Quantitative Assessment of Disparity Vergence ... - Semantic Scholar

Quantitative Assessment of Disparity Vergence Components John L. 5emmlow,*j- George K. Hung.j- and Kenneth J. Ciuffreda^: Earlier evidence suggests qualitatively that at least two control modes may mediate a single vergence response. Thus, in a vergence response to step disparity, the transient component drives the initial fast dynamic portion of the response, while the sustained component maintains the latter slower portion of the response. The authors extended this hypothesis by quantitatively defining the stimulus pattern and dynamics that elicit this dichotomous behavior. The disparity target consisted of vertical lines 2 deg in height presented to each eye. Ramp disparity velocities ranged from 0.7 deg/sec to 36 deg/sec with amplitude of up to 4 deg. Photoelectric recordings of eye movements from both eyes were subtracted to give the vergence response. Fast and slow ramp stimulus velocities were found to elicit transient and sustained component responses respectively. In addition, the finding of staircase-like responses to fast ramp stimuli has strong implications on control mechanisms, indicating a sampling process in the transient component of the disparity vergence system. Invest Ophthalmol Vis Sci 27:558-564, 1986

Division of labor appears as a guiding principle in the neural strategy for controlling ocular movements. A host of specialized neural centers, each responding to a specific stimulus, mediate their own distinctive behavior (saccades, smooth pursuit, vergence movements, vestibular-ocular) with remarkable independence, considering the rich interconnections in neural architecture.1 An exemplary application of this principle is seen in the oculomotor response to near targets, where a single motor behavior (vergence eye movement) is influenced by several separate motor centers each driven by a unique stimulus (disparity, blur, proximity, target size, luminance, etc).2'3 By extension, it is possible that responses currently believed to be the product of a single driving system, such as disparity vergence, are managed by multiple subdivisions of control. For over 150 years it has been known that a target changing in depth produces primarily blur and disparity that evoke both accommodative and vergence eye movements.4 Under controlled stimulus conditions, it is possible to eliminate blur and drive the vergence motor response with disparity alone. The vergence response to disparity stimulation alone consists

of a fairly rapid disjunctive movement requiring 300500 msec5 with the eventual attainment of highly accurate (5-10 min of arc error) bifoveal fixation.6 It has been conventionally viewed that this response is produced and guided by a single neuromuscular feedback control system, and many mathematical models were based on this notion.7"9 Yet, evidence summarized below indicates that this isolated response is the product of at least two separate neural control processes. In an early study of disparity vergence step responses, Westheimer and Mitchell10 noted that vergence position following the initial transient movement "often differs by as much as a degree or more from the one required for binocular fixation." They also observed that this error was subsequently corrected by "very slow changes in convergence." It was later shown that transient disparity vergence movements could be produced by brief flashes (200 msec) of dissimilar targets presented to each eye, a stimulus which could not support sustained binocular fixation." Jones 12 found that the transient movement produced by a standard fusable stimulus (such as identical paired vertical lines) presented in a brief flash (200 msec) was identical with that produced by a long duration nonfusable target (such as vertical line paired with a horizontal line). In the case of the nonfusable target, the normal transient vergence movement was followed by a gradual return to the phoria position. These experiments led Jones12 to surmise that disparity vergence is a "two stage process consisting of a transient fusion-initiating phase and a fusion-sustaining component." Other, less direct evidence indicates that disparity vergence movements may be driven by more than just

From the Department of Surgery,* UMDNJ-Rutgers Medical School, Piscataway, New Jersey, Department of Electrical Engineering,! Rutgers University, Piscataway, New Jersey, and College of Optometry,t State University of New York, New York, New York. Submitted for publication: February 5, 1985. Reprint requests: George K. Hung, PhD, Department of Electrical Engineering, P. O. Box 909, Rutgers University, Piscataway, NJ 08854.

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a single feedback control process. For example, although the transient response appears to be driven by a fast integral controller,13 the sustained response exhibits the behavior of a slow proportionally controlled system.813"15 Another evidence for dual control of disparity vergence is found in the difference in range limits of transient and sustained responses: The maximum amplitude of the sustained disparity vergence response is much greater than the maximum response to steplike stimulation.16 Hence, there is a variety of evidence suggesting dual control of disparity vergence. Actually, additional separate controllers may be involved since convergence and divergence transients may be separately controlled.17 We present below the first comprehensive study of the normal human vergence response to ramp stimuli over a wide range of stimulus velocities (0.7 to 36.0 deg/sec). We were thus able to elicit the two control modalities and quantify the ramp response dynamics. We found that slower ramps were tracked rather smoothly by the sustained component while faster ramps brought out the transient component. In addition, a new finding of staircase-like step responses to faster ramps suggests a sampling process within the transient component.

Materials and Methods Disparity stimuli were generated using the dynamic binocular stimulator described by Semmlow and Venkiteswaran,18 which provides for image viewing through a pinhole (1 mm) located in a plane optically conjugate to the pupil. In this manner blur stimulation is eliminated and cannot either directly or indirectly (through accommodative feedback) influence the vergence response.1920Two different target modes were used. In the fusable mode, the target consisted of thin, paired vertical lines 2° in height, presented as bright bars against a totally dark surround. In the nonfusable mode, the target consisted of a vertical line in the right eye and a horizontal line in the left eye, both 2° in length. The disparity demands of these targets were varied either in 4° steps or in ramps of constant velocities ranging from 0.7 to 36.0 deg/sec (up to 4 deg amplitude). All stimuli required over-convergence beginning (or ending, in the case of divergent stimuli) at the subject's phoria position. A typical experimental run consisted of 15-20 responses over a 3-4-min period with ample time for rest between responses as well as between runs. Horizontal movements of both eyes were measured using the differential infrared reflection technique which provides a resolution of approximately 10 min of arc. The response over a 3-sec interval following the start of the stimulus was digitized by an on-line com-

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TIME (sec) Fig. 1. Variability between two individual disparity vergence responses to a 4 degree step stimulus demonstrates the dichotomous transient/sustained nature of vergence control.

puter at a sampling frequency of 100 hz. Only disjunctively symmetric responses were processed for further calculations, thus eliminating monocular drift movements and smooth versional movements. Using separate calibration of each eye movement, the computed difference between the left and right eye responses was generated as the net vergence response. Both individual responses and computer generated ensemble averages of 8-12 individual responses were used in the analysis. With informed consent, two experienced subjects and one naive subject were tested. All subjects have normal binocular vision. Where required, full refraction correction was provided.

Results Variability of vergence responses to identical stimulus has been known since the earliest objective recordings of vergence responses.21 Researchers have considered it a nuisance and have used averaging methods to reduce this source of noise. Yet, it is in this variability in individual responses that the dichotomous transient/sustained behavior may be observed. Close inspection of the two individual responses from a group of step responses (Fig. 1) shows that final position is not achieved by the transient response, but rather by a slow, drift-like movement, which takes several seconds to reach the final position similar to that reported by Westheimer and Mitchell.10 In the lower response, the peak of the fast transient portion is greater than the 2° stimulus, and the final position is attained through a slow divergence movement, whereas in the upper response the opposite is true. Note that our experimental procedures eliminated proximal cues, blur, and any potential involvement of a blur-driven vergence component; hence, we assume that the slow

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Fig. 2. A set of individual disparity vergence responses to a converging, constant velocity (ramp) stimulus of 1.4 degrees/sec (up to 4 deg amplitude). A shows vergence responses; B shows derivative (velocity) of vergence responses.

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Time (sec) movements as well as the fast transients are pure disparity-driven responses. As the responses for the three subjects were very similar, where appropriate, representative data for one of the subjects is presented. The most identifiable behavioral features of the two response components of Figure 1 are their respective dynamics. To isolate these components under more controlled conditions, we used ramp stimuli of various velocities. Vergence responses to ramp stimuli of 1.4 and 2.7 deg/sec along with their derivatives are shown in Figures 2 and 3 respectively. The slow ramp stimulus elicits primarily smooth tracking behavior (Fig. 2), while the faster ramp stimulus evokes a combination of smooth tracking and step-like dynamic behavior (Fig. 3). The plots of response velocity time course (Figs. 2b, 3b) show increased velocity associated with steplike behavior, identifying their presence in the ramp

Time (sec) responses. Even some of the slower ramp responses appear to contain both step-like and smooth tracking behavior (Figs. 2a-b, lowest traces), and almost all responses show step-like behavior at the onset of the response. Two questions may be posed concerning the steplike behavior in the responses to ramp stimuli (Figs. 2-3). Are the step-like movements seen in ramp responses truly step responses (that is, are they produced by similar neurological signals); and if so, why should such response patterns be generated by ramp stimulation? The answer to the first question can be obtained by comparing the dynamics of the step-like ramp response movements to the dynamics of actual vergence step responses. If two movements have similar dynamics, then they must be produced by similar patterns of

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Fig. 3. Disparity vergence responses to ramp stimuli of 2.7 degrees presented as in Figure 2.

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neuro-muscular innervation. A succinct description of vergence response dynamics can be obtained by plotting maximum velocity against amplitude for a wide range of amplitudes. Such a plot (commonly done on a log-log scale) produces a locus of points, termed the "main sequence,"22 which categorizes the response family according to its dynamics. The plot produced by step-like behavior found in ramp responses (for the three subjects) shows that this behavior can indeed be categorized by a single family (+, X and O points in Fig. 4). Furthermore, this family has the same dynamics as disparity vergence responses of subject 1 to single step stimulus (A in Fig. 4) and closely matches the dynamics of vergence step responses well-documented over a wide range of response amplitudes in a number of subjects by Bahill, et al22 (solid line, Fig. 4). Hence, the use of the term "step-like" for the behavior seen in ramp responses is entirely appropriate. To evaluate control modalities in divergent responses, we repeated the ramp and step response experiments using stimuli that diverged from the initial level. Again, divergent ramp responses were found to contain step-like behavior having dynamic features very similar to true divergence step responses.* While the question regarding the identity of steplike behavior in ramp responses is resolved in Figure 4, the second question regarding the production of this behavior by ramp stimuli is not. Some insight into this question is provided by the interesting pattern seen in the family of average response curves generated at different stimulus velocities (Figs. 5a, b). At the lowest stimulus velocities, predominantly smooth tracking is evident. Moderate velocities produce multiple step-like responses. At the highest velocities, the response is a single step, similar to that produced by actual step stimulation. This pattern of responses demonstrates that the amplitude of step-like movement embedded in ramp responses is related to some feature of the stimulus velocity, either ramp velocity itself or position error within a given time frame. This dependence is explicitly shown in a plot of initial step amplitude as a function of ramp velocity (Fig. 6). While the steplike response is related to stimulus velocity, the process that converts stimulus ramps to response steps is unknown. To demonstrate that the smooth tracking behavior seen primarily in Figure 2 is due to the sustained component, we repeated the ramp stimulus experiments using nonfusable targets. Results show little, if any, consistent smooth tracking to the 1.4 deg/sec stimulus, (Fig. 7a) and primarily random step-like responses to

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Fig. 4. A plot of response velocity verses response amplitude for step-like responses observed during ramp stimulation (+ and X points for experienced subjects; O for naive subject) and in response to actual step stimuli (A). The solid line shows this relationship for normal disparity step responses averaged over a large number of subjects and responses.22 (Subject 1 X and A; Subject 2 +; Subject 3 O.)

the faster 2.7 deg/sec stimulus, (Fig. 7b). These results are evident even in the presence of random vergence drift movements which are to be expected under the vergence "open-loop" conditions of the test procedure, as there is an absence of fusable disparity target. Matching the step-like responses that do appear under these nonfusable stimulus conditions with the "main sequence" vergence plots shows them to be members of the step-like family (Fig. 4). Hence, nonfusable targets can generate step-like response, but smooth tracking requires a fusable target. Another feature of smooth tracking behavior is shown in the plot of maximum smooth tracking velocity as a function of stimulus velocity (Fig. 8). This plot was generated from samples of smooth tracking found in fusable ramp responses to stimulus velocities from 0.7 to 9.0 deg/sec. (No examples of smooth tracking of the ramp stimulus were found in responses to velocities greater than 9.0 deg/sec.) From this plot we see that smooth tracking response velocities are indeed proportional to stimulus velocities up to a maximum response of around 4-5 deg/sec. At this point, a response velocity saturation occurs.

Discussion * Data for divergent responses are not plotted so as to maintain clarity of presentation. A similar dichotomous behavior is seen although the dynamics are slightly slower.

Disparity vergence responses to step and ramp stimuli contain two distinct components characterized by

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Fig. 5. Averaged disparity vergence responses (A) and response velocity (B) to a range of ramp stimuli (up to 4 deg amplitude). Stimulus velocity (in deg/sec) shown next to curves. Top curve is step response.

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Fig. 6. Initial step amplitudes found in the responses of Figure 5 plotted against ramp stimulus velocity. Rightmost data point is for step response.

different stimulus requirements and different dynamic properties. The step-like response family is stimulated by errors greater than about 0.5 to l.O deg (Fig. 3a), and does not require a fusable stimulus (Fig. 7b). It produces responses of 1 deg or more (Fig. 4), and has an amplitude related to ramp velocity (Fig. 6). This family has dynamic features identical to the initial transient of an actual step response (Fig. 4) and thus, represents the transient component identified in previous studies. The slow component response requires a fusable stimulus (Fig. 7). It is capable of smooth tracking (Fig. 2), and has maximum velocity of about 5 deg/sec (Fig. 8). This family represents the sustained disparity component described by others previously. Responses to both convergent and divergent stimuli show similar dichotomous behavior, although divergence steps usually exhibit slightly lower velocities. This difference may be due to separate control processes for convergent and divergent step-like responses, as suggested by Jones,17 or may be the result of a direction

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Fig. 7. A set of individual vergence responses to ramp stimuli presented as a nonfusable target: A stimulus velocity = 1.4 deg/sec; B stimulus velocity = 2.7 deg/sec.

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dependent velocity saturation in the final common pathway. The control characteristics of the slow component had been investigated previously under a different stimulus condition. Using an error clamping procedure, Rashbass and Westheimer12 demonstrated that small, open-loop disparities generated ramp-like movements whose velocities were proportional to disparity. This proportional relationship between velocity and disparity over the range of disparities used (1 deg or less) corresponds closely to our findings on the slow, sustained component. Thus, their findings, as well as ours, indicate that the sustained component responds to small disparities and is mediated by an integral feedback control system. Since the steady state response exhibits a maintained error (ie, fixation disparity), this integrator must be of the "leaky" variety.8-9 The control features of the step-like family are less certain. Rashbass and Westheimer recorded in one of their subjects a step response which showed oscillations during the initial transient movement as well as a sustained oscillation following the initial transient response. As this is not seen in recent recordings of normal subjects, the oscillations they found may reflect an inability of the subject to maintain fixation or an artifactual noise component. Rashbass and Westheimer also recorded ramp response on another subject over a relatively small range of 0.35 to 5.00 deg/sec target velocity. They found oscillations in the ramp responses and indicated that these are similar to the overshoot and oscillations found in the step responses. Normal step responses generally show overshoot with essentially no oscillations (see Fig. 5, step response). If the vergence system is a continuous feedback system, it should respond to ramp stimuli with some overshoot but also essentially no oscillations. However, this is contrary to experimental results. Indeed, our results indicate that the ramp response is closer to a series of relatively accurate step responses than simply random oscillations.

This is more easily seen in individual records (see Fig. 3) than in the averaged records (see Fig. 5), where the responses tend to be smoothed out. Thus other control strategies such as preprogramming or sampling may account for these series of step responses to ramp stimuli. Individual steps in the staircase-like responses to fast ramp stimuli may be preprogrammed as in versional saccadic responses. However, in contrast to the refractory-like character of versional system, responses to pulse disparity stimuli show a decrease in amplitude with decreasing stimulus pulse width.17 This behavior is frequently cited in support of a continuous feedback control process, but may also be explained by a sampling process which can be retriggered by rapid changes in the stimulus. This is not an unreasonable hypothesis since even the saccadic system shows modification of its sampled-data behavior under certain stimulus conditions such as double-step and pulse-reverse step target movements.23"26 The con-

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Stimulus Velocity (deg/sec) Fig. 8. A plot of the maximum velocity of smooth tracking vergence responses as a function of stimulus velocity. A saturation in maximum tracking velocity is clearly seen.

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trol characteristics of the vergence step-like component are currently under study in our laboratory. Although the emergence of dual-mode control processes in the isolated disparity response complicates the rather elegant theory of a simple feedback control system, it has the potential of resolving several fundamental questions regarding disparity vergence control. For example, although separate mathematical models of the dynamic and static disparity vergence control have been well developed, the search for a single quantitative description of both responses has been notably unsuccessful. Specifically, the high closed-loop gain required to account for the very small static response error 27 does not permit stable transient responses. Conversely, accurate models of the dynamic response demonstrate unrealistically large static errors.9 It is in these unreconcilable control problems, the need for very small maintained error coupled with the requirement for rapid, stable movements in a system with unavoidable processing delay times, that we find both an explanation and justification for use of multiple neural control processes to drive a single motor response. Key words: disparity vergence, transient component, sustained components, oculomotor control mechanisms

References 1. Leigh J and Zee D: The Neurology of Eye Movements. Philadelphia, FA Davis, 1983. 2. Hokoda S and Ciuffreda K: Theoretical and clinical importance of proximal vergence and accommodation. In Vergence Eye Movements: Basic and Clinical Aspects, Schor C and Ciuffreda K, editors. Boston, Butterworths, 1983, pp. 75-97. 3. Campbell FW and Westheimer G: Factors influencing accommodation responses of the human eye. J Opt Soc Am 49:568, 1959. 4. Maddox E: Investigation in the relation between convergence and accommodation of the eyes. Journal of Anatomy and Physiology 20:475, 1886. 5. Semmlow JL and Wetzel P: Dynamic contributions of binocular vergence components. J Opt Soc Am 69:639, 1979. 6. Ogle K.N, Avery DeH, and Prangen A: Further consideration of fixation disparity and the binocular fusional process. Am J Ophthalmol 34:57, 1951. 7. Zuber BL and Stark L: Dynamical characteristics of the fusional vergence eye movement system. Institute of Electrical and Electronic Engineers Trans Sys Sci Cyber SSC-4:72, 1968.

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8. Toates FM: Vergence eye movements. Doc Ophthalmol 37:153, 1974. 9. Krishnan VV and Stark L: A heuristic model for the human vergence eye movement system. IEEE Trans Biomed Eng BME24:44, 1977. 10. Westheimer G and Mitchell AM: Eye movement responses to convergence stimuli. Arch Ophthalmol 55:848, 1956. 11. Westheimer G and Mitchell DE: The sensory stimulus for disjunctive eye movements. Vision Res 9:749, 1969. 12. Jones R: Fusional vergence: sustained and transient components. Am J Optom 57:640, 1980. 13. Rashbass C and Westheimer G: Disjunctive eye movements. J Physiol 159:339, 1961. 14. Semmlow J and Hung G: The near response: theories of control. In Vergence Eye Movements: Basic and Clinical Aspects, Schor C and Ciuffreda K, editors, Boston, Butterworths, 1983, pp. 175195. 15. Semmlow J: The oculomotor response to near stimuli: the near triad. In Models of Oculomotor Behavior and Control, Zuber B, editor, Boca Raton, FL, Chemical Rubber Company Press, 1981, pp. 161-191. 16. Holfstetter HW: The zone of clear single binocular vision. Am J Optom and Arch Am Acad Optom 22:301, 1945. 17. Jones R: Horizontal disparity vergence. In Vergence Eye Movements: Basic and Clinical Aspects, Schor C and Ciuffreda K, editors, Boston, Butterworths, 1983, pp. 297-316. 18. Semmlow J and Venkiteswaran N: Dynamic accommodative vergence in binocular vision. Vision Res 16:403, 1976. 19. Ripps H, Chin NB, Siegel IM, and Breinin GM: Effect of pupil size on accommodation, convergence and the AC/A ratio. Invest Ophthalmol 1:127, 1962. 20. Semmlow JL and Heerema D: The synkinetic interaction of convergence accommodation and accommodative convergence. Vision Res 19:1237, 1979. 21. Hung G, Semmlow J, and Ciuffreda K: Identification of accommodative vergence contribution to the near response using response variance. Invest Ophthalmol Vis Sci 24:772, 1983. 22. Bahill AT, Clark MR, and Stark L: The main sequence: a tool for studying eye movements. Math Biosci 24:191, 1975. 23. Wheeless L Jr, Boynton R, and Cohen G: Eye movement responses to step and pulse-step stimuli. J Opt Soc Am 56:956, 1966. 24. Komoda M, Festinger L, Phillips L, Duckman R, and Young R: Some observations concerning saccadic eye movements. Vision Res 13:1009, 1973. 25. Becker W and Jurgens R: An analysis of the saccadic system by means of double step stimuli. Vision Res 19:967, 1979. 26. Hou R and Fender D: Processing of direction and magnitude by the saccadic eye-movement system. Vision Res 19:1421, 1979. 27. Hung G and Semmlow J: Static behavior of accommodation and vergence: computer simulation of an interactive dual-feedback system. IEEE Trans Biomed Eng BME-27:439, 1980.