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Identification of Accommodative Vergence Contribution to the Near Response Using Response Variance George K. Hung,* John L. Semmlow,* and Kenneth J. Guffredaf An experimental method was developed to isolate accommodative and disparity vergence contributions to coordinated near vergence motor responses. The variability normally associated with the neural control signal was used as an identifying marker or tag. Using this approach, the results showed an increased variability associated with the blur-driven, accommodative vergence component that is particularly noticeable during the latter half of the movement. This indicated that accommodative vergence provides a moderate contribution to the near vergence response primarily in the late and post-transient period when the movement is essentially complete. Presence of this accommodative contribution lends further support to the "dual interactive model" of near triad control. Invest Ophthalmol Vis Sci 24:772-777, 1983 namic vergence responses to both combined disparity-blur stimulation and disparity-only (ie, without blur) stimulation. They concluded that accommodative vergence contributed only to the latter half of the transient response. Difference curves (combined disparity-blur minus disparity-only responses) were calculated and presumably reflected the dynamic accommodative vergence contribution. These difference curves indicated that accommodative vergence played a minor role in near vergence responses. However, implicit in this interpretation is the assumption that the disparity component is the same under both stimulus conditions; that is, the presence of blur stimulation and its associated accommodative convergence do not modify the disparity-driven component. Yet disparity vergence operates within a feedback control system, and any additional vergence motor drive (eg, from accommodative vergence) would modify the disparity component. The addition of blur stimulation and the associated accommodative vergence should lead to a compensatory reduction of the disparity component, and, thus, a simple comparison of external responses would erroneously indicate only a small contribution from accommodative vergence. A similar compensatory disparity vergence mechanism was evident in binocular accommodative vergence responses8 (although, instead of combined dynamic stimulation, disparity stimulation was held constant). Thus, to determine the role of accommodative vergence in the combined near vergence response requires a measurement reflecting the internal state of accommodative vergence during these responses. One The contribution of accommodative vergence to the total vergence response during a change in binocular fixation has been of considerable interest to oculomotor physiologists. Maddox1 was the first to define the components of vergence. He believed that blur-driven accommodative vergence was primary, with disparity (fusional) vergence serving only a supplemental role in the attainment of precise binocular fixation. Recently, a qualitative model having such a hierarchical structure was proposed.2 In contrast, Fincham and Walton,3 after carefully collecting static measurements of accommodation and vergence, theorized that disparity provided the dominant vergence drive. Disparity-driven accommodation (vergence accommodation) was found to be nearly sufficient for the target distance, thus necessitating only "fine-tuning" by blur-driven accommodation. Finally, a recent quantitative theory4"6 provided for significant contributions to vergence drive from both major stimuli. Resolution of this long-standing question of stimulus dominance is essential to the development of a comprehensive theory for the coordinated oculomotor activity seen in the binocular near response. Recent experiments specifically addressed this question. Semmlow and Wetzel7 compared average dyFrom Rutgers, the State University of New Jersey,* and the State College of Optometry, State University of New York, New York.f Supported in part by NIH grants EY 03709 and EY 03541. Submitted for publication October 20, 1981. Reprint requests: George K. Hung, PhD, College of Engineering, Rutgers University, Box 909, Piscataway, NJ 08854. 0146-0404/83/0600/772/$ 1.10 © Association for Research in Vision and Ophthalmology 772 Downloaded From: http://iovs.arvojournals.org/pdfaccess.ashx?url=/data/journals/iovs/933342/ on 05/14/2017 No. 6 ACCOMMODATIVE VERGENCE IN NEAR RESPONSE / Hung er ol. parameter uniquely related to accommodative vergence is the response variability associated with this component. As in most physiologic processes, the specific time course of accommodative vergence varies slightly from response to response even though the driving stimulus is unchanging. Through appropriate data analysis, which we term ensemble variability analysis, accommodative vergence variability can be isolated from the variability inherent in other motor components. Ensemble variance, which is calculated from a large number of individual responses, is a measure of this change in dynamic character of a movement from response to response. Although feedback compensation occurs within each response, it does not affect the change in dynamic character of a component from response to response. If response variation is assumed to be Gaussian, variabilities from different motor componets are additive. Hence, ensemble variability analysis coupled with a simple subtraction procedure can be used to extract the variability due to accommodative vergence in the binocular near vergence response. This accommodative variability, in turn, provides information on the relative amount of accommodative vergence contribution to the near response. Further, if variance of responses to different stimulus levels were calibrated, quantitative information can be obtained. The purpose of this investigation was to determine the time course of the accommodative vergence contribution to the total vergence response using ensemble variability analysis. Vergence responses were measured under three viewing conditions: (a) disparity-only stimulation, (b) combined disparity-blur stimulation, and (c) blur-only* stimulation. Average vergence response and variance of vergence responses were constructed to isolate the accommodative vergence contribution. Response and ensemble variance curves from blur-only stimulation were used for comparison with the components isolated by the difference curves. Materials and Methods Experiments Binocular stimulation with disparity-only or combined disparity-blur stimuli required a versatile device capable of generating combinations of binocular stimuli. The dynamic binocular stimulator (DBS)8 was used since it is capable of producing these stimuli. A target, consisting of 1 ° green circle and positioned * While the DBS eliminates major cues to accommodation, other subtle cues may indeed be present. Thus, the use of the term "blur-only" is a concise way of saying that there is no disparity stimulation. 773 by means of motor control in a Badal optical system, served as the stimulus to accommodation. Motor driven translatin^'rotating mirrors in front of both eyes provided disparity stimulation. Interaction of accommodative feedback on disparity9 could be eliminated by reducing the effective entrance pupil to less than 1 mm,| thus providing disparity-only stimulus. Blur-only stimulation was produced by blocking the optical pathway to one eye. For each of three subjects the vergence response was measured for three stimulus conditions: (a) 0 to 3 meter angles (MA) disparity-only step stimulus, (b) 0 to 3 MA and 0 to 3 diopters (D) combined disparity and blur step stimuli, and (c) 0 to 3 D blur-only step stimulus. Each step stimulus presentation was initiated manually by the experimenter, permitting randomization of stimulus onset time. The stimulus trigger signal was used to mark stimulus onset. After the completion of each response, a saccadic eye movement of known amplitude was used to calibrate the response magnitude. Only convergence responses were analyzed. To avoid adaptation effects,10 the subject was required tofixatea far target in the laboratory for 10 sec after every 10 records. Movements of both eyes were measured using the infrared limbus reflection technique," and data were transferred directly to an online computer (PDP 11/ 40). All three subjects had normal visual-motor function, although two subjects with refractive errors were corrected by means of lenses added to the DBS optical system. Data Analysis Because of vergence response variability, the vergence time course was obtained by means of ensemble averaging-^ Usually, the number of individual responses required for accurate representation was determined empirically; however, as the ensemble variability itself is of interest here, a more quantitative approach was used. Specifically, we needed to determine when our limited sample estimate of the ensemble variance approached the true ensemble variance. In other words, how many individual responses were required before our estimate of ensemble varif Measurements in the DBS using a Hartinger coincidence optometer show that there is very little change in static accommodative response to different accommodative stimuli under pinhole viewing conditions. X Given two time series of equal number of data points, the ensemble average is obtained as the point for point average between the two time series, resulting in an averaged time series. An ensemble variance time series can be similarly constructed. This ensemble approach generalizes to any number of time series records with equal number of points. Downloaded From: http://iovs.arvojournals.org/pdfaccess.ashx?url=/data/journals/iovs/933342/ on 05/14/2017 774 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / June 1983 2 7 6 10 15 20 25 30 35 40 45 NUMBER OF RESPONSE RECORDS 50 55 60 Fig. 1. Average of ensemble variance of the vergence responses as a function of the number of individual responses. This curve was used to estimate the number of individual responses required for an accurate average. As number of responses in the average increased, the average ensemble variance became smaller, approaching an asymptote at around 40 responses. Data shown is for subject K.C; those from other subjects were similar. ance was only slightly improved by additional responses? To answer this, the ensemble variance calculated from individual disparity vergence responses was averaged over the transient portion of the response (first 3 sec), and this average plotted as a function of number of responses§ (see Fig. 1). Note that the ensemble variance, as represented by this average is only slightly modified by additional responses after about 40 individual responses. This feature was consistent for other vergence responses and other subjects; hence, ensembles of 40 or more individual responses was considered sufficient for accurate estimation of response variance. Preliminary analysis was applied to some of the data to determine the influence of response latency on the variance time course. These responses, initially synchronized to the stimulus signal, were shifted using an interactive graphical display program to align § The measure of interest is the average of the variance of all the points in the ensemble variance time series given by: 1 Avg.Var.N = - Z where x = vergence response value M = the number of points in the data array i = the ith data point in the response; i.e., the time index N = number of trials j = the j l h trial. The change in average ensemble variance with the addition of each new individual response will converge towards zero as the estimated ensemble variance approaches the true variance. Vol. 24 the transient onset of each response. This provided compensation for latency variations so that influences on the variability calculation could be isolated. Since our preliminary analysis showed that this factor did not significantly affect the interpretation of results (see Results section), latency compensation was not generally used. Responses containing artifacts such as eye blinks or saccades were discarded. After the completion of the ensemble analysis procedure, the ensemble average vergence response time course and the associated ensemble variance time course were plotted. Additionally, the average of the ensemble variance as a function of the number of individual responses was also calculated. Finally, the difference in the ensemble variance of responses obtained with combined disparity-blur stimulation and disparity-only stimulation were calculated and plotted. This procedure was repeated for each subject. Results Ensemble average, ensemble variance, and difference in ensemble variance of vergence responses with and without accommodative stimulation" are presented in Figure 2 for the three subjects. Average vergence response curves (Fig. 2, top row) show slight differences in dynamic behavior under combined and disparity-only stimulation. Variance curves show the time course of response variation (Fig. 2, 2nd row), while curves of difference in vergence response variance (Fig. 2, 3rd row) isolate the added variability due to the addition of blur stimulation. Since this added variability is not influenced by disparity feedback, it represents the actual accommodative vergence contribution to a near response. Accommodative vergence variance curves (Fig. 2, bottom row) show the general dynamic features of this component's variability and confirms the origin of variability isolated by the difference curves (Fig. 2, 3rd row). Evident in comparing variance difference curves (Fig. 2, 3rd row) is the significant contribution of the accommodative component following an initial artifactual peak in all three subjects. The most likely origin of this initial peak, which corresponds in time to the disparity component, is a slight increase in disparity vergence variability during combined stimulation. The second peak is due to the accommodative contribution as can be seen by matching this peak with the transient portion of the accommodative vergence variance curves (Fig. 2, bottom row). As a preliminary check on our analysis procedure, 11 Responses without accommodative stimulation employed pinhole viewing so that the accommodative system is inactivated (open-looped). Downloaded From: http://iovs.arvojournals.org/pdfaccess.ashx?url=/data/journals/iovs/933342/ on 05/14/2017 ACCOMMODATIVE VERGENCE IN NEAR RESPONSE / Hung er ol. No. 6 GH JS 775 KC Fig. 2. Composite figure showing in the top row the ensemble average vergence response to 3 MA disparityonly stimulus (interrupted curves) and combined 3 MA/3D disparity-blur stimulus (solid curves). Ensemble variance curves for 3 MA disparity-only (interrupted curves) and combined 3 MA/3D disparityblur (solid curves) stimulation are shown in the second row. Difference in ensemble variance curves shown in third row were obtained by subtracting ensemble variance curves, (combined disparity-blur variance minus disparity-only variance) of the second row. Ensemble variance of accommodative vergence is shown in the bottom row. Figures are for subjects GH, JS and KC, left to right columns, respectively. we also investigated the effect of latency variation on the ensemble variance curve. The slight reduction in amplitude of the variance curve with latency compensation (Fig. 3) indicated that the effect of latency variation is small when compared to variation in other components of the vergence system. Discussion Statistical Isolation of Motor Components As both blur and disparity stimulation are generated by a near target, and as both separately evoke a vergence response, the normal binocular vergence response must be driven by some combination of these two inputs12 (along with possible contributions from proximal and related higher level compo- nents13). Were it not for disparity feedback, the various component contributions could be isolated easily. For example, a direct comparison of vergence response driven by combined disparity-blur and disparity-only stimulation would identify the blur-driven contribution. Such a comparison7 would suggest that accommodative vergence contributes only slightly to the combined response. It is certainly possible that accommodative vergence is not a major component mediating binocular vergence, but it is just as likely, based solely on a comparison of individual or averaged responses, that the external appearance of a strong accommodative vergence component is diminished by the compensatory action of disparity feedback. Neurophysiologic techniques, probing the appro- Downloaded From: http://iovs.arvojournals.org/pdfaccess.ashx?url=/data/journals/iovs/933342/ on 05/14/2017 776 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / June 1983 < > o or IMA2 TIME, SEC Fig. 3. Ensemble variance for disparity-only stimulation for analysis procedures of no-latency compensation (solid curve) and latency compensation (interrupted curve) showing minor reduction in ensemble variance amplitude due to latency compensation. priate neural pathways,1415 might resolve this question, but our lack of detailed knowledge concerning the anatomical location of these pathways, especially in humans, makes this approach unattractive. As the resolution of component contribution is central to any theory of near triad control,4"6 we have developed a "dry dissection" technique,16 using the variability associated with the neural signals as a "tag" for a specific neural control component. Since ensemble variance is independent of the feedback mechanism, this technique provides a potentially powerful tool for isolating control components in a complex motor response. Accommodative Contribution to Binocular Vergence Comparison of the 2nd peak of the variance difference curves (Fig. 2, 3rd row) and the peaks of response difference curves (by calculating differences seen in Fig. 2, top row) shows the accommodative contribution occurs later than that indicated by the vergence response difference approach.7 Also, evaluation of the variance difference curves indicates a larger accommodative contribution than suggested by differences in vergence responses. Indeed, the responses of subject KC would indicate a large negative contribution from accommodative vergence in the combined-stimulus condition. The absence Of accommodative vergence component from the initial transient portion is explained easily: the latency associated with blur-driven components is substantially longer (by about 100-200 Vol. 24 msec) than the latency seen in disparity-driven components.17 Thus, under simultaneous disparity-blur stimulation, disparity-driven components are well under way before blur-driven components begin to have a motor influence. Additionally, the blur-driven signal has a complex dynamic input due to the effect of the ongoing vergence response in bringing an eccentric target towards central fixation. The effect of nonfoveal stimulation is to reduce the effectiveness of target blur in driving accommodative vergence.1819 However, as convergence continues and the target approaches the fovea, the accommodative and associated accommodative vergence contribution would increase progressively. Meanwhile, convergence accommodation would initiate a lens response that could offset to some extent the increase in blur-driven accommodative stimulation. The presence of accommodative vergence in the late and post-transient portion of the response as suggested by the variance curves, but not in the response difference curves, may be explained by these interaction between vergence and accommodative components. It has long been known that the binocular vergence response is not the summation of the disparity and blur-driven components to the same response.7 This is comforting, since in most individuals simple addition of disparity and accommodative vergence would result in substantial diplopia. In a study comparing combined disparity/blur and disparity-only stimulation, Semmlow and Wetzel7 proposed that reduction in the late transient "apparent" accommodative vergence could be due to compensation in either the disparity or accommodative control system. They further pointed out the relationship between these alternative compensatory mechanisms and two classical views of binocular vergence control: the Maddox hierarchy1 and the theory of Fincham and Walton.3 Essentially, these views are divided on the question of stimulus dominance. Maddox's theory assumes blur-driven dominance (and vergence compensation). Fincham and Walton's theory assumes disparity-driven dominance (and accommodative compensation).5'6 A more recent theory, based on static quantitative representation of the major feedback systems, allows for interactive control by both components and provides for some degree of both disparity and accommodative compensation.4 Simulation of this static model had offered quantification of the relative dominance of disparity and blur components.20 Essentially, dominance goes to the system with the largest interactive influence (AC/A or CA/ C ratio) with some favoritism towards the disparity system due to its higher internal gain. It is interesting to note that even in the limited sample of subjects used in our study, there appears to be a link between Downloaded From: http://iovs.arvojournals.org/pdfaccess.ashx?url=/data/journals/iovs/933342/ on 05/14/2017 No. 6 ACCOMMODATIVE VERGENCE IN NEAR RESPONSE / Hung er ol. the static measure of AC/A (subj. GH 8 A/D; subj. JS 6 A/D; and subj. KC 7 A/D) and the amplitude of the dynamic accommodative contribution (subj. GH .08 MA2; subj. JS .03 MA2; and subj. KC .06 MA2) during combined disparity-blur stimulation (Fig. 2, 3rd row). Applying ensemble variability analysis on a larger sample of subjects and over a larger range of AC/A ratios may further elucidate this correlation. Key words: accommodative vergence, disparity vergence, accommodation, response variance, Maddox hierarchy, Fincham-Walton model, neurological control References 1. Maddox EE: Investigations in the relation between convergence and accommodation of the eyes. J Anat Physiol 20:475, 1886. 2. Toates FM: Control of the eye's intrinsic muscles. Measurement Control 1:129, 1968. 3. Fincham EF and Walton J: The reciprocal actions of accommodation and convergence. J Physiol 137:488, 1957. 4. Hung GK and Semmlow JL: Static behavior of accommodation and vergence: Computer simulation of an interactive dual-feedback system. IEEE Trans Biomed Eng 27:439, 1980. 5. Semmlow JL: Oculomotor responses to near stimuli: The near triad. In Models of Oculomotor Behavior and Control, Zuber BL, editor. Boca Raton, Florida, CRC Press, 1981, pp. 161191. 6. Semmlow JL and Hung GK: The near response: theories of control. In Vergence Eye Movements: Basic and Clinical Aspects, Schor CM and Ciuffreda KJ, editors. Boston, Butterworth's, 1983, pp. 175-195. 7. Semmlow JL and Wetzel P: Dynamic contributions of the components of binocular vergence. J Opt Soc Am 69:639, 1979. 777 8. Semmlow JL and Venkiteswaran N: Dynamic accommodative vergence components in binocular vision. Vision Res 16:403, 1976. 9. Semmlow JL and Hung GK: Accommodative and fusional components of fixation disparity. Invest Ophthalmol Vis Sci • 18:1082, 1979. 10. Schor CM: The influence of rapid prism adaption upon fixation disparity. Vision Res 19:757, 1979. 11. Stark L, Bahill AT, CiufTreda KJ, Kenyon RV, and Phillips S: Neuro-optometry: An evolving specialty clinic. Am J Optom Physiol Opt 54:85, 1977. 12. Semmlow JL and Hung GK: Experimental evidence for separate mechanisms mediating accommodative vergence and vergence accommodation. Doc Ophthalmol 51:209, 1981. 13. Hokoda SC and Ciuffreda KJ: Theoretical and clinical importance of proximal vergence and accommodation. In Vergence Eye Movements: Basic and Clinical Aspects, Schor CM and Ciuffreda KJ, editors. Boston, Butterworth, 1983, 75-97. 14. Keller EL and Robinson DA: Abducens unit behavior in the monkey during vergence movements. Vision Res 12:369, 1972. 15. Mays LE: Neurophysiological correlates of vergence eye movements. In Binocular Vergence Eye Movements: Basic and Clinical Aspects, Schor CM and Ciuffreda KJ, editors. Boston, Butterworth, 1983; 649-670. 16. Stark L: Neurological Control Systems: Studies in Bioengineering. New York, Plenum, 1968. 17. Wilson DC: Accommodation/Accommodative Vergence Synkinesis. Ph.D. dissertation, Berkeley, University of California, 1972. 18. Phillips SR: Ocular Neurological Control Systems: Accommodation and Near Response Triad. Ph.D. dissertation, Berkeley, University of California, 1974. 19. Semmlow JL and Tinor T: Accommodative convergence response to off-foveal retinal images. J Opt Soc Am 68:1497, 1978. 20. Hung GK and Semmlow JL: A quantitative theory of control sharing between accommodative and vergence controllers. IEEE Trans Biomed Eng 29:364, 1982. Downloaded From: http://iovs.arvojournals.org/pdfaccess.ashx?url=/data/journals/iovs/933342/ on 05/14/2017