A shows five downward head rotations at five
different horizontal head positions. As indicated by the head
caricatures, the data are projected onto the horizontal plane from a
perspective above the head. The cartoons in Fig. 9A
illustrate two examples where - -
indicates the average pointing
directions of the head in the first and fifth movement, and
indicates the average axes of rotation.
|
In the main part of Fig. 9A, head position is indicated by
five groups of head direction vectors (dark points labeled 1-5) that
are joined to the origin by - - - (because these downward arcing
vector tips are viewed from above, they do not appear to change very
much during the movement). Also shown are five "velocity loops"
(labeled 1-5), where the individual points (/
) provide the
instantaneous axis and angular speed of head rotation. The numbering
system indicates the correspondence between position and velocity for
each of five movements. In each movement, the velocity vector started
at zero and then grew (accelerated) to some maximum value closely along
some constantly oriented axis of rotation (
) and then shank along
this axis back down to zero, thereby forming a narrow loop. Note that
as the head pointing direction proceeds from left to right (1-5)
across the five different movements, the axes of rotation (1-5) for
the downward head movements stay in the horizontal plane but similarly
rotate stepwise to the right, such that the head axis stays close to
orthogonal to the head pointing vector in each case. Furthermore, the
axes of rotation remained roughly constant throughout each movement.
This dynamic behavior was very much like the rotations that occur about the horizontal axis in a set of Fick gimbals, where this nested axis
initially has been rotated horizontally to different degrees about a
vertical axis.
Figure 9B uses similar conventions but now shows a side view of the vertical velocity loops for five rightward head rotations (1-5) with the head at five different vertical elevations as shown again by the five groups of corresponding head pointing vectors (1-5). The latter form little semicircles because they represent the arcing tips of a vector that was swinging horizontally, and the view of these arcs is not perfectly edge-on. In general, the velocity vertical axes did not align with the gravity vector (the vertical coordinate axis in the plot) but rather showed a consistent upward tilt so that rightward rotations had clockwise components (Fig. 9B) and similarly leftward rotations had counterclockwise components (see Fig. 12A). More importantly, the five sets of velocity loops formed a compact, overlapping set of data points. There was little or no systematic tilting of these five axes with the vertical elevation of the head. Furthermore the orientation of the axis of each rotation remained roughly constant throughout the trajectory (this is further illustrated below in Fig. 12). Thus again, these head rotations strongly resembled those produced by telescope-like Fick gimbals, where the vertical axis for horizontal rotation remained fixed with respect to space throughout the movement, despite various initial displacements about the horizontal axis.
Taken together, Fig. 9, A and B, suggests that the Fick-like constraint observed in the head-fixation range (Fig. 3, H and K) results because the head does indeed rotate about axes like the nested coordinates in Fick gimbals during rotations. These two figures (3 and 9) are linked as follows. First, the upward tilt in the fixed vertical axis (Fig. 9B) accounted for the upward (backward) tilt in the position ranges of Fig. 3, E and H, and the corresponding negative a3 term in Fig. 8. For example, rotation about this tilted axis caused head position to deviate clockwise during rightward movements. Second, and more importantly, the Fick-like nesting of the axes in Fig. 9 gave rise to the bow-tie shape in the fixation range (Fig. 3H). For example, during a downward movement with the head rotated to the left (e.g., Fig. 9A, 1), the "horizontal" axis (for vertical rotation) was rotated similarly to the left so that it then almost aligned with the torsional axis in space-fixed orthogonal coordinates. Thus at this position, downward rotation in Fick coordinates was almost the same as counterclockwise rotation in space-fixed orthogonal coordinates. This explains why downward-leftward positions had a relative counterclockwise twist in the fixed orthogonal coordinates used in Fig. 3H. Similar factors explain the torsional twists at the other corners of the Fick surface (Fig. 3H).
On the basis of these velocity data, it would appear that the Fick
constraint on head position should hold during movements just as
Listing's law holds fairly well during head-fixed saccades (Ferman et al. 1987b; Straumann et al.
1995
; Tweed and Vilis 1990
; Tweed et al.
1994
). To quantitatively test this hypothesis, we reexamined
the head-orientation ranges during the random-gaze task, now focusing
on the range during movement. Figure 10
shows such head-orientation ranges during random-gaze shifts
and their 2-D surfaces of best fit. Figure 10A shows head
positions during steady fixations as a control, whereas B
shows head positions that were selected at the point in time when peak
velocity occurred for each head movement. From this example
(A vs. B), it would appear that the Fick-like
twist remained even during movements. This is quantified in Fig.
10C, which compares the average twist scores (±SE across
experiments) fit to fixation data (as in A) versus average
twist scores fit to the head positions at the time of peak head
velocity (as in B) across all random-task experiments in
each monkey. It would appear that the twist scores remained relatively
constant in both conditions, showing only a slight reduction during
peak head velocities. This reduction was statistically significant in
animal M2 (P
0.001) but not animal
M1 (P
0.15) or M3 (P
0.21).
|
Figure 10D then shows the average torsional standard
deviations (±SE) from these fits, again comparing fixation data versus position data collected at peak head velocities. All three animals showed a modest (mean 15%) increase in torsional variance during peak
head velocities. This increase was statistically significant in two of
the three animals (P 0.012 in M1,
P
0.0005 in M2, P
0.113 in
M3). Thus it appeared that the Donders' law of the head was
relaxed only slightly during head movements, at least when averaged
across all types of movements in the random task.
One explanation for the small but consistent increase in variance of head torsion during head movements could be random biological noise. However, there is still reason to hypothesize that some specific movements were not Fick-like during the movement. Fick-like movement trajectories like the vertical and horizontal rotations shown in Fig. 9 may have dominated the dynamic behavior in the random task (Fig. 10B), masking a less frequent, dynamically non-Fick behavior. In particular, we have not yet addressed the behavior of the head during large oblique movements. The potential complication here is that in a mechanical Fick system, the horizontal component of an oblique axis would be position dependent, whereas the vertical component would be position independent. Thus as described in INTRODUCTION, a mechanical Fick system (or any other system that maintains zero torsion in Fick coordinates) must produce specific nonconstant curvatures in the rotation axis during large oblique movements. A system that did not produce such curved trajectories would therefore not obey Donders' law during large oblique movements even if the endpoints did obey Donders' law.
Consider the hypothetical situation depicted in Fig.
11, A-D, top. A
depicts our paradigm where the head rotates in an "hourglass" pattern, consistently reproducing large oblique movements but without
repetitive back-and-forth motion (to be addressed in a subsequent
section) or circular patterns that might lead to accumulation of
torsion (Tweed and Vilis 1992). Only head position
vectors are depicted, using the right-hand rule, as viewed from behind (left) and from the side (remaining columns).
Assume for the moment that Hs conforms to the ideal Fick constraint
during fixation as depicted schematically in Fig. 11B. In
this case, a large oblique rotation must take the head between
similarly eccentric torsional orientations. For example, the rotation
from down-right (DR) to up-left (UL) begins from a clockwise
orientation in space-fixed orthogonal coordinates and ends at a similar
clockwise orientation. The question is, what path will it take?
|
If head orientation was constrained to the Fick surface mechanically, or maintained in the Fick surface by a neural rule that operates at all times during the movement, then it would follow the 3-D trajectories illustrated in Fig. 11C. It could not pass through the center of the range without crossing a zero-torsion line on the Fick surface. However, if the Fick strategy was preprogrammed before movements such that the control system only really cared about terminating in the Fick surface, it might accept transient violations in the Fick strategy to take the more direct paths illustrated schematically in Fig. 11D.
Figure 11, E-G, shows the experimental result of the
test described above. Other than the irrelevant backward tilt of the
Fick-like range (Fig. 11F), the data closely emulated the
ideal test. From the behind view (Fig. 11E), the oblique
head-position trajectories sometimes showed some slight and variable
curvatures as observed in human head movements (Tweed et al.
1995). However, in the side view critical to the test (Fig.
11G), the head followed remarkably straight trajectories
directly from one torsionally eccentric corner to the next. This was
consistent in other variations of the hourglass paradigm, such as that
shown in Fig. 11H, which depicts the same task only with
gaze/head position rotating around the same sequence in the opposite
direction. Clearly the control system transiently abandoned the
zero-torsion (in Fick coordinates) fixation range during these oblique
trajectories in favor of a more direct trajectory, supporting the
theory illustrated in Fig. 11D.
Task-dependent modifications in the head's Fick strategy
If the observed constraints on head orientation and axes during
gaze shifts were neural in origin, as they appeared to be in Fig. 11,
then they might show some capacity for plasticity or task dependence.
Here we describe two circumstances in which such task dependencies
indeed were observed. First, Tweed and Vilis (1992)
reported that during repetitive back-and-forth movements, the axes of
head rotation showed a tendency to tilt toward the axis perpendicular
to the plane containing the head direction vectors such that the angle
of rotation was minimized. We tested this by having monkeys
M1 and M2 perform repetitive back-and-forth vertical or
horizontal movements at various positions (again, M3 refused
to comply with these task demands). The case where horizontal movements
were repeated at different vertical levels was a more dramatic test of
this effect because it would tend to violate the normal space-fixed
character of the vertical rotation axis.
Figure 12 shows the results of this
test in both monkeys. Angular velocity loops during repetitive
horizontal rotations are viewed from the side perspective in each panel
along with the 2-D directional vectors of the head (- - -).
Left panels show the case where gaze and Hs were
tilted upward, whereas right panels show the case
where gaze and Hs were tilted downward. Unfortunately, the two monkeys
showed two different results. Figure 12, top, (A and B), shows the effect typically observed in animal
M2. This animal did not show the minimum rotation effect observed
in humans. Even after five (as illustrated) or more movement
repetitions in each direction, the axis of rotation remained remarkably
fixed in the Fick-like fashion. However, animal M1
(C and D) did show the minimum rotation effect
reported in humans (Tweed and Vilis 1992). By the second
and third horizontal repetition (as illustrated), the head axis already
had tilted maximally toward a point quasiorthogonal to the head
direction vector. Thus the use of this strategy appeared to be subject
dependent.
|
For a more specific test of the task dependency of these constraints,
we used a second paradigm. In this case, the fixation range of the
random task was reexamined while two trained animals (M1 and
M2) performed gaze shifts wearing opaque plastic goggles with only a small hole positioned over the center of the right eye
(Crawford and Guitton 1997b). This reduced the visual
range to a head-fixed monocular zone of ±4°, which removed several
normal visual task constraints (discussed in the next section) and
forced the head to become the primary mover of gaze. Therefore we
tentatively hypothesized that the head might behave more like Eh in
this task, i.e., obey Listing's law. Remarkably, this simplistic
hypothesis proved to be essentially correct.
Figure 13 illustrates the results of
this test. Note that in this figure, only random-task fixation points
are considered, which in previous sections were confined exclusively to
the twisted Fick-like surface. Figure 13A shows the
second-order fit to a control head range recorded just before putting
on the goggles, revealing the typical Fick-like twist. Figure
13B then shows the analogous fixation range of
head-orientation vectors recorded while the pretrained animal made
randomly directed movements immediately after the goggles were put in
place. As in all other experiments, this produced a slight clockwise
shift in head posture, toward the side with the aperture. More
importantly, the second-order fit to the range flattened out to closely
resemble similar fits to Eh position during saccades (Crawford
and Vilis 1991). Figure 13C quantifies this effect
by showing the average (and SEs across experiments) twist scores (term
a5, Eq. 5) during the random goggle task against the analogous control scores, in both trained animals. On
average (across the means of the 2 animals) the goggles caused a
reduction in the head twist score to only 31.4% of its normal value.
This reduction was statistically significant in both M1 (P
0.011) and M2 (P
0.0005).
|
Moreover, the variance of the head twist score increased substantially during the goggle task, particularly in animal M1. Because this variability might prove to be important in interpreting the goggle effect, several further examples of second-order surface fits to individual experiments have been provided (Fig. 13, D-F). During the goggle task, animal M1 sometimes reproduced the normal Fick-like fixation range (Fig. 13D) but sometimes produced the dramatically opposite twist consistent with Helmholtz coordinates (Fig. 13F). During other goggle experiments, M1 (and M2) produced ranges intermediate between these extremes that were either flattened (Fig. 13B) or curved with little twist (Fig. 13E).
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DISCUSSION |
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The general impact of this experiment can be summarized in three
statements. First, our description of the neural constraints on
orientations of Es, Hs, and Eh during visual fixations following head-free gaze saccades in the monkey largely confirm similar constraints observed in humans (Glenn and Vilis 1992;
Radau et al. 1994
). Such confirmation is useful because
of the inherent stability of coil signals in surgically implanted
animals as opposed to human search coil measurements. More importantly,
it suggests that (despite certain head-neck anatomic differences) the
monkey is an appropriate animal model to investigate the physiological mechanisms of this behavior, and thereby test computational models that
have arisen from experiments with humans (i.e., Tweed
1997
). Second, our analysis of orientation and velocity
trajectories in Eh and Hs address several issues pertaining to 3-D gaze
control that were either left unaddressed or only inferred indirectly in previous 3-D studies. In particular, we have shown that Eh saccades
anticipate torsional violations of Listing's law to land final Eh
position at zero torsion and that Hs dynamically acts like a Fick
gimbal during horizontal and vertical movements but not
during oblique movements. Finally, we have shown for the first time
that the head-fixation constraint is task dependent and modifiable by
visual input. Each of these observations has important implications for
understanding the neural control of gaze direction in 3-D space.
Constraints on Es, Hs, and Eh during visual fixation: implications for perception and control
Listing's law of Eh (with the head stationary) is the
quintessential motor synergy in the sense that it is obeyed with a high degree of precision (Ferman et al. 1987; Tweed
and Vilis 1990
; Tweed et al. 1994
), it has been
known for more than a century (Helmholtz 1867), and it
subsequently has engendered considerable research and controversy
(reviewed in Crawford and Vilis 1995
; Hepp et al.
1994
; Quaia and Optican 1998
). Surprisingly, it
is still not clear which factors determine this particular
implementation of Donders' law, e.g., as opposed to the Fick strategy
observed in Hs. In the 19th century both Hering (1868)
and Helmholtz (1867) formulated arguments for Listing's
law based on the assumption that it provided certain geometric
constancies between the retina and the external world. Such arguments
assume that Listing's law (i.e., a planar range of eye position
vectors) holds with a high degree of precision for eye orientations
in space when the head is free to move in a natural fashion.
It originally appeared that both Es and Hs do obey Listing's law at
least over a relatively central range of positions (Straumann et
al. 1991
; Tweed and Vilis 1992
). However, more
recent data from humans (Glenn and Vilis 1992
;
Radau et al. 1994
), and now monkeys, calls this into question.
First, even for a central target, the torsional range of Es around the
line of sight is highly variable (Fig. 2) (Radau et al.
1994). Second, over a larger 2-D gaze excursion, the 3-D
orientation range of Es is not planar but rather twisted like the range
associated with Fick gimbals (Fig. 3) (Glenn and Vilis
1992
; Radau et al. 1994
). Indeed, even with a
third-order fit, the torsional variance (SD) of our Es data was
consistently larger (average 3.55°) than that of our Eh data (average
1.87°). Even though we analyzed a much more variable and random 2-D
Es/Hs range compared with those used in the human experiments, the
former is almost identical to the analogous human Es data (Radau
et al. 1994
), whereas the latter is slightly smaller than the
human Eh data (perhaps simply due to minor experimental slippage in
human search coil lenses). The torsional SD of our Hs data was slightly
smaller (average 3.10°) than our Es variance but was considerably
smaller than the corresponding human Hs value of 4.75° (Radau
et al. 1994
). Note that the latter value was cut to less than
half when recomputed relative to the chest, which we could not do for
technical reasons. These data suggest that it is the 3-D orientations
of Eh and Hs (or more likely head-relative-to-chest) that are
constrained physiologically and that the apparent constraint on Es is
only the geometric byproduct of the other two constraints (Radau
et al. 1994
).
This by no means suggests that the observed constraints do not have
important implications for perception and the interpretation of visual
information for motor control. Even considering the high torsional
variance observed in Es compared with Eh, the behavioral range of Es
torsion is still relatively small compared with its potential
mechanical range (about ±90° in an upright primate). Moreover, the
Fick-like Es range keeps the para-foveal horizontal meridian of the eye
in better alignment with the horizon than does Listing's law
(Glenn and Vilis 1992; Klier and Crawford
1998
). These constraints are relevant to the problem of space
constancy in high-level object recognition because they reduce the
number of retinal perspectives required to develop object-centered
representations of natural visual targets, which themselves are
normally earth-oriented (e.g., Marr 1982
). Similarly,
although information about 3-D eye and head orientation may be used to
interpret the spatial content of retinal input, this process probably
depends on continual visuomotor calibration for various combinations of
eye/head position (Crawford and Guitton 1997a
;
Haustein and Mittelstaedt 1990
; Helmholtz
1867; Klier and Crawford 1998
). Therefore the
observed constraints on Eh, Hs, and Es orientation probably reduce the
computational load for high-level object recognition and egocentric
localization. This is consistent with the observation that accurate
spatial perception of the roll-tilt of visual stimuli breaks down with large Es torsion (e.g., Wade and Curthoys 1997
).
3-D Eye-in-head constraint and coordination of Eh saccades with slow phases
The previous section suggested that physiological constraints on
eye orientation are controlled at the level of Eh rather than Es. Such
a constraint is necessary for the oculomotor system to convert its 2-D
visual inputs (which only specify desired gaze direction) into actuated
3-D eye positions in an orderly fashion. In other words, Donders' law
solves the degrees-of-freedom problem (Crawford and Vilis
1995). Considerable controversy has persisted over the question
of whether the Eh is constrained solely by its musculature to obey
Donders' law during saccades or whether a specific neural
implementation is required (e.g., Crawford and Guitton
1997
; Crawford and Vilis 1991
; Hepp
1994
; Quaia and Optican 1998
; Raphan
1997
, 1998
; Tweed and Vilis 1990
; Tweed
et al. 1994
; Van Opstal et al. 1996
). This
mostly has been studied in the head-fixed preparation, where the eye
obeys Listing's law. However, it is the range of eye orientations
during head-free fixations that will be most important for
vision in its natural element.
To address these issues, our first goal was to determine the shape (if
possible) and thickness of the Eh fixation range. Unfortunately the 2-D
fixation range of Eh was much smaller than the corresponding Es and Hs
ranges. As a result, it is difficult to be confident in higher-order
terms describing any nonplanar aspects of the shape of the Eh fixation
range for the same reason that it is difficult to fit a line to a small
circular blob of points in an x-y scatter plot: the range of
the independent variables was insufficient to distinguish between
higher-order terms that would only become quantitatively important at
eccentric positions. In a previous paper, Radau et al.
(1994) statistically compared the goodness of fit of first-,
second-, and third-order fits to the Eh fixation range during head-free
gaze saccades across seven human subjects and concluded that the Eh
range was not significantly different from a plane. We could not take
this approach because of the insufficient number of animal subjects.
However, our observations were consistent with their conclusions, i.e.,
despite the statistical improvement in torsional variance with
higher-order fits to the Eh data, these improvements were not
impressive on visual inspection of the data (Fig. 4), and the nonplanar
terms of the fit were highly variable. Therefore we conclude that,
although the monkey Eh fixation range may or may not show some slight
quantitative curvature, there is no practical advantage in
distinguishing these ranges from a plane. Moreover, these
head-free fixation ranges were only slightly thicker in one
animal (M3) and only about twice as thick in the other two
animals compared with the torsional range reported for
head-fixed primates (Crawford and Vilis 1991
; Straumann 1991
; Tweed et al. 1990
). This
is remarkable considering the magnitude of head motion occurring
between these fixations.1
We therefore focused on the mechanisms that maintained this relatively
tight torsional fixation range despite transient large torsional
"violations of Listing's law" observed during various points in
the multistep gaze saccade. It was observed that Eh saccades were
driving eye position away from the quasiplanar fixation plane, such
that subsequent slow phases brought the eye back into the plane with
particular accuracy during the final slow phase that preceded
termination of the associated head movement. This complex goal-directed
torsional behavior contradicts the idea that Listing's law results
from a fixed internal projection of visual representations onto a 2-D
plane of saccade vectors (Raphan 1997, 1998
). Instead,
it supports the idea that Listing's law is upheld by a specific neural
mechanism that (in effect) selects a desired torsional eye position in
Listing's plane2 (Crawford and Vilis
1991
; Tweed 1997
; Van Opstal et al.
1996
).
The inherent difficulty with implementing such a mechanism during
head-free gaze saccades is that they end with movements (slow phases) that are not themselves purposeful, aimed movements but
rather are dictated by head rotation kinematics. Thus it would be up to
the Eh saccade generator to somehow anticipate these subsequent movements (there seems to be no other function to these rapid torsional movements because they do not affect gaze direction). Furthermore as described in more detail elsewhere (Crawford and Vilis 1991; Smith and Crawford 1998
), the
kinematic effects of slow phases on torsional position can only be
predicted from knowledge of both head velocity and eye position.
Therefore to land Eh on a final desired 3-D orientation, the head-free
Eh saccade generator would have to employ an algorithm that accounts
for both Eh position and anticipated head motion (Crawford and
Vilis 1991
). In a recent model, Tweed (1997)
implemented such an algorithm with the use of desired 3-D Es and Eh
orientation commands such that simulated head-free gaze saccades did
ultimately land Eh position within Listing's plane, as we have now
confirmed in the monkey.
At first thought, it might seem like computational overkill to employ
such a complex mechanism to anticipate violations of Listing's law.
However, consider the alternatives: without a torsional corrective
mechanism, huge (>20°) Eh and Es torsions would arise during a
single multiple-step gaze shift (as extrapolated in Fig. 6), which
could disrupt space-centered vision, as discussed earlier, and disrupt
stereo vision in a headcentric frame (Howard and Zacher 1991). Second, if this corrective mechanism was triggered only after the torsional slow phase, it then would transiently
disrupt vision at the end of the gaze shift, when visual stability is most critical. Moreover, these mechanisms probably do not only pertain
to torsional control. In the current experiment, there was no special
distinction among the horizontal, vertical, and torsional aspects of
this anticipatory behavior (e.g., Figs. 5-7) except that the torsional
fixation range was considerably more restricted than the 2-D fixation range.
Perhaps the most dramatic confirmation of this effect was described in
our previous report (Crawford and Guitton 1997b), in which animals M1 and M2, after training on the
original pin-hole aperture (described in the current study), were then
unable (initially) to direct saccades toward a new, slightly displaced
central aperture. Instead, regardless of starting position, Eh saccades
directed the eye toward a location appropriate for the subsequent slow phases to bring the eye back toward the learned 2-D location of the
(now occluded) original aperture. The latter strongly suggests that the
vertical and horizontal components of final post-VOR Eh position also
are preprogrammed, using an algorithm such as that described earlier
(Tweed 1997
). This converging evidence suggests a
mechanism whereby Eh saccades account for initial eye position, desired
target direction, and anticipated head movement to select each
component of desired final 3-D Eh orientation within some internally
delimited central range. In terms of 2-D direction, this Eh fixation
range was flattened in the horizontal dimension (Freedman and
Sparks 1987
; Glen and Vilis 1992
), whereas the
torsional degree of freedom was even more limited to a range
approximating Listing's plane.
Fick operator for the head?
Compared with the oculomotor system, which must point an easily defined 2-D visual axis toward targets, the job of the head-control system in gaze shifts is more difficult to state in quantitative terms. Perhaps it is best stated that the head, in its capacity as the platform for the oculomotor system, must be directed such that in the end, the target is within the internally delimited head-free oculomotor fixation range discussed earlier. Thus instead of a single vector (the visual axis), the head must rotate a binocular pair of 2-D Eh fixation ranges toward the target (think of a head-fixed flashlight, where 2-D Eh direction can only end up within the spread of light). This gives rise to two further degrees-of-freedom problems in choosing head orientation.
First, because a target potentially still can be acquired (by the
eye) at an infinite number of points within the headcentric Eh fixation
zone, the associated range of 2-D head pointing directions is not
severely limited by this ocular fixation range (Radau et al.
1994; Tweed 1997
). The data suggest that the
head probably does not use all of its allowable range of freedom in
thus acquiring targets (if it did, then the associated 2-D Eh range for
one target would be as big as the complete Eh range), and
yet it still showed much more 2-D variation than gaze direction for a
single target (Fig. 2). This suggests that the oculomotor "fixation
range" described earlier is really the amalgamation of smaller zones
for each body-centric target direction, further limiting the allowable
range of 2-D "pointing" directions of the head for each target.
At the extreme, a unique desired head position for a given target could
be selected by first computing the desired final Eh position
(Tweed 1997
), but this does not account for the
variability observed here in final head positions. However, the
possible range of eye-head combinations for a given target probably is
constrained further by the combination used at the previous fixation
point (Becker and Jürgens 1992
; Freedman
and Sparks 1997
; Fuller 1996
; Goossens and Van Opstal 1997
) and the behavioral context
(Crawford and Guitton 1997b
).
The second degrees-of-freedom problem in head control is like that of
the eye, i.e., even with a very narrow headcentric range of desired
facing directions, the head potentially could orient about the
head-centric torsional axis passing through the center of this range
through any arbitrary angle and still have gaze acquire the target.
Again, although Hs torsional variance was slightly larger than Eh
torsional variance, over a large range it was clearly limited compared
with the possible mechanical range of torsional head motion. Moreover,
this range formed a consistent shape (Fig. 3) similar to that observed
in humans (Glenn and Vilis 1992; Radau et al.
1994
). However, the vertical axis of the monkey range was
tilted from the more gravity-aligned head position range reported in
humans (Misslisch et al. 1994b
), even in animal
M3, which was allowed to slouch in a self-selected posture. More
importantly, the shape of this range was twisted like the range
produced by Fick gimbals when torsion (in Fick coordinates) is held at
zero, i.e., rotations about a headcentric torsional axis indeed were minimized. Our more precise quantitative analysis suggested that this
range was intermediate between a pure Fick constraint and a perfect
Listing's law but somewhat closer to the ideal Fick rule than the
ranges reported for humans (Glenn and Vilis 1992
).
In as much as this range is violated easily by voluntary effort and is
not determined by 2-D retinal input, it must be implemented by the
neural equivalent of a "Fick operator" (Tweed
1997). (This does not necessarily imply that this operator is
located in a compact nucleus or in any easily identifiable pattern of
signals.) Moreover, the observation that the head range is modified
readily to a more Listing-like plane by restricting visual input
suggests that this range optimizes task constraints rather than purely mechanical constraints (Radau et al. 1994
;
Theeuwen et al. 1993
). This task dependence may explain
why monkeys and humans show such similar Hs behavior, despite
differences in the gross anatomy of their foramen magnum and neck posture.
In this paper, we tried to address the nature of this Fick
operator by examining it under various conditions of normal fixation and adapted fixation and during rotations about various axes. This is
relevant both to determining the algorithm used by the Fick operator
and determining the behavioral parameters that it might be optimizing
(Glenn and Vilis 1992). From the normal random fixation
data and from the axes of rotation during cardinal horizontal or
vertical movements, it appeared that both the static and dynamic head
ranges were remarkably Fick-like, i.e., it was difficult to distinguish
whether position or velocity was being optimized. However, during
oblique head movements, there was a clear trend to abandon the Fick
constraint during the movement to take the most direct path from one
position to another position in the Fick "surface." Besides
demonstrating again that the head's Fick strategy is not a mechanical
constraint, this has the remarkable implication that the Fick operator
does not operate within a head motor feedback loop but rather only
chooses a final desired head orientation. (The implications
of this for feedback control of gaze direction will be considered in a
later section).
Any one desired head orientation can be reached from a given
initial position by an infinite number of rotational axes, and the data
suggest that the neural algorithm used to select these axes is rather
complex. For example, if the head always rotated about the axis of
minimum rotation (orthogonal to the plane of the initial and final
pointing vectors), then it would not rotate in the observed fashion
about a fixed vertical axis during horizontal gaze shifts. Thus during
randomly directed, normal head-free gaze shifts, the static and dynamic
constraints on head position might be characterized by the following
rule: the head-control system compares current and desired head
position and then chooses the unique (constantly oriented) axis of
rotation that most closely fits the Fick gimbal strategy. This would
explain why horizontal and vertical rotations remain Fick-like
throughout the movement because in these situations the desired Hs
orientation always can be reached by rotating about a constant axis in
Fick coordinates. However, because oblique movements require
nonconstant axes to maintain Fick torsion at zero, the
aforementioned rule only could approximate this ideal curved trajectory
with a single fixed axis, which would lead to the transient deviations
from the Fick surface described earlier. Unfortunately, even this rule
broke down during repetitive horizontal gaze shifts in animal
M1, which showed a tendency to optimize the vertical axis in an
energy efficient, non-Fick fashion, like the minimum rotation strategy
observed in human head movements (Tweed and Vilis 1992)
and to a lesser degree in some human eye movements (DeSouza et
al. 1997
). Therefore, it is probably more accurate to call the
Fick operator a "Donders' operator," whose function is to choose
the best 3-D trajectory for a given behavioral context.
These data thus suggest that the 3-D head-control strategy is
optimized for a number of motor and possibly sensory factors. Perhaps
the best question to focus on next is why the Fick strategy is used
during fixation. Our pin-hole goggle task would tend to suggest that
there is something about normal task constraints on head movement that
maintain the use of a Fick strategy during fixations. Parenthetically,
the increased head range in this task would not artificially lead to a
lower twist score because twist scores tend to be underestimated for
smaller ranges. The flattening of the head range during this task might
indicate that Listing's law was more optimal for the new eye-like role
of the head in directing gaze or it might simply indicate a tendency to
slip toward a default strategy during the removal of some key task constraint. The increased variability in the twist score in this task
might tend to support the latter idea.3 For
example, this constraint could depend on peripheral vision or alignment
of the two seeing eyes with the horizon (Glenn and Vilis
1992), cues that were absent with the pin-hole goggles. In any
case, our result shows that, contrary to a previous suggestion (Radau et al. 1994
; Theeuwen et al.
1993
), the Fick strategy does not appear to optimize purely
mechanical parameters. Further variations of this experiment might
precisely pin down the relevant constraint, but this is beyond the
scope of the current paper.
Another important factor that this study could not address is the
translational component of head movement. Because our animals showed
the same orientation constraints whether the head was allowed to freely
translate (animal M3) or not (M1 and
M2), additional measurement of head translation should
not invalidate our current observations on orientation.
However, measurement of head translations is important for targets
closer to the eye than those that we examined because they
significantly affect gaze direction and vestibulo-ocular compensation
in this range. Moreover, control of head translation and orientation
are probably inseparable in terms of the complex muscular physiology
and joint interactions of the neck (Richmond and Vidal
1988). In particular, head translations probably also affect
the translational locations of the rotational axes that we have
described here (Melis 1996
). Therefore in the future, it
will be useful to place the relatively simple orientation constraints
that we have described here into the broader context of controlling the
head as a six degree-of-freedom rotational/translational body.
Implications for models and the physiology of head-free gaze control
The remarkable accuracy of the visual axis during large
head-free saccades, despite variations in eye-head contribution
(Becker and Jürgens 1992; Freedman and
Sparks 1997
; Fuller 1996
; Guitton and
Volle 1987
) and perturbations to the trajectory
(Goffart et al. 1998a
; Péllison et al.
1995
; Tomlinson 1990
), suggests the existence of
a dynamic gaze error signal that guides and terminates the overall gaze
shift (Galiana and Guitton 1992
; Galiana et al. 1992
; Goosens and Van Opstal 1997
;
Laurutis and Robinson 1986
; Tomlinson and Bahra
1986
). Although 3-D feedback is required to update gaze error
for torsional and noncommutative motion (Henriques et al.
1998
; Tweed 1997
), the output signal is likely
coded in two dimensions at the level of the cortex and colliculus
(Van Opstal et al. 1991
). However, the observed behavior
of the primate suggests that this 2-D signal must be decomposed into
control signals matched to the eye and head in a very complex fashion. For example, like others (as reviewed in Guitton 1992
),
we have observed that large self-paced gaze shifts are broken down into several interim Eh saccades and intervening slow phases. The utility of
this strategy is clear: it allows the visual system to gather brief
snapshots of useful information during the course of a relatively long-lasting gaze shift. However, it now requires the brain to simultaneously specify separate goals, one for the ultimate desired target and several simultaneous goals for the interim Eh saccades. Furthermore introspection seems to suggest that the ultimate goal can
be chosen voluntarily, whereas the precise spatial pattern of the
interim saccades probably is selected by mechanisms that are largely involuntarily.
A reasonable hypothesis to explain this behavior is that
the interim saccades are generated by a quasi-independent brain stem circuit (Paré and Guitton 1998; Tomlinson
and Brance 1992
) that is nested within an overall gaze feedback
loop that specifies the ultimate goal at the level of cortex and the
superior colliculus (Galiana and Guitton 1992
;
Galiana et al. 1992
; Goosens and Van Opstal
1997
; Guitton et al. 1990
; Tomlinson
1990
). Because it has been suggested that visual
representations are remapped in the cortex and colliculus during
saccades to maintain spatial constancy (Duhamel et al.
1992
; Goldberg and Bruce 1990
; Henriques et al. 1998
; Walker et al. 1995
), dynamic gaze
error may be considered to be a special case of this mechanism, wherein
a particular selected target is tracked in 2-D until it is brought into
the foveal zone of internal retinotopic maps (Munoz and Wurtz
1995
; Munoz et al. 1991
; Van Opstal et
al. 1991
). This signal thus could continue to trigger
multiple-step saccades in the brain stem circuit (until gaze feedback
has signaled that the ultimate goal has been reached) through a
mechanism that then becomes refractory until the next slow phases
centers Eh.
In this nested arrangement, the 2-D to 3-D transformation for
Listing's law would need to occur in the brain stem loop that maps
saturated estimates of desired target displacement onto the appropriate
desired final Eh orientation (Guitton and Volle 1987; Tweed 1997
). As argued above, this requires knowledge of
current eye position and either an efferent copy of intended head
movement or a vestibular-derived estimate thereof. The
cortical/collicular drive alone is probably not sufficient to specify
this information. However, the vestibular nuclei and interstitial
nucleus of Cajal collectively possess a 3-D representation of current
eye position, ample vestibular information, and neurons that produce
bursts of action potentials during vestibular driven quick phases
(Crawford et al. 1997
; Fukushima and Fukushima
1992
; Helmchen et al. 1996
; Kitama et al.
1995
). The cerebellum also possesses a rich variety of
information relevant to this task with important 3-D connections to the
brain stem saccade generator (Goffart et al. 1998a
),
including inputs that appear to be involved in correcting torsional
violations of Listing's law (Van Opstal et al. 1996
).
These structures thus collectively could form a circuit that specifies
subgoals of desired final Eh position in a distributed fashion
(Crawford and Guitton 1997b
). In such a nested,
distributed system, it would not be surprising that the brain stem
would possess gaze-related activity in some signals (e.g.,
Cullen and Guitton 1997
; Cullen et al. 1993
), while retaining the ability to dissociate the Eh
trajectory from gaze error in the manner observed in several behavioral
paradigms (e.g., Crawford and Guitton 1997b
;
Tweed et al. 1995
). Moreover, this scheme predicts that
(and thus might explain why) microstimulation of the colliculus
produces near-constant gaze displacements with the head free but then
produces position-dependent goal-directed saccades when the head is
fixed4 (e.g., Freedman et al.
1996
; Paré and Guitton 1998
).
In contrast to the saccades that we quantified in this study, it
would appear that the head movement was triggered only by the ultimate
goal because the head showed no sign of accelerating/decelerating to
match the interim eye movements. Again the brainstem reticular formation is probably important for selecting head movement metrics for
a given gaze error. This being the case, it may form part of the
network that constitutes the Fick gimbal operator discussed earlier.
Note however, that our data suggested that this operator does not
function within any feedback loop (as described earlier). This has the
remarkable implication that head motor error normally is selected at
the beginning of gaze saccades in primates but thereafter operates
independently from gaze-error feedback.5
This is similar to the scheme proposed by Tweed (1997),
wherein the head was triggered by gaze error but only the eye was in
the dynamic gaze feedback loop.
At first glance, this seems to contradict the finding that cat
head motion can be updated by gaze error feedback during large perturbations to the system (Péllison et al.
1995). Assuming that the same is true for primate head
movements, these observations once again can be reconciled by proposing
a nested arrangement: suppose that the Donders' operator for the head
is nested within a dynamic gaze error loop but is only triggered by
gaze error when the target (desired gaze in space) is outside of the
allowable Eh fixation zone (described earlier) at the desired Hs
position. In normal circumstances, this would result in only a single
large head movement toward the target. However, a large head
perturbation (or a change in the desired target) could take the head
trajectory far enough from its optimal goal (as defined in the
preceding text) for dynamic gaze error to reactivate the Donders'
operator and compute a new head motor error command. The possible
utility of this arrangement is that it provides some voluntary
flexibility in the choice of head movement strategies, while
simultaneously making use of the more nimble oculomotor system to make
up for small idiosyncracies or deviations in the head trajectory. In principle, this scheme is no different from the proposed nesting of the
oculomotor circuit (Paré and Guitton 1998
), except
that the larger mechanical range of the head would make multiple-step head movements unnecessary for targets within the visual range. Thus
quasi-independent 3-D eye- and head-control systems (nested within a
dynamic feedback loop that drives 2-D gaze error) may be the optimal
control solution for head-free gaze control in the primate.
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APPENDIX |
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Algorithms for gaze velocity criteria
This section describes the algorithms (in generic code) and
velocity criteria used to select Eh data at various phases in the gaze
shift. Three-dimensional angular velocities of Es and Hs were computed
as described earlier (Crawford and Vilis 1991), and
their magnitudes (speed) were computed by taking the square root of the
sum of squares of the components. The following four measures of speed
are employed further in the following text, measured in degrees/second,
as well as generic string variables H, G, and VOR.
SH = current head speed; SG = current gaze (Es) speed; SH(next) = head speed over the subsequent data interval; SG(next) = gaze speed over the subsequent data interval.
Fixation
If SH < 10°/s and SG < 10°/s then [analyze data].
Eh(head-free) saccade starts
If SH(next) < 10°/s then H = off. If SH(next) > 25°/s then H = on. If SG < (SH + 50°/s) then G = off. If H = on and G = off and SG(next) > 100 and SG(next) > SH then: [G = on, analyze data.] End if.
Eh (head-free) saccade ends
If SH(next) < 10°/s then H = off. If SH(next) > 25°/s (or sometimes 150°/s) then H = on. If H = on and SG > (SH + 100°/s) then G = on. If G = on and SG(next) < (SH + 30°/s) then: [G = on, analyze data] End if.
Slow phase ends
If SH(next) > 25°/s and SG > (SH + 100°/s) then G = on. If G = on and SH > 25°/s and SG < SH/2 then [VOR = on, G = off] End if. If VOR = on and SH(next) < 5°/s then [G = off, VOR = off, analyze data] End if. If VOR = on and SH(next) > (SH + 50°/s) then [VOR = off, analyze data] End if. If SG(next) > SH then G = on. If SH(next) < 5°/s then G = off.
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ACKNOWLEDGMENTS |
---|
J. D. Crawford thanks J. Roi, L. Volume, W. Lezama, and J. Laurence for technical assistance, Dr. D. Tweed for critical editorial comments, and S. N. for inspiration.
This work was funded by Canadian Medical Research Council grants to J. D. Crawford and D. Guitton and by the Human Frontiers Science Organization (D. Guitton). J. D. Crawford is an Alfred. P. Sloan Fellow and holds a Canadian Medical Research Council Scholarship.
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FOOTNOTES |
---|
Address for reprint requests: J. D. Crawford, Dept. of Psychology, York University, 4700 Keele St., Toronto, Ontario M3J 1P3, Canada.
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.
1
Part of the increase in the head-free Eh fixation
range compared with the head-fixed range may have been due to
dependencies of static eye torsion on static head orientation. For
example, the systematic clockwise/counterclockwise deviation of head
orientations during right/left head positions, respectively, may have
induced a small ocular counter-roll. This static counter-roll could
cause the Eh fixation plane to apparently tilt or widen, depending on the variability between eye and head position for a given gaze direction. Moreover, even zero-roll horizontal head orientations have
been shown to affect the orientation of Listing's plane relative to
the head (Misslisch et al. 1998) possibly leading to
similar widening effects during our random task.
2
This does not contradict the idea that muscular
position-dependencies might facilitate and simplify the neural
maintenance of Listing's law when the head is fixed, where eye
position remains within Listing's plane (Crawford and Guitton
1997; Demer et al. 1995
; Quaia
and Optican 1998
; Raphan 1998
).
3
The greater variability of twist in the pin-hole goggle
range of animal M1 might be related to its tendency to
more readily optimize rotation axes as seen during the repetitive task.
If all axes are optimized to minimize the angle of rotation, Donders' law would break down (Tweed and Vilis 1990) and random
range twists could appear, depending on the idiosyncratic paths of the
head in the random task.
4
This can be explained as follows. Assume that
1) the colliculus encodes retinal error, i.e., desired
gaze displacement, 2) a brain stem circuit drives Eh to
a final desired position that is matched to a desired head position,
and 3) to do this, the latter circuit uses feedback
information about actual head movement to anticipate subsequent slow
phases (Crawford and Guitton 1997b), as we have
proposed. First, stimulation of the colliculus in a head-free animal
should correctly activate the brain stem circuit and produce natural
looking eye-head movements with only a mild position-dependent
convergence in gaze. The latter effect can be explained simply on the
basis of the inherent position dependence of retinal error
(Crawford and Guitton 1997a
; Klier and Crawford 1998
). However, with the head fixed, initial Eh position would tend to fall outside of the normal orbital zone associated with that
particular head position and gaze direction. When activated, the
colliculus/brain stem circuit would "attempt" to shift gaze and
center the eye toward the normal Eh zone for that target direction. Because the head cannot move and because head feedback would inform the
system that no subsequent slow phase is coming, saccades would simply
drive the eye toward the desired Eh position, producing the observed
goal-directed behavior (Freedman et al. 1996
;
Paré and Guitton 1998
). The absence of this
phenomenon in some stimulation preparations probably corresponds to
extensive head-fixed training.
5
Note, however, that the head movement signal, either in
the form of efference copy or vestibular re-afference, still would have
to be fed back to the common gaze error signal to make maintain the
spatial registry of visual targets (Henriques et al.
1998) and ensure that gaze gets onto the target
(Péllison et al. 1995
).
Received 17 August 1998; accepted in final form 5 January 1999.
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