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Evidence for separate control of slow version and vergence eye movements: support for Hering's Law
Pergamon
PH: S0042-6989(97)00251-4
Vision Res., Vol. 38, No. 8, pp. 1145-1152, 1998 © 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0042-6989/98 $19.00 + 0.00
Evidence for Separate Control of Slow Version and Vergence Eye Movements: Support for Hering' s Law JOHN L. SEMMLOW,*t"$ WEIHONG YUAN,* TARA L. ALVAREZ* Received 29 January 1997; in revised form 8 July 1997
When a visual stimulus changes direction and distance simultaneously, Hering's Law argues that the resulting eye movements are the result of combined version and vergence control processes. Recently, it has been suggested that slow asymmetrical eye movements might be guided by monocular control processes wherein each eye is driven by its own retinal image. Experimental results presented here show behavioral differences between slow version and slow vergence eye movements, indicating that different control processes drive the two "pure" responses. Specifically, version tracking of constant velocity stimuli (i.e., smooth pursuit) is more precise, showing less variation in tracking velocity than movements of equal velocity produced by vergence stimuli. When the two stimuli are combined, the variability in tracking is consistent with the addition of the two components in proportion to their respective stimuli. These results provide support for Hering's Law, at least for low velocity, smooth tracking movements (i.e., slow version and slow vergence). © 1998 Elsevier Science Ltd. All rights reserved.
Vergence Disparityvergence Smoothpursuit Hering's law
INTRODUCTION Division of labor is a major strategy used by the brain in oculomotor control. For example, smooth tandem ocular movements (i.e., slow version) are mediated by the appropriately termed smooth pursuit system, a system that can produce highly accurate tracking of slowly moving targets. The smooth pursuit system has been well studied and has been represented as a feedback control process driven by target velocity (Robinson, Gordon & Gordon, 1987; Krauzlis & Lisberger, 1989; Goldreich, Krauzlis & Lisberger, 1992). Targets moving smoothly inward are also accurately followed by the two eyes as long as the movement is slow enough (Semmlow, Hung & Ciuffreda, 1986). The behavior of smooth vergence has not been extensively studied and its fundamental control structure is unknown, but the accuracy and smoothness of the tracking movements shown later suggest the action of feedback control. When called upon to track targets moving slowly across and inward (a combined slow version/vergence *Department of Biomedical Engineering, Rutgers-The State University of New Jersey, Piscataway, NJ 08855, U.S.A. tDepartment of Surgery (Bioengineering), UMDNJ-Robert Wood Johnson Medical School, New Brunswick, NJ 08903, U.S.A. STo whom all correspondence should be addressed at: Department of Biomedical Engineering, P.O. Box 909, Rutgers University, Piscataway, NJ 08855, U.S.A. [Email: [email protected]. edu]
Eye movement
stimulus), the eyes respond with smooth tracking movements similar to those produced by version or vergence alone. Traditional thinking about responses generated by combinations of version and vergence stimuli are embodied in Hering's law of equal (muscle) innervation (Hering, 1978 transl.). The contemporary interpretation of this law is that combined stimuli are divided into their respective version and vergence components, then implemented by the independent action of the two control systems. This interpretation implies that a combined version/vergence stimulus produces separate motor commands from the smooth pursuit and disparity vergence systems that then summate at (or before) the final common pathway to produce the combined smooth response. Early experiments both defined and supported the modem interpretation of Hering's law for fast (Yarbus, 1957; Rashbass & Westheimer, 1961) and slow (Rashbass & Westheimer, 1961) movements. To explore the interactions between slow version and vergence, Rashbass and Westheimer (1961) used low frequency sinusoidal stimuli. Simultaneously stimulating both slow version and slow vergence, but at slightly different frequencies, they qualitatively demonstrated "complete independence of the response mechanism of lateral eye tracking and vergence tracking". Specifically, they were able to generate combinations of version and vergence stimuli that exceeded the limits of vergence tracking while version tracking (i.e., smooth pursuit) continued
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normally. Based on these qualitative findings they concluded that combined version and vergence stimuli "were resolved into two components corresponding to mean target position and target vergence, respectively, and that appropriate responses to these components are made by two independent systems". Recent experiments have challenged the validity of Hering' s law to both fast and slow eye movements. When both version and vergence are quickly changed, the resulting eye movements exhibit an asymmetrical behavior that indicates significant and complex interactions between the two control systems (Ono, Nakamizo & Steinbach, 1978; Kenyon & Stark, 1983; Enright, 1992; Maxwell & King, 1992; Collewijn, Erkelens & Steinman, 1995). When a combined version and vergence stimulus changes slowly, the tracking is so smooth and accurate that it is difficult to see the action of separate control processes in the combined response. This performance in conjunction with other factors led Enright (1996) to conclude that the control of such slow-velocity movements is primarily monocular; that is "...the response is determined for each eye by its own visual stimuli". King and Zhou (1995) similarly concluded that "oculomotor commands are organized in a coordinate space defined by right and left eye movements" as opposed to version and vergence. This statement was motivated by their finding in monkey that the monocular acceleration gain of each eye was the same whether stimulated by pure version or combined version/vergence stimuli. Here we first present qualitative evidence that, contrary to the above, slow tracking behavior is influenced by more than its own retinal image. In other words, the binocular stimulus environment influences monocular tracking behavior. We then present qualitative and quantitative evidence indicating that slow version and slow vergence are mediated by different control processes. Finally, we will present quantitative evidence suggesting that when slow version and slow vergence are stimulated simultaneously, the two control systems respond in a manner consistent with Hering's law; that is, the two systems are active in proportion to the relative magnitude of their respective conjunctive or disjunctive stimuli. METHODS
Experiments were designed to acquire horizontal eye movements of both eyes in response to slow conjunctive, slow disjunctive, and combined slow conjunctive/disjunctive stimuli. The stimulus consisted of two stereoscopically paired vertical lines (0.15 deg in width and 5 deg in height) presented on separate oscilloscopes (P31 phosphor and a bandwidth of 20 MHz) at a distance of 40 cm from each eye. The oscilloscopes were arranged as a haploscope and were viewed through partially reflecting mirrors. Two real-world targets viewed directly through the mirrors provided well defined vergence reference points that were used to calibrate the stimulus device prior to each experiment. During the experiment, only the oscilloscope targets were visible to the subject:
no other objects on the stimulus device or in the laboratory could be seen. Proximal influences related to changes in target disparity appeared to be minimal in the device, presumably due to a lack of depth information related to the target (Rosenfield & Ciuffreda, 1991). Slow constant velocity changes in target version, vergence, or version/vergence combinations were generated by the laboratory computer at velocities of either 1.5 or 3 deg/sec. Stimulus velocities were limited by the ability of the vergence system to track fast targets smoothly: stimuli much above approximately 4 deg/sec evoke fast component responses in the vergence pursuit response (Semmlow e t al., 1986). Four different stimulus types were used as schematically illustrated in Fig. 1: (A) pure version; (B) pure vergence; (C) pure version immediately followed by pure vergence; and (D) combined version/vergence in which one eye was stationary. In addition to stimulus presentation, the laboratory computer controlled stimulus selection, response calibration, data acquisition, and data storage. To discourage prediction, the type of stimulus and the time of presentation were randomized for each trial. Once the subject indicated readiness by pressing a button, stimulus presentation and data acquisition followed after a random delay of 0.5-2 sec. The stimulus and recording period lasted for 3 sec. During each experimental run, 12-16 responses were recorded for each stimulus pattern, of which about half were sufficiently saccade and artifactfree to be suitable for analysis. Experimental runs were repeated at least three times on each subject on separate days producing data sets of between 8 and 25 clean responses. Binocular eye position was recorded by means of a Skalar infrared eye movement monitor (Model 6500). This device has a linear range (within 3%) of +25 deg and a resolution of 1.5 min arc. A two-point calibration was performed before and after each response. The baseline position (prior to stimulus onset) was taken as the first calibration point, and the maximum extent of the response was taken as the second point. Calibrations were stored in the computer and used to construct a separate calibration curve for each eye. Data acquisition was done at a sampling rate of 200 Hz, which is well above the Nyquist frequency for vergence eye movements. Six subjects, between 24 and 54 years of age, participated in the experiment. Each subject had normal binocular vision and acuity (20/20). One of these subjects, JS, was experienced and was aware of the goals of this study, while the others were relatively inexperienced and were na]'ve to the study's objectives. RESULTS
Figure 2 shows the typical response of both eyes to a pure version stimulus followed by a pure vergence stimulus [see Fig. I(C)]. The velocities of the two stimuli were selected so that the response velocity of the right eye would be the same under both stimulus conditions. That is, a leftward-moving 2.5 deg/sec version stimulus was followed by a symmetrical 5.0 deg/sec convergent
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FIGURE 1. Schematic illustration of the four stimulus types used in this study. (A) Pure version. (B) Pure vergence. (C) Pure version followed immediately by pure vergence. (D) Combined version and vergence (following a brief period of pure version) in which the stimulus to the left eye is fixed. Note that the line indicates the apparent motion produced by a stereoscopic image pair. The actual images are always at the same physical depth.
stimulus.* T h e starting p o i n t o f the v e r s i o n stimulus was s e l e c t e d so that the e y e s w o u l d be centered w h e n the stimulus s w i t c h e d to c o n v e r g e n c e [Fig. I(C)]. U n d e r this c o n d i t i o n the right e y e m o v e s c o n t i n u o u s l y l e f t w a r d at 2.5 deg/sec, first d r i v e n b y pure version, then b y pure vergence. W i t h r e s p e c t to the right eye, the stimulus does not change, y e t the b e h a v i o r o f the fight e y e is subtly different u n d e r the t w o stimulus conditions. Specifically, *By convention, version stimuli are defined in terms of the monocular amplitude (or velocity) of one eye, while vergence stimulus amplitudes are defined in terms of the summed amplitudes (or velocities) in both eyes. Hence, a 2 deg/sec movement is generated in each eye in response to a 2 deg/sec version stimulus, but a 4 deg/ sec vergence stimulus is required to generate a 2 deg/sec movement (oppositely directed) in each eye. Throughout this paper, we pair version stimuli with vergence stimuli of twice the amplitude in order to compare stimuli that produce the same monocular velocities.
an oscillation is o b s e r v e d during the v e r g e n c e control p e r i o d that was m u c h less w h e n this e y e was driven b y version ( f o l l o w i n g the initial transient period). Note that this oscillation is also seen in the other eye, d e m o n s t r a t ing the b i n o c u l a r i t y o f this behavior. T h e difference in b e h a v i o r o f the right e y e in Fig. 2 is t y p i c a l o f r e s p o n s e s to these stimulus conditions and reflects the o p e r a t i o n o f the u n d e r l y i n g control processes. In general, slow v e r g e n c e tracks less a c c u r a t e l y and has larger oscillations than slow version for the s a m e tracking velocities. This is illustrated in Fig. 3, w h i c h shows t y p i c a l r e s p o n s e s to pure version and pure v e r g e n c e constant v e l o c i t y stimuli [see Fig. I ( A ) and (B)]. T h e s e qualitative b e h a v i o r a l differences were o b s e r v e d in all subjects and indicate that the two r e s p o n s e s are m e d i a t e d b y different control processes. T h e o r g a n i z a t i o n o f slow e y e m o v e m e n t control is illustrated in r e s p o n s e s to stimuli in w h i c h both
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FIGURE 2. Left and right eye movements in response to a constant velocity stimulus first presented as pure version then as a pure vergence: a 2.5 deg/sec version stimulus is followed, after 1.25 sec, by a 5.0 deg/sec convergent stimulus. Position and velocity traces are shown with leftward movements plotted as positive. The initial position of the stimulus was adjusted so that the convergent stimulus would fall along the centerline [see Fig. I(C)]. The response of the fight eye should be the same under both stimulus conditions, but small differences in tracking behavior can be seen. Subject CC.
c o n j u n c t i v e and disjunctive c o m p o n e n t s are present. F i g u r e 4 ( A ) shows the r e s p o n s e o f the two e y e s to a stimulus that is h e l d fixed for the left e y e and m o v e s at 3 d e g / s e c in the right. In this stimulus, a brief, 0.5 sec p e r i o d o f pure v e r s i o n is first p r e s e n t e d to separate out the initial transients o f v e r s i o n and v e r g e n c e [Fig. I(D)]. In terms o f version and vergence, this stimulus can be v i e w e d as a c o m b i n e d 1.5 deg/sec version and a 3 deg/sec vergence. T h e s e two stimuli create equal m o n o c u l a r velocities that cancel in one e y e and a d d in the other. Both eyes are seen to f o l l o w their respective retinal targets, but with s o m e slight variability. T h e source o f this v a r i a b i l i t y is better seen w h e n the left and right e y e m o v e m e n t s are replotted as a version and v e r g e n c e response. W h i l e the version r e s p o n s e is quite s m o o t h (adding further c r e d i b i l i t y to the t e r m s m o o t h pursuit), the v e r g e n c e r e s p o n s e shows well defined oscillations. Such v e r g e n c e oscillations are not u n c o m m o n and are p r o b a b l y due to f e e d b a c k instabilities. F e e d b a c k i n d u c e d oscillations are also s o m e t i m e s o b s e r v e d in s m o o t h pursuit m o v e m e n t s , but at higher velocities than used here ( R o b i n s o n et al., 1986; G o l d r e i c h et al., 1992). A s i m p l e m e a s u r e was d e v e l o p e d to quantify the b e h a v i o r a l differences b e t w e e n the two c o m p o n e n t s . Since the m o s t o b v i o u s differences were in the ability to track a constant v e l o c i t y stimulus s m o o t h l y , the m e a s u r e
c a l c u l a t e d the m e a n d e v i a t i o n o f r e s p o n s e velocity from a s m o o t h trajectory. Specifically, the best straight line was fitted to a section o f the velocity r e s p o n s e using a least m e a n s squared algorithm. T h e variability metric was then taken as the R M S d e v i a t i o n from this straight line.* The section a n a l y z e d was g e n e r a l l y 0 . 7 - 2 . 0 sec in length and was chosen to a v o i d the early transients: saccades for version and initial c o m p o n e n t s for vergence. This m e a s u r e was a p p l i e d to a n u m b e r o f m o v e m e n t s o f the s a m e e y e to facilitate the v e r s i o n / v e r g e n c e c o m p a r i s o n . T a b l e 1 presents the R M S d e v i a t i o n values obtained f r o m constant v e l o c i t y responses to pure version, pure vergence, and c o m b i n e d version and vergence. The n u m b e r o f responses, n, used to c o m p u t e each value are also presented. In all cases the values are for the right eye m o v i n g leftward, and the stimulus values s h o w n are for the m o n o c u l a r v e l o c i t y stimulus to this eye. In the case o f pure v e r s i o n and pure vergence, the stimulus velocity to the fight eye was 1.5 deg/sec, while for c o m b i n e d version/vergence, the fight e y e stimulus velocity was twice that at 3.0 deg/sec. A l s o s h o w n for c o m p a r a t i v e p u r p o s e s are the R M S deviation values obtained for pure version and v e r g e n c e responses f r o m stimuli that drive *Essentially, this measure is mathematically equivalent to a detrended measure of velocity variance over the time period analyzed.
S L O W V E R S I O N A N D V E R G E N C E EYE M O V E M E N T S
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Time (sec) Time (sec) FIGURE 3. (A) The version response to a pure version stimulus of 1.5 deg/sec. The plot shows the time trace of the s u m of the two individual eye m o v e m e n t s divided by two along with the velocity. Leftward version is plotted as positive. (B) The vergence response to a pure vergence stimulus of 3.0 deg/sec from the same subject. The plot shows the time trace of the difference of the two individual eye m o v e m e n t s along with the velocity. Convergence is plotted as positive. Subject CC.
the right eye at 3.0 deg/sec. In all subjects, the RMS deviations show quantitative differences between version and vergence responses, even though the response velocities generated were the same, as were the retinal stimuli in the measured eye. Specifically, the RMS deviation of the tracking eye was considerably greater when driven by vergence control processes. In other words, vergence control processes produced less accurate tracking for the same ocular velocities, as seen qualitatively in Fig. 2.
When the two stimuli are combined, the right eye was driven at 3.0 deg/sec. As would be expected, the RMS deviation for the right eye under combined stimulation was, in all subjects, greater than the RMS deviation seen in either the version or vergence response to a 1.5 deg/sec stimulus. However, the RMS deviation to this combined version/vergence stimulus was also greater than that from a pure version stimulus, producing an equivalent right eye velocity (i.e., 3 deg/sec; Table 1). This indicates that the combined movement is not solely the result of slow
T A B L E 1. R M S deviation* of constant velocity responses to version, vergence, and combined stimuli Subject Stim.t
Version 1.5 deg/sec
Vergence 1.5 deg/sec
Combined 3.0 deg/sec
CC
0.23 (0.04) n = 13 0.26 (0.04) n = 10 0.38 (0.09) n=17 0.39 (0.08) n=13 0.32 (0.06) n=ll 0.34 (0.09) n = 11
0.36 (0.05) n = 10 0.33 (0.06) n = 18 0.49 (0.11) n=12 0.46 (0.08) n=ll 0.40 (0.09) n=12 0.46 (0.12) n=20
0.42 (0.06) n = 21 0.39 (0.06) n=8 0.59 (0.08) n=ll 0.55 (0.11) n=22 0.47 (0.09) n=12 0.52 (0.7) n=16
BS JI MS CA JS
Expected:~ 0.43 0.42 0.56 0.53 0.48 0.57
Version 3.0 deg/sec
Vergence 3.0 deg/sec
0.36 (0.10) n = 18 0.36 (0.10) n = 15 0.56 (0.12) n=15 0.49 (0.10) n=14 0.39 (0.40) n=14 0.40 (0.9) n=21
0.60 (0.11) n = 20 0.58 (0.10) n = 12 0.68 (0.11) n = 13 0.78 (0.14) n = 18 0.55 (0.40) n=17 0.65 (0.9) n=25
*RMS deviation given in deg/sec RMS for the right eye. Standard deviation is shown in parentheses. t G i v e n in terms of the effective velocity to the right eye. :~Calculated by taking the square root of the version RMS deviation squared plus the vergence RMS deviation squared.
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FIGURE 4. The response of the eyes to a combined conjunctive and disjunctive constant velocity stimulus. In version/vergence coordinates: version = 1.5 deg/sec, vergence = 3.0 deg/sec. (A) Left and right eye movements are plotted with velocity as in Fig. 2. (B) Plotted as separate version and vergence responses as in Fig. 3. Subject BS.
version control processes. Moreover, the RMS deviation of the right eye to combined version/vergence was less than that found for a vergence stimulus that produced the same ocular velocity (Table l), again indicating that the combined movement is not guided solely by vergence control components. Since the RMS deviation associated with the combined version/vergence movement is greater than that expected from pure version, but less than that expected from pure vergence, it is likely that some combination of the two could account for the observed variability. Under the assumption that both version and vergence control components are active in proportion to their respective stimulus amplitudes, then the 3 deg/sec response velocity of the right eye during combined stimulation is due to equal contributions from the version and vergence controllers (i.e., each controller provides half of the movement's drive). If the two components are independent, then the RMS deviation associated with each controller should add as the square root of the sum of squares. As shown in Table 1, the RMS deviation in right eye tracking to a combined stimulus is quite close to that predicted by the hypothesis that the driving stimulus
consists of the components.
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DISCUSSION The remarkable ability of the oculomotor control system to track slow velocity targets with little error masks the operation of Hering's law under these circumstances. As both eyes appear to accurately track their respective retinal images, it is difficult to resolve the activity of the two distinct underlying components. In addition to this absence of clearly identifiable control features, other evidence has recently been presented to suggest the monocular guidance of slow version and vergence eye movements. King and Zhou (1995) have shown in monkey a similarity in the early dynamics of all slow movements, whether evoked by pure version, pure vergence, or combined version/vergence. Their analysis was limited to the brief 100 msec period of the response when, due to the response latency, the movement would not be subject to feedback. During this period, the velocity (or acceleration, which they also calculated) would be an indication of the open-loop velocity (or acceleration) gain of the underlying controller, assuming
SLOW VERSION AND VERGENCE EYE MOVEMENTS that the velocity or acceleration reached steady-state during that period. However, their finding of dynamic similarity does not preclude the existence of separate controllers: it merely infers that if separate control processes exist, they have similar gains.* Finally, the stimulus conditions they used were quite different f r o m ours and this could also account for the behavioral differences. A simple qualitative examination of m o v e m e n t dynamics demonstrates that slow m o v e m e n t s generated by version are not the same as those controlled by vergence. This qualitative finding is quite similar in spirit to that of Rashbass and Westheimer (1961), when they showed qualitative differences in the tracking of simultaneous version/vergence sinusoids. W e have chosen to quantify these differences in terms o f "tracking error" as represented by a variability measurement. This feature was chosen as a marker for the two components because it is clearly different in the two components, it is easy to measure, and it appears to be relatively consistent f r o m m o v e m e n t - t o - m o v e m e n t . t (Note the low standard deviations in the variability measurements o f Table 1.) The source o f the increased variability in vergence tracking is unknown, and one reviewer suggested interaction with the a c c o m m o d a t i o n system as a possible explanation. For example, since a c c o m m o d a t i o n was closed-loop in these experiments, the combination o f the vergence and a c c o m m o d a t i v e feedback pathways in conjunction with the crosslink pathways (accommodative vergence and vergence accommodation) establish a positive feedback network that could induce oscillation. Irrespective o f the source of the variability, as long as the variability or tracking error of version and vergence are independent from one another (but not necessarily from other systems), variability will provide a reliable indicator o f the relative proportions of the two c o m p o nents. While the independence o f version and vergence control processes has been questioned, both for the slow tracking m o v e m e n t s addressed here and for the faster m o v e m e n t s produced by step changes in the version/ vergence stimulus, the independence of vergence from version during steady fixation is firmly established. In response to sustained vergence stimuli, the vergence control system responds as a proportional feedback control system: a small, sustained error exists between
*Our finding that tracking accuracy is different in slow version vs slow vergence might indicate differences in open-loop gains, but these behavioral differences could also be due to other dynamic control properties such as latency, gain distribution, or nonlinearities. tOther features could have been used such as the frequency of oscillations in the two responses, but such features were not found to be as consistent as variability. ~Indeed, the concept of the horopter is predicated on version/vergence independence. §The only alternative is a complex switching process that engages the steady-state feedback control system only after the vergence movement has been completed and inhibits or overrides it during the transient response.
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the stimulus and response that increases with the level o f response (Toates, 1974; S e m m l o w & Hung, 1979). The sustained error, termed fixation disparity, depends only on the vergence stimulus (or response), it is not altered by the steady-state version position (Ogle, Martens & Dyer, 1967). Since this error is dependent on, and highly sensitive to, the gain of the vergence control system, its independence from version shows that the vergence control system is independent o f the version system in steady-state or static conditions.:~ It is highly probable that the feedback control processes that mediate sustained behavior also control the smooth tracking movements studied here.§ Thus, the well established steady-state behavior o f vergence strongly supports the experimentally based conclusions reached here: that slow version and vergence are independent o f one another.
CONCLUSION
Slow constant velocity version movements (smooth pursuit) exhibit different tracking behavior than those of slow vergence. W h e n the two stimuli are combined, the resultant eye m o v e m e n t behavior is consistent with the hypothesis that version and vergence control processes are independently active, in proportion to their respective conjunctive and disjunctive stimuli. In other words, slow tracking movements do appear to be organized in terms o f independent version and vergence control signals. This supports the modern interpretation of Hering's law, at least for slow tracking movements.
REFERENCES
Collewijn, H., Erkelens, R. & Steinman, R. M. (1995). Voluntary binocular gaze-shifts in the plane of regard: dynamics of version and vergence. Vision Research, 35, 3335-3358. Enright, J. (1992). The remarkable saccades of asymmetrical vergence. Vision Research, 32, 2261-2276.
Enright, J. T. (1996). Slow-velocity asymmetrical convergence: a decisive failure of Hering's law. Vision Research, 36, 3667-3684. Goldreich, D., Krauzlis, R. J. & Lisberger, S. G. (1992). Effect of changing feedback delay on spontaneous ringing in smooth pursuit eye movements of monkeys. Journal of Neurophysiology, 67, 625638. Hering, E. (1978). In B. Bridgeman (trans.), B. Bridgeman & L. Stark (Eds), The theory of binocular vision. New York: Plenum Press (originally published 1868). Kenyon, R. V. & Stark, L. (1983). Unequal saccades generated by velocity interactions in the peripheral oculomotor system. Mathematical Biosciences, 63, 187-197. King, W. M. & Zhou, W. (1995). Initiation of disjunctive smooth pursuit in monkeys: evidence that Hering's law of equal innervation is not obeyed by the smooth pursuit system. Vision Research, 35, 3389-3400. Krauzlis, R. J. & Lisberger, S. G. (1989). A control systems model of smooth pursuit eye movements with realistic emergent properties. Neural Computing, 1, 116-122. Maxwell, J. S. & King, M. (1992). Dynamics and efficacy of saccadefacilitated vergence eye movements in monkeys. Journal of Neurophysiology, 68, 1248-1260. Ogle, K. N., Martens, T. C. & Dyer, M. (1967). Binocular vision and fixation dispari~. Philadelphia, PA: Lea and Febiger. Ono, H., Nakamizo, S. & Steinbach, M. J. (1978). Nonadditivity of vergence and saccadic eye movement. Vision Research, 18, 735739.
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Rashbass, C. & Westheimer, G. (1961). Independence of conjugate and disjunctive eye movements. Journal of Physiology London, 159, 361-364. Robinson, D. A., Gordon, J. L. & Gordon, S. E. (1986). A model of the smooth pursuit eye movement system. Biological Cybernetics, 55, 43-47. Rosenfield, M. & Ciuffreda, K. J. (1991). The effect of surround propinquity on the open-loop accommodative response. Investigative Ophthalmology and Visual Science, 32, 142-147. Semmlow, J. L. & Hung, G. (1979). Accommodative and fusional components of fixation disparity. Investigative Ophthalmology, 18, 1082-1086.
Semmlow, J. L., Hung, G. K. & Ciuffreda, K. J. (1986). Quantitative assessment of disparity vergence components. Investigative Ophthalmology and Visual Science, 27, 558-564. Toates, F. M. (1974). Vergence eye movements. Documenta Ophthalmologica, 37, 153-214. Yarbus, A. L. (1957). Motion of the eye on interchanging fixation points at rest in space. Biofizika, 2, 698-702.
Acknowledgement--This work was supported in part by a grant from the National Science Foundation IBN-9511655.
PH: S0042-6989(97)00251-4
Vision Res., Vol. 38, No. 8, pp. 1145-1152, 1998 © 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0042-6989/98 $19.00 + 0.00
Evidence for Separate Control of Slow Version and Vergence Eye Movements: Support for Hering' s Law JOHN L. SEMMLOW,*t"$ WEIHONG YUAN,* TARA L. ALVAREZ* Received 29 January 1997; in revised form 8 July 1997
When a visual stimulus changes direction and distance simultaneously, Hering's Law argues that the resulting eye movements are the result of combined version and vergence control processes. Recently, it has been suggested that slow asymmetrical eye movements might be guided by monocular control processes wherein each eye is driven by its own retinal image. Experimental results presented here show behavioral differences between slow version and slow vergence eye movements, indicating that different control processes drive the two "pure" responses. Specifically, version tracking of constant velocity stimuli (i.e., smooth pursuit) is more precise, showing less variation in tracking velocity than movements of equal velocity produced by vergence stimuli. When the two stimuli are combined, the variability in tracking is consistent with the addition of the two components in proportion to their respective stimuli. These results provide support for Hering's Law, at least for low velocity, smooth tracking movements (i.e., slow version and slow vergence). © 1998 Elsevier Science Ltd. All rights reserved.
Vergence Disparityvergence Smoothpursuit Hering's law
INTRODUCTION Division of labor is a major strategy used by the brain in oculomotor control. For example, smooth tandem ocular movements (i.e., slow version) are mediated by the appropriately termed smooth pursuit system, a system that can produce highly accurate tracking of slowly moving targets. The smooth pursuit system has been well studied and has been represented as a feedback control process driven by target velocity (Robinson, Gordon & Gordon, 1987; Krauzlis & Lisberger, 1989; Goldreich, Krauzlis & Lisberger, 1992). Targets moving smoothly inward are also accurately followed by the two eyes as long as the movement is slow enough (Semmlow, Hung & Ciuffreda, 1986). The behavior of smooth vergence has not been extensively studied and its fundamental control structure is unknown, but the accuracy and smoothness of the tracking movements shown later suggest the action of feedback control. When called upon to track targets moving slowly across and inward (a combined slow version/vergence *Department of Biomedical Engineering, Rutgers-The State University of New Jersey, Piscataway, NJ 08855, U.S.A. tDepartment of Surgery (Bioengineering), UMDNJ-Robert Wood Johnson Medical School, New Brunswick, NJ 08903, U.S.A. STo whom all correspondence should be addressed at: Department of Biomedical Engineering, P.O. Box 909, Rutgers University, Piscataway, NJ 08855, U.S.A. [Email: [email protected]. edu]
Eye movement
stimulus), the eyes respond with smooth tracking movements similar to those produced by version or vergence alone. Traditional thinking about responses generated by combinations of version and vergence stimuli are embodied in Hering's law of equal (muscle) innervation (Hering, 1978 transl.). The contemporary interpretation of this law is that combined stimuli are divided into their respective version and vergence components, then implemented by the independent action of the two control systems. This interpretation implies that a combined version/vergence stimulus produces separate motor commands from the smooth pursuit and disparity vergence systems that then summate at (or before) the final common pathway to produce the combined smooth response. Early experiments both defined and supported the modem interpretation of Hering's law for fast (Yarbus, 1957; Rashbass & Westheimer, 1961) and slow (Rashbass & Westheimer, 1961) movements. To explore the interactions between slow version and vergence, Rashbass and Westheimer (1961) used low frequency sinusoidal stimuli. Simultaneously stimulating both slow version and slow vergence, but at slightly different frequencies, they qualitatively demonstrated "complete independence of the response mechanism of lateral eye tracking and vergence tracking". Specifically, they were able to generate combinations of version and vergence stimuli that exceeded the limits of vergence tracking while version tracking (i.e., smooth pursuit) continued
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normally. Based on these qualitative findings they concluded that combined version and vergence stimuli "were resolved into two components corresponding to mean target position and target vergence, respectively, and that appropriate responses to these components are made by two independent systems". Recent experiments have challenged the validity of Hering' s law to both fast and slow eye movements. When both version and vergence are quickly changed, the resulting eye movements exhibit an asymmetrical behavior that indicates significant and complex interactions between the two control systems (Ono, Nakamizo & Steinbach, 1978; Kenyon & Stark, 1983; Enright, 1992; Maxwell & King, 1992; Collewijn, Erkelens & Steinman, 1995). When a combined version and vergence stimulus changes slowly, the tracking is so smooth and accurate that it is difficult to see the action of separate control processes in the combined response. This performance in conjunction with other factors led Enright (1996) to conclude that the control of such slow-velocity movements is primarily monocular; that is "...the response is determined for each eye by its own visual stimuli". King and Zhou (1995) similarly concluded that "oculomotor commands are organized in a coordinate space defined by right and left eye movements" as opposed to version and vergence. This statement was motivated by their finding in monkey that the monocular acceleration gain of each eye was the same whether stimulated by pure version or combined version/vergence stimuli. Here we first present qualitative evidence that, contrary to the above, slow tracking behavior is influenced by more than its own retinal image. In other words, the binocular stimulus environment influences monocular tracking behavior. We then present qualitative and quantitative evidence indicating that slow version and slow vergence are mediated by different control processes. Finally, we will present quantitative evidence suggesting that when slow version and slow vergence are stimulated simultaneously, the two control systems respond in a manner consistent with Hering's law; that is, the two systems are active in proportion to the relative magnitude of their respective conjunctive or disjunctive stimuli. METHODS
Experiments were designed to acquire horizontal eye movements of both eyes in response to slow conjunctive, slow disjunctive, and combined slow conjunctive/disjunctive stimuli. The stimulus consisted of two stereoscopically paired vertical lines (0.15 deg in width and 5 deg in height) presented on separate oscilloscopes (P31 phosphor and a bandwidth of 20 MHz) at a distance of 40 cm from each eye. The oscilloscopes were arranged as a haploscope and were viewed through partially reflecting mirrors. Two real-world targets viewed directly through the mirrors provided well defined vergence reference points that were used to calibrate the stimulus device prior to each experiment. During the experiment, only the oscilloscope targets were visible to the subject:
no other objects on the stimulus device or in the laboratory could be seen. Proximal influences related to changes in target disparity appeared to be minimal in the device, presumably due to a lack of depth information related to the target (Rosenfield & Ciuffreda, 1991). Slow constant velocity changes in target version, vergence, or version/vergence combinations were generated by the laboratory computer at velocities of either 1.5 or 3 deg/sec. Stimulus velocities were limited by the ability of the vergence system to track fast targets smoothly: stimuli much above approximately 4 deg/sec evoke fast component responses in the vergence pursuit response (Semmlow e t al., 1986). Four different stimulus types were used as schematically illustrated in Fig. 1: (A) pure version; (B) pure vergence; (C) pure version immediately followed by pure vergence; and (D) combined version/vergence in which one eye was stationary. In addition to stimulus presentation, the laboratory computer controlled stimulus selection, response calibration, data acquisition, and data storage. To discourage prediction, the type of stimulus and the time of presentation were randomized for each trial. Once the subject indicated readiness by pressing a button, stimulus presentation and data acquisition followed after a random delay of 0.5-2 sec. The stimulus and recording period lasted for 3 sec. During each experimental run, 12-16 responses were recorded for each stimulus pattern, of which about half were sufficiently saccade and artifactfree to be suitable for analysis. Experimental runs were repeated at least three times on each subject on separate days producing data sets of between 8 and 25 clean responses. Binocular eye position was recorded by means of a Skalar infrared eye movement monitor (Model 6500). This device has a linear range (within 3%) of +25 deg and a resolution of 1.5 min arc. A two-point calibration was performed before and after each response. The baseline position (prior to stimulus onset) was taken as the first calibration point, and the maximum extent of the response was taken as the second point. Calibrations were stored in the computer and used to construct a separate calibration curve for each eye. Data acquisition was done at a sampling rate of 200 Hz, which is well above the Nyquist frequency for vergence eye movements. Six subjects, between 24 and 54 years of age, participated in the experiment. Each subject had normal binocular vision and acuity (20/20). One of these subjects, JS, was experienced and was aware of the goals of this study, while the others were relatively inexperienced and were na]'ve to the study's objectives. RESULTS
Figure 2 shows the typical response of both eyes to a pure version stimulus followed by a pure vergence stimulus [see Fig. I(C)]. The velocities of the two stimuli were selected so that the response velocity of the right eye would be the same under both stimulus conditions. That is, a leftward-moving 2.5 deg/sec version stimulus was followed by a symmetrical 5.0 deg/sec convergent
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FIGURE 1. Schematic illustration of the four stimulus types used in this study. (A) Pure version. (B) Pure vergence. (C) Pure version followed immediately by pure vergence. (D) Combined version and vergence (following a brief period of pure version) in which the stimulus to the left eye is fixed. Note that the line indicates the apparent motion produced by a stereoscopic image pair. The actual images are always at the same physical depth.
stimulus.* T h e starting p o i n t o f the v e r s i o n stimulus was s e l e c t e d so that the e y e s w o u l d be centered w h e n the stimulus s w i t c h e d to c o n v e r g e n c e [Fig. I(C)]. U n d e r this c o n d i t i o n the right e y e m o v e s c o n t i n u o u s l y l e f t w a r d at 2.5 deg/sec, first d r i v e n b y pure version, then b y pure vergence. W i t h r e s p e c t to the right eye, the stimulus does not change, y e t the b e h a v i o r o f the fight e y e is subtly different u n d e r the t w o stimulus conditions. Specifically, *By convention, version stimuli are defined in terms of the monocular amplitude (or velocity) of one eye, while vergence stimulus amplitudes are defined in terms of the summed amplitudes (or velocities) in both eyes. Hence, a 2 deg/sec movement is generated in each eye in response to a 2 deg/sec version stimulus, but a 4 deg/ sec vergence stimulus is required to generate a 2 deg/sec movement (oppositely directed) in each eye. Throughout this paper, we pair version stimuli with vergence stimuli of twice the amplitude in order to compare stimuli that produce the same monocular velocities.
an oscillation is o b s e r v e d during the v e r g e n c e control p e r i o d that was m u c h less w h e n this e y e was driven b y version ( f o l l o w i n g the initial transient period). Note that this oscillation is also seen in the other eye, d e m o n s t r a t ing the b i n o c u l a r i t y o f this behavior. T h e difference in b e h a v i o r o f the right e y e in Fig. 2 is t y p i c a l o f r e s p o n s e s to these stimulus conditions and reflects the o p e r a t i o n o f the u n d e r l y i n g control processes. In general, slow v e r g e n c e tracks less a c c u r a t e l y and has larger oscillations than slow version for the s a m e tracking velocities. This is illustrated in Fig. 3, w h i c h shows t y p i c a l r e s p o n s e s to pure version and pure v e r g e n c e constant v e l o c i t y stimuli [see Fig. I ( A ) and (B)]. T h e s e qualitative b e h a v i o r a l differences were o b s e r v e d in all subjects and indicate that the two r e s p o n s e s are m e d i a t e d b y different control processes. T h e o r g a n i z a t i o n o f slow e y e m o v e m e n t control is illustrated in r e s p o n s e s to stimuli in w h i c h both
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FIGURE 2. Left and right eye movements in response to a constant velocity stimulus first presented as pure version then as a pure vergence: a 2.5 deg/sec version stimulus is followed, after 1.25 sec, by a 5.0 deg/sec convergent stimulus. Position and velocity traces are shown with leftward movements plotted as positive. The initial position of the stimulus was adjusted so that the convergent stimulus would fall along the centerline [see Fig. I(C)]. The response of the fight eye should be the same under both stimulus conditions, but small differences in tracking behavior can be seen. Subject CC.
c o n j u n c t i v e and disjunctive c o m p o n e n t s are present. F i g u r e 4 ( A ) shows the r e s p o n s e o f the two e y e s to a stimulus that is h e l d fixed for the left e y e and m o v e s at 3 d e g / s e c in the right. In this stimulus, a brief, 0.5 sec p e r i o d o f pure v e r s i o n is first p r e s e n t e d to separate out the initial transients o f v e r s i o n and v e r g e n c e [Fig. I(D)]. In terms o f version and vergence, this stimulus can be v i e w e d as a c o m b i n e d 1.5 deg/sec version and a 3 deg/sec vergence. T h e s e two stimuli create equal m o n o c u l a r velocities that cancel in one e y e and a d d in the other. Both eyes are seen to f o l l o w their respective retinal targets, but with s o m e slight variability. T h e source o f this v a r i a b i l i t y is better seen w h e n the left and right e y e m o v e m e n t s are replotted as a version and v e r g e n c e response. W h i l e the version r e s p o n s e is quite s m o o t h (adding further c r e d i b i l i t y to the t e r m s m o o t h pursuit), the v e r g e n c e r e s p o n s e shows well defined oscillations. Such v e r g e n c e oscillations are not u n c o m m o n and are p r o b a b l y due to f e e d b a c k instabilities. F e e d b a c k i n d u c e d oscillations are also s o m e t i m e s o b s e r v e d in s m o o t h pursuit m o v e m e n t s , but at higher velocities than used here ( R o b i n s o n et al., 1986; G o l d r e i c h et al., 1992). A s i m p l e m e a s u r e was d e v e l o p e d to quantify the b e h a v i o r a l differences b e t w e e n the two c o m p o n e n t s . Since the m o s t o b v i o u s differences were in the ability to track a constant v e l o c i t y stimulus s m o o t h l y , the m e a s u r e
c a l c u l a t e d the m e a n d e v i a t i o n o f r e s p o n s e velocity from a s m o o t h trajectory. Specifically, the best straight line was fitted to a section o f the velocity r e s p o n s e using a least m e a n s squared algorithm. T h e variability metric was then taken as the R M S d e v i a t i o n from this straight line.* The section a n a l y z e d was g e n e r a l l y 0 . 7 - 2 . 0 sec in length and was chosen to a v o i d the early transients: saccades for version and initial c o m p o n e n t s for vergence. This m e a s u r e was a p p l i e d to a n u m b e r o f m o v e m e n t s o f the s a m e e y e to facilitate the v e r s i o n / v e r g e n c e c o m p a r i s o n . T a b l e 1 presents the R M S d e v i a t i o n values obtained f r o m constant v e l o c i t y responses to pure version, pure vergence, and c o m b i n e d version and vergence. The n u m b e r o f responses, n, used to c o m p u t e each value are also presented. In all cases the values are for the right eye m o v i n g leftward, and the stimulus values s h o w n are for the m o n o c u l a r v e l o c i t y stimulus to this eye. In the case o f pure v e r s i o n and pure vergence, the stimulus velocity to the fight eye was 1.5 deg/sec, while for c o m b i n e d version/vergence, the fight e y e stimulus velocity was twice that at 3.0 deg/sec. A l s o s h o w n for c o m p a r a t i v e p u r p o s e s are the R M S deviation values obtained for pure version and v e r g e n c e responses f r o m stimuli that drive *Essentially, this measure is mathematically equivalent to a detrended measure of velocity variance over the time period analyzed.
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Time (sec) Time (sec) FIGURE 3. (A) The version response to a pure version stimulus of 1.5 deg/sec. The plot shows the time trace of the s u m of the two individual eye m o v e m e n t s divided by two along with the velocity. Leftward version is plotted as positive. (B) The vergence response to a pure vergence stimulus of 3.0 deg/sec from the same subject. The plot shows the time trace of the difference of the two individual eye m o v e m e n t s along with the velocity. Convergence is plotted as positive. Subject CC.
the right eye at 3.0 deg/sec. In all subjects, the RMS deviations show quantitative differences between version and vergence responses, even though the response velocities generated were the same, as were the retinal stimuli in the measured eye. Specifically, the RMS deviation of the tracking eye was considerably greater when driven by vergence control processes. In other words, vergence control processes produced less accurate tracking for the same ocular velocities, as seen qualitatively in Fig. 2.
When the two stimuli are combined, the right eye was driven at 3.0 deg/sec. As would be expected, the RMS deviation for the right eye under combined stimulation was, in all subjects, greater than the RMS deviation seen in either the version or vergence response to a 1.5 deg/sec stimulus. However, the RMS deviation to this combined version/vergence stimulus was also greater than that from a pure version stimulus, producing an equivalent right eye velocity (i.e., 3 deg/sec; Table 1). This indicates that the combined movement is not solely the result of slow
T A B L E 1. R M S deviation* of constant velocity responses to version, vergence, and combined stimuli Subject Stim.t
Version 1.5 deg/sec
Vergence 1.5 deg/sec
Combined 3.0 deg/sec
CC
0.23 (0.04) n = 13 0.26 (0.04) n = 10 0.38 (0.09) n=17 0.39 (0.08) n=13 0.32 (0.06) n=ll 0.34 (0.09) n = 11
0.36 (0.05) n = 10 0.33 (0.06) n = 18 0.49 (0.11) n=12 0.46 (0.08) n=ll 0.40 (0.09) n=12 0.46 (0.12) n=20
0.42 (0.06) n = 21 0.39 (0.06) n=8 0.59 (0.08) n=ll 0.55 (0.11) n=22 0.47 (0.09) n=12 0.52 (0.7) n=16
BS JI MS CA JS
Expected:~ 0.43 0.42 0.56 0.53 0.48 0.57
Version 3.0 deg/sec
Vergence 3.0 deg/sec
0.36 (0.10) n = 18 0.36 (0.10) n = 15 0.56 (0.12) n=15 0.49 (0.10) n=14 0.39 (0.40) n=14 0.40 (0.9) n=21
0.60 (0.11) n = 20 0.58 (0.10) n = 12 0.68 (0.11) n = 13 0.78 (0.14) n = 18 0.55 (0.40) n=17 0.65 (0.9) n=25
*RMS deviation given in deg/sec RMS for the right eye. Standard deviation is shown in parentheses. t G i v e n in terms of the effective velocity to the right eye. :~Calculated by taking the square root of the version RMS deviation squared plus the vergence RMS deviation squared.
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FIGURE 4. The response of the eyes to a combined conjunctive and disjunctive constant velocity stimulus. In version/vergence coordinates: version = 1.5 deg/sec, vergence = 3.0 deg/sec. (A) Left and right eye movements are plotted with velocity as in Fig. 2. (B) Plotted as separate version and vergence responses as in Fig. 3. Subject BS.
version control processes. Moreover, the RMS deviation of the right eye to combined version/vergence was less than that found for a vergence stimulus that produced the same ocular velocity (Table l), again indicating that the combined movement is not guided solely by vergence control components. Since the RMS deviation associated with the combined version/vergence movement is greater than that expected from pure version, but less than that expected from pure vergence, it is likely that some combination of the two could account for the observed variability. Under the assumption that both version and vergence control components are active in proportion to their respective stimulus amplitudes, then the 3 deg/sec response velocity of the right eye during combined stimulation is due to equal contributions from the version and vergence controllers (i.e., each controller provides half of the movement's drive). If the two components are independent, then the RMS deviation associated with each controller should add as the square root of the sum of squares. As shown in Table 1, the RMS deviation in right eye tracking to a combined stimulus is quite close to that predicted by the hypothesis that the driving stimulus
consists of the components.
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DISCUSSION The remarkable ability of the oculomotor control system to track slow velocity targets with little error masks the operation of Hering's law under these circumstances. As both eyes appear to accurately track their respective retinal images, it is difficult to resolve the activity of the two distinct underlying components. In addition to this absence of clearly identifiable control features, other evidence has recently been presented to suggest the monocular guidance of slow version and vergence eye movements. King and Zhou (1995) have shown in monkey a similarity in the early dynamics of all slow movements, whether evoked by pure version, pure vergence, or combined version/vergence. Their analysis was limited to the brief 100 msec period of the response when, due to the response latency, the movement would not be subject to feedback. During this period, the velocity (or acceleration, which they also calculated) would be an indication of the open-loop velocity (or acceleration) gain of the underlying controller, assuming
SLOW VERSION AND VERGENCE EYE MOVEMENTS that the velocity or acceleration reached steady-state during that period. However, their finding of dynamic similarity does not preclude the existence of separate controllers: it merely infers that if separate control processes exist, they have similar gains.* Finally, the stimulus conditions they used were quite different f r o m ours and this could also account for the behavioral differences. A simple qualitative examination of m o v e m e n t dynamics demonstrates that slow m o v e m e n t s generated by version are not the same as those controlled by vergence. This qualitative finding is quite similar in spirit to that of Rashbass and Westheimer (1961), when they showed qualitative differences in the tracking of simultaneous version/vergence sinusoids. W e have chosen to quantify these differences in terms o f "tracking error" as represented by a variability measurement. This feature was chosen as a marker for the two components because it is clearly different in the two components, it is easy to measure, and it appears to be relatively consistent f r o m m o v e m e n t - t o - m o v e m e n t . t (Note the low standard deviations in the variability measurements o f Table 1.) The source o f the increased variability in vergence tracking is unknown, and one reviewer suggested interaction with the a c c o m m o d a t i o n system as a possible explanation. For example, since a c c o m m o d a t i o n was closed-loop in these experiments, the combination o f the vergence and a c c o m m o d a t i v e feedback pathways in conjunction with the crosslink pathways (accommodative vergence and vergence accommodation) establish a positive feedback network that could induce oscillation. Irrespective o f the source of the variability, as long as the variability or tracking error of version and vergence are independent from one another (but not necessarily from other systems), variability will provide a reliable indicator o f the relative proportions of the two c o m p o nents. While the independence o f version and vergence control processes has been questioned, both for the slow tracking m o v e m e n t s addressed here and for the faster m o v e m e n t s produced by step changes in the version/ vergence stimulus, the independence of vergence from version during steady fixation is firmly established. In response to sustained vergence stimuli, the vergence control system responds as a proportional feedback control system: a small, sustained error exists between
*Our finding that tracking accuracy is different in slow version vs slow vergence might indicate differences in open-loop gains, but these behavioral differences could also be due to other dynamic control properties such as latency, gain distribution, or nonlinearities. tOther features could have been used such as the frequency of oscillations in the two responses, but such features were not found to be as consistent as variability. ~Indeed, the concept of the horopter is predicated on version/vergence independence. §The only alternative is a complex switching process that engages the steady-state feedback control system only after the vergence movement has been completed and inhibits or overrides it during the transient response.
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the stimulus and response that increases with the level o f response (Toates, 1974; S e m m l o w & Hung, 1979). The sustained error, termed fixation disparity, depends only on the vergence stimulus (or response), it is not altered by the steady-state version position (Ogle, Martens & Dyer, 1967). Since this error is dependent on, and highly sensitive to, the gain of the vergence control system, its independence from version shows that the vergence control system is independent o f the version system in steady-state or static conditions.:~ It is highly probable that the feedback control processes that mediate sustained behavior also control the smooth tracking movements studied here.§ Thus, the well established steady-state behavior o f vergence strongly supports the experimentally based conclusions reached here: that slow version and vergence are independent o f one another.
CONCLUSION
Slow constant velocity version movements (smooth pursuit) exhibit different tracking behavior than those of slow vergence. W h e n the two stimuli are combined, the resultant eye m o v e m e n t behavior is consistent with the hypothesis that version and vergence control processes are independently active, in proportion to their respective conjunctive and disjunctive stimuli. In other words, slow tracking movements do appear to be organized in terms o f independent version and vergence control signals. This supports the modern interpretation of Hering's law, at least for slow tracking movements.
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Acknowledgement--This work was supported in part by a grant from the National Science Foundation IBN-9511655.