1Laboratory of Sensorimotor Research, National Eye Institute, National Institutes of Health, Bethesda, Maryland 20892; and 2Department of Physiological Optics, School of Optometry, University of Alabama at Birmingham, Birmingham, Alabama 35294
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ABSTRACT |
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Busettini, C.,
E. J. Fitzgibbon, and
F. A. Miles.
Short-Latency Disparity Vergence in Humans.
J. Neurophysiol. 85: 1129-1152, 2001.
Eye movement
recordings from humans indicated that brief exposures (200 ms) to
horizontal disparity steps applied to large random-dot patterns elicit
horizontal vergence at short latencies (80.9 ± 3.9 ms, mean ± SD; n = 7). Disparity tuning curves, describing the
dependence of the initial vergence responses (measured over the period
90-157 ms after the step) on the magnitude of the steps, resembled the
derivative of a Gaussian, with nonzero asymptotes and a roughly linear
servo region that extended only a degree or two on either side of zero
disparity. Responses showed transient postsaccadic enhancement:
disparity steps applied in the immediate wake of saccadic eye movements
yielded higher vergence accelerations than did the same steps applied
some time later (mean time constant of the decay, 200 ms). This
enhancement seemed to be dependent, at least in part, on the visual
reafference associated with the prior saccade because similar
enhancement was observed when the disparity steps were applied in the
wake of saccadelike shifts of the textured pattern. Vertical vergence
responses to vertical disparity steps were qualitatively similar:
latencies were longer (on average, by 3 ms), disparity tuning curves
had the same general form but were narrower (by 20%), and their
peak-to-peak amplitudes were smaller (by
70%). Initial vergence
responses usually had directional errors (orthogonal components) with a
very systematic dependence on step size that often approximated an
exponential decay to a nonzero asymptote (mean space constant ± SD, 1.18 ± 0.66°). Based on the asymptotes of these orthogonal
responses, horizontal errors (with vertical steps) were on average more
than three times greater than vertical errors (with horizontal steps). Disparity steps >7° generated "default" responses that were
independent of the direction of the step, idiosyncratic, and generally
had both horizontal and vertical components. We suggest that the
responses depend on detectors that sense local disparity matches, and
that orthogonal and "default" responses result from globally
"false" matches. Recordings from three monkeys, using identical
disparity stimuli, confirmed that monkeys also show short-latency
disparity vergence responses (latency
25 ms shorter than that of
humans), and further indicated that these responses show all of the
major features seen in humans, the differences between the two species being solely quantitative. Based on these data and those of others implying that foveal images normally take precedence, we suggest that
the mechanisms under study here ordinarily serve to correct small
vergence errors, automatically, especially after saccades.
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INTRODUCTION |
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Vergence eye
movements are critical for good binocular vision, serving to align both
eyes on the same object: the nearer the object of regard, the greater
the required convergence. The visual control of vergence depends
heavily on the slight difference in the positions of the images on the
two retinas, which is referred to as binocular disparity and
effectively defines the vergence error. Although there are a number of
complex visual cues to viewing distance that can influence vergence,
here we shall be concerned solely with disparity, which is the most
potent (for recent review, see Collewijn and Erkelens
1990). The ability of pure disparity errors to drive vergence
was first demonstrated by Rashbass and Westheimer
(1961)
, who used a Wheatstone stereoscope to present identical
targets independently to the two eyes. Targets with crossed disparity
errors (equivalent to objects nearer than the plane of fixation)
elicited increased convergence, and targets with uncrossed disparity
errors (equivalent to objects farther than the plane of fixation)
elicited decreased convergence, exactly as expected of a negative
feedback system working to achieve and maintain appropriate binocular
alignment. Most studies have been concerned with horizontal
vergence, perhaps in large measure because it is the means by which
binocular alignment is shifted between objects in different depth
planes. However, good binocular vision requires that the two lines of
sight be aligned vertically as well as horizontally, and vertical
disparities have been shown to elicit appropriate vertical vergence,
although the effective range of disparities is much smaller, the
responses have much more sluggish dynamics, show more extensive spatial
integration, and are less sensitive to instruction, than the horizontal
vergence responses associated with horizontal disparities
(Howard et al. 1997
, 2000
; Kertesz
1983
; Stevenson et al. 1997
).
In the present study on humans, we have been concerned solely with the
initiation of vergence by disparity steps applied to large random-dot
stereograms. Previous studies on humans have generally, although not
always, used small targets and reported latencies ranging from 150 to
200 ms (Erkelens and Collewijn 1991; Houtman et
al. 1977
, 1981
; Jones 1980
;
Mitchell 1970
; Rashbass and Westheimer
1961
; Westheimer and Mitchell 1956
). Using
monkeys, we have recently reported that, when large textured
patterns are used, horizontal disparity steps of suitable magnitude
consistently elicit horizontal vergence eye movements with latencies of
<55 ms (Busettini et al. 1994a
, 1996b
).
These short-latency vergence responses were in the appropriate
direction only when steps were small (<2-3°), and large steps (up
to 12.8°) yielded responses with both isogonal and orthogonal
components that were largely independent of whether the steps were
crossed or uncrossed, horizontal or vertical (so-called, "default"
responses). We argued that the responses to small disparity steps
reflected the operation of a servomechanism that normally functions to
correct residual vergence errors, and the (default) responses to large
steps were due to residual local correlations. We also reported that
small disparity steps applied in the immediate wake of a saccadic eye
movement yielded appropriately directed vergence eye movements with
much higher initial accelerations than did the same steps applied some time later. Further, this transient postsaccadic enhancement seemed to
be dependent, at least in part, on the visual stimulation associated with the prior saccade because similar, although sometimes weaker, enhancement was observed when the disparity steps were applied in the
wake of saccadelike shifts of the textured pattern (so-called, "simulated saccades"). In the present paper on humans, we report similar findings: latencies are short (although 25 ms or so longer than
in monkeys), there are default responses with large steps, and there is
transient enhancement in the wake of real and simulated saccades. The
only significant methodological difference between the present study
and our previous one on monkeys was the visual stimulus: the collage of
arbitrary geometrical shapes used previously was replaced by a
random-dot pattern, permitting a more formal description of the
stimulus. We also report here that initial vergence responses have
orthogonal components that reach an asymptote with steps of a few
degrees and persist (as default responses) with large steps. Further,
we show that the initial vergence responses to small disparity steps
(<2-3°) are relatively insensitive to eightfold changes in the size
of the texture elements (random dots), although responses to steps of
intermediate size (3-6°) are larger with larger elements. In
addition, we report that the vertical vergence responses to vertical
disparity steps have only slightly longer latencies but are appreciably
smaller in magnitude than the horizontal responses to horizontal steps,
although the general form of the disparity tuning curves is very
similar. Finally, we use the same new random-dot stimuli to extend our
earlier report on monkeys and show that the initial vergence responses
of monkeys share most of the features of the human, the differences
between the two species being quantitative rather than qualitative.
Some of these findings on humans have been published in abstract form (Busettini et al. 1994b
).
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METHODS |
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The eye movements evoked by brief exposure to disparity steps
applied to large projected random-dot patterns were recorded from seven
adult human subjects. All procedures were approved by the Institutional
Review Committee concerned with the use of human subjects, and all
subjects provided informed consent. Three of the subjects (FM,
RK, and GM) each participated in numerous recording
sessions, and four more (MB, KP, HA, and JG) each
participated in only a few sessions on selected abbreviated paradigms.
All of these subjects had stereoacuities better than 40 s of arc
(Titmus test) and no known oculomotor or visual problems other than
refractive errors that were corrected with spectacles when necessary.
Only two subjects (FM and RK) had prior
experience (as subjects) in eye-movement studies. We also recorded the
vergence responses of three rhesus monkeys using the exact same stimuli
as for the human recordings to permit a quantitative comparison between
the two species. Except for the details of the stimuli (described in
Recording and stimulation procedures), the
methodology used on monkeys was exactly the same as in our earlier
study and will not be described here (Busettini et al.
1996b).
Recording and stimulation procedures
The presentation of stimuli and the acquisition, display, and
storage of data were controlled by a PC (Hewlett Packard Vectra, 486)
using a Real-time EXperimentation software package (REX) developed by
Hays et al. (1982). The horizontal and vertical
positions of both eyes were recorded with an electromagnetic induction
technique (Robinson 1963
) using scleral search coils
embedded in silastin rings (Collewijn et al. 1975
).
Coils were placed in each eye following application of 1-2 drops of
anesthetic (proparacaine HCl), and wearing time ranged up to 73 min for
the three main subjects and 30 min for all others. The AC voltages
induced in the scleral search coils were led off to a phase-locked
amplifier that provided separate DC voltage outputs proportional to the
horizontal and vertical positions of the two eyes with corner
frequencies (
3 dB) at 1 kHz (CNC Engineering). The outputs from the
coils were calibrated at the beginning of each recording session by
having the subject fixate small target lights located at known
eccentricities along the horizontal and vertical meridia. Peak-to-peak
voltage noise levels were equivalent to an eye movement of 1-2 min of arc. Interocular distance was measured to the nearest millimeter.
The subject was seated in a fiberglass chair with his/her head stabilized by means of a chin support and forehead rest combined with a head strap and faced a translucent tangent screen (distance, 33.3 cm; subtense, 85 × 85°) onto which two identical, overlapping patterns were back-projected. Orthogonal polarizing filters in the two projection paths and matching filters in front of each eye ensured that each pattern was visible to only one eye: dichoptic stimulation. The screen was constructed of material specially designed to retain the polarization (Yamaboshi, Tokyo, Japan). The patterns consisted of black circular dots with randomly distributed centers on a white background; overlaps were freely allowed, resulting in irregular clustering, and the screen image had equal amounts of black and white (50% coverage). Dot diameters were 2° except for one special study in which this parameter was varied systematically (when all dots had one of the following diameters in a given experiment: 0.5, 1.1, 2.2, or 4.4°). The luminance of the images on the screen was measured with a photometer (Spectra Pritchard), sampling the screen through the polarizing filters so as to mimic the subjects' view. With this arrangement, the luminance measured through the matching polarizing filters was 0.13 cd/m2 in the light areas of the patterns and 0.0026 cd/m2 in the dark areas. The equivalent measures through the nonmatching (orthogonal) polarizing filters were 0.0011 cd/m2 in the light areas and 0.00060 cd/m2 in the dark areas. Subjects were unaware of the "ghost" images seen through the orthogonal filters. Pairs of mirror galvanometers (General Scanning, M3-S with vector tuning) positioned in each of the two light paths in an X/Y configuration were used to control the horizontal and vertical positions (and thereby the horizontal and vertical disparities) of the two images. These galvanometers were driven by the DAC outputs of the PC at a rate of 1 kHz with a resolution of 12 bits (optical range, ±50°). Voltage signals separately encoding the horizontal and vertical positions of both eyes together with the positions of the four mirror galvanometers were low-pass filtered (Bessel, 6-pole, 180 Hz) and digitized to a resolution of 16 bits, sampling at 1 kHz. All data were stored on a hard disk and, after completion of each recording session, were transferred to a workstation (Silicon Graphics) for subsequent analysis. The rise time of the mirror galvanometers was <2 ms, and to determine their true dynamics and exact timing they were monitored with a Tektronix digital storage oscilloscope linked to a PC (386).
Paradigms
In a given experiment, the stimulus parameter(s) under study were varied from trial to trial in a pseudorandom sequence, in part to discourage prediction/anticipation, and in part to distribute any effects due to short-term changes in nonvisual factors such as arousal, attention, fatigue, and so forth. It was usual to collect data over several sessions until each condition had been repeated a sufficient number of times to permit good resolution of the responses to be achieved (through averaging) even when we were exploring the limit of the responsive range with stimuli of marginal efficacy.
STANDARD PARADIGM. At the beginning of each trial, the two patterns on the screen were positioned in register and overlapped exactly (zero disparity) for a minimum period in excess of 1 s to allow adequate time for the subject to acquire a convergent state appropriate for the near viewing (33.3 cm). Disparity steps were initiated in the wake of a saccade into the center of the screen because preliminary experiments had shown that the vergence responses were subject to transient postsaccadic enhancement. This was accomplished by having the subject transfer fixation between suitably positioned target spots projected onto the scene through polarizing filters so as to be seen by the right eye only (to avoid any possible disparity conflict with the background patterns). The initial target spot appeared 10° right of center 1 s after the beginning of the trial. When the subject's right eye had been positioned within 1-2° of the spot for a period of time that was randomly varied (1-1.5 s), the spot was extinguished and a new one appeared at the center of the screen. This new target was extinguished as soon as the computer detected a saccadic eye movement, using as a criterion an eye speed >54°/s. If this saccade achieved a speed in excess of 180°/s and arrived within 4° of the position of the new target (which was now no longer visible), then it was deemed appropriate and the disparity step was initiated with a postsaccadic delay of 50 ms (measured from the time when eye speed fell below 36°/s). We used the convention that rightward and upward movements were positive, and stimulus disparity was computed by subtracting the horizontal (or vertical) position of the right image from the horizontal (or vertical) position of the left image. This meant that horizontal disparity steps were positive when the left stimulus stepped to the right and/or the right stimulus stepped to the left (crossed-disparity steps), and negative when the left stimulus stepped to the left and/or the right stimulus stepped to the right (uncrossed-disparity steps); vertical disparity steps were positive when the left stimulus stepped upward and/or the right stimulus stepped downward (left-hyper disparity steps), and negative when the left stimulus stepped downwards and/or the right stimulus stepped upward (right-hyper disparity steps). The disparity steps had a rise time of <2 ms and were applied symmetrically to the patterns seen by each of the two eyes (equal amplitudes, opposite directions), except when stated otherwise. The amplitude of the disparity steps varied from trial to trial (absolute values: 0.2, 0.4, 0.8, 1.2, 1.6, 2.0, 2.4, 3.2, 4.0, 4.8, 5.6, 6.4, 9.6, and 12.8°), with crossed, uncrossed, left-hyper, and right-hyper steps being randomly interleaved. Because we were interested only in the initial vergence responses, exposure to the disparity steps lasted only 200 ms, and, if there were no saccades during this time, then the data were stored on a hard disk; otherwise, the trial was aborted and subsequently repeated. At this point in the paradigm, electro-magnetic shutters in the light paths were used to blank both images for 500 ms, marking the end of the trial; when the images reappeared, they were once more in register for the start of the next trial. The projected patterns always filled the entire screen, and their initial positions were pseudorandomized (9 positions, with horizontal and/or vertical offsets of 0 or 10°) to reduce the impact of local anisotropies in the patterns on the mean vergence responses. Subjects were instructed to make saccades into the center of the pattern by following the projected target spots and then to refrain from making any further saccades until the screen was blanked, signaling the end of the trial. Subjects were given no instructions in regard to the disparity step stimuli but were asked to restrict their blinks to the inter-trial period. Direct observation, in addition to the eye movement profiles (blinks being associated with transient horizontal convergence and downward version), indicated that subjects had no problem following this instruction. By applying the disparity steps in the immediate wake of centering saccades we ensured that 1) the subject was alert during the steps, 2) the stimulus pattern was always centered on the retina at the onset of the steps, and 3) the vergence responses were enhanced (postsaccadic enhancement). Note that all experiments included control trials in which no steps were applied (saccade-only trials).
DEPENDENCE ON A PRIOR SACCADE OR SIMULATED SACCADE.
Preliminary experiments (Busettini et al. 1994b) had
revealed that, like ocular following (Gellman et al.
1990
), disparity vergence was subject to transient postsaccadic
enhancement, and we now conducted a series of experiments in which the
postsaccadic delay was varied systematically to characterize the time
course of the enhancement. Stimuli were 1.6° crossed- and
uncrossed-disparity steps, and the postsaccadic delay intervals were
50, 100, 200, 400, and 800 ms (randomly interleaved).
OCULAR FOLLOWING: DEPENDENCE ON A PRIOR SACCADE OR SIMULATED
SACCADE.
To allow a direct comparison of the effects of a prior saccade or
simulated saccade on disparity vergence with those on ocular following
(Gellman et al. 1990), additional experiments were
undertaken that were identical to those just described except that the
disparity steps were replaced with conjugate steps in which the
patterns seen by both eyes stepped together 0.8° (leftward or
rightward): ocular following stimulus. Note that the previous study of
the dependence of human ocular following on a prior saccade used
velocity step stimuli (Gellman et al. 1990
).
Data collection and analysis
The horizontal and vertical eye position data obtained during
the calibration procedure were each fitted with a third-order polynomial that was then used to linearize the horizontal and vertical
eye position data recorded during the experiment proper. The latter
were then smoothed with a cubic spline of weight
107, selected by means of a cross-validation
procedure (Eubank 1988), and all subsequent analyses
utilized these splined data. To be consistent with our conventions for
defining the polarity of the disparity stimuli, rightward and upward
eye movements were defined as positive, and vergence position was
computed by subtracting the horizontal (or vertical) position of the
right eye from the horizontal (or vertical) position of the left eye.
This meant that horizontal vergence was positive (denoting increased
convergence) when the left eye moved rightward with respect to the
right eye, or the right eye moved leftward with respect to the left
eye. Likewise, vertical vergence was positive when the left eye moved upward with respect to the right eye, or the right eye moved downward with respect to the left eye (so-called, left sursumvergence or right
deorsumvergence). Horizontal (or vertical) version position, equivalent
to cyclopean gaze position, was computed by averaging the horizontal
(or vertical) positions of the two eyes. Vergence (or version) velocity
was obtained by two-point backward differentiation of the vergence (or
version) position data.
The vergence position and vergence velocity temporal profiles recorded in all of the trials using a given stimulus condition were displayed together (synchronized to the disparity step) with an interactive graphics program that allowed the deletion of the occasional trials with saccades or blinks.
To best illustrate the temporal structure of the responses, mean vergence velocity profiles were computed for each stimulus condition. To eliminate any effects due to postsaccadic vergence drift, the mean vergence velocity profile recorded during the control saccade-only trials was subtracted from the mean vergence velocity profiles obtained for each stimulus condition. All of the vergence velocity traces in the figures have been so adjusted, and upward deflections of these traces represent convergent or left sursumvergent velocities.
LATENCY MEASURES.
An objective algorithm was used to estimate the latency of onset of
vergence using data obtained with disparity steps that gave
close-to-maximal responses. Visual inspection of the mean vergence
velocity profiles had indicated that the average latencies were
generally 75-85 ms. Accordingly, the individual vergence velocity
profiles over the time window, 52-118 ms (measured with respect to the
onset of the disparity step), were fitted with a function that assumed
that, up to a time, T, the response profiles were flat
(preresponse period), and then incremented linearly (response period).
The fitting was done using the nonlinear regression method implemented
in BMDP 3R (Dixon et al. 1990), based on a modified
Gauss-Newton algorithm (Jennrich and Sampson 1968
). For times <T, the function had a constant value
(P1), and for times
T,
the function had a value, at time t, of
P1 + [P2(t
T)]. The value of the baseline
(P1), the starting point of the linear segment (T, which was our estimate of the response latency),
and the slope of the linear segment
(P2), were all free parameters. Starting values were 75 ms (T), 0°/s
(P1), and
0°/s2 (P2).
AMPLITUDE MEASURES. Estimates of the amplitude of the initial disparity vergence response were obtained by measuring the change in vergence position over a 67-ms time interval starting 90 ms after the onset of the disparity step. It will be seen that the mean latency of onset is about 80 ms so that this amplitude measure is restricted to the period prior to the closure of the feedback loop, when eye movements begin to influence the disparity: initial open-loop response. The measures from all trials were then used to calculate the mean change in vergence, together with the SD, for each stimulus condition. Of course, sampling the response at a fixed time with respect to the onset of the stimulus meant that the sample would be sensitive to changes in the latency of onset of the response. The latency of vergence showed little dependence on any of the stimulus parameters examined in the present study, although the initial vergence responses could become vanishingly small as the limits of the response range were explored. (At such times, response-locked measures would default to later components of the response.) To eliminate any effects due to postsaccadic vergence drift, the mean change in vergence during the saccade-only (control) trials was subtracted from the mean change in vergence for each stimulus condition, and these adjusted measures are the ones given in the text and plotted in the figures (where they are referred to as "change in vergence position").
OCULAR FOLLOWING. The analysis of the ocular following data was very similar to that of the vergence data except that it was carried out on the splined position measures obtained from the right eye. Quantitative estimates of the amplitudes of the initial responses were obtained by measuring the change in eye position during the 67-ms time interval starting 90 ms after the onset of the conjugate position step, and two-point backward differentiation was used to obtain eye velocity profiles. The position measures and velocity temporal profiles obtained for all trials were then averaged for each stimulus condition, and any effects due to postsaccadic drift were eliminated by subtracting the data obtained from saccade-only (control) trials. These adjusted eye-position measures (referred to as "change in eye position") and eye-velocity temporal profiles are used for all figures and textual references.
Phoria measurement
Dissimilar target images were presented to the two eyes
dichoptically, and the subjects' verbal reports of their relative positions were used to bring the targets into subjective alignment using a staircase procedure, thereby providing an estimate of each
subject's phoria. Subjects viewed the tangent screen in the usual way,
and separate projectors with orthogonal polarizers were used to present
an upright cross (+) continuously to one eye and an oblique cross (×)
transiently to the other. Each cross was black on a white background
and spanned 2.3° with arms 10 min of arc thick. The subject fixated
the upright cross, and, following a warning tone, the oblique cross
appeared for 50 ms. The subject was required to report the horizontal
and vertical position of the oblique cross with respect to the upright
cross, i.e., right/left/aligned, above/below/aligned. If the subject reported misalignment, then, on the next trial, the oblique cross was
repositioned, by a discrete amount, so as to reduce its apparent horizontal and vertical separation from the upright cross. If the
subject reported alignment along one or the other axis, no adjustment
was made along that axis for the next trial. At the start of each block
of trials, the oblique cross could have horizontal and vertical offsets
(relative to the upright cross) of 0, +5, or 5° (varied randomly).
The repositioning steps were initially 2°, and then reduced with each
successive report of alignment or reversal in the apparent
misalignment, to 1°, then to 0.5°, and finally to 0.2°. When the
horizontal and vertical steps had both decremented to 0.2°, the
oblique cross had invariably reached an asymptotic position, and the
block was continued for 20 more trials before starting a new block with
a new misalignment. Each subject completed 9-20 blocks of trials, and
his/her phoria was estimated from the average misalignment of the 2 crosses for the last 20 trials in each block.
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RESULTS |
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Vergence responses to horizontal disparity steps
Horizontal disparity steps of suitable amplitude applied to large random-dot patterns elicited consistent horizontal vergence responses at short latencies. Figure 1 shows sample horizontal vergence velocity temporal profiles from 1 subject in response to 174 horizontal crossed-disparity steps of 2° applied 50 ms after 10° leftward centering saccades. Data are shown for all trials except the few (8) contaminated with saccades. Also shown in Fig. 1 is the mean horizontal vergence velocity profile (±SD), together with the mirror galvanometer feedback signals indicating the horizontal positions of the images seen by the left and right eyes. The estimated mean latency (objectively determined, see METHODS) for the data shown in Fig. 1 was 82.5 ms and is indicated by the arrows. For 2° crossed-disparity steps such as those used in Fig. 1, the mean latency for seven subjects was 80.9 ± 3.9 (SD) ms. Individual mean latencies (±SD), together with the number of measures contributing to the estimates (when the latency algorithm converged) and the total number of trials from which the data were drawn (after rejecting trials with saccades or blinks), were as follows: 82.5 ± 4.8 ms (subject RK, n = 174/174), 86.0 ± 8.7 ms (FM, 140/144), 84.6 ± 11.6 ms (GM, 147/177), 78.0 ± 6.2 ms (JG, 147/148), 77.7 ± 9.2 ms (KP, 165/168), 81.6 ± 7.0 ms (MB, 169/172), and 75.6 ± 9.2 ms (HA, 31/32). Because our major concern was with the initial open-loop vergence responses, the temporal profiles in all figures are discontinued 180 ms after the onset of the disparity steps.
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BINOCULAR RESPONSE TO A BINOCULAR STIMULUS.
These short latencies are similar to those reported for the ocular
following elicited by conjugate ramps applied to large textured
patterns (Gellman et al. 1990). Because visual motion detectors can integrate position steps over time to generate an apparent motion signal (Mikami et al. 1986a
,b
;
Newsome et al. 1986
), it was possible that the
short-latency vergence responses resulted from independent monocular
tracking, in which each eye tracked the apparent motion that it saw,
rather than from the binocular misalignment per se. To test this idea,
we restricted the step to one eye only, leaving the other eye to view a
stationary pattern. The movements of the eye that saw the stationary
pattern were of particular interest; any effects on this eye due to the monocular apparent-motion cues should have been either negligible (if
motion stimuli affected only the eye that saw the motion) or in the
same direction as the motion (if motion stimuli at either eye affected both eyes), whereas any effects on this eye due to the
binocular misalignment (stereo) cues should have been in the direction
opposite to the apparent motion stimulus.
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DEPENDENCE ON THE MAGNITUDE AND DIRECTION OF THE STEPS. Vergence responses were often not exactly aligned with the direction of the disparity steps and could include appreciable orthogonal components ("directional errors"). That is, responses to horizontal steps included vertical vergence, and responses to vertical steps included horizontal vergence. Like the isogonal components, these orthogonal components showed a highly systematic dependency on the amplitude and direction of the disparity step, but the form of this dependency differed markedly for the two components and will be described separately.
Isogonal components. With small horizontal disparity steps (<3°), the very earliest isogonal (i.e., horizontal) components of the vergence responses were always in the compensatory direction, i.e., the direction that reduced the seen disparity, so that crossed steps resulted in increased convergence and uncrossed steps resulted in decreased convergence. This is evident from the horizontal vergence velocity profiles shown for each of three subjects in the middle rows of Fig. 3 (stimuli, crossed steps) and Fig. 4 (stimuli, uncrossed steps): see data labeled
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Vergence responses to vertical disparity steps
Vertical disparity steps of suitable amplitude elicited consistent vertical vergence responses at short latencies. Using the vertical vergence velocity data obtained with 1.2° left-hyper steps, mean latency (±SD) determined by our objective method was 85.1 ± 3.4 ms for four subjects. Individual mean latencies (±SD), together with the number of measures contributing to the estimates and the total number of trials from which the data were drawn, were 86.9 ± 12.4 ms (subject RK, n = 159/179), 84.9 ± 12.3 ms (FM, 122/145), 88.2 ± 14.3 ms (GM, 152/177), and 80.5 ± 11.5 ms (HA, 26/31). These latencies are on average 3 ms longer than those listed earlier for the isogonal vergence responses (of these same 4 subjects) to horizontal disparity steps.
BINOCULAR RESPONSE TO A BINOCULAR STIMULUS.
Once again, we tested the possibility that these short-latency
(isogonal) vergence responses might have resulted from independent monocular tracking, rather than from disparity per se, by restricting the steps to one eye only, leaving the other eye to view a stationary pattern. The results of one such experiment on subject RK
are shown in Fig. 7, in which vertical
positive-disparity steps (that is, left-hyper steps) of 1.2° were
applied by 1) shifting the pattern seen by the left eye
0.6° upward and the pattern seen by the right eye 0.6° downward
(), 2) shifting the pattern seen by the left eye 1.2°
upward (· · ·), or 3) shifting the pattern seen by
the right eye 1.2° downward (- - - - -). The outcome was essentially the same as for horizontal vergence in that monocular steps
were almost as effective as binocular ones in producing (isogonal)
vergence, and the eye that saw the stationary pattern always
moved in a direction appropriate for a stereo-driven response: when
only the right eye saw a step (downward), the left eye moved upward,
and when only the left eye saw a step (upward) then the right eye moved
downward. Essentially identical data were obtained from two other
subjects (FM and GM).
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DEPENDENCE ON THE MAGNITUDE AND DIRECTION OF THE STEPS.
The vergence data obtained with vertical steps showed a pattern of
dependence on the amplitude and direction of the steps strongly
resembling that reported above for horizontal steps. The relevant data
for vertical steps are shown in Figs.
810, which are organized like Figs. 3-5 to permit a ready comparison with
the data for horizontal steps. It is evident from these figures that
the disparity tuning curves for the data obtained with vertical steps
had the same general form as the curves obtained with horizontal steps:
the curves for the isogonal component resembled the derivative of a
Gaussian, and the curves for the orthogonal component were exponential
(with the same polarity for positive and negative stimuli). However,
there were consistent quantitative differences between the two sets of
data.
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Quantitative comparison of the disparity tuning curves for horizontal and vertical steps
We fitted mathematical functions to the change-in-vergence measures for both the isogonal and orthogonal components of the vergence responses, and these functions are plotted as smooth curves in Figs. 6 and 10. The function parameters provide a succinct summary of the data and permit quantitative comparisons of the responses of the different subjects and, for a given subject, of the responses to horizontal versus vertical steps. Later, the function parameters will be used to compare the data for different stimulus patterns (large-dot patterns vs. small-dot patterns), as well as for human versus monkey.
The following exponential function (Eq. 1) was fitted to the
mean orthogonal responses of each subject
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(1) |
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The following function (Eq. 2) was fitted to the isogonal
responses
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(2) |
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Dependence on the size of the elements in the visual patterns
All of the above vergence responses were obtained with random-dot
patterns in which the individual dots each had a diameter of 2°, and
we now report the effects of changing the diameter of the dots up to
eightfold while maintaining the same overall coverage (50%). These
experiments were carried out on monkeys as well as humans to allow a
comparison of the two species. We know from the study of
Busettini et al. (1996b) that the disparity tuning
curves for the isogonal horizontal responses of the monkey have the
same general form as the curves of humans, resembling the derivative of
a Gaussian with a nonzero asymptote. However, that earlier study did
not document the orthogonal responses or the responses to vertical
disparity steps and employed visual stimuli (irregular patterns) that
cannot be formally described, so that direct quantitative comparisons
with the present human data were not possible. We therefore undertook a
comparison study on three monkeys and three humans using the same
stimulus patterns.
The vergence responses of humans and monkeys showed a similar dependence on the size of the individual dots in the disparity stimuli, and Fig. 12 shows some representative data from one human subject. The most obvious effect on the isogonal disparity tuning curves was on the falling phase: for both horizontal and vertical steps, the transition from the peak to the asymptote tended to be more gradual as the dot size increased. The peak responses tended to occur at slightly higher disparities with the larger dots, but effects on the initial rapid rise to the peak were generally small and effects on the asymptote were somewhat variable. The latter was also evident in the orthogonal disparity tuning curves, and, in Fig. 12, B and D, this effect partially obscures a tendency for the space constant to increase with dot size.
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Such quantitative effects were assessed by fitting Eq. 1 to the orthogonal data and Eq. 2 to the isogonal data, and the best-fit parameters are summarized in Tables 3 and 4, respectively, which show average data for the three humans and the three monkeys. The fits for the isogonal data were all extremely good for the human data (r2, 99.4 ± 0.2% mean ± SD) and only slightly less so for the monkey data (r2, 97.9 ± 1.5% mean ± SD).1 The fits for some of the orthogonal data were poor, especially for the monkey vertical responses (to horizontal steps), mostly because the latter were vanishingly small and sometimes showed a very slight transient overshoot similar to that of subject FM seen in Figs. 6B and 10B. (Note that this was of little consequence for the fits of Eq. 2 to the monkey's vertical isogonal responses because the latter had correspondingly small asymptotes: see Ai in Table 4.) If the monkey vertical response data are excluded, however, r2 for the orthogonal fits exceeded 0.8 in 32/36 data sets; again, the (4) data sets that were fitted poorly were of very small amplitude and showed slight overshoot.
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Regarding the best-fit isogonal parameters, the only one that
consistently showed a systematic dependence on dot size was the
Gaussian width (), which increased with increasing dot size. For
example, the value of
with the largest dots exceeded that with the
smaller ones (on average) by 47% in humans (horizontal, 41%;
vertical, 53%) and 152% in monkeys (133%, 172%). The compression factor, F, and the spatial frequency, f,
sometimes showed a slight tendency to decrease with increasing dot
size, and this, together with the changes in
, largely accounted for
the more gradual transition from the peak to the asymptote as the dot
size increased. The only orthogonal parameter consistently showing a
systematic dependence on dot size was the space constant
(Bo), which increased with increasing
dot size. For example, for the fits for which r2 > 0.8, the value of
Bo with the largest dots exceeded that
with the smaller ones (on average) by 68% in humans (for both
horizontal and vertical vergence responses) and by 159% in monkeys
(horizontal responses).
HORIZONTAL VERSUS VERTICAL RESPONSES.
In general, responses were larger and the spatial tuning was slightly
broader for the horizontal responses than for the vertical. Thus the
peak-to-peak measure, P, was always much greater for horizontal steps than for vertical, on average by a factor of more than
two in monkeys and more than three in humans. Further, the Gaussian
width, , was larger for horizontal steps than for vertical, the
values with horizontal steps exceeding those with vertical on average
by more than 40% in both humans and monkeys. Also of interest was the
compression factor, F, which showed very little variation
between subjects (on average, SDs were 11% of the mean for humans, and
13% for monkeys) but, for humans, was always a little larger for
horizontal than for vertical (on average, by nearly 17%), consistent
with there being greater asymmetry between the rising and falling
phases of the tuning curves for the vertical data. However, Table 4
also indicates that this factor showed no consistent differences
between horizontal and vertical in the monkey data. Regarding the
orthogonal responses, the asymptotic values
(Ao + C), for the
horizontal responses (to vertical steps) were always appreciably larger
than for the vertical responses (to horizontal steps), on average by a
factor of 25 in monkeys and more than 3 in humans.
HUMANS VERSUS MONKEYS.
The spatial tuning was broader in the humans than in the monkeys. This
was apparent from the the spatial frequency, f, which was on
average two to three times higher for the monkeys (19.8 cycles/deg vs.
8.1 cycles/deg), and the space constant,
Bo, which was on average twice as
large for the humans (1.15 vs. 0.55° for the horizontal). In
addition, if the data obtained with 4.4° dots are excluded, the
Gaussian width, , was on average 21% larger for humans (1.23 vs.
1.02°).
Could the default responses with large disparity steps be due to the emergence of a phoria?
Because the responses to large steps were independent of the
direction of the step, it was possible that they were not actively generated by the binocular visual stimuli but rather represented the
emergence of a phoria. This explanation assumes that the largest steps
exceeded the system's ability to sense disparity and that the two eyes
then passively assumed a (mis)alignment characteristic for each subject
(Leigh and Zee 1999). We measured the subjects' steady-state phorias in our near-viewing situation by assessing the
binocular alignment of the eyes during monocular viewing (see METHODS), and the findings are listed in Table
5. (Note that the phoria values listed in
Table 5 are given with respect to the plane of the screen, 0 indicating
that the 2 lines of sight intersected exactly at the screen, positive
values that the eyes converged in front of the screen, and negative
values that the eyes converged beyond the screen.) Vertical phorias
were generally very small and showed little variability, the absolute
values averaging only 0.30° and the SDs averaging only 0.11°. The
corresponding values for the horizontal phorias were appreciably
larger: 3.71 and 0.55°. Table 5 also lists (under the heading
"Default") the average change-in-vergence measures for the largest
(12.8°) disparity steps for each of the subjects, and it is clear
that these measures often have the opposite sign to the subjects'
phorias. In particular, all (6) subjects had negative horizontal
phorias, indicating that, with monocular viewing, their eyes were
converged well beyond the screen, yet the horizontal default responses
of four subjects (RK, FM, HA, and KP) were
positive and involved increased convergence.
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Dependence on a prior saccadic eye movement
All of the above vergence responses were obtained with disparity
steps applied 50 ms after the centering saccade. Busettini et
al. (1996b) showed that, in monkey, disparity steps applied at
such times generated much more vigorous responses than when applied
some time later: disparity vergence showed transient postsaccadic enhancement. That the same is true of human disparity-vergence responses is readily apparent from the sample data in Fig.
13A (left side),
which shows the mean horizontal vergence velocity responses elicited in
subject FM, by 1.6° crossed-disparity steps applied at
selected times after the centering saccades. Effects on response
latency were generally minor, and our usual change-in-vergence measures
were used to quantify the dependence on postsaccadic delay by
expressing them as a percentage of the measures obtained with the
shortest delay interval (50 ms). The (isogonal) data obtained from two
subjects using crossed and uncrossed horizontal disparity steps are
plotted in filled symbols and continuous lines in Fig.
14A. The magnitude and time
course of the postsaccadic decay in response amplitude clearly varied
considerably between the two subjects and the two kinds of disparity
step. For example, the response with the longest postsaccadic interval
ranged from 15 to 67% (mean ± SD 43 ± 23%) of that with the
shortest interval. The decay over time was roughly exponential, and the
following function (Eq. 3) was fitted to the isogonal
responses
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(3) |
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COMPARISON WITH OCULAR FOLLOWING.
These effects of a prior saccade on the vergence responses to disparity
steps were reminiscent of the transient postsaccadic enhancement of
ocular following described by Gellman et al. (1990), and
we made a direct comparison of the two phenomena. For this, the
disconjugate steps used to elicit disparity vergence were replaced with
conjugate steps to elicit ocular following (see METHODS).
Some sample ocular following data obtained from subject FM
are assembled in Fig. 13B (left side), which
shows the mean (right) eye velocity profiles elicited by
0.8° rightward conjugate steps applied at selected times after the
centering saccades. Effects on latency were again clearly negligible,
and mean change-in-eye-position measures were used to quantify the
dependence on postsaccadic delay by expressing them as a percentage of
the measures obtained with the shortest delay interval (see
METHODS). These data are plotted as open symbols and
discontinuous lines in Fig. 14A, and it is immediately
apparent that the ocular following data strongly resemble the disparity
vergence data. Once more the magnitude of the enhancement varied
considerably between the two subjects and the two kinds of conjugate
steps. For example, the response at the longest interval ranged from 15 to 56% (mean ± SD 32 ± 18%) of that at the shortest interval,
the average decrement being 19% greater than that seen (at the same
interval) with disparity vergence. As previously reported by Gellman et
al., the decay over time was roughly exponential, and the time
constants estimated from best-fitting exponentials (Eq. 3) were 151 ms (subject FM) and 230 ms (GM)
for rightward steps, 124 ms (subject FM) and 149 ms
(GM) for leftward steps (mean ± SD 164 ± 46 ms).
These values are on average 18% smaller than those for the
disparity-vergence data, but the differences for a given individual
again clearly varied widely. Thus on average, the postsaccadic
enhancement of ocular following was slightly greater and more transient
than that of disparity vergence.
Are the effects of a prior saccade due to the associated visual reafference?
We investigated the possibility that the effects of a prior saccade resulted from the visual reafference associated with the saccade sweeping the image of the pattern across the retina. For this, we applied the disparity steps in the wake of saccadelike (conjugate) shifts of the visual patterns ("simulated saccades": see METHODS). Note that the trials yielding the data in this section were interleaved with others in which the disparity steps were delivered after real saccades (data in the previous section).
The simulated saccades resulted in transient enhancements of the initial isogonal vergence responses to horizontal disparity steps that roughly resembled those seen in the wake of real saccades: Figs. 13A (right side) and 14B (filled symbols, continuous lines). When expressed in terms of the responses at the shortest interval after the saccadelike shift, the responses at the longest interval ranged from 11 to 59% (mean ± SD 39 ± 20%), which values are comparable with those seen at the same interval after a real saccade, although there was considerable individual variation. The decay over time was only roughly exponential, and the time constants estimated from best-fitting exponentials (Eq. 3), were 221 ms (subject FM) and 33 ms (GM) for crossed steps, and 228 ms (subject FM) and 119 ms (GM) for uncrossed steps (mean ± SD 150 ± 93 ms). These values are on average 25% smaller than those for the disparity-vergence data in the wake of a real saccade, although again the differences for a given individual varied widely. Thus on average, the enhancement of disparity vergence after a simulated saccade was comparable in amplitude to, but somewhat more transient than, that after a real saccade.
COMPARISON WITH OCULAR FOLLOWING. Simulated saccades were also used to examine the extent to which the postsaccadic enhancement of ocular following might also involve visual reafference. For this, the disconjugate steps used to elicit disparity vergence were again replaced with conjugate steps to elicit ocular following (see METHODS). A prior saccadelike shift of the pattern resulted in a transient enhancement of the initial ocular following responses to conjugate steps (Fig. 13B, right side; Fig. 14B, open symbols and discontinuous lines), although the response waveforms were rather different from those in the wake of a real saccade. When expressed in terms of the responses at the shortest interval after the saccadelike shift, the responses at the longest interval ranged from 11 to 47% (29 ± 15%), which averages 91% of that seen at the same interval after a real saccade. The decay over time was roughly exponential, and the time constants estimated from best-fitting exponentials (Eq. 3) were 159 ms (subject FM) and 139 ms (GM) for rightward steps, and 28 ms (subject FM) and 288 ms (GM) for leftward steps (mean ± SD 153 ± 106 ms). These values are on average only slightly smaller (7%) than those for the real-saccade data, but the differences for a given individual varied widely. Thus on average, the enhancement of ocular following after a simulated saccade was roughly comparable with that of disparity vergence in that it was slightly weaker and more transient than that after a real saccade.
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DISCUSSION |
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Short latencies and machinelike consistency
The vergence responses induced by small disparity steps applied to
large textured patterns had ultra-short latencies and almost machinelike consistency despite the fact that subjects were never given
explicit instructions to respond to the steps. For example, the mean
latencies of the horizontal vergence responses to 2° horizontal
crossed-disparity steps ranged from 75.6 to 86.0 ms for the seven
subjects examined, with individual SDs ranging from 4.8 to 11.6 ms. The
data for vertical vergence responses to vertical disparity steps were
very similar except that response amplitudes were much smaller and
latencies were on average 3 ms longer. These latency measures were
obtained using steps that were close to optimal, but it is evident from
the vergence velocity temporal profiles in Figs. 3, 4, 8, 9, and 13
that latency was largely independent of the specific parameters of the
steps and of the exact times at which the steps occurred with respect
to a prior saccade. The small variance of the (objectively determined)
latency estimates coupled with the total absence of any negative
latencies indicates that these ultra-rapid responses were
stimulus-driven and not the result of anticipation such as described by
Kowler and Steinman (1979a,b
). In a comparable study on
monkeys, we previously reported mean latencies ranging from 52.2 to
53.4 ms with SDs ranging from 3.8 to 5.2 ms (Busettini et al.
1996b
).
As pointed out in the INTRODUCTION, published estimates of
the latency of disparity vergence in humans are generally in the range
of 150-200 ms, and although most of these studies used small targets,
some also used larger ones like our random-dot patterns (e.g.,
Erkelens and Collewijn 1991). Our use of a prior saccade (to boost response amplitudes), together with vergence
velocity profiles rather than the more usual
position profiles (to improve temporal resolution), might
have increased the probability that the earliest responses would be
detected sooner in our study. However, we think it unlikely that such
methodological considerations can account for a difference that often
exceeds 100 ms.
Response to the binocular misalignment
The experiments in which the step of disparity was applied to one eye only while the other eye viewed a stationary pattern (Figs. 2 and 7) indicate that the short-latency vergence responses were not the result of monocular visual tracking in which each eye independently tracked the apparent motion that it saw; the eye that saw the stationary scene always moved in a direction that was opposite to the motion seen by the other eye, exactly as expected of a stereoscopic mechanism that responds to the binocular misalignment.
It is also of interest that, even though the binocular stereoscopic
cues here were asymmetric, they resulted in vergence eye movements that
affected the two eyes almost equally. From Figs. 2 and 7 it is very
evident that the version responses were appreciably weaker than the
vergence responses. It seems unlikely that the low amplitude of the
version was due merely to the fact that the version stimulus had only
one-half the magnitude of the vergence stimulus (1.2 vs. 2.4°),
especially given the vigorous version responses (ocular following) in
Fig. 13B (left side) to 0.8° conjugate steps. A
possible factor is that the earliest version responses to
frontoparallel motion are best for binocular images moving in the plane
of fixation and attenuate considerably if those images have disparity
(Busettini et al. 1996a). Thus the version component of
the response to the asymmetric steps may have been compromised by the
fact that the 2.4° monocular steps shifted the binocular image out of
the plane of fixation.
Dependence on a prior saccade
The initial horizontal vergence elicited by horizontal
crossed-disparity steps showed clear transient enhancement in the
immediate wake of a saccade (Figs. 13A, left side, and
14A). This enhancement was greatest with the shortest
postsaccadic delay intervals, decreasing roughly exponentially as the
delay interval increased, and was probably in part visual in origin
because similar (although sometimes more transient) enhancement was
seen after simulated saccades (Figs. 13A, right side, and
14B). Some of the differences in the enhancement due to real
and simulated saccades might have resulted from the fact that the
associated visual events did not exactly match (see Busettini et
al. 1996b for discussion of the optical factors). Because of
this, it is difficult to know how much weight to attach to the
(sometimes minor) quantitative discrepancies between the effects of
real and simulated saccades in our experiments. In sum, it is possible
that the postsaccadic enhancement of disparity vergence is due in large
part to the visual reafference resulting from the saccade sweeping the
image of the pattern across the retina, but a contribution from
nonvisual mechanism(s) cannot be excluded. Others have described
nonvisual "priming effects" whereby stimulus-evoked eye movements
can be influenced by another, prior eye movement (Cullen et al.
1991
; Das et al. 1999
; Lisberger 1998
).
The postsaccadic enhancement of disparity vergence is strongly
reminiscent of the postsaccadic enhancement of ocular following described by Gellman et al. (1990). In the present study
we sought to compare the two directly using conjugate position steps to induce ocular following (in place of the conjugate position ramps in
the study of Gellman et al.). On average, the peak enhancement after
real and simulated saccades was slightly less for vergence than for
ocular following (Fig. 14, A and B), although the
enhancement of ocular following was sometimes slightly more transient.
These data clearly suggest that the effects of a prior saccade on
vergence and ocular following have a similar, if not exactly identical, etiology (for a discussion of the possible neural mechanisms that might
mediate postsaccadic enhancement see Kawano and Miles
1986
).
Busettini et al. (1996b) pointed out that most saccades
involve a transfer of fixation between locations at different viewing distances and suggested that the postsaccadic enhancement of disparity vergence might help to speed the alignment of the two eyes on the newly
acquired location. Kawano and Miles (1986)
argued that by raising the gain only transiently (when needed most), the system avoids the potentially destabilizing effects of a permanently high
gain. One possible problem with this scheme is that it assumes that the
vergence control system can distinguish the object of regard from the
background, yet our responses were obtained with very large stimuli.
The recent findings of Howard et al. (2000)
might offer
a solution. These workers measured vergence responses while modulating
disparity sinusoidally and found that the gain of the (isogonal)
vergence responses for images centered on the fovea increased with
stimulus size. Surprisingly, horizontal responses (to horizontal
disparities) saturated when the stimulus subtended only 0.75°,
whereas the vertical responses (to vertical disparities) did not
saturate until the stimulus subtended 20°. This accords with the
optical challenges faced by the two systems: the horizontal system must
be able to respond to local differences in horizontal disparity to
produce a convergent angle appropriate for the viewing distance of the
object in the fovea, whereas a large integration area is preferred for
the maintenance of the vertical alignment of the two eyes (see
Howard et al. 2000
for detailed discussion of this
point). One of the several differences between our study and that of
Howard et al. was that the latter examined the closed-loop performance
of the disparity vergence mechanism, whereas our analysis dealt solely
with the initial open-loop response. Popple et al. (1998)
used nonius lines to monitor the initial vergence
responses elicited by brief disparity steps applied to the center part
of a random-dot stereogram (while the surround remained at a fixed depth) and found that the initial vergence response increased with the
area of the central region but, idiosyncratically, saturated when this
region subtended 2-16° (average, 6°). The recent study of
Stevenson et al. (1999)
also indicates that foveal
inputs carry much more weight than peripheral inputs, as though scaled
in accordance with the cortical magnification factor. These studies
raise the possibility that vergence responses similar to those we have
studied might be obtainable with images much smaller than the ones we have used.
Responses of monkeys are similar to those of humans
The earlier studies of Busettini et al. (1996b) on
the ultra-short-latency vergence responses of monkeys were largely
restricted to horizontal isogonal responses. The present report extends
this earlier study by including the disparity tuning of orthogonal as
well as isogonal responses (vertical as well as horizontal) and is the
first to provide such data for humans. As a result, it is now clear
that the short-latency disparity-vergence responses of monkeys and
humans have much in common: their disparity tuning curves, based on
isogonal (or orthogonal) responses to horizontal (or vertical)
disparity steps, have qualitatively similar forms and show a similar
pattern of dependence on a prior saccade as well as on stimulus factors
such as dot size. Of course, there are clear quantitative differences
between the responses of the two species. For example, the monkey's
responses have a shorter latency (on average, by about 25 ms) and
narrower disparity tuning curves (on average, the spatial frequency of
the isogonal components, f, is more than 2 times higher and
the space constant of the orthogonal components,
Bo, is about 1/2). The
responses of both species also show transient enhancement after
saccades, real or simulated, although again, there are quantitative
differences. For example, the time constants of the best fitting
exponentials for the decay in postsaccadic enhancement averaged 52 ms
in monkeys (Busettini et al. 1996b
) and 200 ms in the
two subjects in the present study. (Unfortunately, the 2 studies
employed different visual stimuli: irregular geometrical patterns vs.
random dots.) In our view, most of the differences between the two
species involve scaling factors, and we conclude that the monkey is an
excellent model for studying the neural basis of human short-latency
disparity vergence.
Negative feedback depth-tracking system using disparity selective neurons?
It has often been pointed out that disparity-selective neurons
provide a direct measure of vergence error and so have the potential to
provide the primary drive for vergence eye movements like those
described in the present paper. Such neurons have been recorded in a
number of areas in monkey cortex, including striate and extrastriate
visual areas (Burkhalter and Van Essen 1986; Cumming and Parker 1999
, 2000
;
Felleman and Van Essen 1987
; Hubel and
Livingstone 1987
; Hubel and Wiesel 1970
;
Poggio and Fischer 1977
; Poggio and Talbot
1981
; Poggio et al. 1988
; Prince et al. 2000
; Smith et al. 1997
; Trotter et al.
1996
), as well as the middle temporal (MT) area (Bradley
and Andersen 1998
; Bradley et al. 1995
;
DeAngelis and Newsome 1999
; DeAngelis et al.
1998
; Maunsell and Van Essen 1983
), the medial
superior temporal (MST) area (Eifuku and Wurtz 1999
;
Roy et al. 1992
; Takemura et al. 1999
),
the posterior parietal area (Sakata et al. 1983
), the
lateral bank of the intraparietal sulcus (LIP) (Gnadt and Mays
1995
), and the frontal eye field (FEF) (Ferraina et al.
2000
; Gamlin and Yoon 2000
; Gamlin et al.
1996
). The recent preliminary findings of Takemura et
al. (1999)
in MST are of particular interest because they were
obtained using stimuli and behavioral paradigms identical to those in
the present study. Takemura et al. reported that the earliest vergence
eye movements were attenuated after chemical lesions in MST and that,
although the individual MST cells encoded only some aspect(s) of the
disparity stimulus, the disparity tuning curve for the summed activity
of the population of disparity-selective cells in MST resembled the
derivative of a Gaussian and closely matched the entire tuning curve
for the associated (isogonal) vergence responses.
The large random-dot patterns that we (and Takemura et al.) have used,
confront the disparity-sensing mechanisms with a matching problem
because a given dot at one eye can be matched to many dots at the other
eye, even though only one match is globally "correct." In fact,
disparity-selective neurons in V1 have been shown to respond solely to
local matches regardless of whether globally "correct" or
"false" (Cumming and Parker 2000). One consequence of this is that most of these neurons respond to the disparity of
patterns that have opposite contrast in the two eyes: so-called, anticorrelated patterns (Cumming and Parker 1997
). It is
further known that disparities applied to anticorrelated patterns
generate (isogonal) vergence eye movements at short latency that are
very similar to those in the present study except that they are in the
opposite (i.e., "wrong") direction (Masson et al.
1997
). This is consistent with the idea that the vergence eye
movements in the present study rely on disparity-selective neurons that
respond to purely local matches between the two visual images.
Interestingly, such anticorrelated stimuli are seen as rivalrous and do
not give rise to percepts of depth (Cogan et al. 1993
;
Cumming and Parker 1997
; Cumming et al.
1998
; Masson et al. 1997
), leading to the suggestion that the associated vergence eye movements are reflexlike and generated independently of perception (Miles 1998
).
Takemura et al. (1999)
also reported that individual MST
cells responded to (horizontal) disparity steps applied to
anticorrelated patterns and that the summed activity of the population
once more closely matched the associated ("wrong") vergence
responses. The clear suggestion is that, in the monkey, horizontal
vergence eye movements like those described in the present study are
mediated at least in part by the aggregate activity of
disparity-selective neurons in MST. The neuronal mediation of the
vertical vergence responses remains open. Neurons sensitive to vertical
disparity have been described in cat visual cortex (Bishop et
al. 1971
; Ferster 1981
; Nikara et al.
1968
; von der Heydt et al. 1978
) as well as
monkey MT (Maunsell and Van Essen 1983
), but there have
been no formal studies concerning the neural mediation of vertical
vergence. It is commonly assumed that vertical vergence is entirely
involuntary, and there is strong evidence that human subjects are
unable to ignore small vertical disparities in the foveal region (see
Stevenson et al. 1997
for recent review).
Functional neuroimaging studies have identified a human homologue of
area MT-MST (Greenlee 2000; Tootell et al.
1995
; Watson et al. 1993
; Zeki et al.
1991
), although there is some debate as to whether MST lies
adjacent to MT in the human (de Jong et al. 1994
). These
human studies have all identified MT-MST on the basis of its motion
sensitivity, and none have looked for sensitivity to disparity stimuli
or vergence eye movements. Studies in monkeys have identified direct,
subcortical pathways by which MST might produce horizontal vergence eye
movements, including the dorsolateral pontine nuclei (Boussaoud
et al. 1992
; Glickstein et al. 1980
, 1985
), which contain cells that discharge in relation to
horizontal vergence (Zhang and Gamlin 1997
) and project
in turn to regions of the cerebellum known to be concerned with eye
movements (for review, see Leigh and Zee 1999
). There
have been some preliminary reports that MST projects to the superior
colliculus (Colby and Olson 1985
; Lock et al.
1990
), a structure also recently implicated in the production
of vergence (see Chaturvedi and Van Gisbergen 2000
for
recent review). Other studies in monkeys indicate that MST projects to
two cortical areas that are interconnected and contain neurons that
discharge in relation to horizontal disparity stimuli and/or horizontal
vergence eye movements: LIP (Gnadt and Mays 1995
) and
FEF (Ferraina et al. 2000
; Gamlin and Yoon
2000
; Gamlin et al. 1996
). Neurons in LIP that
carry depth-related information project directly to the superior
colliculus (Gnadt and Beyer 1998
), and FEF neurons
project directly to the medial part of the nucleus reticularis tegmenti
pontis (Huerta et al. 1986
; Leichnetz et al.
1984
; Stanton et al. 1988
), which shows
vergence-related activity (Gamlin and Clarke 1995
) and
projects in turn to the premotor neurons for vergence (in the
supraoculomotor and adjacent reticular formation) via the posterior
interposed and fastigial nuclei of the cerebellum (see Gamlin et
al. 1996
and Gamlin 1999
for review).
Default responses and directional errors (orthogonal components)
The isogonal vergence responses in the present study peaked with
disparity steps of only 1-3°, so that the servo operating range,
over which increases in disparity gave rise to roughly proportional
increases in vergence, was often restricted to disparities of less than
1° (Figs. 6A and 10A). We infer from this that
the disparity-selective mechanism mediating our responses has a
relatively small range and is able to make globally "correct"
matches only for disparities up to a degree or two. The power spectrum
of our random-dot patterns indicated that most of the power in our
stimuli is at low spatial frequencies, the overall screen size (85°
in our case) setting the lower limit, and the dot size determining the
high-frequency roll-off. Thus increasing the dot size reduced the
high-frequency content: 3 dB points were
0.15 cycles/deg with the
4.4° dots and
0.75 cycles/deg with the 1.1° dots. This indicates
that the limited servo-range is not due to a lack of low spatial
frequencies in our stimuli. Large disparity steps (12.8°), which far
exceeded what we are defining as "the servo range," generated
vergence responses that were independent of the direction of the step
(crossed, uncrossed, right hyper, left hyper). Because these so-called
"default" responses often had the opposite sign to the subjects'
phorias (Table 5), we conclude that they were not simply a passive
response to a loss of binocular fusion but were actively generated by a
disparity-driven mechanism. Busettini et al. (1996b)
were the first to report nonselective vergence responses to large
disparity steps (in monkeys) and suggested that such large stimuli are
seen as uncorrelated by the disparity detectors, hence the vergence
system's indifference to their
direction.2
Interestingly, it is known that at least some of the
disparity-selective neurons in visual cortex respond when the patterns
at the two eyes change from correlated to uncorrelated (Gonzalez
et al. 1993
; Poggio 1989
, 1990
;
Poggio et al. 1988
). Our default vergence responses to
large disparity steps were presumably generated by globally "false"
matches and had both isogonal and orthogonal components that varied in
amplitude from one subject to another (although, for a given subject,
were always greatest in the horizontal direction; see Figs. 6 and 10).
Being independent of stimulus direction, the isogonal components of the
default responses were often anticompensatory.
We have failed to find any mention of orthogonal components (i.e.,
directional errors) in the literature on the disparity-induced vergence
eye movements of normal humans. Further, we found only one report of
anticompensatory responses unrelated to any phoria; Jones
(1977) used small, briefly presented, visual stimuli and described anomalous vergence responses that were clearly very different
from those in the present study in that they were found in <20% of
subjects and invariably consisted of small decreases in convergence
with crossed disparity steps.
The disparity tuning curves for the orthogonal component of the
vergence responses were often well fitted by an exponential with a
space constant that averaged 1.18 ± 0.66° (SD): see Figs. 6B and 10B and Table 3. (Some curves, especially
those of the monkeys, showed slight overshoot, and this, combined with
the fact that some orthogonal responses were very weak, rendered some of the exponential fits less satisfactory; see Table 3.) One might
expect that the shape of the orthogonal tuning curves would in part
reflect the orthogonal structure of the binocular receptive fields of
the disparity detectors: clearly, whatever the disparity detection
mechanism, it must be two-dimensional and show dependence on orthogonal
as well as isogonal disparities. The only data available on the
two-dimensional field structure of disparity-selective neurons are in
the study of Maunsell and Van Essen (1983), who plotted
the responses of monkey MT neurons to horizontal and vertical disparities. These plots, which were of low resolution, did not always
show clear orientation (elongation), and no attempt was made to define
isogonal and orthogonal axes. However, whereas the optimal horizontal
disparity varied from cell to cell, "the optimal vertical disparity
was never significantly different from zero," which we take to
indicate that the primary disparity-encoding (isogonal) axis was
probably horizontal in most of the (19) units so studied. Not
surprisingly, these plots were too sparse to define the exact
mathematical form of the dependency on disparity. An attempt has been
made to construct very detailed three-dimensional surface plots of the
binocular receptive fields of V1 cells from the two monocular receptive
fields, which are commonly represented by Gabor functions along the
primary disparity-encoding (isogonal) axis and by Gaussian functions
along the orthogonal axis (Cumming and DeAngelis 2001
).
In these models, the responses to orthogonal disparities have a roughly
Gaussian envelope, which is slightly different from the exponential
form that we chose to fit to our orthogonal data. In fact, we found
that Gaussian functions fitted the orthogonal data in Figs. 6 and 10 as
well as the exponentials did, insofar as both functions accounted, on
average, for 90% of the disparity-induced variation in
vergence.3 Given
the steepness of the initial rise in the orthogonal components, however, it is perhaps not surprising that the Gaussian functions were
sometimes less successful than the exponentials in fitting the
responses to the very smallest disparity steps. On the basis of this,
we feel that the exponential is a slightly more appropriate function
for describing our data.
We have suggested that the short-latency vergence responses are
mediated by disparity detectors that respond solely to local disparity
matches, and further that the so-called default responses to large
disparity steps are a product entirely of globally "false" matches.
In fact, it seems likely that, in our experiments, the recorded
isogonal vergence responses were never solely the product of globally
"correct" matches and were always "contaminated" by responses
to globally "false" matches. One possibility is that the
contributions from these two sources are effectively given by the two
terms of Eq. 2 that we have used to describe the isogonal tuning curves. In our attempts to provide a mathematical description of
the isogonal responses (Eq. 2), we at first sought to use
simple Gabor functions, which have been much used to describe and
compare the disparity tuning curves of neurons in various regions of
the cortex (see Cumming and DeAngelis 2001 for recent
review). However, an additional term was required to provide the
nonzero asymptote (default), and, because this was independent of the
direction of the step, we assumed that it shared the exponential
development of the response to the orthogonal stimulus. This might
indicate that the two terms in Eq. 2 approximate the
contributions of globally false matches (the exponential function) and
globally correct matches (the Gabor function).
Automatic correction of small vergence errors
The (isogonal) disparity tuning curves in our study resemble the
derivative of a Gaussian, with a roughly linear servo region that
extends only a degree or two on either side of zero disparity, indicating that the vergence mechanism that we have studied can deal
only with small disparities. Erkelens (1987) used line
targets and random-dot patterns to study horizontal vergence responses to crossed disparity steps that were stabilized on the retina (using
eye-movement feedback) and reported that responses were sustained only
for steps up to 2°: responses to larger steps were transient, as
though beyond the position-servo range. We envisage a rapid automatic
(reflex?) mechanism that functions solely to correct small (i.e.,
residual) vergence errors independently of perception. This means that
another, voluntary, mechanism would be needed to deal with the larger
disparities involved when shifting binocular alignment to other
surfaces in other depth planes, a process requiring some kind of target
selection and a depth-sensing mechanism that can deal with disparities
well beyond the range of the system that we have studied. Schor
et al. (1992)
already proposed such a dual vergence control
mechanism, using inputs derived from perceived distance and disparity
in a "coarse to fine sequence" in which "perceptual spatiotopic
errors" are used to initiate the voluntary transfer of gaze to a
target in a new depth plane and the disparity-driven subsystem then
completes the binocular realignment by eliminating any residual
vergence error.
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ACKNOWLEDGMENTS |
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We thank E. King and L. Optican for doing the spectral analysis of our visual stimuli. We also thank T. Ruffner, A. Nichols, and L. Jensen for technical assistance, J. McClurkin and A. Hays for software support, J. Steinberg for secretarial assistance, and our subjects for their patience.
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FOOTNOTES |
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1 Note that the shorter response latencies of the monkeys (approximately 60 ms) necessitated the use of an earlier, and shorter, time interval to assess their vergence responses: 60-93 ms from stimulus onset. For this reason, scaling factors in the mathematical fits for human and monkey data cannot be compared directly.
2
Although Busettini et al. (1996b)
emphasized the relative insensitivity to direction, their data showed
small, idiosyncratic anisotropies in the default responses for the
different directions. We noticed similar response differences in our
initial pilot studies on humans and attributed them to slight
differences in the net (local) matches between the disparity detectors
(that are assumed to mediate the vergence responses) and the dots in
our stimulus pattern. For all of the experiments described here, we
decided to randomize the initial starting position of the random dot
stereo pairs on each trial (see METHODS), hypothesizing
that this would reduce the likelihood of consistent local correlations
and thereby homogenize the responses to large steps. With
randomization, the mean vergence responses of a given subject to the
largest steps generally showed only very weak dependence on the
direction of the step (Fig. 5).
3 Visual inspection (and the exponential fits) indicated that the orthogonal responses were often not symmetrical about zero disparity (see the space constants in Table 1 for right-hyper vs. left-hyper steps, and for crossed vs. uncrossed steps), so it was necessary to treat the data for the 4 directions of steps (right hyper, left hyper, crossed, uncrossed) separately. Given that there were 3 subjects, this meant that there were 12 data sets in all. For the Gaussian fits, we assumed simply that each datum point in each data set had a mirror image on the other side of zero disparity, thereby artificially creating 12 symmetrical data sets, and then fitted a Gaussian function to each of these using a least-squares criterion. The Gaussian envelopes in the receptive field models decay to zero, whereas in our data the peak of the Gaussian started out near zero and "decayed" to the "default" level. This was achieved by subtracting a Gaussian function from a constant representing the "default" level.
Address for reprint requests: F. A. Miles, Laboratory of Sensorimotor Research, National Institutes of Health, Bldg. 49, Rm. 2A50, 49 Convent Dr., Bethesda, MD 20892-4435 (E-mail: fam{at}lsr.nei.nih.gov).
Received 21 August 2000; accepted in final form 8 December 2000.
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REFERENCES |
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